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Some aspects of the yielding and flow of lithium fluoride Martinson, Riho Hans 1963

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SOME ASPECTS OF THE YIELDING AND FLOW OF LITHIUM  FLUORIDE  by  RIHO HANS MARTINSON  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE IN THE DEPARTMENT OF METALLURGY  We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e standard r e q u i r e d from c a n d i d a t e s f o r t h e d e g r e e o f MASTER OF APPLIED SCIENCE  Members o f t h e D e p a r t m e n t •f Metallurgy  THE UNIVERSITY OF BRITISH COLUMBIA F e b r u a r y 1963  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study.  I further agree that permission  for extensive copying of this thesis for scholarly purposes may  be  granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  Metallurgy  The University of British Columbia, Vancouver 8, Canada. Date  March 13,  196$  J  ABSTRACT  Tension tests The  results  current  ing  of s t r a i n rate  theories  locations  have been p e r f o r m e d on L i F s i n g l e change t e s t s  crystals.  are not wholly c o n s i s t e n t  of deformation processes.  with  The number o f m o b i l e  a p p e a r s t o depend s e n s i t i v e l y on t h e s t r e s s  prevailing  disdur-  straining.  A short.investigation ers  o f the e f f e c t o f removing s u r f a c e  d u r i n g d e f o r m a t i o n was u n d e r t a k e n .  polished  L i F single  The ical  effects  properties  tensile  crystals  stress,  lay-  The s u r f a c e s o f c h e m i c a l l y  are not s i t e s o f s t r o n g  o f magnesium-rich s u r f a c e  o f L i F have been s t u d i e d . and w o r k - h a r d e n i n g s l o p e  work-hardening.  layers  on t h e mechan-  The y i e l d s t r e s s , increase  critical  l i n e a r l y with  layer  thickness, while the s t r a i n to f r a c t u r e  decreases r a p i d l y  with i n -  creasing  of tension  supplemented  by  layer  thickness.  metallographic evidence,  critical  tensile stress  The r e s u l t s indicate  that  tests,  the y i e l d s t r e s s  a r e n o t d e t e r m i n e d by s u r f a c e  and t h e  source  operation.  ACKNOWLEDGEMENT  The and  Professor  ulating cation  author thanks h i s r e s e a r c h W. M. A r m s t r o n g f o r t h e i r  d i s c u s s i o n s with o f many p o i n t s .  fellow  advice  and e n c o u r a g e m e n t .  graduate students  aided  Stim-  i n the c l a r i f i -  Thanks a r e due t o M e s s r s . R. G. B u t t e r s and  R. J . R i c h t e r f o r t e c h n i c a l a s s i s t a n c e . Mr.  d i r e c t o r s , Dr. E . T e g h t s o o n i a n  S p e c i a l thanks are extended t o  W. R. I r v i n e f a r h i s many h e l p f u l s u g g e s t i o n s  and f o r t h e l o a n o f  equipment.  Financial Canada, L i m i t e d lurgy,  assistance  i n the form  and by The N a t i o n a l  awards a r e g r a t e f u l l y  was p r o v i d e d  by The S t e e l Company o f  o f The 5 t e l c o G r a d u a t e F e l l o w s h i p Research  acknowledged.  Council  i n Metal-  under G r a n t #A-1463.  Both  ii TABLE OF CONTENTS Page INTRODUCTION  1  PREVIOUS WORK  3  EXPERIMENTAL PROCEDURE  5  (1)  Material  5  (2)  Specimen P r e p a r a t i o n  5  (i)  5  (ii)  Annealing  (iii)  Polishing  (iv) (v) (vi) (3)  Cleaving •  (ii)  Etching  . . . . . . . .  7  Diffusion  9 . . . . . .  11  Mounting  .•  Tensile testing  Uncoated c r y s t a l s (i) (ii) (iii) (iv) (v) (vi)  . . . . . . . . . . . . . . . .  . . . . . . . . .  . . . . .  (iii)  12  14  Q u a l i t y o f the specimens  14  Tensile tests  15  B i r e f r i n g e n c e observations  . . . . . . . . .  IB  . . . . .  18  S t r a i n r a t e change t e s t s  Surface removal during i n t e r r u p t e d t e n s i l e t e s t s  ...  19  Removal o f surface l a y e r s during s t r a i n r a t e . i . .  ( I I ) -Coated c r y s t a l s  (ii)  11  14  change t e s t s  (i)  6  Production of evaporated coatings . . . . . .  EXPERIMENTAL RESULTS (1)  6 6  T e s t i n g procedures (i)  . . . .  19 32  P r o p e r t i e s o f as-evaporated coatings  . . . . . . . . .  32  P r o p e r t i e s o f the d i f f u s e d coatings  32  Properties of surface layers  33  . . . . . .  iii TABLE DF-CONTENTS CONTINUED Page (iv) (v)  Tensile properties  o f coated c r y s t a l s  crystals  44  . . . . . .  46  Uncoated c r y s t a l s  46  (i)  Tensile tests  46  S t r a i n r a t e change t e s t s  47  Polishing effects  51  (ii) (iii) (II)  35  M e t a l l o g r a p h i c observations on coated and deformed  DISCUSSION (I)  . .  . . .  Coated c r y s t a l s ( i ) . The p r o p e r t i e s (ii)  Tensile tests  . . . . . of the d i f f u s e d l a y e r s  53 53  . . . . . . . .  54  SUMMARY AND CONCLUSIONS  59  SUGGESTIONS FOR FURTHER WORK  60  REFERENCES  61  APPENDICES  63 .  iv FIGURES Page 1.  Cleaving apparatus  2.  Geometry during evaporation of magnesium  3.  Longitudinal  4.  Cooling  5.  Longitudinal  6.  Grown-in d i s l o c a t i o n structure  7.  T y p i c a l s t r e s s s t r a i n curves .  8.  Summary of mechanical properties  of c r y s t a l s A and  9.  Log-log p l o t of i n i t i a l strength  properties  14.  . . . . . . .  s e c t i o n of a d i f f u s i o n v i a l  8  . . . . . . . .  9  curve of furnace #1  ID  s e c t i o n of mounted specimen in LiF  11  . . . . . . . . . . . . . . .  14 15  B . . . . . .  versus s t r a i n rate  .  16  . .  17  T y p i c a l s t r e s s - s t r a i n curves obtained during s t r a i n rate change experiments  . . . . . . . . . . .  15.  Results of 10:1  16.  Results of 100:1  17.  Results of 10:1  18.  Smoothed plots of  19.  Strengthening of L i F during i n t e r r u p t e d  20.  Change i n flow s t r e s s induced by removing a 76 )\  21.  E f f e c t of removing surface change t e s t s E f f e c t of removing surface  22.  5  21  s t r a i n r a t e change experiments . . . . . . . . . .  24  s t r a i n rate change experiments  23  s t r a i n rate change experiments versus CS"  24  . . . . . . . . . . . . . . . . . . . . tensile tests  24  . . . . . .  25  . . . . .  26  layer  l a y e r s during 10:1  s t r a i n rate . . . . . . . . l a y e r s during 100:1 s t r a i n r a t e .  27  change t e s t s i n uncoated c r y s t a l s  28  23.  Birefringence  . . . . . .  29  24.  Microhardness p r o f i l e s of s e l e c t e d d i f f u s e d l a y e r s  25.  Microhardness indentations  26.  V a r i a t i o n of y i e l d s t r e s s with layer thickness . . . . . . . . . .  36  27.  V a r i a t i o n of c r i t i c a l t e n s i l e s t r e s s with l a y e r thickness  ....  37  28.  T y p i c a l s t r e s s s t r a i n curves f o r coated c r y s t a l s  . . . .  38  '.  34 .  35  V  FIGURES CONTINUED Page 29.  Variation of work-hardening slope with layer thickness . . . . . .  39  30.  Variation of strain to fracture with layer thickness . . . . . . .  40  31.  Birefringence  at the interface between the diffused layer and  the crystal interior  .  . . . . . . . .  41  32.  Photo-micrographs of diffused layers  42  33.  Photo-micrographs of diffused layers  43  34.  Short pile-up of dislocations against the diffused layer . . . . .  45  35.  Parameters observed in an idealized strain rate change test  48  ...  INTRODUCTION The mechanical properties of LiF are, at present, understood i n greater d e t a i l than those of any other material. investigations by J . J . Gilman and W.G.  A recent series of elegant experimental  Johnston has yielded detailed quantitative  information regarding the behaviour of individual dislocations i n both strained and unstrained LiF -- information which i s currently exerting a profound influence on the development of a general microscopic p l a s t i c i t y theory.  Since the work of  Gilman and Johnston i s described i n numerous readily available reviews i g i n a l communications  4-13  1-3  and or-  , i t w i l l not be surveyed here.  However, i n spite of this intensive and f r u i t f u l study, certain fundamental aspects of the p l a s t i c i t y of LiF remain obscure.  For instance, one ques-  t i o n awaiting a satisfactory resolution i s : Does the nucleation and/or m u l t i p l i cation of dislocations i n LiF occur p r e f e r e n t i a l l y near the c r y s t a l surface?.  It  i s known'' that mobile dislocation half-loops are readily introduced into LiF by 1  surface damage and that the mechanical properties of LiF are affected by such surface damage.  However, i t i s not known whether  i n the absence of large numbers of  a r t i f i c i a l l y introduced surface sources, dislocations arise more e a s i l y near the c r y s t a l surface than i n the c r y s t a l i n t e r i o r .  I t i s also not known to what ex-  tent existing mobile dislocations multiply p r e f e r e n t i a l l y near.the c r y s t a l surface. A study of the influence of alloyed surface layers on the mechanical properties of LiF was undertaken i n order to answer these questions. Fundamental differences exist between the work—hardening theories pro9  posed for LiF j and those currently thought to apply to face-centered cubic metals. In view of this,, i t seemed,desirable to perform certain standard experiments on LiF —  the Cottrell—Stokes behaviour of copper, f o r instance, i s commonly r a t i o n -  alized i n terms of the interaction of mobile dislocations with barriers possessing long-range stress f i e l d s .  The behaviour of individual dislocations i n strained  LiF^ suggests that s t a t i c barriers possessing long-range stress f i e l d s either do  not exist or do not strongly impede the motion of dislocations, at least not i n the early stages of p l a s t i c flow.  The existence of a Cottrell-Stokes law i n LiF  would therefore imply that the current interpretation of Cottrell-Stokes behaviour i s not unique. One reason why the macroscopic p l a s t i c properties of i o n i c crystals have not been studied i n the same d e t a i l as those of metals i s that i t has long been thought d i f f i c u l t to perform adequate mechanical tests on non-metallic crystals.  The simple tension test has frequently been eschewed i n principle because  of "the inherent d i f f i c u l t y of performing tensile tests on b r i t t l e materials". i  Instead, recourse i s often had to bend tests with an attendant uncertainty i n stres and a non-uniformity of s t r a i n .  It i s part of the purpose of the present work to  show that i t i s possible to perform adequate t e n s i l e tests on LiF with only moderat precautions.  Any i r r e p r o d u c i b i l i t y i n strength properties i s shown to be a t t r i -  butable to random variations i n testing procedure which, at least i n p r i n c i p l e , apply equally well to tensile tests on metallic c r y s t a l s .  -  3  -  PREVIOUS WORK Recent reviews of the e f f e c t s of environments ( s o l i d ^ l i q u i d , gaseous) on the mechanical properties  of c r y s t a l s are a v a i l a b l e . " ^ ' ^  s u f f i c e to s t a t e here that the observed e f f e c t s are many and i n t e r n a l l y consistent of the  i n the l i g h t of current t h e o r i e s ,  fundamental e f f e c t s according to the  following  and  varied,  and i t will  not  always  that a c l a s s i f i c a t i o n  scheme has  recently  been  proposed: (1) the  The  d i s l o c a t i o n egress e f f e c t —  c r y s t a l provided by,  say,  the mechanical p r o p e r t i e s (2) has  The  a s o l i d surface f i l m may  s t r e s s , a new  with i t .  Dislocations  may  slip-step.  be expected to  be anchored at the surfaces of c r y s t a l s  influence  by:  dislocations."^  pinning e f f e c t s .  surface anchoring e f f e c t may  on  dislocations.  be detectable i n measurements of the  critical  solved shear s t r e s s i f surface sources are important i n determining the resolved  shear s t r e s s .  (4)  force f i e l d e f f e c t —  The  applied  of c r y s t a l s .  (c) s e l e c t i v e p r e c i p i t a t i o n of i m p u r i t i e s The  surface  A change in' surface energy or  surface may  (a) s e l e c t i v e etching to produce hollow (b) s o l u t e  from  influence  As the screw d i s l o c a t i o n moves under  a mechanical b a r r i e r to the formation of new  (3)  be expected to  a screw d i s l o c a t i o n i n t e r s e c t i n g a clean  surface i s formed at the  the mechanical p r o p e r t i e s  egress of d i s l o c a t i o n s  of c r y s t a l s .  surface drag e f f e c t —  a s l i p - s t e p associated  a b a r r i e r to the  re-  critical  a change i n the e l a s t i c constants or l a t t i c e para-  meters near a c r y s t a l surface may  influence  the  course of deformation by  causing  an e l a s t i c i n t e r a c t i o n with the s t r a i n f i e l d s of d i s l o c a t i o n s moving near the surface.  17,18 '  '  Any c r y s t a l s may Only (2)  observed e f f e c t of environment on the mechanical properties  be regarded as a superposition  19 20 ' and  of  of these four fundamental e f f e c t s .  17 (4)  have been analysed ( s e m i - q u a n t i t a t i v e l y ) ;  a resolution  of  an observed effect into i t s components i s therefore v i r t u a l l y impossible at present. A short investigation of the effect of magnesium-alloyed surface layers 21  on the deformation of L i F single crystals has been published by A.R.C. Westwood. The relevant conclusions from t h i s research are: (1)  Metallographic evidence shows that surface coatings can act as barriers to  the egress of edge dislocations from the L i F c r y s t a l . (2)  Tests on as-cleaved, chemically polished, coated and uncoated specimens show  that a coating can r e s t r i c t the operation of a r t i f i c a l l y introduced surface sources, thereby r a i s i n g the y i e l d s t r e s s .  A coating also decreases the i n i t i a l  rate of work-hardening of as-cleaved L i F crystals by reducing the number of active dislocation sources, so that mutual dislocation interference effects are lessened. (3)  A catastrophic break-through of groups of edge-dislocations piled up against  the coating can cause stress drops i n the stress-strain curve. (4)  A surface coating can act as a stable barrier to the egress of dislocations,  causing pile-up, coalescence, and the formation of crack-nuclei beneath the f i l m . This can reduce the stress and s t r a i n to fracture of coated crystals to half that of uncoated c r y s t a l s .  - 5EXPERIMENTAL PROCEDURE (1)  Material Two L i F c r y s t a l s (A and B) were purchased from The Harshaw Chemical  Company, Cleveland, Ohio, i n the form of cleaved rectangular blocks, approximately l x l x l  inches i n dimension.  No a n a l y s i s was a v a i l a b l e from the s u p p l i e r ,  haw-  ever, i t proved possible to estimate the impurity content by comparing the mechani c a l p r o p e r t i e s of A and B with those of other c r y s t a l s obtained from the same source. (2)  Specimen preparation (i)  Cleaving Rods of the nominal dimensions 2.5  the  x 2.5  x  25  mm were cleaved from  as-received c r y s t a l s using the apparatus shown i n F i g . 1.  Fig.  1.  Clsaving  Apparatus  - 6 P r i o r to c l e a v i n g , a g r i d was c r y s t a l s with a tool-maker's of constant specimen (ii)  s c r i b e d onto one face of the as-received  surface gauge i n order to f a c i l i t a t e the maintenance  dimensions.  Annealing The as-cleaved specimens were annealed  During annealing, the specimens were supported  f o r 24 hours at 600°C i n a i r .  on high density 99.9%  alumina  a platens.  The  (iii)  annealing furnace was  cooled at the mean r a t e of 50 C per hour.  Polishing A l l specimens were chemically p o l i s h e d before t e s t i n g .  treatments Fast —  were used (Fast and  The  c r y s t a l was  Two  polishing  Slow).  r o t a t e d at approximately  \ r p s . i n 5D%  HBF4.  This t r e a t -  ment removed m a t e r i a l at the r a t e of 38 yUL per minute. Slow —  A standard c y c l e was  employed, c o n s i s t i n g of:  (a) Immersion of the specimen i n 5 0 % HF f o r 1 minute, r i n s i n g and drying, and (b) Rapid r o t a t i o n i n a 2 v o l . % aqueous NH^OH s o l u t i o n f o r 4 minutes. s t i r r i n g speed, was  The  c r i t i c a l , optimum surface appearance r e s u l t i n g from a  s t i r r i n g speed of the order of 1 0 r p s . The Slow p o l i s h i n g treatment  removed  L^jUL per minute from the c r y s t a l  surface. During p o l i s h i n g operations, the c r y s t a l s were mounted on a glass rod with a drop of "Pyeseal".  The rod was  r o t a t e d at the required r a t e s by a portable  s t i r r i n g motor. In a l l cases, at l e a s t 25 jU  was  p o l i s h e d o f f the surfaces of  as-annealed  c r y s t a l s before the c r y s t a l s were e i t h e r coated or t e s t e d . (iv)  Etching The standard d i s l o c a t i o n etching reagents f o r L i F were s l i g h t l y modified  for this investigation.  The approximate compositions  of the two  etches  (A_ and  used were: Etch A —  Equal parts of cone. HF and g l a c i a l CH3COOH plus 1 v o l . % cone. HF  W)  saturated with FeCl -4 Etch W — A.2 x 10 'molar solution of FeCl^ ^ d i s t i l l e d water. The exact optimum concentrations of the reagents were found by t r i a l n  3+ and error for individual crystals.  The Fe  concentration required i n Etch A  was especially c r i t i c a l . The specimens were rinsed i n ethyl alcohol and dried i n a warm a i r stream between individual polishing and etching operations. It was found that polishing i n HBF^ did not usually produce a surface amenable to etchpitting.  The surface structure resulting from HBF^ polishing  could, however, be removed quickly by polishing i n the NH^OH solution.  It was a  certained that the surface structure resulting from HBF^ polishing did not affect the mechanical properties of the specimens, (v)  Production of evaporated coatings Evaporated magnesium coatings were produced i n a b e l l jar, using the  geometry shown i n Fig. 2. The magnesium strip (approximately -J- x 0.01 i n . i n cross-section) was wound onto frames as shown and was heated by the passage of an e l e c t r i c current. The strip was cleaned i n dilute HCl, rinsed i n alcohol, and dried prior to sealing off the apparatus.  immediately  During the evaporation process, each spec-  imen was supported near the axis of the frame by a wire to which i t had been attached with "Pyeseal".  The evaporation process was carried out i n a vacuum of  -4 2 x 10  mm of Hg, produced by a mechanical fore pump and an o i l diffusion pump. As i t proved impossible to control accurately the amount of magnesium  deposited on the specimens., the following standard procedure was employed which maximized i t : (!) The euto-transformer controlling the input to the main step-down transformer was preset to give an output of approximately 50 volts. (2) Powe. was applied instantaneously to the step-down transformer. (.3) The evaporation process was allowed to continue u n t i l i t was terminated  - 6  e i t h e r by l o c a l f a i l u r e  o f t h e magnesium s t r i p , o r by a s h o r t  c a u s e d by magnesium d e p o s i t e d on t h e a l u m i n a The  circuit  rods of t h e s u p p o r t i n g  amount o f magnesium d e p o s i t e d on each s p e c i m e n was a s s e s s e d  weighing.  F i g . 2, Geometry d u r i n g e v a p o r a t i o n o f magnesium.  -  by  frame,  - 9(vi)  Diffusion After a satisfactory  magnesium coating had been produced, the specimens  were sealed o f f under vacuum i n Pyrex vials as shown i n F i g . 3.  A carbon sheath  was used to prevent the possibility of a chemical reaction between the magnesium and Pyrex.  Fig, 3. Longitudinal section of a diffusion v i a l . Efforts were made to reduce the oxygen partial pressure i n the diffusion vials by alternately pumping and back-filling with tank nitrogen.-  Before the  vials were sealed, a f i n a l pumping"reduced the total gas pressure to approximately -3 2 x 10  mm of Hg.  - 10 -  The majority o f d i f f u s i o n runs were made i n two i d e n t i c a l tube furnaces whose temperatures were c o n t r o l l e d  to within - 1°C by c a l i b r a t e d  thermocouples d r i v i n g Minneapolis-Honeywell c o n t r o l l e r s .  Chromel-Alumel  A check o f the temper-  ature of each run was obtained from an independent, c a l i b r a t e d  Chromel-Alumel  thermocouple placed i n contact with the d i f f u s i o n v i a l s i n s i d e the furnace tube. Because o f t h e i r high s p e c i f i c heats, the furnaces cooled quite slowly when the power was shut o f f at the end of a d i f f u s i o n run.  A furnace cooling  curve from 500°C i s shown i n F i g . 4. A f t e r d i f f u s i o n , the specimens were r i n s e d  i n approximately 0.1 M HCl  f o r 30 seconds i n order t o remove adherent portions o f the MgF2 l a y e r produced during d i f f u s i o n annealing.  600  F i g . 4.  Cooling curve o f furnace #1.  (3)  Testing procedures (i) Mounting The specimens were mounted  Fig. 5.  in mild steel grips of the design shown in  A commercially available epoxy resin (Epon 828 plus Curing Agent D,  marketed by The Shell Chemical Company, and mixed according to directions) was used to bond the specimens to the grips.  The epoxy was cured at approximately  95°C in a water bath, the total curing cycle requiring 90 minutes per end mounted.  NOT TO SCALE:  Fig. 5.  Longitudinal section of. mounted specimen.  - 12 -  During mounting, the speeimens and the grips were supported in a special j i g to ensure axial alignment of the grips and reasonably central positioning of the specimen relative to the grips.  Shims were sometimes used to correct the  position of the specimens relative to the grips. Specimen dimensions were measured ling microscope accurate to 1 Jil .  after mounting, by a Gaertner travel-  Two measurements were usually made of each  dimension* (ii)  Tensile testing. A l l tensile tests were performed on two Instron mechanical testing 22  machines, models TT-B.  