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Slip continuity across grain boundaries in aluminum Davis, Keith Gordon 1959

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SLIP CONTINUITY ACROSS GRAIN BOUNDARIES IN ALUMINUM by KEITH GORDON DAVIS  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of MINING AND METALLURGY  We accept t h i s thesis as Conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE.  Members of the Department of Mining and Metallurgy  THE UNIVERSITY OF BRITISH COLUMBIA May, 1959  .ABSTRACT  A study of s l i p continuity across grain boundaries i n highpurity aluminum has been carried out, both on bicrystals and on polycrystal strip.  Metaliographic methods have been used to show that s l i p continuity  i s not confined to the surface, but i s a true continuity present within the metal. Orientations favouring continuity have been determined, which indicate that screw dislocations can pass through grain boundaries more easily than edge or mixed dislocations.  In p r e s e n t i n g  this thesis i n partial fulfilment of  the r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t t h e L i b r a r y s h a l l make i t freely  a v a i l a b l e f o r r e f e r e n c e and s t u d y .  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  I further  copying of t h i s  thesis  f o r s c h o l a r l y purposes may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s .  I t i s understood  that 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 g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n  Department The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver 8, Canada. Date  i^rfay  iqg-q  financial  permission.  ACKNOWLEDGEMENTS  The author i s grateful f o r the advice and encouragement given by his research director, Dr. E. Teghtsodnian, and for technical assistance given by Mr. R.G. Butters and Mr. R, Richter. The work was carried out with the help of the Defence Research Board Grant Number 7510-29.  Financial assistance was also received from the  National Research Council and i n the form of an Inco Fellowship.  TABLE OF CONTENTS Page INTRODUCTION  .  The Deformation of P o l y c r y s t a l s  „  Previous Work on P l a s t i c i t y i n B i c r y s t a l s  . .  1  . . . . . . . . . . .  3  The Problem  .•  EXPERIMENTAL PROCEDURE  5  . .  B i c r y s t a l Work  7  . . . . . . . . . .  Preparation  1  .  .  , . . . « '  Orientation determination •  7 7  . . . . . . . . .  7  Electropolishing  . . . . . . . . . . . . . . . . . . . . .  9  Testing  ....«.©«  ....  •.*••.  10  Work on Thin P o l y c r y s t a l S t r i p  10  Methods Used t o Try t o see S l i p Bands i n the I n t e r i o r as Revealed by Further P o l i s h i n g A f t e r Testing (a)  X-ray microscopy  (b)  Etching  (c)  P r e c i p i t a t i o n o f a second phase  .  BICRYSTAL ORIENTATIONS RESULTS  •  •  o  o  a  o  o  .  .  6  o  12 i 12  .  .  o  .  .  .  .  ... »  . . . . . . . .  .  .  .  .  .  .  .  .  .  .  .  .  o  12  ..... e  o  a  Observations on Continuity  o  .  »  o  *  *  12  o  *  15  *  »  »  o  «  o  o  o  a  o  . . . . . . . . . . . . . . . . .  S l i p at the Boundaries  17 17 19  (1)  Where s l i p i s continuous  19  (2)  Where there i s no c o n t i n u i t y  19  Stress-St r a i n Curves  •  O  »  »  o  o  *  »  Observations on Thin P o l y c r y s t a l S t r i p  o  *  o  o  o  o  e  * • o »  o  o  9  o  »  o  20 20  si'  TABLE OF CONTENTS (continued)  Page 20  S l i p Below the Surface (1)  X-ray microscopy  20  (2)  Etching  22  (3)  A l - k% Ag alloy s t r i p  S l i p Continuity i n Annealed Bicrystals  22 23  ......  23  S l i p Continuity Observed on Anodised Surfaces  24  DISCUSSION 1.  The S l i p Systems Active i n Symmetric T i l t Bicrystals  2.  