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UBC Theses and Dissertations

Critical evaluation of hypotheses on the nature of the earth's core McFadden, Charles 1965

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A C r i t i c a l E v a l u a t i o n of Hypotheses on the Nature of the E a r t h ' s Core  by C h a r l e s McFadden  Sc., The U n i v e r s i t y of B r i t i s h Columbia,  1964  A T h e s i s Submitted i n P a r t i a l F u l f i l l m e n t of the Requirements f o r the Degree of Master of S c i e n c e i n the department of Geophysics  We  accept t h i s t h e s i s as conforming to the  /'  r e q u i r e d standard.  The U n i v e r s i t y of B r i t i s h August,  1965  Columbia  In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y  of  B r i t i s h C o l u m b i a , I agree t h a t the L i b r a r y s h a l l make i t  freely  a v a i l a b l e f o r r e f e r e n c e and s t u d y .  per-  I f u r t h e r agree t h a t  mission f o r extensive copying of t h i s t h e s i s f o r  scholarly  purposes may be g r a n t e d by the Head o f my Department o r by his representatives,,  It  i s understood t h a t c o p y i n g o r p u b l i -  c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n .  P.P. MnFflflden  Department o f ftftriphyMflS The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada D a  te  February  ^rd  r  1966.  ABSTRACT  Arguments and evidence from many r e l a t e d branches of geophysics  are used  to e v a l u a t e the p r i n c i p a l  on the nature of the e a r t h ' s core. on the composition  No d e f i n i t e c o n c l u s i o n s  of the core are reached.  with improved data from seismology,  hypotheses  Nevertheless,  high p r e s s u r e p h y s i c s and  p l a n e t a r y astronomy, i t should be p o s s i b l e to o b t a i n f u r t h e r i n s i g h t on the nature of the earth's core on the b a s i s of the arguments summarized i n t h i s  thesis.  ii TABLE OF CONTENTS  1.  INTRODUCTION 1.1  1.2 2.  1  Summary of major arguments on the nature of the core mantle boundary.  5  Origin  7  of the s o l a r  system  EVIDENCE FROM METEORITES  13  2.1  C l a s s i f i c a t i o n of meteorites  14  2.2  Parent bodies of meteorites  17  2.3  N u c l e o s y n t h e s i s and e x t i n c t  2.4  Genetic r e l a t i o n s 2.41 2.42  2.43 2.5  radioactivity  among meteorites  24 33  The hypothesis o f an igneous o r i g i n of meteorites Carbonaceous c h o n d r i t e s , o r d i n a r y c h o n d r i t e s and Wood's theory on the o r i g i n of meteorites  36  L e v i n ' s theory on the o r i g i n of meteorites  41  Observations and c o n c l u s i o n s  33  44  3.  CHEMICAL ABUNDANCES  47  4.  TRANSITION TO A METALLIC PHASE  51  5.  THE MOON  63  5.1  The o r i g i n of the moon  63  5.2  F u r t h e r evidence from a study of the moon  67  6.  EVIDENCE FROM THE ABUNDANCES OF Th, U AND Pb  76  7.  THERMAL HISTORY OF THE EARTH  83  7.1  Sources of heat and the primeval temperature of the e a r t h  83  -  iii  TABLE OF CONTENTS (Cont'd.)  7.2  7.3  8.  M e l t i n g p o i n t and a c t u a l temperatures in the earth  89  Thermal h i s t o r y and the core of the earth  96  THE POSSIBILITY OF CONVECTION AND DIFFERENTIATION IN THE EARTH 8.1 8.2  Chemical evidence on the p o s s i b i l i t y of d i f f e r e n t i a t i o n  10.  11.  12.  105  The p o s s i b l e r o l e of convection i n the e a r t h  9.  1°5  107  THE EQUATION OF STATE OF THE EARTH  119  THE CONSTITUTION OF THE EARTH  131  10.1  The upper mantle  131  10.2  The lower mantle  138  10.3  The core  141  PLANETARY MODELS  149  11.1  A s t r o n o m i c a l data  149  11.2  P l a n e t a r y models  151  CONCLUSIONS  162  BIBLIOGRAPHY  167  - iv TABLES  1.  I ^  2.  Weight Percents of Irons, Stony-Irons Stones of T o t a l M e t e o r i t e " F a l l s "  3.  4.  5.  -Xe  ^ Decay I n t e r v a l s  27  and 47  A s t r o n o m i c a l Data: Diameters and Mean D e n s i t i e s of the T e r r e s t r i a l Planets  52  Estimates of the Content Chondrites  84  of K, U and Th i n  I n t e r n a l Layers of the E a r t h  119  FIGURES The c a l c u l a t e d v a r i a t i o n of the mean d e n s i t y with the mass of t h e planet ( a f t e r RAMSEY, 1948)  Schematic r e p r e s e n t a t i o n of the e l e c t r o n i c energy l e v e l s ( a f t e r RAMSEY, 1949)  The t r a n s i t i o n to the m e t a l l i c phase. The s u b s c r i p t s 1 and 2 r e f e r to the normal and m e t a l l i c phases r e s p e c t i v e l y ( a f t e r RAMSEY, 1949) Estimates of m e l t i n g temperatures and a c t u a l temperatures i n t h e earth Equations of s t a t e f o r the earth  - v i-  ACKNOWLEDGEMENTS  I am indebted  to Professor  J . A„ Jacobs not only f o r  h i s help as s u p e r v i s o r of t h i s t h e s i s but a l s o i n such matters as a s s i s t a n c e i n o b t a i n i n g summer employment and encouragement of my i n t e r e s t i n geophysics, materially contributed  to this t h e s i s .  a l l of which  I am e s p e c i a l l y  g r a t e f u l t o Dr. B. J . L e v i n f o r h i s correspondence and considerable helped  a s s i s t a n c e and encouragement.  by many d i s c u s s i o n s with  I was a l s o  P r o f e s s o r s R. D. R u s s e l l ,  W. F. Slawson and G. P. E r i c k s o n .  1.  INTRODUCTION Most problems of fundamental  importance  i n geophysics  are yet unsolved or o n l y p a r t i a l l y or i n c o n c l u s i v e l y answered However, w i t h the a i d of e l e c t r o n i c computers, the present advanced s t a t e of p h y s i c a l and chemical s c i e n c e and  the  g r e a t e r number of people c u r r e n t l y engaged i n s c i e n t i f i c work the means probably e x i s t blems .  today f o r s o l v i n g some of these pro-  I t i s not surprising,, then, that g e o p h y s i c a l problems  occupy the a t t e n t i o n of a l a r g e and growing  number of  scientists.  In s p i t e of the f a c t  that many fundamental  blems remain  unsolved,, the accomplishments of t h i s young  branch of s c i e n c e are by no means s m a l l . theoretical,  s e i s m i c , g r a v i t y , magnetic,  pro-  The amount of heat flow, h i g h -  p r e s s u r e , a s t r o n o m i c a l and geochemical work that has been done which has a b e a r i n g on the c o n s t i t u t i o n and behaviour of the e a r t h i s q u i t e i m p r e s s i v e . In view of the l a r g e amount of experimental and  theoreti  c a l work that has been c a r r i e d out i n geophysics, i t might. seem strange that such a fundamental  problem  as the nature of  the e a r t h ' s core - whether i t i s b a s i c a l l y a n i c k e l - i r o n alloy_ or a m e t a l l i c phase of s i l i c a t e c l u s i v e l y solved.  However, our knowledge of the earth's core  is necessarily indirect Furthermore,  - has not yet been con-  s i n c e we cannot  t h i s problem  reach i t by  and the i n d i r e c t  drilling.  evidence b e a r i n g  on i t are c l o s e l y connected with other unsolved  problems,  e.g.,  the o r i g i n of m e t e o r i t e s , the o r i g i n of the moon and  the p o s s i b l e r o l e of c o n v e c t i o n i n the e a r t h . At l e a s t  s i x hypotheses  the chemical composition  and  can be c o n s t r u c t e d which r e l a t e i n t e r n a l s t r u c t u r e of the e a r t h  to that of the other t e r r e s t r i a l p l a n e t s , although the e v i dence e v a l u a t e d i n t h i s t h e s i s does not g i v e them a l l equal support. .,' Two  hypotheses  chemically d i s t i n c t  can be c o n s t r u c t e d f o r a core which i s from the mantle, i . e . , c o n s i s t i n g  p r i n c i p a l l y of i r o n .  On  hypothesis I, the chemical  composi-  t i o n of each of the t e r r e s t r i a l p l a n e t s i s e s s e n t i a l l y  the  same,except that of Mercury, which has a h e a v i e r , more r e f r a c t o r y composition because of i t s p r o x i m i t y to the  sun.  On hypothesis II,, the t e r r e s t r i a l p l a n e t s have d i f f e r e n t chemical  compositions.  Four hypotheses  can be c o n s t r u c t e d f o r a core which i s a  h i g h - p r e s s u r e , m e t a l l i c phase of q u a r t z - p l u s - o x i d e s or cates.  A c c o r d i n g to hypotheses  I I I and  IV, the moon and  t e r r e s t r i a l p l a n e t s have the same chemical whereas on hypotheses  variation hypotheses  the  composition  V and VI they are d i f f e r e n t .  IV and VI d i f f e r from hypotheses  sili-  Hypotheses  I I I and V by assuming some  i n chemical composition with depth  i n the e a r t h .  I I I and V, the e n t i r e e a r t h below the c r u s t  and  upper mantle i s homogeneous ( i n c o m p o s i t i o n ) . A v a r i a n t of hypothesis I I I , i n which the inner core i s considered t o be n i c k e l - i r o n , has been proposed (1949c, 1952a, b) .  by B U L L E N  In  - 3 Hypotheses I and I I f o r an e s s e n t i a l l y  i r o n core  neces-  s i t a t e a s p e c i a l e x p l a n a t i o n f o r a d i f f e r e n c e i n chemical comp o s i t i o n between the e a r t h and the moon.  Such an e x p l a n a t i o n  must be s o u g h t i n the answer t o the question of the o r i g i n of the moon.  In t u r n , i f a l l evidence  o r i g i n a t e d with an average  i n d i c a t e s that the moon  composition  c l o s e to that of the  e a r t h , then t h i s evidence would be a s t r o n g argument a g a i n s t hypotheses  I and I I .  The problem of the o r i g i n of the s o l a r  system i s c o n s i d e r e d b r i e f l y i n s e c t i o n 1.2 o f t h i s and  thesis  the problem of the o r i g i n of t h e moon i n s e c t i o n 5.1. Hypotheses I I , V and VI r e q u i r e s p e c i a l e x p l a n a t i o n s  f o r F e / S i f r a c t i o n a t i o n i n the c i r c u m s o l a r gas-dust or i n the process of the growth of the p l a n e t s . cated inhomogeneity  cloud  The i n d i -  by hypothesis I I i s a lower F e / S i r a t i o  f o r Venus and Mars than f o r the earth (see Chapter  11).  It  must be noted that Venus i s c l o s e r and Mars more d i s t a n t from the sun than the e a r t h ;  hence two e x p l a n a t i o n s would  be r e q u i r e d . f o r the lower Fe content Conversely, hypotheses  i n both Venus and Mars.  V and VI imply that both Venus and  Mars have a higher content of Fe than the e a r t h (see s e c t i o n 1.1,  Chapter  4 and 11).  On the b a s i s of the evidence and  arguments considered i n t h i s t h e s i s , the f o l l o w i n g observat i o n s can be made.  I f improved s e i s m i c and a s t r o n o m i c a l data  together with the i r o n - c o r e hypothesis imply that the e a r t h has a h e a v i e r composition than both Venus and Mars, t h i s may  - 4 be an argument against the i r o n - c o r e hypotheses  i n the absence  of s p e c i a l e x p l a n a t i o n s f o r such an inhomogeneity.  On  the  other hand, reasonable arguments have been advanced i n support of the inhomogeneity s e c t i o n 1.2  and  suggested by hypotheses  section  V and VI  (see  2.43).  Hypotheses I and II and to a l e s s e r extent perhaps  also  IV and V depend on the p o s s i b i l i t y of c o n v e c t i o n i n the mantle.  In a d d i t i o n to a t h e o l o g i c a l d i s c u s s i o n , t h i s r e -  q u i r e s c o n s i d e r a t i o n of the thermal h i s t o r y of the e a r t h and, consequently, an e v a l u a t i o n of t h e o r e t i c a l and m e l t i n g p o i n t temperatures  experimental  and a c o n s i d e r a t i o n of sources of  heat i n the e a r t h (Chapters 7 and 8). F u r t h e r c o m p l i c a t i o n s a r i s e from the circumstance there i s no d i r e c t way of the e a r t h . mantle,  that  of determining the gross composition  Soon i t may  be p o s s i b l e to sample the upper  but so f a r only the s i a l i c  c r u s t has been sampled,  representing, an i n s i g n i f i c a n t f r a c t i o n of the volume of the earth.  Estimates of the gross composition of the e a r t h are  made from a c o n s i d e r a t i o n of the abundances of the  elements  i n m e t e o r i t e s and are u s u a l l y i n f l u e n c e d by the assumption  of  a n i c k e l - i r o n core by analogy with n i c k e l - i r o n m e t e o r i t e s . It i s t h e r e f o r e necessary to g i v e c a r e f u l c o n s i d e r a t i o n to s t u d i e s of m e t e o r i t e s i n order t o determine  the best e s t i m a t e  of m e t e o r i t i c abundances and e v a l u a t e p o s s i b l e and. probable  - 5 r e l a t i o n s between such abundances and the composition of the earth. 1.1  Summary of major arguments on the nature of the core-mantle boundary. It w i l l prove i n t e r e s t i n g l a t e r t o cpmpare the evidence  considered i n t h i s t h e s i s w i t h the arguments which have been advanced  (a) a g a i n s t the hypothesis of a t r a n s i t i o n of  cates to a m e t a l l i c phase at the core-mantle  boundary and  a g a i n s t the h y p o t h e s i s of a c h e m i c a l l y d i s t i n c t c o r e . arguments are presented here by way  sili(b)  These  of i n t r o d u c t i o n and as a  reference for l a t e r discussion. Arguments a g a i n s t a phase t r a n s i t i o n : a.  Experiments  with s i l i c a t e s under shock p r e s s u r e s  equal t o those p r e s s u r e s i n the earth's core g i v e no  evidence  of a phase t r a n s i t i o n . b.  Estimates of the dimensions  and masses of Mercury and  Venus obtained from Rabe's work on the o r b i t on the assumption  of Eros show that,  that the t e r r e s t r i a l p l a n e t s are c h e m i c a l l y  homogeneous, Ramsey's hypothesis i s untenable. c.  I f a m e t e o r i t i c model i s assumed f o r the e a r t h , then  Ramsey'shypothesis i s a u t o m a t i c a l l y excluded because i t i s i n c o n s i s t e n t with m e t e o r i t i c abundances of i r o n to s i l i c o n magnesium (RINGWOOD, 1959). d. will  It i s u n l i k e l y that a non metal - metal  result  transition  i n such a l a r g e i n c r e a s e i n d e n s i t y as that  and  - 6 i n d i c a t e d at the core-mantle (RINGWOOD, 1959; e.  boundary (a r a t i o of 1.6-1.7)  BIRCH, 1961).  C a l c u l a t i o n s based  on the Thomas-Fermi method, which  gives d e n s i t i e s f o r completely i o n i z e d elements,  suggest  that  a compound such as Mg2SiC>4 of mean atomic number equal to 10 would reach a d e n s i t y of 10gm/cm o n l y at a p r e s s u r e ten times 3  as great as that at the core mantle boundary, even i n the fully  i o n i z e d c o n d i t i o n (BIRCH, 1952).  Arguments a g a i n s t a c h e m i c a l l y d i s t i n c t a.  core:  The hypothesis of a c h e m i c a l l y d i s t i n c t  an e s s e n t i a l l y  core, i . e . ,  i r o n core, i s i n c o n s i s t e n t w i t h the  observed  mean d e n s i t i e s of the t e r r e s t r i a l p l a n e t s i f i t i s assumed that the chemical c o n s t i t u t i o n s of these p l a n e t s are to that of the e a r t h (JEFFREYS, 1937;  RAMSEY, 1949).  any case, t h e r e has been no success i n e x p l a i n i n g how d i f f e r e n c e s arose b.  similar And  in  such  (LEVIN, 1962a, 1964a).  I f gravity.were the c o n t r o l l i n g f a c t o r , then the jump  i n d e n s i t y would be spread over at l e a s t  300 km.  Thus, a  sharp boundary, as i n d i c a t e d by s e i s m i c data, i s d i f f i c u l t , i f not i m p o s s i b l e , to r e c o n c i l e with a change i n chemical composition  (RAMSEY, 1949). c.  Using the r e s u l t s of a t h e o r e t i c a l study of the  i n g p o i n t temperatures  of s i l i c a t e s ,  s i l i c a t e s by Zharkov (1959), who  melt-  i r o n and m e t a l l i z e d  obtained somewhat d i f f e r e n t  r e s u l t s from Uffen's p r e v i o u s s t u d i e s , the hypothesis of an  - 7 i r o n core i s not capable of e x p l a i n i n g i t s molten s t a t e and at the same time the s o l i d s t a t e of the adjacent  lower  mantle  (LEVIN, 1962a, 1964a). d. Stoke's  Based on c a l c u l a t i o n s of L u s t i k (1948), formula  who  used  to c a l c u l a t e the speed of s i n k i n g of i r o n  i n c l u s i o n s of v a r i o u s s i z e s and cate i n c l u s i o n s ,  the speed of r i s i n g of  sili-  g r a v i t a t i o n a l d i f f e r e n t i a t i o n of stone  and  i r o n i n the i n t e r i o r proceeds too slowly to g i v e the e a r t h an i r o n core e.  (LEVIN, 1962a, 1964a). Shock compression  of i r o n up to p r e s s u r e s of s e v e r a l  m i l l i o n atmospheres shows that i t s d e n s i t y under these cond i t i o n s i s somewhat g r e a t e r than the a c t u a l d e n s i t y of the e a r t h ' s core, n e c e s s i t a t i n g a n admixture of l i g h t e r m a t e r i a l , thus d e s t r o y i n g t h e analogy  with i r o n meteorites  (LEVIN,  1962a, 1964a). f.  There i s a l a r g e d i s c r e p a n c y between estimates  the content i r o n , and core  of i r o n i n meteorites, p a r t i c u l a r l y of m e t a l l i c  the i r o n content  (RAMSEY, 1949; We  will  of  of an e a r t h with a n i c k e l - i r o n  LEVIN, p e r s o n a l  communication).  see that many of these n e g a t i v e arguments are  i n c o r r e c t w h i l e a l l but the l a s t argument against a chemically distinct evidence 1.2  core are q u e s t i o n a b l e , or unsupported by  considered i n t h i s  thesis.  O r i g i n of the s o l a r system I f the nature of the e a r t h ' s core were known, such  the  knowledgewould haveto be taken i n t o account  i n the study of  the q u e s t i o n of the o r i g i n of the s o l a r system. if  In p a r t i c u l a r ,  i t were e s t a b l i s h e d that the e a r t h ' s core were a n i c k e l -  i r o n a l l o y , then a l a r g e d i f f e r e n c e i n composition  between the  earth and the moon would have to be e x p l a i n e d by any acceptable theory of the o r i g i n of the moon.  Moreover, a more  d e f i n i t e d e t e r m i n a t i o n of the equation of s t a t e of the m a t e r i a l of the e a r t h ' s mantle and core, together with more p r e c i s e data on the diameters  and masses of the t e r r e s t r i a l p l a n e t s ,  would determine the nature o f the v a r i a t i o n of the t e r r e s t r i a l p l a n e t s .  i n the i r o n  content  This v a r i a t i o n would have t o be  e x p l a i n e d by any theory of the o r i g i n of the s o l a r system. On the other hand, i f the processes which gave r i s e to the s o l a r system were known i n s u f f i c i e n t d e t a i l ,  t h i s know-  ledge would help i n e v a l u a t i n g hypotheses on the nature of the earth's core.  Although  there i s some d i f f e r e n c e of o p i n i o n  about the l e v e l o f c u r r e n t knowledge on the question of the o r i g i n of the s o l a r system, i t i s n e v e r t h e l e s s f a i r  to con-  c l u d e that t h i s knowledge i s not yet adequate to d e f i n i t e l y d i s t i n g u i s h between d i f f e r e n t hypotheses on the nature o f the earth's core.  At the same time,  the c l o s e connection between  these two problems cannot be n e g l e c t e d . T h i s t h e s i s was o r i g i n a l l y undertaken i n order to e v a l u ate the v a l i d i t y of the c o n c l u s i o n of the Schmidt theory on the o r i g i n of the s o l a r system that the moon and the t e r r e s t -  _ 9 _  r i a l p l a n e t s , except Mercury, have n e a r l y i d e n t i c a l t i o n s and t h a t , t h e r e f o r e , Ramsey's hypothesis i s a high-pressure  composi-  that the core  phase of mantle m a t e r i a l i s c o r r e c t .  b r i e f i n t r o d u c t i o n t o t h i s t h e o r y . i s , thus,  A  i n c l u d e d here.  Adherents of the Schmidt theory b e l i e v e that the w e l l known r e g u l a r i t i e s and even the i r r e g u l a r i t i e s of the o r b i t s of p l a n e t s and s a t e l l i t e s ,  the e x i s t e n c e of an a s t e r o i d zone,  meteors and comets and c u r r e n t composition  knowledge of the chemical  of the p l a n e t s , p a r t i c u l a r l y the chemical  i n t o two groups, have permitted  the e l a b o r a t i o n of a reason-  ably complete, q u a n t i t a t i v e l y developed theory of the s o l a r system (SCHMIDT, 1944, 1958; 1960b; 1960,  GUREVICH and LEBEDINSKY, 1950; 1962;  RUSKOL, 1960c).  the sun i s considered A major question  of the o r i g i n  LEVIN, 1958,  SAFRONOV, 1958, 1960a,  T h e i r use of the term " s o l a r  system" i n c l u d e s the p l a n e t s , t h e i r s a t e l l i t e s , meteors and comets;  division  the a s t e r o i d s ,  the sun i s excluded s i n c e the o r i g i n of a separate  problem.  t o which the theory  has not given a  c o n c l u s i v e answer, i s the o r i g i n of the gas-dust cloud which at one time surrounded the sun and had at l e a s t 98% of the angular  momentum of the s o l a r system i n c l u d i n g the sun.  p o s s i b i l i t i e s a r e now being c o n s i d e r e d . ents of the Schmidt theory captured  Originally,  Two  adher-  thought that t h i s cloud was  by the sun, which p o s s i b i l i t y was d i s c u s s e d  three body problem s o l v e d by Schmidt and Hilmy  in a  (SCHMIDT, 1958)  - 10 and i n subsequent work by o t h e r s .  The other p o s s i b i l i t y i s  that mass and angular momentum were t r a n s f e r r e d from a r a p i d l y r o t a t i n g , sun by e l e c t r o m a g n e t i c f o r c e s , a hypothesis which was  first  suggested  by ALFVEN (1954) and which has been put  i n t o a more a c c e p t a b l e , yet s t i l l  i n c o n c l u s i v e form by  HOYLE (1960, 1963). A s i d e from the problem of the o r i g i n of a c i r c u m s o l a r gas-dust  c l o u d with over 98% of the angular momentum of the  s o l a r system, the Schmidt theory i s b a s i c a l l y a q u a n t i t a t i v e e l a b o r a t i o n of the e v o l u t i o n of the gas-dust  cloud under the  i n f l u e n c e of constant s o l a r r a d i a t i o n of t h e same amount as the sun emits today.  The e v o l u t i o n i s t r a c e d through the  v a r i o u s stages which l e d f i n a l l y to the development of an i n n e r and outer zone of p l a n e t s , some with s a t e l l i t e s , a l l l y i n g n e a r l y i n a plane with an a s t e r o i d zone i n between the two groups.  I t proved p o s s i b l e to e x p l a i n q u a n t i t a t i v e l y the  process of growth of the p l a n e t s , the r e g u l a r i t i e s of the p l a n e t a r y o r b i t s , the a x i a l r o t a t i o n of the p l a n e t s , the o r i g i n of s a t e l l i t e s ,  the o r i g i n of Saturn's  r i n g s and, based  on a  c o n s i d e r a t i o n o f the v a r i a t i o n of b l a c k body temperature  with  d i s t a n c e from the sun and of the change i n time of the opaqueness of t h e two groups,  the chemical composition  p l a n e t s and the o r i g i n of the a s t e r o i d zone and comets. short review a r t i c l e (1962b).  of the A  ( i n E n g l i s h ) has been given by L e v i n  - 11 A c c o r d i n g to the Schmidt theory, the bodies which accumulated  i n t o the t e r r e s t r i a l  ponent of the gas-dust  p l a n e t s formed from the dust com-  c l o u d , which i s thought  p r i n c i p a l l y and u n i f o r m l y of o x i d e s . s e p a r a t e d out from the gas-dust  t o be composed  T h i s dust  component  c l o u d c o n c e n t r a t i n g towards  the L a p l a c e plane of the s o l a r system, the plane d e f i n e d by the a n g u l a r momentum v e c t o r of the whole system of gas dust.  The  and  gas component of the c l o u d only condensed onto  dust p a r t i c l e s and p a r t i c i p a t e d to a s i g n i f i c a n t  the  degree i n  the f o r m a t i o n of the bodies i n the more d i s t a n t , c o l d e r r e g i o n s , that i s i n the a s t e r o i d zone and giant planets.  i n the zone of the  (See UREY (1957) f o r chemical support  of the  a c c r e t i o n of c o l d dust p a r t i c l e s i n the f o r m a t i o n of the terrestrial  planets.)  Supporters of the Schmidt theory u s u a l l y adopt  Ramsey's  h y p o t h e s i s of a m e t a l l i c phase t r a n s i t i o n because the  nickel-  i r o n core h y p o t h e s i s would r e q u i r e a s p e c i a l h y p o t h e s i s f o r the o r i g i n of the moon, because of i t s low mean d e n s i t y . A l s o , on the assumption  that the p l a n e t s formed under the i n -  f l u e n c e of s o l a r r a d i a t i o n having the same s t r e n g t h at the time of f o r m a t i o n as i t does today,  s u p p o r t e r s of the Schmidt  t h e o r y b e l i e v e that the e n t i r e dust c l o u d , except f o r the innermost  zone, had  an e s s e n t i a l l y homogeneous composition  s i s t i n g p r i m a r i l y of o x i d e s . terrestrial  con-  Hence they p r e d i c t e d t h a t the  p l a n e t s , which formed from t h i s dust component of  - 12 the gas-dust c l o u d , have an e s s e n t i a l l y homogeneous composit i o n , except f o r Mercury. was  unacceptable  i m p l i e s chemical  Therefore  the i r o n core  hypothesis  on the a d d i t i o n a l grounds t h a t i t apparently inhomogeneity of the t e r r e s t r i a l p l a n e t s i n  the sense that the e a r t h has  a g r e a t e r percent  iron  content  than Venus and Mars, LEVIN (1965a), one theory,  of the c h i e f proponents of the Schmidt  has h i m s e l f drawn a t t e n t i o n to the f a c t that  the  d e n s i t y of Mercury i s an i n d i c a t i o n of a t h e o r e t i c a l l y  pre-  d i c t e d e a r l y high temperature stage i n the h i s t o r y of the when the sun's l u m i n o s i t y was  sun  s u f f i c i e n t l y high f o r tempera-  tures i n the innermost zone of opaque c o n c e n t r a t i o n of dust t o exceed 440°K, the temperature r e q u i r e d f o r i r o n to i n m e t a l l i c r a t h e r than oxide  state.  This c o n c l u s i o n negates  a fundamental assumption i n the development of the theory that the o r i g i n and neglected.  As d i s c u s s e d  Schmidt  e a r l y h i s t o r y of the sun  i n Chapters 2, 5 and  of o x i d a t i o n of the p l a n e t s and  occur  11,  could  be  the s t a t e  hence the percentage  content  of i r o n depends both on the temperatures i n the gas-dust cloud b e f o r e , and  the p o s s i b l e r o l e of reducing  d u r i n g the formation problems and known and  of the p l a n e t s .  The  compounds  answers to  these  of the o r i g i n of the gas-dust cloud are  not  no d e f i n i t e c o n c l u s i o n s can be reached, on  the  b a s i s of any  theory of the o r i g i n of the s o l a r system, on  s i m i l a r i t y i n chemical  composition  of the t e r r e s t r i a l  the  planets.  - 13 -  2.  EVIDENCE FROM METEORITES The study of the o r i g i n and nature of meteorites  e s p e c i a l l y complex one.  i s an  S c i e n t i s t s s e r i o u s l y engaged i n t h i s  study u s u a l l y advise c a u t i o n i n adopting hypotheses or t h e o r i e s which attempt t o r e l a t e or u n i f y the e x i s t i n g But  the r a p i d accumulation  data.  of evidence has two e f f e c t s .  While on the one hand, new data u s u a l l y i n c r e a s e the number of problems t o be s o l v e d , at the same time they b r i n g us c l o s e r t o the c o r r e c t answers t o the major q u e s t i o n s :  (1)  what are the parent bodies of meteorites and (2) what are the g e n e t i c r e l a t i o n s h i p s among meteorites, of  i . e . , the o r i g i n  meteorites. Given  cerned,  the answers to these two q u e s t i o n s , we are con-  f i r s t , with the b e a r i n g of t h i s i n f o r m a t i o n on the  composition  of the e a r t h and moon, and second, with any i n d i -  c a t i o n that t h i s i n f o r m a t i o n might g i v e of processes t a k i n g p l a c e i n the e a r t h .  Thus, i f answers to the major questions  i n the study of meteorites are u n c e r t a i n , answers to our problems w i l l  be even more u n c e r t a i n .  F o r t u n a t e l y , there seems  to be a reasonably w e l l - e s t a b l i s h e d answer to q u e s t i o n (1) and, at l e a s t , some good ideas with regard to question ( 2 ) . In c o n c l u s i o n , we w i l l  c o n s i d e r the i m p l i c a t i o n s o f these  answers on the nature of the earth's c o r e .  - 14 2.1  C l a s s i f i c a t i o n of meteorites Of a l l meteorites  observed  to f a l l ,  are stony i r o n s and 6% are i r o n s . 85%,  5%, and 10%, r e s p e c t i v e l y .  over 80% of a l l meteorites  92% are stones, 2%  The weight percent Of the stones,  observed  to f a l l ,  ages are  90%, i . e . ,  are c h o n d r i t e s  (LEVIN, 1965). At l e a s t s i x groups of c h o n d r i t e s have been d i s t i n g u i s h e d . These groups are shown by the d i f f e r e n t  r a t i o s of metallic  i r o n t o o x i d i z e d i r o n i n a p l o t of weight percent metal and FeS a g a i n s t weight percent 1962). first  of Fe i n  of o x i d i z e d i r o n  (MASON,  The e x i s t e n c e of a low and a high t o t a l Fe group, observed  by UREY and CRAIG (1953), i s a l s o evident on  such a plot„ The found  overwhelming m a j o r i t y of c h o n d r i t e s which have been  are o l i v i n e - b r o n z i t e c h o n d r i t e s  hypersthene c h o n d r i t e s  (270).  called ordinary chondrites. are n e a r l y i n chemical chondrules  (196) and o l i v i n e -  Together they comprise the soThe minerals  equilibrium;  have n e a r l y constant  i n these  chondrites  f o r example, the o l i v i n e  Fe content.  Another c h a r a c t -  e r i s t i c f e a t u r e of o r d i n a r y c h o n d r i t e s i s that they are d e p l e t e d of such v o l a t i l e elements as Hg and Cd (MASON, 1963; ANDERS, 1964). Enstatite drites  (9), p i g e o n i t e (12) and carbonaceous chon-  (12) are much r a r e r (MASON, 1963).  The o l i v i n e -  p i g e o n i t e and carbonaceous c h o n d r i t e s are d i s e q u i l i b r i u m  - 15 assemblages;  the o l i v i n e chondrules i n them are of d i f f e r e n t  composition and i n carbonaceous  c h o n d r i t e s there i s a s t r o n g  d i s e q u i l i b r i u m between the chondrules and the matrix. e n s t a t i t e c h o n d r i t e s are h i g h l y reduced; i s almost  the s i l i c a t e phase  i r o n - f r e e and even some of the s i l i c o n has been r e -  duced to i r o n s i l i c i d e .  The presence of w a t e r - s e n s i t i v e  m i n e r a l s such as CaS and MgS  i n d i c a t e s very d r y c o n d i t i o n s .  The content of i r o n , t r o i l i t e and t r a c e elements f a c t o r s of two,  v a r i e s by  three and g r e a t e r , r e s p e c t i v e l y , evidence of  a d i v e r s e and heterogeneous  group (ANDERS, 1964).  Wiik d i s t i n g u i s h e d three types of carbonaceous rites.  The  chond-  Type I has a composition very s i m i l a r to that  i n s o l i d matter condensed i n a moderately  expected  c o l d nebula of s o l a r  composition, c o n t a i n i n g s i g n i f i c a n t amounts of hydrated magnesian s i l i c a t e s ,  ferro-  somewhat s i m i l a r to s e r p e n t i n e , but  chondrules and no o l i v i n e .  no  Of the three types, Type I con-  t a i n s the l a r g e s t amount of v o l a t i l e s , probably i t s cosmic complement of a l l elements noble gases.  h e a v i e r than oxygen, except  Type II c o n t a i n s 10 - 15% water and  10 - 30%  o l i v i n e chondrules, w h i l e the main mass i s hydrated Type I I I c o n t a i n s 1% water; cates dominate. cluded.  the  silicate.  o l i v i n e and other anhydrous  sili-  Small amounts of n i c k e l - i r o n are a l s o i n -  While the t h r e e types have n e a r l y the same propor-  t i o n s of n o n v o l a t i l e s  (Mg.  S i , Fe, e t c . ) ,  the p a t t e r n i s a  decrease of v o l a t i l e s by f a c t o r s of approximately two  and  - 16 f o u r r e s p e c t i v e l y , and a marked decrease i n the s t a t e of o x i d a t i o n i n going from I t o I I I (ANDERS, 1964; The Renazzo  LEVIN,  carbonaceous c h o n d r i t e f i t s  1965).  i n t o Type I I but  i t s chondrules a r e v i r t u a l l y F e - f r e e f o r s t e r i t e and e n s t a t i t e , a s s o c i a t e d w i t h l a r g e amounts of Ni-poor metal.  I t s matrix  c o n t a i n s N i i n o x i d i z e d form, as w e l l as magnetite and hydrated s i l i c a t e , but no metal.  (ANDERS, 1964).  These f e a t u r e s form  the b a s i s o f a theory by Wood, supported by Anders, on the o r i g i n of m e t e o r i t e s .  We s h a l l consider: t h i s  later.  The a c h o n d r i t e s , which are a group of stones that have no chondrules and comprise about 9% of a l l m e t e o r i t e s observed to f a l l ,  are h i g h l y d i f f e r e n t i a t e d and c o a r s e l y  crystallized.  They resemble remelted s i l i c a t e p a r t s of c h o n d r i t e s 1965).  (LEVIN,  Another group of stones a r e the b r e c c i a s which are  b e l i e v e d to be the product of c o l l i s i o n s of m e t e o r i t e parent bodies. The i r o n s a r e , to some e x t e n t , d i s t i n g u i s h e d by t h e i r content of N i .  Depending  on both temperature and N i content,  Fe e x i s t s i n ex" and ^ phases at the p r e s s u r e s p r e v a i l i n g i n asteroids.  From a phase diagram of Fe, i t can be seen that  at constant p r e s s u r e , c o o l i n g of l a r g e monocrystals from temperatures when only the )&-phase e x i s t s , proceeds t o a t r a n s i t i o n t o the (/-phase.  T h i s occurs above 600 - 700° K  f o r normal N i - c o n t e n t i n m e t e o r i t e s .  For N i content l e s s  than 6%, the Fe i s e n t i r e l y r e c r y s t a l l i z e d  i n t o kamacite  - 17 (the of-phase)  and some i s transformed by l a t e r thermal meta-  morphism i n t o the n i c k e l - p o o r a t a x i t e s .  Iron meteorites w i t h  a content o f N i of 6 - 14% are u s u a l l y o c t a h e d r i t e s , kamacite and t a e n i t e  (the X-phase) separated i n a r e g u l a r p a t t e r n , known  as the Widmanstatten p a t t e r n .  The N i r i c h a t a x i t e s a r e i r o n s  with a g r e a t e r content of N i .  The c o r r e l a t i o n between percen-  tage N i and type i s not exact, however,  In a d d i t i o n there i s  some evidence that i r o n s o r i g i n a t e from d i f f e r e n t bodies with d i f f e r e n t  2.2  i n t e r n a l pressures  parent  (LEVIN, 1965).  Parent bodies of meteorites ANDERS (1964) has reviewed  the a s t r o n o m i c a l evidence f o r  the l o c a t i o n of the o r i g i n of meteorites and the s i z e of the parent b o d i e s .  H i s o b s e r v a t i o n s and c o n c l u s i o n s are d i s c u s s e d  briefly in this  section.  Of about seventy m e t e o r i t e o r b i t s c a l c u l a t e d from o b s e r v a t i o n s , about ten are considered t o l e r a b l y  visual  reliable.  In a d d i t i o n one o r b i t , that of the Pribram b r o n z i t e c h o n d r i t e , was determined  photographically.  The r e s u l t s f o r the l a t t e r  are semi-major a x i s a, 2.42 AU, e c c e n t r i c i t y e, 0.67, and inclination  i , 10.4.  