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The surface tension of solid nickel Saaremaa, Eino 1957

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THE SURFACE TENSION OF SOLID NICKEL by EINO SAAREMAA  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE  DEGKEE  GE  MASTER OF APPLIED SCIENCE i n the Department of M i n i n g and M e t a l l u r g y at the University of B r i t i s h  We accept t h i s t h e s i s as conforming  Columbia.  t o the standard r e q u i r e d  from candidates f o r t h e degree o f 'Master of A p p l i e d S c i e n c e ' i n M e t a l l u r g i c a l Engineering  Members o f the Department o f M i n i n g and M e t a l l u r g y THE UNIVERSITY OF BRITISH COLUMBIA  JANUARY, 1957.  ABSTRACT  The s u r f a c e t e n s i o n of s o l i d commercially pure n i c k e l was determined by the f o r c e measurement technique u s i n g f i n e wires as proposed by Udin, S h a l e r , and Wulff.  Grain  boundary measurements were a l s o made on t h e same m e t a l . A f t e r f i n d i n g e x p e r i m e n t a l l y that t e s t s i n a vacuum -5 of approximately 5 x 10  y  mm Hg were u n s u c c e s s f u l because of  the h i g h power vapour p r e s s u r e of n i c k e l a t h i g h temperatures, s i m i l a r t e s t s were made i n helium and argon atmospheres, the pressure being kept constant a t 7&0 mm Hg d u r i n g the experiments. The average s u r f a c e t e n s i o n o f n i c k e l i n argon was found t o be 2220 ± 300 dynes per c e n t i m e t e r f o r a temperature range from 1370°C t o 1390°C. The r e l a t i v e g r a i n boundary energy of s o l i d was  determined by measuring  nickel  the d i h e d r a l g r a i n boundary groove  angles of t h e r m a l l y etched n i c k e l .  The i n t e r f e r o m e t r i c method  developed by H i l l i a r d and H a r r o l d was used f o r t h i s  purpose.  An average value of l 6 l degrees was found f o r the d i h e d r a l angle. The g r a i n boundary energy was c a l c u l a t e d t o be 7 4 0  ±  300 dynes  per centimeter. Examination o f t h e r m a l l y etched n i c k e l s u r f a c e s was i n c o n c l u s i v e w i t h r e s p e c t to p h y s i c a l evidence f o r d i s l o c a t i o n .  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  the requirements f o r an advanced degree at the  University  of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may of my  be granted by the  Department or by h i s r e p r e s e n t a t i v e .  stood that  I t i s under-  copying or p u b l i c a t i o n of t h i s t h e s i s f o r  f i n a n c i a l gain  s h a l l not be  allowed without my  permission.  Department of  M i n i n g and  The U n i v e r s i t y of B r i t i s h Vancouver #, Canada. Date  Head  January 24th, 1957  Metallurgy  Columbia,  written  ACKNOWLEDGMENT  The author i s g r a t e f u l t o the N a t i o n a l Research C o u n c i l and Defence Research Board of Canada f o r f i n a n c i a l aid  i n the form o f a Research A s s i s t a n t s h i p granted d u r i n g  the  past year. The work was c a r r i e d out with t h e h e l p of funds  p r o v i d e d by t h e Defence Research Board of Canada. The experimental work was done i n the l a b o r a t o r i e s of  the Department of M i n i n g and M e t a l l u r g y , and the author  wishes t o thank P r o f e s s o r F.A. Forward, Head of t h e Department, f o r the f a c i l i t i e s and the a s s i s t a n c e made a v a i l a b l e to the  him.  S p e c i a l thanks a r e extended t o Dr. Vernon  Griffiths,  d i r e c t o r of t h i s r e s e a r c h , and t o R.G. B u t t e r s f o r  t e c h n i c a l a d v i c e and encouragement. Thanks a r e extended t o P r o f e s s o r A.M. Crooker, of the  P h y s i c s Department,  f o r providing the f a c i l i t i e s to  prepare t h e p a r t i a l l y r e f l e c t i v e o p t i c a l  flats.  TABLE OF CONTENTS Page I.  INTRODUCTION  . . . . . . . . . . . . . . . . . .  -L  II.  PREVIOUS WORK . . . . . . . . . . . . . . . . . .  3  Experimental  Techniques . . . .  »  Energy measurements  . . . . . . . . . . .  3  Force measurements  . . . . . . . . . . .  4  G r a i n boundary energy measurements . . . . Theoretical Considerations.  IV  H e r r i n g theory Theories  .  19  . .  22  .  23  •  23  of d i f f u s i o n a l v i s c o s i t y  of s u r f a c e t e n s i o n o f s o l i d s  EXPERIMENTAL Materials  . . . . . . .  23  Equipment Procedures . . . . . .  . . . .  Difficulties IV.  RESULTS  . . . . . . . . . . . . . . . . . . . . .  33  . .  The Surface Tension of S o l i d N i c k e l  S u r f a c e Energy Measurements . . . . . . .  33 42  DISCUSSION  Thermal E t c h i n g  23 30  The G r a i n Boundary Energy of S o l i d N i c k e l  V.  12 17  . . . . . . . . .  Viscosity  III.  3  . . .  .  48  •  48  . . .  52  VI.  CONCLUSIONS  58  VII.  APPENDICES  60  A  Definitions . . . . .  dl  B  Nominal Composition o f Commercially Pure N i c k e l of Type "A" Grade  63  TABLE OF CONTENTS-: (cont'd. ) 0  E l e c t r i c a l Power Supply, Thermocouple, and Vacuum Gauge C i r c u i t s . . . . . . 64  D  P r e p a r a t i o n of 50 Percent L/Il 1 I* 01* k  E VIII.  Page  ^  Q  o  o  w  o  O  O  Transmitting O  O  O  O  O  O  O  O  O  C a l c u l a t i o n of the Surface Tension o f Solid Nickel .. . . . . . . . . .  BIBLIOGRAPHY  . . . . . . . . . . . . . . . . . .  ^3  .  66  70  LIST OF ILLUSTRATIONS  Fig.  Page  1.  The Stress Analysis of Loaded Wire  2.  Surface Tension of S o l i d Copper as a Function of Temperature  . . . , „ .  . . . . . . . .  . . . . . . . .  . ./.  3.  A Typical Experimental Stress-Strain Diagram  4.  A Drawing showing the Marking of Reference Points on the Wire „ . . . , . . . . . . . . , Dihedral Groove Angle of a Thermally Etched  5.  Specimen  vHcy-Mi,'.  ,  .  .  .  .  .  .  .  .  .  .  .  7  ...  .  .  8  ? 11  .  . . . . . . . . . . . . . . . . . .  15  6.  Vacuum furnace  24  7.  I n t e r i o r Arrangement of the Vacuum Furnace . . . .  26  8.  Vacuum Furnace with Control Instruments  . . . . .  33  9.  Vacuum Furnace with Control Instruments  . . . . .  33  10.  Micrograph showing the Fizeau Fringes along the Grain Boundary of a Thermally Etched Nickel  11.  Micrograph showing the Fizeau Fringes  12.  Micrograph showing the Fizeau F r i n g e s . . . . . . .  37  13.  Micrograph showing the Fizeau F r i n g e s . . . . . . .  37  14.  Elevation P r o f i l e No. 1 pf the Grain Boundary Groove Plotted from the Interferometric Data Micrograph showing the Mierosection of Grain Boundary Groove, of Thermally Etched Nickel  15.  "'• . .  36  .,- 39  16.  A Typical Experimental Stress-Strain  17.  Micrograph showing the 'Bamboo-like' Structure of Experimental Wires . . . . . . , .  47  Thermally Etched Nickel Specimen showing a Sub-boundary. . . . . . . . . . . . . . . . . . .  54  18. 19.  Diagram. . >  Thermally Etched Nickel Specimen showing a Sub-boundary . . . . . ... '. . . .. , . , . . .  45  54-  LIST OF ILLUSTRATIONS  (cont'd.)  Fig. 20.  Thermally Etched  N i c k e l Specimen . . . . . . . . . .  54  21.  Thermally Etched  N i c k e l Specimen . . . . . . . . . .  54  22.  Thermally Etched  N i c k e l Specimen . . . . . . . . . .  55  23.  Thermally Etched  N i c k e l Specimen . . . . . . . . . .  55  24.  Thermally Etched  N i c k e l Specimen  25.  Thermally Etched  N i c k e l Specimen . . . . . . . . . . .  55  26.  Thermally E t c h e d  N i c k e l Specimen ' . . . . . . . , . . „  56  27.  Thermally Etched  N i c k e l Specimen .• . . • . . . .  0  . . . . . . . . . .  55  , . .  56  LIST OF TABLES  Table  I. II.  Page  H o r i z o n t a l D i s t a n c e s between the F i z e a u F r i n g e s Measured from the Experimental M i c r o g r a p h s . . Values of D i h e d r a l G r a i n Boundary Groove Angle of Thermally Etched Commercially Pure Nickel. . •. . •  III.  Experimental S t r e s s and S t r a i n Measurements. . . .  IV.  Experimental Values of the S u r f a c e T e n s i o n and G r a i n Boundary E n e r g i e s of S o l i d N i c k e l .  V. VI.  38  4-0 43 . 46  C a l c u l a t e d Values of the S u r f a c e T e n s i o n f o r Solid Nickel  50  C a l c u l a t e d and Observed Values of S u r f a c e T e n s i o n f o r Some Metals  50  THE  SURFACE TENSION QF SOLID NICKEL  I. The  INTRODUCTION  present work on s o l i d n i c k e l was  the growing need f o r numerical  motivated  by  values of the s u r f a c e t e n s i o n  of s o l i d s , as a r e s u l t of i n c r e a s i n g i n t e r e s t i n the r o l e of i n t e r p h a s e boundary phenomena i n m e t a l s . The has  e x i s t e n c e of s u r f a c e t e n s i o n f o r c e s i n s o l i d s  been known f o r almost a century.  progress was when C.S.  made i n the study  Smith  1  D. Harker and E.R. metals i s due  Only very  1948  of t h i s phenomenon up to  extended to multiphase a l l o y s the i d e a o f Parker  t h a t c r y s t a l growth i n heated  to g r a i n boundary f o r c e s .  Smith a l s o showed  the nature of the dependence of c r y s t a l l i t e f a c i a l t e n s i o n s between s o l i d i f i e d alloy.  little  shape on  c r y s t a l s and  inter-  still  Since some of the mechanical p r o p e r t i e s of  liquid  engineering  a l l o y s are s t r u c t u r e s e n s i t i v e , many m e t a l l u r g i s t s were a l e r t e d by t h i s paper. Hollomon and h i s co-workers r e a l i z e d t h a t the phase  7 n u c l e a t i o n theory  of Volmer,  state transformation,  4  extended by Becker  r e q u i r e d some data on s o l i d  t e n s i o n to a c t i v a t e i t t o p r a c t i c a l I n the study  to  solid-  surface  use.  of s i n t e r i n g of metal powders i t was  found t h a t a more b a s i c understanding  of the  operating 5  mechanisms was  needed f o r f u r t h e r development.  Shaler  showed  t h a t an exact value of s u r f a c e t e n s i o n of s o l i d metals i s  necessary f o r s o l u t i o n of the k i n e t i c s of s i n t e r i n g , because t h i s f o r c e p l a y s a p r i n c i p a l r o l e i n d e n s i f i c a t i o n and strengthening  of powder compacts«  Welding m e t a l l u r g i s t s r e a l i z e d that s u r f a c e determine the soundness of welded or brazed j o i n t s . B a i l e y and H.C.  Watkins were l e d to a study of the  f o r c e s i n metals by t h e i r i n t e r e s t i n the  forces G-.L.C.  surface  j o i n i n g of m e t a l s .  B e s i d e s the m e t a l l u r g i s t s , chemical engineers i n t e r e s t e d i n c a t a l y s i s , mechanical engineers working l u b r i c a t i o n problems had  shown a p p r e c i a t i o n of the  of the s u r f a c e f o r c e s i n metals, but had determine e x p e r i m e n t a l l y facial  on  importance  been unable to  the  s o l i d : l i q u i d and  solid:gas  inter-  surface forces  ( d e f i n i t i o n s and  terms used  tensions. The  are  g i v e n i n Appendix A) are a d i r e c t r e s u l t of chemical f r e e energy.  The  i n t e r f a c i a l atoms are at energy s t a t e s between  those of i n t e r i o r atoms and between the  vaporized  atoms.  energy of s u r f a c e atoms and  The  difference  i n t e r n a l atoms i s i n  terms of the energy r e q u i r e d to form a u n i t area of s u r f a c e , and  i s c a l l e d s u r f a c e energy.  the s u r f a c e provides may  T h i s excess energy i n  the d r i v i n g f o r c e f o r any  induce a decrease i n s u r f a c e a r e a .  the  process which  Such a process i s  capable of doing work at the expense of the energy of  decreasing  surface. G-ibbs^ has i n t e r f a c e between two  proved t h a t t h i s excess energy at phases i s a p a r t i a l f u n c t i o n of  the the  i n t e r f a c i a l area, thus  3 „  ^ Or  OF  ^  ^  =  S  "  where - ^ j i s the r a t e of change of f r e e energy of the system w i t h  changing s u r f a c e area at  temperature, p r e s s u r e , and V  i s the i n t e r f a c i a l  constant  composition.  