S l i p i n the Interior  3.  S l i p Band Continuity  4.  Possible Mechanisms for S l i p Band Continuity  2k  ...  2k 25  . .  25  (a) A theoretical treatment of dislocation source 27  activation across a boundary (b) An examination of the possible movement of dislocations ,.  30  the Angle of Dislocation Twist (0) at the Boundary . .  32  through a boundary 5.  Theoretical Considerations on the Effect on Continuity of  6. Theoretical Estimation of the Frequency of Continuous S l i p Across Boundaries i n a Polycrystal . . . . . . . 7.  34  Further Evidence for the Transparency of Crystal Boundaries to Screw Dislocations  ..........  34  8. Reasons Why Screw Dislocations Should Pass More E a s i l y Through Grain Boundaries than do Edge or Mixed Dislocations 9.  Conclusions  37 ' 38  TABLE OF CONTENTS (continued)  Page  APPENDIX I  40  Electropolishing Large Areas of Aluminum Introduction  40  »  40  Experimental details Results  40 ......  41  Perchloric acid-ethyl alcohol solution  41  An electropolish for rapid removal of metal  42  Summary  42  APPENDIX I I  43  The Shear Stresses Acting on S l i p Planes Ahead of a Pile-up of Dislocations  ,  43  APPENDIX I I I  .  45  An Analysis of the Energy Considerations i n the Formation of a Stepped Dislocation at a Twist Boundary  45  BIBLIOGRAPHY MICROGRAPHS  50 r• • •  5 2  LIST OF FIGURES Page 1.  Experiment of Bainbridge et a l on a zinc b i c r y s t a l  2  2.  Orientations of the: aluminium b i c r y s t a l s used by F l e i s c h e r and Chalmers  3  3.  The c r y s t a l growing furnace  4.  The t e n s i l e t e s t i n g apparatus  5.  Schematic diagram f o r Berg-Barret X-ray microscopy  6.  Orientation  of the symmetric b i c r y s t a l s  13  7.  Orientation  o f the t w i s t boundary b i c r y s t a l  16  8.  Orientation  o f the b i c r y s t a l s Q l , Q2  16  9.  S l i p traces on the symmetric t i l t b i c r y s t a l s  10.  -. . .  8 11  ...  13  18  Standard cubic stereographic plot showing the s t r e s s axis f o r the symmetric t i l t b i c r y s t a l s  18  11.  Work hardening slopes i n the symmetric b i c r y s t a l s  12.  The formation o f a stepped d i s l o c a t i o n i n c r y s t a l 2 when a  21  d i s l o c a t i o n crosses from c r y s t a l 1  26  13.  Values of N f o r bent c o n t i n u i t y  14.  Values of N f o r s t r a i g h t c o n t i n u i t y  15.  As i n F i g . 12, when steps i n the d i s l o c a t i o n  :  . . . 28 29  . i n crystal 2 join  neighbouring s l i p planes 16.  26  Area of the boundary plane favourable t o s l i p band c o n t i n u i t y if  0 max  * 15°  35  17.  D i s l o c a t i o n structure  f o r a low angle t i l t boundary -  18.  The passage of a d i s l o c a t i o n through a boundary  35 . v .  47  LIST OF TABLES Page 1,  Test f o r accuracy of orientation determination  2,  Orientation of the symmetric bicrystals  15  3,  Observations on bent continuity  17  k»  The angle  between s l i p direction and the boundary plane f o r  the symmetric t i l t boundary 5.  ......  9  Angle of dislocation twist 0  . .  31 31  SLIP CONTINUITY ACROSS GRAIN BOUNDARIES IN ALUMINUM  INTRODUCTION  The Deformation of P o l y c r y s t a l s . S i n g l e c r y s t a l s are weaker than p o l y c r y s t a l s .  One o f the b a s i c  problems i n p h y s i c a l metallurgy i s t o f i n d out p r e c i s e l y why t h i s i s so. I t i s hoped that such knowledge w i l l help i n the development of p o l y c r y s t a l m a t e r i a l w i t h greater s t r e n g t h . Two mechanisms strengthen p o l y c r y s t a l s r e l a t i v e t o s i n g l e crystals.  