These o r b i t s a r e compared  (1) with the  A p o l l o Group of a s t e r o i d s , which i s that group of a s t e r o i d s with e a r t h - c r o s s i n g o r b i t s and (2) with a t h e o r e t i c a l t r i b u t i o n of o r b i t a l elements c a l c u l a t e d by A r n o l d f o r bodies o r i g i n a t i n g i n c o l l i s i o n s with the moon.  dis-  (1964) There  - 18 appears to be no s t a t i s t i c a l l y meteorites and  s i g n i f i c a n t d i f f e r e n c e between  the A p o l l o Group of a s t e r o i d s ;  these, however,  c l e a r l y do not match the d i s t r i b u t i o n f o r a l u n a r o r i g i n . Moreover, g e o c e n t r i c v e l o c i t i e s c a l c u l a t e d by Arnold f o r bodies  of lunar o r i g i n  f o r meteorites  range from 5 - 8  of a s t e r o i d a l o r i g i n are approximately  sec, i n agreement with the observed i t e s and  18.2  16.6  which i s r a t h e r l a r g e . the stony meteorites  15  km/  Furthermore,  from the moon i s 2.4  Opik concludes  those  km/sec f o r 8 meteor-  km/sec f o r 8 A p o l l o a s t e r o i d s .  the escape v e l o c i t y of bodies  must be due  km/sec, whereas  km/sec,  that at most 0.2%  might have come from the moon and  of  these  to c o l l i s i o n s with comet n u c l e i i n retrograde  o r b i t s s i n c e these are the only bodies whose o r b i t s  possess  the r e q u i r e d v e l o c i t i e s of g r e a t e r than 45 km/sec. Whipple and Hughes have a l s o r u l e d out comets as a major source of meteorites  on the grounds that the e l o n g a t i o n s of  apparent r a d i a n t s of meteorites ent of high i n c l i n a t i o n .  do not show a cometary compon-  These r e s u l t s suggest  that the most  s e r i o u s c o n s i d e r a t i o n should be given to the A p o l l o Group of asteroids.  These a s t e r o i d s were probably d e r i v e d from the  Mars a s t e r o i d s , i . e . , those which cross the o r b i t of Mars, by p e r t u r b a t i o n s or c o l l i s i o n s that made t h e i r o r b i t s and more e c c e n t r i c . probably  Anders suggests  that t h e i r o r b i t s  c h a r a c t e r i s t i c of a l l s t r a y bodies  space i n the f i n a l stage before E a r t h  smaller are  from t r a n s - M a r t i a n  capture.  - 19 It  i s n a t u r a l to f i r s t  -  consider  the problem of p l a c i n g  asteroidal material into Earth-crossing  orbits.  For  this,  c o l l i s i o n s producing v e l o c i t y changes of 5 km/sec. are  required.  Even head-on c o l l i s i o n s among a s t e r o i d s are i n e f f e c t i v e i n t h i s respect.  Moreover, the p o s s i b i l i t y of an  stage where a t r a n s i t i o n of a s t e r o i d s to orbits f i r s t  Mars-crossing  occurs i s r u l e d out because the change i n the  o r b i t a l v e l o c i t y required This leaves  intermediate  is s t i l l  too great  (1-3  the 34 a s t e r o i d s which are a l r e a d y  o r b i t s as most probable candidates f o r  km/sec).  i n Mars c r o s s i n g  meteorites,  Anders suggests that because A p o l l o a s t e r o i d s and  the  Mars a s t e r o i d s have capture l i f e - t i m e s which are short compared to the age  of the s o l a r system, they must be  by some source.  He  replenished  narrows down t h i s source to w i t h i n 0.2  AU  of those a s t e r o i d s a l r e a d y having Mars c r o s s i n g o r b i t s . As w i l l be d i s c u s s e d  below, there  ous p r o p e r t i e s of meteorites explained 4 or 5.  are c e r t a i n d i s c o n t i n u -  which Anders b e l i e v e s are e a s i e s t  i n terms of a small number of parent bodies, In t h i s regard  i t i s probably s i g n i f i c a n t  e.g.,  that  four  f a m i l i e s of Mars a s t e r o i d s account f o r 98% of the mass and 92% of the c r o s s - s e c t i o n of the Mars a s t e r o i d s and f o u r , two  of these  predominate.  Another p o s s i b l e source of meteorites, Anders, i s h e a v i l y shocked e j e c t a from the the a s t e r o i d b e l t .  A few  discussed  by  c e n t r a l funnel  small fragments of these may  of  sur-  - 20 v i v e and reach us. ureilities,  Anders b e l i e v e s the m e s o s i d e r i t e s and  which appear to be h e a v i l y shocked  meteorites,  are such examples. On omy  the q u e s t i o n of the s i z e of the parent bodies, a s t r o n -  p r o v i d e s three p i e c e s of evidence.  First,  the mass of  the a s t e r o i d zone at present i s no g r e a t e r than 1 x l O ^ tons, 1  which i s l e s s than 1/7 of  of a l u n a r mass - and l e s s than  mass d i s t r i b u t i o n  Moreover, evidence of symmetry of the  i n the a s t e r o i d b e l t  gives no support to a  systematic d e p l e t i o n of the r e g i o n c l o s e r to J u p i t e r . f o r e , i f there was matter  There-  ever much more than the present amount of  i n the a s t e r o i d b e l t ,  the d i f f e r e n c e must have been  l o s t as dust, not as s o l i d fragments. i t does not seem p o s s i b l e to produce  Anders concludes a s t e r o i d s i n the  that 1-770  range by c o l l i s i o n s of l u n a r - s i z e d b o d i e s . Anders g i v e s another p i e c e of evidence from  to  3  the i n i t i a l mass could have l e f t the a s t e r o i d b e l t by the  Martian escape hatch.  km  10~  support h i s c o n c l u s i o n .  astronomy  Four of the l a r g e s t f i v e  o i d s appear s p h e r i c a l i n the t e l e s c o p e , i n d i c a t i n g , that they are primary a c c r e t i o n s .  asterprobably,  A l s o , by c o n s i d e r i n g the  present masses of the f o u r f a m i l i e s of Mars a s t e r o i d s , Anders estimates r a d i i of 104,  105 and 46 km f o r t h r e e of the  parent bodies, although these estimates do not take account mass a l r e a d y l o s t asteroids.  into  i n the form of m e t e o r i t e s and A p o l l o  - 21 The  above r e s u l t s d i s p u t e the commonly supported  hypo-  t h e s i s that meteorites have a s i n g l e l a r g e parent body.  The  chemical evidence d i s c u s s e d by ANDETRS (1964) and LEVIN (1965) i s considered below. Some geochemists b e l i e v e that the l a r g e monocrystals of t a e n i t e i n i r o n meteorites o r i g i n a t e d by c o o l i n g from t h e molten s t a t e .  However, Ringwood observed  that c e r t a i n f e a t u r e s  of these m e t e o r i t e s , e.g., the Widmanstatten p a t t e r n , are uns t a b l e at very high temperatures  and low p r e s s u r e s ;  in fact  p r e s s u r e s g r e a t e r than 30 kb are : r e q u i r e d f o r chemical stability.  But i f a pressure of 30 kb i s to p r e v a i l i n only  1/8 of the volume f o r a d e n s i t y of 3.5 gm/cm^, the radius must be at l e a s t  1530 km (that of the moon i s 1738 km).  But a  molten body of l u n a r s i z e would not c o o l to 300 - 400°C i n the e n t i r e age of the s o l a r system, even i f h e a t i n g by U, 40 . Th and K  i s ignored.  Moreover, the Washington county  iron  meteorite c o n t a i n s i r r e g u l a r pores which become n o t i c e a b l y rounded when heated  t o 1300°C f o r 100 h r . This evidence  putes both very high pressures and temperatures parent  dis-  i n meteorite  bodies.  The presence  of small diamonds, d e f i n i t e l y e s t a b l i s h e d  f o r the Canyon D i a b l o meteorite, has been the main reason f o r the p e r s i s t e n c e o f the hypothesis of lunar s i z e d bodies.  T h i s evidence  parent  has played a p a r t i c u l a r l y prominent  r o l e i n Urey's t h e o r i e s o f the o r i g i n o f the s o l a r system,  - 22 the o r i g i n of the moon, and, of course, the o r i g i n of meteorites . ANDERS (1964) has marshalled evidence  a c o n s i d e r a b l e amount of  a g a i n s t a high s t a t i c p r e s s u r e o r i g i n of these  monds, arguing i n s t e a d f o r a shock o r i g i n . dence of the l o c a l i z e d occurrence  Included  dia-  i s evi-  of the diamonds, evidence of  r e h e a t i n g l a t e i n t h e i r h i s t o r y i n a time of 1-5 seconds and quenching i n l e s s than 20 seconds.  F u r t h e r evidence  f o r the  view that diamond formation took p l a c e d u r i n g impact  has come  from the d i s c o v e r y of shock-produced c o e s i t e and s t i s h o v i t e i n sandstone below the c r a t e r f l o o r of the Canyon D i a b l o meteorite,  i n d i c a t i n g pressures of g r e a t e r than 20 and 100  kb r e s p e c t i v e l y d u r i n g impact.  Moreover, the diamonds occur  i n c a v i t i e s which should have c o l l a p s e d i f the i r o n  meteorites  were ever subjected to h y d r o s t a t i c p r e s s u r e s g r e a t e r than 4 kb f o r a p p r e c i a b l e p e r i o d s of time. More r e c e n t l y , CARTER and KENNEDY (1964) renewed the arguments f o r an o r i g i n of diamonds i n the Canyon D i a b l o and Novo U r e i meteorites under l a r g e h y d r o s t a t i c p r e s s u r e s . argued that the evidence  f o r the l o c a l i z e d occurrence  They  of d i a -  monds i n Canyon D i a b l o was m i s l e a d i n g , and t h a t , i n f a c t , most samples had been taken from one area, i . e . , the rim of the crater.  Moreover, they found  that the one sample from the  p l a i n s r e g i o n s t u d i e s by them was diamond b e a r i n g . to C a r t e r and Kennedy, t h i s sample was not reheated.  According  - 23 ANDERS (1965) c r i t i c a l l y concluded that i t f a i l s first  evaluated  to support  t h e i r evidence and  their contention.  In the  p l a c e , t h e i r "unheated" specimen a c t u a l l y d i s p l a y s con-  s i d e r a b l e evidence of shock i n the 150 to 1000 kb range. Furthermore, there was apparently  some misunderstanding on the  p a r t o f C a r t e r and Kennedy concerning and  number of samples.  the data  on t h e l o c a t i o n  The c o r r e l a t i o n s between diamond con-  t e n t , shock and l o c a t i o n are s t a t i s t i c a l l y  s i g n i f i c a n t , the  p r o b a b i l i t y that diamonds are e q u a l l y common among p l a i n s and -54 rim specimens being 4 x 10  . Moreover, Anders argues that  thermodynamic and k i n e t i c data  show c o n c l u s i v e l y that any  diamonds made p r e t e r r e s t r i a l l y by the Carter-Kennedy model could not have s u r v i v e d the slow c o o l i n g p e r i o d d u r i n g which the Widmanstatten p a t t e r n  formed.  F u r t h e r evidence comes from g a s - r e t e n t i o n ray exposure ages of stone m e t e o r i t e s . gas  r e t e n t i o n ages as great  on the l a r g e parent parent  body occurred  rapid heating  L e v i n p o i n t s out that  as 4.5 - 4.6 x 10^ years  body hypothesis, 10  ages and cosmic  years  require,  that d i s r u p t i o n of the  a f t e r i t s formation.  While  of the i n t e r i o r of such a body might be a s c r i b e d  to s h o r t l i v e d r a d i o a c t i v i t y . ,  i t s c o o l i n g i n t h i s short  val  of time i s i m p o s s i b l e .  mic  ray...exposure ages of b r o n z i t e and hypersthene  inter-  Anders notes the tendency of coschondrites  to c l u s t e r around 3.8 - 5.5, 7-13 and 16-31 and a u b r i t e s , d i o g e n i t e s and p i g e o n i t e s around 45, 20 and 35 m.y. r e s p e c t i v e l y .  - 24 These probably i n d i c a t e times of c o l l i s i o n and break up of parent bodies of the m e t e o r i t e s . I f meteorites were samples of a s i n g l e parent body, they might be expected composition  t o show continuous  and s t r u c t u r e .  i t i e s are prominent. hypersthene  transition  i n chemical  However, s i g n i f i c a n t d i s c o n t i n u -  While  o l i v i n e - b r o n z i t e and  olivine-  c h o n d r i t e s are so homogeneous that each group must  be fragments of the same parent body or some l a y e r of the same body, the e n s t a t i t e c h o n d r i t e s have a range of i r o n content i n chondrules  and the carbonaceous c h o n d r i t e s a range of content  of v o l a t i l e s which i n d i c a t e that they come from parent bodies or d i f f e r e n t  different  l a y e r s of the same body (LEVIN,  1965). The mole percent of FeO  i n ferromagnesian  silicates  is a  good example of the d i s c o n t i n u o u s p r o p e r t i e s of m e t e o r i t e s . While we might expect  a continuous  complete r e d u c t i o n of i r o n , favored 16%.  range of values f o r the i n -  i n f a c t a few  s p e c i f i c values are  (0, 18 and 25%), l e a v i n g a l a r g e h i a t u s between 0 and  A s i m i l a r r e s u l t has been observed  f o r g a l l i u m and  manium, where f o u r groups have been found. 2.3  N u c l e o s y n t h e s i s and e x t i n c t A d i s c u s s i o n of e x t i n c t  (ANDERS,  ger-  1964)  radioactivity  radioactivity i s appropriately  i n c l u d e d at t h i s time because it-., p r o v i d e s some i n f o r m a t i o n on the g e n e t i c r e l a t i o n s and o r i g i n of m e t e o r i t e s .  We  are a l s o  - 25 concerned  with the p o s s i b l e r o l e of e x t i n c t  radioactivity in  the h e a t i n g of meteorite parent bodies, as w e l l as the e a r t h , moon and other t e r r e s t r i a l p l a n e t s .  Indeed, the question of  whether n u c l e o s y n t h e s i s occurred i n the matter p l a n e t s accumulated,  from which the  at a time s h o r t l y before t h e i r accumula-  t i o n , i s r e l e v a n t to the question of the o r i g i n of the  gas-  dust c l o u d and hence, i n d i r e c t l y , to the subject of t h i s  thesis.  HARRISON BROWN (1947) p o i n t e d out the p o s s i b i l i t y that Q  e x t i n c t r a d i o n u c l i d e s with h a l f - l i v e s of 10  years or l e s s  might once have been present i n the e a r l y s o l a r system i f nucleogenesis had taken p l a c e s h o r t l y before i t s f o r m a t i o n . 129  In p a r t i c u l a r , Xe  1 2 9  ,  i t was  suggested  that the decay of I  to  (with a h a l f - l i f e of 17 m.y.), would be e s p e c i a l l y  to d e t e c t because of the low abundance of the i s o t o p e s . o f xenon.  easy  nonradiogenic  The d i s c o v e r y of excess Xe^-  29  would  f i r m the r o l e of nucleogenesis s h o r t l y before formation  conand  would p r o v i d e a method of d a t i n g the i n t e r v a l from the end of TOO  t h e p r o d u c t i o n of I  to the time of the r e t e n t i o n of X e  x  1 2 9  .  (This i n t e r v a l i s known as the formation i n t e r v a l or, more correctly., as the decay i n t e r v a l , unsupported without  decay•of  I  1 2 9  s t r e s s i n g the p o i n t that  , without  chemical f r a c t i o n a t i o n  r e t e n t i o n of the decay product,  c a l event being measured.) (ANDERS,  and  i s the a c t u a l p h y s i -  1962)  129 Xe  would be r e t a i n e d i n the parent body of a meteorite  only a f t e r the temperature  fell  to some 300°K or lower.  This  - 26 c o o l i n g time depends not only on the s i z e of the meteorite parent body but a l s o on the depth of b u r i a l w i t h i n the body, r e s u l t i n g i n a wide spread of I - Xe decay i n t e r v a l s .  (ANDERS, .  1962) It  i s u s u a l l y assumed that a l l m e t e o r i t i c matter  contained i o d i n e with a constant I present s t a b l e j}-27  ^  s  a  m  e  a  s  u  r  e  Q  / i  initially  r a t i o and that the  f i t s one-time 1^29  c o n  tent.  Hence there i s some a r b i t r a r i n e s s i n the time t , when Q  1 of  / i  had  i t s assumed i n i t i a l  value.  If I  n u c l e o s y n t h e s i s i n the galaxy, then t  which p r o d u c t i o n of I  129  ceased.  But  Q  if  i s a product  i s the time at i?o  ±  a.product  s  n u c l e o s y n t h e s i s i n the e a r l y s o l a r system, then t at  which the s o l a r system became i s o l a t e d from galaxy.  e i t h e r case, the i n i t i a l and  i s the  Q  10  -3  .  value o f I  129 / 127 /I  of time  In  i s between  10"  2 1  Most authors assume thxs r a t i o to be 1.25  x 10" ,  which i s the steady s t a t e value f o r a model i n which the elements are s y n t h e s i z e d c o n t i n u o u s l y at a constant r a t e f o r 2 x 10  1 0  years.  Thus, the decay i n t e r v a l s measured are u s e f u l  only i n a r e l a t i v e sense. 55 m.y.  The e r r o r i n the decay i n t e r v a l i s  f o r the maximum e r r o r i n the r a t i o  f a c t o r of 10.  (REYNOLDS, 1960;  ANDERS,  (I  1  2  9  /l  1  2  7  )  0  of a  1964) 129  As  i s now  w e l l known-, excess xenon  several meteorites. by ANDERS (1964),  has been found i n  Measured decay i n t e r v a l s , as summarized  are presented  i n Table 1, which f o l l o w s .  - 27 TABLE 1 I  1  2  - Xe  9  DECAY INTERVALS  1 2 9  Decay I n t e r v a l C a l c u l a t e d From: Meteorite  Class  Abee Indarch St. Marks Beardsley Richardtonj Bruderheim Renazzo Murray Sardis ( T r o i l i t e )  Total I m. y.  E E E B B H  ...  . "Correlated" I m.y.  47 . ... 77 52 254  51.5  97  51,5 .34.3 . .66  107  7  ••  K  -  +  2  4.71 4.29 3.78 4.30 4.27 1.81 3.8 1.58  + 2 + 6 + e>  128 238  0  Average K-A age AEONS +  0.28 + 0.26 + 0.18 + 0.08 + 0.07 2.51  -  where E = e n s t a t i t e c h o n d r i t e , B = b r o n z i t e c h o n d r i t e , H = hypersthene c h o n d r i t e , K = carbonaceous c h o n d r i t e , 0 = coarse octahedrite  ( a f t e r ANDERS, 1964).  In 1962 ANDERS, on the b a s i s of measured Xe i s o t o p e abundances f o r eleven meteorites ordinary chondrites Xe contents  (e.g., Richardton  and zero to moderate Xe  s t a t i t e chondrites  and very  and Bruderheim) have low enrichment.  large X e  the carbonaceous c h o n d r i t e s  large. Xe contents with only s l i g h t , O l d e r estimates total  that  The en-  (e.g., Abee, Indarch and St. Marks) have  i n t e r m e d i a t e Xe content Finally,  and the e a r t h , observed  1 2 9  anomalies.  (e.g., Murray) have very i f any, X e  1 2 9  enrichment.  of the decay i n t e r v a l s were b a s e d o n  i o d i n e content, but Anders argues that decay i n t e r v a l s  - 28 should be based only upon i o d i n e c o r r e l a t e d with xenon, r a t h e r than the t o t a l i o d i n e content  of the meteorite.  Therefore  more recent measurements of decay i n t e r v a l s , which c o r r e l a t e xenon r e l e a s e d at d i f f e r e n t  temperatures and hence from  different  produced by neutron a c t i v a t i o n  sites,, with Xe  127 of I  , are more r e l i a b l e than the e a r l i e r work. A l l o w i n g f o r an u n c e r t a i n t y of 60 m.y.  i n the  absolute  value of the decay i n t e r v a l , ANDERS (1964) makes s e v e r a l comparisons:  (1)  the e n s t a t i t e c h o n d r i t e Abee and  b r o n z i t e c h o n d r i t e Richardton temperature to r e t a i n X e  1 2 9  the  friable  both cooled to a low enough  some 50 * 60 m.y.  after t .  more h i g h l y r e c r y s t a l l i z e d b r o n z i t e c h o n d r i t e Beardsley 129 not begin  to r e t a i n Xe  u n t i l some 100  The  Q  - 200  m.y.  did  later,  i n d i c a t i n g an o r i g i n i n e i t h e r a deeper l o c a t i o n or a l a r g e r body.._  (2)  retain X e (3)  The  The  1 2 9  hypersthene c h o n d r i t e Bruderheim began to  17 m.y.  e a r l i e r than Abee and  Richardton.  carbonaceous c h o n d r i t e Murray seems to c o n t a i n  no  129 r a d i o g e n i c Xe from the present  , but no d e f i n i t e c o n c l u s i o n can be drawn data  s i n c e carbonaceous c h o n d r i t e s  more readily, than o r d i n a r y cJiondrites and gas  r e t e n t i o n ages.  (4)  ently. began to r e t a i n . X e  The 129  lose  gas  g e n e r a l l y have  low  i r o n meteorite  100  - 200  c h o n d r i t e s , i n d i c a t i n g a deeper o r i g i n  m.y.  S a r d i s appar-  l a t e r than most  i n a l a r g e r body.  From the value of 66 t 6 m.y. f o r Renazzo, Anders a l s o made the comparison that, w i t h i n the s t a t e d e r r o r , the p r i m i -  - 29 t i v e c h r o n d r i t e Renazzo has the same decay i n t e r v a l as Abee and Xe  Richardton, 1 2 9  but that Renazzo contains a l o o s e l y bound  component not present  and TURNER  i n other m e t e o r i t e s .  (1964) c o n s i d e r 66 t  REYNOLDS  6 m.y. to be a minimum decay  i n t e r v a l and taking. i n t o account gas evolved at low temperat u r e s as w e l l as at high, they o b t a i n a value of 82 t 4 m.y. Thus, from what l i t t l e has been a l r e a d y s a i d i t appears that there are some d i f f i c u l t i e s  i n determining  v a l s and i n t e r p r e t i n g t h e i r s i g n i f i c a n c e . scope of t h i s t h e s i s to adequately  decay  inter-  I t i s beyond the  compare and evaluate the  v a r i o u s arguments and data, but i t i s worthwhile to at l e a s t mention some of the d i f f i c u l t i e s  which have been encountered  i n t h i s subject and some of the ways i n which the d i f f i c u l t i e s have been answered. Problems a l r e a d y a r i s e i n the c h o i c e of a r e f e r e n c e  iso-  tope and the n e c e s s i t y f o r making a c o r r e c t i o n f o r primeval Xe  i s o t o p e abundances.  There i s some v a r i a t i o n  i n the decay  i n t e r v a l depending on the c h o i c e of r e f e r e n c e i s o t o p e . ANDERS (1962) f o r reasons the r e f e r e n c e i s o t o p e .  d i s c u s s e d by him p r e f e r s X e  as  Abundances of i s o t o p e s of Xe i n the  earth's atmosphere a r e u s u a l l y taken as the primeval dances.  1 3 0  abun-  There are good.reasons f o r t h i s c h o i c e , but there i s  a l s o the p o s s i b i l i t y that e x t i n c t some of the observed  r a d i o a c t i v i t y contributed  atmospheric Xe.  e r r o r s a r e not s e r i o u s f o r meteorites  At any r a t e , p o s s i b l e like  Richardton,  - 30 Bruderheim and Indarch which have l a r g e anomalies  i n Xe  129  A more s e r i o u s problem f o r the exact d e t e r m i n a t i o n of decay i n t e r v a l s may be atmospheric  contamination.  T h i s can be  q u i t e severe even f o r cases of meteorites with a r e l a t i v e l y high Xe content and has perhaps had a s i g n i f i c a n t e f f e c t on the i s o t o p e abundances observed  f o r Murray and Beardsley,  which g i v e v a l u e s c l o s e t o atmospheric 1962),  abundances.  (ANDERS,  In t h i s regard the p o s s i b i l i t y of shock emplacement  of r a r e gases i n a meteorite has been e x p e r i m e n t a l l y v e r i f i e d by FREDERIKSSON et a l . (1964). A p o s s i b l e e r r o r i n the theory on which t h i s method of dating., is. based  i s that the decay of I ^  2  9  might have taken  p l a c e i n the s o l a r nebula long before the formation of any s o l i d bodies and i n t h i s case, d i f f e r e n c e s between m e t e o r i t i c and t e r r e s t r i a l xenon might have a r i s e n from p a r t i a l I-Xe f r a c t i o n a t i o n i n the nebula where the chemical  fractionation  f a c t o r v a r i e d i n the p r o t o - e a r t h and p r o t o - a s t e r o i d a l r e g i o n s . Two t e s t s have been d e v i s e d to t r y and answer t h i s problem. I f n u c l e o s y n t h e s i s and the decay of s h o r t - l i v e d occurred b e f o r e formation of meteorite parent  radioactivity  bodies and the  e a r t h , then Xe i n a given meteorite should have the same i s o t o p i c c o m p o s i t i o n r e g a r d l e s s of the I content of the host. Separate  i n v e s t i g a t o r s , however, have come to o p p o s i t e c o n c l u -  s i o n s based  on the r e s u l t s of t h i s t e s t .  The second  (ANDERS, 1962)  t e s t , which Anders c o n s i d e r s more c o n c l u s i v e ,  - 31 i s the p o s s i b l e c o r r e l a t i o n of Xe anomalies r e l a t i v e l y . high I content.  If X e  1 2 9  with phases of  has been produced  in  s i t u i n the meteorite parent bodies, then the anomaly should vary from phase to phase.  By i r r a d i a t i n g the sample with  127 128* neutrons, c a u s i n g I —5>Xe and comparing the r e l e a s e of l9fi* 129 Xe with Xe at v a r y i n g temperatures, JEFFREY and REYNOLDS (1961) obtained " c o n c l u s i v e " evidence of in. s i t u decay i n the c h o n d r i t e Abee.  However, l a t e r work on  the  R i c h a r d t o n and Bruderheim meteorites gave much l e s s r e s u l t s and the authors suggest would be h e l p f u l  that f u r t h e r o b s e r v a t i o n s  (REYNOLDS, 1963;  and TURNER, 1964).  MERRIHUE, 1963;  A p r e d i c t i o n by Merrihue  Pantar would show an enrichment  -j pa by I , now A  REYNOLDS  that i o d i n e i n  by a f a c t o r of 53 i n the  f r a c t i o n of the meteorite, on the assumption 129 Xe . ... was,; produced  obvious  that  dark  excess  seems u n l i k e l y to be t r u e .  REED (1963) p o i n t s out that i f i t were t r u e , i o d i n e must c l e a r l y , depart from the trend toward l e s s enrichment i e r elements i n the dark f r a c t i o n of the Pantar In view of these d i f f i c u l t i e s ,  i n heav-  meteorite.  i t seems unsafe t o draw  any d e f i n i t e c o n c l u s i o n s on the time of occurrence of nucleogenesis and ites.  on the v a r i a t i o n i n decay i n t e r v a l s among meteor-  There i s at l e a s t one more s i g n i f i c a n t problem connec-  ted with Xe been s o l v e d .  i s o t o p e abundances which a p p a r e n t l y has FOWLER et a l . (1962) suggested  129 a c t i v e nucleus - I  i s produced  not as yet  that the  p r i m a r i l y by neutron  radiocapture  - 32 128 in; Te  which has a s o l a r system abundance approximately  t h r e e t i m e s that of I  1 2 7  .  MANUEL and KURODA (1964) s t a t e that  they are carrying, out an i n v e s t i g a t i o n of t h i s p o s s i b i l i t y f o r the F a y . e t t e v i l l e meteorite - the r e s u l t s of t h e i r study w i l l be of i n t e r e s t .  The s t u d i e s by REYNOLDS and TURNER (1964)  i n d i c a t e d an i o d i n e r a t h e r than t e l l u r i u m c o r r e l a t i o n f o r Abee, but t h e i r experiments on Richardton as mentioned above, l e s s c o n c l u s i v e .  and Bruderheim were,  Of i n t e r e s t a l s o i n t h i s 124  regard  i s the suggestion  126  t h a t , s i n c e Xe  and Xe  are e v i -  d e n t l y produced i n some kind of s p a l l a t i o n r e a c t i o n , the a s s o c i a t i o n of very abundant X e and X e with excess 129 12Q Xe would support Fowler et a l . i n t h e i r view that Xe 1 2 4  1 2 6  was produced by p a r t i c l e i r r a d i a t i o n of heavy elements l a t e i n the development of t h e s o l a r system.  T h i s suggestion of  Fowler et a l . , i f confirmed, would remove the n e c e s s i t y f o r a short time s c a l e f o r the e v o l u t i o n of the matter of the s o l a r system. .  (REYNOLDS, 1963) .  .  131-6  F i s s i o n o g e n i c Xe bility.  from Plutonium 244 i s a l s o a p o s s i -  One measurement of a P u  has been made.  2 4 4  Pasamonte.  m e t e o r i t e they f i n d no e x c e s s - X e ^ anomaly, f o r t h i s  A search  1 3 6  decay  ROWE and KURODA (1965) get a value  m.y. f o r the a c h o n d r i t e ,  negative  - Xe  for A g  been u n s u c c e s s f u l .  1 0 7  29  interval of 300  However, f o r t h i s same and even report a s l i g h t l y  isotope.  produced by t h e decay of P d  No enrichment of A g  1 0 7  1 0 7  was detected  has i n 18  - 33 samples of 7 i r o n m e t e o r i t e s .  (CHAKRABURTY et a l . 1964)  The d i s c o v e r y , that chondrules from the Bruderheim meteor129 i t e are e n r i c h e d i n excess Xe pleted  •  J  while at the same time de-  i n p r i m o r d i a l Xe r e l a t i v e to the t o t a l meteorite  con-  tent has been used as evidence f o r a theory by Wood on the o r i g i n of m e t e o r i t e s .  (MERRIHUE, 1963), We s h a l l c o n s i d e r  t h i s theory., i n s e c t i o n 2.42. 2.4  Genetic r e l a t i o n s among meteorites  2.41  The hypothesis of an igneous  o r i g i n of meteorites  The a s t r o n o m i c a l and chemical evidence reviewed i n s e c t i o n 2.2 r a t h e r c o n v i n c i n g l y r e f u t e d the hypothesis of l u n a r - s i z e d parent bodies of m e t e o r i t e s .  Here we s h a l l  b r i e f l y , c o n s i d e r hypotheses  o r i g i n proposed by  Ringwpod;  of an igneous  F i s h , Goles and Anders;  ments a g a i n s t these hypotheses RINGWOOD (1961) proposed  and Urey.  F u r t h e r argu-  are a l s o presented. that a l u n a r - s i z e d  meteorite  parent body a c c r e t e d from c o l d , h i g h l y o x i d i z e d dust of the composition  of Type I carbonaceous c h o n d r i t e s .  the m e l t i n g p o i n t was depressed by the presence amounts of HgO and CC^, so that m e l t i n g a n d i n t h i s parent body.  In h i s view of l a r g e  volcanism occurred  D i s p e r s i o n of the lava produced  q u a n t i t i e s of chondrules w h i l e other chondrules by. the c r y s t a l l i z a t i o n of s p h e r u l e s . c h o n d r i t e s were a l s o produced  large  formed i n s i t u  Metal p a r t i c l e s of  i n s i t u by the r e a c t i o n of  - 34 carbonaceous matter with o x i d i z e d i r o n and n i c k e l . assumption  Ringwood's  that at l e a s t one meteorite parent body was  s i z e i s founded  of l u n a r  on h i s b e l i e f that Widmanstatten p a t t e r n s have  a high p r e s s u r e o r i g i n . C r i t i c i s m s of t h i s hypothesis have been summarized ANDERS (1964):  (1) Gases i n e q u i l i b r i u m with  matter would be mainly H2.and CO (2)  chondritic  r a t h e r than HgO  and  the absence of bubbles  understand  (3)  2  The p r e s e r v a t i o n of g l a s s  and hydrated minerals i s hard to  on Ringwood's model.  (4)  There i s no f e a s i b l e  of c o o l i n g a l u n a r - s i z e d body to the r e q u i r e d low (5)  C0 .  These gases would not cause d e p r e s s i o n of the m e l t i n g  p o i n t as r e q u i r e d by Ringwood. and  by  N e i t h e r m e t a l l i c chondrules  way  temperatures.  nor h i g h l y reduced  chondrules  i n e n s t a t i t e c h o n d r i t e s can be e x p l a i n e d i n terms of a v o l c a n i c process based  on water.  (6)  There i s no obvious  way  of accounting, f o r most .of the chemical f r a c t i o n a t i o n s i n chond r i t e s by. Ringwood ' s model.  (7)  Disequilibrium chondrites  such as Renazzo have no p l a c e i n t h i s scheme, FISH, GOLES, and ANDERS (1960) a l s o proposed generation of a s t e r o i d a l b o d i e s . to have melted followed.  a single  The parent body was  assumed  by e x t i n c t r a d i o a c t i v i t y and phase s e p a r a t i o n  The p r o d u c t i o n of chondrules was  a s c r i b e d to a  c y c l i c mechanism f o r d e p l e t i n g , t h e c h o n d r i t i c mantle of c h a l c o p h i l e elements.  The v a r i o u s c l a s s e s of meteorites were  b e l i e v e d to come from s u c c e s s i v e l a y e r s of t h i s body.  Anders  -  h i m s e l f now  35  -  r e j e c t s t h i s hypothesis.  drules beingproduced  The suggestion of chon-  by volcanism i s open to a l l the above  objections. Urey has w r i t t e n s e v e r a l papers on the o r i g i n of meteori t e s i n which a fundamental bodies.  r o l e i s played by  Some of the d i f f i c u l t i e s  with the thermal h i s t o r y of  such bodies have already, been d i s c u s s e d . are enhanced by Urey's  latest  lunar-sized  These  difficulties  idea that at an e a r l y stage the  meteorite parent bodies were i n t e n s e l y heated from the outs i d e because they were s i t u a t e d at c e n t r e s of massive t r a c t i n g gas spheres  (LEVIN,  1965).  con-  F u r t h e r arguments are  given by.Anders but w i l l not be considered here. It  i s important a l s o to c o n s i d e r the p o s s i b i l i t y of an  igneous o r i g i n  i n a s t e r o i d a l bodies s i n c e these s m a l l e r  bodies would c o o l more r a p i d l y and hence the major problem the thermal h i s t o r y of l a r g e r bodies would not e x i s t .  of  Earlier  estimates of the content of U and Th i n meteorites were used in a c a l c u l a t i o n which showed that m e l t i n g would occur i n the i n t e r i o r s of bodies l a r g e r than 2 0 0 1959)  km i n diameter  (MAJEVA,  - with more recent values Of the content of U and  Th,  only the i n t e r i o r s of bodies g r e a t e r than 1 0 0 0 km would melt due to l o n g - l i v e d r a d i o a c t i v i t y  (LEVIN,  1965).  Because of the p o s s i b l e r o l e of s h o r t - l i v e d  radioactivity,  the melting_of. . a s t e r o i d a l bodies cannot be d e f i n i t e l y out.  However, i f excess Xe i s evidence of s h o r t - l i v e d  ruled radio-  - 36 a c t i v i t y , i n t h e h i s t o r y of a s t e r o i d s , then h e a t i n g and subsequent, r a p i d cooling.., must have indeed occurred very Evidence  early.  from the e x c e s s i v e abundance of Xe and t h e suggestion  of melting, and  then r a p i d c o o l i n g i n a s t e r o i d s a r e probably  inconsistent.  I t may a l s o be d i f f i c u l t  to e x p l a i n how a s t e r -  o i d a l - s i z e d bodies c o u l d have molten i n t e r i o r s at an e a r l y stage and s t i l l  remain c o l d enough near the s u r f a c e to have a  " c r u s t " and "mantle" composition chondrites  2.42  of carbonaceous and o r d i n a r y  respectively.  Carbonaceous c h o n d r i t e s , o r d i n a r y c h o n d r i t e s and Wood's theory on the orig_in of m e t e o r i t e s . The presence  chondrules  of presumed high temperature minerals i n  i n d i c a t i n g , a high temperature o r i g i n of these  chondrules, w h i l e strong evidence the c h o n d r i t e s themselves,  supports a c o l d h i s t o r y f o r  poses a s e r i o u s problem.  been r e s o l v e d i n two d i f f e r e n t ways. the c h o n d r i t e s are regarded  First,  i n Wood's theory,  as the r e s u l t of an a c c r e t i o n of  a low temperature and a high temperature f r a c t i o n , r i x and the chondrules,  respectively.  proposes a high temperature, h i s t o r y of the s o l a r system; (WOOD, 1963; and  evidence  I t has  In t h i s regard, Wood  high p r e s s u r e event caused  the mat-  i n the e a r l y  by s o l a r eiuptions.  ANDERS,.. 1964). We s h a l l c o n s i d e r Wood's theory relating, to i t i n this section.  A l t e r n a t i v e l y . L e v i n c o n s i d e r s i t h i g h l y improbable shock waves produced by. s o l a r e r u p t i o n s could reach the  that  - 37 a s t e r o i d z o n e t r a v e l l i n g , some 300 km i n the l a y e r of dust which has s e t t l e d towards the c e n t r a l plane of the s o l a r nebula, and doubts the evidence f o r a high-temperature h i s t o r y of c h o n d r u l e s .  He c o n s i d e r s that d i f f u s i o n  played a prominent part bodies  i n the s o l i d  i n the e v o l u t i o n of m e t e o r i t e parent  (LEVIN, 1965), and h i s ideas and arguments  s i d e r e d i n the next  state  w i l l be con-  section.  The m i n e r a l s and p a r t i c u l a r l y the presence of abundant q u a n t i t i e s of v o l a t i l e s i n carbonaceous c h o n d r i t e s are i n d i c a t i v e of low temperature h i s t o r i e s .  In a p i e c e of s t r a i n e d  g l a s s i n the m e t e o r i t e Mighei, the s t r a i n disappeared a f t e r annealing. f o r two days at 206°C  (ANDERS, 1964).  LEVIN (1965)  concludes that the carbonaceous c h o n d r i t e s were never heated above 200 - 300°C.  