f o r c e per u n i t l e n g t h or  f r e e energy per u n i t area, being  expressed  e i t h e r i n dynes/cm or i n orgs/cm. T h e r e f o r e , two  approaches are p o s s i b l e to measure the  s u r f a c e energy of the s o l i d s .  The  s u r f a c e t e n s i o n may  be  deter-  mined e i t h e r by thermodynamic measurement of the s u r f a c e energy or by a mechanical measurement of the s u r f a c e f o r c e by a p p l i c a t i o n of a b a l a n c i n g At present Au and Ag,  counterforce.  the values of the s u r f a c e f o r c e s of  a l l being metals of r e l a t i v e l y  nave been determined by the use The  the  Cu,  low m e l t i n g p o i n t s ,  of the second method.  present work to determine the s u r f a c e t e n s i o n of  s o l i d n i c k e l i s an attempt to use the f o r c e measurement technique  first  developed by Udin and h i s c o l l a b o r a t o r s , on a  metal of h i g h e r m e l t i n g  point.  II, Experimental  PREVIOUS WORK  Techniques  Energy measurements. Thermodynamical measurements to determine s u r f a c e energy have been c a r r i e d out by the a p p l i c a t i o n of  heat-of-  s o l u t i o n method,  F r i c k e and Meyer^ measured the heat of  s o l u t i o n of massive gold i n i o d i n e t r i c h l o r i d e , and found i t t o be lower than t h a t of f i n e gold p a r t i c l e s . evaluated  Surface  area  was  on the b a s i s of cubic p a r t i c l e s , the diameter of t h e  p a r t i c l e s being determined from the amount of broadening of the x-ray d i f f r a c t i o n l i n e s of the gold powder.  T h i s area and t h e  excess heat of s o l u t i o n y i e l d e d a s u r f a c e energy equal t o 670 ergs per square  centimeter. o  H i i t t i g and h i s c o l l a b o r a t o r s f a c i a l t e n s i o n copper:copper sulphate square centimeter  determined the i n t e r -  to be 40,000 ergs per  by measuring the e l e c t r o m o t i v e  f o r c e between  e l e c t r o d e s of copper powder and massive copper r e s p e c t i v e l y , i n a copper sulphate  solution.  S i n c e copper tends t o d i s s o l v e from  the powder e l e c t r o d e and p r e c i p i t a t e on the massive m e t a l , an e q u i l i b r i u m emf. due t o the excess s o l u t i o n t e n s i o n of p a r t i c l e s of r a d i u s r , and with an i n t e r f a c i a l t e n s i o n y a g a i n s t the electrolyte,  can be measured. v  frf  w h e r e t o " i s the r a t i o of atomic weight t o d e n s i t y of the particle F  i s Faraday's  constant.  C e r t a i n errors are introduced  i n estimating the  s u r f a c e area or p a r t i c l e s i z e , and i n u s i n g the e l e c t r o c h e m i c a l method, due t o t h e s i d e r e a c t i o n s and n o n - e q u i l i b r i u m  conditions,  F o r c e measurements The techniques  f o r determining  the f o r c e of s u r f a c e  t e n s i o n have been more f a v o r e d than those i n v o l v i n g measurement of energy, because of fewer experimental uncertainties.  difficulties  These methods i n v o l v e t h e b a l a n c i n g  tension with a counterforce.  and  of  surface  T h i n w i r e s or f o i l s are loaded  with  weights of v a r y i n g magnitude and heated t o . a temperature below the m e l t i n g f o r c e , and The  point. negative  The  straixis  i f due  ( p o s i t i v e i f due  to the  t o the  s u r f a c e t e n s i o n ) are  observed.  l o a d which e x a c t l y balances the upward p u l l of the  t e n s i o n i s estimated  from the p l o t of s t r a i n a g a i n s t  i n t e r p o l a t e d l o a d allows  the d e t e r m i n a t i o n  counter-  surface  stress.  of the value pf  The  the  s u r f a c e t e n s i o n i n a simple c a l c u l a t i o n . T h i s technique has  been known f o r many y e a r s ,  and  s u r f a c e t e n s i o n v a l u e s have been r e p o r t e d by Chapman and Schottky  1 0  and B e r g g r e n  f i l a m e n t technique was  Porter,^  i n the e a r l i e r p a r t of the century.  1 1  The  l a t e r used s u c c e s s f u l l y to determine the 12  s u r f a c e t e n s i o n of v i s c o u s l i q u i d s . Sawai and  Tammann and  co-workers,  IJ  '  c o l l a b o r a t o r s , ^ ' ^ and M a c k ^ r e p o r t e d good agreement 1  1  between t h i s technique and more c o n v e n t i o n a l methods of measuring the s u r f a c e t e n s i o n of g l a s s e s and A l l these experimental in reliability  r e s u l t s supported the  of the technique and  success on s o l i d metals. 20 Boehme  tars.  Sawai and  soon i t was Nishida,  belief  employed '  with  and Tammann and  made q u a n t i t a t i v e measurements on gold f o i l s and  attempted  to c a l c u l a t e from t h e i r r e s u l t s the i n t e r f a c i a l t e n s i o n of non-equilibrium  the  system g o l d : a i r .  In experiments f o r determining loaded w i r e s r a t h e r than loaded  f o i l s may  the s u r f a c e  tension,  be used, although  the  s e n s i t i v t y of the t e s t i s somewhat., d i m i n i s h e d due to the. u n f a v o r a b l e s u r f a c e area to , c r o s s - s e c t i o n a l area r a t i o of t h i n ;  For example,. Sawai^s gold f o i l s b e i n g ' 7 . 7 x  wires.  10~^  centimeters thick.,,-.,,were s u b j e c t e d to a shrinkage s t r e s s of 19 centimeter at a s u r f a c e t e n s i o n of 1500  per square  dynes per  c e n t i m e t e r , whereas i n 0,008-centimeter r a d i u s wire the i s o n l y 0.57  kg. per square  i n the experiments  centimeter.  kg.  stress  Hence, the use of w i r e s  r e q u i r e s an o p e r a t i o n very near the m e l t i n g  p o i n t f o r a reasonable d u r a t i o n .  The i n s e n s i t i v i t y i n u s i n g  wires i s counterbalanced by the f o l l o w i n g c o n s i d e r a t i o n s .  The  c y l i n d r i c a l w i r e , i n e q u i l i b r i u m , i s i n a s t a t e of h y d r o s t a t i c compression,  the s t r a i n r a t e i n a l l d i r e c t i o n s being zero, which  i s not t r u e i n the case of f o i l s . energy,  undoubtedly  Secondly,  the g r a i n boundary  one of the components of the f o r c e a c t i n g  on the specimens, can be d e a l t w i t h i n case of w i r e s , i f the m a j o r i t y of. g r a i n boundaries  are p e r p e n d i c u l a r t o the w i r e  axis.  F i n a l l y , s t r a i n a n i s o t r o p y i s n e g l i g i b l e i n the case o f w i r e s compared t o  as  foils.  Consider a w i r e of l e n g t h 1 and r a d i u s r c o n t a i n i n g n+1  g r a i n s w i t h a c r o s s - s e c t i o n equal t o that of the w i r e w i t h  boundaries  p e r p e n d i c u l a r to the a x i s of the w i r e  (Fig,  1).  I f t h e shrinkage f o r c e of the s u r f a c e t e n s i o n i s j u s t counterbalanced by a. suspended weight W , then the a x i a l Tir  'x -  where along  stress (l)  1  if i s the s u r f a c e t e n s i o n o f the w i r e , the x - a x i s  being  the wire with t e n s i o n p o s i t i v e .  F i g . 1 . . The S t r e s s A n a l y s i s of Loaded Wire The s t r e s s e s p e r p e n d i c u l a r  t o t h e w i r e are due t o  the c i r c u m f e r e n t i a l f o r c e of t h e s u r f a c e t e n s i o n and the l i n e f o r c e s due t o each g r a i n boundary.  These f o r c e s are equal and  can be expressed by  where  fc^is  t h e g r a i n boundary  tension.  - 8 ' F o r the case of zero s t r a i n i n the x - d i r e c t i o n , the s t r a i n w i l l a l s o be zero i n the y- and z - d i r e c t i o n s , s i n c e the wire i s under h y d r o s t a t i c s t r e s s .  G^L =. (T^  Hence  =  and thus  w = nc^ - 1 - n c V .... From t h i s equation  ^\  the s u r f a c e t e n s i o n can be.  determined i n a s i n g l e experiment i f the g r a i n boundary  tension  i s known, o r i f t h e r a t i o of g r a i n boundary t e n s i o n t o s u r f a c e tension i s available. 21 Udin, S h a l e r , and Wulff  first  applied t h i s  to evaluate t h e s u r f a c e t e n s i o n of copper i n vacuum.  technique Their  value f o r the s u r f a c e t e n s i o n of s o l i d copper was 1670 dynes per 0 ' 22 centimeter at 1030 G, as c o r r e c t e d by U d i n a c c o r d i n g t o the E q u a t i o n 3.. The r e s u l t s are summarized g r a p h i c a l l y i n F i g . 2, and a t y p i c a l s t r e s s - s t r a i n diagram i s shown i n F i g . 3.  1  .  1  'll  !  •i_ 2 0 0 0  1 — — _ _ _ _ _  |  A O  ____A  L egend 0.005" C io.Wrie 0003" 0io. Wrie C Coorprepeee lr;dI0/4E 103/50.  A  1  1  -  C 1 O 0_  — Mel  rii  O -  1200  I'600 Temoeroiure  Fig. 2  1  0  K  Surface Tension of S o l i d Copper as a F u n c t i o n o f Temperature ( a f t e r H . UdinJ.  Funk, Udin, and Wulff  23 J  experimented  9 -  on s i l v e r i n a  helium atmosphere ,• a f t er they found t h a t the vapor p r e s s u r e of s i l v e r was t o o hi'gh t o a t t a i n the metal:vapour t h e i r experiments  i n vacuum.  equilibrium i n  The s u r f a c e t e n s i o n o f s i l v e r  i n helium was found t o be 1 1 4 0 i 9 0 dynes p e r c e n t i m e t e r f o r the temperature  range from 875°C t o 952°C, which i s a t r u e s u r f a c e  t e n s i o n , because  helium i s i n s o l u b l e i n s i l v e r and w i l l not be  p h y s i c a l l y adsorbed a t h i g h temperatures, to a metal  and cannot  chemisorb  surface.  1  1  1  1  0.006 0.004  X /  0.002 c S  -  X  0  fl  -0.002  -  -  .—x  -0.004 -0.006  -  Test No. 13  1  i  1  i  2 3 Siress, Dynes per Cm.  5«I0  :  1  Fig.  3.  A T y p i c a l Experimental S t r e s s - S t r a i n Diagram ( a f t e r H. U d i n ) , 24  Alexander, Kuczynski and Dawson gold w i r e s suspended similar d i f f i c u l t i e s .  who worked with  i n t u b u l a r n i c k e l h e a t e r s i n vacuum, had S i n c e a complex g o l d : g p l d v a p o r . n i c k e l  vapor system w i t h no p o s s i b i l i t y o f g o l d . g o l d vapor was  equilibrium  used, no r e p r o d u c i b l e v a l u e s f o r the i n t e r f a c i a l t e n s i o n o f  the system were o b t a i n e d .  - 10 Buttner, Udin and Wulff i n helium gold.  25  experimented on gold  wires  atmosphere t o determine the s u r f a c e t e n s i o n of  solid  They determined a value of 1400-65 dynes per  centimeter  f o r the temperature range from-1017°C°to 1042°C.  26 Buttner,  Funk  on s u r f a c e t e n s i o n .  ^nd U d i n  s t u d i e d the  effect  They found the i n t e r f a c i a l t e n s i o n o f the  system g o l d : g o l d v a p o r : a i r a t 1040°C t o te 1 2 1 0 as compared to 1 3 7 0  centimeter  of oxygen  dynes per  dynes per centimeter  system g o l d : g o l d vapor at the same temperature;  f o r the  and the  inter-  f a c i a l t e n s i o n of the system s i l v e r : s i l v e r v a p o r : a i r at 930°C only 450  dynes per centimeter  centimeter  as compared to 1140. dynes per  f o r the s u r f a c e t e n s i o n of s i l v e r .  e x p e r i m e n t a l l y determined values are a c c u r a t e no f u r t h e r experiments were c a r r i e d out The  Since  the  only t o about  i n the case of g o l d .  e f f e c t of oxygen on s u r f a c e t e n s i o n of s i l v e r was  more f u l l y . helium  oxygen.  The  r e s u l t s showed a  l i n e a r r e l a t i o n s h i p between s u r f a c e t e n s i o n and the of oxygen p a r t i a l p r e s s u r e . adsorb approximately  pressure  1.7  I t was  concluded  logarithm  that s i l v e r  x l O ^ atoms of oxygen per  i n the range i n v e s t i g a t e d , and  The  on  form a s u r f a c e -  oxide.  experimental  technique  i s a d e l i c a t e one.  marking of r e f e r e n c e p o i n t s on the wire presents P a i n t i n g or p l a t i n g the wires  l e n g t h i s not  will  square  1  of s u r f a c e , the amount not b e i n g dependent  s t a b i l i z e d f i l m of  problem.  studied  Tests were run i n v a r i o u s mixtures of p u r i f i e d  plus dried e l e c t r o l y t i c  centimeter  ±5%i  a  The  difficult  o u t s i d e a g i v e n gage  s a t i s f a c t o r y because a n y t h i n g adhering  to the  - 11  s u r f a c e lowers the s u r f a c e energy. p o i n t s was  -  K n o t t i n g the w i r e s at two  used by Udin and co-workers  i n the case of copper.  