A universal gripping arrangement previously described  was used i n order to minimize bending moments on the specimens caused by noncentral positioning of the specimens during mounting. A majority of the tensile tests performed during the course of this i n vestigation were done on a machine which did not incorporate a "quick-change" crosshead speed changer.  It was necessary to change gears manually between speed  changes; the process requiring approximately 4D seconds.  A "quick-change" mod-  i f i c a t i o n enables the speed change to be effected in approximately 1 second, during which time certain transient effects exist i n the motion of the crosshead.  A de-  tailed account of the procedures used to effect the changes i n crosshead speed may be found i n the Experimental Results section. A preliminary investigation of the effect of surface removal on the mechanical properties of LiF was made. (1)  The procedures used were:  The specimen was strained a given amount and removed from the testing machine.  (2)  The specimen, complete with grips, was rotated slowly in cone. HBF^ for a given time.  (3)  The specimen was replaced i n the machine, care being taken that i t was replaced i n the same position relative to the universal grips as previously.  - 13 The specimens subjected t o p o l i s h i n g during the t e s t were a l s o p o l i s h e d i n HBF^ p r i o r t o mounting, and were g e n e r a l l y given a second s h o r t (20 sec.) HBF^ p o l i s h immediately (iii)  before being t e s t e d .  Metallography A R e i c h e r t m e t a l l o g r a p h i c microscope (model MeF) and a R e i c h e r t p e t r o -  graphic microscope were used f o r m e t a l l o g r a p h i c observations and observations o f birefringence respectively. (iv)  Microhardness  measurements.  A l l coated specimens were s e c t i o n e d l o n g i t u d i n a l l y a f t e r t e s t i n g and etched i n order t o determine the t h i c k n e s s o f the magnesium-rich l a y e r .  Micro-  hardness t r a v e r s e s were made across the d i f f u s e d l a y e r s on a group o f specimens • i n order t o assess the s t r e n g t h p r o p e r t i e s o f the l a y e r s . The microhardness p r o f i l e s were obtained using a Tukon hardness t e s t e r with a Knoop diamond pyramid i n d e n t e r .  The i n d e n t a t i o n s were made with the long  d i a g o n a l o f the i n d e n t e r p o s i t i o n e d along the ^100^ d i r e c t i o n p a r a l l e l t o the edge of the specimen.  A 5 gram l o a d was used t o produce most o f the i n d e n t a t i o n s .  Each data p o i n t on the p l o t t e d p r o f i l e s represents the mean o f three measurements on each o f four i n d e n t a t i o n s .  The i n d i v i d u a l i n d e n t a t i o n s i n a  group of f o u r were no c l o s e r than three times the long d i a g o n a l o f each i n d e n t a t i o n . I t d i d not prove p o s s i b l e to perform adequate microhardness measurements on d i f f u s e d l a y e r s t h i n n e r than 20 JJl .  - 14  EXPERIMENTAL RESULTS (I)  Uncoated c r y s t a l s (i)  Q u a l i t y of the specimens: Metallographic examination  of annealed and polished specimens showed  the f o l l o w i n g : (1)  The grown-in d i s l o c a t i o n density was  between 5 x 10  and 1 x 10' d i s -  2 l o c a t i o n s per cm (2)  , excluding d i s l o c a t i o n s i n subgrain boundaries.  The mean subgrain s i z e was  2 mm.  Most of the subgrains were equiaxed  some very narrow subgrains whose boundaries l a y i n (110) planes were, however, o c c a s i o n a l l y observed near the ends of the specimens. (3)  Cleavage  steps were very small (approximately 1 j\ high) and were w e l l  rounded o f f . (4)  No evidence of micro-cracks or other damage was  found at the corners o  polished specimens. (5)  The specimen faces were u s u a l l y p a r a l l e l to w i t h i n 1 0 j j .  F i g . 6. Grown-in d i s l o c a t i o n s t r u c t u r e in L i F . E t c h - p i t density = 4.0 x 10 /cm . M a g n i f i c a t i o n - 110 X  End damage in the form of large cleavage steps and short transverse cracks often occurred on cleaving these relatively slender specimens.  The damage  was, however, confined to regions which were immersed in the epoxy during mounting and thus did not affect the quality of the specimens within the gauge length. It did not prove possible to control the specimen dimensions more closely.than to approximately - 0.2 mm.  This variation in specimen dimensions  proved troublesome in that i t caused a certain non-axiality in the loading in the very early stages of plastic flow.  The use of shims during mounting compensated  to some extent for this dimensional variation. (ii)  Tensile tests The parameters obtained from the load-elongation curves are defined in  F i g . 7.  600r  ELONGATION Cd)  ULTIMATE TENSILE STRESS (U.T.S.)  TANe - WORKHARDENING SLOPE  .05  F i g . 7. Typical stress-strain curves.  - 16 The appearance of the i n i t i a l region of the load-elongation curves varied from specimen to specimen —  typical curves are shown i n Fig. 7.  The  strain to fracture also varied greatly; total tensile strains between 3% and 13% being observed.  The results of simple tension tests on uncoated crystals are  tabulated i n Appendix TL An attempt wa's made to assess the mechanical properties of the epoxy by mounting a steel rod in the grips and performing a tensile test on i t .  The  relevant observations are: (1)  The elastic modulus of the epoxy was so small that i t alone determined the slope of the elastic portion of the stress-strain curve.  After  corrections for machine deflection had been applied, the as-measured Young's modulus of the rod was approximately 5 times lower than the true value. (2)  Slipping of the epoxy-metal bond did not start u n t i l loads i n excess of 25 lbs.--were applied. -4 At a strain-rate of 4.3 x 10  between the average  -1. sec , systematic differences appear  properties of specimens prepared from crystals A and B as  shown i n Fig. 8. 2 (g/mm )  6 (%)  Y.S. (g/mm^)  C.T.S, (g/mm^)  Crystal A  305 ± 19  385 - 30  6.8 i 1.5 x 10  3  3.8  Crystal B  254 ± 18  295 ± 6  4.4 * 0.4 x 10  3  4.3 ± 0.7  Fig. 8.  ©  1  Summary of the mechanical properties of crystals A and B. Strainrate — 4,-3 x 10 sec  The standard deviation i s used as a measure of error throughout this thesis.  0.8  0 3 I  1  L  1  1  -3.0  -4.0  LOG, F i g . 9.  -2.0 0  £  CSEC ) 1  Log-log p l o t of the i n i t i a l strength p r o p e r t i e s versus s t r a i n r a t e .  1  - IB The v a r i a t i o n of the i n i t i a l s t r a i n - r a t e i s shown i n F i g . 9. with s t r a i n - r a t e was  strength p r o p e r t i e s of c r y s t a l B with  No systematic v a r i a t i o n of worki-hafdefiing.rate  observed.  Fracture occurred by cleavage along the (100") plane normal to the axis of  t e n s i o n , g e n e r a l l y near the middle of-the gauge l e n g t h .  Very d u c t i l e  (those e x h i b i t i n g more than 7% elongation) always f r a c t u r e d near the  crystals  grips.  U s u a l l y the f r a c t u r e surfaces were plane, showing no d e t a i l except small cleavage steps.  In three instances i t was  observed  that i n a d d i t i o n to the cleavage  crack  causing f a i l u r e , s e v e r a l smaller cleavage cracks i n the neighbourhood of the main crack had been nucleated and had begun to propagate across the specimen.  These  a r r e s t e d cracks seemed to have o r i g i n a t e d oh or hear the c r y s t a l s u r f a c e . (iii)  B i r e f r i n g e n c e observations S l i p occurred on a l l of the four e q u a l l y s t r e s s e d ^ 1 1 0 } < 1 1 0 >  slip  systems from the beginning of p l a s t i c flow, subject to the f o l l o w i n g two  general  observations: (1)  U s u a l l y , s l i p occurred predominantly  on the planes  p o r t i o n of the gauge length and on ( 1 0 1 ) and (2)  ( O i l ) and  (QTl) f o r a  (TQl) f o r an adjacent p o r t i o n .  Unusually d u c t i l e c r y s t a l s s l i p p e d predominantly  on two  orthogonal  slip  planes along the whole gauge l e n g t h . Strong b i r e f r i n g e n c e bands were i n a l l cases observed v i c i n i t y of the g r i p s . tile  Kink bands were o c c a s i o n a l l y observed  i n the immediate  i n extremely  duc-  crystals. (iv)  S t r a i n - r a t e change t e s t s S t r a i n - r a t e change t e s t s were conducted  according to three  different  procedures: Procedure I —  The' specimen was  the crosshead motion was \  extended, at a s t r a i n - r a t e £  stopped,  , where 20 s e c . 4 t < 3 0 sec.  (  , to a s t r a i n  6^ ;  and the load was  allowed to r e l a x f o r a time  The  then extended at a s t r a i n - r a t e  specimen was  - 19 £ e j to a strain 6*>, and the process was repeated until the specimen fractured. Procedure II — The same procedure as I was used, except that T" =• \ second. Procedure III — The crystal was extended  at a strain rate  £^  to a strain 6 , V  the crosshead motion was then reversed u n t i l only a few grams of the load r e mained on the specimen.  A time  V  15Q sec. was allowed to elapse, after which  the specimen was extended at a strain -rate €^ . . Typical stress-strain curves obtained from strain rate change experiments are shown in F i q . 14.  Graphs of £><S and £2" as functions of  in F i g . 15, F i g . 16,Fig .17.,.. Fig. 18. Graphs of  versus  <S are shown  <5" obtained when n_g_  changes in strain-rate are made are shown in F i g . 19. (v)  Surface removal during interrupted tensile tests The effect pf removing a 76 ^Jl surface layer by chemical polishing at  various points on the stress-strain curve is i l l u s t r a t e d in F i g . 20. It is apparent that the work-hardening slope is not changed by the polishing treatment, but that the flow stress is changed discontinuously by an amount ACS" which varies linearly with the flow stress (vi)  Removal of surface layers during strain rate change tests The effect of removing 76 Jj. and 38 jU surface layers during strain rate  change tests is shown i n F i g . 21 and F i g . 22. The change in the flow stress is irreversible by an amount varies with strain and with the amount of material removed.  which  It should be r e -  alized that this is an i r r e v e r s i b i l i t y of a second kind since the strain rate changes were conducted according to Procedure III, which does not produce an i r reversible effect of the f i r s t kind, as may be seen from F i g , 19.  - 02  - 21 -  - 22 -  - 23  .20 r  6  INCREASING  4  200  400  600  C;||)  , E  DECREASING  800  1200  IOOO  cr, e g / m m ) 2  F i g . 17.  Results o f 10:1 s t r a i n rate change experiments. S t r a i n r a t e c y c l e d between 4.28 x 10 s e c and 42.8 x 10" s e c - 1  4  - 1  -i  - 24  40  I £00  I  400  I  600  1 800 0",  Fig. IB.  :  ' 1000  (9/mm ) 2  Smoothed plots ofA<S versus GT  ' " 1200  —  -  1  1400  -  80  -  •  0  r  25  • PROCEDURElje^ea^^XlO^Sec"  *tf60  ID  UJ  h  o —I U-  40 -  O 2 <  zr.  20  P R O C E D U R E I , €, = e = a  SUxicf  4  sec  1  PROCEDURE!!, •  »  -I  PROCEDURETI, ^ % = 2 l . 4 X l " - S e C 4  0  450  550  650  T50  850  FUOWSTRESS  F i g . 19.  Q50  cr, c g/mm )  Strengthening observed i n L i F during interrupted tension tests.  2  1050  1  /  - 26 -  60  0  ON  \  0  «40 tf) (0  LU  cc h-  o 20 -  AC-"= .1430"  LU  -50  0  vD  < a:  o i.  -20 200  600  400 FLOW  Fig. 20.  S T R E S S  Chenge in flaw stress induced by removing a 76 surface layer during tension testing. Strain rate 4.28 x I D sec - 4  - 1  800  - 27 -  200  400  600  800  FLOWSTRESS  F i g . 21.  1000  1200  CT, Cg/mnni ) 2  E f f e c t of removing surface l a y e r s during 10:1' s t r a i n r a t e change experiments. S t r a i n rate c y c l e d between 2.14 x . l O sec" and 21.4 x I O " s e c - 4  4  - 1  - 28 -  300  400  500  600  FLOWSTRESS Fig. 22.  TOO CT^  800  (9/mffP)  Effect of removing surface layers during strain rate change experiments. Strain rate cycled between 21.4 x 10~ sec -'" and 214 x ID" sec" 4  4  1  -  Fig.  23.  Birefringence  i n uncoated  crystals  SOX  - 30 Summary o f e x p e r i m e n t a l (l)  The  yield  imately  observations  stress  5 ppm.  and  f o r uncoated  critical  tensile  magnesium v a r y w i t h  -  specimens.  s t r e s s of L i F c o n t a i n i n g approx-  strain  4*  r a t e a c c o r d i n g to the  equations:  144  where  (2)  The  i n i t i a l work h a r d e n i n g  rate i n the (3)  (4)  above r a n g e o f s t r a i n  L i F does n o t  obey t h e  c h a n g e s ; the  plot  of  &<S  v e r s u s . <s  p o r t i o n o f the  non-zero  at  A«5  <S =  The  change i n f l o w  and  II i s i r r e v e r s i b l e  closely  l o a d f o r 45 The  by  strain  e q u a l to the  r e s p e c t to s t r a i n  exhibiting versus  a minimum.  <5*  curve  rate  The  approx-  extrapolates to a  an amount t h a t i n c r e a s e s w i t h rate.  The  change i n t h e  seconds, f o r both  s m a l l i f the  with  o f L i F as measured a c c o r d i n g t o p r o c e d u r e s  amount o f i r r e v e r s i b i l i t y  ligibly  strain  O.  stress  faster  independent of  rate.  C o t t r e l l - S t o k e s law  imately l i n e a r  './Value o f t h e  (5)  rate i s substantially  10:1  i n the  absolute  amount o f i r r e v e r s i b i l i t y  flow and  the  stress 100:1  induced  by  aging  changes i n s t r a i n  is under  rate.  change o f f l o w s t r e s s becomes  s t r a i n r a t e change i s c o n d u c t e d  I  a c c o r d i n g to  negpro-  cedure I I I . (6)  The  change i n f l o w  surface i s  ^(S*  stress  caused  by  polishing  76  o f f the  crystal  , where:  £><s" =^ . \ 4 3 <r - 5 0 (7)  During  1:10  strain  r a t e change t e s t s ,  from the s u r f a c e o f the second  effect  s p e c i m e n i s to c a u s e an  k i n d to appear i n the  (a) i n c r e a s e s w i t h  the  flow stress  increasing stress  which:  o f removing m a t e r i a l irreversibility  of  the  -  31  -  (b) increases with the amount of m a t e r i a l removed. (8)  During 100:1 s t r a i n rate change t e s t s , the e f f e c t of p o l i s h i n g the c r y s t a l surface i s :  (a) the same for Z^^S f as f o r ^<s'"^ (b) such as to decrease  uniformly.  off  (II)  COATED CRYSTALS  (i)  Properties  o f as-evaporated  coatings.  The a s - e v a p o r a t e d magnesium a p p e a r e d l u s t r o u s and " s i l v e r y " a t t h e magnesium-crystal greyish. imately  i n t e r f a c e , whereas  t h e m a g n e s i u m - a i r i n t e r f a c e a p p e a r e d d u l l and  The amount o f magnesium d e p o s i t e d 1 milligram  to 3 milligrams.  w i t h magnesium i n t h e e v a p o r a t i o n  on t h e s p e c i m e n s v a r i e d from, a p p r o x -  A l l t h e c r y s t a l s were c o m p l e t e l y  p r o c e s s , a l t h o u g h no way was f o u n d t o a s s e s s t h e  uniformity' o f t h e as-evaporated coatings.  Evidence that the coating  s p e c i m e n was, i n . f a c t , s u f f i c i e n t l y u n i f o r m w i l l be p r e s e n t e d (ii)  Properties  of diffused  covered  on any one  later.  coatings.  A f t e r d i f f u s i o n , t h e MgF£ e x c e s s magnesium c o a t i n g s . w h i c h had formed as a c o n s e q u e n c e o f t h e r e a c t i o n between t h e magnesium and L i F were brown i n c o l o u r . The d e g r e e o f a d h e r e n c e o f t h e MgF2 c o a t i n g t o s p e c i m e n and f r o m p l a c e  t o place  to the substrate  on any one s p e c i m e n .  v a r i e d from specimen  U s u a l l y , most o f t h e  coating  s p a l l e d o f f i n l a r g e p a t c h e s on r e m o v a l o f t h e s p e c i m e n f r o m t h e d i f f u s i o n  vial.  The r e m a i n d e r was l o o s e n e d i n d i l u t e H C l as d e s c r i b e d  previously.  Gas  e v o l u t i o n was o f t e n o b s e r v e d t o accompany t h e H C l t r e a t m e n t . No d i s c o l o r a t i o n o f t h e P y r e x v i a l was observed, when t h e s p e c i m e n s were completely enclosed i n the graphite  sheaths,, a l t h o u g h e v i d e n c e o f a  reaction.be-  tween t h e g l a s s and t h e magnesium t o form MgO was.found i n c e r t a i n e a r l y r u n s d u r i n g ' w h i c h t h e s p e c i m e n s were n o t c o m p l e t e l y  protected.  Debye-Sherrer X-ray d i f f r a c t i o n patterns  of typical as-diffused  coat-  i n g s showed t h e f o l l o w i n g : (1)  The a s - d i f f u s e d c o a t i n g s  consisted  o f MgF2.  ' F a i n t magnesium l i n e s were  o b s e r v e d i n one i n s t a n c e . . (2)  The l a t t i c e p a r a m e t e r s o f t h e a s - d i f f u s e d c o a t i n g s  were i d e n t i c a l  (O.OOS  t h o s e o f p u r e MgF  ?  within experimental error  (Q. 05' ft).  f\)  with  - 33 (iii)  Properties  of the surface  layers.  LaUB X-ray d i f f r a c t i o n patterns of s e l e c t e d fused l a y e r s  specimens with t h i c k  dif-  (150 jji ) did not appear e s s e n t i a l l y d i f f e r e n t from patterns obtained  from pure L i F c r y s t a l s .  In p a r t i c u l a r , Debye rings were not observed i n the  patterns obtained from c r y s t a l s with magnesium-rich surface  layers.  Debye-Sherrer d i f f r a c t i o n patterns of powder ground from the surface  (150Jd).  a specimen with a t h i c k LiF patterns.  of  d i f f u s e d l a y e r were s u c c e s s f u l l y indexed as pure  No l a t t i c e parameter change greater than 0.005? was  observed  and  no' extra l i n e s appeared. No second phase was  observed by focussing  the surfaces of c r y s t a l s with thick d i f f u s e d The  etching  a microscope s l i g h t l y below  layers.  behaviour of the d i f f u s e d surface  32 l a y e r i s shown i n Fig.£3%  It should be noted that the photo-micrographs show l o n g i t u d i n a l sections  of  de32  formed c r y s t a l s . The  The  "thickness"  d i f f u s e d surface  5% of the l a y e r thickness, sectioned  c r y s t a l . ' The  and  s e n s i b l y equal i n thickness on both sides of  one  runs. and  No  by varying  c r y s t a l varied from one  the  the duration  the  p o s i t i o n to another.  to c o n t r o l the thickness of the  diffused  and/or temperature of the d i f f u s i o n  c o r r e l a t i o n between the amount of magnesium deposited on the  the thickness of the d i f f u s e d l a y e r s was  established.  thicknesses as w e l l as corresponding times and ulated  within  response of the l a y e r s did not suggest that  It did not provB possible layers accurately  i n Fig.33-.  l a y e r s were u s u a l l y uniform i n thickness to  etching  character of the l a y e r on any  of the d i f f u s e d l a y e r i s as defined  The  crystals  measured l a y e r  temperatures of d i f f u s i o n are  tab-  i n Appendix IV-. Micro-hardness p r o f i l e s of t y p i c a l d i f f u s e d l a y e r s are -shown i n Fig,24. The  LiF i s unity.  p r o f i l e s have been normalized so that the micro-hardness of "pure" No systematic d i f f e r e n c e s were observed between the micro-hardnesses  of c r y s t a l s A and  B.  - 35 -  The quality of the micro-hardness indentations is shown in F i g . 25.  F i g . 25.  (iv)  Micro-hardness indentations in LiF. ^ 2 0 X  Tensile properties of coated crystals The variation of the yield stress and the c r i t i c a l tensile stress of  surface-alloyed crystals with the thickness of the alloyed layer is shown in F i g . 26 and F i g . 27. abraded  The properties of three surface-alloyed crystals which had been  equal amount (20 strokes) on 4/0 emery paper are also shown in the  figures. Typical stress-strain curves for coated crystals are shown in F i g . 26. No stress drops or yield drops were observed in the stress-strain curves of the coated crystals.  - 36 -  LAYER F i g , 26.  T H I C K N E S S C/L)  Variation of yield stress with layer thickness  - 37 -  LAYER THICKNESS CjU.) Fig.  27.  Variation of c r i t i c a l tensile stress with layer thickness.  F i g . 28.  Typical stress-strain curves for coated crystals.  - 39 -  6  0  r  <D<D 0  PIP  ©  LU CL O  m  4  0  z z o  ©  3  O 0  X  §  2  h  ©  ©  ©  LU 0)  bo  © 0  ©0  o  20  40  60  LAYER T H I C K N E S S  F i g . 29.  80  I0O (}X)  V a r i a t i o n of i n i t i a l work-hardening slope with l a y e r t h i c k n e s s .  120  LAYER  F i g . 3D.  THICK N E S S  C ju)  V a r i a t i o n of the s t r a i n to f r a c t u r e with l a y e r t h i c k n e s s .  -  F i g . 31.  Birefringence at the d i f f u s e d layer crystal interior interface. TSK  —  41  42 -  F i g . 32.  Photo-micrographs of diffused layers.  2.SOX  - 43 -  F i g . 33.  Photo-micrographs of diffused layers.  2.00 X  - 44 The  work-hardening slopes of those specimens which exhibited  p l a s t i c i t y f o r the slopes to be measurable are p l o t t e d against Fig.  -  enough  l a y e r thickness i n  29. Coatings t h i c k e r than 30 p  in Fig.  embrittled  the specimens severely  as shown  30.  T The (v)  r e s u l t s pertaining  to coated c r y s t a l s are tabulated  Metallographic observations on coated and (a)  Observations of  deformed c r y s t a l s .  birefringence.  S l i p bands were observed i n every specimen which had i n those which had  f a i l e d i n an e s s e n t i a l l y b r i t t l e manner.  photographs obtained under crossed n i c o l s . l a y e r s and Fig.  i n Appendix iV-.  The  been tested,  even  F i g . 31 shows t y p i c a l  i n t e r f a c e s between the  the specimen i n t e r i o r s exhibited marked b i r e f r i n g e n c e ,  diffused  as i s shown i n .  31. (b)  Etch-pit The  observations.  d i s l o c a t i o n density  specimens which had (1)  (2)  i n the c r y s t a l i n t e r i o r was  been s t r a i n e d and  The  density  any  one  The  mean d i s l o c a t i o n density  sectioned.  