In a l l c h o n d r i t e s , l i t h o p h i l e ,  chalcophile  and s i d e r o p h i l e elements mingle together, evidence that melting., ... which would cau;se s e p a r a t i o n of these phases, never occurred  (WOOD, 1963).  ANDERS (.1964) b e l i e v e s that the presence of high-temperat u r e m i n e r a l s and other evidence suggest that the minerals of chondrules formed from a melt at a temperature of 1200 2000°C and were quenched  r a p i d l y , w h i l e the c h o n d r i t e as a  whole could not have melted. achieve i n a s i z e a b l e mass. s i t u o r i g i n of chondrules.  Moreover,  quenching i s hard to  This evidence i s against an i n Furthermore, t e x t u r a l evidence  a c c o r d i n g to Anders, supports the view that chondrules are  - 38 s o l i d i f i e d drops of ' f i e r y r a i n ' . cave i n d e n t a t i o n s ;  Some chondrules  show con-  others are wholly enclosed w i t h i n l a r g e r ,  m i n e r a l o g i c a l l y d i f f e r e n t chondrules, suggesting the p o s s i b i l i t y that chondrules f r e q u e n t l y c o l l i d e d with each other while still  i n a l i q u i d or p l a s t i c  state.  In the same paper ANDERS (1964) a l s o concludes that metal p a r t i c i T e s i n c h o n d r i t e s appear to have developed  their  struc-  tures i n s i t u , and that i n order f o r t h i s to happen, temperatures of at l e a s t 450° C must have p r e v a i l e d i n the parent bodies of the c h o n d f i t e s f o r long times, perhaps up to 10  -  Q  10  m.y.  Hence the hypothesis to be evaluated i s that chon-  d r u l e s were not formed iji s i t u , whereas metal p a r t i c l e s were. S i n c e Anders gives only three p i e c e s of i n f o r m a t i o n to support a high temperature t h i s evidence of Wood r e s t s , suggested  o r i g i n of chondrules and  i s the main support  since  on which the whole theory  t h i s i n f o r m a t i o n w i l l be r e s t a t e d here.  that t h i s evidence may  It i s  not be c o n c l u s i v e and that i t  i s c r u c i a l t o c o n s i d e r i n the l i g h t of the hypothesis of L e v i n , to be d i s c u s s e d i n the next s e c t i o n , of the n u c l e a t i o n and growth i n s i t u of many s m a l l g l o b u l e s and gation into "1.  their further  aggre-  chondrules.  P r i m i t i v e r e l a t i v e l y unmetamorphosed c h o n d r i t e s (Renazzo,  Mezo - Madaras) f r e q u e n t l y c o n t a i n b a s a l t i c g l a s s of r e f r a c t i v e index 1.55  - 1.60.  g l a s s e s of t h i s composition  In t e r r e s t r i a l  resist  settings,  devitrification  - 39 only at f a i r l y 2.  r a p i d c o o l i n g r a t e s , e.g., 10°C/min.  O l i v i n e and pyroxene c r y s t a l s i n chondrules a r e  elongated s h e e t - l i k e , r a t h e r than equidimensional t h e i r t e r r e s t r i a l analogues. crystallographic direction cooled systems. cooling 3.  Non-equidiraensional  i s c h a r a c t e r i s t i c of super-  Supercooling, i n turn, implies a f a s t  rate.  O r d i n a r y c h o n d r i t e s c o n t a i n the high-temperature  v a r i e t y of p l a g i o c l a s e .  T h i s i m p l i e s formation above  700°C, f o l l o w e d by f a i r l y no q u a n t i t a t i v e data e x i s t low  like  rapid cooling.  Regrettably,  on the r a t e of i n v e r s i o n at  temperatures."  ANDERS (1964) and LEVIN (1965) have both reviewed Wood's theory, a theory which was proposed 1958  and developed  by Wood from  to 1963. A c c o r d i n g t o t h i s theory, chondrules were  a l r e a d y present i n the p r i m o r d i a l dust b e f o r e a c c r e t i o n .  As  s t a t e d above, t h i s theory assumes that the p r i m i t i v e m a t e r i a l of the s o l a r nebula once passed ( 10  atm) and high-temperature  l i q u i d drops  through  a brief  high-pressure  ( 2000°K) stage.  On c o o l i n g ,  of s i l i c a t e and metal condensed from vapor,  ducing the chondrules and metal g r a i n s of c h o n d r i t e s . r e s t of the m a t e r i a l d i d not pass through  a liquid  went d i r e c t l y from a vapor to a sub-micron-sized,  pro-  The  stage but dust-like  s o l i d which a c c r e t e d as the matrix o f the c h o n d r i t e s .  In  - 40 p a r t , t h i s condensation  presumably occurred from a gas with  s o l a r H/O r a t i o s i n order to g i v e n e a r l y pure magnesium s i l i c a t e s with l e s s than 1% FeO.  (In f a c t ,  i n t h e Renazzo  m e t e o r i t e , the FeO c o n t e n t . i s as low as 0.5 to 2%.) c o o l i n g , the dust o x i d i z e d and absorbed  On  volatiles.  Anders p a r t i c u l a r l y l i k e s t h i s theory because i t supports the o b s e r v a t i o n of two chemical f r a c t i o n s i n c h o n d r i t i c m e t e o r i t e s , a f r a c t i o n A which a c c r e t e d at low and  temperatures  a f r a c t i o n B which formed i n a h i g h l y reducing, presumably  hydrogen-rich,  environment.  Anders suggests  that a l l three  c l a s s e s of c h o n d r i t e s , carbonaceous, o r d i n a r y and e n s t a t i t e , are a blend of these two f r a c t i o n s .  In t h i s theory type I  carbonaceous c h o n d r i t e s c o n s i s t of the matrix o n l y . According: tP Wood's theory, the c h o n d r i t e s a c c r e t e d i n a s t a t e of d i s e q u i l i b r i u m . ample .  Renazzo i s considered the only ex-  T h i s c o n t r a s t s with L e v i n ' s theory, i n which Renazzo  i s considered l e s s p r i m i t i v e than the carbonaceous c h o n d r i t e s i d e n t i f i e d as type I I .  In Wood's theory, thermo-metamorphism  converts the Renazzo type to the other carbonaceous chondrites and  (except type I which i s considered to be a l l matrix)  to the o r d i n a r y c h o n d r i t e s .  The other c l a s s e s of meteor-  i t e s are produced by c o n v e n t i o n a l m e l t i n g and d i f f e r e n t i a t i o n processes  i n the a s t e r o i d .  Anders mentions some d i f f i c u l t i e s  i n t h i s theory, i n  p a r t i c u l a r that of a t t a i n i n g a combination  of high p r e s s u r e s  - 41 (10  3  atm) and low temperatures  ( £ 2000° K) .  He a l s o p o i n t s  out the d i f f i c u l t y i n e x p l a i n i n g r a p i d c o o l i n g , although he has some answers to these d i f f i c u l t i e s . sure can be reduced  The necessary p r e s -  by a decrease o f the hydrogen/metal  e.g.., by s e t t l i n g of dust p a r t i c l e s to the e c l i p t i c A l s o , T. T a u r i s t a r s a r e observed  to e j e c t  ratio,  plane.  l a r g e amounts of  mass d u r i n g . b r i e f p e r i o d s of g r e a t l y i n c r e a s e d l u m i n o s i t y and Anders suggests passed  through  propagated  that i t i s l i k e l y that the sun, too, once a T T a u r i stage.  by such e r u p t i o n s would compress and heat the  nebular gas, v o l a t i l i z i n g panding.,  High p r e s s u r e shock waves  the dust g r a i n s .  some o f the gas might pass through  where chondrules  On c o o l i n g and exa l i q u i d phase  and metal g r a i n s would condense.  T h i s per-  mits f a s t c o o l i n g of the chondrules, as r e q u i r e d by the e v i dence .  There seems to be an i n c o n s i s t e n c y i n Anders' d i s c u s -  s i o n , however.  He e a r l i e r concludes  that the evidence f a v o r s  an iin s i t u formation of the metal p a r t i c l e s  i n chondrites,  while l a t e r , without c r i t i c i s m , he d e s c r i b e s Wood's theory, which p r e d i c t s the condensation  from the dust cloud of metal  d r o p l e t s as w e l l as s i l i c a t e ones.  2.43  L e v i n ' s theory on the o r i g i n of meteorites L e v i n ' s theory on the o r i g i n of meteorites and on the  g e n e t i c r e l a t i o n s h i p s among meteorites i s based  on what he  c a l l s the hypothesis of non-melted parent bodies, i . e . , the hypothesis that a l l the f e a t u r e s of meteorites developed  in ;  - 42 the s o l i d  state.  Mason p r e v i o u s l y proposed that a l l the f e a -  tures of c h o n d r i t e s developed  i n t h e s o l i d s t a t e from p r i m i t i v e  m a t e r i a l s i m i l a r t o that of carbonaceous c h o n d r i t e s - but he considered o r d i n a r y melting, and d i f f e r e n t i a t i o n t o be respons i b l e f o r the f e a t u r e s of the other types o f m e t e o r i t e s . Mason's ideas r e c e i v e d some c r i t i c i s m .  I t was objected  that carbonaceous c h o n d r i t e s d i f f e r from o r d i n a r y c h o n d r i t e s i n many c o m p o s i t i o n a l d e t a i l s  (e.g., Mg/Si, Na/Si,  B i , T l , e t c . ) and cannot be converted i n a c l o s e d system.  Fe/Se, Pb,  to ordinary chondrites  T h i s o b j e c t i o n i s based on t h e supposed  problem o f removing Mg, Fe, Na, B i , e t c . from s o l i d temperatures below t h e i r m e l t i n g p o i n t ever, t h e r o l e of s o l i d cant  i n t h i s regard.  (ANDERS, 1964).  s t a t e d i f f u s i o n may be very  Solid  rock at How-  signifi-  state d i f f u s i o n also plays a  minor r o l e i n Wood's theory, and f o r t h i s reason he s t u d i e d e x p e r i m e n t a l l y the p o s s i b i l i t y o f o b t a i n i n g other from parent by thermal  chondrites  m a t e r i a l s i m i l a r t o that of t h e Renazzo c h o n d r i t e metamorphism.  (WOOD, 1965).  H i s r e s u l t s have been p o s i t i v e  Moreover, Anders' suggestion  that small  bodies  at s u f f i c i e n t d i s t a n c e s from the sun may r e t a r d the escape of water by means of a permafrost  l a y e r below the s u r f a c e  (and hence make p o s s i b l e a r o l e f o r " i n t e r n a l atmospheres" i n m e t e o r i t e s ) might very w e l l account f o r many of the f e a t u r e s of  meteorites. According  t o L e v i n , t h e more p r i m i t i v e chondrules i n  -  carbonaceous c h o n d r i t e s and  43  -  other non-metamorphosed  chondrites  are only, p a r t i a l l y c r y s t a l l i n e , c o n t a i n i n g g l a s s , and f o r e are not  s t r i c t l y a product  of c r y s t a l l i z a t i o n .  suggests that the metastable s e p a r a t i o n of two  thereLevin  immiscible  l i q u i d s by means of the n u c l e a t i o n and  growth of many small  g l o b u l e s and  i n t o chondrules  t h e i r f u r t h e r aggregation  b e t t e r to f i t the experience  obtained  high-temperature s p h e r u l i t i c  crystallization.  seems  i n g l a s s technology  than  Without going, i n t o d e t a i l s , which r e q u i r e f u r t h e r study, L e v i n agrees with Mason on the f o l l o w i n g scheme: bonaceous c h o n d r i t e s  (no c h o n d r u l e s ) T y p e I I  (chondrules  formed by decomposition of serpentine)-»Type I I I completely  converted  brium) .  (serpentine  to o l i v i n e and pyroxene, although  "high temperature" minerals ordinary chondrites  Type I c a r -  are s t i l l  these  in disequilibrium)  ("high temperature" minerals  in e q u i l i -  However, L e v i n c o n s i d e r s e n s t a t i t e c h o n d r i t e s to  s i m i l a r to Type I I I , but formed i n a more reducing  be  environment,  r a t h e r than as the end member i n the above scheme. The  major new  f e a t u r e of L e v i n ' s  of the range of a c t i o n of s o l i d  theory  s t a t e processes  the e v o l u t i o n of a l l m e t e o r i t i c types. diffusion  i n the s o l i d  parent  bodies  extension  to i n c l u d e  L e v i n b e l i e v e s that  s t a t e , the g r e a t e r s o l u b i l i t y of  s m a l l e r g r a i n s l e d to t h e i r d i s s o l u t i o n and of n i c k e l - i r o n  i s the  into larger inclusions.  the  the  agglomeration  In the p a r t s of  which a t t a i n e d temperatures of 800  by  the  - 1000° C,  - 44 the agglomeration  of n i c k e l - i r o n i n t o l a r g e r and l a r g e r  bodies  must have proceeded f a r enough, a c c o r d i n g t o L e v i n , th produce i n c l u s i o n s of the s i z e of the l a r g e s t on the e a r t h .  i r o n meteorites  found  In t h i s scheme a c h o n d r i t e s a r e considered t o  represent samples o f t h e surrounding or completely f r e e of n i c k e l - i r o n .  s i l i c a t e s , being  almost  A l s o i n t h i s scheme, stony-  i r o n s are samples i n which the s e p a r a t i o n of metal and s i l i cates was stopped  at some i n t e r m e d i a t e stage.  A possible  d i f f i c u l t y of L e v i n ' s hypothesis that a l l f e a t u r e s of meteori t e s developed  i n the s o l i d  s t a t e i s considered i n Chapter  6.  D i s c u s s i n g , the g e o p h y s i c a l i m p l i c a t i o n s o f h i s theory, L e v i n notes that i n t h e e a r t h ' s zone of the s o l a r nebular the temperature was higher than i n the a s t e r o i d a l zone and hence he suggests t h a t a s m a l l e r q u a n t i t y of carbonaceous compounds condensed i n the earth's zone than i n the type I carbonaceous c h o n d r i t e s , that no s u b s t a n t i a l r e d u c t i o n of o x i d i z e d i r o n occurred i n bodies which accumulated l a t e r i n the e a r t h ' s zone.  This i s i n agreement with the d e n s i t y of the moon which  i s s m a l l e r than  that of o r d i n a r y c h o n d r i t e s .  contains l i t t l e  or no m e t a l l i c i r o n .  Hence the moon  The v a l i d i t y of these  arguments would support Ramsey's h y p o t h e s i s .  2.5  Observations  and C o n c l u s i o n s  It would seem that the present s t a t e of knowledge o f the r o l e of s h o r t - l i v e d  r a d i o a c t i v i t y i n the e a r l y h i s t o r y of the  -  45  -  s o l a r system i s i n c o n c l u s i v e . A l s o without f u r t h e r study no d e f i n i t e c o n c l u s i o n s can be drawn with regard to the question of the o r i g i n of m e t e o r i t e s . t i o n has been o b t a i n e d .  However, some u s e f u l  informa-  In the f i r s t p l a c e , i t can be s a i d  with reasonable c e r t a i n t y that the f a m i l i e s of Mars a s t e r o i d s 1  represent the parent bodies of most, i f not n e a r l y a l l meteorites.  A l s o some l i m i t s can be placed on the p o s s i b l e r o l e of  s h o r t - l i v e d r a d i o a c t i v i t y , as w i l l be d i s c u s s e d i n chapter 7. Moreover, we a r e i n a p o s i t i o n to e s t a b l i s h l i m i t s on the t o t a l content of Fe i n the parent bodies of meteorites by c o n s i d e r i n g e i t h e r L e v i n ' s or Wood's t h e o r i e s of t h e i r Furthermore, graph,  origin.  according, t o the reasoning i n the above para-  the average  composition  of the e a r t h i s by e i t h e r  theory l i g h t e r or at l e a s t no h e a v i e r than that o f the meteori t e parent b o d i e s .  We s h a l l see i n the next chapter that the  evidence from meteorites f a v o r s a composition  of the e a r t h  which i s l i g h t e r than that r e q u i r e d by the i r o n core hypothesis. solid  The v a l i d i t y of L e v i n ' s hypothesis of the r o l e o f  s t a t e d i f f u s i o n w i l l probably be determined  chemical study of meteorites  (or, perhaps,  by f u r t h e r  as d i s c u s s e d i n  chapter 6, by f u r t h e r study of uranium and lead, i s o t o p e abundances) r a t h e r than by experimental  study of s o l i d  d i f f u s i o n , because the time f a c t o r cannot laboratory.  I f h i s hypothesis i s found  state  be d u p l i c a t e d i n the  to be c o r r e c t , i t  might be u s e f u l to i n v e s t i g a t e the p o s s i b i l i t y o f an even  - 46 g r e a t e r r o l e played by s o l i d s t a t e d i f f u s i o n i n the h i s t o r y of the earth than has p r e v i o u s l y been c o n s i d e r e d .  The  earth  has presumably e x i s t e d f o r the same length of time as that f o r the meteorites temperatures.  and  with s i g n i f i c a n t l y g r e a t e r  Solid state d i f f u s i o n  interior  i n the earth might  be  s i g n i f i c a n t f o r the problem of t h i s t h e s i s i f the content f r e e metal i n the e a r t h i s g r e a t e r than the arguments presented  above allow.  of  - 47 3„  CHEMICAL ABUNDANCES In t h i s chapter we c o n s i d e r e s t i m a t e s o f the abundances  of elements i n meteorites and i n the earth.. A t t e n t i o n i s centered on t o t a l Fe (or Fe + Ni) content because  indirect  d e t e r m i n a t i o n s o f the composition of the e a r t h based variation  on the  of t h e d e n s i t y of the e a r t h can only r e f l e c t a v a r i a -  t i o n i n the Fe content  (atomic weight 55.85).  Possible varia-  t i o n s i n the content of other major elements i n the e a r t h 0, S i , and Mg (atomic weights l i k e l y to cause s i g n i f i c a n t  16.00, 28.09 and 24.32) are un-  changes i n d e n s i t y .  It seems reasonable to assume that those called  "falls",  observed  meteorites  i . e . , those which a r e recovered a f t e r  to f a l l ,  being  g i v e a maximum estimate of the Fe and N i  contents o f the meteorite parent bodies r e g a r d l e s s of which theory of the o r i g i n  of meteorites we adopt.  The necessary  data i s g i v e n i n Table 2, taken from MASON (1962) and LEVIN (1965). TABLE 2  Irons Stony-irons Stones  The 8.59%  Falls  %  Weight. %  42 12 628  6 2 92  10 5 85  i r o n s a r e almost  N i (MASON, 1962).  e n t i r e l y Fe + N i ;  90,78% Fe and  A c c o r d i n g t o MASON (1964) c h o n d r i t e s  are f a r more common than a c h o n d r i t e s , making up over 90% of  - 48 all  stones.  The t o t a l Fe content of a c h o n d r i t e s i s about 14%  (MASON, 1962) and the t o t a l Fe + N i content of c h o n d r i t e s about 26%. percentage  T h e r e f o r e , we can take 25% as a maximum weight o f Fe + N i i n stony m e t e o r i t e s .  The Fe + N i con-  tent of s t o n y - i r o n s i s q u i t e v a r i a b l e , but c e r t a i n l y does not exceed  50%. T h e r e f o r e , the maximum content o f Fe + N i i n  meteorites appears  to be 35%.  In L e v i n s theory, carbonaceous c h o n d r i t e s and, i n Wood's theory, a l l c h o n d r i t e s can be taken as a c l o s e d system i n determining the composition  of the parent bodies of m e t e o r i t e s .  In e i t h e r case the t o t a l content of Fe + N i i s about 26%. Estimates of the composition determined  of the earth? are n e c e s s a r i l y  i n d i r e c t l y and depend on the hypothesis  f o r the -nature of the earth's core.  adopted  A comparison of s e i s m i c  data with the r e s u l t s of high p r e s s u r e experiments  result in  v a r y i n g estimates of the t o t a l i r o n content of the e a r t h , but on the assumption  of an i r o n core, these estimates a r e a l l  h i g h e r than even the maximum p o s s i b l e content of Fe + N i i n the parent bodies of m e t e o r i t e s .  BIRCH (1964, and p e r s o n a l  communication, 1965), who supports the i r o n core hypothesis, f a v o r s a value o f 10% FeO f o r the mantle, thereby o b t a i n i n g a 38% t o t a l Fe + N i content f o r the e a r t h .  A c t u a l l y , as we  s h a l l see l a t e r , h i s own data are c o n s i s t e n t with a h i g h e r FeO content i n the mantle.  Independently  comparing shock  wave p r e s s u r e data with s e i s m i c data, MCQUEEN et a l . (1964)  - 49 obtained f o r the Fe + N i content of an e a r t h with an n i c k e l core values of 42.5  iron-  to 45.3%, depending on the d e n s i t y  assumed at the top of the mantle. Hence we may  conclude that the evidence from  meteorites  combined with estimates of the earth's composition based  on  seismic and high p r e s s u r e data f a v o r s Ramsey's hypothesis of a m e t a l l i z e d s i l i c a t e core i f L e v i n ' s reasoning on the abundance of carbonaceous compounds and t h e i r r o l e i n meteorites and the e a r t h i s c o r r e c t .  Specifically,  t h i s evidence f a v o r s  e i t h e r hypothesis V or VI, d i s c u s s e d i n the I n t r o d u c t i o n . I n homogeneity of the e a r t h as compared to Mars i s e x p l a i n e d by a g r e a t e r content of m e t a l l i c  i r o n i n Mars, an expected  sequence of the g r e a t e r p a r t i c i p a t i o n of reducing  con-  agents,  p a r t i c u l a r l y carbonaceous compounds, i n the formation of bodies i n the Mars zone. Hypotheses I and  II cannot  be r u l e d out by the above e v i -  dence unless adequate c r i t i c a l c o n s i d e r a t i o n and c o n c l u s i v e support  i s g i v e n to L e v i n ' s argument that the e a r t h and moon  have a l i g h t e r composition than the p r i m i t i v e m a t e r i a l which formed the meteorite parent bodies and to Anders' c o n c l u s i o n on the l o c a t i o n of the o r i g i n of m e t e o r i t e s .  However, i f  these c o n c l u s i o n s are s u b s t a n t i a t e d by f u r t h e r r e s e a r c h on meteorites and by c a r e f u l c o n s i d e r a t i o n of a l l p o s s i b l e causes of a v a r i a t i o n  i n composition between the meteorite parent  bodies and the e a r t h , i t might be p o s s i b l e to give a more  - 50 definite,  i f not f i n a l ,  of an i r o n c o r e . f a i r l y detailed  c o n c l u s i o n concerning the p o s s i b i l i t y  Such s u b s t a n t i a t i o n , of course, r e q u i r e s a knowledge of the o r i g i n of the s o l a r  system.  - 51 4.  TRANSITION TO A METALLIC PHASE In  t h i s chapter the theory of a t r a n s i t i o n t o a m e t a l l i c  phase, as d i s c u s s e d by RAMSEY (1948, 1949, 1950, 1954), i s considered.  In 1939, the g e o l o g i s t V. N. Lodochriikov suggested  that the hypothesis of an i r o n core was i n c o r r e c t and ment i o n e d that l i t t l e was known about the behaviour  of matter at  the tremendous p r e s s u r e s e x i s t i n g i n the earth's c o r e . 1948,  In  i n a d i s c u s s i o n of the c o n s t i t u t i o n of the t e r r e s t r i a l  p l a n e t s , Ramsey hypothesized that a t r a n s i t i o n t o a m e t a l l i c phase of mantle m a t e r i a l occurs at the p r e s s u r e ,  approximately  1.4 x 10^ atmospheres, which i s found at the core-mantle boundary i n the e a r t h . lized  With the new hypothesis o f a metal-  s i l i c a t e core, Ramsey attempted  s i t i e s of the t e r r e s t r i a l  p l a n e t s with the hypothesis that  they were of uniform composition. 1954), he developed to  to r e c o n c i l e the den-  L a t e r (1949, 1950, 1951,  and d i s c u s s e d the theory of a t r a n s i t i o n  a m e t a l l i c phase. In  1948, adopting the hypothesis of a phase t r a n s i t i o n ,  u s i n g B u l l e n ' s p r e s s u r e - d e n s i t y r e l a t i o n f o r the e a r t h (Model A - see chapter 9) and c o n s i d e r i n g the mass of the p l a n e t s as g i v e n , Ramsey made a t h e o r e t i c a l c a l c u l a t i o n of the diameter planets.  and the mean d e n s i t y of each of the t e r r e s t r i a l  The a s t r o n o m i c a l data which he used, more recent  data, and the diameters are given i n Table 3.  and d e n s i t i e s c a l c u l a t e d by Ramsey  TABLE 3 Mean Diameter  D(km)  Core  Diameter  Mean D e n s i t y Measured* Measured** Theoretical 1945 1965 Ramsey, 1948  Theoretical Measured* Measured** Ramsey, 1948 1945 1965 EARTH  12742  12742  12742  0.550  5.52  5.52  5.52  VENUS  12570  12400+100 12246  0.340  4.70  4.89+0.12 5.06  MARS  7020  6793+ 16  6664  3.56  3.93+0.03 4.12  MERCURY  5285  5000+250  4840  3.41  4.0 +0.9  MOON  3480  3476  3476  3.334  3.34+0.01 3.34  *  5.46  Ramsey used t h e data of R u s s e l l , Dugan and Stewart, 1945.  ** David Goodenough, 1965, k i n d l y p r o v i d e d t h i s data t o the a u t h o r . It i s considered by him to be the most recent and r e l i a b l e data on t h e t e r r e s t r i a l p l a n e t s . (See Chapter 11 f o r a summary of v a r i o u s e s t i m a t e s of the mass, diameter and mean d e n s i t y o f Venus, Mars and Mercury.)  to  - 53 Ramsey c a l c u l a t e d the t h e o r e t i c a l d e n s i t i e s of s e v e r a l other masses to c o n s t r u c t the curve shown i n F i g u r e 1. astronomical  data which he used are shown by open c i r c l e s ,  c u r r e n t data by c l o s e d c i r c l e s . curve  The  at 0.793 Mg,  where Mg  The  d i s c o n t i n u i t y i n the  i s the mass of the e a r t h , i s a  consequence of the assumption that the core boundary has a c h a r a c t e r i s t i c pressure  and of the circumstance,  RAMSEY (1948, 1950)  LIGHTHILL (1950), that very  and  p l a n e t a r y cores are u n s t a b l e .  shown by small  Thus, i f the cores are a p r e s -  sure phenomenon, the p l a n e t s to the r i g h t of the d i s c o n t i n u i t y do not have c o r e s . It i s obvious from Table  3 and  F i g u r e 1 that  the  t h e o r e t i c a l d e n s i t i e s of Venus, Mars and Mercury are  signi-  ficantly  from  lower than the d e n s i t i e s determined i n 1948  astronomical with  observations.  This s i t u a t i o n i s even worse  respect to the current data.  Ramsey found on the b a s i s  of the o l d data that the t h e o r e t i c a l d e n s i t i e s of Mars and Venus could be made to agree with the observed d e n s i t i e s i f Bullen's pressure-density  r e l a t i o n , which assumed a c h e m i c a l l y  homogeneous lower mantle, was effect  of the condensation  q u i r e d was  modified  of matter.  by c o n s i d e r i n g The  the  condensation  such that the average atomic weight  re-  increased  from i t s value below the c r u s t to an average value f o r the e a r t h 8% g r e a t e r than the s u b c r u s t a l value. s u b c r u s t a l average atomic weight i s 20.0,  Thus, i f the  the mean f o r the  - 54 -  MEAN DENSITY o (g/crn) 1 3  -1.5 L0G  -2.0 |0  M  /M  E  FIGURE 1. The c a l c u l a t e d v a r i a t i o n of t h e mean d e n s i t y w i t h t h e mass o f t h e planet ( a f t e r Ramsey, 1943).  ENERGY  EXCITED  GROUND STATE  MOLAR VOLUME FIGURE 2. Schematic r e p r e s e n t a t i o n of t h e e l e c t r o n i c energy l e v e l s (Ramsey, 1949)•  - 55 e a r t h i s 21.8. 9, but  We  s h a l l c o n s i d e r t h i s suggestion  in  chapter  observe here that a s i g n i f i c a n t l y g r e a t e r c e n t r a l  condensation  would be r e q u i r e d to meet c u r r e n t  astronomical  data. Since the chemical  composition  of the e a r t h i s complex,  Ramsey d i s c u s s e s the phase t r a n s i t i o n u s i n g helium ample. at  The  m e t a l l i c phase of helium  very high pressures  as an  ex-  should be s t a b l e only  s i n c e the n o n - m e t a l l i c phase has  s m a l l e r i n t e r n a l energy at lower p r e s s u r e s .  the  F i g u r e 2 shows  a schematic r e p r e s e n t a t i o n of the e l e c t r o n i c energy  levels.  When the volume i s very l a r g e , the i n t e r a c t i o n s between atoms are n e g l i g i b l e , and  the energy spectrum c o n s i s t s of sharp  l i n e s c h a r a c t e r i s t i c of the i s o l a t e d atoms.  In the  s t a t e , as the matter i s compressed there i s at f i r s t  solid a  s l i g h t decrease i n the e l e c t r o n i c energy l e v e l s owing to weak van der Waals a t t r a c t i o n .  With f u r t h e r compression, however,  r e p u l s i v e i n t e r a c t i o n comes i n t o p l a y and  the energy  i n c r e a s e s r a p i d l y as the volume i s d i m i n i s h e d . energy l e v e l of helium  i s a non-conductor.  of the helium  atom, however, one  the 2S l e v e l .  incompletely split  first  i s a complete s h e l l and hence the  normal s o l i d  to  The  In the f i r s t  excited state  of the e l e c t r o n s i s r a i s e d  T h i s s t a t e i s degenerate, as the s h e l l s  filled.  are  T h i s energy l e v e l w i l l t h e r e f o r e be  i n t o a quasi-continuous  band by mutual i n t e r a c t i o n s  when the atoms combine to form a s o l i d .  This band can  never  - 56 be completely f i l l e d  and hence a net c u r r e n t can be e s t a b -  l i s h e d through e l e c t r o n s jumping to unoccupied l e v e l s i n the band. solid  When a l l the atoms are in. t h i s conducting s t a t e , the i s r e f e r r e d t o as the m e t a l l i c phase of helium.  This  phase i s achieved by compression i n the f o l l o w i n g manner. In forming the s o l i d ,  the conduction band i s depressed t o -  wards the ground s t a t e , the m e t a l l i c b i n d i n g f o r c e s being much g r e a t e r than those a r i s i n g from van der Waal's f o r c e s , and the r e p u l s i o n which e v e n t u a l l y s e t s i n i s l e s s  strong  than the f o r c e between the atoms i n the ground s t a t e ,  result-  ing, at s u f f i c i e n t l y high p r e s s u r e s , i n the conduction band c r o s s i n g the ground  s t a t e , as shown i n F i g u r e 2.  In theory,  a s i m i l a r diagram might be drawn f o r the a c t u a l m a t e r i a l s of the e a r t h , but the c a l c u l a t i o n s are p r o b a b l y too complicated (RAMSEY, 1949,  1954).  The t o t a l i n t e r n a l energy U per mole of the s o l i d f o l l o w s d i r e c t l y from a knowledge of the energy l e v e l s i n F i g . 2, and the Helmholtz f r e e energy F at any f i x e d  tempera-  t u r e T i s then given by F = U-TS where S i s the entropy per mole.  (1) The f r e e energy F at f i x e d  temperature i s shown s c h e m a t i c a l l y as a f u n c t i o n of volume i n F i g u r e 3, the s u b s c r i p t s 1 and 2 r e f e r r i n g to the normal m e t a l l i c phases  respectively.  and  The two phases can c o - e x i s t i n  e q u i l i b r i u m at p r e s s u r e P and temperature T i f t h e i r Gibbs  - 57 -  FREE ENERGY  MOLAR VOLUME  FIGURE 3. The t r a n s i t i o n t o m e t a l l i c phase. The s u b s c r i p t s 1 and 2 r e f e r t o the normal and m e t a l l i c phases r e s p e c t i v e l y (Ramsey, 1949)  - 58 f r e e energies  are equal, U  where  and  V  2  1 +  P  V l  i.e •  - TS  if  >  = U  X  2  +  PV  2  -  TS  (2)  2  are r e s p e c t i v e l y the volumes occupied  mole of the normal s o l i d and t u r e T and  -  pressure  P.  by  one  of the m e t a l l i c phase at tempera-  In v i r t u e of the thermodynamic  rela-  t ion (3) the c o n d i t i o n  (2) f o r e q u i l i b r i u m i s e q u i v a l e n t  common tangent T^ T  t o the two  2  to drawing a  curves i n F i g . 3.  tude of the slope of the tangent i s the c r i t i c a l (RAMSEY 1949,  The  magni-  pressure  1954).  T h i s d i s c u s s i o n , Ramsey p o i n t e d  out,  i s equally  appli-  cable to i o n i c c r y s t a l s and  to s o l i d s composed of  molecules.  a t r a n s i t i o n to a m e t a l l i c phase  However, before  saturated  c o u l d occur i t would f i r s t be necessary t o i o n i z e the i.e.,  to break the molecular bond.  latter,  Ramsey estimated that  an  energy i n the neighbourhood of ten e l e c t r o n - v o l t s per  mole-  c u l e would be r e q u i r e d .  pres-  sure i s i n c r e a s e d , great,  He  then observed that i f the  a c r i t i c a l pressure,  i s eventually  which may  be  very  reached at which the work done by  h y d r o s t a t i c f o r c e s during  the c o l l a p s e to the m e t a l l i c phase  s u p p l i e s j u s t the amount of energy r e q u i r e d . zero temperature the c o n d i t i o n U  2  -  the  U  l =  P  At  absolute  (2) of e q u i l i b r i u m reduces to C 1 V  -  V) 2  (4)  - 59 from which an order of magnitude estimate can be made of the necessary p r e s s u r e .  For an i n t e r n a l energy d i f f e r e n c e of ten  e l e c t r o n v o l t s and a change i n molar volume o f 10 cm , the r e 3  q u i r e d p r e s s u r e i s of the order o f magnitude of a m i l l i o n a t mospheres.  The only cases a c t u a l l y c a l c u l a t e d a r e f o r hydro-  gen where i t was found 10 10  that the c r i t i c a l p r e s s u r e i s 0.8 x  atm, and f o r helium where the c r i t i c a l p r e s s u r e i s 18 x 6  3 atm, and the d e n s i t y changes from 4.8 t o 5.7 gm/cm . A change i n d e n s i t y of mantle m a t e r i a l of about 50% at  a p r e s s u r e of 1.4 x 10  atmospheres i s probably c o n s i s t e n t  with the theory of a t r a n s i t i o n to a m e t a l l i c phase (RAMSEY, 1949,  1954).  RAMSEY (1951) a l s o considered the i n n e r core  boundary t o represent a second phase t r a n s i t i o n which i n creases the number of " f r e e " e l e c t r o n s . RAMSEY (1949) strengthened  the argument f o r h i s hypo-  t h e s i s by a c a l c u l a t i o n , u s i n g equation in  (4), of the change  i n t e r n a l energy i m p l i e d by s e i s m i c d a t a .  mate from t h e s e i s m i c a l l y determined d e n s i t y at t h e core-mantle  H i s rough  p r e s s u r e and change o f  boundary was 13.6 e l e c t r o n - v o l t s ,  although a c o r r e c t i o n f o r l a t e n t heat would lower t h i s somewhat.  esti-  value  A c c o r d i n g to Ramsey "13 e.v. i s a reasonable  e x c i t a t i o n energy f o r a very s t a b l e molecule, s t a b l e molecules  will  occur i n t h e e a r t h .  and only very  T h i s shows that  the p r e s s u r e and d e n s i t y jump at the boundary of t h e e a r t h ' s core are j u s t what one would expect  at a t r a n s i t i o n t o  - 60 m e t a l l i c phase."  Ramsey t e n t a t i v e l y a t t r i b u t e d the c o r e -  mantle d i s c o n t i n u i t y to the e x c i t a t i o n of the molecule  Si02,  n o t i n g that the conduction band i n quartz l i e s about 10.9 above the ground  e.v.  level.  In h i s arguments, Ramsey i n c l u d e d s e v e r a l c r i t i c i s m s of the hypothesis of an i r o n c o r e .  One  of them, that the hypo-  t h e s i s i s i n c o n s i s t e n t with the observed  mean d e n s i t i e s of  the t e r r e s t r i a l p l a n e t s , assuming that t h e i r chemical stitution mentioned.  con-  i s s i m i l a r to that of t h e e a r t h , has a l r e a d y been Ramsey a l s o considered the sharpness  of the boun-  dary of the core t o be i n c o n s i s t e n t with the i r o n core hypothesis  (RAMSEY, 1949).  However, BIRCH (1952) p o i n t e d out  that g r a v i t y i s not the f a c t o r which c o n t r o l s the  distribu-  t i o n of atoms between the s i l i c a t e and metal phases, as assumed by Ramsey;  i t merely  c o n t r o l s the r e l a t i v e p o s i t i o n s  of the phases, w h i l e the d i s t r i b u t i o n of the elements depends upon chemical  potentials.  In c o n s i d e r i n g the p o s s i b i l i t y of a m e t a l l i z e d s i l i c a t e core, many s c i e n t i s t s emphasize the negative r e s u l t s of e x p e r i ments with o l i v i n e , u s i n g shock, waves t o o b t a i n p r e s s u r e s exceeding  those i n the e a r t h ' s c o r e .  conducted  these experiments,  The  investigators  ALTSHULER and KORMER  (1961),  conclude that " i t would be premature to t o t a l l y r e j e c t Lodochnikov-Ramsey theory on the b a s i s of these f o r the f o l l o w i n g c o n s i d e r a t i o n s :  (a)  who  the  experiments  the temperature  of  - 61 p e r c u s s i v e compression of o l i v i n e exceeds the temperature i n the e a r t h ' s core;  (b) the exact composition  of the  s h e l l i s unknown;  (c) the t r a n s i t i o n to a more, dense  l i c phase could be a s s o c i a t e d with prolonged cesses."  silicate metal-  diffusional  pro-  In t h i s regard, LEVIN (1964a) has drawn p a r t i c u l a r  a t t e n t i o n to the case of g r a p h i t e .  