The gage p o i n t s are taken as i n t e r s e c t i o n of the i n n e r loops of the knot w i t h the s t r a i g h t p o r t i o n of the w i r e  (Fig.4).  L a t e r Udin and h i s group i n s c r i b e d the marks by r o t a t i n g the wire mounted i n a jeweler's l a t h e a g a i n s t a p a i r of r a z o r blades spaced the r e q u i r e d gage l e n g t h a p a r t .  *1 Fig. 4  A Drawing Showing the Marking of Reference P o i n t s on the Wire. .  The weights, r a n g i n g from zero t o about two t o t h r e e times the estimated weight  r e q u i r e d f o r balance, are f u s e d t o  the ends of the gage-marked w i r e s .  E i g h t t o s i x t e e n w i r e s used  - 12 i n each t e s t a r e suspended weights, l i d , the specimen.  from the l i d of the metal c e l l .  The  and the box are made o f the same metal used f o r Thus a t temperature the w i r e s hang i n an  e q u i l i b r i u m w i t h metal vapor  atmosphere.  The w i r e s are s t r a i g h t e n e d and annealed at or above the experimental temperature f o r at l e a s t one hour i n the vacuum or t e s t atmosphere.  A f t e r c o o l i n g , the specimens  measure the gage l e n g t h and count the g r a i n s .  are removed to  The assembly i s  r e t u r n e d t o the f u r n a c e and h e l d at the t e s t temperature f o r a time s u f f i c i e n t f o r measurable dependent  creep t o take p l a c e , the time being  on the temperature and a c c u r a c y r e q u i r e d .  The f u r n a c e  i s cooled to room temperature, the specimens are removed and re-measured.  I t ha$ been found that no f u r t h e r g r a i n growth t a k e s  p l a c e d u r i n g the t e s t because the t h e r m a l l y etched grooves produced d u r i n g the anneal anchor the g r a i n boundaries. The change i n l e n g t h i s transformed t o e n g i n e e r i n g s t r a i n and p l o t t e d a g a i n s t the s t r e s s due t o the suspended weights, which^ are c o r r e c t e d by t a k i n g i n t o account the weight of the wire below the p o i n t midway between the upper and lower gage marks.  The  i n t e r c e p t of t h i s p l o t w i t h the .strain a x i s g i v e s the v a l u e of the s t r e s s at zero s t r a i n or the v a l u e of w from E q u a t i o n 3,  G r a i n boundary  energy measurements.  I n o r d e r to c a l c u l a t e the s u r f a c e t e n s i o n f o r t h e g i v e n metal, e i t h e r the value o f the g r a i n boundary  energy  must be known, or the r a t i o between 194-8  assumed.  no s a t i s f a c t o r y methods to determine the  energies, new  and  showed that the g e o m e t r i c a l  proposed by G.S.  whose s u r f a c e  tensions  along the  Smith" "  A  who  1  shapes of g r a i n s r e s u l t from  approach to an e q u i l i b r i u m between phase and geometrically  to  interfacial  such as g r a i n boundary energy, were a v a i l a b l e .  a t t a c k to the problem was  p o i n t s and  Up  an  grain interfaces  balance each o t h e r at  l i n e s of contact  the  when annealed at  s u f f i c i e n t l y high temperatures f o r a s u f f i c i e n t  length  T h i s r e l a t i o n s h i p between g r a i n boundary t e n s i o n s  and  of time. grain  27 boundary geometry had  been suggested e a r l i e r by Desch.  ment of angles e s t a b l i s h e d between the  i n t e r f a c e s when i n  e q u i l i b r i u m , p r o v i d e s a method t o determine the of s u r f a c e f o r c e s i n v o l v e d a c c o r d i n g  JL  Sinvy,  =  Si^a.  energies,  and  y  '  3  a  r  e  r e l a t i v e values  t o the r e l a t i o n s h i p  » J a  5inv^  Where E s are the r e s p e c t i v e f  Measure-  (4) s  specific  interfacial  "the d i h e d r a l angles between the i n t e r -  faces measured i n the plane p e r p e n d i c u l a r However, t h i s r e l a t i o n s h i p w i l l be  t o the  junction.  complicated by the  t i o n dependence of g r a i n boundary e n e r g i e s .  The  orienta-  evidence  a v a i l a b l e concerning the o r i e n t a t i o n dependence of s o l i d i n t e r f a c e energies i s sparse but and  i t seems t h a t both  t h e o r e t i c a l l y i t s e f f e c t may  experimentally  be expected t o be  small,  except f o r a l i m i t e d number of cases when g r a i n boundaries have cusp o r i e n t a t i o n s . P h y s i c a l measurement of m i c r o s c o p i c  dihedral  angles  - 14 i s d i f f i c u l t because,  by d e f i n i t i o n , they must be measured i n  a plane p e r p e n d i c u l a r t o the l i n e of j u n c t i o n of the i n t e r f a c e s , 2  which a c t u a l d i r e c t i o n i s unknown.  Harker and Parker  proposed  a s t a t i s t i c a l method which, i f employed, would give the v a l u e of d i h e d r a l angle w i t h i n the l i m i t s of ~5°  when a l a r g e number of  d i h e d r a l angles were measured at random.  T h i s method has been  used i n some cases w i t h c e r t a i n m o d i f i c a t i o n s by  different  researchers, A more s u b t l e method i s the c a l i b r a t i o n of  solid:solid  i n t e r f a c i a l t e n s i o n i n a b s o l u t e u n i t s when the e n e r g i e s of such solid:liquid  or s o l i d : g a s s u r f a c e s are known or can be  by the methods d e s c r i b e d above.  determined  Calibration with solid:gas  t e n s i o n i s p r e f e r r e d t o the c a l i b r a t i o n w i t h a  solid:liquid  t e n s i o n because an i n e r t gas or vacuum can be used t o a v o i d contamination of the i n t e r f a c e under study. e q u i l i b r a t i n g heat treatment,  During the  shallow grooves on the f r e e  s u r f a c e of the specimen at the g r a i n boundaries are formed, the process b e i n g c a l l e d groove angles ^  'thermal e t c h i n g ' .  I f the d i h e d r a l or  are measured and the s u r f a c e t e n s i o n of the  s o l i d i n the gas i s known, the g r a i n boundary energy c a l c u l a t e d from the formula  ( F i g . J5)  Ztfcos^ Or, subsequently,  _? and tf* may  -  (5)  i f the s u r f a c e t e n s i o n and  boundary t e n s i o n are determined unknowns  can be  s i m u l t a n e o u s l y , the  be c a l c u l a t e d  from  two  grain  - 15 -  .  2-*> cos  (6)  |  where a l l o t h e r v a l u e s can be measured,  Fig. 5  D i h e d r a l Groove Angle of a Thermally Etched Specimen.  Because of the small s i z e of the grooves  (approx,  1 micron deep) and the obtuseness of the groove angle  (usually  160 degrees o r g r e a t e r ) , a small experimental e r r o r i n measuri n g the angle produces a l a r g e r e l a t i v e e r r o r i n the c a l c u l a t e d g r a i n boundary  energy, the experimental technique i s d i f f i c u l t .  B a i l e y and Watkins  28  measured the groove angles of  t h e r m a l l y etched copper i n m i c r o s e c t i o n s taken normal t o the 29  surface,,  B u t t n e r , U d i n and Wulff  determined the a b s o l u t e  g r a i n boundary energy of g o l d at 1300°K t o be 365±j?0 dynes per centimeter by measuring d i h e d r a l a n g l e s ,  Greenough and K i n g - ^  used both m i c r o s e c t i o n s and t a p e r - s e c t i o n s t o measure d i h e d r a l groove angles i n s i l v e r , and checked t h e i r r e s u l t s by a method o f o p t i c a l gpniometry.  successfully  The l a t t e r method, however,  i s not s u f f i c i e n t l y a c c u r a t e because of the very small s i z e o f the groove  and continuous c u r v a t u r e of the groove  s u r f a c e s and 31  of the magnitude of the wave l e n g t h of l i g h t . determined  Fullman  the groove angle f o r copper coherent twin  t h e r m a l l y etched i n l e a d vapor and demonstrated  boundaries  that there i s  an optimum t a p e r - s e c t i o n i n g angle f o r most a c c u r a t e measurement of a p a r t i c u l a r groove. 32 33 Hess and others used the method of  multiple-beam  34 i n t e r f e r o m e t r y developed by Tolansky  t o measure the  groove  angles of pure copper but found that l a r g e e r r o r s i n the c a l c u - r l a t e d g r a i n boundary e n e r g i e s r e s u l t , i f the r e f e r e n c e p l a t e  and  the s u r f a c e d e v i a t e from p a r a l l e l i s m more than approximately 2 degrees.  On the o t h e r hand, H i l l i a r d ^  the i n t e r f e r o m e t r i c  has demonstrated  that  method i s s u f f i c i e n t l y a c c u r a t e , i f t h e  r e f e r e n c e p l a t e and the experimental s u r f a c e are p a r a l l e l , measuring  g r a i n groove angles i n the Cu-Au T h i s method c o n s i s t s i n matching  silvered, optically f l a t , approximately 0,50 monochromatic l i g h t  by  system. an a l u m i n i z e d or  g l a s s s u r f a c e of r e f l e c t i v i t y  a g a i n s t the metal s u r f a c e , and the use of i n the f o r m a t i o n of F i z e a u f r i n g e s which  represent the contour l i n e s i n the s u r f a c e topography.  Knowing  the necessary c o n s t a n t s , the e l e v a t i o n p r o f i l e of the s u r f a c e slope i n the g r a i n boundary may angle measured.  be c o n s t r u c t e d and the d i h e d r a l  The equation governing f r i n g e s of minimuna  r e f l e c t i o n from the i n t e r f erometric  e-n ^~ -*- £  =  UM+  gap  I)TT  , is (7)  according  to H a r r o l d ^  multiple dielectric  who used g l a s s s l i p s coated w i t h  films.  When the o b j e c t i v e i s focused i n  the a i r gap between the r e f l e c t i v e s u r f a c e of t h e o p t i c a l  flat,  the metal specimen r e v e a l s contour l i n e s at i n t e r v a l s of as  S  v a r i e s w i t h i r r e g u l a r i t y of the metal s u r f a c e and  assumes s u c c e s s i v e  i n t e g r a l values.  phase changes at r e f l e c t i o n , No c r i t i c a l  i s fixed i n this  case.  evaluation f o r the interferometric  method developed by H i l l i a r d present.  £ , the sum of a l l r e l e v a n t  However, present  and H a r r o l d  i s a v a i l a b l e at the  work has demonstrated  convincingly  the a p p l i c a b i l i t y and the r e l a t i v e s i m p l i c i t y of the method w i t h respect  t o other  conventional  techniques.  T h i s method makes i t  p o s s i b l e t o p i c k the g r a i n boundary grooves s u i t a b l e f o r the measurement of d i h e d r a l angles by o b s e r v i n g Fizeau  fringes.  No time-consuming work i s r e q u i r e d as i n t h e  case of m i c r o s e c t i o n s , use  the symmetry o f the  o r d e t e r m i n i n g t h e d i h e d r a l angle by the  of s t a t i s t i c a l methods.  Furthermore, the accuracy o f t h e  method i s b e l i e v e d t o be h i g h e r  than t h a t of t h e other methods  because of the fewer experimental d i f f i c u l t i e s and u n c e r t a i n t i e s involved. Theoretical  Considerations.  Viscosity Knowing the s u r f a c e t e n s i o n of s o l i d metals, i t i s p o s s i b l e t o c a l c u l a t e t h e i r v i s c o s i t y , i f c e r t a i n assumptions are made. uniformly  I t i s assumed that t h e m a t e r i a l c o n t r a c t s o r extends along the l e n g t h of t h e specimen, and a l s o t h a t i t  flows i n a v i s c o u s f a s h i o n , i . e . t h a t the s t r a i n r a t e s a r e  - 18 p r o p o r t i o n a l t o the s t r e s s a p p l i e d . no change i n l a t t i c e energy s t r a i n energy  -  I f v i s c o u s flow i s assumed,  should be p r e s e n t , and a l l the  should appear as heat.  The k i n e t i c energy  moving weight being n e g l e c t e d , the time r a t e of heat equals the r a t e of change of p o t e n t i a l energy  of the  generation  by changing  both  the p o s i t i o n of the weight and the a r e a of the metal s u r f a c e . T h e r e f o r e , under i s o t h e r m a l c o n d i t i o n s ,  TJt  -  . , cLt  d£  w  ds * "3*  v  (8)  where Q i s the heat of v i s c o u s flow.  37 A c c o r d i n g to F r e n k e l  the.energy  d i s s i p a t e d i n flow  f o r a v i s c o u s rod under l o n g i t u d i n a l s t r a i n i s  dl  ~~  where  jb* ^7jb>  (?)  