measured on  selected  Three general observations were:  of d i s l o c a t i o n s v a r i e d by a f a c t o r of approximately two  in  specimen. was  approximately 5 x 10^  dislocations/ 2 c m  as determined by area counts. (3)  The  d i s l o c a t i o n density  was  always low  t h i c k d i f f u s e d l a y e r s , the density c r y s t a l s (5 x 10^/ J  The —  cm  was  l i t t l e evidence of d i s t i n c t s l i p bands was Fig.  In  equal to that of unstrained  2)  d i s t r i b u t i o n of e t c h - p i t s was,  are shown i n F i g . 32 and  i n the d i f f u s e d l a y e r s .  i n the majority of cases, uniform found.  T y p i c a l photo-micrographs  33.  A band.of high d i s l o c a t i o n density, ways observed at the d i f f u s e d l a y e r —  approximately 10 |^wide, was  pure c r y s t a l i n t e r f a c e .  al-  Recognizable  - 45 dislocation pile-ups were only rarely observed,  An example of a pile-up is shown  in F i g . 34.  F i g . 34.  A short pile-up of dislocations against the diffused layer. 4 2 0 /  DISCUSSION (I) (l)  Uncoated c r y s t a l s , Tensile tests I t has been e s t a b l i s h e d by W.G.  Johnston t h a t the mechanical p r o p e r t i e s  of L i F are h i g h l y s e n s i t i v e to i m p u r i t y content, and t h a t the i m p u r i t y content of c r y s t a l s obtained from The Harshaw Chemical Co. i s v a r i a b l e . c e n t r a t i o n of magnesium from 3 ppm. t o 75 ppm.  can change the c r i t i c a l  shear s t r e s s of L i F (at room temperature) from 170 g/mm to 1750 g/mm LiF  2  , depending on heat treatment  11  .  A change i n the con-  2  resolved  t o a value from 300  g/mm  The s t r e n g t h p r o p e r t i e s of impure  are s t r o n g l y dependent on the c o o l i n g r a t e from temperatures greater than  200°C, i n c r e a s i n g r a p i d l y with c o o l i n g r a t e .  The s t r e n g t h p r o p e r t i e s of r e l a -  t i v e l y pure L i F are independent of c o o l i n g r a t e f o r r a t e s l e s s than 10^ °C min  \  A comparison of the c r i t i c a l r e s o l v e d shear s t r e s s e s of c r y s t a l s A and B with those used i n the i n v e s t i g a t i o n s of Johnston''""'" suggests t h a t the magnesium contents of both A and B were approximately 10  ppm.  A theory of the r a p i d hardening induced i n L i F by t r a c e amounts of 23 magnesium has very r e c e n t l y been proposed by F l e i s c h e r The causes of the i r r e p r o d u c i b i l i t y (observed by a l l current  investi-  gators) i n : (1)  The appearance o f the i n i t i a l region of the s t r e s s - s t r a i n curve of L i F , and  (2)  The amount of s t r a i n to f r a c t u r e are w e l l understood. Pure L i F t e s t e d at room temperature under v e r y . c a r e f u l l y c o n t r o l l e d  c o n d i t i o n s has been shown to e x h i b i t a l a r g e (30%) y i e l d drop"^.  However, the  specimen alignment must be c o n t r o l l e d by r a t h e r e l a b o r a t e procedures i n order t o .observe a r e p r o d u c i b l e y i e l d drop. sent i n v e s t i g a t i o n .  Such procedures were not a p p l i e d i n the pre-  I t should be noted, however, t h a t a moderate degree of non-  a x i a l i t y of l o a d i n g has ( e m p i r i c a l l y ) been shown not to change the c r i t i c a l r e -  2  - 47 -  solved shear s t r e s s by more than B%  1 9 21  I t has been shown that cracks can be generated during p l a s t i c flow i n ionic crystals.by  the i n t e r a c t i o n o f d i s l o c a t i o n s moving on i n t e r s e c t i n g  p l a n e s . I n  L i F , cracks l y i n g i n {100~^ planes have been found t o nucleate ->  slip  24  at the i n t e r s e c t i o n o f p a i r s of conjugate £110 j s l i p planes.  I t i s therefore  apparent that the s t r a i n to f r a c t u r e i n L i F c r y s t a l s i s a s e n s i t i v e f u n c t i o n of the slip distribution.  The s l i p d i s t r i b u t i o n , i n t u r n , depends s e n s i t i v e l y on the  geometrical d i s t r i b u t i o n of d i s l o c a t i o n sources o p e r a t i n g i n the very e a r l y (none l a s t i c ) p o r t i o n of the s t r e s s - s t r a i n curve, since i t has been shown that a whole s l i p band can a r i s e from one i n i t i a l mobile d i s l o c a t i o n h a l f - l o o p by m u l t i p l i c a t i o n processes.  Mobile surface h a l f - l o o p s  are i n e v i t a b l y introduced during h a n d l i n g .  ( I t has r e c e n t l y been s e r i o u s l y suggested that s t a b l e d i s l o c a t i o n h a l f - l o o p s  can  be introduced i n t o r e l a t i v e l y pure L i F by atmospheric dust p a r t i c l e s impinging on the c r y s t a l s . ^ )  Hence, i t i s not unreasonable to expect that the s t r a i n t o  f r a c t u r e w i l l vary g r e a t l y i n L i F unless very s t r i n g e n t c o n t r o l indeed i s e x e r c i s e d during handling and t e s t i n g . The r e l a t i o n s h i p between the amount' o f d u c t i l i t y and the d i s t r i b u t i o n of s l i p observed i n t h i s i n v e s t i g a t i o n i s c o n s i s t e n t nucleation iii)  with current t h e o r i e s  o f crack  i n ionic solids.  S t r a i n r a t e change t e s t s I t i s known"^ that the average v e l o c i t y of an i n d i v i d u a l d i s l o c a t i o n i n  s t r a i n e d L i F can be a c c u r a t e l y  where  expressed i n the form:  = dislocation <5" = a p p l i e d  density  stress  \ff\ = a constant, 1 6 ^ 25, independent of <^ and G~ For any p l a s t i c deformation process, the f o l l o w i n g r e l a t i o n holds:  e - c b9 v s  Q  (2  )  - 4B -  where  £  = the tensile strain rate of the specimen  C e , = an appropriate geometrical factor ^  = burger's vector = the area density of moving dislocations  Consider an idealized strain rate change test (one in which the change of crosshead speed is instantaneous) resulting in an observed load-elongation curve similar.,to the'one shown in F i g . 35.  F i g . 35.  Parameters observed in an idealized strain rate change test.  - 49 Let the parameters points P-^ and P 2 .  CTj  CT  and  2  sj  and ^> take the values  CVij^V)  ^  anc  j^a,^ ^ ^ a  e  Let the c o n v e n t i o n a l l y defined flow s t r e s s e s at Pj_ and P 2 be Then:  where  = a constant independent of s t r e s s  I f i t i s now assumed that:  (2) 5^' = CS^ ( i . e . The flow s t r e s s at P2 i s s u f f i c i e n t l y w e l l represented by <  the usual convention.) then: N^VY\  ve.  _  C  ^  ^  - &  m  \ >  v  (4)  0  (5)  That i s , a C o t t r e l l - S t o k e s law follows from the premises:  (2) gc^ = OCcsn A C o t t r e l l Stokes law i s not pbserved i n L i F . mental f a c t s . of  ( l ) and (2) are e x p e r i -  I t follows that equation (4) i s i n e r r o r and t h a t the c o r r e c t form  (5) i s :  _\_  That i s , the observed A<5 i s not even approximately a t t r i b u t a b l e to the change i n the mean d i s l o c a t i o n v e l o c i t y .  Instead, the magnitude of £>^ i s gov-  erned by a combination of a change i n the number of mobile d i s l o c a t i o n s (caused by 26 m u l t i p l i c a t i o n processes, perhaps according to the theory of Wiedersich  .) and  a change i n the mean d i s l o c a t i o n v e l o c i t y .  acti-  The a s s i g n a t i o n of a s i n g l e  v a t i o n energy to the process r e s u l t i n g i n the observed  i s t h e r e f o r e meaningless.  Independent evidence of the v a l i d i t y o f t h i s c o n c l u s i o n e x i s t s . equation (2) i t follows that:  dOo^e) _ dfloqv) + dQo9?\  (7)  From  - 50  D i r e c t measurements of L i F ^ " ' ^ , s i l i c o n i r o n ^ ' ^ , and 2  have been performed Ge"^'  -  on:  For a l l of these materials i t has been  shown, that:  That i s , a change i n s t r a i n rate i s accompanied by a change i n both, the number and the mean v e l o c i t y of mobile d i s l o c a t i o n s .  It should  be noted that the  increase  i n the number of mobile d i s l o c a t i o n s i s not p h y s i c a l l y unreasonable i n that i t does not imply extensive  motion of d i s l o c a t i o n s i n a p e r f e c t l y e l a s t i c region  the s t r e s s - s t r a i n curve.  The  i m p l i c a t i o n i s simply  of  that f o r a given increase i n  p l a s t i c s t r a i n , the mean number of d i s l o c a t i o n s moving i s a s e n s i t i v e f u n c t i o n ofthe mean s t r e s s p r e v a i l i n g during the s t r a i n i n c r e a s e .  Studies of i n d i v i d u a l •  8 d i s l o c a t i o n m u l t i p l i c a t i o n events i n unstrained deed so.*  -  LiF  have shown that t h i s i s i n -  .  When the crosshead of a t e s t i n g machine i s suddenly stopped, an i n s t a b i l i t y occurs i n the dynamic e q u i l i b r i u m between the- time rates of change of d i s l o c a t i o n production,  debris production,  and  d i s l o c a t i o n v e l o c i t y which i s estab-  l i s h e d during a t e n s i l e t e s t . . It does not, however, immediately f o l l o w that one  of these q u a n t i t i e s becomes zero instantaneously,  zero at .approximately equal r a t e s .  or even that they approach  It i s premature to speculate  on the d e t a i l s  of the events o c c u r r i n g during s t r a i n rate changes i n view of the f a c t that  * I t has been shown t h a t :  where  <S  =  the  _  f\ = ' number of loops emitted'in moves.  1 second when a d i s l o c a t i o n  applied stress 8  The measurements were conducted i n the domain 1.6 5 x 10^  d y n e s / 2 j the corresponding range of  A  —3 10  loops/sec  Z. GMft ^ 10  x 10  is:  cm  any  3 loops/sec  dynes/ 2 ^ cm  ^  ^  - 51 current t h e o r i e s of work-hardening i n L i F are not yet f u l l y q u a n t i t a t i v e . should  It  be noted, however, t h a t :  (1)  The 100:1  irreversibility  of the f i r s t  s t r a i n r a t e changes, the amount of extension  quired to account f o r the ing  kind i s not caused by creep.  observed strengthening  i s approximately 4" mm.  The  For  of the specimen r e -  by normal work-harden-  amount of ( e l a s t i c ) extension  required  -2 to completely unload the specimen i s c a l c u l a t e d to be 10 (2)  Known s t r a i n - a g i n g processes are not i n v o l v e d i n the observed.  