Under prolonged  s i o n , 20,000 atmospheres i s s u f f i c i e n t  compres-  for transition  to  diamond, whereas under l a b o r a t o r y c o n d i t i o n s where p r e s s u r e s are a p p l i e d f o r minutes, a pressure  of the order of hundreds  of thousands of atmospheres i s necessary.  For shock compres-  s i o n , m i l l i o n s of atmospheres are r e q u i r e d , i . e . , a shock pressure  two  pressure  i s r e q u i r e d f o r the same t r a n s i t i o n , g r a p h i t e to  diamond. and  orders of magnitude g r e a t e r  than the  static  L e v i n d e s c r i b e s g r a p h i t e as a " s l u g g i s h " substance  suggests that Si02 i s a l s o " s l u g g i s h " , i n c o n t r a s t  to  substances which behave i n the same manner at shock pressures and  at s t a t i c  compression.  In the theory of the formation  of the core by a  transi-  t i o n to a m e t a l l i c phase, the c a t a s t r o p h i c c h a r a c t e r of formation  and the energy r e l e a s e d i n the process  tant c o n s i d e r a t i o n s  (RAMSEY, 1951).  Ramsey has  are  impor-  shown that  small p l a n e t a r y cores formed by compression are u n s t a b l e that a core d i d not e x i s t accumulated 0.8 pressure  i n the earth u n t i l  of i t s contemporary mass.  core  i t had  and  already  At that time,  the  i n the i n t e r i o r exceeded that r e q u i r e d f o r a phase  - 62 transition.  The beginning of the formation of the core  vated the c e n t r a l p r e s s u r e and caused  ele-  more mass to reach  p r e s s u r e s above the c r i t i c a l even b e f o r e a d d i t i o n a l mass was accumulated. i t s diameter p h i c nature.  In t h i s way, the formation of the core, reached  1/3 that o f the e a r t h , was of a c a t a s t r  A rough c a l c u l a t i o n by Ramsey gave a value of  l O ^ ergs, f o r the energy r e l e a s e d , s u f f i c i e n t 3  temperatures  until  o i n the e a r t h by 15 .  to r a i s e  ft In the subsequent 10  years, when the e a r t h completed i t s accumulation, grew t o 0.55 o f the diameter  of the e a r t h .  the core  - 63 5.  THE MOON  5.1 The o r i g i n of t h e moon An is  important boundary c o n d i t i o n on the o r i g i n of the moon  i t s average d e n s i t y .  JEFFREYS (1937) and, more r e c e n t l y ,  LYTTLETON (1963) have shown that the uncompressed d e n s i t i e s of t h e moon and the outer  400 km of the e a r t h a r e i d e n t i c a l .  Moreover, i f the i n c r e a s e i n d e n s i t y i n the t r a n s i t i o n zone of t h e e a r t h ' s  mantle can be f u l l y accounted f o r by a more  t i g h t l y packed c r y s t a l s t r u c t u r e p l u s normal compression and if  the jump i n d e n s i t y at the core-mantle boundary i s due t o  a t r a n s i t i o n to a m e t a l l i c phase, then the composition moon must be n e a r l y i d e n t i c a l t o that of t h e e a r t h  of the  (LYTTLETON,  1963). Of  course,  i f the moon o r i g i n a t e d by r o t a t i o n a l f i s s i o n  from the e a r t h t h i s might e x p l a i n t h e s i m i l a r i t y of i t s comp o s i t i o n with  that of the e a r t h ' s outer 400 km.  t h e s i s as f i r s t  T h i s hypo-  developed by DARWIN (1880) was based on t i d a l  resonance, but was l a t e r r e j e c t e d because damping of the t i d a l bulges would prevent f i s s i o n  (JEFFREYS, 1930).  Without o f f e r i n g s o l u t i o n s to important dynamical d i f f i c u l t i e s , WISE (1963) has r e v i v e d the f i s s i o n in a new form.  According  of t h i s hypothesis, fission  hypothesis  to Wise's q u a l i t a t i v e development  the o r i g i n of the moon by r o t a t i o n a l  i s connected w i t h the formation  WISE (1963) h i m s e l f l i s t s  of the earth's  core.  several objections to this  - 64 hypothesis.  H i s c r i t i c i s m s are q u i t e severe, and he has no  answer t o the most s e r i o u s o b j e c t i o n .  The angular  momentum  of the earth-moon system i s only 27% of the value r e q u i r e d by the f i s s i o n theory of the o r i g i n o f the moon.  The present  r o t a t i o n a l k i n e t i c energy p l u s the g r a v i t a t i o n a l p o t e n t i a l energy a r i s i n g from the s e p a r a t i o n of the e a r t h and moon are about 6 per cent of the t h e o r e t i c a l o r i g i n a l energy.  The p o s s i b i l i t y  that magnetic f i e l d s or a change i n  the g r a v i t a t i o n a l constant suggested  rotational  might answer these o b j e c t i o n s , as  by Wise, has c e r t a i n l y not been demonstrated.  Furthermore, as Wise p o i n t e d out, out on the f i s s i o n hypothesis  the c a l c u l a t i o n s c a r r i e d  by J e f f r e y s , Moulton and  L y t t l e t o n do not have as a f i n a l r e s u l t two unequal masses with n e a r l y c i r c u l a r r e l a t i v e  orbits.  Perhaps the most p e r s u a s i v e argument against such a hypothesis  i s the e x i s t e n c e of an a l t e r n a t i v e hypothesis of  the o r i g i n of the moon which i s i n agreement with the c u r r e n t l y known laws of p h y s i c s and recognized p h y s i c a l processes, which i s an i n t e g r a l p a r t of a theory which encompasses the o r i g i n of a l l the p l a n e t s and t h e i r s a t e l l i t e s and to which no o b j e c t i o n has as yet been made. ing t h i s h y p o t h e s i s ,  yet another  hypothesis  Before  consider-  on t h e o r i g i n of  the e a r t h , c u r r e n t l y e n j o y i n g some p o p u l a r i t y , w i l l be critically  discussed.  Because Urey assumes the v a l i d i t y of t h e i r o n  core  - 65 h y p o t h e s i s , he must have a s p e c i a l hypothesis f o r the o r i g i n of the moon i n order t o e x p l a i n i t s l i g h t e r composition compared with the e a r t h . solar  as  H i s theory of the o r i g i n of the  system from lunar s i z e d  bodies has a l r e a d y been men-  t i o n e d and the chemical support which he found f o r t h i s theory from m e t e o r i t e s , p a r t i c u l a r l y from the e x i s t e n c e of diamonds in some m e t e o r i t e s , was  critically  evaluated i n Chapter  A c c o r d i n g to Urey (1960) the moon was an event which even he admits  captured by the e a r t h ,  has a very low p r o b a b i l i t y . '  Urey h i m s e l f d i d not propose a concrete scheme f o r the ture, but g r a v i t a t i o n a l  2.  capture i s r e a l i z a b l e  when three bodies approach one another:  cap-  in principle  the growing e a r t h  and two bodies s i m i l a r i n mass to the moon.  RUSKOL (1963)  demonstrated that the p r o b a b i l i t y  of capture of a ready-made  moon was  2  c o n s i d e r a b l y less than 10~  even assuming that the  mass of the zone from which the e a r t h accumulated  was  made up  p r i n c i p a l l y of moon-sized b o d i e s . RUSKOL (1960a, 1960b, 1963a) concluded realistic  that the only  view of the problem i s to e n v i s i o n the growth of  the moon i n a swarm of s a t e l l i t e bodies g i r d l i n g the e a r t h . T h i s hypothesis made e a r l i e r by Schmidt was t i v e l y by Ruskol  i n the three papers  developed q u a n t i t a -  r e f e r r e d to above.  Ruskol c o n s i d e r s that c o n v i n c i n g evidence i n f a v o r of the formation of a l l major s a t e l l i t e s planets l i e s  i n the neighbourhood of  i n the r e g u l a r c h a r a c t e r of t h e i r o r b i t s , which  - 66 i s incompatible with the capture of s a t e l l i t e s a l r e a d y formed. The capture i n the "grown-up" s t a t e , a c c o r d i n g to Ruskol, be assumed only f o r s o - c a l l e d " i r r e g u l a r " s a t e l l i t e s , remote from t h e i r p l a n e t s and having n e g l i g i b l y Ruskol considered the capture of p a r t i c l e s circumterrestrial  ticle.  - the growing  A change i n p a r t i c l e energy  the E a r t h .  demonstrated  by  into  circular  i s necessary to enable the around  the Sun to an  The e f f e c t i v e n e s s of t h i s process  orbit  was  Ruskol.  He found that a mass of the c i r c u m t e r r e s t r i a l tween 0.01  the  e a r t h , the sun and the par-  p a r t i c l e to t r a n s f e r from an o r b i t around  usually  s m a l l masses.  swarm i n terms of a r e s t r i c t e d  three-body problem  can  Q and 0.1 Q was  s,warm be-  necessary f o r the moon's formation,  where Q i s the t o t a l mass of a l l bodies i n the annular zone of the earth's supply source (from approximately 0.8 1.3 AU from the sun).  AU  Such a mass could have been obtained  d u r i n g the time of the e a r t h ' s growth, i f the average  proba-  b i l i t y of capture at one c o l l i s i o n were of the order of and  the average  e f f e c t i v e dimensions  were 10 to 100 km.  While  i t was  l e v e l of 0.001, the  would be 1 to 10 km  impossible to determine  (RUSKOL, 1960). the d i s t a n c e from  the e a r t h at which the embryonic moon o r i g i n a t e d , an mate was  0.01,  of c o l l i d i n g bodies  At the p r o b a b i l i t y  e f f e c t i v e dimensions  to  esti-  made of the d i s t r i b u t i o n of the d e n s i t y of matter i n  the swarm as a f u n c t i o n of d i s t a n c e from the e a r t h ,  In t h i s  - 67 regard, c o n s i d e r a t i o n was given to the f a c t "Roche l i m i t ,  i . e . , w i t h i n approximately  that w i t h i n the  two and one-half  times the r a d i u s of t h e embryonic e a r t h , the t i d a l f o r c e separating p a r t i c l e s  i s g r e a t e r than t h e i r  gravitational  a t t r a c t i o n and hence the embryonic moon must have formed out side t h i s of  limit,  matter.  yet i n a r e g i o n of reasonably high d e n s i t y  Thus the minimum p o s s i b l e d i s t a n c e depends on t h  mass of the e a r t h at the time when the formation of t h e moon commenced.  Although  i t i s i m p o s s i b l e to c a l c u l a t e t h i s mass  with any degree of accuracy,  i t can be a s s e r t e d d e f i n i t e l y  that the ,earth-moon system d i d not o r i g i n a t e as a double p l a n e t from some double  embryo.  Ruskol estimates t h a t the  formation of the moon commenced when the earth's mass amounted t o 0.3 - 0.5 of i t s present mass and at a d i s t a n c e of between 5 and 10 e a r t h r a d i i . This theory of the o r i g i n o f the moon i s a p p a r e n t l y i n c o n s i s t e n t with a l a r g e d i f f e r e n c e i n chemical between the e a r t h and the moon. which supports  Therefore, any evidence  t h i s theory l i k e w i s e supports Ramsey's hypo-  t h e s i s of a m e t a l l i z e d s i l i c a t e 5.2  composition  core.  F u r t h e r evidence from a study of the moon All  of the major problems connected  i t s thermal h i s t o r y ,  with the moon, e.g.  i t s f i g u r e and r h e o l o g i c a l  behaviour,  the t i d a l e v o l u t i o n of t h e earth-moon system and t h e o r i g i n  - 68 of i t s s u r f a c e f e a t u r e s , a r e r e l a t e d to i t s composition and its origin.  Hence a c o n s i d e r a t i o n of i n v e s t i g a t i o n s o f these  problems i s of i n t e r e s t  i n an attempt t o e v a l u a t e hypotheses  on t h e nature of t h e earth's core. matters  We s h a l l c o n s i d e r these  ,  only b r i e f l y , however, s i n c e t h e i r r e l e v a n c e to the  t h e s i s problem i s somewhat remote, although not i n s i g n i f i c a n t . The t i d a l e v o l u t i o n of t h e earth-moon system i s c e r t a i n l y r e l a t e d to the o r i g i n o f the moon; cant source of heat  i t may a l s o be a s i g n i f i -  i n the e a r t h , a matter which w i l l be con-  s i d e r e d i n s e c t i o n 7.1.  From the present  observed  l a g i n the  t i d e s of t h e s o l i d body of t h e e a r t h , RUSKOL (1963b) has cons t r u c t e d a p i c t u r e o f the r e c e s s i o n of the moon t o i t s present d i s t a n c e d u r i n g the l a s t 4.5 b i l l i o n  years which i s c o n s i s t e n t  with i t s formation from a swarm of small s a t e l l i t e s moving about the e a r t h at d i s t a n c e s of 5 - 20 e a r t h r a d i i . evidence  f o r the r e c e s s i o n of the moon comes from  Other  astronomical  measurements (GAMOW, 1957; MUNK AND MACDONALD, I960),,  The  length of time d u r i n g which the moon has been r e c e d i n g has not yet been d e f i n i t e l y determined mates v a r y i n g from l e s s than years.  from t h i s evidence,  esti-  1 b i l l i o n years to 4.5 b i l l i o n  Moreover, i t does not seem p o s s i b l e , on the b a s i s o f  t h i s evidence,  to d i s t i n g u i s h between an o r i g i n of the moon  by capture, f i s s i o n o r c i r c u m t e r r e s t r i a l accumulation, a l though an exact d e t e r m i n a t i o n o f the d u r a t i o n of r e c e s s i o n coupled with a knowledge of t h e thermal  h i s t o r y of the e a r t h  - 69 could p o s s i b l y accomplish  this.  P o t e n t i a l l y useful information mination of the f i g u r e of the moon.  a l s o comes from a d e t e r Deviation  of the lunar  f i g u r e from i t s h y d r o s t a t i c form may impose l i m i t a t i o n s on the thermal s t a t e of i t s i n t e r i o r and t h i s i n turn would be a boundary c o n d i t i o n on the o r i g i n and composition of the moon.  A c c o r d i n g t o LEVIN (1964b), t h i s d e v i a t i o n  cated  not by the geometrical  i n e r t i a , the t r i a x i a l i t y times greater  is indi-  form, but by the e l l i p s o i d of  of t h i s e l l i p s o i d being  than can be e x p l a i n e d  t i d a l i n f l u e n c e o f the e a r t h .  several  by r o t a t i o n plus the  I f A, B, C are the moments of  i n e r t i a about three mutually p e r p e n d i c u l a r  axes (C being the  moment about the a x i s of r o t a t i o n ) , the t r i a x i a l i t y sented by the r a t i o  (C - A)/(B  hydrostatic equilibrium,  -A).  I f the moon were i n  t h i s r a t i o would be 4/3, whereas  the observed value i s s e v e r a l times g r e a t e r deviation  i s more commonly d i s c u s s e d  (BALDWIN, 1949; 1962). 1.09  i s repre-  KOPAL, 1962;  than t h i s .  i n geometrical  RUNCORN, 1962;  This  terms  MACDONALD,  KOPAL (1962) noted that t h e moon has a t i d a l bulge of  km., which corresponds t o h y d r o s t a t i c e q u i l i b r i u m f o r a  moon 2.57 times c l o s e r to the e a r t h  than i t i s now,  The  p o l a r f l a t t e n i n g of a moon i n h y d r o s t a t i c e q u i l i b r i u m t h i s c l o s e t o the e a r t h would be 0.28 km., corresponding to a r a t i o of p o l a r f l a t t e n i n g to t i d a l bulge of 0.25, whereas estimates of the r a t i o based on present observations  vary  - 70 between 0.60 and 0.71. Whether t h e f i g u r e of the moon i s c o n s i d e r e d  geometrically  or i n terms of i t s e l l i p s o i d of i n e r t i a , and i n s p i t e o f unc e r t a i n t i e s i n astronomical  measurements, LEVIN  (1964b),  RUNCORN (1962), KOPAL (1962) and MACDONALD (1962) are a l l i n agreement that the observed d i f f e r e n c e s between the r e a l moon and a moon i n h y d r o s t a t i c e q u i l i b r i u m a r e s i g n i f i c a n t . The  f i g u r e of the moon d e v i a t e s  ponding t o h y d r o s t a t i c the e x i s t e n c e  so much from values  e q u i l i b r i u m as to r u l e out,  of exact h y d r o s t a t i c  corresnot only  e q u i l i b r i u m at the present  time, but a l s o any p o s s i b i l i t y that the moon's dynamical c h a r a c t e r i s t i c s may have preserved a f o s s i l form of hydros t a t i c e q u i l i b r i u m p r e v a i l i n g i n the past. against  Another argument  the suggestion made by JEFFREYS (1959), that the  shape of the moon i s a f o s s i l solidified  at a d i s t a n c e  that an i n i t i a l l y  r e l i c o f i t s shape when i t  c l o s e r to t h e e a r t h than now, i s  molten moon would remain molten i f i t s con-  tent of r a d i o a c t i v i t y were greater chondrites  than one-fourth that of  (MACDONALD, 1962).  KOPAL (1962) and RUNCORN (1962) have suggested that convection  i n the moon i s r e s p o n s i b l e  for i t s  nonequilibrium  figure.  On t h i s suggestion the moon need not have a f i n i t e  strength  to support i t s n o n e q u i l i b r i u m  figure.  By comparing  estimates of the a d i a b a t i c and conductive temperature g r a d i ents,  Kopal concludes that  i f as a r e s u l t of r a d i o g e n i c  - 71 h e a t i n g any p a r t of the l u n a r i n t e r i o r becomes molten, conv e c t i o n c u r r e n t s are bound to a r i s e which w i l l i n a d d i t i o n to conduction argues,  or r a d i a t i o n .  t r a n s p o r t heat  Moreover, Kopal  i n order that t h i s be t r u e , i t i s not  necessary  for  a c t u a l melting of the rocks to take p l a c e , because convect i o n can a r i s e i n a visiCo-elast i c medium c h a r a c t e r i z e d by a f i n i t e viscosity,  no matter how  l a r g e , provided  only that  the  conductive g r a d i e n t i s much l a r g e r than the a d i a b a t i c and that the time s c a l e of the f l o w i s s u f f i c i e n t l y p a r i s o n with the Maxwellian r e l a x a t i o n time. are shown to be s a t i s f i e d  i n the moon.  v e c t i v e v e l o c i t y as low as 10"^^ meter per 1000 conduction  These c o n d i t i o n s  Furthermore, a  cm/sec i.'e., about one  years, i s s u f f i c i e n t  con-  centi-  to render c o n v e c t i o n  of comparable importance f o r heat  lunar i n t e r i o r .  long i n com-  and  t r a n s p o r t i n the  For higher v e l o c i t i e s , convection should  pre-  dominate. RUNCORN (1962) suggests  that the bulge towards the e a r t h  can be e x p l a i n e d by a second-degree c o n v e c t i o n  current  i t s a x i s of symmetry d i r e c t e d towards the e a r t h .  with  Further-  more, because the moments of i n e r t i a about the p o l a r a x i s and the e q u a t o r i a l a x i s i n the plane of the sky are unequal, there must be superposed on t h i s p a t t e r n an e x a c t l y s i m i l a r symmetrical  one  about the l a t t e r a x i s , with v e l o c i t i e s 0.6  of the former.  Runcorn gives no e x p l a n a t i o n f o r the  dence of c o n v e c t i o n c u r r e n t and  g e o m e t r i c a l axes;  -  0.7  coinci-  perhaps  - 72 v a r i a b l e thermal expansion near the s u r f a c e , as d i s c u s s e d below,  i s r e l a t e d to t h i s r e s u l t .  Runcorn r e q u i r e s the e x i s t e n c e  I t should of a core  be noted that  i n the moon, which  may be as small as 0.06 or as l a r g e as 0.36 of the lunar diameter, i n order t o e x p l a i n the proposed convection  cur-  rents . Taking account of the m i g r a t i o n  of most of the r a d i o -  a c t i v e elements towards the s u r f a c e at the time of g r e a t e s t heating,  LEVIN (1964b) argues that t h e present  is p r a c t i c a l l y  thermal s t a t e  independent of the mean r a d i o a c t i v e content,  but depends only on the content i n t h e i n t e r i o r a f t e r d i f f e r e n t i a t i o n and on the thermal c o n d u c t i v i t y .  Calculations f o r  a number of models (LEVIN, 1960) show that because of the c o o l i n g of the moon which would begin a f t e r d i f f e r e n t i a t i o n , an outer  l a y e r some 500 - 700 km i n t h i c k n e s s  at the present  must be s o l i d  time and the i n t e r i o r below t h a t , molten.  i  The  nonequilibrium  shape of the moon i s maintained by the  s t r e n g t h of i t s c r u s t .  L e v i n o f f e r s an e x p l a n a t i o n  of t h i s  shape based on t h e f a c t  that the s u r f a c e temperature main-  t a i n e d by s o l a r r a d i a t i o n must s u b s t a n t i a l l y decrease from the lunar equator, which almost c o i n c i d e s with the e c l i p t i c , lunar p o l e s .  Levin's  c a l c u l a t i o n s show that because of the  temperature dependence of the c o n d u c t i v i t y , temperatures i n the s o l i d increases.  l a y e r are not e q u a l i z e d Instead,  to the  with-  i n l a t i t u d e as the depth  d i f f e r e n c e s at depths of 200 - 300 km  - 73 are about twice as great as at the s u r f a c e . 150°  i n sub-surface  A d i f f e r e n c e of  temperature between the equator and p o l e s ,  leads t o a d i f f e r e n c e o f about 200° i n t h e mean temperature of the s o l i d l a y e r . Lower temperature i n any part of the l a y e r , L e v i n p o i n t s out,  i s accompanied by an i n c r e a s e i n i t s r a d i a l t h i c k n e s s .  According  to h i s c a l c u l a t i o n s , s o l i d i f i c a t i o n at the p o l e s  extends about 50 km deeper than at the equator.  Since the  d e n s i t y of s o l i d matter exceeds that o f i t s l i q u i d form,  iso-  s t a t i c adjustment of the outer l a y e r as a whole leads t o a f l a t t e n i n g of the p o l a r r e g i o n s . creased  T h i s would be f u r t h e r i n -  by the g r e a t e r thermal expansion of e q u a t o r i a l mater-  i a l because of i t s higher  temperature.  Levin considers that this explanation  of .the f l a t t e n i n g  of the dynamical f i g u r e of the moon has t h e advantage that the s t r e s s e s i n the s o l i d  layer after i s o s t a t i c  adjustment  would be s u f f i c i e n t l y small to a l l o w permanent support by rigidity.  F i n a l l y , L e v i n gives a method f o r e s t i m a t i n g  (C - A)/C a c c o r d i n g t o h i s hypothesis f i g u r e of the moon. not  f o r the n o n e q u i l i b r i u m  In h i s view, the q u a n t i t i e s i n v o l v e d are  know s u f f i c i e n t l y a c c u r a t e l y to prove or d i s p r o v e the  v a l i d i t y of the hypothesis,  although  i n d i c a t e s that the hypothesis  a rough estimate  i s probably  adequate.  by him KOPAL  (1965), however, on the b a s i s of a more r i g o r o u s treatment of the problem, concluded  that d i r e c t i o n a l h e a t i n g of the lunar  - 74 s u r f a c e by t h e sun could not deform the moon by more than a few p e r cent o f t h e amount i n d i c a t e d by the observed  value  of the d i f f e r e n c e s i n the moments of i n e r t i a . It seems p o s s i b l e that a combination o f Runcorn's and L e v i n ' s hypotheses can e x p l a i n the n o n - e q u i l i b r i u m the moon.  The t h i n n i n g of the s o l i d i f i e d  towards the e c l i p t i c ,  s u r f a c e of the moon  as proposed by L e v i n , suggests that  heat t r a n s f e r r e d by c o n v e c t i o n  to this s o l i d i f i e d  more e a s i l y conducted away at the e c l i p t i c .  surface i s  Combined  the t i d a l i n f l u e n c e of the e a r t h t h i s suggestion r i s i n g convection  shape of  with  explains  c u r r e n t s along an a x i s d i r e c t e d towards the  earth's c e n t r e and f a l l i n g c u r r e n t s at the p o l e s , as proposed by Runcorn. The  problem o f the o r i g i n of the s u r f a c e f e a t u r e s of t h e  moon has been considered  f o r i t s p o s s i b l e b e a r i n g on the  q u e s t i o n of t h e o r i g i n of the moon and on the thermal h i s t o r y of the moon.  The strong evidence  f o r an impact o r i g i n of  l u n a r c r a t e r s and p a r t i a l melting of the moon's s u r f a c e (SYTINSKAYA, I960;  STAYUKOVICH and BRONSHTEN, 1960;  SHOEMAKER, 1964) i s c o n s i s t e n t with the theory  of the o r i g i n  of the moon developed by Ruskol and the thermal h i s t o r y put forward  by L e v i n .  While i n agreement with the work of Ruskol  and L e v i n , the observed s u r f a c e f e a t u r e s are by no means conc l u s i v e evidence  supporting  t h e i r work.  I t i s conceivable  that a moon which o r i g i n a t e d i n a d i f f e r e n t way and with a  - 75 chemical  composition  nevertheless  d i f f e r e n t from that of the e a r t h  have the observed s u r f a c e f e a t u r e s .  could  - 76 6.  EVIDENCE FROM THE ABUNDANCES OF Th, U AND  Pb  P o t e n t i a l l y s i g n i f i c a n t and p o s s i b l y d e c i s i v e evidence f o r the problems  c o n s i d e r e d i n t h i s t h e s i s comes from the  measured abundances i n the e a r t h and m e t e o r i t e s of the i s o topes of thorium, uranium and l e a d .  About  o n e - t h i r d of the  lead at the e a r t h ' s s u r f a c e i s the r e s u l t of the decay of uranium and thorium formed d u r i n g the l i f e t i m e of the e a r t h . For t h i s reason, lead, more than any other element,  i s unique  and powerful as a geochemical t o o l f o r t r a c i n g the h i s t o r i c a l sequence  of g e o l o g i c a l events (PATTERSON, 1963).  Moreover,  the measured abundances of lead are the b a s i s f o r what i s considered the most p r e c i s e d e t e r m i n a t i o n of t h e age of the earth  (OSTIC et a l . ,  1963).  The success of the uranium-lead method i n determining the age of the earth depends on the v a l i d i t y of a p p l y i n g the theory of s i n g l e - s t a g e leads to samples s e l e c t e d samples from the e a r t h ' s c r u s t .  from m e t e o r i t e s and T h i s theory assumes  . _ . . , 238 235 . ^232 204 that the r a t i o s of U , U and Th to Pb remained TT  constant, except f o r the r a d i o a c t i v e decay of U  2 3 8  , U  2 3 5  and  232 Th  , i n l o c a l l y c l o s e d systems from the time t  Q  to the pre-  sent time i n meteorites and to a time t-^ f o r samples  i n the  crust, where t± i s the time when m i n e r a l i z a t i o n i s o l a t e d the lead from the i n i t i a l (KANASEWICH, 1962).  uranium and thorium environment The success of t h i s method a l s o depends  on a knowledge of the " p r i m o r d i a l " i s o t o p i c abundances of  - 77 l e a d , i . e . , the abundances at time t . Q  Using the theory of s i n g l e - s t a g e leads and assuming that uranium-free  l e a d i n the t r o i l i t e phase of some i r o n meteor-  i t e s g i v e s the p r i m o r d i a l abundances of lead i s o t o p e s , i t has been found existed  that l e a d - b e a r i n g samples from m e t e o r i t e s have  i n l o c a l l y c l o s e d systems f o r 4.56 ± 0.02 aeons  (OSTIC et a l . , 1963).  The value f o r the earth a l s o depends  on the hypothesis that leads were emplaced i n the c r u s t  from  a s i n g l e c l o s e d system, i . e . , that the U/Pb r a t i o i n the mantle i s c o n s t a n t . The  " c e s s a t i o n of m e l t i n g " i n the parent bodies of meteor-  i t e s has been dated by two other independent R7  Rb  - Sr  method g i v e s an age of 4,37 t 0.2 aeons (ANDERS,  A c c o r d i n g to Anders, the f r a c t i o n a t i o n s i n v o l v e d  temperatures era  The  7  ft  1964).  methods.  above 1000°C and hence he concludes  that the  of i n t e n s e m e l t i n g i n the meteorite parent bodies ended  about 4.4 - 4.6 aeons ago.  K  4 0  - A  4 0  and R b  8 7  - Sr  87  ages  of c r u s t a l rocks a r e s i m i l a r l y c o n s i s t e n t with age determinat i o n s based  on lead i s o t o p e abundances (KANASEWICH, 1962).  When considered i n r e l a t i o n t o the observed  concentra-  t i o n s of uranium and thorium i n the c r u s t , evidence f o r and a g a i n s t the s i n g l e - s t a g e theory has important  implications.  Knowledge of the thermal s t a t e of the e a r t h , chemical t i e s and the composition  affini-  of c h o n d r i t i c meteorites a l l i n d i -  cate that uranium and thorium are concentrated  i n the c r u s t ,  - 78 perhaps to the extent of 75 per cent or more of the e a r t h ' s t o t a l content  of these elements (ADAMS et a l . , 1959).  Assum-  ing that uranium f r a c t i o n a t e d with respect to lead i n the process which concentrated  uranium i n the c r u s t , t h i s  l e d Ringwood (1960) to conclude approximately  4.55  that an age of the e a r t h of  aeons r e f e r s to the time when d i f f e r e n t i -  a t i o n of the whole mantle and completed;  evidence  s e g r e g a t i o n of the core  s i m i l a r l y , d i f f e r e n t i a t i o n and  was  s e g r e g a t i o n of the  m e t e o r i t e parent bodies must have been completed at the same time.  The only other p o s s i b i l i t y  i s that the e a r t h was  c l o s e d system b e f o r e the meteorite parent seems unreasonable  i n view of the evidence  a  bodies, which considered  in this  t h e s i s of p o s s i b l e g e n e t i c r e l a t i o n s h i p s between the e a r t h and m e t e o r i t e s .  To e x p l a i n these r e s u l t s , Ringwood  has  evolved an e l a b o r a t e theory, which i n c l u d e s a m e t e o r i t i c planet.  He  attempts to give a p h y s i c a l b a s i s f o r an  early  high temperature h i s t o r y of both the l a r g e m e t e o r i t i c p l a n e t s and  the e a r t h and  a chemical and p h y s i c a l b a s i s f o r the  formation of an i r o n core and  the formation of a moon of  l i g h t e r d e n s i t y than the e a r t h (RINGWOOD, 1960, 1965).  Evidence  on the l o c a t i o n and  parent bodies and evidence  1961,  s i z e of the  1963,  meteorite  of the low temperature h i s t o r y of  carbonaceous c h o n d r i t e s , considered i n Chapter  2, and  r e l a t i n g to the thermal h i s t o r y of the earth and  evidence  the p o s s i -  b i l i t y of the formation of an i r o n core, considered i n  - 79 Chapters  7 and 8, a l l argue against Ringwood's theory, a s i d e  from the a r b i t r a r i n e s s of many of i t s f e a t u r e s . Yet Ringwood's c o n c l u s i o n of the meaning of the measured age of the e a r t h and meteorites may be i n e s c a p a b l e i f the s i n g l e stage theory o f leads and h i s assumption t i o n of v o l a t i l e s  i n the c r u s t  that the concentra-  and upper mantle  corresponded  to a f r a c t i o n a t i o n of uranium with respect to l e a d , are both correct. I f there i s no f r a c t i o n a t i o n of uranium with r e s p e c t to lead i n any of the p r o c e s s e s t h a t have taken p l a c e i n the mantle or deep i n t e r i o r of the e a r t h or i n meteorite parent b o d i e s , then there i s probably no d i f f i c u l t y with the s i n g l e stage model.  The agreement between the age of the e a r t h and  the age of the meteorites i s then e x p l a i n e d by i d e n t i f y i n g t h i s age as the time o f formation of both the meteorite parent bodies and the e a r t h . However, i f t h e r e has been s i g n i f i c a n t f r a c t i o n a t i o n of uranium and thorium with r e s p e c t to l e a d , then arise.  difficulties  In t h i s case e i t h e r the s i n g l e stage theory i s g r o s s l y  i n e r r o r o r , a f t e r Ringwood, we must c o n s i d e r that a l l processes which might have f r a c t i o n a t e d uranium with respect t o lead were completed of  this  result.  The ceased  4.55 aeons ago and look f o r an e x p l a n a t i o n  i m p l i c a t i o n of Ringwood's reasoning that m e l t i n g  at the same time, t , i n both the meteorite parent Q  - 80 bodies and  the e a r t h and  that at that time the l e a d  r a t i o s were the same i n bodies formed i n d i f f e r e n t environments and deed very  .A f u r t h e r c o m p l i c a t i o n f o r any  t i o n that d i f f e r e n t i a t i o n and  segregation  meteorites  aeons ago  the e a r t h 4.55  t u r e s of meteorites suggests,  due  chemical  a f t e r a p e r i o d of r a d i o a c t i v e decay i s i n -  remarkable.  and  isotope  was  sugges-  completed i n  a r i s e s i f the f e a -  were i n p a r t or e n t i r e l y , as LEVIN (1965)  to d i f f u s i o n  i n the s o l i d  state.  Solid  d i f f u s i o n might a l s o have been a s i g n i f i c a n t process e a r t h , perhaps even being  state i n the  e n t i r e l y r e s p o n s i b l e f o r the  con-  c e n t r a t i o n of v o l a t i l e s i n the c r u s t . I f s o l i d s t a t e d i f f u s i o n has been an important i n meteorites  and  the e a r t h f o r 4.55  process  aeons, then the hypo-  t h e s i s that measured samples of lead from the upper mantle or from meteorites  have e x i s t e d i n c l o s e d systems depends on  f u r t h e r hypothesis  that there i s no U-Pb, or Th-Pb f r a c t i o n a -  t i o n i n d i f f u s i v e processes. t h i s f u r t h e r hypothesis not be  the  The  importance of e v a l u a t i n g  t h e o r e t i c a l l y and  experimentally  can-  over-emphasized*  However, measurements of modern lead i s o t o p e abundances i n meteorites  are reasonably  c o n s i s t e n t with the  that a l l f r a c t i o n a t i o n of uranium with completed 4.55  aeons ago.  to lead  was  Lead i s o t o p e abundances i n c r u s t a l  samples b e l i e v e d to have a recent give f u r t h e r agreement.  respect  hypothesis  o r i g i n i n the upper mantle  T h i s evidence seems f a i r l y  convincing.  - 81 An attempt to combine an equation d e s c r i b i n g the d i f f u s i o n of uranium out of, or i n t o a l e a d environment with the of  equation  r a d i o a c t i v e decay l o o k i n g f o r p o s s i b l e c o n s i s t e n c i e s of  such a model w i t h the observed  abundances, might l e a d t o  more d e f i n i t e c o n c l u s i o n s . In the u n c e r t a i n t i e s of the d e t e r m i n a t i o n of p r i m o r d i a l abundances and the observed  s c a t t e r of the present-day  lead  i s o t o p e r a t i o s i n meteorites about an i s o c h r o n d e f i n e d by s i n g l e stage theory, may r o l e of d i f f u s i o n  perhaps be found evidence  of the  i n the f r a c t i o n a t i o n of uranium and  In t h i s regard, ANDERS (1962) notes that there i s too uranium i n the t r o i l i t e phase of the Toluca i r o n to  account  f o r the observed  lead. little  meteorite  amounts of r a d i o g e n i c l e a d ;  n e v e r t h e l e s s , the i s o t o p i c composition T o l u c a l e a d f a l l s between the 4.6  and  of the r a d i o g e n i c 4.7  aeon  isochrones  a g r e e i n g r a t h e r w e l l with r e s u l t s from other m e t e o r i t e s . Furthermore, the " p r i m o r d i a l - l e a d " p o i n t s of S t a r i k d i f f e r from those of P a t t e r s o n by being higher i n P b  2 0 7  ,  indicating  e i t h e r a systematic e r r o r i n l a b o r a t o r y measurements or "the e x i s t e n c e of more than one type of p r i m o r d i a l l e a d . " evidence  should be considered  Such  carefully.  U n t i l f u r t h e r work has been done, the merit of the  evi-  dence d i s c u s s e d i n t h i s chapter cannot be p r o p e r l y e v a l u a t e d . However, three p o s s i b i l i t i e s e x i s t :  (1)  The  processes  which concentrated the v o l a t i l e s i n the c r u s t gave r i s e to a  - 82 core of the e a r t h and were r e s p o n s i b l e f o r the f e a t u r e s of meteorites d i d hot f r a c t i o n a t e uranium and respect to lead i n the e a r t h ' s i n t e r i o r . meteorite parent bodies formed 4.55  thorium  with  The e a r t h and (2)  The  cesses i n q u e s t i o n f r a c t i o n a t e d uranium and thorium  with  respect t o l e a d . ago  aeons ago.  the  These processes were completed  i n both meteorites and  the e a r t h .  (3)  4.55  aeons  The observed i s o -  t o p i c abundances are c o n s i s t e n t with f r a c t i o n a t i o n due d i f f u s i o n of uranium and  thorium i n t o and  ments d u r i n g the h i s t o r y of meteorites and  the e a r t h .  The  recon-  The t h i r d p o s s i b i l i t y seems r a t h e r u n l i k e l y ,  must be t e s t e d .  to  out of lead environ-  meaning of age d e t e r m i n a t i o n s i n t h i s case must be sidered.  pro-  but  Other evidence c o n s i d e r e d i n t h i s t h e s i s i s  i n c o n f l i c t with the second  possibility.  The f i r s t  i t y depends on the n o n - f r a c t i o n a t i o n of uranium and  possibilthorium  with respect to lead i n the processes which separated p h i l e , c h a l c o p h i l e and perhaps s i d e r o p h i l e  elements.  litho-  - 83 7.  THERMAL HISTORY OF THE EARTH Any  knowledge of the thermal  h i s t o r y of the e a r t h i s  r e l e v a n t to an e v a l u a t i o n o f the p o s s i b i l i t y and time o f formation  of an i r o n c o r e .  Seismic  studies provide  evidence  that the outer core of the e a r t h i s l i q u i d , whereas the mantle is solid.  The inner core i s probably  comparisons of estimates  m e l t i n g temperatures of i r o n ,  and e x p e r i m e n t a l l y  determined  s i l i c a t e s and m e t a l l i z e d  cates can p r o v i d e a d d i t i o n a l evidence  7.1  Therefore,  o f the a c t u a l temperatures i n the  e a r t h with the t h e o r e t i c a l l y  earth's  also s o l i d .  sili-  on the nature o f the  core.  Sources of heat  and the primeval  temperature o f the e a r t h  The most s i g n i f i c a n t source of heat probably  i n the e a r t h i s  the decay o f the l o n g - l i v e d r a d i o a c t i v e n u c l i d e s of  uranium, thorium,  and potassium.  Estimates  of the content of  U, Th and K i n the e a r t h are u s u a l l y based on t h e i r abundance i n c h o n d r i t e s .  T h i s procedure can only g i v e very  rough e s t i m a t e s , however. o x i d a t i o n o f meteorites  different  A d i f f e r e n c e i n the s t a t e of  and the e a r t h might a l s o mean a d i f f e r -  ence i n the t o t a l content t h e r e i s evidence  average  o f K, U and Th.  In t h i s  regard,  that the r e l a t i v e abundances of K and U a r e  i n the e a r t h ' s c r u s t and i n c h o n d r i t e s - i n the  sense that i n the e a r t h K and other a l k a l i metals a r e depleted with  respect t o U (GAST, 1960).  an i r o n core, the composition  Furthermore, i f the e a r t h has  of the e a r t h i s o b v i o u s l y not  - 84 chondritic; lic  the e a r t h ' s content o f i r o n , p a r t i c u l a r l y  i r o n , would be much too high i n t h i s  metal-  case.  TABLE 4 E s t i m a t e s o f the content o f K, U and Th (ppm) i n c h o n d r i t e s LEVIN et a l .  LEVIN  MASON  MACDONALD  LOVERING & MORGAN* 1964  1956  1961  1962  1959  Th  0.2  0.105  0.04  0.044  0.073  U  0.052  0.026  0.014  0.011  0.0256  K  700  700  1000  800  *Average values from 2 samples o f the carbonaceous c h o n d r i t e Orgueil. More recent estimates o f the content o f U, Th, and K, based  on the method of neutron a c t i v a t i o n , a r e lower than the  o l d e r estimates as can be seen by comparing L e v i n ' s (1956) estimate with Mason's o r MacDonald's.  Recently reported values  f o r the carbonaceous c h o n d r i t e s are regarded to the p r i m i t i v e composition of the Mars a s t e r o i d s .  as being nearest  of bodies accumulated  i n the zone  I t i s noteworthy that the measurements  i n d i c a t e a content o f U and Th twice as great as i n o r d i n a r y c h o n d r i t e s , suggesting that the use of the above estimates i n c a l c u l a t i n g the heat p r o d u c t i o n i n the e a r t h should be r e garded  with c a u t i o n u n t i l the causes o f the v a r i a t i o n s i n the  K, U and Th content among meteorites and the p o s s i b l e ences i n content between meteorites and t h e e a r t h a r e  differ-  - 85 understood. Assuming that the c o n c e n t r a t i o n of r a d i o a c t i v e at the present time can be w r i t t e n i n the form U n Th = 4n x 10"  8  g/g and K  4 0  - 0.91  x 10"  7  g/g,  elements x 10~  8  g/g,  RUSKOL (1963b)  o b t a i n s approximately 2000 j / g f o r n = 1 and 2500 j / g f o r n » 2 as the i n t e g r a t e d c o n t r i b u t i o n from l o n g - l i v e d to the heat produced  radioactivity  i n the e a r t h over the l a s t 4.5  aeons.  S i m i l a r l y , TOZER (1965) g i v e s a value of 2250 j / g as the heat p r o d u c t i o n of a c h o n d r i t i c e a r t h i n 4.5 Another  significant  total  aeons.  source of heat i n the h i s t o r y of the  e a r t h has been the d i s s i p a t i o n of t i d a l energy i n the  interior.  The t o t a l g e n e r a t i o n of heat by earth-moon t i d e s d u r i n g the e n t i r e h i s t o r y of the e a r t h , a c c o r d i n g to a c a l c u l a t i o n RUSKOL (1963b),  amounts to 20 - 30% of the r a d i o g e n i c heat,  the major p a r t being due An  by  to t i d e s generated at small d i s t a n c e s .  important f e a t u r e of t h i s heat i s that i t s g e n e r a t i o n was  probably l o c a l i z e d , perhaps mainly or e n t i r e l y i n the  upper  mantle. The c o n t r i b u t i o n of s h o r t - l i v e d the most s i g n i f i c a n t h i s t o r i e s proposed  r a d i o a c t i v i t y i s one of  sources of d i f f e r e n c e s among the thermal  f o r the e a r t h .  A c c o r d i n g t o UREY (1960),  the o n l y n u c l i d e that can reasonably be assumed to have been present i n s u f f i c i e n t amounts to produce heat i s A L  2 6  l a r g e q u a n t i t i e s of  with a h a l f - l i f e of only 0.74  i t s short h a l f - l i f e ,  m.y.  Because of  i t s c o n t r i b u t i o n to the h e a t i n g of the  - 86 e a r t h must have been n e g l i g i b l e ;  15 m i l l i o n years a f t e r nucleo-  genesis i t could have c o n t r i b u t e d only a few j / g . However, MACDONALD (1959) argues are U  2 3 6  , Sm  146  , Pu  that the important and C m  2 4 4  247  .  s h o r t - l i v e d isotopes  A l l these have h a l f - l i v e s  s u f f i c i e n t l y l o n g t o have c o n t r i b u t e d heat d u r i n g the p e r i o d 7 10  8 - 10  years a f t e r the i n i t i a l formation o f the e a r t h .  MacDonald obtains a temperature  i n c r e a s e of 3000°c due t o the  decay, of these f o u r s h o r t - l i v e d  i s o t o p e s , i . e . , twenty times  that due t o potassium genesis.  d u r i n g the f i r s t  In t h i s regard i t i s important  1 0 years a f t e r 8  nucleo-  t o r e c a l l that t h e  minimum formation i n t e r v a l measured f o r meteorites i s 3.4 x 7 . • 10 years and that s e v e r a l values have been obtained o f t h e 7  order of 5 x 10  years.  Anders assigns an a b s o l u t e e r r o r o f  7 6 x 10  years as a measure o f the u n c e r t a i n t y i n the model o f  nucleogenesis used f o r these c a l c u l a t i o n s .  Apparently,  it is  not p o s s i b l e on t h i s evidence alone to come to a d e f i n i t e c l u s i o n on the r o l e o f s h o r t - l i v e d r a d i o a c t i v i t y . the c o n t r i b u t i o n t o the temperature  con-  Certainly,  o f the e a r t h was l e s s  than 3000°C, but i t may have been a s u b s t a n t i a l f r a c t i o n o f this J Other s i g n i f i c a n t  u n c e r t a i n t i e s are the heat which the  e a r t h acquired i n the process of accumulation cess o f the formation o f the core. e a r t h depends on the circumstances  and i n the pro-  The i n i t i a l heat of the of i t s b i r t h .  The high  negative p o t e n t i a l energy of t h e e a r t h i m p l i e s that a l a r g e  - 87 amount o f energy, must have been l i b e r a t e d d u r i n g i t s formation (SAFRONOV, 1959).  Some of t h i s energy was undoubtedly  d u r i n g the formation  o f the core  t i o n o f t h i s energy would  (TOZER, 1965).  A small  frac-  s u f f i c e to heat the e a r t h t o a tempera-  t u r e o f some thousands of degrees. protoplanetary  liberated  cloud f i r s t  I f ones assumes that a  gave b i r t h to p r o t o p l a n e t s c o n s i s t i n g  of gases and dust, which subsequently c o n t r a c t e d q u i c k l y t o form p l a n e t s , then one o b t a i n s an i n i t i a l l y  hot e a r t h .  On the  other hand, i f one assumes that the p l a n e t s have grown gradua l l y as the r e s u l t of c o a g u l a t i o n of very f i n e p a r t i c l e s one a r r i v e s at a primeval  cold earth.  On t h i s l a s t  assumption,  SAFRONOV (1959) has c a l c u l a t e d the maximum temperature  which  the e a r t h could have a t t a i n e d by impacts i n the process formation, at  A f u r t h e r c a l c u l a t i o n of the  h e a t i n g due t o compaction gave only an i n s i g n i f i c a n t Considering  contri-  a l s o the c o n t r i b u t i o n of l o n g - l i v e d  r a d i o a c t i v i t y , Safronov obtained at  of i t s  o b t a i n i n g a value of 400°K f o r a l a y e r now l o c a t e d  a depth of about 2000 km.  bution.  then  the end of the formation  a maximum c e n t r a l temperature  of the e a r t h o f 950°K.  BECK (1964) i n v e s t i g a t e d t h e e f f e c t of t a k i n g i n t o account the e s s e n t i a l l y non-uniform d i s t r i b u t i o n of energy per gram a v a i l a b l e from both the i n i t i a l subsequent  energy of a c c r e t i o n and the  energy r e l e a s e d d u r i n g g r a v i t a t i o n a l r e o r g a n i z a t i o n .  He found that the maximum value of the a v a i l a b l e energy  occurs  i n the mantle and i s between 4 and 6 times that a v a i l a b l e i n  - 88 the c o r e . radiated  H e n c e , i f a l l or most of the a c c r e t i o n energy i s i n t o space, as i s the case i n the c o l d - o r i g i n  theory computed by Safronov, then the mantle l i k e l y to melt than the core because from g r a v i t a t i o n a l  i s f a r more  of the energy  available  reorganization.  TOZER (1965) computed that the t o t a l change i n g r a v i t a t i o n a l energy  i n the f o r m a t i o n of an i r o n core i s n e a r l y 2000  j/g, s u f f i c i e n t  to heat the e a r t h by 2000°C.  U n l i k e Beck's  c a l c u l a t i o n s , however, Tozer's work does not take i n t o the non-uniform  d i s t r i b u t i o n of the r e l e a s e d energy.  account The  s i g n i f i c a n t consequence of Tozer's work i s that the amount of heat that would be generated i f an i r o n core formed e a r t h , i s n e a r l y as great as that produced  by  i n the  radioactivity.  Because the p r e s e n t l y observed heat flow agrees with that expected from r a d i o a c t i v e decay, Tozer concludes that the process of f o r m a t i o n of an i r o n core must now  be proceeding much  more s l o w l y than i n the p a s t , i f i t i s o c c u r r i n g at a l l . . RAMSEY (1950b) made a crude estimate of the energy r e leased i n the f o r m a t i o n of a m e t a l l i c s i l i c a t e c o r e .  His  36 value of 10  ergs i m p l i e s an i n c r e a s e i n temperature  of only  15° i f the energy were shared by the whole volume of the earth  (LEVIN,  1964a).  I t may  w e l l be that t h i s crude estimate  i s too low and that a c t u a l l y the energy produced c r e a t e d were many times g r e a t e r .  and the heat  - 89 7.2  M e l t i n g p o i n t and a c t u a l temperatures M e l t i n g p o i n t temperatures  mated by combining s o l i d p r e s s u r e data 1962)  and  i n the e a r t h  i n the e a r t h have been  s t a t e theory with s e i s m i c or high  (UFFEN, 1952;  GILVATTCY, 1956; 1957;  ZHARKOV, 1959,  a l s o by e x t r a p o l a t i o n of the m e l t i n g p o i n t tempera-  t u r e s measured at low p r e s s u r e s  (SIMON, 1953;  1962;  BOYD and  CLARK, 1963;  1964;  STERETT et a l . , 1965).  f o r an i r o n and  ENGLAND, 1963;  STRONG,  Estimates have been made both  a "non-iron" m e t a l l i c  to a p r e s s u r e of 1.4  1959,  BOYD et a l . ,  core.  E x t r a p o l a t i n g data obtained f o r p r e s s u r e s l e s s 0.090 Mb  esti-  than  Mb by means of the Simon  equation, STRONG (.1959) suggested  a value of 2340 - 50°C as  the m e l t i n g temperature of i r o n at the core-mantle  boundary.  More recent estimates have been c o n s i d e r a b l y h i g h e r , however. Combining Strong's  o r i g i n a l data with data obtained from  shock wave experiments on i r o n , KNOPOFF and MACDONALD (1960) e x t r a p o l a t e d the m e l t i n g p o i n t curve t o a value of about 4000°C at 1.4 al.  (1965),  Mb.  In a p e r s o n a l communication t o STERETT et  Strong suggested,  on the b a s i s of r e v i s e d data,  (STRONG, 1962), a m e l t i n g p o i n t temperature as h i g h as 5000°C at 1.4  Mb.  S i n c e the m e l t i n g p o i n t i s probably  at 3.2  Mb,  at the boundary between the i n n e r and  encountered outer core,  CLARK's (1963) estimate, obtained from an e x t r a p o l a t i o n of Strong's data, of a melting temperature there of about 7500°C i s perhaps more meaningful.  STERETT et a l . (1965),  extra-  - 90 p o l a t i n g t h e i r low p r e s s u r e data t o 3.2 Mb, i n g temperature  obtained a melt-  there of 10,600°C, but emphasize that such a  lengthy e x t r a p o l a t i o n probably has  l i t t l e validity  - the  e r r o r s being p o s s i b l y as great as 5000°C. S i m i l a r e x t r a p o l a t i o n s of low p r e s s u r e data on d i o p s i d e (BOYD and ENGLAND, 1963)  and e n s t a t i t e  g i v e lower values- (3750°C and m e l t i n g p o i n t temperatures  (BOYD et a l . , 1964)  3725°C, r e s p e c t i v e l y ) f o r the  of these s i l i c a t e s at the c o r e -  mantle boundary than the more recent estimates f o r i r o n . T h i s r e s u l t would be s i g n i f i c a n t  i f any r e l i a n c e could be  p l a c e d on the lengthy e x t r a p o l a t i o n s i n v o l v e d . s t a t e of the mantle and the l i q u i d  The  solid  s t a t e of the outer core  would be i n e x p l i c a b l e on the i r o n core hypothesis i f i t were confirmed that the m e l t i n g p o i n t of an i r o n - n i c k e l a l l o y i s h i g h e r than the melting p o i n t of s i l i c a t e s or a mixture s i l i c a t e s at 1.4  Mb.  of  In f a c t , a c o n s i d e r a b l e d i f f e r e n c e i n  m e l t i n g p o i n t temperatures  i s probably r e q u i r e d by the  core hypothesis f o r an e a r t h which has heated  up from  iron an  i n i t i a l l y c o l d s t a t e to i t s present c o n d i t i o n and which has a l i q u i d outer core and s o l i d  i n n e r core  now  (see s e c t i o n  7.3). T h e o r e t i c a l estimates of m e l t i n g p o i n t temperatures  are  a c t u a l l y considered more r e l i a b l e than e x t r a p o l a t i o n s from pressure data.  Using the Einstein-Debye  theory of s o l i d s  low and  Lindemann's theory of f u s i o n , UFFEN (1952) computed the r a t i o  - 91 of  the m e l t i n g p o i n t at v a r i o u s depths i n t h e mantle t o that  at a depth of 100 km.  He found  ent decreases with depth.  that the m e l t i n g p o i n t g r a d i -  Using data f o r s o l i d o l i v i n e ,  Uffen  got a value of 5300°K f o r the m e l t i n g p o i n t at the core-mantle boundary, which gives an upper l i m i t f o r the a c t u a l temperatures there.  (See F i g u r e 4.)  Using a g e n e r a l i z a t i o n of the Lindemann law i n conjunct i o n with the Murnaghan equation o f s t a t e f o r a s o l i d , GILVARRY (1956),  i n an attempt  t o improve the estimates o f  Uffen, d e r i v e d a law of reduced is valid  states f o r fusion.  T h i s law  f o r the case of c l a s s i c a l e x c i t a t i o n o f the l a t t i c e  v i b r a t i o n s at melt ing[,  i . e. , f o r the a l k a l i metals, and i s  i d e n t i c a l i n form t o the Simon e q u a t i o n .  Because of. t h i s ,  GILVARRY (1957) used the Simon equation f o r the core where the Lindemann theory i s i n a p p l i c a b l e because o f the l i q u i d s t a t e o f the outer core. P where P  m  and T  m  m  = A (T /T ) r t  t  B  -1  are the f u s i o n p r e s s u r e and a b s o l u t e tempera-  t u r e , r e s p e c t i v e l y , Tt i s the t r i p l e p o i n t of temperature, i s a constant.  A  Curves corresponding t o a low, high and aver-  age estimate of the exponent, B, i n Simon's equation, assuming c e r t a i n e l a s t i c  and thermal p r o p e r t i e s of the core, a r e  shown i n F i g u r e 4.  A l s o i n F i g u r e 4, Lindemann's law f o r the  mantle i s compared with Uffen's and with three Simon curves,  - 92a -  FIGURE 4. E s t i m a t e s of m e l t i n g temperatures and temperatures i n the e a r t h .  actual  - 92b -  FIGURE 4. E s t i m a t e s of m e l t i n g temperatures and a c t u a l temperatures i n the e a r t h . E s t i m a t e s of A c t u a l Temperatures 1. 2. 3.  Convection Theory, Present Heat Flow (Tozer, Convection Theory. Twice Present Heat Flow (Tozer, 1965) Conduction Theory (Tozer, 1965)  E s t i m a t e s o f M e l t i n g Point  Temperatures  a. b. c. d. e. f.  U f f e n (1952) Lindemann Law ( G i l v a r r y , Zharkov (1959) Simon E q u a t i o n ( G i l v a r r y . I r o n Core (Zharkov, 1962)  g.  M e t a l l i z e d S i l i c a t e Core (Zharkov,  1957) 1957) 1962)  1965)  - 93 the l a t t e r corresponding, t o ii maximum, minimum and most probable value of the exponent B. C o n s i d e r i n g i t necessary t o apply a d i f f e r e n t  semi-  e m p i r i c a l method, one which would be e q u a l l y a p p l i c a b l e to simple as w e l l as more complex substances,  ZHARKOV (1959)  a p p l i e d a r e l a t i o n a c c o r d i n g to which f u s i o n i s a t t a i n e d i f the d e n s i t y of thermal d e f e c t s i n the c r y s t a l l i n e reaches  a certain c r i t i c a l  p o i n t temperature  value.  solid  By t h i s method, the m e l t i n g  i s s m a l l e r by approximately  1000°K than  Uffen's value f o r depths around 1000 km (see F i g u r e 4 ) .  The  v a l i d i t y of t h i s method f o r the deeper mantle, however, has not yet been demonstrated. C a l c u l a t i o n s by ZHARKOV (1959) f o r an i r o n core gave practically  i d e n t i c a l r e s u l t s using Lindemann's method and  the method of c r i t i c a l  d e n s i t y of d e f e c t s .  Zharkov e x p l a i n e d  that the indeterminate r e s u l t s o f G i l v a r r y a r e due to the f a c t that he d i d not use an adequate equation o f s t a t e f o r i r o n , and a l s o that he was handicapped mental o b s e r v a t i o n s that determine  by a s c a r c i t y of e x p e r i -  the i n i t i a l slope of the  m e l t i n g p o i n t curve by means of Clapeyron's  e q u a t i o n . Zharkov  used the s e m i - e m p i r i c a l equation of s t a t e f o r metals by Davydov, based of  iron.  proposed  upon Bridg.man's data f o r the c o m p r e s s i b i l i t y  More r e c e n t l y , ZHARKOV (1962) repeated h i s c a l c u l a -  t i o n s , t a k i n g i n t o account  the r o l e of t h e r m a l l y e x c i t e d  e l e c t r o n s and a phase change at high p r e s s u r e s from C< -Fe t o  - 94 -  -Fe.  The  r e s u l t i n g m e l t i n g temperatures  which are c o n s i d e r -  a b l y h i g h e r than h i s e a r l i e r c a l c u l a t i o n s , are a l s o shown i n Figure  4.  In c o n s i d e r i n g c a l c u l a t i o n s o f the m e l t i n g of Fe,  temperature  i t must be borne i n mind that i f the core of the e a r t h  i s predominately  Fe, t h i s Fe i s probably a l l o y e d with N i  perhaps w i t h S i .  High p r e s s u r e work and t h e o r e t i c a l  t i o n s f o r i r o n a l l o y s are t h e r e f o r e of the utmost  and  calcula-  importance.  A c t u a l l y , very l i m i t e d work has been done i n t h i s regard, but With s i g n i f i c a n t  results.  At a p r e s s u r e of 300  TAKAHASHI and BASSETT (1965) found and  kilobars,  that i r o n - a l l o y s with  10% n i c k e l were l e s s dense than pure i r o n .  5%  Moreover,  the a l l o y e d i r o n at these p r e s s u r e s e x i s t s i n a p r e v i o u s l y undiscovered phase, £ -Fe, i n hexagonal c l o s e packing, which is The  less tight importance  than  £-Fe,  of t h i s  Here i t i s s u f f i c i e n t  the f a c e centred c u b i c s t r u c t u r e .  r e s u l t w i l l be d i s c u s s e d i n Chapter  to p o i n t out that the m e l t i n g tempera-  t u r e s of the a l l o y s are probably somewhat d i f f e r e n t m e l t i n g temperature  9.  of pure i r o n and  may  be lower,  from  the  i n accord  with the g e n e r a l r e s u l t f o r a l l o y s . ZHARKOV (1962) a l s o s t u d i e d the m e l t i n g temperature non-iron core, i . e . , a core composed p r i n c i p a l l y of atoms i n the m e t a l l i c s t a t e .  of a  lighter  The s i g n i f i c a n t d i f f e r e n c e  be-  tween such a core and an i r o n core i s that at e x a c t l y the same c o n d i t i o n s and temperatures,  the amplitude  of the  thermal  - 95 v i b r a t i o n s of atoms of m e t a l l i z e d s i l i c a t e s must be than  that of atoms of i r o n , and  of m e l t i n g lower.  the corresponding  temperature  The m e l t i n g curve of a m e t a l l i z e d s i l i c a t e  core, c a l c u l a t e d by Zharkov u s i n g Debye's theory, shown i n F i g u r e  greater  i s also  4.  ZHARKOV (1962) a l s o c a l c u l a t e d the temperature d i s t r i b u t i o n r e q u i r e d i n an i r o n core to o b t a i n agreement between the shock adiabat of i r o n determined by ALTSHULER AND (1961) and  s e i s m i c data.  would imply,  The  r e s u l t i n g temperature  of the r e s u l t s of TAKAHASHI AND i r o n a l l o y i s probably  However, i n view  BASSETT (1965), a n i c k e l -  i n accord with much lower temperatures  t o i t s g r e a t e r i n c o m p r e s s i b i l i t y as compared to i r o n . According  d u c t i o n and  to the c a l c u l a t i o n s of TOZER (1965), both  c o n v e c t i o n heat  d i s t r i b u t i o n a c c o r d i n g to c o n v e c t i o n heat c a l c u l a t e d f o r both  present heat  flow.  the present heat  The  temperature  transport  theory  flow and twice  the  These r e s u l t s are a l s o g i v e n i n F i g u r e  I f c o r r e c t , these r e s u l t s would probably b i l i t y of an i r o n  con-  transport theories give core-  mantle boundary temperatures below 3000°C.  was  curve  i f the core were pure i r o n , that the whole core  and at l e a s t the deeper mantle are molten.  due  KORMER  4.  r u l e out the p o s s i -  core.  LEVIN (1962a) has a l r e a d y p o i n t e d out that i f the method of c r i t i c a l d e n s i t y of thermal d e f e c t s gives the c o r r e c t melti n g p o i n t curve,  as c a l c u l a t e d by Zharkov, then  the  - 96 p o s s i b i l i t y of an i r o n core of an  i r o n core  i s c o r r e c t , one  b i l i t i e s must be t r u e : high melting  i s r u l e d out.  (1)  of the two  Uffen's,  rather  G i l v a r r y ' s lower  esti-  p o i n t curve f o r the core or s i m i l a r l y  estimates are p r e f e r r e d ;  7.3  similarly  p o i n t temperature curves f o r the mantle  mate of the melting  point  following possi-  G i l v a r r y ' s or  than Zharkov's curve must be c o r r e c t ;  the core  I f the h y p o t h e s i s  is incorrect.  Zharkov's melting (2)  A l l recent  Thermal h i s t o r y and  the core  p o i n t curve f o r  estimates of  temperatures i n an i r o n core are too of the  melting  high.  earth  Other s e c t i o n s of t h i s t h e s i s have i n c l u d e d b r i e f , c a l d i s c u s s i o n s of some of Ringwood's ideas. appropriate  to i n c l u d e a c o n s i d e r a t i o n  of the e a r t h e n v i s i o n e d U n t i l recent whole earth was  by him  years,  at one  Because of  d i f f e r e n t i a t i o n of the earth was With regard melting  and  the  the core f r a c t i o n a t e d  (3) h i s adherence to  hypothesis of an i r o n core, Ringwood continues idea of a once molten e a r t h and  the  of more  (2) h i s assumption that  p r o c e s s e s which formed the c r u s t and to lead and  that  a s i l i c a t e mantle  (1) the c o n c e n t r a t i o n  v o l a t i l e elements i n the c r u s t ,  uranium with respect  1965).  During i t s molten stage  i t d i f f e r e n t i a t e d to form an i r o n core, a lighter crust.  of the thermal h i s t o r y  generally believed  time molten.  criti-  Here i t i s  (RINGWOOD, 1960,  i t was  low  the  to support  furthermore concludes that completed 4.55  aeons  ago.  to p o s s i b l e sources of heat f o r the e a r l y  of the e a r t h , Ringwood b e l i e v e s that g r a v i t a t i o n a l  the  - 97 energy i s c h i e f l y r e s p o n s i b l e . been converted  G r a v i t a t i o n a l energy may  i n t o heat energy a v a i l a b l e f o r warming  e a r t h i n the process  of a c c r e t i o n and  z a t i o n of the earth's matter.  i n subsequent  have  the  reorgani-  SAFRONOV (1959), as mentioned  above, c a l c u l a t e d that i n the process the energy r e l e a s e d as heat was  of a c c r e t i o n most of  r a d i a t e d away i n t o space  and  that t h i s p o s s i b l e source of energy c o n t r i b u t e d very l i t t l e the h e a t i n g of the e a r t h .  Ringwood, however, suggests that a  dense c l o u d cover of reducing and,  to  gases trapped  much of t h i s heat  what i s perhaps more important, reduced the i r o n i n  oxides  t o metal.  quently  Convective  overturn  segregated the metal phase and  by l i b e r a t i n g g r a v i t a t i o n a l energy. f o r m e l t i n g was process  i n the e a r t h subseformed the core,  there-  Thus the energy r e q u i r e d  presumably l i b e r a t e d i n l a r g e measure i n the  of c o n v e c t i v e  overturn  r a t h e r than d u r i n g the  time  preceding i t . The  tremendously dense atmosphere of reducing  q u i r e d f o r reducing  enough i r o n f o r an i r o n core  of 2 gm/cm" and a pressure 3  gases r e -  (a d e n s i t y  of 300,000 atmospheres at  s o l i d s u r f a c e i s suggested) was ready r a p i d l y s p i n n i n g e a r t h was  the  presumably l o s t when the a l caused t o r o t a t e even more  r a p i d l y by the r e d u c t i o n i n i t s p o l a r moment of i n e r t i a the formation  of the c o r e .  during  Without c o n s i d e r i n g the escape of  a l a r g e atmosphere, the hypothesis  that the moon o r i g i n a t e d by  f i s s i o n from the e a r t h i n t h i s process  has been d i s c u s s e d  - 98 above. There a r e some obvious  d i f f i c u l t i e s with Ringwood's  ideas, one o f which has a l r e a d y been mentioned:  the problem  of the t r a n s f e r o f angular momentum and indeed a l o s s of perhaps t h r e e q u a r t e r s of the o r i g i n a l angular momentum o f the earth-moon system. thermal  h i s t o r y o f t h e e a r t h are not supported  tive calculations; cusses  U n f o r t u n a t e l y , Ringwood's ideas on the  the p o s s i b i l i t i e s of the processes  t h i s i r o n ) have not been demonstrated. gradual growth o f the c r u s t beginning cates t h a t the composition argument f o r the completion  of a core from  A l s o , evidence  of the  3.5 aeons ago, i n d i -  o f the c r u s t cannot be used as an of d i f f e r e n t i a t i o n i n the e a r t h  aeons ago. The thermal  h i s t o r y o f the e a r t h was c a l c u l a t e d by JACOBS  AND ALLAN (1956) f o r a combination  of s e v e r a l p o s s i b l e i n i t i a l  d i s t r i b u t i o n s o f temperature and r a d i o a c t i v i t y . and  he d i s -  ( r e d u c t i o n i n a reducing atmosphere of enough i r o n f o r  the core and c o n v e c t i v e o v e r t u r n and formation  4.55  by q u a n t i t a -  " c o l d " o r i g i n s o f t h e e a r t h were c o n s i d e r e d .  Both " h o t " Constant  thermal d i f f u s i v i t y was assumed, but Jacobs has p o i n t e d out more r e c e n t l y that t h e c a l c u l a t i o n s of Lubimova  (1952-1958),  t a k i n g i n t o account v a r i a b l e d i f f u s i v i t y and a probable i n crease i n the thermal  c o n d u c t i v i t y at depth due t o r a d i a t i v e  t r a n s f e r o f energy, do not change t h e i r general (JACOBS et a l . , 1959).  conclusions  These g e n e r a l c o n c l u s i o n s a r e that  - 99 for  a l l models,  the temperature at depth has continued to  r i s e throughout g e o l o g i c time, that there has been m e l t i n g or r e m e l t i n g of matter i n the upper mantle about 3.5 aeons ago and that t h e near s u r f a c e c o n d i t i o n s were dominated first  aeon o r so by the i n i t i a l  f o r the  temperature d i s t r i b u t i o n .  MACDONALD (1959) c a l c u l a t e d the thermal h i s t o r y of the e a r t h f o r a great number of models, dependent  although i n the time-  s o l u t i o n s only the d i s t r i b u t i o n of temperature i n  the  mantle was  for  minimal v a l u e s of uranium and thorium content, o b t a i n e d  in  calculated.  A l l h i s c a l c u l a t i o n s were made  recent analyses of m e t e o r i t e s by the n e u t r o n - a c t i v a t i o n  method (K = 8.0 x 1 0 " x 10~  8  g/g)•  g/g, U = 1.1 x 1 0 ~  As mentioned  rather high i n i t i a l MAJEVA  4  4  g/g and Th -  4.4  e a r l i e r , MacDonald c o n s i d e r s  temperatures of the e a r t h .  LEVIN  AND  (1961) have c a l c u l a t e d the thermal h i s t o r y of the  e a r t h assuming  a l i n e a r i n c r e a s e i n the c o n c e n t r a t i o n of r a d i o -  a c t i v e elements towards the s u r f a c e beginning 3 aeons ago and t a k i n g Safronov's i n i t i a l these two assumptions  temperature d i s t r i b u t i o n .  With  they f i n d agreement w i t h the observed  s u r f a c e heat flow, whereas MacDonald found rough agreement o n l y with h i g h i n i t i a l  temperatures.  A l s o , MacDonald d i d not take  i n t o account the low c o n d u c t i v i t y l a y e r at a depth 100-200 km and t h e r e f o r e , a c c o r d i n g to L e v i n and Majeva, he o v e r - e s t i mated the heat f l o w through the s u r f a c e .  L e v i n and  Majeva  considered two models of the r a d i o a c t i v e content of the earth,  - 100  -  but even t h e i r lower estimate of the content thorium  of uranium  and  i s more than twice as high as that of MacDonald.  temperature d i s t r i b u t i o n s c a l c u l a t e d by them vary depending on the heat  c a p a c i t y , the content  The  immensely  of r a d i o a c t i v i t y  and the r o l e p l a y e d by r a d i a t i v e c o n d u c t i v i t y . In view of the u n c e r t a i n t i e s and models i n the estimates  the v a r i e t y of p o s s i b l e  of m e l t i n g p o i n t temperatures  and  a c t u a l temperature d i s t r i b u t i o n s , comparisons are riot p a r t i cularly useful.  Unless  some of the u n c e r t a i n t i e s can  e l i m i n a t e d , no c o n c l u s i o n s can be reached  be  from thermal  studies  on the p o s s i b i l i t y of an i r o n or a m e t a l l i z e d s i l i c a t e But  the thermal  core.  h i s t o r y i s so i n t i m a t e l y r e l a t e d to t h i s  q u e s t i o n that c o n s i d e r a t i o n of the r e l a t i o n between  these  two problems must e v e n t u a l l y h e l p i n t h e i r s o l u t i o n . arguments on the thermal h i s t o r y of the e a r t h are  Further  considered  below. The  c a l c u l a t i o n s d i s c u s s e d above a l l n e g l e c t the p o s s i b l e  r o l e of c o n v e c t i o n i n the mantle. s i d e r e d by TOZER (1965) and  i s s i g n i f i c a n t f o r convective  v e l o c i t i e s of the order of 1 0 ~ of at l e a s t 10 suggested.  The  cm/s  T h i s r o l e has been con-  1 0  cm/s.  Convective  velocities  i n the c r u s t and mantle have been  most important  f e a t u r e of c o n v e c t i o n  i s that  8 the time of c o n v e c t i o n o v e r t u r n i s 10 on the c o n v e c t i o n theory  i t may  years or l e s s , i . e . ,  be p o s s i b l e to ignore  i n the earth's h i s t o r y which occurred more than a few  events hundred  - 101 m i l l i o n years ago.  The r e s u l t s of Tozer's e v a l u a t i o n o f the  p o s s i b i l i t y and c h a r a c t e r o f the formation of an i r o n core i n a c o n v e c t i n g e a r t h a r e d i s c u s s e d i n Chapter  8.  He showed  that r a d i a l departures from t h e s t a t e o f uniform entropy i n the mantle can amount t o temperature of 300°C.  Another important  d i f f e r e n c e s of the order  r e s u l t f o r a convecting earth i s  that changes i n the s t r e n g t h of the heat sources have f u r t h e r e f f e c t on the temperature sufficient  little  d i s t r i b u t i o n once they a r e  t o maintain s u p e r a d i a b a t i c c o n d i t i o n s .  Tozer's thermal h i s t o r y and d i s c u s s i o n o f the p o s s i b i l i t y of formation of an i r o n core a r e l i n k e d w i t h h i s c a l c u l a t i o n that the t o t a l change i n g r a v i t a t i o n a l and s t r a i n energy i s very n e a r l y 2000 j / g .  However, as p r e v i o u s l y mentioned,  BECK (1964) has c a l l e d a t t e n t i o n t o the importance  o f the d i s -  t r i b u t i o n i n t h e e a r t h of t h e a v a i l a b l e g r a v i t a t i o n a l Any  energy.  c a l c u l a t i o n o f t h i s a v a i l a b l e energy depends on the assump-  t i o n s made about the a c c r e t i o n process and the d e n s i t y of the original material. original /  Beck c o n s i d e r e d two extreme cases f o r the  ( i . e . , zero-pressure) d e n s i t y , 2.85 gm/cm" and 4.4 3  -3  gm/cm  , and assumed that the e a r t h was formed by m e t e o r i t i c  aggregation from t h i s m a t e r i a l .  The t o t a l amount o f energy  a v a i l a b l e from g r a v i t a t i o n a l r e o r g a n i z a t i o n i s then  determined  by f i n d i n g the d i f f e r e n c e between the g r a v i t a t i o n a l p o t e n t i a l energy  (GPE)  of the present e a r t h and that o f the o r i g i n a l  e a r t h of uniform d e n s i t y .  The c a l c u l a t e d amount should be  - 102 considered  a maximum r a t h e r than the expected v a l u e .  The  important q u a n t i t y , however, i s the energy p e r gram a v a i l a b l e in the various  regions of t h e e a r t h , which Beck c a l c u l a t e d  from the d i f f e r e n c e between the a c c r e t i o n energy p e r gram f o r a given r e g i o n o f a uniform  sphere and the c o n t r i b u t i o n o f t h i s  r e g i o n t o the GPE of the present  earth.  Beck found f o r e i t h e r  value of the o r i g i n a l d e n s i t y that t h e a v a i l a b l e energy i s considerably i n n e r core,  l e s s than the energy r e q u i r e d f o r m e l t i n g  i n the  reaches a maximum, perhaps enough f o r melting, i n  the lower mantle and decreases towards the s u r f a c e .  Beck con-  s i d e r e d the i m p l i c a t i o n of t h i s r e s u l t f o r t h e thermal h i s t o r y of the core, assuming that the r o l e of s h o r t - l i v e d r a d i o a c t i v i t y was i n s i g n i f i c a n t  i n heating  the p r i m e v a l  earth.  