The f i r s t , and i n many cases probably the most important mechanism,  a r i s e s ' f r o m the need f o r s e v e r a l s l i p systems to act i n each g r a i n i n order to keep neighbouring grains i n contact. Von Mises"'" has shown that unless at l e a s t f i v e s l i p systems per g r a i n are a c t i v e , gaps w i l l appear at the boundaries, a r e s u l t that has never been challenged. s l i p systems w i l l cause hardening.  I n t e r a c t i o n between these  The question of which e x t r a s l i p systems  w i l l be a c t i v a t e d and how much s l i p each w i l l give has been the subject of extensive research based on comparison between s t r e s s - s t r a i n curves f o r s i n g l e c r y s t a l s and f o r p o l y c r y s t a l specimens (see Refs. 2, 3, U, 5 ) . I n l a t e r remarks the term •complexity hardening' w i l l be used t o describe t h i s type o f mechanism. The second mode of strengthening i n p o l y c r y s t a l s i s the holding up of moving d i s l o c a t i o n s at g r a i n boundaries.  McLean^ c a l l s t h i s ' b a r r i e r  hardening', and h i s terminology w i l l be f o l l o w e d . Where two s l i p systems o f neighbouring c r y s t a l s n e a r l y c o i n c i d e , lower b a r r i e r hardening might be expected.  For F.C.C. and B.C.C. metals w i t h many s l i p systems per g r a i n , .  - 2 b a r r i e r hardening w i l l be l e s s important than i n C.P.H. metals,(polyc r y s t a l l i n e G.P.H. metals tend t o have very rapid rates of work hardening compared w i t h t h e i r s i n g l e c r y s t a l s ) .  A l l o y s with a hard phase may be  considered an extreme case of b a r r i e r hardening where the b a r r i e r v i r t u a l l y never breaks down. The strength of a boundary as a d i s l o c a t i o n b a r r i e r appears t o be g r e a t l y enhanced by the presence of a solute with s m a l l atomic diameter which gives C o t t r e l l l o c k i n g .  Sharp  y i e l d of the type observed i n mild  s t e e l i s now generally held to be caused, i n the cases i n v e s t i g a t e d , by the presence of such s o l u t e s : the y i e l d i s thought of as a catastrophic break through of d i s l o c a t i o n s across boundaries. That even a low angle boundary can act as a d i s l o c a t i o n t r a p has 7 been demonstrated c l e a r l y by  Bainbridge et a l .  b i c r y s t a l was stressed as shown In F i g . 1.  A low angle boundary zinc  As the s t r e s s was increased,  d i s l o c a t i o n s t r a v e l l i n g along the b a s a l planes were trapped i n the boundary and the boundary angle increased. There must therefore be some degree of b a r r i e r hardening even from such low angle boundaries.  To c l a r i f y the  r e l a t i v e importance of complexity hardening and b a r r i e r hardening, studies have been c a r r i e d out on the deformation c h a r a c t e r i s t i c s of b i c r y s t a l s .  ,low angle boundary s l i p (basal) planes  load  F i g . 1.  Experiment of Bainbridge et a l on a zinc b i c r y s t a l .  - 3 -  F i g . 2.  Orientations o f A l Bi-x's used by F l e i s c h e r and Chalmers. In A, s l i p d i r e c t i o n s are p a r a l l e l t o the boundary. I n B, one c r y s t a l has i t s s l i p d i r e c t i o n p a r a l l e l and the other nearly normal t o the boundary.  Previous Work on P l a s t i c i t y i n B i c r y s t a l s . B i c r y s t a l s of Zn, Sn and A l h a v e been t e s t e d .  In a l l the cases t o  be described the boundary was kept p a r a l l e l t o the s t r e s s a x i s . Zn (a) Kawada^ grew symmetric b i c r y s t a l s w i t h b a s a l planes i n c l i n e d at equal angles t o the boundary.  They showed the same strength as s i n g l e c r y s t a l s .  