mm.  irreversibilities  A time of the order of 1 hour at a temperature of 120°C i s  r e q u i r e d to lock d i s l o c a t i o n s i n r e l a t i v e l y impure L i F ^ . f a c t that n e g l i g i b l e strengthening r a p i d l y unloaded and  Also,  the  of the specimens occurs i f they are  held i n the unloaded c o n d i t i o n f o r times comparable  to the time required to e f f e c t the s t r a i n r a t e changes  excludes the pos-  s i b i l i t y of s t r a i n - a g i n g processes o c c u r r i n g . The  f a c t remains, however, that L i F does harden on unloading  and  that  the amount of hardening increases with the s t r e s s p r e v a i l i n g during s t r a i n i n g . This suggests that, during  unloading,  the debris production  r a t e decreases l e s s  r a p i d l y with s t r e s s than does the d i s l o c a t i o n v e l o c i t y . Haasen has r e c e n t l y reported  s i m i l a r " i r r e v e r s i b l e e f f e c t s " while i n 31 v e s t i g a t i n g s t r a i n r a t e change phenomena i n NaCl. . The e a r l y portion of the 29 &<S versus <S" curve i n s i l i c o n i r o n also e x h i b i t s i r r e v e r s i b i l i t i e s . i i i i ) Polishing effects Only very general conclusions may  be drawn from the e s s e n t i a l l y ex-  p l o r a t o r y i n v e s t i g a t i o n of the e f f e c t of removing surface l a y e r s during  tension  testing: (1)  The  e q u i l i b r i u m d i s l o c a t i o n d i s t r i b u t i o n i n s t r a i n e d L i F i s not  the  same throughout the whole c r y s t a l . (2)  The  d i s t r i b u t i o n of d i s l o c a t i o n s i n L i F i s not the same i n a l l stages  of the s t r e s s s t r a i n curve.  - 52 (3)  The surface is not a preferred site of work-hardening in L i F .  (4)  The effects of surface removal are not large unless relatively thick layers (more than 20 |A) are removed. Conclusion (3) is in agreement with Mendelson's work on NaCl, 33  in disagreement with the results of Suzuki for KC1. experimental procedure has recently been questioned.  32  but is  (The adequacy of Suzuki's  32.  )  \  II  Coated c r y s t a l s  (i)  The p r o p e r t i e s of the d i f f u s e d l a y e r s Two  obvious i n c o n s i s t e n c i e s i n the p r o p e r t i e s of the magnesium-rich  l a y e r s are: (1)  The micro-hardness p r o f i l e s suggest t h a t s o l u t i o n s of the d i f f u s i o n equation r e l a t i n g to d i f f u s i o n from an instantaneous plane source of s t r e n g t h (X are a p p r o p r i a t e .  Q  (viz. couft = (2)  The  e"Dt  observation t h a t magnesium was  ')  present i n excess suggest t h a t s o l -  u t i o n s of the form  C t t ; b * C C 0 e r f c JL_ o  HOV  are r e l e v a n t .  In view of these i n c o n s i s t e n c i e s and s i n c e no systematic time dependence of the l a y e r t h i c k n e s s was  temperature or  e s t a b l i s h e d , i t i s apparent t h a t some  e s s e n t i a l l y u n c o n t r o l l e d v a r i a b l e governed the d i f f u s i o n k i n e t i c s during t h i s i n vestigation.  A c c i d e n t a l surface contamination and a v a r i a b l e r e s i d u a l gas com-  p o s i t i o n i n the d i f f u s i o n v i a l s may  conceivably  have i n f l u e n c e d the d i f f u s i o n  k i n e t i c s markedly, although the remarkable u n i f o r m i t y of the c h a r a c t e r of the d i f fused l a y e r on any one c r y s t a l suggests t h a t s u r f a c e contamination was portant . f a c t o r .  The  not an .im-  c o r r e l a t i o n s attempted i n t h i s i n v e s t i g a t i o n are, i n any  case, based on the independently measured p r o p e r t i e s of the d i f f u s e d l a y e r s . The q u a n t i t a t i v e c o r r e l a t i o n of hardness measurements with t e n s i l e perties i s d i f f i c u l t .  pro-  For any given m a t e r i a l and w i t h i n r e s t r i c t e d ranges of  hardness, the e x i s t e n c e of a general c o r r e l a t i o n of the form:  h  H  , i •,. I ,34  U.T.S.CQ ,  VL01  \1XS.(£)  HC8)  (9)  has been e s t a b l i s h e d . . I t has proved p o s s i b l e to e s t a b l i s h an analogous e m p i r i c a l c o r r e l a t i o n between Knoop hardness and the flow s t r e s s of L i F at 0.06% 35  i n bending) from the data of Nadeau. .  s t r a i n (as measured  - 54  -  It i s :  Unfortunately,  t h i s c o r r e l a t i o n i s e s t a b l i s h e d from data r e l a t i n g . t o  L i F c r y s t a l s ten times harder than those used i n the present i n v e s t i g a t i o n and must t h e r e f o r e be regarded as t e n t a t i v e . I f an e x t r a p o l a t i o n of (10) i s accepted as v a l i d , the y i e l d s t r e s s of the- i s o l a t e d d i f f u s e d l a y e r s was crystals.  approximately three times t h a t of the pure L i F  Even i n view of the u n c e r t a i n t i e s i m p l i c i t i n the a p p l i c a t i o n of  to the present case, i t seems safe to conclude that the y i e l d s t r e s s of the fused l a y e r s was. at most s i x times greater  (10) dif-  than t h a t of the pure L i F .  The X-ray i n v e s t i g a t i o n of the nature of the d i f f u s e d l a y e r s shows t h a t : (1)  The  amount of second phase (MgF2) present, i f any,  was  too s m a l l to be  detected by the Debye-Sherrer technique. (2)  The  l a t t i c e parameter of the magnesium-rich L i F was  i d e n t i c a l with  that  o of pure L i F to w i t h i n 0.002A. (3)  The  d i f f u s e d surface  l a y e r s were s i n g l e c r y s t a l s , coherent with the sub-  strate. (2)  Tension t e s t s Assume that no i n t e r a c t i o n occurs between the c r y s t a l i n t e r i o r and  d i f f u s e d l a y e r during a tension t e s t . <S  Q  =  ."S = =  the  Define:  y i e l d s t r e s s of the pure c r y s t a l y i e l d s t r e s s of the d i f f u s e d l a y e r y i e l d s t r e s s of the combination  ( " y i e l d s t r e s s " i s to be i n t e r p r e t e d as the s t r e s s necessary to e s t a b l i s h a given small d i s l o c a t i o n v e l o c i t y ) I t f o l l o w s immediately t h a t :  £ = &where  X  Cl -  fr).  =  t h i c k n e s s of the d i f f u s e d l a y e r  =  the s i d e of the cross s e c t i o n of the specimen  - 55 -  From the data i n F i g . 26,  5.=:g2  CQV X-I001A)  (12)  A value o f 55D0 g/ 2 f o r the y i e l d s t r e s s o f magnesium doped L i F canmm  not be r e j e c t e d a p r i o r i , i n view o f the known strong hardening e f f e c t o f magnesium on L i F .  S e v e r a l reasons a r e , however, apparent why such a l a r g e value f o r  the y i e l d s t r e s s of the d i f f u s e d l a y e r s i s not c r e d i b l e : (1)  The micro-hardness measurements suqqest t h a t  (2)  When a d i f f u s i o n run was terminated, mately .2"°C per minute.  ~? — So  6.  the furnace was cooled a t a p p r o x i - .  I t i s known t h a t i n order to o b t a i n great  s t r e n g t h e n i n g , magnesium-containing L i F must be coaled at r a t e s of the order of 1 0 (3)  min  \  L i F c o n t a i n i n g 0.5 mol. % magnesium has a y i e l d s t r e s s of 6000 g/mm2 when slow cooled"^.  approximately  However, l a r g e c h a r a c t e r i s t i c MgF2 pre-  c i p i t a t e p a r t i c l e s are.seen i n such h i g h l y a l l o y e d L i F .  No evidence of  a p r e c i p i t a t e was found i n the d i f f u s e d l a y e r s during the present i n v e s t igation. (4)  The maximum s o l u b i l i t y of magnesium i n L i F v a r i e d from 0,03 mol. % to 0.40 mol. % at the temperatures p r e v a i l i n g during the d i f f u s i o n runs. In view o f the f a c t t h a t l i t t l e v a r i a t i o n i n the e t c h i n g behaviour of 'the l a y e r s on d i f f e r e n t c r y s t a l s was observed, i t i s apparent t h a t the s o l u b i l i t y l i m i t was not a t t a i n e d . approximately  This e s t a b l i s h e s an upper bound of  300 ppm on the c o n c e n t r a t i o n of magnesium i n the l a y e r s .  Such a value i s a l s o c o n s i s t e n t with the micro-hardness measurements. I t can t h e r e f o r e be concluded t h a t a l a r g e degree o f i n t e r a c t i o n e x i s t s between the d i f f u s e d l a y e r s and the c r y s t a l i n t e r i o r during t e n s i o n t e s t s . Of the four fundamental mechanisms proposed by Machlin, three a r e , i n p r i n c i p l e , a p p l i c a b l e to the present system.  The " f o r c e - f i e I d " e f f e c t and the 17  a s s o c i a t e d edge d i s l o c a t i o n p i l e - u p s proposed by Head  may be excluded  since  Nadeau has shown t h a t the Young's modulus of L i F i s not changed g r e a t l y by  - 56  -  „ . : 35 magnesium a l l o y i n g . .. The  l i n e a r dependence of the y i e l d s t r e s s on the  very t h i c k l a y e r s suggests that (1)  Fisher type surface  (2)  The  l a y e r thickness up  to  either:  sources do not e x i s t i n L i F , or  y i e l d s t r e s s i s not the s t r e s s required  to a c t i v a t e surface  sources  (or both). The metallographic evidence shows that, i n specimens possessing t h i c k d i f f u s e d l a y e r s , d i s l o c a t i o n s were nucleated and  m u l t i p l i e d much more r e a d i l y i n  the c r y s t a l i n t e r i o r than i n the d i f f u s e d l a y e r s .  The  evidence was  less clear  i n the case of t h i n l a y e r s since the specimens were s t r a i n e d a large amount before being sectioned.  Even i n these cases, however, l e s s d i s l o c a t i o n a c t i v i t y  apparently occurred i n the  layers than i n the c r y s t a l i n t e r i o r .  that the mechanical properties follows  of thick and  had  I f i t i s assumed  t h i n l a y e r s were nearly  identical, i t  that at the beginning of p l a s t i c flow, d i s l o c a t i o n s were i n a l l cases gen-  erated more e a s i l y i n the  c r y s t a l i n t e r i o r than i n the l a y e r s .  s t r e s s of a specimen with a 20 Jjl l a y e r was c r y s t a l , i t follows operation.  only 50%  that the y i e l d s t r e s s was  Since t h e ' y i e l d  greater than that of pure  not determined by surface  Instead, d i s l o c a t i o n s were nucleated i n the  source  c r y s t a l i n t e r i o r at  stresses below the macroscopically determined y i e l d s t r e s s , and m u l t i p l i e d  pro-  f u s e l y before emerging from the c r y s t a l s . The  processes whereby d i s l o c a t i o n s are nucleated i n L i F are not  understood at present, as i t has been shown that the  grown—in Frank network.does  not act as a source of d i s l o c a t i o n s , at l e a s t i n c r y s t a l s of presently purity.^"  It has  fully  available  also been shown that d i s l o c a t i o n s do not a r i s e homogeneously  i n p e r f e c t regions of L i F c r y s t a l s even at stresses  as high as G_ B5  The  pre-  sent work i n d i c a t e s that d i s l o c a t i o n s either do not a r i s e p r e f e r e n t i a l l y near the c r y s t a l surface,  or the y i e l d s t r e s s i s not determined by source operation, or  both. Evidence has  been presented that edge d i s l o c a t i o n s p i l e up at the.interface  - 57 between the d i f f u s e d l a y e r and the c r y s t a l i n t e r i o r .  The strengthening caused  by the l a y e r s i s probably a s s o c i a t e d with t h i s p i l e - u p phenomenon.  