He  concluded that i t i s extremely u n l i k e l y that the e a r t h reached a completely  molten s t a t e 4.5 x 1 0  9  noted that the case f o r a completely  years  ago. He furthermore  molten core at any stage  of the earth's h i s t o r y i s b o r d e r l i n e and that i t seems p o s s i b l e that not only has the e a r t h always had a s o l i d core, but that t h e c e n t r a l p o r t i o n o f i t may c o n t a i n  inner  compressed  primary m a t e r i a l . While Beck's c a l c u l a t i o n s and c o n c l u s i o n s c o n s i s t e n t with the hypothesis  a r e probably  of a m e t a l l i z e d s i l i c a t e  they a r e d e f i n i t e l y not c o n s i s t e n t with an i r o n c o r e .  core, I f the  outer core were molten i r o n , how i s i t p o s s i b l e that the i n n e r core  i s a denser s o l i d s i l i c a t e ?  T h e o r e t i c a l s t u d i e s of  - 103 m e l t i n g p o i n t curves c a t e s than f o r i r o n  support  -  lower values f o r m e t a l l i z e d s i l i -  (see F i g u r e 4 ) .  i n n e r core i s compressed primary  Hence, evidence  m a t e r i a l supports  that  the  the hypo-  t h e s i s that the whole core i s a m e t a l l i z e d s i l i c a t e . However, a c a l c u l a t i o n of the d i f f e r e n c e between the p r e sent and former GPE  of a given mass does not e x p l a i n where and  how  liberated.  t h i s energy was  The c a l c u l a t i o n might have a  d i f f e r e n t meaning depending upon which hypothesis s i d e r s f o r the nature of the e a r t h ' s c o r e .  one  con-  I t i s a l s o impor-  tant to note t h a t Beck assumes low i n i t i a l temperatures of the e a r t h , c o n s i d e r i n g the r o l e of s h o r t - l i v e d r a d i o a c t i v i t y to be insignificant  i n the h e a t i n g of the e a r t h .  A c c e p t i n g B i r c h ' s suggestion boundary between the i n n e r and  that the temperature at the  outer core i s the m e l t i n g p o i n t  temperature, JACOBS (1954) has g i v e n a q u a l i t a t i v e d i s c u s s i o n of the thermal mantle and  h i s t o r y , which e x p l a i n s the s o l i d s t a t e of the  i n n e r core and the l i q u i d s t a t e of the outer core.  He assumes an i n i t i a l l y molten e a r t h , c o o l i n g a d i a b a t i c a l l y . The  key f e a t u r e s of h i s e x p l a n a t i o n are that the a d i a b a t i c  g r a d i e n t i s l e s s steep than the m e l t i n g - p o i n t  curve and  the m e l t i n g - p o i n t curve i s d i s c o n t i n u o u s , having on the core s i d e of the core-mantle boundary. cools, a l i q u i d layer i s l e f t core and the s o l i d mantle.  that  a lower value  As the e a r t h  trapped between the s o l i d  inner  At p r e s e n t , the a c t u a l temperature  curve can be a d i a b a t i c i n the core, but must be  superadiabatic  - 104 i n the mantle, approaching  the melting p o i n t curve.  Evidence t h a t the c o r e may be more complicated than the "thermostat  model" d e s c r i b e d above i s d i s c u s s e d i n Chapter  10.  A l t e r n a t i v e models of the core, c o n s i s t e n t w i t h recent s e i s m i c v e l o c i t y d e t e r m i n a t i o n s , are presented i n Chapter  8.  - 105 8.  8.1  THE POSSIBILITY OF CONVECTION AND DIFFERENTIATION IN THE EARTH Chemical evidence on the p o s s i b i l i t y o f d i f f e r e n t i a t i o n RINGWOOD'S (1959) arguments f o r complete  differentiation  of the e a r t h , which have a l r e a d y been d i s c u s s e d i n t h i s can be summarized b r i e f l y :  thesis,  (a) There i s evidence o f concen-  t r a t i o n of uranium and thorium i n the c r u s t . p r o b a b l y has an i r o n - n i c k e l c o r e .  (b)  The e a r t h  (c) The chemical e v o l u t i o n  of the m e t e o r i t e parent p l a n e t was s i m i l a r t o t h e e a r t h . The last  two arguments, however, a r e not chemical evidence but  hypotheses.  Support  f o r Ringwood's f i r s t  argument i s given  by ADAMS e t a l . (1959) who conclude from a survey study of the geochemistry  of thorium and uranium that " d e s p i t e quan-  t i t a t i v e uncertainties,  i t i s e v i d e n t that the c o n c e n t r a t i o n  of thorium and uranium must f a l l e l s e t h e e a r t h would be molten Arguments a g a i n s t complete  o f f r a p i d l y with depth or  today." m e l t i n g and d i f f e r e n t i a t i o n  based on chemical evidence, a r e g i v e n by UREY (1962) and DUKE (1965),  Urey maintains that t h e r e a r e no c o m p e l l i n g reasons  f o r the b e l i e f that t h e e a r t h has at any time been i n a comp l e t e l y molten c o n d i t i o n . completely molten  Whereas the usual argument f o r a  e a r t h i s that many elements  i n a c r u s t some 15 km t h i c k on the average, we see b a s a l t and g r a n i t e b e i n g produced  a r e concentrated  Urey argues  i n l a v a flows  that today  and the r a t e of these p r o c e s s e s i s not i n c o n s i s t e n t with t h e  - 106  -  s u p p o s i t i o n that the e n t i r e c r u s t was  produced i n t h i s  He a l s o argues that there i s no evidence  way.  that the more v o l a -  t i l e elements are s y s t e m a t i c a l l y concentrated  i n the e a r t h ' s  c r u s t and that apart from the very v o l a t i l e compounds such  as  carbon d i o x i d e , n i t r o g e n and water, the elements so concent r a t e d are very s o l u b l e i n water at o r d i n a r y  temperatures.  DUKE (1965) has compared the n i c k e l content a c h o n d r i t e s , measured by him,  in basaltic  with the n i c k e l content  o l i v i n e s from d u n i t e i n c l u s i o n s i n b a s a l t s .  He  i n nine  concludes  that the low t o t a l n i c k e l content of most b a s a l t i c  achondrites  i s best e x p l a i n e d by s e p a r a t i o n of a n i c k e l r i c h metal phase d u r i n g magmatic c r y s t a l l i z a t i o n . the data suggest  He furthermore  observes  that  an i n c o n s i s t e n c y i n upper mantle models f o r  an e a r t h of c h o n d r i t i c composition  because i t i s d i f f i c u l t  r e c o n c i l e the r e l a t i v e l y high n i c k e l content of u l t r a b a s i c rocks w i t h the s e p a r a t i o n of a m e t a l l i c core, which should e f f i c i e n t l y remove n i c k e l . "Nine o l i v i n e s from d u n i t e i n c l u s i o n s i n b a s a l t s have Ni:Fe = 1:20, has Ni:Fe = 1:1000-  whereas the o l i v i n e of c h o n d r i t e s This large d i f f e r e n c e challenges  Ringwood's c o n t e n t i o n that the e a r t h i s composed of more h i g h l y reduced  material.  In f u r t h e r reducing  c h o n d r i t i c m a t e r i a l , n i c k e l should be h i g h l y concent r a t e d i n the m e t a l l i c phase, and ..the : s i l i c a t e s should decrease.  the Ni:Fe  r a t i o of  However, the Ni:Fe i s  to  - 107 much g r e a t e r  i n the s i l i c a t e o f the earth's  than i n the s i l i c a t e s of c h o n d r i t e s ,  mantle  thereby b a r r i n g  the mantle's d e r i v a t i o n by d i r e c t r e d u c t i o n of chondritic material  "Considering  . . .  the l a r g e f r a c t i o n a t i o n of n i c k e l be-  tween metal and s i l i c a t e s  i t isdifficult  to explain  the presence of any o x i d i z e d n i c k e l i n t h e mantle i f a m e t a l l i c core and s i l i c a t e mantle were  separated  under c o n d i t i o n s approaching e q u i l i b r i u m .  To e x p l a i n  the content of n i c k e l i n the upper mantle i t may be necessary t o assume that i t d i d not take p a r t p r o c e s s o f core  8.2  separation."  (Emphasis i s mine.)  The p o s s i b l e r o l e o f convection The  exact  i n the  i n the e a r t h  r h e o l o g i c a l behaviour of the e a r t h  i s not known,  although., i n many c a l c u l a t i o n s o f the nature and p o s s i b i l i t y of convection  o r g r a v i t a t i o n a l d i f f e r e n t i a t i o n of the e a r t h i t i s  assumed that the e a r t h behaves l i k e a Newtonian (LYUSTIK, 1948; RUNCORN, 1960, 1963, 1964).  liquid  It i s generally  b e l i e v e d that r h e o l o g i c a l behaviour depends on the time v a l o f the process; state describes  e.g.,  inter-  a d i f f e r e n t r h e o l o g i c a l equation o f  an earthquake t o that which a p p l i e s to long-  enduring processes such as convection  i n the mantle.  0R0WAN  (1964) has questioned the assumption of Newtonian behaviour f o r the mantle, p r o p o s i n g that  i t behaves l i k e the c r y s t a l l i n e  - 108 solids  s t u d i e d i n the l a b o r a t o r y .  T h i s behaviour approaches  i d e a l p l a s t i c i t y , although the r a t e of change of s t r a i n becomes non-zero b e f o r e the c r i t i c a l infinity  as the s t r e s s approaches the c r i t i c a l  d e s c r i b e s t h i s as Andradean who r e c o g n i z e d i t as t y p i c a l elastic  s t r e s s i s reached, approaching  behaviour ( a f t e r of c r y s t a l l i n e  range) or " t h e r m a l l y rounded  stress.  the s c i e n t i s t matter beyond the  ideal-plasticity."  By a r a t h e r simple, but p o s s i b l y q u e s t i o n a b l e , tion,  Orowan demonstrated  mantle has Andradean  in the e a r t h by assuming plastic  the l i k e l i h o o d  behaviour.  Orowan  calcula-  o f c o n v e c t i o n i f the  He approximated  conditions  i d e a l p l a s t i c i t y and equated the  r e s i s t a n c e to the r i s e of a prism to the buoyancy  f o r c e and hence c a l c u l a t e d the c r i t i c a l stress.  Assuming  v a l u e of the y i e l d  a temperature d i f f e r e n c e of 100°C between  a 1000 km square-faced p r i s m and i t s surroundings and a coefficient critical  of thermal expansion of 1 0 ^ , Orowan o b t a i n e d a  yield  -  s t r e s s of 40.3 b a r s .  estimates of the y i e l d energy r e l e a s e d  He compared t h i s t o  s t r e s s down to 700 km based on the  i n earthquakes and concluded that the y i e l d  s t r e s s of the mantle at that depth i s of the same order of magnitude  as the y i e l d  s t r e s s at which p l a s t i c  c o n v e c t i o n can  take p l a c e under p l a u s i b l e dimensional and temperature  condi-  tions. GORDON (1965) has shown that the phenomenon known as diffusion  creep, i f i t occurs at s i g n i f i c a n t  r a t e s i n the  - 109 e a r t h ' s mantle,  agrees with the assumption  v i s c o s i t y f o r l a r g e - s c a l e flow p r o c e s s e s .  o f Newtonian On the other hand  creep mechanisms i n v o l v i n g d i s l o c a t i o n s can r e s u l t i n more r a p i d non-Newtonian flow.  Since i t i s slower, the d i f f u s i o n  creep r a t e s e t s an upper l i m i t t o r e s i s t a n c e t o non-hydrostatic  stresses.  Whether d i s l o c a t i o n creep or d i f f u s i o n creep i s the a c t u a l f l o w mechanism i n the mantle depends on the temperature and pressure conditions. m a t e r i a l deforming ideal p l a s t i c i t y ,  In the l a b o r a t o r y a p o l y c r y s t a l l i n e  by s t e a d y - s t a t e creep d i s p l a y s n e a r l y a f a c t emphasized by OROWAN  (1964).  How-  ever, GORDON (1965) p o i n t s out that when the temperature i s high but the a p p l i e d s t r e s s r e l a t i v e l y low, a d i f f e r e n t of creep response, d i f f u s i o n creep, i s observed c r y s t a l l i n e materials.  type  i n poly-  From t h e o r e t i c a l c o n s i d e r a t i o n s ,  Gordon concludes that d i f f u s i o n creep can reasonably be expected t o be a s i g n i f i c a n t flow process i n the mantle, but does not r u l e out creep deformation at a more r a p i d r a t e due to motion  of dislocations.  The l a t t e r i s expected  to occur  i n r e g i o n s of orogenic and s e i s m i c a c t i v i t y . These arguments, however, do not enable us t o conclude what the r e a l behaviour o f the e a r t h i s and has been f o r long-enduring processes and whether the p o s s i b i l i t y o f convect i o n i s more c o r r e c t l y s t u d i e d using equations d e s c r i b i n g p l a s t i c or Newtonian behaviour.  E i t h e r behaviour i s a d m i s s i b l e  - 110  -  and perhaps the a c t u a l behaviour has changed i n the course of time, depending on the thermal  s t a t e of the e a r t h and  the  magnitude of the n o n - h y d r o s t a t i c s t r e s s e s . I t i s important  t o d i s c u s s the c a l c u l a t i o n s of LYUSTIK  (1948) on the p o s s i b i l i t y of d i f f e r e n t i a t i o n  i n the e a r t h be-  cause supporters of Ramsey's hypothesis o f t e n r e f e r to these c a l c u l a t i o n s as an argument a g a i n s t the i r o n core h y p o t h e s i s . L y u s t i k attempted  only an order of magnitude c a l c u l a t i o n  the time r e q u i r e d f o r d i f f e r e n t i a t i o n , using Stokes'  on  law.  However, t h i s law i s o n l y s t r i c t l y a p p l i c a b l e to a Newtonian liquid.  Using v i s c o s i t i e s of 10  p o i s e (upper l i m i t )  and  20 10  p o i s e (lower l i m i t ) f o r the mantle, L y u s t i k found that  the s e t t l i n g o f  h e a v i e r i n c l u s i o n s or the r i s i n g of  ones i n such a v i s c o u s medium would proceed  lighter  o n l y a few hun-  dred km i n a b i l l i o n years i n the case of i n c l u s i o n s 100 m to 3 km  i n diameter.  However, L y u s t i k c o n s i d e r e d t h i s to be an  argument i n favour of d i f f e r e n t i a t i o n s i n c e the of  such i n c l u s i o n s i n any  accumulations  l a y e r i n the e a r t h would hasten  process of d i f f e r e n t i a t i o n .  Moreover, a p o s s i b i l i t y which  L y u s t i k d i d not c o n s i d e r , the l i b e r a t i o n of energy  i n the  process of d i f f e r e n t i a t i o n would lower the v i s c o s i t y hence a l s o have the e f f e c t  the  and  of h a s t e n i n g the p r o c e s s .  There are s e v e r a l unanswered questions r e l a t i n g to t h i s calculation.  First  of a l l , i f the e a r t h does not behave as  a Newtonian l i q u i d , but r a t h e r deforms by d i s l o c a t i o n  creep  - I l li n long-enduring  processes,  t i a t i o n i s greater. or formation  On  then the p o s s i b i l i t y of d i f f e r e n -  the other hand, the p o s s i b l e e x i s t e n c e  of l a r g e i r o n i n c l u s i o n s i n the p r i m i t i v e e a r t h  i s an unanswered q u e s t i o n .  The p o s s i b i l i t y and  such i n c l u s i o n s depends of course on the content i r o n i n the e a r t h . the content  Evidence  of m e t a l l i c i r o n i s r a t h e r small i n the e a r t h ,  approximately  i n m e t e o r i t e s , and  35 per cent by weight, as r e q u i r e d f o r an  However, as was  suggested  of m e t a l l i c  d i s c u s s e d above i n d i c a t e s that  even s m a l l e r than i t s average content  core.  importance of  iron  a l s o d i s c u s s e d e a r l i e r , Ringwood  that an important  r o l e was  not  has  played by a tremendous  reducing atmosphere i n the p r i m e v a l e a r t h , a p o s s i b i l i t y which has not been d i s p r o v e d . ELSASSER (1963) has  given a more s o p h i s t i c a t e d treatment  of the problem of f a l l i n g i r o n masses i n c l u d i n g a c o n s i d e r a t i o n of i t s connection with t e c t o n i c t h e o r i e s .  Assuming a  Newtonian l i q u i d he c o n s i d e r s the problem of a T a y l o r i n s t a b i l i t y r e s u l t i n g from a l a y e r of i r o n o v e r l y i n g l e s s dense silicates. and  He  shows that such a l a y e r would form i n t o a drop  sink rapidly.  i n c l u s i o n s , but  Here the s t a r t i n g p o i n t i s not l a r g e i r o n  r a t h e r a l a y e r of i r o n .  of accounting, f o r a l a r g e content  The problem remains  of m e t a l l i c i r o n i n the  earth. The  s m a l l departures  from a s p h e r i c a l l y symmetric  t i o n a l geopotential provide d i r e c t  gravita-  arguments f o r c o n v e c t i o n i n  - 112 the e a r t h from one p o i n t of view (RUNCORN, 1962, 1963, 1964; TOZER, 1965) and f o r minimum s t r e n g t h another point of view (MACDONALD, point  of the e a r t h from  1962;  CAPUTO, 1965).  Which  of view i s c o r r e c t and hence which c a l c u l a t i o n has any  meaning depends on whether convection e a r t h at the present  time.  i s taking place  i n the  I f i t i s not, the c a l c u l a t i o n s o f  MacDonald and Caputo, who have each c a l c u l a t e d the s t r e n g t h of the e a r t h necessary to support the n o n - h y d r o s t a t i c are s i g n i f i c a n t .  stresses,  MacDonald has c a l l e d a t t e n t i o n t o the f a c t  that the observed d e v i a t i o n s from e q u i l i b r i u m a r e l a r g e r than and o f o p p o s i t e  s i g n to those expected from the known  s t r u c t u r e near t h e s u r f a c e .  He has used t h i s o b s e r v a t i o n  an argument f o r the deep s t r u c t u r e o f c o n t i n e n t s ,  as  although the  same data have been used t o support the hypothesis o f a conv e c t i v e mechanism f o r c o n t i n e n t a l Caputo s l i g h t l y modified  drift.  the de S i t t e r theory  of hydro-  s t a t i c f l a t t e n i n g and c a l c u l a t e d the i n t e r n a l s t r e n g t h to maintain the g l o b a l departures from h y d r o s t a t i c brium. bars,  He concluded that the most probable value or approximately the same as the s t r e s s e s  with the r e g i o n a l anomalies o f the earth's In an attempt drift,  to p r o v i d e  RUNCORN (1962) p o s t u l a t e d  o c c u r r i n g i n the earth's  mantle.  equilii s about 30  associated  gravity  an e x p l a n a t i o n  needed  field.  of c o n t i n e n t a l  that convection  c u r r e n t s were  T h i s supposes the mantle to  have zero s t r e n g t h under s t r e s s e s p e r s i s t i n g over m i l l i o n s of  years and t o have a Newtonian v i s c o s i t y .  Applying  Chandrasekhaf's theory of c o n v e c t i o n i n s p h e r i c a l under a r a d i a l g r a v i t a t i o n a l f i e l d  and supposing  shells that an i r o n  core o f the e a r t h separated g r a d u a l l y d u r i n g the e a r t h ' s Runcorn concluded  life,  that a change i n the number o f c o n v e c t i o n  c e l l s i n t h e mantle with consequent c o n t i n e n t a l d r i f t have o c c u r r e d r e c e n t l y .  might  I f core formation began 3 aeons ago,  t h e r e i s agreement, a c c o r d i n g t o h i s theory, between the times when the number of c o n v e c t i v e c e l l s changed and the observed peaks i n the d i s t r i b u t i o n o f r a d i o a c t i v e age d e t e r m i n a t i o n s . However, these peaks, i n d i c a t i n g a p e r i o d i c c h a r a c t e r i n t e c t o n i c a c t i v i t y , while they a r e c e r t a i n l y s i g n i f i c a n t , have only been r e l i a b l y obtained f o r t h e North American c o n t i n e n t . RUNCORN (1964) noted  that i n t e r p r e t i n g the observed non-  h y d r o s t a t i c s t r e s s e s i n terms of a f i n i t e s t r e n g t h of the e a r t h r e q u i r e s that creep r a t e s i n the mantle be l e s s  than  -12  10  of those i n l a b o r a t o r y experiments,  although the s t r e s s  d i f f e r e n c e s a r e of the order of 10 t o 100 bars and the temp e r a t u r e s are e l e v a t e d .  T h e r e f o r e , RUNCORN (1963, 1964)  i n t e r p r e t e d s a t e l l i t e g r a v i t y measurements i n terms o f convect i o n i n the mantle. tinental drift  He a l s o i n c l u d e d an e x p l a n a t i o n of con-  i n his interpretation.  The d e t a i l s of h i s  arguments w i l l not be d i s c u s s e d here nor w i l l g e o l o g i c a l support f o r them, although such support on the l i k e l i h o o d of c o n v e c t i o n .  o b v i o u s l y has a b e a r i n g  It isfelt  that encumbering  - 114 the present d i s c u s s i o n with dubious offers l i t t l e the e a r t h ' s  g e o l o g i c a l arguments  hope at present o f h e l p i n g to s o l v e problems o f  interior.  The problem of the formation o f an i r o n core i n a convect i n g . e a r t h has been c o n s i d e r e d by TOZER (1965) with some significant results. tial in  imply d e n s i t y v a r i a t i o n s on s p h e r i c a l s u r f a c e s o f 1 p a r t  10 . 4  due  The t e s s e r a l harmonics of the geopoten-  These d e n s i t y v a r i a t i o n s may be thermal i n o r i g i n o r  t o departures from u n i f o r m i t y i n composition.  Assuming  the l a t t e r , Tozer estimated the r a t e at which i r o n has been e n t e r i n g the core d u r i n g some p e r i o d l e s s than the l a s t 10® years.  With a v e l o c i t y o f 1 0 ~ cm/sec, he c a l c u l a t e d 7  gm/sec as the present r a t e of growth of the c o r e .  10  7  Compared  OH  to  the present mass of the core (2 x 10  tion it  g), this  i n d i c a t e s that core formation i s v i r t u a l l y complete, i f  is still  o c c u r r i n g at a l l .  On the b a s i s o f s t u d i e s , which he proposes in  calcula-  a l a t e r paper,  Tozer concluded  to d e s c r i b e  that w i t h any reasonable  d i s t r i b u t i o n of s i z e s of the i r o n masses i n the s i l i c a t e phase, the f o r m a t i o n o f the core c o u l d not proceed  u n t i l the s i l i c a t e  v i s c o s i t y was reduced by r a d i o a c t i v e h e a t i n g t o about i t s present v a l u e .  Subsequently,  v e c t i o n would be the energy  the major d r i v i n g f o r c e o f con-  r e l e a s e d by v i s c o u s d i s s i p a t i o n  i n the f o r m a t i o n of the c o r e .  In t h i s regard, Tozer c o n s i d e r s  i t probable that the v i s c o s i t y o f the mantle i s p r i m a r i l y  - 115  -  c o n t r o l l e d by t h e r m a l l y - a c t i v a t e d "creep" mechanisms, which have a very s t r o n g temperature dependence. When c o n v e c t i o n  i n a body the s i z e of the mantle s u p p l i e s  one-half of the s u r f a c e heat  flow, the c a l c u l a t e d v i s c o s i t y  20 i s about 10  poise.  dependent estimates, Bonneville  Tozer c o n s i d e r s t h i s agreement with i n 21 10  p o i s e f o r the unloading  (CRITTENDEN, 1963)  and  10  2 2  p o i s e f o r the  ing of Fennoscandia, to be good evidence i n a s t a t e of  of Lake unload-  that the mantle i s  convection.  Tozer c o n s i d e r s that before d i f f e r e n t i a t i o n commenced, all  the core m a t e r i a l was  i n a molten s t a t e .  ates the k i n e t i c s of core formation  He then  a c c o r d i n g to two  evaludiffer-  ent models.  In model I he e n v i s i o n s masses of i r o n i n  cate phase.  In model I I he c o n s i d e r s masses of s i l i c a t e  i r o n phase.  The  model i s the f a l l  mechanism of s e p a r a t i o n of i r o n i n the  in first  of l i q u i d masses through a v i s c o u s medium.  In the second model, i r o n flows along channels. to r e j e c t model I as the process convection  sili-  i s added to the  BIRCH (1952) has  He i s f o r c e d  of core formation  even when  theory.  s t a t e d that estimates  of the  viscosity  20 of the e a r t h of the order 10  p o i s e are f a r too h i g h .  But  Tozer argues that such low v i s c o s i t i e s as B i r c h assumes p l u s the i n e v i t a b l y high temperature g r a d i e n t s they imply would lead to an enormous heat  l o s s from the p l a n e t and  that a  source of energy that would get the e a r t h i n t o such a s t a t e  - 116  -  i s u n l i k e l y , unless perhaps i t were a s s o c i a t e d with planet's  the  formation.  The p o s s i b i l i t y of core formation by model II  depends on  the d i s t a n c e over which i r o n can move along channels the s i l i c a t e phase. i s l i k e that observed i s unable,  The  structure visualized  through  i n t h i s model  i n stony-iron, m e t e o r i t e s .  T h i s model  however, to e x p l a i n the p e r i o d s of c o n t i n e n t a l  growth and d r i f t  suggested  by Runcorn because the core r a d i u s  cannot have changed enough i n Mesozoic and T e r t i a r y  times.  Furthermore, Tozer argues that Runcorn's f a s t e r r a t e of core growth at the present time leads to impossibly high temperat u r e s at depths of the order of 100  km.  Tozer concludes  the l a r g e amount of energy r e l e a s e d and the great  that  sensitivity  of v i s c o s i t y to temperature favours the view that core format i o n by d i f f e r e n t i a t i o n was past. it  v i r t u a l l y complete i n the remote  Of course, such arguments do not prove or d i s p r o v e that  ever occurred, but o n l y l i m i t  the  possibilities.  The dearth of r a d i o a c t i v e elements i n i r o n meteorites been used as an argument a g a i n s t the i r o n core hypothesis cause a heat  source i s needed f o r a convecting  has be-  (outer) core  and c o n v e c t i o n i n the outer core i s r e q u i r e d t o e x p l a i n the e a r t h ' s magnetic f i e l d .  JACOBS (1954),  that a r a d i o a c t i v e content  i n the i n n e r core of only 2 per  cent of c r u s t a l values i s s u f f i c i e n t t r a n s f e r of heat  however, has shown  i n the outer c o r e .  f o r maintaining  convective  - 117 Jacobs a l s o i n v e s t i g a t e d t h e problem heat from t h e core. core might  of the t r a n s f e r of  He found that the heat generated i n the  be removed by conduction alone.  In the heat conduc-  t i o n equation he used the m e l t i n g point g r a d i e n t c a l c u l a t e d by U f f e n f o r the lower mantle as an approximation t o the a c t u a l temperature  gradient there.  Such an approximation i s i n  accord with the hypothesis of s o l i d i f i c a t i o n of a once molten earth.  However, f o r an e a r t h that has g r a d u a l l y been h e a t i n g  up, the a c t u a l temperature  g r a d i e n t i n the lower mantle  might  be c o n s i d e r a b l y s m a l l e r than the m e l t i n g point g r a d i e n t . r e s u l t might  This  imply c o n v e c t i v e t r a n s f e r o f heat i n the mantle,  but the q u e s t i o n i s f u r t h e r complicated by the probable r o l e of the r a d i o a c t i v e t r a n s f e r o f heat.  T h e r e f o r e , Jacobs' con-  c l u s i o n t h a t the heat generated i n the core might be removed by conduction alone i s perhaps  t r u e f o r an e a r t h which i s  e i t h e r h e a t i n g . u p or c o o l i n g down. Another  important q u e s t i o n r e l a t e d to the g e n e r a l problem,  of d i f f e r e n t i a t i o n and c o n v e c t i o n i n the e a r t h i s the p o s s i b i lity  of d i f f e r e n t  outer c o r e .  chemical compositions f o r the i n n e r and  ZHARKOV (1962) noted that the core cannot  of a conglomerate  consist  o f substances s i n c e i t s s m a l l v i s c o s i t y must  of n e c e s s i t y l e a d t o g r a v i t a t i o n a l d i f f e r e n t i a t i o n .  He then  concluded that the e x i s t e n c e between the outer and i n n e r core of a wide t r a n s i t i o n l a y e r  (  200 km) r e f u t e s the hypothesis  of t h e i r d i f f e r e n t chemical composition s i n c e with a  - 118 v i s c o s i t y of l e s s than 10  12  • p o i s e , which must c h a r a c t e r i z e  t h i s zone, g r a v i t a t i o n a l d i f f e r e n t i a t i o n would  inevitably  occur l e a d i n g to a sharp boundary between the outer and core.  However, h i s c o n c l u s i o n i s based  inner  on the assumed v a l i d -  i t y of Gutenberg's s e i s m i c v e l o c i t y d i s t r i b u t i o n i n the c o r e . T h i s s o l u t i o n i s not unique d i s c u s s e d i n Chapter correct.  and there are s t r o n g arguments,  10, that t h i s p a r t i c u l a r s o l u t i o n i s i n -  N e v e r t h e l e s s , Gutenberg's s o l u t i o n does correspond  to a t r a n s i t i o n of the same substance solid state.  from a l i q u i d to a  If i t i s incorrect, this fact  i m p l i e s that the  core i s more complicated than the simple model assumed i n c o n s i d e r i n g i t s thermal h i s t o r y .  A possibility  of the three zones which comprise  the core i s composed of  normal metals, whereas the other two metallized s i l i c a t e s .  In p a r t i c u l a r ,  i s that  one  zones are composed of i t i s suggested  that  the o u t e r core i s m e t a l l i z e d s i l i c a t e i n a l i q u i d s t a t e , " t r a n s i t i o n " zone i s composed of denser normal metals, marily iron also in a l i q u i d  the  pri-  s t a t e and that the i n n e r core  is metallized s i l i c a t e in a solid state.  Of course, i t might  be p o s s i b l e that three d i s t i n c t phase changes of the same m a t e r i a l occur i n the core, each change corresponding to the f a c t that a h i g h e r numbered energy one.  l e v e l i s the more s t a b l e  E i t h e r p o s s i b i l i t y corresponds  to B o l t ' s v e l o c i t y  t r i b u t i o n i n the core, which should be accepted distribution i s rejected.  dis-  i f Gutenberg's  119 9.  THE  EQUATION OF STATE OF THE  . I t i s intended  EARTH  that t h i s chapter,  which i s l i m i t e d to a  d i s c u s s i o n of v a r i o u s proposed d e n s i t y - p r e s s u r e  relations for  the e a r t h , serve as a framework f o r the f o l l o w i n g chapter, which the c o n s t i t u t i o n of the e a r t h i s considered.  The v a r i e t y  of models proposed gives some idea of the u n c e r t a i n t y the a c t u a l s t a t e of the e a r t h .  The  are determined from s e i s m i c data under high p r e s s u r e s ,  together  v a r i o u s assumptions.  The  and  in  density-pressure from s t u d i e s of  about relations materials  with boundary c o n d i t i o n s  and  u n c e r t a i n t y about the a c t u a l s t a t e  of the e a r t h a r i s e s from u n c e r t a i n t i e s i n the data  and  i n the  assumpt i o n s . B u l l e n ' s d i v i s i o n of the e a r t h i n t o l a y e r s , based J e f f r e y s ' v e l o c i t i e s i n the mantle and the core,  i s given  i n Table  on  Bolt's v e l o c i t i e s in  5. TABLE 5  INTERNAL LAYERS OF THE Layer  EARTH  Depth to Boundaries, 0  Crust  33 B  413  C D'  Mantle  D"  984 2700 2898  E' 45 60 4710  Core F  5160  G 6371  km  - 120 The e a r l i e s t r e l a t i o n s based (BULLEN, 1936,  and perhaps the best known d e n s i t y - p r e s s u r e  on seismology 1949a, 1950,  are B u l l e n ' s Model A and Model B  1963).  B u l l e n used  J e f f r e y s ' velo-  c i t y d i s t r i b u t i o n as the b a s i s f o r these d e n s i t y - p r e s s u r e relations;  more r e c e n t l y  (BULLEN, 1965b), he has  s e v e r a l p o s s i b l e models f o r the core based city  proposed  on B o l t ' s v e l o -  distribution. Both compressional  have been determined  and shear wave v e l o c i t y - d e p t h curves  from t r a v e l - t i m e t a b l e s .  The f a i l u r e of  the outer core to pass shear waves i s evidence that i t i s liquid. of  A c c o r d i n g to the theory of e l a s t i c i t y ,  compressional waves, 0( , and  the v e l o c i t y  the v e l o c i t y of shear waves,  /3 , are r e l a t e d to the d e n s i t y , ^ , the modulus of r i g i d i t y ,  /A , and the a d i a b a t i c i n c o m p r e s s i b i l i t y , k, by the f o l l o w i n g two  equations: CV  In  = / k  +  3  the mantle, whereCx* and  (1)  are known f u n c t i o n s of the  r a d i u s , s e i s m i c data give two equations i n t h r e e unknowns. In the c o r e , there i s one equation i n two ary  unknowns.  to i n t r o d u c e the v a r i a b l e Q9 and t r e a t  one equation i n two dj  I t i s custom-  the whole e a r t h with  unknowns: -.  * \ f>\  Seismic data g i v e ^ as a f u n c t i o n of the r a d i u s , r.  (3) Thus,  - 121 s e i s m i c data alone, even i f there were no u n c e r t a i n t i e s i n the v e l o c i t i e s , cannot Furthermore,  g i v e an equation of s t a t e f o r the e a r t h .  there e x i s t s no other independent  equation i n  these v a r i a b l e s that can be shown from d i r e c t evidence to be a p p l i c a b l e t o the e a r t h as a whole.  Every procedure f o r  determining an equation of s t a t e f o r the e a r t h has i n c l u d e d s e v e r a l assumptions about the nature of the v a r i o u s zones i n the e a r t h .  Often these assumptions are supported  by experiments  on m a t e r i a l s at high p r e s s u r e s .  or  suggested  In each model,  the t o t a l mass and moment of i n e r t i a of the e a r t h are used boundary c o n d i t i o n s .  P o s s i b l e s o l u t i o n s are d e f i n i t e l y  fined within certain l i m i t s ,  as  con-  i r r e s p e c t i v e of assumptions on  the nature of v a r i o u s zones;  but there i s s t i l l c o n s i d e r a b l e  v a r i e t y i n the s o l u t i o n s that have been o f f e r e d . to the composition of the earth-and  With regard  the nature of the earth's  core, such d i f f e r e n c e s between s o l u t i o n s are q u i t e s i g n i f i c a n t . Combining equation  (3) with the equation of h y d r o s t a t i c  e q u i l i b r i u m and the assumption  that the temperature  i s adia-  b a t i c , g i v e s the w e l l known Adams-Williamson equation. equation i n v o l v e s o n l y the v a r i a b l e s ^ , ^ and Y  and  cable wherever the f o l l o w i n g three c o n d i t i o n s are (1)  The  (2)  phase throughout batic.  is appli-  satisfied:  n o n - e q u i l i b r i u m s t r e s s e s are much s m a l l e r than  pressures.  This  the  There i s no change i n chemical composition the zone.  (3)  The temperatures  are a d i a -  Using a form of the Adams-Williamson equation which  or  - 122 i n c l u d e s the mass m of a sphere of r a d i u s r , i t i s f o r m a l l y p o s s i b l e to d e r i v e a d e n s i t y d i s t r i b u t i o n f o r any range of values of r f o r which P i s known, p r o v i d i n g that t h e s t a r t i n g values  of (? and m are known.  In a p r e l i m i n a r y e f f o r t  to o b t a i n t h e d e n s i t y  distribution  i n the e a r t h , BULLEN (1936) a p p l i e d the Adams-Williamson equation  t o the e n t i r e mantle, i . e . , from 33 km to 2898 km,  t a k i n g the value o f ^ at the top of the mantle equal t o 3.32 g/cm  and m equal  t o the mass o f the e a r t h l e s s a small  allowance f o r that of the c r u s t .  To t e s t t h i s  preliminary  d i s t r i b u t i o n , he c a l c u l a t e d the r a t i o I / M R , where I , M C  C  C  c  and  R  The  c a l c u l a t e d value 0.57 exceeds the value 0.40 f o r a u n i -  c  c  are the moment of i n e r t i a , mass and r a d i u s of the core.  form sphere and a c t u a l l y i m p l i e s a decrease of d e n s i t y depth i n the c o r e .  with  The assumption u n d e r l y i n g the t r i a l  l a t i o n o f the d e n s i t y d i s t r i b u t i o n which was considered  calcumost  l i k e l y t o be i n e r r o r was that there i s no change i n chemical composition ous  or phase throughout the zone.  s l o p e s of the v e l o c i t y - d e p t h curve suggest at l e a s t  zones B, C and D i n the mantle. c a l t o apply and  Indeed, d i s c o n t i n u -  As a next step i t was l o g i -  the Adams-Williamson equation  to regions B and D  t o t r e a t r e g i o n C, because o f i t s steeper  ent , as a t r a n s i t i o n r e g i o n .  