V) i s the c o e f f i c i e n t  By making necessary  of v i s c o s i t y  substitutions, a  simplified  relationship  € - £ c c - f v  (io,  i s d e r i v e d , i f the s t r a i n s measured are s m a l l , <T* being s t r e s s . Udin has c a l c u l a t e d the c o e f f i c i e n t of v i s c o s i t y from h i s experimental data on s u r f a c e t e n s i o n of copper u s i n g equation 10,  and p l o t t e d the l o g a r i t h m of the v i s c o s i t y a g a i n s t  the r e c i p r o c a l of a b s o l u t e temperature.  The  equation of the  resulting line i s OOQ  7 The a c t i v a t i o n energy  = Bo  e,  *r  (ll)  of 59,000 c a l o r i e s per mole i s w i t h i n the  - 19  -  range of values r e p o r t e d f o r s e l f - d i f f u s i o n of copper by Steigman,^  However, the constant i s 10^ times l a r g e r than 38 that p r e d i c t e d by Kauzmann a c c o r d i n g to the e q u a t i o n  V  =  Udin concluded  *GT  (  t h a t an atomic vacancy i s the u n i t of  flow, but only a very s m a l l f r a c t i o n of v a c a n c i e s i n the  }  can  participate  flow.  H e r r i n g theory of d i f f u s i o n a l  viscosity.  Since the c o r r e c t n e s s of the r e p o r t e d values f o r s u r f a c e t e n s i o n of v a r i o u s metals and the f u t u r e  experimental  work i s based on the assumption t h a t the specimens deform i n a v i s c o u s f a s h i o n , i t i s necessary  t h a t a mechanism be e s t a b l i s h e d  that would e x p l a i n both the v i s c o u s flow and the uniform  deforma-  40 tion.  Such a mechanism has  e x p l a i n s the deformation  been proposed by H e r r i n g  t a k i n g p l a c e under  c o n d i t i o n s by means of a flow of vacancies a r i e s and  surfaces.  who  experimental between g r a i n bound-  T h i s theory, which i s a d i r e c t  but 41  independent e x t e n s i o n of the theory put forward  by Nabarro  i n an attempt t o e x p l a i n the microcreep observed by Chalmers i n s i n g l e t i n c r y s t a l s , suggests t h a t any shape by s e l f - d i f f u s i o n i n such a way  c r y s t a l can change i t s as to y i e l d t o an a p p l i e d  shearing s t r e s s .  T h i s can cause the macroscopic behaviour of  a polycrystalline  s o l i d to be l i k e t h a t of a v i s c o u s l i q u i d .  is- assumed t h a t t h i s phenomenon i s the predominant cause of creep at very high temperatures and  very low s t r e s s e s , though  not under normal c o n d i t i o n s . I t i s p o i n t e d out t h a t a p o l y c r y s t a l l i n e s o l i d under a shearing s t r e s s , can, because of  It  - 20 selfr-diffusion within  the g r a i n s , y i e l d as a r e s u l t of  d i f f u s i o n a l flow of matter w i t h i n each c r y s t a l away from g r a i n boundaries where t h e r e where t h e r e  i s a normal p r e s s u r e ,  i s a normal t e n s i o n .  a l l y describable  The  y i e l d i n g i s macroscopic-  grains.  explana-  been observed f o r f o i l s  w i r e s being suspended w i t h very small loads  the  T h i s t h e o r y of  'diffusional viscosity'-provides a possible  t i o n f o r the behaviour which has  elevated  towards those  by an e f f e c t i v e v i s c o s i t y p r o p o r t i o n a l to  square of the l i n e a r dimensions of the so-called  and  and  h e l d at  and an  temperature. The  r a t e o f y i e l d i n g of the  specimen to the  applied  f o r c e s understandably depends on the d e t a i l e d d i s t r i b u t i o n of the s i z e s and not the  shapes of i t s c r y s t a l g r a i n s , and  g r a i n boundaries are able  on whether or  to w i t h s t a n d s h e a r i n g  stress  f o r times as l o n g as are necessary f o r measurable d i f f u s i o n a l flow to take p l a c e . across  I t has  been found t h a t  boundaries.  The  property  at  of  r a t e of creep, u n t i l t h i s r e l a x a t i o n  become complete, w i l l u s u a l l y be  considerably  high  grain has  f a s t e r than t h a t  to d i f f u s i o n a l v i s c o s i t y . Compared to the  the  stresses  m e t a l l i c g r a i n boundaries are r a p i d l y r e l a x e d  temperatures, which seems t o be a g e n e r a l  due  shearing  low  stresses i n ordinary  creep experiments,  s t r e s s e s used i n experiments to determine the  surface  t e n s i o n of metals i n d i c a t e t h a t the mechanism proposed Nabarro and H e r r i n g  to e x p l a i n the d e f o r m a t i o n o f the  i s most probable, although i t i s , of course, q u i t e t h a t the mechanism of o r d i n a r y  by specimen  conceivable  creep and microcreep are  the  - 21 same, the t h r e s h o l d being lower and the r a t e s f a s t e r at the higher  temperatures. H e r r i n g ' s v i s c o s i t y equation f o r a w i r e w i t h  'bamboo-  l i k e ' structure i s 2 kTRL  .  .  where T i s the a b s o l u t e temperature R i s the r a d i u s o f the g r a i n L i s the l e n g t h of the g r a i n D i s the s e l f - d i f f u s i o n  coefficient  B i s a f u n c t i o n of g r a i n shape L R SI i s atomic The theory was  volume  v e r i f i e d by the work of Udin  and  42 others who determined that the v i s c o s i t y of 3 m i l g o l d w i r e s i s much h i g h e r than t h a t of 1 m i l w i r e s . G-ood agreement w i t h 43 theory was a l s o found by Greenough who observed s t r a i n r a t e s i n s i l v e r single crystals. Opposed t o these o b s e r v a t i o n s were 21 the r e s u l t s of Udin and h i s c o l l a b o r a t o r s which case the v i s c o s i t y was  on s o l i d copper i n  found to decrease as g r a i n s i z e  increased. A s e r i e s of experiments were c a r r i e d out by P r a n a t i s 44 and Pound  w i t h copper f o i l s of v a r y i n g g r a i n s i z e t o c o n f i r m  the H e r r i n g t h e o r y of d i f f u s i o n a l v i s c o s i t y . between, c a l c u l a t e d and observed  v a l u e s o f the c o e f f i c i e n t  v i s c o s i t y , a c t i v a t i o n energy, and found.  T h i s a d d i t i o n a l evidence  A good agreement of  self-diffusion coefficient  was  i n f a v o r of H e r r i n g ' s theory of  v i s c o u s flow i n d i c a t e s t h a t the v a l u e s of s u r f a c e t e n s i o n  o b t a i n e d by f o r c e measurement techniques may be regarded confidence.  The r e l a t i o n s h i p s determined  between v i s c o s i t y and  g r a i n s i z e , and v i s c o s i t y and temperature, of observed  viscosities,  deformation  under the experimental  with  as w e l l as the values  s t r o n g l y support the p r o p o s a l t h a t c o n d i t i o n s develops  e n t i r e l y by means of vacancy d i f f u s i o n . .  almost  S l i p , kinking, o f f -  s e t t i n g , and g r a i n boundary s l i d i n g a r e assumed t o make o n l y limited contributions. T h e o r i e s of s u r f a c e t e n s i o n of s o l i d s Not  only a r e t h e a v a i l a b l e data concerning the  numerical values of the s u r f a c e t e n s i o n o f s o l i d s  incomplete,  but i n a d d i t i o n , no s a t i s f a c t o r y theory of the s u r f a c e t e n s i o n 45  of nonionic s o l i d s i s a v a i l a b l e at p r e s e n t .  Stratton's  e l e c t r o n t h e o r y of s u r f a c e t e n s i o n of s o l i d metals  i s one of  the best of the e x i s t i n g ones, but i t s p r e d i c t i o n s are c o n s i d e r a b l y lower than the e x p e r i m e n t a l l y known s u r f a c e t e n s i o n s o f ' l i q u i d metals, and hence has to be c o n s i d e r e d at l e a s t  in its  q u a n t i t a t i v e p r e d i c t i o n s inadequate. L a t e l y a new theory of s u r f a c e t e n s i o n of s o l i d s based on the elementary  next-neighbor  approach has been  46  presented by S k a p s k i .  T h i s theory allows one t o c a l c u l a t e  the s u r f a c e t e n s i o n of n o n - i o n i c s o l i d s from the arrangement o f next neighbors, from the heat t e n s i o n o f the l i q u i d  of f u s i o n , and from t h e s u r f a c e  substance  at the m e l t i n g - p o i n t .  Comparison o f t h e t h e o r e t i c a l values w i t h experimental obtained from f o i l good agreement.  data  o r w i r e - s t r e t c h i n g experiments has g i v e n  Ill,  EXPEEIMEOTAL  Materials Commercially pure n i c k e l o f Type "A" grade was s u p p l i e d by Johnson and Matthey Company L t d , , London, England.  T h i s was  i n t h e form of 1/2''* round bar f o r g r a i n boundary energy measurements and 1/8'* wire f o r s u r f a c e t e n s i o n measurements. a n a l y s i s f o r t h i s m a t e r i a l i s g i v e n i n Appendix B.  The  I n the l a t t e r  stages of the experimental work, n i c k e l w i r e o f 0.010 i n c h  size  manufactured by Hoskins A l l o y s Canada L t d . , Toronto, became available. Equipment The vacuum furnace ( F i g . 6 ) used i n t h e experimental work was of m i l d s t e e l , w i t h a diameter of 8 inches and a h e i g h t of 20 inches, i n s i d e dimensions.  I t was evacuated by'a 275  l i t e r / s e c o i l d i f f u s i o n pump backed by a 140 l i t e r / m i n mechanical pump. P r e s s u r e was measured by a thermocouple vacuum gauge, and by an i o n i z a t i o n gauge.  The vacuum measuring u n i t allowed _7  an e f f e c t i v e range from 1 mm to 10 ' mm Hg, and p r e s s u r e s of _5 2*10 - mm Hg were r e a d i l y o b t a i n e d . One p l a t i n u m thermocouple, used f o r c o n t r o l l i n g the temperature, and t h e power leads were i n s e r t e d through the furnace arm which was s p e c i a l l y designed f o r t h a t purpose.  The  other thermocouple was i n t r o d u c e d i n t o t h e furnace through t h e bottom p l a t e of t h e f u r n a c e .  The c o n t r o l l i n g thermocouple was  connected t o a Honeywell r e c o r d e r - c o n t r o l l e r and t h e emf. o f t h e  -  TAP 3 PEEP fe HOLES OKI TOP 12 HOLES IN BOTTOM  J DRILL  Fie  6  Vacuum Furnace  24  -  o t h e r thermocouple  was measured w i t h a T i n s l e y potentiometer,,  A h e a t i n g c o i l of molybdenum  0 . 0 2 5  i n c h w i r e , wound  on a grooved alundum tube 1 2 inches l o n g and of 1 ^ i n c h  diameter,  s u p p l i e d the f u r n a c e w i t h power. Heat l o s s e s by r a d i a t i o n f r o m the heated decreased by the use of t h r e e c o n c e n t r i c r a d i a t i o n made of molybdenum  zone were shields  sheet.  F i g u r e 7 shows the i n t e r i o r arrangement of t h e furnace.  A complete  thermocouple,  drawing of t h e e l e c t r i c a l power s u p p l y ,  and vacuum gauge c i r c u i t s  i s g i v e n i n Appendix C.  Procedures. N i c k e l w i r e s of 0 , 0 1 0 i n c h diameter were prepared by drawing  the 1 / 8 i n c h w i r e w i t h jeweler's drawing  plates.  It  was found necessary to anneal the c o l d worked wires q u i t e o f t e n . The best l u b r i c a n t f o r the work was t h i n l u b r i c a t i n g o i l f o r scientific  instruments.  A f t e r every i n d i v i d u a l step o f  r e d u c t i o n , the w i r e s were cleaned t h o r o u g h l y w i t h carbon c h l o r i d e , and annealed i n hydrogen a t about i m a t e l y 3 0 minutes.  1200°G  tetra-  f o r approx-  S t e e l boats f i l l e d w i t h f i n e alundum  powder were used i n t h i s o p e r a t i o n .  The process was repeated  u n t i l the minimum s i z e of the w i r e was  established.  The Udin technique o f f o r c e measurement was  used.  K  N i c k e l w i r e s of 0 . 0 1 0 i n c h diameter were c o l d worked about J>% by s t r e t c h i n g and then annealed grains.  to grow s u f f i c i e n t l y  large  The most e f f e c t i v e range o f c o l d working was obtained  - 26 -  fONU/ttlON  4 A 0 E  Fig. 7  Interior Arrangement of the Vacuum Furnace A R S W T.C.  -  Radiation shells Refractory Specimen Winding tube Thermocouple  - 27  e x p e r i m e n t a l l y by s t r e t c h i n g wires at d i f f e r e n t r a t e s of and determining m i c r o s c o p i c a l l y the  -  strain  effects.  The w i r e s , cut t o s u i t a b l e l e n g t h s , were knotted at two p o i n t s l e a v i n g the approximately between them.  Great care was  order t o minimize  c o l d working of the wire between the knots. attached to each w i r e .  ranging from zero t q about two  estimated weight r e q u i r e d f o r balance, had center.  The wire was  box,  to three times  below the l o a d .  pushed through the h o l e i n the top of the n i c k e l A f t e r seven or  eight wires were mounted to the top of the box, a t t a c h e d t i g h t l y t o the box,  box.  touched  the top  was  a f t e r making sure t h a t t h e w i r e s  n e i t h e r each o t h e r nor the w a l l s of the  The box t o g e t h e r w i t h the top p l u s w i r e s and  removable n i c k e l bottom was a small  secured  The other end of the  and wedged t h e r e by a small n i c k e l p l u g .  and the weights  the  a hole d r i l l e d i n i t s  pushed through the h o l e and then  by making another knot loaded wire was  gage l e n g t h  taken i n making the knots i n  A l o a d of known weight was The weight,  predetermined  the  i n t r o d u c e d i n t o the f u r n a c e u s i n g  electromagnet. The wires were annealed  and  s t r a i g h t e n e d at or above _5  the experimental temperature approximately temperature,  one hour.  i n a vacuum of 5<LQ  The furnace was  y  mm  c o o l e d to room  a process r e q u i r i n g about twelve hours.  n i c k e l box was  removed from the f u r n a c e w i t h the  the gage l e n g t h s of the w i r e s , s t i l l  A f t e r the  electromagnet,  attached to the top of the  box, were measured w i t h the t r a v e l l i n g h o r i z o n t a l and the g r a i n s were counted.  Hg f o r  The box was  microscope,  reassembled,  returned  -  28  -  to the. furnace, and brought t o the experimental temperature f o r a time s u f f i c i e n t l y l o n g f o r a measurable  creep t o take  p l a c e , t h i s time being l o n g e r the lower the temperature.  The  f u r n a c e was cooled a g a i n t o room temperature, specimens were removed and re-measured.  The change i n l e n g t h was c o n v e r t e d  to e n g i n e e r i n g s t r a i n , and p l o t t e d a g a i n s t s t r e s s a r i s i n g from the suspended  weights.  To measure the g r a i n boundary  energy of s o l i d  nickel,  the f o l l o w i n g work had t o be c a r r i e d out. Glass proof p l a t e s of 1 mm a g a i n s t a standard o p t i c a l f l a t , picked out.  t h i c k n e s s were t e s t e d  and the s a t i s f a c t o r y ones were  These g l a s s e s were cleaned t h o r o u g h l y i n n i t r i c  a c i d and washed w i t h d i s t i l l e d water and soap.  They were d r i e d  c a r e f u l l y and mounted f i v e at a time on a s p e c i a l l y prepared support.  Aluminum was evaporated i n a s u i t a b l e apparatus.  The  d e t e r m i n a t i o n of t h e t h i c k n e s s of t h e f i l m f o r f i f t y percent t r a n s m i s s i o n and the weight i n Appendix D.  of the c o a t i n g m a t e r i a l a r e shown  A complete d e s c r i p t i o n of t h e apparatus and t h e 47  procedure used i n s i l v e r i n g the m i r r o r s i s g i v e n by S t r o n g . F o r t h i s work the apparatus from t h e P h y s i c s Department of t h e U n i v e r s i t y of B r i t i s h Columbia was k i n d l y made a v a i l a b l e . Aluminum was used as a c o a t i n g m a t e r i a l s i n c e s i l v e r was c o n s i d e r e d t o be u n s a t i s f a c t o r y because of i t s tendency t o form sulphides;  the m u l t i p l e d i e l e c t r i c  f i l m s proposed by H a r r o l d ^  were not used because of the e x p e r i m e n t a l d i f f i c u l t i e s i n p r e p a r i n g them.  O p t i c a l f l a t s were produced w i t h the f o l l o w i n g  reflectivities:  20%, 30%, 40%, 5 0 % , and 70%,  -  P i e c e s approximately commercially  c o n v e n t i o n a l methods. for  -  1/2 i n c h l o n g were cut from a  pure n i c k e l bar of 1/2 i n c h diameter,  t h r e e percent by compression  29  c o l d worked  and p o l i s h e d a c c o r d i n g t o the best  These specimens were annealed  a few days i n t h e temperature  i n vacuum  range from 1200°G t o 1 3 0 0 ° C ,  The p r i o r c o l d work o f t h e specimens allowed t h e g r a i n s t o grow to  a s u f f i c i e n t l y l a r g e s i z e , and t o r e a c h thermodynamical  e q u i l i b r i u m at t h e experimental t e m p e r a t u r e d u r i n g the allowed.  A f t e r t h e furnace was  time  c o o l e d t o room, temperature,  the  specimens were removed f o r m i c r o s c o p i c o b s e r v a t i o n of t h e t h e r m a l l y etched g r a i n The  boundaries.  contour f r i n g e s of the g r a i n boundary grooves  v i s i b l e i n monochromatic l i g h t , when the t h e r m a l l y etched s u r f a c e was  observed  through  the p a r t i a l l y r e f l e c t i n g  were  metal  optical  f l a t with i t s coated s u r f a c e a g a i n s t the specimen, p r o v i d e d t h a t the r e f e r e n c e p l a t e and the s u r f a c e of the specimen were p a r a l l e l . The mercury green l i n e of wave l e n g t h 5461 Angstroms used obtained from an i n t e r f e r e n c e f i l t e r made by B a r r and The o b j e c t i v e , focused i n the a i r gap, l i n e s at i n t e r v a l s of  A / 2 as the i n t e r f e r o m e t r i c  w i t h the i r r e g u l a r i t y of the metal was  r e v e a l e d the  surface.  was  Stroud.  contour gap  The f i e l d  varied of view  photographed t o study the s u r f a c e p r o f i l e s obtained from t h e  f r i n g e s of equal chromatic  order.  By the a p p l i c a t i o n of  experimental data i n the c a l c u l a t i o n s , the p r o f i l e of the g r a i n boundary groove was  p l o t t e d , and the d i h e d r a l angle measured.  A number of micrographs  were t a k e n t o r e c o r d some of  the i n t e r e s t i n g phenomena i n the s t r u c t u r e of the t h e r m a l l y  r 30 etched  nickel.  Difficulties. Temperature measurement and c o n t r o l . Temperature measurement i n s i d e the experimental zone, and temperature c o n t r o l were s u b j e c t t o c o n s i d e r a b l e difficulties.  In the f i r s t  t e s t when t h e platinum thermo-r  couples were i n t r o d u c e d i n t o t h e n i c k e l that they became contaminated w i t h  box. It was  condensed n i c k e l  making the r e a d i n g s completely u n r e l i a b l e .  observed vapor,  I n t h e attempts  which f o l l o w e d , the thermocouples had t o be removed from t h e a c t u a l experimental zone and covered w i t h s u i t a b l e  shielding  m a t e r i a l , thus i n t r o d u c i n g u n c e r t a i n t y i n the experimental temperature.  The magnesium s i l i c a t e  (AlSiMag2Z2Z)  tube which  served as t h e support f o r the n i c k e l box c o n t a i n i n g the specimens, was found to be s a t i s f a c t o r y .  Metal shields,  as t i t a n i u m and molybdenum, were e n t i r e l y  unsatisfactory  because  such  of t h e i r tendency t o form a l l o y s w i t h condensing  n i c k e l , and t o melt around the thermocouple. The thermocouples were observed to p i c k up an induced A.C. v o l t a g e o f up t o 70 v o l t s from the f u r n a c e winding  d u r i n g the experiments at h i g h temperatures.  the  s i t u a t i o n , thermocouples i n s e r t e d  silicate  To c o r r e c t  i n the magnesium  support were s h i e l d e d w i t h grounded molybdenum s h e e t s .  T h i s method decreased the A.C. v o l t a g e i n the thermocouple t o l e s s than 1 v o l t , but the o t h e r thermocouple.used  for control  purposes and s i t u a t e d o u t s i d e the furnace winding was never f r e e from an A.C. v o l t a g e o f at l e a s t about 15 v o l t s .  - 31 Temperature g r a d i e n t . During the p r o d u c t i o n o f t h e r m a l l y etched m e t a l l o g r a p h i c specimens,  nickel,  as w e l l as the thermal treatment  of  n i c k e l wires t o determine the s u r f a c e t e n s i o n of the m e t a l , the presence of a c o n s i d e r a b l e temperature furnace was  observed,  g r a d i e n t i n s i d e the  Although the e f f e c t  of t h i s g r a d i e n t  would be somewhat diminished by the h i g h thermal c o n d u c t i v i t y of n i c k e l , i t s u n d e s i r a b l e e f f e c t s on the experimental specimens were e a s i l y • d e t e c t a b l e .  M e t a l l o g r a p h i c specimens prepared f o r  i n t e r f e r o m e t r i c technique t o determine the g r a i n boundary of s o l i d n i c k e l were found to be u n s a t i s f a c t o r y because s u b l i m a t i o n of n i c k e l atoms on the p o l i s h e d s u r f a c e s . o r i g i n a l wire s i z e was diameter because  energy  of the The  i n c r e a s e d up to 50 percent of i t s o r i g i n a l  of the condensation o f n i c k e l vapour  i n the  c o o l e r r e g i o n s of the hot zone, and p a r t i a l l y decreased at the hotter spots.  Furthermore,  the weights  suspended  on the w i r e s  were found to have i n c r e a s e d up to 50 percent with r e s p e c t to the o r i g i n a l l y determined  loads f o r the same reason.  the thermal g r a d i e n t i n the furnace the f o l l o w i n g steps were taken: was  To  improve  corrective  the o r i g i n a l gage l e n g t h of the w i r e s , which  approximately 8 c e n t i m e t e r s , was  decreased t o about  2  c e n t i m e t e r s ; more r a d i a t i o n s h i e l d s were i n t r o d u c e d , and t h e h e a t i n g c o i l re-designed. However, t h e r e was  still  C o n s i d e r a b l e improvement was  observedo  some i n d i c a t i o n of a thermal g r a d i e n t  i n s p i t e of t h i s , the n i c k e l box appeared t o l i e i n a r e g i o n of reasonably uniform  temperature.  - 32 High vapour pressure of n i c k e l . To decrease the h i g h r a t e of e v a p o r a t i o n of n i c k e l atoms at e l e v a t e d temperatures,  i t was d e c i d e d t o use i n e r t  gas atmospheres i n s t e a d of vacuum.  A helium atmosphere o f 760  mm Hg was found t o be u n s a t i s f a c t o r y because thermal c o n d u c t i v i t y , the maximum temperature below 1200°C.  o f i t s very h i g h reached  staying  An argon atmosphere of 760 mm Hg was used  s u c c e s s f u l l y , the maximum a t t a i n a b l e temperature  approaching  1400°G. The s t r u c t u r e of experimental w i r e s . The f i n e wires employed employed i n t h e f o r c e measure ment technique t o determine t h e s u r f a c e t e n s i o n of s o l i d  nickel  were two t o three times g r e a t e r i n diameter than those used by other workers on copper, g o l d , and s i l v e r .  In the previous  work the r e p o r t e d diameters of t h e w i r e s used were 0.003 and 0.005 inches compared to 0.010 inches i n t h e present case.  The  use of f i n e r w i r e s i s c o n s i d e r e d t o be a f a c t o r i n s e c u r i n g a s a t i s f a c t o r y bamboo-like experimental t e s t s .  s t r u c t u r e of t h e w i r e s d u r i n g t h e  As a consequence, an i d e a l  bamboo-like  s t r u c t u r e of the wires was seldom observed a f t e r experimental runs.  Furthermore, much l o n g e r d u r a t i o n s of t h e experimental  runs had t o be a p p l i e d t o a c h i e v e measurable  strains.  I n t e r f e r o m e t r i e work A f t e r many u n s u c c e s s f u l attempts t o observe the F i z e a u f r i n g e s a c c o r d i n g t o the method d e s c r i b e d p r e v i o u s l y , o p t i c a l immersion  o i l was employed between the specimen and  Fig. 9  Vacuum Furnace w i t h C o n t r o l Instruments  -34.-  the coated detected  s l i p , as proposed by H i l l i a r d .  