A r e l a t i v e r o t a t i o n about the s t r e s s axis gave some strengthening. , (b) Gilman^ confirmed Kawada's r e s u l t s  that i n symmetric b i c r y s t a l s  the boundary gives no hardening. He also found a high degree of strengthening i n b i c r y s t a l s w i t h a r e l a t i v e r o t a t i o n about an a x i s normal t o the boundary. Sn  Chalmers  the s l i p d i r e c t i o n s . was measured. (1)  grew symmetric b i c r y s t a l s , varying the angle between The s t r e s s needed t o produce a standard s m a l l extension  He found that the s t r e s s increased l i n e a r l y w i t h o r i e n t a t i o n d i f f e r e n c e  between the two c r y s t a l s from 0 - 9 0 ° . (2) to  varying the o r i e n t a t i o n of the boundary so that i t was I n c l i n e d  the s t r e s s a x i s gave no d i f f e r e n c e i n strength f o r the same r e l a t i v e  o r i e n t a t i o n between the two c r y s t a l s .  High-purity A l (a) Clark and Chalmers  11  carried out experiments on  two crystals with a common {111} s l i p plane at U5° t o the stress axis, rotations being made i n these {111} planes to vary the angle 0 between favoured s l i p directions.  They found that -  (1) the y i e l d stress increases with 0 up to 0 = 30°, and then remains steady. ...... (2) the i n i t i a l work hardening rate increases l i n e a r l y with 0 up to 0 = 60°. 12 (b) Aust and Chen  grew symmetric bicrystals based on a  seed crystal with a<110> stress axis and a {"100} plane facing upwards. Rotations were made about the ^110> axis.  Yield stress and i n i t i a l work  hardening rate both increased with misorientation angle0 from 9 = 5° to 0 = 85°, but the effect was less than that with Clark and Chalmers• bicrystals. (c)  Fleischer and Chalmers  grew two series of bicrystals. In  one (A) the preferred s l i p direction was p a r a l l e l to the boundary i n both crystals.  In the other (B) the preferred s l i p direction i n one crystal was  p a r a l l e l to the boundary and i n the other crystal nearly normal to the boundary (see F i g . 2). Series A bicrystals showed l i t t l e strengthening due to the boundary. Series B showed a large boundary effect.  Double s l i p near the  boundary was observed only i n series B bicrystals. No clear conclusions about the relative importance of barrierhardening and complexity hardening can be drawn from these data. The important factors that do emerge are (1) the strengthening effect of a boundary depends on the relative orientation of the component crystals i n a f a i r l y systematic manner. (2) aluminum i s strengthened only when double s l i p occurs near the boundary.  - 5 -  The Problem. When metals are polished and deformed, surface s l i p bands i n general fade out near to the grain boundaries.  In some cases, however, the  s l i p bands pass right through a boundary. Ogilvie" "^' has studied this i n 1  polycrystalline aluminum and 3-brass.  He found that continuity of s l i p  occurred only (1)  across straight boundaries.  (2)  where the line of intersection with the boundary of the two active  s l i p planes i n neighbouring crystals had <110> , <112> and <123> directions (within 2 ° ) . The directions were not necessarily the same i n both grains. Other observations of s l i p across grain boundaries have been published.  Lacombe and Beaujard^ observed s l i p across low angle boundaries  i n high-purity aluminum. Observations of s l i p continuous across twin boundaries 16  have been made i n several metals, and Gilman  has recently noted that s l i p i s  always continuous i n symmetric zinc bicrystals. It was thought that a further investigation of s l i p across boundaries may be useful.  