three  velocity gradi-  The d e t a i l s of such c a l c u l a t i o n s  have been b r i e f l y d e s c r i b e d by BULLEN (1963). a p p l i c a t i o n o f the Adams-Williamson equation  A similar t o the outer  core  - 123 i.e.,  -  region E, l e d to a d e n s i t y d i s t r i b u t i o n d e s c r i b i n g most  of the earth's mass.  There i s , however, a wide margin of  c e r t a i n t y f o r the d e n s i t y d i s t r i b u t i o n i n region G. d e n s i t y d i s t r i b u t i o n s were c a l c u l a t e d using two hypotheses f o r the d e n s i t y at the earth's 22.3  g/cm .  The  3  Later,  fairly  centre,  un-  12.3  extreme and  average of the r e s u l t i n g d i s t r i b u t i o n s , known  as B u l l e n ' s Model A,  i s shown i n F i g u r e  5.  A p l o t of the v a r i a t i o n of the i n c o m p r e s s i b i l i t y with depth, u s i n g the d e n s i t y d i s t r i b u t i o n of Model A i n (3),  has  the f e a t u r e that the i n c o m p r e s s i b i l i t y at the base of  region D and 6.5  and  6.2  at the top of r e g i o n E d i f f e r by only 5%, x 10-*- dynes/cm , r e s p e c t i v e l y . 2  2  s e r v a t i o n s combined with positionally distinct  (BULLEN, 1949a).  1000  km  On  com-  indepenand  deep  the b a s i s of t h i s hypothesis  subsequently developed a new  equation  he  of s t a t e ,  assuming that k and dk/dp change c o n t i n u o u s l y  and  smoothly throughout the whole earth below a depth of (BULLEN, 1949a, 1950).  the Adams-Williamson equation 200  be  c o n s t i t u t i o n at pressures  temperatures of the order p r e v a i l i n g i n the earth's  fairly  is  from the mantle l e d B u l l e n to hypo-  dent of the p a r t i c u l a r chemical  Model B,  These ob-  the assumption that the core  t h e s i z e that the c o m p r e s s i b i l i t y of substances may  suggested and  being  dk/dp i s a l s o  n e a r l y continuous across the core-mantle boundary.  interior  equation  kilometers  T h i s hypothesis  i m p l i e s that  cannot be a p p l i e d to the  of the mantle, region D.  lowest  In h i s Model B,  - 124  FIGURE 5.  -  E q u a t i o n s of s t a t e f o r the  earth.  - 125  -  B u l l e n used h i s c o m p r e s s i b i l i t y - p r e s s u r e hypothesis the d e n s i t y d i s t r i b u t i o n  between the c e n t r e of the e a r t h  the base of r e g i o n E and between the top of E and D".  In regions E and D',  to compute and  the top of  he a p p l i e d the Adams-Williamson  equation. RAMSEY (1948, 1949)  modified B u l l e n ' s Model A to  to an i n c r e a s e i n d e n s i t y with depth due i n composition.  The  amount and  nature  to a gradual change  of t h i s i n c r e a s e i n  d e n s i t y were chosen a c c o r d i n g to the c r i t e r i a Chapter 4. Figure  correspond  Ramsey's d e n s i t y d i s t r i b u t i o n  discussed i n  i s a l s o shown i n  5.  BIRCH (1952) added to the Adams-Williamson equation c o r r e c t i o n : f a c t o r f o r non-adiabatic mated that a departure  temperatures.  and  esti-  from the a d i a b a t i c gradient by l°/km  would l e a d to an e r r o r of 10 to 20 per cent gradient.  He  a  C o n s i d e r i n g the estimates  i n the d e n s i t y  of m e l t i n g - p o i n t  gradients  a c t u a l temperature g r a d i e n t s i n the e a r t h , there i s no  reason  to expect  approaching  departures  l°/km except  from the a d i a b a t i c g r a d i e n t even  i n the uppermost p a r t of the mantle  where i n any case the Adams-Williamson equation cannot applied.  For pressures between 0.4  (1950) found  and 3.2  that the f o l l o w i n g equation k = 2.25  megabars, BULLEN  gives k to w i t h i n  + 2.86p + 0.16p  2  (4)  T h i s leads to llS = 2.86 dp  + 0. 32p .  be  (5)  2%.  - 126 In these two equations k and p are i n megabars. A s i g n i f i c a n t o b s e r v a t i o n made by BIRCH (1952) i s that the v a r i a t i o n o f  has not been used d i r e c t l y to f i n d dk/dp;  i n s t e a d , the d e n s i t y d i s t r i b u t i o n has f i r s t with the a i d o f v a r i o u s assumptions, lation k  =(  pr^-  been c a l c u l a t e d ,  and then k from the r e -  B i r c h made a d i r e c t c a l c u l a t i o n of dk/dp from  (j> and has compared h i s r e s u l t s with the p r e d i c t i o n of f i n i t e s t r a i n theory f o r a homogeneous l a y e r , u s i n g parameters d e t e r mined e x p e r i m e n t a l l y f o r matter  at r e l a t i v e l y low p r e s s u r e s .  The f o l l o w i n g comparisons have been made by B i r c h between h i s r e s u l t s and the s i m p l i f y i n g assumptions of B u l l e n and Ramsey.  F i r s t , d i r e c t c a l c u l a t i o n of dk/dp from s e i s m i c  data i s not c o n s i s t e n t with an i n c r e a s i n g slope i n the lower mantle, as given by equation  (5).  T h i s c a l c u l a t i o n may be  c o n s i s t e n t , however, with the suggestion by RAMSEY (1949) that dk/dp i s constant f o r the d i f f e r e n t phases i n the lower mantle and core, although B i r c h ' s values are 3,3 i n r e g i o n D compared with 3.7 by Ramsey, and 3.6 (using J e f f r e y s ' . v e l o c i t i e s ) o r 3.0 ( u s i n g Gutenberg's v e l o c i t i e s ) i n region E, compared with 3.8 by Ramsey. BIRCH (1961) found that measurements of the v e l o c i t y of compressional waves in; s i l i c a t e s and oxides having a range of / d e n s i t y from 2.6 t o 5 g/cm  3 suggest  a simple dependence of  v e l o c i t y upon d e n s i t y and mean atomic weight. ated v a r i o u s proposed  He then e v a l u -  d e n s i t y d i s t r i b u t i o n s i n the mantle by  - 127 comparing them with s e m i - e m p i r i c a l v e l o c i t y - d e n s i t y He found by p l o t t i n g d e n s i t y density  relations  d i s t r i b u t i o n s on a v e l o c i t y -  diagram that many o f those which were determined on t  assumption that one l a y e r or another i s homogeneous are c l e a r l y inconsistent  with t h i s assumption.  Bullen's  Model B  and  two models proposed by B u l l a r d f a l l  i n t o t h i s category.  The  v e l o c i t y - d e n s i t y p l o t of these models a c t u a l l y i m p l i e s a  decrease i n i r o n content with depth through the t r a n s i t i o n region  i n the mantle.  B i r c h r e j e c t s these models.  A p l o t of Ramsey's d e n s i t y d e n s i t y diagram showed that t i o n s made i n c o n s t r u c t i n g  d i s t r i b u t i o n s on the v e l o c i t y  i t i s consistent the model.  with t h e assump-  However, the agreement  found by BIRCH (1952) between f i n i t e - s t r a i n theory f o r a homo geneous l a y e r and the observed v e l o c i t i e s i n region c a t e s that  D indi-  r e g i o n D i s the most homogeneous i n the mantle.  Because Ramsey's d e n s i t y  d i s t r i b u t i o n i s inconsistent  with  t h i s r e s u l t i t i s a l s o r e j e c t e d by B i r c h . The construct  i n v e s t i g a t i o n s mentioned above l e d B i r c h a new d e n s i t y  (1964) t o  d i s t r i b u t i o n f o r the e a r t h .  In the  upper mantle and t r a n s i t i o n l a y e r , d e n s i t y was assumed t o be proportional  to the v e l o c i t y of compressional waves, with  ratios consistent  with experimental s t u d i e s  lower mantle and outer core, the d e n s i t y by the Adams-Williamson method.  of rocks.  In the  v a r i a t i o n was found  The estimated d e n s i t y  of the  inner core was based on shock-wave measurements of metals and  -  abundance c o n s i d e r a t i o n s .  128 -  B i r c h a l s o used a s i g n i f i c a n t l y  d i f f e r e n t v a l u e of the moment of i n e r t i a from that p r e v i o u s l y accepted, t h i s new value r e s u l t i n g from s t u d i e s of the e x t e r n a l p o t e n t i a l as revealed by p e r t u r b a t i o n s o f s a t e l l i t e (The o l d value of the r a t i o l/MR value i s 0 . 3 3 0 6 . )  2  orbits.  was 0 . 3 3 3 6 , whereas the new  A c t u a l l y , B i r c h c a l c u l a t e d two s l i g h t l y  d i f f e r e n t d i s t r i b u t i o n s , depending on whether  the d e n s i t y or  the s l o p e of the v e l o c i t y - d e n s i t y p l o t i s assumed known at the top of the mantle.  S o l u t i o n I, i n which the s l o p e at the top  of the mantle i s assumed to be 0 . 3 2 8 (g/cm )/(km/sec.), i s 3  approximately the same as B u l l e n ' s Model A i n the upper mantle and l i e s between B u l l e n ' s Models A and B i n the lower mantle.  In the outer core B i r c h ' s S o l u t i o n I i s approximately  the same as Model B. A method of c a l c u l a t i n g the equation of s t a t e of the earth based on J e f f r e y s ' s e i s m i c v e l o c i t i e s and which i s p a r t i c u l a r l y s u i t a b l e f o r comparison with the r e s u l t s ' - o f h i g h p r e s s u r e experiments on s i l i c a t e s , by McQUEEN et a l . (1964).  oxides and metals was used  The form o f the equation of s t a t e  used throughout t h e i r i n v e s t i g a t i o n was based on the r e s u l t s of shock-wave experiments.  E s s e n t i a l l y , the Adams-Williamson  equation was r e p l a c e d by the Hugoniot, w r i t t e n as a f u n c t i o n of volume and known c o n s t a n t s .  There a r e s i g n i f i c a n t  differ-  ences i n the r e s u l t i n g d e n s i t y d i s t r i b u t i o n s depending on the c h o i c e o f the d e n s i t y , (?  Q  e  at the top of the mantle.  The  - 129 density d i s t r i b u t i o n = 3.2 g/cm A.  With  resulting  i s essentially =  from the assumption, that  the same as that of B u l l e n ' s Model  3.6 g/cm , a d e n s i t y d i s t r i b u t i o n  s i m i l a r to  B u l l e n ' s Model B r e s u l t s . Data from the f r e e v i b r a t i o n s of the e a r t h , i . e . , love wave v e l o c i t i e s from t o r s i o n a l  o s c i l l a t i o n s and R a y l e i g h wave  v e l o c i t i e s from s p h e r o i d a l o s c i l l a t i o n s , a r e a d d i t i o n a l seismic i n f o r m a t i o n which can h e l p r e s o l v e the u n c e r t a i n t i e s i n the earth's density d i s t r i b u t i o n . permits  a determination  This a d d i t i o n a l information  of the d e n s i t y d i s t r i b u t i o n  e a r t h independent of assumptions of chemical the mantle.  However i t i s s t i l l  assumptions about the composition  necessary  i n the  homogeneity i n  t o make some  or homogeneity of the core.  KOVACH and ANDERSON (1965) modified a d e n s i t y d i s t r i b u t i o n f o r the e a r t h , determined by Anderson from analyses of the p e r i o d s of f r e e o s c i l l a t i o n s of the e a r t h , so that i t would be i n accord with the more recent value of the moment of i n e r t i a and shock wave data on i r o n .  According  t o Kovach  and Anderson, t h i s d e n s i t y d i s t r i b u t i o n was not r e s t r i c t e d by assumptions r e g a r d i n g homogeneity, thermal h y d r o s t a t i c c o n d i t i o n s , but the equation  g r a d i e n t s and  of s t a t e f o r t h e  core was chosen to be p a r a l l e l to the 0°K isotherm f o r i r o n computed from the shock wave Hugoniot 1958), corresponding  (ALTSHULER et a l . ,  t o a core composition  i r o n and 16 per cent mantle m a t e r i a l .  o f 84 per cent  The v a l i d i t y of t h i s  - 130 procedure,  -  p a r t i c u l a r l y i n view of high p r e s s u r e  experiments  on i r o n by TAKAHASHI and BASSETT (1965). i s q u e s t i o n a b l e . However the r e s u l t i n g d e n s i t y d i s t r i b u t i o n  i s reasonably  to B u l l e n ' s Model A i n the upper mantle and  close  outer c o r e .  In  the lower mantle, i t l i e s roughly between B u l l e n ' s Model A and  B. Significant  new  work i n e s t i m a t i n g the d e n s i t y d i s t r i b u -  t i o n i n the e a r t h u s i n g data on the f r e e o s c i l l a t i o n s of the earth  (measured d u r i n g the 1960  carried  Chikan earthquake) has been  out by LANDISMAN et a l . , (1965).  They  initially  assumed B u l l e n ' s Model A d e n s i t y d i s t r i b u t i o n and velocities.  Gutenberg's  For the gravest modes of o s c i l l a t i o n they  that the observed  f r e e p e r i o d s are longer than  by the Gutenberg-Bullen  A model.  d e n s i t i e s i n the lower mantle.  those p r e d i c t e d  To remove t h i s  they modified B u l l e n ' s Model A by approximately  found  discrepancy, 10%  smaller  T h e i r curve shows n e a r l y con-  stant d e n s i t i e s between depths of 1600  and  2800 km,  which  they e x p l a i n by a s u p e r - a d i a b a t i c temperature g r a d i e n t of about 2°C/km, coupled with a d e p l e t i o n of i r o n towards the bottom of the mantle.  - 131 10.  THE CONSTITUTION OF THE  -  EARTH  It i s p o s s i b l e that the combination cities  of s e i s m i c wave v e l o  i n the core with the r e s u l t s of h i g h - p r e s s u r e e x p e r i -  ments on p o s s i b l e m a t e r i a l s i n the core w i l l e v e n t u a l l y g i v e a c o n c l u s i v e answer to the question of i t s c o n s t i t u t i o n . the p r e s e n t , however, i t i s s t i l l d i r e c t evidence.  important  For  to c o n s i d e r l e s s  T h e r e f o r e i n a d d i t i o n to evidence on  the  c o n s t i t u t i o n of the core, evidence on the c o n s t i t u t i o n of the lower and upper mantle i s c o n s i d e r e d below. 10.1  The upper mantle The most s i g n i f i c a n t f e a t u r e of the upper mantle i s the  s o - c a l l e d "20° d i s c o n t i n u i t y " , which corresponds i n the s e i s m i c v e l o c i t y g r a d i e n t .  A c c o r d i n g to J e f f r e y s '  v e l o c i t y d i s t r i b u t i o n t h i s occurs at about 413 surface.  Between 30 and 413  to a change  km below the  km J e f f r e y s ' s o l u t i o n shows a  n e a r l y l i n e a r i n c r e a s e i n v e l o c i t y w i t h depth,  agreeing c l o s e  with the t h e o r e t i c a l i n c r e a s e i n a homogeneous, i s o t h e r m a l layer.  However, Gutenberg's s o l u t i o n shows a low  l a y e r between about 50 and  100 km,  v e l o c i t y beginning at 200 km, at about 600 km.  velocity  then a r a p i d i n c r e a s e of  meeting J e f f r e y s '  distribution  Thus, i n Gutenberg's s o l u t i o n , the d i v i s i o n  between regions B and C becomes i n d e f i n i t e but might occur around 200 km  r a t h e r than at 413  km.  The e f f e c t of p r e s s u r e i s t o increase., the s e i s m i c v e l o c i t i e s whereas the e f f e c t of temperature  i s to decrease  them.  - 132 BIRCH (1952) has  -  shown that a negative  v e l o c i t y gradient  the c r u s t corresponds to a temperature gradient 6.6°/km.  On  below  greater  than  the other hand, J e f f r e y s ' v e l o c i t y d i s t r i b u t i o n  corresponds to a temperature gradient  of l°/km.  Whether  there  i i s a shadow zone or not, gradient  greater  B i r c h concludes that a temperature  than l°/km seems p r o b a b l e .  On  the  that the r a d i o a c t i v e elements completely separated i n t e r i o r and  are concentrated  ture gradient  i s 5°/km.  mately c o r r e c t and  assumption from  the  i n the c r u s t , the minimum tempera-  I f t h i s assumption i s even  i f J e f f r e y s ' v e l o c i t y gradients  approxiare  the  a c t u a l ones, then l a y e r B must be c h a r a c t e r i z e d by a p r o g r e s s i v e change of composition.  Therefore,  the Adams-Williamson  equation i s not  a p p l i c a b l e i n t h i s region  This conclusion  must be considered  (BIRCH, 1952).  an o b j e c t i o n to  Bullen's  Model A. The  "20°  d i s c o n t i n u i t y " was  explained  by BERNAL (1936) as  a t r a n s i t i o n to a c r y s t a l s t r u c t u r e which i s more s t a b l e at high p r e s s u r e s .  R e c a l l i n g Goldschmidt's a s s e r t i o n  that  magnesium germanate (MgGeO^J i s transformed under pressure a denser m o d i f i c a t i o n , Bernal probably apply constituent  to f o r s t e r i t e  to  suggested t h a t the same would ( M g S i 0 ) , which i s a p r i n c i p a l 2  4  of o l i v i n e rocks such as d u n i t e .  The  density  jump  at the t r a n s i t i o n would be about 9% f o r f o r s t e r i t e . It  i s now  perhaps, 400  b e l i e v e d that the e n t i r e region from 200,  to 900  km  or  i s a t r a n s i t i o n zone (B'lRCH, 1952) .  - 133 B i r c h has concluded  that t h e r e must be changes of phase, com-  p o s i t i o n , or both i n this zone.  He suggested  that the t r a n s i -  t i o n zone i s a system with s e v e r a l major components. MgO - FeO S i 0 . Then a gradual change may be i n t e r p r e t e d as a s h i f t 2  with  p r e s s u r e i n the r e l a t i v e p r o p o r t i o n s of h i g h - p r e s s u r e and lowp r e s s u r e phases.  More recent i n v e s t i g a t i o n s by B i r c h a r e d i s -  cussed below which i n d i c a t e that the inhomogeneity C may be f u l l y accounted  of region  f o r by changes of phase.  Between 1958 and 1960, Ringwood s t u d i e d the s o l i d t i o n of M g S i 0 2  4  in spinel Ni Ge0 . 2  He found  4  solu-  that t h e t r a n s i -  t i o n of f o r s t e r i t e t o s p i n e l occurred at a p r e s s u r e of 1.3 x 10  1 1  dynes/cm  2  (- 10%) and a temperature  a p r e s s u r e of 1.75 x 1 0 t u r e of 1500°C. respectively. found  1 1  dynes/cm  These correspond Corresponding  that f a y a l i t e  0.38 x 1 0  1 1  2  ( t 30%) and at a tempera-  to depths of 400 and 500 km,  to a depth o f 1 2 0 km, Ringwood  ( F e S i 0 ) transformed  dynes/cm  2  o f 600°C and a l s o at  4  to a s p i n e l at  and 600°C.  Other probable t r a n s i t i o n s i n v o l v e the conversion of o l i v i n e or s p i n e l forms of magnesium-iron s i l i c a t e to h i g h p r e s s u r e oxide phases.  Even at moderate p r e s s u r e s the open  framework of q u a r t z i s not s t a b l e .  At a temperature of  930°C, a p r e s s u r e o f 30,000 atmospheres i s r e q u i r e d to conv e r t q u a r t z to c o e s i t e .  A further t r a n s i t i o n of S10 to  s t i s h o v i t e occurs at h i g h e r p r e s s u r e s  2  (MACDONALD, 1962) .,  Recently, SCLAR et a l . (1964) have proposed  a detailed  - 134 p e t r o l o g i c a l model of the 200 t o 900 km d i s c o n t i n u i t y zone. They c o n s i d e r e d the f o l l o w i n g reactions  with i n c r e a s i n g  sequence of t r a n s f o r m a t i o n s and  depth t o be the most probable on  the b a s i s of experimental evidence, c r y s t a l l o c h e m i c a l (coordination) considerations, A.  and r e l a t i v e d e n s i t i e s of phases:  Pyroxene (MgSiC>3) (1)  2MgSi0  3  — 5 ? Mg SiC>4 + S i 0 , 2  clinoenstatite (2)  Mg Si0 2  + Si0  4  2  -5> f o r s t e r i t e + s t i s h o v i t e ~*> M g S i 0 2  + Si0 ,  4  Mg Si0 2  + Si0  4  3  spinel + stishovite (4)  2MgSi0  3  = -318 c c / mole  spinel + stishovite  2MgSi0 ,  2  Av  2  forsterite + stishovite (3)  A v = -513 cc/mole  2  A v = -2.4cc/mole  —$> corundum A v = -0.3 cc/mole  —9- 2MgO + 2 S i 0 , 2  corundum —"S> p e r i c l a s e + s t i s h o v i t e B.  Olivine (1)  (Mg Si0 ) 2  Mg Si0 2  4  Mg Si0 ,  4  2  forsterite (2)  Mg Si0 2  spinel (3)  4  -*>  A'v .= -3.8 cc/mole  4  spinel  -v> MgO + MgSiOg, —periclase  MgO + M g S i 0  3  + corundum  — 2 M g O  p e r i c l a s e + corundum  ZJv = -2.9 cc/mole  + Si0 , 2  4 v = -0.5 cc/mole  periclase + stishovite  S c l a r et a l . combine these two sequences i n a t a b l e summarizing t h e i r p e t r o l o g i c a l model.  The authors suggest  s u c c e s s i v e phase t r a n s i t i o n s and r e a c t i o n s  with  that the increasing  - 135 depth  l i s t e d above c o u l d account  f u l l y f o r the broad 200 to  900 km s e i s m i c d i s c o n t i n u i t y . B i r c h ' s equations r e l a t i n g the v e l o c i t y of compressional waves to d e n s i t y and mean atomic weight m, because they are i n f l u e n c e d r e l a t i v e l y l i t t l e by d i f f e r e n c e s of c r y s t a l s t r u c t u r e , can i n theory be a p p l i e d t o the t r a n s i t i o n region as a t e s t o f homogeneity, i . e . , f o r uniform For a homogeneous, self-compressed curve should be a s t r a i g h t stant m.  iron  content.  l a y e r , the v e l o c i t y - d e n s i t y  l i n e p a r a l l e l t o the l i n e s of con-  In f a c t , B i r c h used  this result  to t e s t v a r i o u s  equations of s t a t e f o r c o n s i s t e n c y with t h e assumptions made i n c o n s t r u c t i n g them, as d i s c u s s e d i n the l a s t chapter.  He  f u r t h e r used t h i s r e s u l t t o c a l c u l a t e a mean atomic weight f o r the e a r t h , o b t a i n i n g the value m = 22.5 t 0.5. of temperature,  The e f f e c t  which i s q u a n t i t a t i v e l y Unknown, makes i t  p o s s i b l e t h a t t h i s value i s too high. c o n s t r u c t e d by B i r c h , on the assumption  A density d i s t r i b u t i o n o f uniform m through-  out the e a r t h , would approach B u l l e n ' s Model A i f t h e e f f e c t of temperature  were s i g n i f i c a n t .  The v a l u e o f the mean atomic weight i s c r i t i c a l d e t e r m i n a t i o n of the i r o n content i n the mantle. experiments  t o determine  the e f f e c t  of temperature  v e l o c i t y - d e n s i t y - a t o m i c weight r e l a t i o n s a r e very Using the formula f o r pyroxene (Mg, Fe) S i 0 , 3  for a  Therefore, on B i r c h ' s important.  the i r o n  a s s o c i a t e d w i t h a range of v a l u e s of m c l o s e t o 22.5 i s  content  t a b u l a t e d below. m  Weight Percent  21.5  12.2  22  15.3  22.5  19.3  . 23  ' ' .24.6  N e a r l y i d e n t i c a l r e s u l t s were found olivine  Iron  (Mg, F e ^ S i O ^ .  u s i n g the formula f o r  A mean atomic  weight f o r the mantle  of 22.5 or g r e a t e r would s t r o n g l y favour Ramsey's h y p o t h e s i s . On t h e other hand, a mean atomic weight of 21.5 o r l e s s would be a s e r i o u s argument i n f a v o u r of t h e i r o n core h y p o t h e s i s . In order to determine whether known changes o f c r y s t a l s t r u c t u r e a r e f u l l y adequate to account zone, BIRCH (1961) developed equations.  The f i r s t  f o r the t r a n s i t i o n  and evaluated the f o l l o w i n g two  of these i s the Adams-Williamson  equation g e n e r a l i z e d t o i n c l u d e the e f f e c t content  o\\  and of phase,  i s an i n t e r v a l of depth,  i n g o r mean atomic adiabatic gradient. fined.  of change of i r o n  y d e f i n e s the c l o s e n e s s o f pack-  volume and ^ i s t h e departure  from the  The other symbols a r e as p r e v i o u s l y de-  The second equation r e l a t e s q u a n t i t i e s which can be  measured i n h i g h - p r e s s u r e  experiments,  - 137  -  (2)  dV  i s the change i n v e l o c i t y of compressional waves i n the  i n t e r v a l dz. following  These two  equations can be combined to g i v e the  relation,  " (SL LV«'" ) *\  M  M  It  i s assumed that the constants  ^V/p^)  obtained from experimental data, remain transition  zone.  , may  (3) was  km with the f o l l o w i n g 2.32 The f i r s t  constant through  be n e g l e c t e d .  =1.09  + 3.3lAy  y  the  to  920  - 0.36dm.  r e p r e s e n t s the r e s u l t  and accounts  v e l o c i t y change.  3  p ,  result,  term on the r i g h t  = 0.48g/cm .  T  With these assump-  of o r d i n a r y  f o r l e s s than h a l f of the  For B u l l e n ' s Model A,  t i o n which s a t i s f i e s the v e l o c i t y r e l a t i o n Ay  (<^£/^m)  i n t e g r a t e d by B i r c h from 413  a d i a b a t i c compression, observed  and  I t i s f u r t h e r assumed that the departure  from a d i a b a t i c i t y , ^ t i o n s , equation  m  (3)  the combina-  i s A m =1.0  I f A m = 0, then H y = 0.37g/cm . 3  and  From the  a v a i l a b l e data on the volume changes i n t r a n s i t i o n s to d i f f e r ent c r y s t a l s t r u c t u r e s f o r the probable m a t e r i a l s of the mantle,  B i r c h concludes  that i t appears  l i k e l y that there i s  - 138 little  -  change of i r o n content throughout  the t r a n s i t i o n  BIRCH (1964) has more r e c e n t l y argued  layer.  that the data are  c o n s i s t e n t with u n i f o r m i t y of i r o n content throughout  the  lower mantle, being roughly equal to that of o r d i n a r y diabase or about 10% FeO.  Of course, i f the e a r t h has an i r o n core,  the s u g g e s t i o n of such a low content of i r o n i n the mantle i s undoubtedly  correct.  However, the c o n s i s t e n c y t o which B i r c h  c a l l s a t t e n t i o n does not seem to be c o n c l u s i v e evidence i n favour of such a low i r o n content.  He has shown that the mean  mantle v a l u e of m(22.5) given by him i n 1961  i s consistent  with a c o n s i d e r a b l y g r e a t e r content of i r o n . 10.2  The  lower mantle  I d e n t i f i c a t i o n of the composition of the v a r i o u s zones by comparison of h i g h - p r e s s u r e data with data from seismology i s the most promising method of determining the composition the e a r t h and,  i n p a r t i c u l a r , the nature of the core.  of  Birch  p l a c e d s u f f i c i e n t r e l i a n c e on the s t a t i c h i g h - p r e s s u r e data that he c o n s t r u c t e d an equation of s t a t e f o r the upper mantle using i t .  Such a procedure  r e s t r i c t s p o s s i b l e equations of  s t a t e i n the lower mantle and outer core determined  from  s e i s m i c data . With regard t o extending t h i s procedure  to the lower mantle,  i t must be noted that the p r e s s u r e s i n the lower mantle and core are o n l y a t t a i n a b l e i n the l a b o r a t o r y by the use of shock waves, and any  r e s u l t s w i l l depend on the accuracy  and  - 139 validity  -  of such shock-wave experiments.  Discussing  the  r e s u l t s of shock-wave experiments on d u n i t e , BIRCH (1961) concluded  that "the a p p l i c a t i o n of shock-wave techniques  such m a t e r i a l s has  still  to be p e r f e c t e d , and  that  to  reserva-  t i o n s r e g a r d i n g these p i o n e e r i n g s t u d i e s are warranted."  More  r e c e n t l y , BIRCH (1964) noted that phase t r a n s i t i o n s appear to take p l a c e at somewhat higher than e q u i l i b r i u m p r e s s u r e s shock c o n d i t i o n s and  t h a t , t h e r e f o r e , a complete correspondence  between the d e n s i t y - p r e s s u r e for  under  curves  rocks i s not to be expected.  improvements i n both s e i s m i c and  f o r the mantle and  I t may  be concluded  shock-wave data are  i n order t o s o l v e the problem of the composition  those that  required  of the lower  mantle. The theory  simplest s o l u t i o n f u l l y c o n s i s t e n t with  and  seismology i s that region D between 800  core i s s u b s t a n t i a l l y uniform s t r o n g l y supports cates.  finite-strain  a composition  Since the v a r i a t i o n of  u n i f o r m i t y and applied there.  (BIRCH, 1952). of oxides  The  km  and  the  evidence  r a t h e r than  sili-  i n l a y e r D i s c o n s i s t e n t with  a d i a b a t i c i t y , the Adams-Williamson equation However, as B i r c h p o i n t e d out,  to g i v e p r e c i s e answers to such questions  as:  i t is difficult "Just  great an excess of the temperature g r a d i e n t above the abatic i s permissible? mean temperature?  How  is  how adi-  What are the p e r m i s s i b l e l i m i t s of the much departure  r e c o n c i l e d with the data,?"  from u n i f o r m i t y can  be  At l e a s t approximate answers to  - 140 these questions are r e q u i r e d f o r s o l v i n g the problem  of the  c o n s t i t u t i o n of r e g i o n D. McQUEEN et a l . (1964) u s i n g B i r c h ' s v e l o c i t y - d e n s i t y r e l a t i o n s and t h e i r own equation of s t a t e , c a l c u l a t e d a value of m = 22.7 f o r r e g i o n D, i n agreement with B i r c h ' s value f o r a uniform mantle with m = 22.5  I t i s important  that  although  the data used by McQueen et a l . and by B i r c h are a p p a r e n t l y the same, there i s a l a r g e d i s c r e p a n c y i n t h e i r estimates o f the t o t a l i r o n content, as mentioned i n Chapter 3.  McQueen  et a l . p o i n t out that t h e i r own c a l c u l a t i o n s a r e by no means c o n c l u s i v e and that b e t t e r experimental data a r e needed to e s t a b l i s h the mean composition o f r e g i o n D and whether or not t h i s composition i s uniform.  LANDISMAN et a l . (1965) f i n d  that there i s a s l i g h t decrease of atomic weight  i n the lower  mantle,  i n the upper  mantle. weight  preceded  by a s l i g h t  i n c r e a s e with depth  S i g n i f i c a n t l y , they a l s o i n f e r an average f o r the mantle between 22 and 23.  The lowest 200 km o f the mantle, posed  atomic  some problems.  The V a r i a t i o n of  t a b l e s i s zero i n t h i s r e g i o n .  known as r e g i o n D", has  Atf/AA"  in Jeffreys'  BIRCH (1952) p o i n t e d out that  i f the v e l o c i t y curves a r e continued from r e g i o n D' to the core boundary with no change o f s l o p e , the d i f f e r e n c e o f v e l o c i t y i s l e s s than 0.2 km/sec, an amount i n s u f f i c i e n t t o produce  a s i g n i f i c a n t change i n t r a v e l time;  furthermore,  the angle of emergence o f a r a y g r a z i n g the core i s probably  - 141 u n c e r t a i n by s e v e r a l degrees.  BULLEN (1949, 1963a, 1963b)  has shown, n e g l e c t i n g temperature e f f e c t s , that the f l a t t e n i n g of the v e l o c i t y g r a d i e n t i m p l i e s s i g n i f i c a n t region D",  inhomogeneity i n  with an i n c r e a s e of d e n s i t y t h r e e times g r e a t e r  than that due to compression alone.  Assuming  that  the  f l a t t e n i n g i n region D" i s r e a l , "RAMSEY (1949) has o f f e r e d a different  explanation.  Using s e i s m i c data i n the thermo-  dynamic equation f o r the f r e e energy, he c a l c u l a t e d an e x c i t a t i o n energy of about 7e.v. j u s t o u t s i d e the core boundary about 24 e.v. j u s t which now  inside.  Assuming  and  :  a temperature o f 10,000°,  seems to be at l e a s t twice the a c t u a l  temperature  there, he observed that only one molecule i n 10^^ would  be  e x c i t e d at the top of the core whereas the e x c i t a t i o n of e l e c t r o n s at the bottom of the mantle could be  significant.  S i n c e 7.e.v. r e p r e s e n t s the c e n t r e of the conduction band* the bottom of the band at such high p r e s s u r e s i s p r o b a b l y only 4 or 5 e.v. above the ground s t a t e .  At a temperature of 10,000°.  the f r a c t i o n of the molecules e x c i t e d by thermal a g i t a t i o n would be of the order of 1 per cent and t h i s would modify the e l a s t i c constants i n region D".  The anomaly would  decrease e x p o n e n t i a l l y with d i s t a n c e from the core because of the decrease of e x c i t a t i o n  10.3  appreciably  boundary  energy.  The Core Based on i n t e r p o l a t i o n s between equations of s t a t e  - 142 experimentally pressures  -  determined by Bridgman f o r v a r i o u s m a t e r i a l s at  up to 1 0  5  atmospheres and  equations  of s t a t e of  v a r i o u s elements determined using a g e n e r a l i z e d Fermi-Thomas theory by FEYNMAN et a l . (1949) a p p l i c a b l e only at g r e a t e r than 1 0  7  atmospheres, ELSASSER (1951) concluded  a s i l i c a t e composition cluded."  pressures that  f o r the region E "appears to be  ex-  BULLEN (1952a, b ) , however, has demonstrated t h a t  E l s a s s e r ' s r e s u l t s are u n s a t i s f a c t o r y , a c r i t i c i s m by E l s a s s e r .  accepted  B u l l e n p o i n t e d out that E l s a s s e r ' s i n t e r p o l a -  t i o n s g i v e d e n s i t y g r a d i e n t s i n r e g i o n D which are more than twice those curves  i n Models A and B and he modified  Elsasser's  to g i v e a d e n s i t y g r a d i e n t i n region D i n accord  the r e s u l t s from seismology.  with  I f t h e r e were no d i s c o n t i n u i t y  at the core-mantle boundary, then the modified  curve  would  g i v e an unreasonably low value of the atomic weight i n region D,  too low to f i t an u l t r a - b a s i c rock composition.  On  the  other hand, "the d e n s i t y data f o r the mantle of Model A or Model B,  considered  i n r e l a t i o n t o the Feynman r e s u l t s ,  f u l l y c o n s i s t e n t with and a c t u a l l y g i v e some f u r t h e r  are  support  to the view that the r e g i o n E c o n s i s t s of modified u l t r a b a s i c rock that has undergone a d i s c o n t i n u o u s B u l l e n used h i s modified  density increase."  i n t e r p o l a t i o n s to estimate  the  c h a r a c t e r i s t i c atomic number f o r each of the regions D, E G;  but the s i g n i f i c a n c e of these estimates  the v a l i d i t y ,  questioned  depends  and  on(1)  by Ramsey, of a p p l y i n g the Thomas-  - 143 Fermi-Dirac model even at p r e s s u r e s as "low" as 30 m i l l i o n atmospheres and (2) the v a l i d i t y o f the c o m p r e s s i b i l i t y p r e s s u r e hypothesis between pressures of 3.2 x 10^ and 30 x 10  6  atmospheres.  I f (1) and (2) are v a l i d , then the  c h a r a c t e r i s t i c atomic  number i n region E i s a p p r e c i a b l y  than 28 and the c h a r a c t e r i s t i c atomic  lower  number at the top o f the  i n n e r core i s at l e a s t 7 u n i t s g r e a t e r than f o r r e g i o n E. f u r t h e r c o n c l u s i o n that the c h a r a c t e r i s t i c atomic  A  number i n  the i n n e r core i n c r e a s e s by 7 u n i t s towards t h e c e n t r e , g i v i n g a minimum value of 37 at the e a r t h ' s c e n t r e , depends on the v a l i d i t y of J e f f r e y s ' v e l o c i t y g r a d i e n t s i n regions F and G. KNOPOFF and UFFEN (1954) improved the i n t e r p o l a t i o n of E l s a s s e r by extending Bridgman's data u s i n g the Birch-Murnaghan s e m i - e m p i r i c a l theory o f f i n i t e s t r a i n .  T h e i r r e s u l t s are i n  s u b s t a n t i a l agreement with B u l l e n ' s estimate of 23 f o r the c h a r a c t e r i s t i c atomic  number i n r e g i o n E.  A l a t e r comparison,  by KNOPOFF and MACDONALD (1960) of s e i s m i c data with the r e s u l t s o f AL'TSHULER et a l . ' s (1958) shock-wave experiments on i r o n r e v e a l e d that the d i s c r e p a n c y between the d e n s i t y of solid cent.  i r o n at 0°K and the d e n s i t y of the core i s about 20 per To account  f o r the s m a l l e r d e n s i t y o f the core, Knopoff  and MacDonald suggested  that i t i s an a l l o y of i r o n and  silicon. Various authors have s i m i l a r l y estimated  the d i s c r e p a n c y  - 144  -  between the d e n s i t y of i r o n and  the d e n s i t y of the  o b t a i n i n g values between 10 and  20 per cent  BIRCH, 1952,  1961,  LYTTLETON, 1963; estimates The  1964;  (RAMSEY,  AL TSHULER.and KORMER,  1949;  1961;  1  McQUEEN et a l . , 1964).  core,  The more recent  have p l a c e d the d i s c r e p a n c y c l o s e r to 10 per  usual e x p l a n a t i o n i s that i r o n i s a l l o y e d with  cent.  lighter  elements, i t being assumed that an a l l o y with n i c k e l or other h e a v i e r elements would i n c r e a s e the d i s c r e p a n c y . recent experimental p r e s s u r e s of 300  work with  However,  i r o n - n i c k e l a l l o y s up to  kb i n d i c a t e t h a t an a l l o y of 90% i r o n  and  10% n i c k e l would be about 10% l i g h t e r than pure i r o n at to 3500 kb and  3000°C (TAKAHASHI and BASSETT).  