i n the regions where o i l was  specimen and  No f r i n g e s were  squeezed between the  the g l a s s p l a t e , but they were c l e a r l y  i n the r e g i o n s where no o i l was  present.  I t i s assumed t h a t  t h i s t h i n l a y e r of o i l c a r r y i n g the weight of the  specimen  promotes an almost p e r f e c t p a r a l l e l i s m between the etched  s u r f a c e and  RESULTS  G r a i n Boundary Energy of S o l i d N i c k e l . The  was  thermally  the r e f e r e n c e p l a t e ,  IV. The  visible  r e l a t i v e g r a i n boundary energy of s o l i d  nickel  determined by measuring the d i h e d r a l g r a i n boundary groove  angle  of t h e r m a l l y etched  commercially  pure n i c k e l specimens.  The  i n t e r f e r o m e t r i c method as proposed by H i l l i a r d and  was  used. Matching an aluminized  of r e f l e c t i v i t y etched of 5461  approximately  specimen, and  optically flat  glass surface  0 . 3 0 , a g a i n s t the  u s i n g monochromatic l i g h t  thermally  (Hg green l i n e  Angstroms), F i z e a u f r i n g e s r e p r e s e n t i n g the  l i n e s i n the s u r f a c e topography were observed and at a m a g n i f i c a t i o n of 1170  times.  Distances  contour  photographed  between t h e  r e s p e c t i v e F i z e a u f r i n g e s were measured to 0 . 0 0 5 cm a microscope.  Harrpld  by  using  Knowing the m a g n i f i c a t i o n of the micrograph,  the  h o r i z o n t a l d i s t a n c e s between the F i z e a u f r i n g e s were c a l c u l a t e d and  p l o t t e d a g a i n s t the constant  f r i n g e s , which were equal to  v e r t i c a l d i s t a n c e s between the or to 2.7305xlO~5 cms.  From  -  35  -  the r e s u l t i n g e l e v a t i o n p r o f i l e of the s u r f a c e slope i n the . g r a i n boundary groove, the d i h e d r a l angle A few of the micrographs  ^  was  ( F i g u r e s 10,  measured,  11,  12,  15)  and  showing the F i z e a u f r i n g e s along the g r a i n boundaries of t h e r m a l l y etched  n i c k e l specimens, and the d e t e r m i n a t i o n  d i h e d r a l angles from those  are presented  on pages 36  of 37.  and  Table I gives the h o r i z o n t a l d i s t a n c e s between the f r i n g e s , measured at the c r o s s - s e c t i o n s as i n d i c a t e d on the micrographs, and c a l c u l a t e d , t a k i n g i n t o account the m a g n i f i c a t i o n . Fig.  14  shows one  of the e l e v a t i o n p r o f i l e s of  the  gra,in boundary groove p l o t t e d from the a t t a i n e d i n t e r f erometric data. The  t e s t s to produce t h e r m a l l y  etched  specimens of -5  f o u r hours d u r a t i o n were c a r r i e d out Hg  at 1375°C.  i n vacuum of 5 x 10  Because of the e x p e r i m e n t a l  difficulties,  three d i f f e r e n t g r a i n boundaries have been s t u d i e d metrically.  ^  mm  only  interfero-  -  F i g . 10  HOOx  Micrograph Showing the F i z e a u F r i n g e s along t h e G r a i n Boundary of a Thermally Etched N i c k e l Specimen.  F i g . 11  HOOx  Micrograph Showing the F i z e a u F r i n g e s .  36 -  - 37 -  F i g . 15 Micrograph Showing the F i z e a u  1  1  0  0  X  Fringes.  -  38 -  TABLE I H o r i z o n t a l D i s t a n c e s Between t h e F i z e a u F r i n g e s Measured from t h e Experimental Micrographs.  Profile 1  2  3  5  4  •  a*  b  A  a*  b*  a*  b*  ft a•  b*  b  T  &  • 'i  0.205  17.5  0.190  16.3  0.195  16.7  0.160  13 = 7  0.190  16.3  0.155  13.2  0.250  21,4  0.275  23.5  0.190  16.3  0.170  14.6  0.145  12.4  0.220  18.8  0.240  20.5  oa8o  15.4  0  0  0  0  0  0  0  0  0  .. 0  0.175  15.0  0.160  15.7  0,230  19.7  0.260  22.0  0.175  15.0  0.205  17.5  0.185  15.8  0.260  22.2  0.300  25.5  0.210  18.0  0.215  18.4  0.215  18.4  .0,265  22.7  0.245  21.0  A  a g i v e s the measured d i s t a n c e between f r i n g e s i n cm.  A  b g i v e s t h e c a l c u l a t e d r e a l d i s t a n c e s between f r i n g e s i n 10  _5 cm.  o  g i g . 14  E l e v a t i o n P r o f i l e No. 1 of the G r a i n Boundary Groove P l o t t e d from the I n t e r f e r o m e t r i c Data.  (  ^  - 40 The  values  o f d i h e d r a l a n g l e s determined from  -  the  above data are recorded i n Table I I . Table I I i  Values of D i h e d r a l G r a i n Boundary Angles of Thermally Etched Commercially Pure N i c k e l . Profile  Dihedral Angle M>  4> 2  cos  2  1  159  79.5  0.182  0.364  2  156  78  0.208  0.41b  3  164  82  0,139  0.278  4  165  82.5  0.131  0.262  5  159  79.5  0.182  0.J64  The  s c a t t e r i n g of the  v a l u es  obtained f o r .the  d i h e d r a l angle causes, as seen from the above t a b l e , a v a r i a t i o n of the  up t o ±30 percent w i t h r e s p e c t  the r a t i o  average v a l u e ,  explained  0.33.  T h i s l a r g e v a r i a t i o n cannot  be  by the o r i e n t a t i o n dependence of the g r a i n boundary  energies.  I t i s expected that the average g r a i n boundary l i e s  between g r a i n s so d i f f e r e n t i n o r i e n t a t i o n that the angle would be v i r t u a l l y constant.  dihedral  Hence, the reason f o r the  s c a t t e r most probably l i e s i n the experimental technique conditions.  case the  F i r s t , the  or  I t i s not b e l i e v e d t h a t H i l l i a r d ' s i n t e r f e r o -  m e t r i c method has present  to  very  i n h e r e n t l y low  p r e c i s i o n , r a t h e r , i n the  s c a t t e r r e s u l t s from two  contributing factors.  shallow nature o f the g r a i n boundaries  i n the specimens, i . e . , only two not permit the a c c u r a t e  revealed  t o f o u r f r i n g e s i n depth d i d  p l o t t i n g of p r o f i l e .  H i l l i a r d , however,  - 41 was  a b l e to get boundaries  so was  s i x t o e i g h t f r i n g e s i n depth  and  a b l e t o draw b e t t e r and more a c c u r a t e p r o f i l e s .  Secondly,  only a very few  boundaries were found where f r i n g e s  c o u l d be observed, w h e r e a s , i d e a l l y , a f a i r l y l a r g e number would be necessary i n order t o get t r u l y r e p r e s e n t a t i v e v a l u e s . An attempt  was  made t o measure the d i h e d r a l g r a i n  boundary groove angles of t h e r m a l l y etched n i c k e l i n m i c r o s e c t i o n s taken p e r p e n d i c u l a r to the s u r f a c e . etched g r a i n boundaries  The t h e r m a l l y  of the specimen were observed  in  p r o f i l e and the s u i t a b l e ones were photographed a t a m a g n i f i c a t t i o n of 1100  times.  groove was magnified angle measured. was  The r e g i o n c o n t a i n i n g the g r a i n boundary ( F i g . 1_?)  from the p r i n t s and  the d i h e d r a l  A c c o r d i n g t o t h i s method the d i h e d r a l angle  found to be equal t o 146  degrees.  As s t a t e d on t h e p r e v i o u s pages (page 17)>  the  i n t e r f e r o m e t r i c method i s c o n s i d e r e d t o be more a c c u r a t e than the m i c r o s e c t i o n a l one because of i t s r e l a t i v e s i m p l i c i t y involvement  of fewer experimental u n c e r t a i n t i e s .  and  Hence, i n the  f o l l o w i n g c a l c u l a t i o n s , d e s p i t e i t s u n c e r t a i n t y because pf the small number of experimental d e t e r m i n a t i o n s , an average of l 6 l  degrees  i s used to determine  value  t h e r e l a t i v e g r a i n boundary  t e n s i o n of s o l i d n i c k e l a c c o r d i n g t o the  equation  = 2 $ cos From t h i s equation the r a t i o of g r a i n boundary to s u r f a c e t e n s i o n f o r s o l i d n i c k e l was l y 0.33  f o r the average  found t o be  v a l u e of d i h e d r a l a n g l e .  energy  approximate-  This ratio  has  - 42  been proposed and c o n f i r m e d f o r copper, g o l d , and  F i g . X5  -  silver.  M i c r o g r a p h Showing t h e M i c r o s e c t i o n o f G r a i n Boundary of T h e r m a l l y E t c h e d N i c k e l a t 1375°C f o r 4 Hours. O r i g i n a l M a g n i f i c a t i o n llOOx, enlarged 8 x .  The S u r f a c e T e n s i o n of S o l i d  Nickel  S t r a i n and s t r e s s measurements w i t h i n the r e c o r d e d temperature range f o r a determined l e n g t h of t i m e a r e g i v e n i n Table I I I .  The atmosphereic c o n d i t i o n s o f t h e s u c c e s s f u l  experiments a r e a l s o  indicated.  These r e s u l t s are p l o t t e d g r a p h i c a l l y i n a s t r e s s s t r a i n diagram, t o determine t h e l o a d which e x a c t l y b a l a n c e s t h e upward p u l l of the s u r f a c e t e n s i o n .  F i g u r e 16 i s a t y p i c a l  plot.  A c t u a l l y t h e val,ue f o r s t r e s s at z e r o s t r a i n , as w e l l as t h e s l o p e , was c a l c u l a t e d by u s i n g t h e method o f l e a s t  squares.  T a b l e IV g i v e s the v a l u e s of s u r f a c e t e n s i o n and g r a i n boundary energy d e t e r m i n e d from t h e s t r e s s a t zero  - 43 -  Table I I I Experimental S t r e s s and S t r a i n Measurements •1  Test No. Temp.°C. Time hours Atm. mm Hg Wire r a d i u s cm. Spec. No.  1300*5 20 5xl0~5 0.01425 Stress dyne/cm^ x 10 -  1 2 3 4 5 6 7 8  5  Spec. No.  1300-5  1391*5  5x10-5 ^ 0.0129  5x10-5 0.0127  Stress dyne/cm.2 -5 x IO 0.568 1.065  Strain cm/cm 5 x IO  1.44 1.91  -2.71 -1.01  4.26 5.41  -0.29 1.00  -6.15 -3,18  Stress _ S t r a i n dyne/cm cm/cm5 - 5 x IO - x IO -5.77 -6.45 -4.05 -1.88 -0.405  2.56 3.75 4.30 5.77 6.40  6'  7  10  1595*5 20 5x10"^ 0.0127  1350*5  1375±5  5x10 ? 0.0127  5x10 ^ 0.0127  Stress dyne/cm x 10"-  Strain cm/cm x 10  Stress dyne/cm, 5 x IO"  Strain cm/cm x 10  2.09 3.92  -6.02 -4.93  2.37 4.36 6.02 7.97 10.82 12.27 13.67  -0.774 -0.543 -0.056 0.728 1.32 1.94 1.79  5  1 2 3 4 5 6 7 8  5  -2.43 -1.61 0.328  Test No. Temp. °C Time hours Atm. mm Hg Wire r a d i u s cm.  4  7 0  Strain cm/cm x 10  1.75 3.23 4.07  2  9.61  5  1.46  5  Stress dyne/cm - 5 x IO -  Strain cm/cm x 10?  0.92  -0.70  2.21 4.04 5.42 5.50 7.46  -0.115 0.97 1.73 1.98 3.41  - 44 TABLE I I I (cont»d.)  Test; No.  11 1327*10 73 760 (Argon)  Temp.°C Time hours Atm, mm Hg Wire r a d i u s cm. Spec. No,  2 3 5 6 1  4  7  0,0123  Stress dyne/cm x  10  Spec. No.  t,  T  x 10  5  13  1380*10 760  (Argon) 0,0127  Stress dyne/cm 2  Strain cm/cm  -1,003 -0.843  x 10"^  0,076 0,327  1.44 2.92  71  x 10  x IO'  5  1.55  15  14  1366±10  1380±10 24 760 (Argon) 0,0126  760  70  (Argon 0,0117  Stress dyne/cm^ x 10**-  Strain cm/cm. x 10  Stress dyne/cm 2 x 10*  Strain cm/cm. x IO  0.728 0.930 1,525 2,52  -1.32 -0.19 0,382 1.79  0 . 836 1.05 / 1. ^6 2,98  ™ * *1» 0 2 2 -0.55  5  5  4.87 6,73  (Argon) 0,0126  Stress Strain dyne/cm 2 cm/cm  -1.38  4.01  6  Strain cm/cm  0. .0 48 67 4,06 1,006 3; -1 1.087 1,58 2.63  5  1 2 3 4 5 6 7 •  ^  0.749 O.949  Test No, Temp„°C. Time hours Atm. mm Hg Wire r a d i u s cm.  2  760  12 1 93 600*10  5  0,207 0.738  1.68 2.14  1.52; 2,52 3.87 4.18  5  x  10*  0.115 0.972  1.752 1,977  i-  46 -  TABLE IV Experimental Values of the Surface Tension' and'Grain Boundary Energies of Solid Nickel, X  "  1  11  "  Surface Tension dyne/cm  Grain Bound, Energy , dyne/cm,-  4V07  . 6760  2^53  79  4,22  6370  2123  1391±5  19  6o97  10320  3440  Vacuum  1395+5  20  8,30  1230O  4100  3  Vacuum  139015  50  11130  mo  10  Vacuum  1375±5  50  - 2.50  44160  13B7  Argon  1327iJ0  75  2„08  2990  997  12  Argon  1300+10  96  2,95  . 4410  1470  13  Argon  1380+10  6  1.67  2470  825  14 .  Argon '  1380±10  24  1.33  I97O  657  if-  Argon  1366iio  70  2.16  2920  973  Duration of test hours,  Test No,  .:"Atmos,  Temp °.0.  1  Vaquum  130015  42  2  Vacuum  1300+5  4  Vacuum  6  p  dyne/cm'r 10-5  '  - 47 • s t r a i n , by use of the two simultaneous l i n e a r equations, w . i r r * - (^Trr -*?* 2  a/ = 2 if cos y where, as before w = suspended  weight  & = surface tension jf*= g r a i n boundary energy r - r a d i u s of the wire = number of g r a i n s p e r u n i t l e n g t h . The value f o r ft/1, the number of g r a i n s per u n i t l e n g t h of the wire, was determined a f t e r every run by c u t t i n g p i e c e s of the n i c k e l wire specimens, i n lucite, polishing,  e t c h i n g , and o b s e r v i n g these specimens  under the microscope. determined  1 cm. l o n g , and mounting  to be 30110.  