Information was sought on the following questions:  (a) Is s l i p band continuity as observed on polished surfaces a true continuity or purely a surface effect? (b) What i s the orientation dependence? (c)  What i s the actual mechanism for s l i p through grain boundaries?  Do  dislocations pass through the boundary, or do pile-ups i n one crystal activate dislocation sources i n a neighbour? (d) Is there a connection between barrier hardening and s l i p band continuity?  - 6Answers to the f i r s t two questions should shed light on the t h i r d , which i s of course the crux of the problem.  Of interest i s the investigation  17 by Urie and Wain ' on the deformation of polycrystalline aluminum. They deposited photographically a fine grid on the surface before deformation, and found that i n general deformation was less at grain boundaries than near grain centres. However, where s l i p passed through, the grain boundary had no effect 18 on deformation. Other interesting work was carried out by Kawada  on coarse  polycrystal aluminum. Sensitive measurements of extension under load showed that, i n the early stages of deformation, commercial aluminum between 100°C and 350°C showed sudden elongation »jumps* of the order of a few microns. There were no jumps when s l i p was continuous across the boundary, and such jumps were never seen i n high-purity aluminum.  EXPERIMENTAL PROCEDURE  B i c r y s t a l Work. Preparation B i c r y s t a l s of 99.99% pure aluminum w i t h approximate dimensions 4 1/2" -x 3/4" x 3/S" were prepared by a modified Bridgman technique.  Seed  c r y s t a l s were l a i d i n a graphite boat i n contact w i t h a machined s l u g o f aluminum which was covered by a l i d .  The boat was placed i n a Vycor tube,  through which helium was slowly passed.  A r e s i s t o r - t y p e furnace was drawn  along over the tube by a s m a l l e l e c t r i c motor (see F i g . 3). I t was found necessary t o j o i n the seeds to the melt by mechanical a g i t a t i o n .  The s o l i d -  l i q u i d i n t e r f a c e was approximately 3 " w i t h i n the furnace. Some t r o u b l e was encountered w i t h shrinkage on s o l i d i f i c a t i o n .  Shrinkage was reduced by providing  a s m a l l r e s e r v o i r of aluminum joined t o the melt by a narrow h o l e .  After  s o l i d i f i c a t i o n the aluminum remaining i n the r e s e r v o i r could be e a s i l y cut o f f . Growth rate was c o n t r o l l e d by the speed of furnace t r a v e l .  This was  kept a t four cms. per hour, higher growth rates g i v i n g pronounced lineage structures.  S t r a y c r y s t a l s or changes i n o r i e n t a t i o n were r a r e .  of the c r y s t a l s showed a few coarse lineage t i l t boundaries d i f f e r e n c e s of around 1 1/2*.  About 20%  with orientation  There r a r e l y occurred more than two such  boundaries per c r y s t a l , and i n a l l cases they could be etched up e a s i l y . O r i e n t a t i o n determination. C r y s t a l s were taken from the boat, etched i n 'Tucker's etch' and oriented by the X-ray Laue b a c k - r e f l e c t i o n method.  The accuracy o f the method  was t e s t e d by repeatedly mounting a c r y s t a l on the X-ray s e t , taking a p i c t u r e , demounting the c r y s t a l , and repeating the procedure.  A t y p i c a l example of the  Fig. 3»  The crystal growing furnace.  - 9 -  values obtained i s given i n Table 1. I n t h i s case the o r i e n t a t i o n desired had a {100} plane f a c i n g the f i l m holder and a < 1 1 0 > a x i s v e r t i c a l .  The  values 9 , 0 represent r o t a t i o n s about the v e r t i c a l and h o r i z o n t a l axes i n the f i l m needed t o give a p e r f e c t (100) <110> o r i e n t a t i o n , and a represents the r o t a t i o n needed about an a x i s perpendicular t o the f i l m . three needed t o define the m i s o r i e n t a t i o n completely.  