However, i t  i s i m p o s s i b l e , a t the present s t a t e o f knowledge, to develop a q u a n t i t a t i v e theory of the s t r e n g t h e n i n g . I t should be noted that the mere e x i s t e n c e o f short p i l e - u p s cannot g r e a t l y change the increment o f p l a s t i c s t r a i n o c c u r r i n g at a given mean s t r e s s , since:  e where  X  bp  t  (i3)  = mean s l i p d i s t a n c e o f the moving d i s l o c a t i o n s  and hence:  , 3 :=4*U) That i s , i t i s not p o s s i b l e to a t t r i b u t e the increased r a t e o f workhardening  o r the increased y i e l d s t r e s s merely to the s m a l l changes i n the mean  s l i p d i s t a n c e o f g l i d e d i s l o c a t i o n s which a short p i l e - u p causes. The m u l t i p l i c a t i o n r a t e o f screw d i s l o c a t i o n s may be a f f e c t e d by back s t r e s s e s from the p i l e d - u p groups, but i n view o f t h e ' f a c t t h a t the mechanism o f 26 36 37 38 d i s l o c a t i o n m u l t i p l i c a t i o n i n L i F i s not yet f u l l y understood,  '  ' .'  specul-  a t i o n on t h i s p o i n t i s premature. The decrease i n d u c t i l i t y caused by the presence o f a d i f f u s e d l a y e r i s undoubtedly a s s o c i a t e d w i t h the p i l i n g up o f edge d i s l o c a t i o n s a g a i n s t the 39 layer.  Crack n u c l e a t i o n by the mechanism proposed by Stroh  o r by a v a r i a t i o n  40 thereof  probably occurs at the i n t e r f a c e , and the cracks grow according t o the 41  mechanism proposed by G r i f f i t h s . •The r e s u l t s o f the present i n v e s t i g a t i o n cannot be compared i n d e t a i l with the work o f Westwood f o r the f o l l o w i n g reasons: (1)  The a l l o y e d l a y e r s were prepared  by d i f f e r e n t techniques  i n the two  investigations. (2)  The greater part of Westwood's work was concerned with.the!:locking of a r t i f i c i a l l y introduced surface sources.  - 58 There are certain points of conflict, however, between the results of Westwood and those of the present author: (1)  Westwood observed that the i n i t i a l rate of work-hardening increased rather less rapidly with layer thickness than the trend established in this investigation indicates.  (2)  Largely as a consequence of ( l ) , Westwpod observed that the ultimate tensile stress of the coated crystals was often reduced to half of that of uncoated crystals.  In the present investigation, the ultimate ten-  s i l e strength of coated crystals was always larger than the average value for uncoated crystals. (3)  Regarding (apparently) one experiment on a polished and coated crystal Westwood states  the reaction treatment had very l i t t l e effect on  i t s yield stress (an increase of 3%) and caused only a small increase in the c r i t i c a l resolved shear stress (13%)".  Unfortunately, no data on  the coating thickness are provided.(Generally, Westwood differentiates only between thin ("^TlO  ) and thick ( £i 25 JJl and ^ 50 JUL ) coatings.)  The present investigation shows that i t is possible to increase both the yield stress and the c r i t i c a l resolved shear stress of polished crystals by 250% by producing 50 )& thick alloyed layers. It seems to be implied throughout Westwood's communication that a magnesium-alloyed layer has relatively l i t t l e effect on the strength properties of polished LiF crystals.-  The hardening observed in as-cleaved  and coated crystals is .attributed to the locking of a r t i f i c i a l l y i n t r o duced surface dislocation sources by magnesium.  However, the present  investigation shows that i t is possible to strengthen polished LiF crystals appreciably by producing a magnesium rich surface layer.  Sur-  face source locking effects seem to contribute l i t t l e to .the strengthening.  SUMMARY AND CONCLUSIONS (1)  It is possible to perform adequate tensile tests on LiF single crystals while  taking only moderate precautions. (2)  The change of flow stress observed during strain rate change tests i s not de-  termined solely by a change in the mean velocity of previously mobile dislocations. The number of mobile dislocations apparently changes greatly during both increases and decreases of strain rate.  Hence, an a p r i o r i application of the current rate  theory formalism to work-hardening processes constitutes a serious over-simplification. (3)  During stress relaxation, dislocation activity prevails i n LiF.  The hard-  ening caused by this activity increases with the level of stress from which relaxation occurs.  This implies that macroscopic, plastic deformation is not prerequi-  site to strain hardening. (4)  Preliminary  evidence exists that the distribution of dislocations i n a rather  thick ( 8 D JUL) surface layer is not identical with that existing . in the interior of strained LiF crystals.  The difference i n distribution appears to be associa-  ted with macroscopic effects which are more complex than a preferential surface layer hardening phenomenon. (6)  The y i e l d stress and/or the c r i t i c a l resolved shear stress of chemically pol-  ished LiF are not the stresses required to activate dislocation sources existing near the crystal surface.  - 6D SUGGESTIONS FOR  The  present  work c o u l d be  FURTHER WORK  e x t e n d e d i n many  directions:  -2 (1) be  The  p r o p e r t i e s of L i F at high  interesting.  strain rates  -1  (10  sec  Adequate i n s t r u m e n t a t i o n f o r t h e i r  study  -1 to 1 sec  should  ) appear  prove easy  to  develop. (2)  A c a r e f u l p h o t o - e l a s t i c study,  prove f r u i t f u l ,  contingent  l o c a t i o n models o f the (3)  The  refined  on t h e  utilizing  high  speed cinematography,  d e v e l o p m e n t o f unambiguous q u a n t i t a t i v e d i s -  birefringence effects.  p r e s e n t work on s u r f a c e c o a t i n g s might w e l l be  techniques  (4)  The  effects  gated  more  (5)  A study  should  repeated,  u s i n g more  of coating preparation. o f removing  surface l a y e r s during deformation  should  be  invest  thoroughly.  would p r o b a b l y  o f the t e m p e r a t u r e v a r i a t i o n not  prove i l l u m i n a t i n g  of the mechanical  at the present  time.  properties of LiF  - 61 REFERENCES  1.  J.J, Gilman and W.G. Johnston, Dislocations and Mechanical Properties of Crystals. J.C. Fisher ed., Wiley, N.Y. 116, (1957)  2.  J.J. Gilman, Progress in Ceramic Science v o l . I. J.E. Burke ed., Pergamon Press N.Y.  (i960)  3.  J.J, Gilman and W.G.  Johnston, Solid State Physics 13, D. Turnbull ed. (1962)  4.  J.J. Gilman and W.G.  Johnston, Jour. App.. Phys. 29., 877 (195B)  5.  J.J. Gilman and W.G.  Johnston, Jour. App. Phys. 3D, 129 (1959)  6.  J.J. Gilman, Jour. App. Phys. 20, 1584  7.  W.G.  8.  J.J, Gilman and W.G.  9.  J.J. Gilman, Jour. App. Phys. 33, 2703 (1962)  (1959  Johnston and J.J. Gilman, Jour. App. Phys. 31., 632 (i960) Johnston, Jour. App. Phys. .31, 687 (I960) <  10.  W.G.  Johnston, Jour. App. Phys. 33, 2716 (1962)  11..  W.G.  Johnston, Jour. App. Phys. .33, 2050 (1962)  12.  J.J. Gilman, Jour. App. Phys. 4., 601 (1958)  13.  J.J. Gilman, Acta Met. ±, 123, (1961)  14.  I.R. Kramer and L.J. Demer, Prog, in Metal Phys. 9., (i960)  15.  E.S. Machlin, Strengthening Mechanisms in Solids. A.S.M. Seminar, 375 (1962)  16.  A.C.R. Westwood, Phil. Mag. 6, ;542 (1961)  17.  A.K. Head, Proc. P h i l . Mag. 44,. 92 (1953)  18.  E.D. Shchukin, Proc. Acad. S c i . U.S.S.R. 118, 1105 (1958)  19.  F.R.N. Nabarro, Advances in Physics .1, 269- (1952)  20.  J.J. Gilman, P h i l . Mag. 6,, .159 (1961)  .21. 22.  A.R.C. Westwood, P h i l . Mag. 5., 981 (i960) R.F. Snowball, Unpublished M.A.Sc. thesis, The University of British Columbia (I960)  23.  R.L. Fleisher, Jour. App. Phys. 33,, 3504 (1962)  24.  W.G.  Johnston, P h i l . Mag. 5,, 407 (i960)  - 62 REFERENCES CONTINUED  25.  R.J. Stokes, T.L. Johnston,  and C H .  L i , Strengthening Mechanisms i n S o l i d s ,  A.S.M. Seminar, 341 (1962) 26.  H. Wiedersich, Jour. App. Phys. 33, 854 (1962)  27.  W.L.  28.  D.F. S t e i n and J.R. Low, Jour. App. Phys. 31, 362 (1960)  29.  R.W.  30.  A.R. Chaudhuri,  31.  P. Haasen, Jour. App. Phys. 2£, 718 (1958)  32.  S. Mendelson  33.  T. Suzuki, D i s l o c a t i o n s and Mechanical P r o p e r t i e s of C r y s t a l s . J.C. Fisher ed. Wiley* N.Y. 215 (1957)  34.  Oata by Wilson Mechanical Instrument D i v i s i o n , American Chain &. Cable  P h i l l i p s , Trans. A.I.M.E. 218, 939  Guard, Acta Met. 9,  f  (i960)  163 (1961)  J.R. P a t e l , and L.G. Rubin, Jour. App. Phys. 33, 2737 (1962)  Jour. App. Phys. 33., 2182  (1962)  Inc. 35.  F, Nadeau, Unpublished  Ph.D. Thesis, U n i v e r s i t y of C a l i f o r n i a ,  36.  F. Tetelman, Acta Met. 10, 1021 (1962)  37.  J.C.M. L i and C.D. Needham, Jour. App. Phys. 31, 1318  38.  A.S. Argon, Acta Met. 10, 574 (1962)  39.  A.N. Stroh, P h i l . Mag. 46, 986 (1955)  40.  A.H. C o t t r e l l , Trans. A.I.M.E. 212, 192 (1958)  41.  A.A. G r i f f i t h s , Trans. Roy. Soc. (London) A 221. 180 (1921)  (i960)  (1959)  Co.,  - 63 APPENDIX  I  ESTIMATES DF ERROR  (1)  Uncertainties in measurements It is apparent that:  &s =  cLL  S where  A =  i.e.  (2)  +  =  CU  +  &_F F  A,  F  2&X. X  stress  F  =  force  A  =  specimen  X  =  edge of  &P = P  .01  cross-section cross-section  +  (2)(.005) 2.5  =  .015  Uncertainties in parameter measurements from the chart. (a)  The yield point could be determined to £(Y.P.)  =  00  =  .10 l b s . in 4 lbs.  .025  4 (b)  The c r i t i c a l tensile stress could be determined to 0.01 lbs. in 4 lbs. .*.  £>(C.T.S.)  = jDl 4  =  .003  Therefore, the total uncertainties in the absolute values of the strength parameters due to errors of measurement are: 5 (C.T.S.) t  (3)  2%  The effect of non-axiality. On the basis of e l a s t i c i t y theory, the distribution of stress on the  specimen cross-section sufficiently far from the grips was linear, such that:  -64 where  S  _  maximum t e n s i l e s t r e s s i n outer f i b e r  ^avg  =  average t e n s i l e s t r e s s  £  =  distance from c e n t r o i d o f specimen to point o load a p p l i c a t i o n  m a x  ^max - 5 Savg  i.e.  a V  g  ^ (6)(.2) ^(2.5,(2)  = 0.25  This i s an upper bound, since the exact value depends on the (unknown d e t a i l s o f the p o s i t i o n of the specimen r e l a t i v e to the g r i p s .  As deformation  proceeds, the s t r e s s d i s t r i b u t i o n w i l l become more uniform. The non-uniformity o f s t r e s s proved troublesome•for specimens possess ing t h i c k a l l o y e d l a y e r s .  However, i t was often p o s s i b l e t o determine which  specimens had been subjected to bending moments by etching longitudinal section.  the s l i p bands on a  The r e s u l t s of t e s t s on specimens which showed evidence  of having been bent were d i s c a r d e d .  - 65 APPENDIX  II  Results of Tensile Tests on Uncoated Specimens  Critical Tensile Stress (g/mm )  Ultimate Tensile Stress (g/mm2)  Total Strain  A 2  349  387  665  .0433  .640  4.28  A 3  318  388  586  .0251  .780  4.28  A 7  336  419  692  ,0471  .581  4.28  , 286  428  581  .0156  .972  4.28  A 9  275  351  732  .0508  .747  4.28  A 19  288  338  556  .0437  .510  4.28  A 27  281 •  386  585  .0359  .566  4.28  B 1  224  285  427  .0359  B 2  236  282  512  .0522  .441  4.28  B 3  299  318  448  .0284  .456  4.28  B 4  278  316  574  .0532  .485  4.28  B 12  259  295  4.28.  