The number of g r a i n s per cm of wire was A c h a r a c t e r i s t i c micrograph  demonstra  t i n g the s t r u c t u r e o f t h e n i c k e l w i r e i s g i v e n i n F i g u r e 17 where the s o - c a l l e d  Fig.  17  'bamboo-like  1  s t r u c t u r e can be observed.  250x  Micrograph Showing t h e 'Bamboo-like* S t r u c t u r e of E x p e r i m e n t a l Wires.  - 48 V,  DISCUSSION  S u r f a c e Energy Measurements. The v a l u e of the d i h e d r a l g r a i n boundary groove f o r t h e r m a l l y etched n i c k e l was  found to be lf-1. degrees  a c c o r d i n g to the i n t e r f e r o m e t r i c method*  angle  .  On the b a s i s of the  present work and as d e s c r i b e d e a r l i e r the accuracy of t h i s method i  s  b e l i e v e d to be. higher- than, t h a t of. other .conventional  techniques.  Furthermore, the i n t e r f e r o m e t r i c method i n comparison  with the m i c r o s e c t i o n a l one was  found t o be  simpler because of the  r e l a t i v e ease i n p i c k i n g v i s u a l l y the g r a i n boundary grooves s u i t a b l e f o r the measurement of d i h e d r a l angle by o b s e r v i n g  the  symmetry of the F i z e a u fringes'.. Hence, the above v a l u e f o r the d i h e d r a l g r a i n boundary groove, angle of t h e r m a l l y etched i s thought  to' be a c c e p t a b l e , a l t h o u g h , -  been made to account boundary angle.  nickel  of course, no attempt  has  f o r the o r i e n t a t i o n dependence of the g r a i n  Furthermore, t h i s value cannot be taken  f i n a l because of the small number of t e s t s c a r r i e d  as  out  successfully. S u b s t i t u t i n g the determined angle i n the  v a l u e of the d i h e d r a l  equation X*=  2 Vcos  ^  g i v e s the r a t i o of g r a i n boundary t e n s i o n over s u r f a c e t e n s i o n for solid nickel. 0.33  T h i s r a t i o was  determined  t o be  approximately  which checks very w e l l w i t h the assumption f o r n i c k e l .  S i m i l a r v a l u e s had f o r copper,  been p o s t u l a t e d and  gold, and  silver.  confirmed  experimentally  - 4? The s u r f a c e t e n s i o n o f s o l i d n i c k e l determined i n a vacuum of 5 x I O ' mm Hg i n t h e temperature range from 1300°C t o 5  13950(3  w  a  s  found t o vary i n c o n s i s t e n t l y from 4160 t o 1 2 , 3 2 0  per c e n t i m e t e r .  dynea  The combination o f t h e h i g h vapour p r e s s u r e o f  n i c k e l under these experimental c o n d i t i o n s , and t h e sharp thermal g r a d i e n t s w i t h i n t h e hot zone, r e s u l t s i n e x c e s s i v e e v a p o r a t i o n from some p a r t s o f t h e system and condensation onto other p a r t s of t h e system.  T h i s produces changes  weights o f t h e t e s t components.  i n t h e dimensions and  T h e r e f o r e , l i t t l e r e l i a n c e may  be p l a c e d i n t h e r e s u l t s o b t a i n e d from t e s t s i n vacuum. To overcome t h e d i f f i c u l t i e s due t o t h e h i g h vapour p r e s s u r e o f n i c k e l , an i n e r t gas atmosphere was employed i n t h e experiments.  The s u r f a c e t e n s i o n o f s o l i d n i c k e l i n argon at  760 mm Hg i n the temperature range from 1300°C t o 138o°C was determined t o vary from 1 9 7 0 t o 4410 dynes p e r c e n t i m e t e r .  The  lower v a l u e s , 1 9 7 0 and 2470 dynes/cm a r e thought t o be moat reliable. I t w i l l be seen that o f t h e runs made w i t h an argon atmosphere,  those made w i t h t h e l o n g e s t times have the g r e a t e s t  surface tension value.  The time f a c t o r may be c o i n c i d e n t a l ,  s i n c e t h e m i c r o s t r u c t u r e s o f t h e w i r e s g i v i n g the l a r g e r v a l u e s were not bamboo-like,  and f o r t h i s reason alone these v a l u e s c a n  be r e j e c t e d . However, s i n c e t h e vacuum runs a r e a l l h i g h , i t may be t h a t e v a p o r a t i o n i s p a r t l y t o blame.  I t should be noted t h a t t h e  argon atmosphere does not prevent t h e e v a p o r a t i o n of n i c k e l , i t merely reduces t h e p a r t i a l pressure o f n i c k e l so t h a t e v a p o r a t i o n  - 50 i s diminished.  The vapour p r e s s u r e of n i c k e l at  the order 10  mm.  -3  1357°C  is in  46 A recent paper by Skapski  enables a c a l c u l a t i o n of  s u r f a c e t e n s i o n t o be made i f c e r t a i n values are known. E shows the c a l c u l a t i o n f o r n i c k e l . p o l a t e data by N o r t o n ^  I t was  Appendix  necessary t o e x t r a -  i n order to get a v a l u e f o r the s u r f a c e  t e n s i o n of l i q u i d n i c k e l at the m e l t i n g p o i n t s i n c e the  capillary  c o e f f i c i e n t of l i q u i d n i c k e l i s unknown. Table V. C a l c u l a t e d Values ilues o f " t h e S u r f a c e . Tension f o r S o l i d N i c k e l (dynes/cm). a  1450 1500 1550 1600 1650 1700 The  1630 1680 1730 1781 1831 1882  ^  1671 1721' 1771 1822 1872 1923  above t a b l e gives the c a l c u l a t e d v a l u e s and  be seen that they agree i n order of magnitude w i t h the  i t will  observed  surface tensions. It  i s i n s t r u c t i v e t o compare the r e s u l t s of Skapski  i n Table VI. Table VI  Metal Ag  Au Cu  (T  , 1056  1267 1417  t?w  1130*60  1350±70 1650-80  as  - 31 A l l the c a l c u l a t e d v a l u e s a r e l e s s than t h e  observed  ones, but the t h e o r y g i v e s good g e n e r a l agreement and  supports  the c h p i c e of the two  lowest  observed v a l u e s , and  a r i t h m e t i c a l average i s h e n c e f o r t h u s e d f i n a l value i s d i f f i c u l t 300  dynes/cm„  0  their  The p r e c i s i o n o f the  t o assess but i s probably b e t t e r t h a n  Hence, i t i s proposed on the b a s i s of the  present  work t h a t the s u r f a c e t e n s i o n of s o l i d n i c k e l i n argon w i t h i n the temperature range from  1370°C  to  1390°C  i s 2220*300 dynes per  centimeter. Thus the g r a i n boundary energy o f s o l i d n i c k e l w i t h i n the p r e v i o u s l y s t a t e d experimental dynes per  c o n d i t i o n s would be 340*300  centimeter. However, these v a l u e s cannot be c o n s i d e r e d as f i n a l  c o n c l u s i v e because of the s m a l l number of t e s t s c a r r i e d  and  out  s u c c e s s f u l l y under s a t i s f a c t o r y experimental c o n d i t i o n s . N e v e r t h e l e s s , i t i s b e l i e v e d t h a t these v a l u e s can be  confirmed  i n f u t u r e t e s t s provided t h a t t h e temperature c o n t r o l i n the experimental  zone i s s u f f i c i e n t l y c l o s e , the temperature g r a d i e n t  i s n e g l i g i b l e , and the s t r u c t u r e of the experimental approaches the s o - c a l l e d size,  0 , 0 0 3  to  0 , 0 0 3  I t had  'bamboo-like' s t r u c t u r e ,  A finer  wire  inches diameter, would be d e s i r a b l e .  been hoped t h a t the v a l u e f o r the  c o e f f i c i e n t o f the  wires  temperature-  s u r f a c e t e n s i o n of s o l i d n i c k e l , and the value  f o r the v i s c o s i t y of s o l i d n i c k e l c o u l d be e s t a b l i s h e d experimenta l l y , but the i d e a had to be abandoned because o f the  shortness  of time and the i n s u f f i c i e n t l y c l o s e c o n t r o l of temperature d u r i n g the  tests.  Thermal E t c h i n g . During the experimental work to determine  the g r a i n  boundary energies of s o l i d n i c k e l , the s t r u c t u r e s of the t h e r m a l l y etched m e t a l l o g r a p h i c specimens were examined f o r evidence i n d i c a t i n g the presence  of d i s l o c a t i o n s .  The d i s l o c a t i o n concept has been found t o be u s e f u l i n explaining crystal structure, diffusion, s o l i d i f i c a t i o n , deformation,  but u n t i l l a t e l y d i r e c t  experimental  and  observations  48 have been s c a r c e .  A c c o r d i n g to F o r t y  very l i t t l e work has  done on metals, most of the o b s e r v a t i o n s being c a r r i e d out  been  on  non-metals. From the c a l c u l a t i o n s based  on a d i s l o c a t i o n model of  a small-angle g r a i n boundary, i t i s expected t h a t 'the spacing of i n d i v i d u a l d i s l o c a t i o n s along such a boundary i s w i t h i n the r e s o l v i n g power of t h e . o p t i c a l m i c r o s c o p e t ^ ^ ? -  c o n c e i v a b l e t h a t a microscope power would r e v e a l the  Hence, i t i s  of s u f f i c i e n t l y h i g h m a g n i f i c a t i o n  dislocations.  The d i s l o c a t i o n s i n low-angle  boundaries  i n the m a t r i x can be r e v e a l e d w i t h methods based  as w e l l as  on the  assumption  that a d i s l o c a t i o n i s a s t r u c t u r a l d i s c o n t i n u i t y c a u s i n g d i f f e r e n c e i n the c r y s t a l l a t t i c e .  energy-  The most u s e f u l method  r e v e a l the d i s l o c a t i o n s i s the s e n s i t i v e e t c h i n g , which may accomplished  to be  by chemical, e l e c t r o c h e m i c a l , i o n i c bombardment, or  by thermal e t c h i n g .  A l l these techniques i n v o l v e the removal o f  atoms from the high-energy m i g r a t i o n from these  d i s l o c a t i o n s i t e s , the r a t e o f  s i t e s being h i g h e r than from the  neighboring  matrix. T h i s method has been employed to show the presence of d i s l o c a t i o n s xn s i l v e r  54  55  and i n chromium.  Commercially pure n i c k e l t h e r m a l l y etched at 135°°C  -5  and at a pressure of 5 x 10 following structure  mm  Hg f o r f o u r hours showed the  ( F i g s . 18-27). 55  The e x i s t e n c e of d i s l o c a t i o n s i n chromium  had been  concluded from the f o l l o w i n g f e a t u r e s r e v e a l e d a f t e r a s u i t a b l e thermal e t c h : 1.  The e x i s t e n c e o f s u b b o u n d a r i e s developed as rows  2.  The occurrence of g e n e r a l l y spaced p i t s w i t h i n  r  of p i t s .  the s u b - g r a i n . 3.  The d i h e d r a l angles between  sub-boundaries  themselves and between the sub-boundaries and the g r a i n boundaries. In the present work no sub-boundaries were d e t e c t e d as rows of etch p i t s ,  Tigs, 18  and 19  boundaries but not as a row of p i t s . boundary  , however, show subThe continuous s o l i d  c o u l d be c o n s i d e r e d as a sub-boundary  of mismatch a c r o s s the.boundary  i s very s m a l l .  s i n c e the degree The absence  of  rows of e t c h p i t s might be due to the decreased s e n s i t i v i t y  of  the thermal etch at the h i g h e r temperatures as i n the work on chromium. S i m i l a r l y , the occurrence of g e n e r a l l y spaced  pits  -  F i g . 18  1100 x  Thermally Etched N i c k e l Specimen Showing a Sue-boundary.  F i g . 20  2J00 x  Thermally Etched N i c k e l Specimen Showing t h e C o n f i g u r a t i o n around an I n c l u s i o n .  F i g . 19  54  -  2300 x  Thermally Etched N i c k e l Specimen Showing a Sub-boundary.  Fig.  21  2300 x  Thermally Etched N i c k e l Specimen Showing the C o n f i g u r a t i o n around an I n c l u s i o n .  2J00 x Thermally Etched N i c k e l Specimen Showing the C o n f i g u r a t i o n around Two Inclusions.  gift. 23  550 X  Thermally Etched N i c k e l Specimen Showing a Symmetrical Deep P i t .  (0) F i g . 24  2300 x  Thermally Etched N i c k e l Specimen Showing the Symmetrical Deep P i t from the F i g . 23.  2300 x Thermally Etched N i c k e l Specimen Showing an Octahedral Deep P i t .  Fig.  26  1100  Thermally Etched N i c k e l Specimen Showing some Symmetrical F e a t u r e s .  x  US*  27  1100  Thermally Etched N i c k e l , C h e m i c a l l y Etched before Thermal Treatment.  