appears p o s s i b l e that shock-wave experiments on a l l o y s w i l l d i s p e l one  1500  I t thus nickel-iron  of the more s e r i o u s arguments a g a i n s t  an " i r o n " c o r e . It would be too much of a c o i n c i d e n c e to f i n d that m e t a l l i z e d s i l i c a t e s and Therefore,  i r o n had  the same equation  of s t a t e .  i f shock-wave experiments confirm the c l o s e  ment observed  agree-  i n "low" p r e s s u r e experiments between the  equation of s t a t e of the core m a t e r i a l and of an a l l o y of i r o n and  10% n i c k e l , which are approximately  of these metals u s u a l l y found  Comparisons of equations  the p r o p o r t i o n s  i n iron meteorites,  be a s t r o n g argument i n favour of an i r o n  90%  t h i s would  core.  of s t a t e f o r m a t e r i a l s under  high p r e s s u r e with the equation  of s t a t e f o r the core are made  - 145  -  e i t h e r by n e g l e c t i n g the " t r a n s i t i o n " region F, i . e . , ' by smoothing out the equation al.,  1964)  of s t a t e of the core  (McQUEEN et  or by n e g l e c t i n g the e n t i r e inner core i n c l u d i n g  region F (BIRCH, 1964).  However, i n the r e a l e a r t h ,  ences between regions E and G and  the e x i s t e n c e of the  mediate region F, are d i s t i n c t i v e f e a t u r e s of the On  the b a s i s of o b s e r v a t i o n s  i n f e r r e d a negative r e g i o n F and F and G.  of two  v e l o c i t y gradient  earthquakes, J e f f r e y s  i n the  "transition" regions  Although the evidence at that time supported v e l o c i t y gradient,  that the s o l u t i o n f o r t h i s region was b a s i s of o b s e r v a t i o n s  s e p a r a t i n g the outer and  not unique.,  of the e x i s t e n c e  increases  amounting to about 10%;  the 1964)  of region  F,  there  i n the v e l o c i t y of compresregion  F.  the v e l o c i t y g r a d i e n t s at the bottom  i n regions  F and G are  BULLEN (1949, 1963b, 1965b) has gradients  On  In B o l t ' s model,  s i o n a l waves i n the core, the t o t a l jump across  (E") of r e g i o n E and  cautioned  inner core, but proposed a d i f f e r e n t  v e l o c i t y d i s t r i b u t i o n i n t h i s region. discontinuous  Jeffreys  the  of 24 more earthquakes BOLT (1962,  supported J e f f r e y s ' c o n c l u s i o n  core.  inter-  core.  a d i s c o n t i n u i t y i n the v e l o c i t y between  i n f e r e n c e of a negative  are two  differ-  i m p l i e d by J e f f r e y s ' and  zero.  considered  the  density  B o l t ' s v e l o c i t i e s f o r the  In h i s e a r l i e r a n a l y s i s , he came to the f o l l o w i n g  conclusions.  Either v e l o c i t y d i s t r i b u t i o n i s consistent  a homogeneous outer core, e x c l u d i n g  r e g i o n E" i n B o l t ' s  with  - 146 distribution.  B o l t ' s d i s t r i b u t i o n f o r E", F and G implies  mild chemical slight  inhomogeneity i n these r e g i o n s .  However, a  v e l o c i t y g r a d i e n t , c o n s i s t e n t with o b s e r v a t i o n s ,  reduce t h i s inhomogeneity.  would  J e f f r e y s ' d i s t r i b u t i o n implies a  l a r g e inhomogeneity i n region F and a mild inhomogeneity i n G. It a l s o i m p l i e s a high c e n t r a l d e n s i t y B u l l e n ' s Model B ) .  (about 18 g/cm on 3  B o l t ' s d i s t r i b u t i o n i s c o n s i s t e n t with a  c e n t r a l d e n s i t y which might be l e s s than 15 g/cm . values  These  should be compared with a value of about 13 g/cm f o r 3  the d e n s i t y o f i r o n at the temperatures and p r e s s u r e s earth's c e n t r e  at the  (BIRCH, 1964).  From equation  (1) i n Chapter 9, a d i s c o n t i n u o u s  increase  i n the compressional wave v e l o c i t y 0< i m p l i e s e i t h e r a d i s continuous i n c r e a s e i n k,^( or both, s i n c e () i s an i n c r e a s i n g f u n c t i o n of depth.  The magnitude o f the i n c r e a s e i n & from  r e g i o n E t o region G (about 10% according according  to Jeffreys),  i n n e r core,  t o B o l t and 20%  i s regarded as evidence of a s o l i d  i.e., a significant  increase i n ^ A .  c o m p r e s s i b i l i t y - p r e s s u r e hypothesis  I f Bullen's  i s c o r r e c t , then d i s c o n -  t i n u i t i e s i n CX n e c e s s i t a t e d i s c o n t i n u i t i e s i n . Further  i n v e s t i g a t i o n s are r e q u i r e d t o determine whether  a discontinuous  jump i n p< i s c o n s i s t e n t with the hypothesis  that such a d i s c o n t i n u i t y marks the boundary between (a) the l i q u i d and s o l i d s t a t e of the same m a t e r i a l , in a l i q u i d  (b) one m a t e r i a l  s t a t e and another a l s o i n a l i q u i d s t a t e , or (c)  - 147 one m a t e r i a l i n a l i q u i d In  s t a t e and another i n a s o l i d  state.  any case, i t i s c l e a r that the v e l o c i t y d i s t r i b u t i o n s of  J e f f r e y s and B o l t are not c o n s i s t e n t with the view that F i s a t r a n s i t i o n r e g i o n between l i q u i d material.  Furthermore,  Gutenberg's  bears some resemblance the neighbourhood  and s o l i d  iron or other  s o l u t i o n f o r F, which  t o the v a r i a t i o n of v e l o c i t y found i n  of the m e l t i n g p o i n t i n the few cases  measured (BIRCH, 1952), does not agree w i t h recent s e i s m i c evidence (CALOI, 1961;  BOLT, 1964);  i t a l s o i m p l i e s a very  l a r g e d e v i a t i o n from the c o m p r e s s i b i l i t y - p r e s s u r e hypothesis over a wide range; o f depths  (BULLEN, 1936).  I t thus  appears  that the nature of the c o r e i s more complex than the "thermos t a t " model d i s c u s s e d i n Chapter 7. In h i s most recent paper, BULLEN (1965b) has c o n s i d e r e d the p o s s i b i l i t y  of a c e n t r a l d e n s i t y ,  ^ , l e s s than 13 g/cm , 3  o  using B o l t ' s compressional wave v e l o c i t i e s f o r the c o r e . E s s e n t i a l l y such a low c e n t r a l d e n s i t y r e q u i r e s negative g r a d i e n t s of the shear wave v e l o c i t y i n both r e g i o n s F and G, i.e.,  r i g i d i t y i n F and G d e c r e a s i n g towards the bottom of  each l a y e r .  H i s minimum v a l u e of ^  , on extreme, but never/  3  t h e l e s s p l a u s i b l e assumptions, i s 12.57 g/cm .  He c o n s t r u c t s  two other models on l e s s extreme assumptions which g i v e £ 13 g/cm However, i f F i s assumed t o be l i q u i d , then the minimum value of ^ liquid,  Q  i s 13.5 g/cm .  then the minimum value o f ^  0  I f both F and G are  / 3 i s 14.67 g/cm ; i f ,  - 148 a l s o , k i s continuous, B u l l e n now  the minimum value of  ^  i s 15.29  g/cm .  c o n s i d e r s the l a t t e r c a l c u l a t i o n s as a d d i t i o n a l  evidence that the i n n e r core i s s o l i d .  3  - 149 11. 11.1  PLANETARY MODELS A s t r o n o m i c a l Data The d i f f e r e n c e s between a c c e p t a b l e estimates o f the mean  diameter, mass and mean d e n s i t y of Mercury, are s i g n i f i c a n t  i n comparative  these p l a n e t s and the e a r t h .  Venus and Mars  s t u d i e s of the c o n s t i t u t i o n of A summary o f some of these  esti-  mates i s u s e f u l before e v a l u a t i n g the p o s s i b l e v a l i d i t y of v a r i o u s p l a n e t a r y models d i s c u s s e d i n the next s e c t i o n . data below were compiled from JEFFREYS (1934, 1937),  The  RAMSEY  (1948), BIRCH (1952, 1964), MACDONALD (1962), PLAGEMANN (1965) and KDVACH and ANDERSON  (1965).  Mean diameter o f Mercury  (km.)  J e f f r e y s , 1934 J e f f r e y s , 1937 Ramsey, 1948 L e v i n , 1962 D o l f u s , 1963  5000 4900 ± 150 5000 t 250 4800 4892  Mean diameter of Venus (km.) J e f f r e y s , 1934 J e f f r e y s , 1937 Ramsey, 1948 Martynov, 1961 Smith, 1964 de Vaucouleurs, 1964  12,400 12,300 12,400 12,200 12,100 12,170  ± 100 + 100 + 68 + 3 + 20  Mean diameter of Mars (km.) Trumpler, 1927 Rabe, 1929 J e f f r e y s , 1937 R u s s e l , Dugan & Stewart, 1945 D o l f u s , 1952 Camichel, 1954 L e v i n , 1962 de Vaucouleurs, 1964  6, 620 6, 846 6,770 6,792 6, 670 6, 720 6,760 6,724  + 274 ± 22 + 16 + 16 +  20  +  20  - 150 Masses of Mercury, Venus and Mars (gm.) Mercury  Rabe, 1950  0.326 +0.002 x 1 0  Venus  J e f f r e y s , 1937 Ramsey, 1948 L e v i n , 1962 Mariner I I v a l u e  4.911 + 4.88 + 4.863 x 4.8695+  J e f f r e y s , 1937 Ramsey, 1948 Brouwer and Clemence, 1961  0.6431+0.0010 x 1 0 0.6443+0.0013 x 1 0  Mars  D e n s i t y of Mercury  (gm/cm ) 3  Urey,1952 Urey, 1957 W i l d t , 1961 D o l f u s , 1963 D e n s i t y of Venus  5.0 5.46 5.46 5.31 + 0.27 (gm/cm ) 3  J e f f r e y s , 1934 J e f f r e y s , 1937 W i l d t , 1942 Rabe, 1950 Smart, 1941 Urey, 1952 Urey, 1957 W i l d t , 1961 L e v i n , 1962 D e n s i t y of Mars Trumpler, 1926 J e f f r e y s , 1934 J e f f r e y s , 1937 Whipple, 1941 Ramsey, 1948 Urey, 1950 Rabe, 1950 Smart, 1951 Urey, 1952 Urey, 1957 W i l d t , 1961 L e v i n , 1962  4.86 5.04 ± 0.12 4. 86 4. 99 5. 21 4. 9 5. 06 5. 06 5. 11 (gm/cm ) 3  4. 21 3. 96 3. 958+ 0.031 3. 96 3. 93 + 0.03 4. 16 3. 93 + 0.04 3. 94 4.2 4.24 4. 12 3. 95  0.015 x 10 0.03 x 1 0 10 0.006 x 1 0  2 7  2 7  2 7  0.6434+0.0006 x 1 0  2 7  2 7 2 7  2 7  - 151 11.2  P l a n e t a r y Models Comparative p l a n e t a r y models must be regarded  siderable caution.  with  con-  The v a l i d i t y o f a p l a n e t a r y model depends  on the v a l i d i t y of the assumptions made i n c o n s t r u c t i n g i t . These assumptions o r hypotheses can be grouped i n t o  three  categories. 1.  Assumptions about the composition and p l a n e t s .  of the e a r t h  2.  Other assumptions made i n c o n s t r u c t i n g an equation of s t a t e f o r the e a r t h and a p p l y i n g i t t o another planet.  3.  Assumptions about the o b s e r v a t i o n a l data from p l a n e t a r y astronomy.  The wide range o f p o s s i b l e d e n s i t i e s i s an i n d i c a t i o n of the u n c e r t a i n t y i n p l a n e t a r y models and i n comparisons a r i s i n g out of i n d e f i n i t e a s t r o n o m i c a l it d i f f i c u l t ,  data.  i f not impossible,  T h i s u n c e r t a i n t y makes  t o t e s t the v a l i d i t y o f the  v a r i o u s p r i n c i p a l hypotheses given i n the i n t r o d u c t i o n t o this thesis.  I t i s p o s s i b l e to r e c o n c i l e widely  hypotheses on the nature  divergent  of the earth's core and the com-  p a r a t i v e c o n s t i t u t i o n of the p l a n e t s with a c c e p t a b l e mical  astrono-  data I f the earth does have an i r o n core, then p l a n e t a r y  comparisons a r e p a r t i c u l a r l y u n c e r t a i n , s i n c e the s t a t e o f each p l a n e t must depend on t h e extent has  o f core formation  which  taken p l a c e i n i t . We a l r e a d y know from determinations o f  the moment o f i n e r t i a of Mars and from recent  satellite  - 152 o b s e r v a t i o n s of i t s s u r f a c e , has  that the h i s t o r y of i t s i n t e r i o r  been s i g n i f i c a n t l y d i f f e r e n t from that Present u n c e r t a i n t i e s  of the e a r t h .  about the o r i g i n of the s o l a r  system make i t impossible t o assume the v a l i d i t y of t h e hypot h e s i s that  the dust c l o u d  formed was c o m p o s i t i o n a l l y  from which the t e r r e s t r i a l  planets  homogeneous, although t h i s hypo-  t h e s i s may be c l o s e to the t r u t h .  Nor can we yet use  a s t r o n o m i c a l arguments to d e f i n i t e l y e s t a b l i s h t h e nature o f variations The  i n composition i n t h i s dust  cloud.  only v a r i a t i o n which can have a s i g n i f i c a n t e f f e c t  on the mean d e n s i t i e s of the p l a n e t s i s a v a r i a t i o n i n i r o n content.  Such a v a r i a t i o n probably depends on d i f f e r e n c e s  i n the s t a t e of o x i d a t i o n highly  reduced p l a n e t  portion  of i r o n .  of the t e r r e s t r i a l p l a n e t s ,  a  being expected t o have a g r e a t e r pro-  Such a reduced s t a t e could  e i t h e r be t r a c e d  to a high-temperature stage i n the e a r l y h i s t o r y of the s o l a r system or to reducing processes i n the e a r l y h i s t o r y of the planets.  In t h i s regard, LEVIN (1964) concluded that  v i c i n i t y of Mercury i r o n would have been o x i d i z e d  i n the  i n the  presence of oxygen i f the s o l a r r a d i a t i o n had always been the same as i t i s today.  Thus, the i n d i c a t e d  Mercury, even though i t i s not a c c u r a t e l y that  high d e n s i t y of known, i s evidence  an e a r l y , high-temperature stage, when some of the i r o n  i n the innermost zone of the dust cloud  existed  i n a reduced  s t a t e , occurred d u r i n g the f o r m a t i o n of the p l a n e t s .  - 153 Chemical processes  -  i n the p l a n e t s which would reduce i r o n  depend on the presence of carbonaceous compounds which are gaseous at r e l a t i v e l y low t e m p e r a t u r e s . that such compounds were present  I t i s probably  true  i n g r e a t e r abundances i n the  a s t e r o i d a l zone of the gas-dust cloud than i n the zones from which Venus, E a r t h and Mars formed.  However, these  abundances  undoubtedly changed i n time because of changes i n the o p a c i t y of the dust  cloud and perhaps a l s o because of changes i n  solar radiation.  These f a c t o r s and  the f u r t h e r p o s s i b i l i t y  that the reducing  r o l e which carbonaceous compounds played  have depended on the s i z e of the p l a n e t g r e a t e r i n a l a r g e r one due make i t impossible  a more exact system and  ( p o s s i b l y being  to the r e t e n t i o n of ah atmosphere)  to d e f i n i t e l y e s t a b l i s h the nature  v a r i a t i o n i n the composition  may  of Venus, E a r t h and Mars  of a without  knowledge of the e a r l y h i s t o r y of the s o l a r  a more thorough study  of the p o s s i b l e  chemical  history. With these be d i s c u s s e d .  r e s e r v a t i o n s , v a r i o u s p l a n e t a r y models can "Ramsey's attempt t o  r e c o n c i l e the  of an o v e r a l l s i m i l a r i t y of composition Venus and Mars with the hypothesis cores of Venus and order  the e a r t h , was  to r e c o n c i l e these two  B u l l e n ' s E a r t h Model A. considered  most probable,  of  now  hypothesis  the moon, e a r t h ,  of m e t a l l i z e d s i l i c a t e discussed  i n Chapter 4.  hypotheses, Ramsey modified  With the mean d e n s i t i e s c u r r e n t l y an even g r e a t e r m o d i f i c a t i o n  of  In  - 154 Model A would be r e q u i r e d .  In Chapter  9, i t was concluded on  the b a s i s of s t u d i e s by B i r c h that the equation of s t a t e which r e s u l t s from modifying Model A t o i n c l u d e a c e n t r a l condensat i o n of h e a v i e r matter  i s probably  incorrect.  A comparison of  h i g h - p r e s s u r e data with s e i s m i c data f a v o r s the hypothesis that region D i s the most homogeneous i n the e a r t h r a t h e r than inhomogeneous as i m p l i e d by Ramsey's modified Model A. As e a r l y as 1937, JEFFREYS showed that the moon and t h e e a r t h ' s mantle could have the same composition  i f Bernal's  hypothesis i s c o r r e c t that the 20° d i s c o n t i n u i t y i s due t o a p r e s s u r e m o d i f i c a t i o n of u l t r a b a s i c rock. KOVACH and ANDERSON  (1965) found  d e n s i t y and moment of i n e r t i a  Furthermore,  that the observed mean  of the moon are only c o n s i s t e n t  with a core which i s l e s s than 8.5% of t h e moon's t o t a l mass. It i s e v i d e n t that any s i g n i f i c a n t d i f f e r e n c e between the i  composition  of the e a r t h ' s core and mantle i s i n c o n s i s t e n t  with the hypothesis that t h e e a r t h and moon have the same o v e r a l l chemical  composition.  The a s t r o n o m i c a l data of Mercury are t h e most u n c e r t a i n of the t e r r e s t r i a l p l a n e t s .  Nevertheless, i t i s possible, t o  conclude that the uncompressed d e n s i t y of Mercury i s g r e a t e r than that of any of the other t e r r e s t r i a l p l a n e t s , probably because of Mercury's p r o x i m i t y to the sun. hypotheses  In the v a r i o u s  on the c o n s t i t u t i o n o f t h e t e r r e s t r i a l p l a n e t s ,  Mercury i s c o n s i d e r e d a s p e c i a l case.  PLAGEMANN  (1965) has  - 155 determined  -  an equation of s t a t e f o r Mercury on the  assumption  that i t has a mantle and core, the mantle having the same c o n s t i t u t i o n as the upper mantle of the e a r t h and the core .  /  composed of a m a t e r i a l approximately iron.  T h i s l a t t e r assumption  3  2 g/cm  l e s s dense than  f o l l o w s from the  observed  d i f f e r e n c e i n d e n s i t y between the e a r t h ' s core and under high p r e s s u r e . Takahashi it  iron  However, the experimental work of  and B a s s e t t with i r o n - n i c k e l a l l o y s , which makes  reasonable to i d e n t i f y the " i r o n - c o r e " hypothesis with a  m a t e r i a l whose composition  i s s i m i l a r to that of m e t e o r i t e s ,  i m p l i e s that at the lower p r e s s u r e s i n Mercury, core m a t e r i a l would not be l e s s dense than i r o n .  Hence, Plagemann's con-  c l u s i o n that Mercury i s composed mostly of core m a t e r i a l i s probably not v a l i d , although a comparatively heavy comp o s i t i o n f o r Mercury i s d e f i n i t e l y  indicated.  A l s o , the  recent d i s c o v e r y of the slow r e t r o g r a d e r o t a t i o n of Mercury i n v a l i d a t e s some of the d e t a i l s of Plagemann's thermal  history  of the p l a n e t , but does not a f f e c t h i s main c o n c l u s i o n that Mercury has a non-molten  interior.  The mean d e n s i t y of the earth's, mantle f a l l s below the minimum mean d e n s i t y of Venus;  hence, JEFFREYS (1937) con-  cluded that Venus has a c e n t r a l dense c o r e . d e n s i t y of 5.04  g/cm  3  Assuming a mean  f o r the whole p l a n e t , J e f f r e y s  calcu-  l a t e d that the r a t i o of the core mass to the t o t a l mass f o r Venus i s 0.22;  the value f o r the e a r t h i s 0.32.  BULLEN  - 156  -  (1952b) concluded from t h i s r e s u l t that the hypothesis  that  r e g i o n E of the e a r t h i s c h e m i c a l l y d i s t i n c t from the mantle i s untenable i f one same composition.  assumes that Venus and  the e a r t h have the  I t i s perhaps s i g n i f i c a n t  that J e f f r e y s was  in this  r e q u i r e d to make p r a c t i c a l l y no  p o l a t i o n of the e a r t h ' s Venus, the pressures  equation  regard  extra-  of s t a t e i n a p p l y i n g  i t to  at the boundary of the core t u r n i n g  to be n e a r l y the same i n both p l a n e t s .  out  This circumstance  must have impressed Ramsey. BULLEN (1949b) attempted to show the c o m p a t i b i l i t y of Ramsey's and  hypothesis  the hypothesis  composition.  of a phase change at the core boundary  that Venus and  Ramsey had  nomical data, M « 4.88  the e a r t h have the same  a l r e a d y found, assuming the a s t r o -  x 10  2 7  g and  R = 6200 km f o r Venus, to  be c o r r e c t , that B u l l e n ' s Model A r e q u i r e d some m o d i f i c a t i o n i n order to make these two the a s t r o n o m i c a l  hypotheses compatible.  data M - 4.91  x 10  2 7  g and  Accepting  R = 6150  km  Venus, B u l l e n found that a m o d i f i c a t i o n of h i s Model A  for along  the l i n e s suggested by h i s c o m p r e s s i b i l i t y - p r e s s u r e hypot h e s i s , a c t u a l l y made things worse. the a s t r o n o m i c a l  data  However, amendment of  i n the d i r e c t i o n of i n c r e a s i n g the  r a d i u s tended to reduce the discrepancy,  but  not  sufficiently,  27 With a mass of 4.88 u s i n g Model A, theses;  x 10  g, a r a d i u s of 6285 km  i s needed,  to o b t a i n c o m p a t i b i l i t y between the two  t h i s value of the radius i s o u t s i d e  hypo-  the range of  - 157 uncertainty. data  and  pressure  -  Having shown that amendment to the  astronomical  m o d i f i c a t i o n of Model A using h i s c o m p r e s s i b i l i t y hypothesis  of the two  are unable to e s t a b l i s h the c o m p a t i b i l i t y  hypotheses, BULLEN (1949b) suggested that  t i o n of the equation  of s t a t e of the e a r t h i n other ways,  such as Ramsey's suggestion c e n t r e , was  necessary.  of i n c r e a s e d d e n s i t y towards the  Later  (1952b), BULLEN suggested that  Venus, as w e l l as the other t e r r e s t r i a l p l a n e t s , has core.  modifica-  an  inner  However he d i d not demonstrate i n the case of Venus  that t h i s a d d i t i o n a l hypothesis  made the other  two  hypotheses  more compatible. KOVACH and ANDERSON (1965) re-examined the question c o m p a t i b i l i t y of the hypothesis  of a c h e m i c a l l y d i s t i n c t  i n both the e a r t h and  the hypothesis  composition  Venus and  of these p l a n e t s  i s the same.  s t a t e which they used i s d e s c r i b e d  The  of  the  core  that the  gross  equation  of  i n Chapter 9.  They found  that the mean d e n s i t y i n t h e i r model i s w i t h i n 0.4  per  cent  of the temperature c o r r e c t e d upper l i m i t f o r the mean d e n s i t y of Venus ( s o l i d body r a d i u s 6050 km and  mean d e n s i t y 5.25g/cm ). 3  A r e d u c t i o n of the core to t o t a l p l a n e t a r y mass r a t i o from 0.32  to 0.30  i s compatible with  i n c r e a s i n g the r a d i u s to  km.  UREY's (1952) c o n c l u s i o n that Venus i s so s i m i l a r to  e a r t h that i t can be made to f i t any the e a r t h i s a p p a r e n t l y  theory  data  and  the  that accounts f o r  t r u e i n view of the present  t a i n t i e s i n both a s t r o n o m i c a l  6100  the equation  uncerof s t a t e  - 158 of the e a r t h .  -  I t i s a l s o apparent,  of the diameter  however, that r e s o l u t i o n  of Venus i n the d i r e c t i o n of one of the  limit-  i n g values would f a v o r one or the other of the models d e s c r i b e d i n the l a s t  two paragraphs.  The most recent measurement of  the diameter by de Vaucouleurs  f a v o r s the lower value and  hence supports the c o m p a t i b i l i t y of the hypothesis of a c h e m i c a l l y d i s t i n c t core and the hypothesis that the composition  of Venus and  overall  the e a r t h i s n e a r l y the same.  When JEFFREYS (1937) c a l c u l a t e d the mean d e n s i t y of Mars, assuming that i t has a c o n s t i t u t i o n s i m i l a r to the e a r t h ' s mantle, he obtained a value of 3.56  g/cm , which i s c o n s i d e r 3  ably below the range of a c c e p t a b l e v a l u e s . a c t u a l mean d e n s i t y of Mars i s 3.96,  Assuming t h a t the  J e f f r e y s c a l c u l a t e d that  the c o r e t o t o t a l p l a n e t a r y mass r a t i o f o r Mars must be about 0.16. In h i s Paper 1 on the c o n s t i t u t i o n of Mars, BULLEN (1949c) found that the d i s c r e p a n c y between the hypothesis of a c h e m i c a l l y i d e n t i c a l composition  f o r Mars and  the e a r t h and  Ramsey's phase change hypothesis i s much l e s s than the d i s crepancy found by J e f f r e y s between the former the hypothesis of an i r o n core. assumptions, moved.  hypothesis  Moreover, with  and  certain  the f i r s t - m e n t i o n e d d i s c r e p a n c y can be f u l l y r e -  I f Model B i s used  i n s t e a d of Model A and  i f Mars and  the e a r t h are assumed to have c h e m i c a l l y d i s t i n c t  i n n e r cores  which are p r o p o r t i o n a l l y of the same s i z e , then the  two  - 159 hypotheses  are compatible f o r a mass of 6.442 x 10  r a d i u s of 3391 Later,  g and a  km.  i n h i s Paper 2, BULLEN (1957) r e c o n s i d e r e d the  problem i n the l i g h t of Kuiper's lower value of the r a d i u s of Mars (3330 km),  and a l s o took i n t o account  e l l i p t i c i t y of the f i g u r e of Mars.  the measured  With the same  hypotheses  as above and with Kuiper's value of the r a d i u s , B u l l e n found that i t i s improbable  that Mars has a core with a r a d i u s  g r e a t e r than 900 km.  Values of the e l l i p t i c i t y f o r core  r a d i i between 900 km and  zero show that a mixture of uncom-  bined i r o n and m a t e r i a l of the composition  of the e a r t h ' s  mantle would c o n t a i n between 2 and 3^ per cent more uncombined i r o n than the e a r t h ' s mantle as given i n Model B. Hence B u l l e n concluded  that o n l y s m a l l m o d i f i c a t i o n s of  Ramsey's hypothesis that the core i s a high p r e s s u r e m o d i f i c a t i o n of the mantle m a t e r i a l , are r e q u i r e d f o r c o m p a t i b i l i t y with the hypothesis that the o v e r a l l composition of Mars and the e a r t h i s the same.  I t must be noted, however, that these  m o d i f i c a t i o n s imply d i f f e r e n t  o v e r a l l chemical  compositions  of  the moon and the e a r t h , thus to some extent negating  of  the b a s i c arguments f o r Ramsey's h y p o t h e s i s .  one  I t i s per-  haps more l i k e l y t h a t , i f Ramsey's hypothesis i s c o r r e c t , Mars has a s l i g h t l y g r e a t e r i r o n content than the e a r t h . D i s c u s s i n g the many "degrees  of freedom" i n c o n s t r u c t i n g  a p l a n e t a r y model, where by "degrees  of freedom" he means  - 160  -  u n c e r t a i n t i e s i n the r e l e v a n t data, MACDONALD (1962) concludes that a unique s o l u t i o n i s not p o s s i b l e . s u r f a c e d e n s i t y and  reaches s i g n i f i c a n t  conclusions.  (3.8 in  - 4.0  i s one g/cm  the dynamically  constructs  i n s p i t e of the  value of the r a d i u s of Mars (~3310 km) model c o n s i s t e n t with  ellipticity,  assuming that  Mars are i r o n , MacDonald  s e v e r a l d i f f e r e n t models f o r Mars and,  ellipticity  the  core r a d i u s as v a r i a b l e s and  the core of the e a r t h and  certainties,  Using  I f the  unlower  i s adopted the  obtained  only  value of  the  i n which the s u r f a c e d e n s i t y i s high  ), and  there i s no l a r g e - s c a l e inhomogeneity  the form o f an inner m e t a l l i c core.  On  the other hand, a  somewhat l a r g e r radius  (~3345 km)  i s c o n s i s t e n t with  surface density  g/cm  a small core, though such  (^3.5  ) and  a core would be l e s s than 1 per Mars.  The  composition  sumed composition  a lower  cent of the t o t a l mass of  of Mars would then d i f f e r from the  of the e a r t h , i f the e a r t h has an i r o n  These r e s u l t s are roughly s i o n s of J e f f r e y s and  c o n s i s t e n t with  the e a r l i e r  precore.  conclu-  Bullen.  KOVACH and ANDERSON (1965) t e s t e d the c o m p a t i b i l i t y of the hypotheses that the e a r t h has and  an  i r o n core and  the e a r t h have the same composition.  that Mars  They concluded  Mars can be s i m i l a r to an u n d i f f e r e n t i a t e d e a r t h , but provided The  the lower value of the r a d i u s , 3310  km,  only  i s correct.  recent work of de Vaucouleurs f a v o r s a high value of  r a d i u s , v i z . 3362 km.  The  that  the  most probable i n t e r p r e t a t i o n of  -  161  -  t h i s value of the r a d i u s , i s that Mars has l e s s i r o n than the e a r t h on the i r o n core hypothesis or more i r o n than the e a r t h on Ramsey's h y p o t h e s i s .  - 162 12.  CONCLUSIONS It has not proved p o s s i b l e on the b a s i s of the evidence  considered i n t h i s t h e s i s t o determine the nature of the earth's core.  This result  i s due to the u n c e r t a i n t i e s i n the  s e i s m i c , high p r e s s u r e and a s t r o n o m i c a l data. summary of how the evidence  A brief  r e l a t e s t o the p r i n c i p a l hypo-  theses and how f u r t h e r r e s e a r c h may h e l p t o s o l v e t h i s problem i s given below.  1.  The agreement between the s e i s m i c a l l y determined  densities  i n the core and the d e n s i t y d i s t r i b u t i o n i n d i c a t e d by an e x t r a p o l a t i o n of the r e s u l t s of low p r e s s u r e experiments on an a l l o y of 10% n i c k e l and 90% i r o n i s c u r r e n t l y the s t r o n g e s t argument i n f a v o r of an i r o n c o r e .  I t would be an unexpected  c o i n c i d e n c e i f both an a l l o y with the m e t e o r i t i c abundances of n i c k e l and i r o n and a m e t a l l i z e d s i l i c a t e had the same d e n s i t y d i s t r i b u t i o n at core p r e s s u r e s . important  It i s , therefore,  that shock wave experiments be performed on an a l l o y  of n i c k e l and i r o n to c o n f i r m at high pressures the behaviour i n d i c a t e d by lower,  s t a t i c p r e s s u r e experiments.  The s t r e n g t h  of comparisons based on high p r e s s u r e experiments,  however,  a l s o depends on more c e r t a i n knowledge of s e i s m i c v e l o c i t i e s in the core.  The p r e f e r r e d v e l o c i t y d i s t r i b u t i o n i n the core  i n d i c a t e s three d i s t i n c t  regions.  Contrary to the simplest  i n t e r p r e t a t i o n , r e g i o n F may not be a t r a n s i t i o n  region  - 163 between the outer and inner core, but may i n f a c t have a d i s tinct  2.  chemical composition from the outer c o r e .  Only one of the major arguments summarized i n the i n t r o -  d u c t i o n i s given adequate support by the evidence c o n s i d e r e d in this thesis. of  T h i s was L e v i n ' s argument that the abundance  iron, p a r t i c u l a r l y metallic  i r o n , does not support the  analogy between i r o n and stony m e t e o r i t e s , on the one hand, and  the i r o n core hypothesis on t h e other.  The  indicated  abundances of i r o n i n the meteorite parent bodies, and the g r e a t e r abundance of i r o n  i n the e a r t h i m p l i e d by t h e ' i r o n  core hypothesis pose one of the g r e a t e s t d i f f i c u l t i e s f o r t h i s hypothesis. of  iron  In t h i s sense, the evidence on the abundance  i n meteorites i s an argument f o r the hypothesis of a  metallized s i l i c a t e  3.  Principal  core.  support f o r the hypothesis of a m e t a l l i z e d  s i l i c a t e core comes from the mean d e n s i t y o f t h e moon.  On  the assumption of a m e t a l l i z e d s i l i c a t e core, .seismic and high p r e s s u r e evidence support and  the hypothesis that the e a r t h  the moon have the same chemical composition.  On the  other hand, the hypothesis of an i r o n core i m p l i e s that the e a r t h and the moon have d i f f e r e n t  overall  compositions.  T h e o r i e s of the o r i g i n of t h e moon which attempt to e x p l a i n the assumed d i s t i n c t composition inadequate;  of the moon are p r e s e n t l y  whereas the theory of the o r i g i n of the moon  - 164 suggested  by Schmidt and developed  satisfactory.  More thorough  by Ruskol seems q u i t e  c r i t i c a l e v a l u a t i o n of Ringwood's  theory on the e a r l y h i s t o r y of the e a r t h and the moon i s r e q u i r e d . Chapters to be  4.  5,  6 and  In p a r t i c u l a r ,  the o r i g i n of  the o b j e c t i o n s g i v e n i n  8 must be answered i f Ringwood's theory i s  accepted.  The d e f i n i t e i d e n t i f i c a t i o n of the composition of the  mantle ( i . e . ,  i t s i r o n content) by a combination  high p r e s s u r e experiments  and  of f u r t h e r  s e i s m i c s t u d i e s , c o u l d lead to  a d e f i n i t e c o n c l u s i o n on the nature of the e a r t h ' s core. average  An  i r o n content of the mantle of about 10% would be a  c o n c l u s i v e argument i n favour of an i r o n core, whereas an average  i r o n content of the mantle of about 20% would be an  e q u a l l y c o n c l u s i v e argument i n favour of a m e t a l l i z e d s i l i c a t e core.  Although B i r c h supports the hypothesis of the  lower  content of i r o n i n the mantle, the evidence does not seem to give any b e t t e r support f o r t h i s value than f o r the higher one.  With the present evidence,  assumptions on the nature of  the e a r t h ' s core probably i n f l u e n c e c o n c l u s i o n s on the content of i r o n i n the mantle, r a t h e r than v i c e v e r s a . 5.  I f the nature of the e a r t h ' s core were known, more  d e f i n i t e a s t r o n o m i c a l data would determine variation  the nature of the  i n i r o n content among the t e r r e s t r i a l  the other hand, i t seems l e s s l i k e l y  planets.  On  that an improvement of  - 165 the present a s t r o n o m i c a l data w i l l p r o v i d e c o n c l u s i v e arguments on the nature of the e a r t h ' s core.  6.  With the s e i s m i c evidence t h a t the outer core i s l i q u i d ,  whereas t h e mantle and inner core of the e a r t h are s o l i d , a more d e f i n i t e knowledge of the m e l t i n g p o i n t curves of i r o n and  s i l i c a t e s might p r o v i d e a c o n c l u s i v e argument on the  nature of t h e earth's c o r e . temperatures, cient  however, cannot  Estimates of the m e l t i n g p o i n t be made at present with  suffi-  accuracy.  7.  Because of the low v i s c o s i t y of the l i q u i d outer core,  any  s i g n i f i c a n t l y denser  m a t e r i a l present i n i t would have  segregated  i n t o a l a y e r at the bottom.  T h e r e f o r e , on the  assumption  that the e a r t h has a m e t a l l i z e d s i l i c a t e core, the  author has o f f e r e d as an e x p l a n a t i o n of t h e s t r u c t u r e i n d i cated by.recent determinations of the s e i s m i c v e l o c i t y  distri-  b u t i o n i n the core, the hypothesis that the region F i s composed of normal metals, p r i n c i p a l l y i r o n . segregated silicates  have  out from the outer core of l e s s dense m e t a l l i z e d in a liquid  metallized s i l i c a t e 8.  These metals  s t a t e and surround  a denser,  solid,  inner core.  A common i n t e r p r e t a t i o n of the observed  abundances of  uranium, thorium and lead i s that a l l processes which f r a c t i o n a t e d lead with respect t o thorium and uranium  ceased  4.55  interior.  aeons ago i n both meteorites and the earth's  - 166 The  implications  known.  and  v a l i d i t y of t h i s c o n c l u s i o n  It i s suggested that  required,  are not  fully  f u r t h e r study of t h i s matter i s  p a r t i c u l a r l y i n view of i t s importance to major geo-  p h y s i c a l problems i n c l u d i n g the nature of the e a r t h ' s core.  9.  F u r t h e r t h e o r e t i c a l i n v e s t i g a t i o n s of the p o s s i b i l i t y  a t r a n s i t i o n of s i l i c a t e s useful.  to a m e t a l l i c phase would a l s o  of be  - 167 BIBLIOGRAPHY  Adams, J . A. S., J . Kenneth Osmond and John J . W. Rogers (1959) The geochemistry of thorium and uranium, P h y s i c s and Chemistry of the E a r t h . V o l . 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