B 13  268  281  • 4.28  B 14  25D  296  4.28  B 35  212 '  289  4.28  B 8  257  307  2,14  B 15  206  231  2.14  B 17.  188  244  2.14  B 19  184  244  2.14  B 21  220  254  2.14  B 22  209  235  2.14  B 23  205  243  2.14  B 25  198  263  2.14  B 3D  222  279  2.14  B 7,  360  421  21.4  B 27  298  329  21.4  B 29  344  445  21.4  2  A. 8  2  ;  WorkHardening Slope (g/WxlQ-*)  Strain Rate  Yield Stress (g/mm )  lecimen Jumber  .395  (sec-ixlO ) 4  4.2B  - 66 -  Specimen Number  Yield Stress (g/W)  Critical Tensile Stress  Ultimate Tensile Stress  (g/mm )  (g/W)  2  B 32  WorkHardening Slope  Total Strain  (g/mm^xlQ- ) 4  (sec-^xlO ) 4  359  21.4  B 33  291  342  21.4  B 18  423  456  214  B 24  501  515 '  214  495  214  B 28  Note:  Only the i n i t i a l strength properties are l i s t e d for the specimens on which Cottrell-Stokes tests were performed.  Average I n i t i a l Tensile Properties of Uncoated Specimens from Crystal A.  Critical Tensile  Strain Rate (sec-1 10 )  Yield Stress (g/mm2)  2.14  209 + 7  255 ± 7  4..28 -  254 ± 18  295 + 6  21.4  322 + 8  354 + 14  214  471 + 50  490 + 24  4  \  Strain Rate  , * f* (g/mm^) S  r B  - 67 A P P E N D I X III  R e s u l t s of S t r a i n Rate Change Tests Specimen B 8 . S t r a i n Rate Cycled by I (2.14 - 21.4 x I O " s e c ) 4  In(l+-S_) (g/mm ) 2  <s\  - 1  <5T (g/mm ) 2  In(l+<5 ) <5\  310  .122  .0012  653  .088  .0381  328  .143  .0036  671  .076  .0402  349  ,185  ,0043  680  .083  .0408  378  .114  .0062  699  .072  .0434  384  .116  .0068  707  i082  .0439  408  .109  .00B7  728  ;068  .0460  ' 409  .150  .0093  738  .077  .0465  433  .117  .0116  755  .068  .04B7  437  .133  .0122  764  .076  .0492  449  .120  .0139  781  ,068  .0513  455  .120  .0144  789  .077  .0519  456  .119  .0166  811  .063  .0539  476  .114  .0172  823  .069  .0545  487  .099  .0192  843  ^063  .0568  494  .114  ,0197  850  .074  .0574  507  .099  .0219  869  .064  .0595  515  .106  .0222  879  .071  .0600  530  .089  .0246  900  .063  .D622  536  -.100  .0250  907  .073  .0626  554  .082  .0273  927  .062  .0646  559  .098  .0279  939  .070  .0652  577  .079  .0298  956  .067  .0671  582  .095  .0303  971  i064  .0678  595  .087  .0322  992  ^060  .0699  604  .090  .0327  1003  .068  .0705  620  .079  .0351  1015  .069  .0725  628  .091  .0356  1029  .067  .0730  643  .076  .0381 .  1050 .  .063  .0750  - 68 Specimen B 5  Specimen B 8  S t r a i n Rate Cycled by I (2.14 - 21.4 x I O sec" ) - 4  (5  In(l+i_)  g/mm ) 2  1  In(l+1_]  .(g/mm ) 2  LQ  10.68  .060  .0755  284  .193  .0035  1083  .065  .0783  323  .185  .0057  1094  .066  .0788  342  .213  .0062  1120  .063  .0810  365  *155  .0083  1137  .062  .0816  368  .203  .•089  1158  .058  .0836  392  .158  .0108  1169  .062  .0840  397  .180  .0110  1192  .055  .0860  400  .131  .0132  1206  .061  .0870  405  .161  .0138  1232  .056  .0889  431  .121  .0163  1244  .059  .0895  432  .160  .0167  1256  .061  .0920  455  .124  .0193  1282  .059  .0925  463  .141  .0197  1314  .050  .0946  487  .088  .0223  1322  .060  .0951  492  .141  .0227  512  .111  .0248  519  .128  .0252  - 69 Strain Rate Cycled by I (2,14 - 21.4 x I O s e c ) - 4  (g/mnr)  AS"  -1  In(l+i£j  In(l+<5 j  (g/mm^) 850  .069  .0695  866  .058  .0705  880  .072  .0723  905  .065  .0741  931  .078  .0760  952  .064  .0778  971  .072  .0797  990  .064  .0814  1020  .067  .0835  252  .233  .0034  276  ,165  ,0054  286  .183  .0071  303  .145  .0089  313  .178  .0106  329  .154  .0123  341  .162  .0144  362  .130  .0163  418  .126  .0232  436  .101  .0250  450  .106  .0272  468  .095  .0290  478  .114  .030B  497  .090  .0327  507  .110  .0344  528  .086  .0362  542  .099  .0380  565  .076  .0401  580  .088  .0420  597  .077  .0438  Specimen B 17  610  .097  .0455  628  .076  .0472  Strain Rate Cycled by I (2.14 - 214 x IO" s e t )  646  .085  .0491  663  .071  .0507  682  .081  .0526  700  .070  .0548  723  .076  .0570  741  .062  .0589  764  .080  .0613  787  .062  .0632  806  .078  .0653  829  .063  .0671  Specimen B 16 Strain Rate Cycled by I (2.14 - 214 x ID" s e c ) 4  -1  In(l+S )  .(g/mnr)  To  370  .702  .0044  625  .212  .0227  633  .369  .0252  794  .173  .0329  824  .274  .0359  4  (g/mnr)  <S\  - 1  In(l+6 )  382  .682  ,0036  586  .252  .0151  599  .403  .0176  802  .173  .0302  820  .236  .0333  1000  jl.49  .0477  1019  .210  .0504  1208  .130  .0626  1229  .193  .0659  1414  .124  .0780  - 70 Specimen B 18  Specimen B 35  S t r a i n Rate Cycled by I (2.14 - 214 x IO" s e c " ) 4  1  In(l+<S )  (g/mm ) 2  ~E~o  S t r a i n Rate Cycled by II (4.28 - 42,8 .x I O sec" ) - 4  cs;  1  In(l+6)  (g/mm ) 2  585  .239  .0216  230  .710  .0013  . 615  .469  .0254  395  .121  ,0110  839  .186  .0357  406  4144  .0132  880  .252  .0411  456  .107  .0213.  1330  .120  .0683  464  ;122  .0231  533  .095  .0347  546  .102  .0366  613  ^083  .0472  626  .093  .0490  702  .077  .0607  720  .085  .0629  766  .078  .0695  S|pecimen B 34 S t r a i n Rate Cycled by II (4.28 - 42.8 x ID" s e c " ) 4  (g/mm^)  AS  -  CSv  1  In(l+&)  396  .162  .0027  478  .096  .0088  488  .118  ,0095  655  .067  .0176  683  .082  .0183  852  .058  .0270  894  .067  .0284  1041  .053  .0349  Specimen B 26 S t r a i n Rate Changed by III (2.14 - 214 x 10-4 s e c " ) 1  (g/mm  2  (g/mm ) 2  In(l+<5 )  To ,  • 306  189  .0131  429  125  .0224  493  .38  .0317  703  .0405  - 71 -  Specimen B 28  Specimen B 29 Strain Rate 21.4 x I D sec (^decay and reload"} - 4  <T  £,<ST  - 1  Strain Rate 214 x I O sec" (relax and reload^ - 4  (g/mm )  (g/mm )  In(l+&) ~~  CS" (g/mm )  (g/mm )  498  5  .0090  624  81  .0205  557  6  ..0182  1231  110  .0541  597  10  .0244  656  11  .0319  695  12  .0358  770  13  .0439  845  9  .0514  2  2  Speciman B 27 Strain Rate 21.4 X I D sec" (relax and reload} - 4  cr _ (g/mrrr)  (g/mm^)  519  • In(l=5) .0087  581  5  .0180  642  6  .0272  720  5  .0386  808  2  .0518  855  1  .0581  2  In(l+S )  A P P E N D  I X  IV  Effect of.Surface Removal on Mechanical Properties Specimen B 12 Strain Rate 4.28 x 10'-4 ,sec" 76 jX, removed betweench.anges 1  . (g/mm )  ACT (g/mm )  295  - 15  .0015  373  + 15  .0295  521  + 26  i0595  745  + 59  .0955  2  In(l+6 )  2  931  . .1029  Specimen B 11 Strain Rate Cycled by III (2.14 - 21,4 x IO" sec- ) 76 removed between changes 4  (g/mnr)  1  In(l+ 6) »-o  (g/mm ) 2  374  +  38  553  +  25  ,.0313  616  + 112  .0406  950  -  30  .0646  + =68  .0812  1082  '.0005 •  2010  ,1346  Specimen B 32 Strain Rate Cycled by III (2.14 - 21.4 x IO" sec"" ) 76 Jj\ removed between changes 4  (g/mnr)  (g/mnr)  1  In(l+6 )  405  70  .0065  463  103  .0207  607  111  .0336  798  19  *0484  923  .0632  Specimen B 3D S t r a i n Rate Cycled by I I I (2.14 - 21.4 x 10-4 s e c - ) 3B IL removed between changes 1  ACS' (g/mm ) 12  i(g/mnr)  In(l+&)  2  447  .0268  464 '  59  '.-0372  555  19  .0489  617  56  .0607  723  22  .0734-  765  60  ^0829  881  38  .0961  941  89  .1061  1109  13  *1206  1180  ;1268  t  Specimen B 31 Strain/Rate Cycled 1by I I I (2.14 - 21.4 x 10-4 s e c ) 38 )i removed between changes - 1  . (g/mm^)  A<S - (g/mm )  In(l+S )  2  8  3B1  -.0105  Specimen B 24 S t r a i n Rate Cycled by I I I (2.14 - 214 x 1 0 - s e c " ) 76 removed between•changes 4  ^ 2 .(g/mm ) 470  1  In(1+6 )  .'(g/mm) 106 2  "Co  .0137  515  145  .0194 •  645  105  .0326  690.  . 32  .0387 *0650  945 Specimen B 23  S t r a i n Rate Cycled by I I I (2.14 - 214 x I O " -l) 76 removed.between changes • ACT In(l+6 ) ,(g/mm ) ." (g/mm ) to 4  s e c  2  341  2  154  .0140  - 74 A P P E N DH X V  Properties of Coated Specimens Tested at 4.3 x I O  Specimen Number .  - 4  sec  - 1  WorkC r i t i c a l Ultimate TempeJPa^ Diffusion Yield Layer Tensile Tensile Total . Hardening ture Time Thickness Stress 'Stress ' Stress Strain Slope (g/mm2) (°C) (hrs) (|» (g/mm?) (g/mm ) (g/mm xl0- ) 2  11  500*  41  12  450  570  6T3  15  500*  50  47  675  1000  1000  16  500*  24  18  471  750  18  500*  12  15  365  20,  500*  41  137  1700  22  500*  41  150  1860  1860  24  500*  41  160  1920  1920  25  500*  20  125  1880  1880  26  500*  11  91  1290  1700  1700  28  500*  20  144  1670  2320  2320  35  510*  21  47  760  880  55  421  11  30  270  56  3T6  18  22  57  405  20  58  422  60  2  .0205  .860  845  .0098  .970  580  775  .0160  1.22  1970  1970  975  .0051  1.51  297  339  .0102  353  425  506  .0062  20  230  424  575  .0189  .800  20  30  444  517  580  .0089  .'712  485  21  50  411  466  529  .0036  61  485  . ' 18  94  901  953  970  64  590  18  27  310  481  535  ^0091  .595  66  422  14  5  296  322  434  .0264  .425  • .69  485  21  91  1000  1140  1210  A  0026  2.68  70  433  25  34  470  .612  1087  • 0210  2.26  71  440  18  38  340  361  495  .0116  1.15  72  590  18  69:  806  873  873  73  433  25  25  474  621  621  74  422  14  10  344  395  578  *0212  .87  77  433  25  37  362  543  550  40182  .38  81**  410  21  63  640  779  779  82  410  21  45  413  624  624  .411 1.32  1.76  4  - 75 -  Specimen Number  Temperature  (°C)  Diffusion Layer Time Thickness (hrs) (fl)  Critical Yield Tensile Stress Stress (g/mm?) (g/mm ) 2  WorkUltimate T e n s i l e T o t a l Hardening Slope , ' Strese S t r a i n (g/mmZxlO- ) (g/mm ) 4  2  83**  410  21  '35 '•  325  390  390  84  410  21  46  644  ,700  700  85**  582  4  105  1164  1290  1300  87  582 .  4  107  1164  1385  1505  .0055  2.16  88  582  4  85  1050  4185  1215  ,0021  1.45  89  536  3  3  230  264  90.  536  3  5  269  ' ' 285  Notei  *  .0573  .352  4 044 5  ;351  —« Temperature not known more a c c u r e t e l y than - 15°C  ** —  One face abraded.  Given 20 s t r o k e s on'4/o p o l i s h i n g  paper.  - 76 A P P E N D I X  VI  Representative X-ray data CuK .radiation, Ni F i l t e r  Powder ground from specimen #20 Line#  Q  1  (hkl)  C U D  i  c  Parameter (8)  2  19.3D 22.45  (111) (200)  (Film shrinkage correction applied)  3  32.71  (220)  4  39.32  (311)  5  40.81  (222)  6  69.65  (422)  7  59.00  (420)  4.023  8  50,15  "• (400)  4.020  1  Powder ground from specimen #24 1  19*31  (111)  2  22.46  (200)  3  32.73  (220)  4  39.33  (311)  5  ' 41,43  (222)  . 6  69.85  (422)  7  59.03  (420)  4.020  8  50.13  (400)-  4.021  Powder ground from specimen #18 1  19.34  (111)  2  22.70  (200)  3 .  32.95  (220)  4  38.89  (311)  5  40.35  (222)  6  69.85  (422)  7  59.00  (420)  4.022  8  50.IB  (400)  4.021  •  - 77 -  :•: Coating from specimen #29 L  © _  1  30.06  2  33.07  (110)  c.= 4.64a = 3.06  3  50.62  (200)  c = 4.66a = 3.07  4  59.39  (103)  . c = 4.69a = 3.08  5  64.72  (211)  c = 4,67a = 3.07  6  70.71  (113)  e  ( n k l )  tetragonal .  Parameter (A)  i" #  Coating from specimen #34 1'  30.01  2  32.85  (110)  c = 4.6Ba = 3.07  3  50.48  (200)  c = 4.67a = 3.08  4  53.12  (103)  5  55.75  6  59.20  7  64.55  (211)  8  70.52  (113)  c = 4.69a = 3.10  

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