x  w i t h i n the g r a i n s was  dubious,,  However, i n t e r e s t i n g c o n f i g u r a -  t i o n s around the i n c l u s i o n s were rioted i n the study of t h e r m a l l y  etched  nickel.  Such p a t t e r n s around  i n c l u s i o n are demonstrated i n F i g u r e s 2 0 , Figures-23  21 and  22.  at h i g h e r temperatures only  r e l a t i v e l y deep p i t , shown i n F i g u r e 2 5 ,  symmetry at i t s base.  The  those (1500°G).  e x h i b i t s octagonal  i n c l u s i o n of F i g u r e 23 magnified  F i g u r e 24 shows hexagonal symmetry at i t s base and i n the second and  an  to 25 show the s t r u c t u r e s s i m i l a r t o  noted i n the chromium etched The  metallographic  t h i r d l e v e l s from the base.  p o s t u l a t e d that t h i s symbolizes  in  dodecahedral  I t has  the r e v e r s e process  been  of  spiral  56 growth as proposed by Frank i o d i d e c r y s t a l s by Newkirk,  and  d i r e c t l y observed i n cadmium  Thus, screw d i s l o c a t i o n s may  o p e r a t i v e i n p e r m i t t i n g s u b l i m a t i o n to take p l a c e at at which the vapour pressure 57 Danko and  Griest  corresponds to low  temperatures  supersaturations.  observed s i m i l a r s u b l i m a t i o n f i g u r e s on the  s u r f a c e of pure n i c k e l , copper, and  zinc specimens.  They found  t h a t the geometry of the s u b l i m a t i o n f i g u r e of n i c k e l and corresponded to t h e i r r e s p e c t i v e c r y s t a l  of the present work no  Griest.  n i c k e l specimens, as  However, t r i a n g u l a r , hexagonal,  c i r c u l a r c o n f i g u r a t i o n s were e x h i b i t e d i n some cases The  specimen seen i n the F i g u r e 27 was  to the thermal treatment.  In the  cubic s u b l i m a t i o n f i g u r e s were  observed on the t h e r m a l l y etched by Danko and  zinc  s t r u c t u r e s , the  f i g u r e s on the copper specimens being of c i r c u l a r nature. course  be  reported and (Fig,26).  c h e m i c a l l y etched  prior  - j>8 VT.  1.  -  CONCLUSIONS  The s u r f a c e t e n s i o n of s o l i d n i c k e l i n argon a t  760 mm Hg and w i t h i n the temperature range from 1370°C t o 1390°C was determined t o he 2220*300 dynes p e r c e n t i m e t e r , 2,  The g r a i n boundary  energy o f s o l i d J i l c k e l i n  argon w i t h i n t h e p r e v i o u s l y s t a t e d temperature range was found t o be 740*300 dynes p e r c e n t i m e t e r , assuming t h e r a t i o o f g r a i n boundary  energy t o s u r f a c e t e n s i o n f o r n i c k e l t o be 1 / 3 . 3„  The d i h e d r a l g r a i n boundary groove angle o f  t h e r m a l l y etched s o l i d n i c k e l was determined  interferometrically  and measured t o be l 6 l degrees, 4.  The r a t i o o f g r a i n boundary  energy t o s u r f a c e  t e n s i o n f o r s o l i d n i c k e l , u s i n g t h e measured dihedral, a n g l e , was c a l c u l a t e d t o be approximately 0,33 which checks w e l l w i t h t h e assumption o f 1 / 3 , 5.  The p h y s i c a l evidence f o r d i s l o c a t i o n s i n n i c k e l  was i n c o n c l u s i v e on t h e b a s i s o f o b s e r v a t i o n s on t h e s t r u c t u r e s of t h e t h e r m a l l y etched n i c k e l specimens mm Hg and at 1350°C.  i n vacuum of 3 x 10"^  N e v e r t h e l e s s , a more s e n s i t i v e thermal  e t c h at lpwer temperatures i s expected t o produce more c p n v i n c i n g p h y s i c a l evidence o f d i s l o c a t i o n s i n n i c k e l . t>„  Udin's technique t o determine t h e s u r f a c e t e n s i o n  of metals by f o r c e measurement on s t r e t c h e d w i r e s wag found t o be s a t i s f a c t o r y on a metal o f h i g h e r m e l t i n g p o i n t , p r o v i d e d  - 59 p r e c a u t i o n s were taken t o reduce the h i g h vapour pressure of the metal. 7.  H i l l i a r d ' s i n t e r f e r o m e t r i c method t o measure the  d i h e d r a l g r a i n boundary groove angles was found t o be a p p l i c a b l e and  simple.  The accuracy of the method was not v e r y h i g h i n the  present work, but t h i s c o u l d be blamed on the small number of t e s t s c a r r i e d out.  I t i s b e l i e v e d t h a t the p r e c i s i o n of t h i s  method i s not i n h e r e n t l y low.  -  VII.  APPENDICES  60  -  - 61 ^  APPENDIX A  DEFINITIONS Interface • M  . ......  i .  A n e i h t e r f a c e i s def ined; t o . be: a .bounding,;surface a c r o s s  which a d i s c o n t i n u i t y can be observed, - v . . G r a i n boundary I n the s o l i d s t a t e the observed i n t e r f a c e s due t o a d i s c o n t i n u i t y may be caused by d i f f e r e n t changes. i n t e r f a c e i s due t o a sudden change i n l a t t i c e  I f the  orientation  w i t h i n a s i n g l e phase, i t i s c a l l e d a g r a i n boundary, I n t e r f a c i a l energy Atoms i n the d i s c o n t i n u o u s regions o r i n t e r f a c e s do not have t h e i r normal number of neighbors at normal d i s t a n c e s , they are i n h i g h e r energy s t a t e s compared t o t h e atoms i n n e i g h b o r i n g homogeneous r e g i o n s .  The t o t a l excess energy of these i n t e r -  f a c i a l atoms due t o t h e abnormal s t r u c t u r a l arrangement, i s c a l l e d i n t e r f a c i a l energy. G r a i n boundary energy G r a i n boundary energy i s t h e excess.energy of the i n t e r f a c i a l atoms due t o the abnormal c r y s t a l l o g r a p h i c  arrangement.  S p e c i f i c i n t e r f a c i a l energy The s p e c i f i c  i n t e r f a c i a l f r e e energy may be d e f i n e d as  the i n c r e a s e o f f r e e energy of a system per u n i t i n c r e a s e of i n t e r f a c i a l area under c o n d i t i o n s so that the new i n t e r f a c e has i t s minimum energy c o n f i g u r a t i o n .  -  62  -  I n t e r f a c i a l force The f i c t i t i o u s f o r c e per u n i t l e n g t h which i s assumed to r e p l a c e t h e f r e e energy per u n i t area of i n t e r f a c e i n c a l c u l a t i o n s has t h e same p h y s i c a l dimensions and i s considered to be a t e n s i o n as the i n t e r f a c i a l Surface  energies  a r e always p o s i t i v e .  tension.  The s u r f a c e t e n s i o n i s d e f i n e d t o be the i n t e r f a c i a l f o r c e , i f a s o l i d o r l i q u i d i s i n e q u i l i b r i u m w i t h t h e vapour i n a vacuum o r i n a noble gas atmosphere.  - 63 -  APPENDIX B  Nominal Composition o f Commercially  Pure  N i c k e l of Type "A" Grade  Ni  (Co)  99.4%  Ee  0.15%  Mn  0.20%  Cu  0.10%  c  0.10%  Si  0.05%  S  0.005%  £1  ED  F  3>  HO  R.C.  H CO  o  V.  c+ HO  P ' I— 1  ^0  P *d  o o d 6 S:  Q CO  P d d *c(  -QJMUULgJJUU  UOv.  01} CD  w  hj  H *<  Ox.  H  K3  iy  o  CD  e g  v.a  O O O d •d i—  1  CD  P d  no v.  A - Ammeter L - Lamp  R P S T  - Relay - Potentiometer - Specimen - Time elapse meter  V.G. IsG. T.C.G. T.C. C.J. O.P.  - Vacuum gauge control - Ionization gauge -• Thermocouple gauge - Thermocouple - Cold junction - Diffusion pump  M.P. - Mechanical pump R.C. - Recorder-controller  - 65 APPENDIX D  P r e p a r a t i o n of 50 Percent  Transmitter^ Mirrors.  of the t h i c k n e s s of the f i l m f o r 50 transmission.  Determination  percent  Formulas: 0.695  \ Data:  =  4-n  /*»  y  Absorption index k  \  Refractive index n  nk f o r green Hg s p e c t r a l l i n e of 5461 A  Silver  17.9  0.175  3.30  Aluminum  3.48  1.16  4.04  Calculation: 4(1.14)(4.04) ' x  Determination  =  Q  o  9  2  8  x  1 Q  6  c  m  - l  5461 x 10-° v 0.928xlO  =  x  = 0.747 x 1 0 "  b  6  cm  of the weight o f metal needed f o r 50 t r a n s m i s s i o n t o coat the glass,'  Formula  x.t where  percent  m  4-npc  x  i s the d e n s i t y of the metal. r i s the d i s t a n c e between source metal and g l a s s  of c o a t i n g  . m i s the weight of metal needed Data:  r i s 15  cm.  m  Thickness  10.5 2.7  Silver Aluminum Calculation:  Density  0 . 9 H x 1 0 " § cm 0.747 x 1 0 cm - b  = 4(3.14)(2,7)(15 )(0.747 x 10" ) 2  A1  of F i l m  6  = 27  mg.  - 66 APPENDIX E C a l c u l a t i o n of the Surface Tension  of S o l i d  Nickel  53 According  t o Skapski  the s u r f a c e t e n s i o n of metals  can be c a l c u l a t e d from t h e arrangement o f t h e i r next-neighbors, from the heat o f f u s i o n , and from the s u r f a c e t e n s i o n o f the l i q u i d at the m e l t i n g p o i n t .  The f o l l o w i n g  equation:  (1) holds  f o r t h e c a l c u l a t i o n of the s u r f a c e t e n s i o n o f a s o l i d i n  i t s most densely  populated  planes  t o r e v e a l the minimum  surface  t e n s i o n , where  Zo,= number of next-neighbors on t h e surface ~ 2j= number of next-neighbors i n the l a t t i c e .  Qp= heat o f f u s i o n P = d e n s i t y o f s o l i d at m e l t i n g £  fl  = d e n s i t y o f l i q u i d at m e l t i n g  Ct = s p e c i f i c T= M  A£ L u  melting  point, point  surface t e n s i o n of l i q u i d p o i n t i n °K  = c o n f i g u r a t i o n a l entropy f o r the l i q u i d " i " surface.  = c o n f i g u r a t i o n a l entropy f o r the s o l i d *u>*^ s u r f a c e . f\ = molar a r e a .  where  |  = density f a c t o r  N = Avogadro's number  M = molecular  where  Oj  67  -  weight  gravity acceleration  X = height of the lower s u r f a c e of the p l a t e above the u n d i s t u r b e d l e v e l of the l i q u i d . F o l l o w i n g Skapski, cubic metal,  the minimum s u r f a c e t e n s i o n can be c a l c u l a t e d i n  the most densely For  f o r n i c k e l , which i s a f a c e - c e n t r e d  populated  planes,  Ill-planes.  nickel: 12  V  9  Z„= 1 2 - 9  5 ~o Is = 3 / 1 2 = 1/4 \ =  1.09  M = 58.69 T  I455°c.  = rn  = 4,48x10^  «t  U  ergs/degree  K  7  AS = 3 . 9 0 x 1 0 ' ergs/degree 6^ = I 8 . l 8 x l 0 ergs/gram-atom  (Metals Handbook)  1 0  j> i s c a l c u l a t e d from the l a t t i c e parameter of nickel. 6  el = 3.517x10"^ cm, and from the c u b i c a l thermal expansion c o e f f i c i e n t ^ jb - 3 8 . 1 x 1 0 a ?  cm/m,  a c c o r d i n g t o Mott and  1455°C  = (3.517 10" ) (l +  l455°G  ~  c u 3  p J  6  $  8  4  d  . °c  3  x  X  1  0  ~  2  4  3.8lxio" (1455-20)) 6  <? ^ m  ^(58.69)  6.0235xl0 3(46xio 2  . j  8  o  4  8  g  /  c  m  3  Johnson  59  Since no d a t a i s  s o l i d n i c k e l at the same temperature  i n d e n s i t y of  i s assumed t o be  similar  Hence, the d e n s i t y of l i q u i d n i c k e l at the  m e l t i n g p o i n t i s taken t o be equal to 8.26  From equation  g/cm.3  fa  = 8 . 2 6 g/cm?  A  , 1 = 1.09(6.0235xlO°J3  (2)  ?  g  Because the c a p i l l a r y unknown, the v a l u e s of G[ presented by Norton  . 2 n o ( 5 8 . 6 9 ) 3 = 3 3 . 4 x 1 0 'cur  constant f o r l i q u i d  nickel i s  has been e x t r a p o l a t e d from t h e 58  et a l .  and r e s u l t s a r e presented  below:  ( S^Sj^x^o) 8.26  +  +  y  =136  + 1.018(1550)  = 136  + 1579  = 1730  +  1455±273 .(4.48^3.90)xlo7 2(33.4x10/  2.59(0.58)  + 15  dynes/cm at 1455°C.  Assuming the thermal c o e f f i c i e n t solid  v a l u e s of  (1)  £ . l ( % l 8 x l ^ ) V p 4 33.4x107  q!  data  Owing to the u n c e r t a i n t y of t h i s  e x t r a p o l a t i o n , c a l c u l a t i o n s were made f o r s i x d i f f e r e n t  From equation  -  a v a i l a b l e c o n c e r n i n g t h e d e n s i t y of  l i q u i d n i c k e l at t h e m e l t i n g p o i n t , t h e d e c r e a s e  to t h a t of copper.  68  n i c k e l be equal to that of s o l i d ^ v w c  =  1  7  3  0  = 1730 „ = 1771  +  ° » 3 5 (1455  -  f o r s u r f a c e t e n s i o n of  copper, 1380)  + 41 dynes/cm at 1 3 8 0 ° C .  0.55  dynes/cm/°C  TABLE V. C a l c u l a t e d Values of the S u r f a c e Tension f o r S o l i d N i c k e l .  1450 1500 155Q 1600 1650 1700  1630 1680 1730 1781 1831 1882  1671 1721 1771  1822 1872 1923  - 7P VIII.  BIBLIOGRAPHY  Trans. A.I.M.E. , v o l . 175,  1... Smith, C.S., 2.  Harker, D. and Parker, E,R., p. 156.  5.  Volmer, M.  4.  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