0 , 0 and a are a l l  The method appears  accurate t o w i t h i n -1°. Traverses across a specimen surface were sometimes taken t o t e s t f o r low angle lineage boundaries.  Except f o r the e a s i l y etched  boundaries of some 1/2 t o 1 1/2°, the structures were perfect w i t h i n the l i m i t s of the method. TABLE 1 Test f o r accuracy of o r i e n t a t i o n determination. Test Number 1 1 1 1 1 0  1 2 3 4 5 6  0°  0° 1/2 1/2 1/2  2 2 2 1 2  1/2 1/2  3  a° 0 1/4 1 0 1/2 0  E l e c t r o p o l i s h i n g ( f o r d e t a i l s see Appendix l ) Several e l e c t r o p o l i s h e s were t r i e d , the f i n a l choice being 15$. perchloric acid i n acetic acid.  With a current of some 3/4 amp at 25-35  V, a good p o l i s h was obtained i n about 1 1/2 hours. a jacket of cold running water.  Cooling was e f f e c t e d by  The best r e s u l t s were obtained when s t i r r i n g  was kept very slow, j u s t s u f f i c i e n t t o prevent the specimen from overheating A region about 1 " long i n t h e middle of the specimen was p o l i s h e d , the r e s t being masked o f f by e l e c t r i c a l tape.  P r e l i m i n a r y treatment was r e s t r i c t e d  to g r i n d i n g w i t h a coarse-grade emery paper.  I t i s b e l i e v e d t h a t the worked  - 10 l a y e r was t o t a l l y removed.  X-ray p i c t u r e s of the polished surface showed no  asterism, and annealing caused no r e c r y s t a l l i s a t i o n . Testing. E l e c t r o p o l i s h e d c r y s t a l s were mounted i n a Hounsfield tensometer (see  F i g . 4). Simple V-block f r i c t i o n grips were machined from aluminum a l l o y ,  and the g r i p p i n g surface covered w i t h coarse emery paper.  I t . was thought that  the  more u s u a l serrated g r i p p i n g surfaces would give unnecessary deformation a t  the  ends of the specimens.  i n s u f f i c i e n t l y strong.  Thin rubber was at f i r s t t r i e d , but proved  Even the l i g h t aluminum g r i p s gave appreciable bending  stresses from t h e i r own weight.  The tensometer was therefore mounted i n the  v e r t i c a l p o s i t i o n from a w a l l bracket. To look f o r s l i p c o n t i n u i t y , w i d e l y spaced s l i p bands were p r e f e r a b l e .  To observe the formation of s l i p bands a  t r a v e l l i n g microscope w i t h m a g n i f i c a t i o n around lOOx was placed i n f r o n t of the  specimen.  The load was removed when s l i p bands were f i r s t seen t o form,  at 70 - 100 l b s .  S t r e s s - s t r a i n curves were recorded while t e s t i n g .  The g r i p p i n g system was not r i g i d , and some bending i n e v i t a b l y accompanied the t e n s i l e t e s t s .  For two b i c r y s t a l s , SR 4 e l e c t r i c a l r e s i s t a n c e  strain-gauges were cemented on t o opposite f a c e s .  Both showed extension up  to approximately 0.5$ on one face, w i t h e i t h e r a s l i g h t compression o r a s m a l l extension on the other. the  This was r e f l e c t e d i n the frequent d i s p a r i t y between  density of s l i p bands on opposite faces.  Work on Thin P o l y c r y s t a l S t r i p . Thin p o l y c r y s t a l s t r i p , a few hundredths of a mm.-thick'was prepared to see i f any c o r r e l a t i o n between s l i p bands on the two opposite surfaces could be found.  I d e n t i f i c a t i o n o f the same boundary on both sides i s much  e a s i e r i f the grains are l a r g e .  The s t r i p was therefore r o l l e d , annealed a t  - 12 -  640°C, given a further small reduction and re-annealed at 640°C for several days.  Grains passing right through the s t r i p with diameters of the order of  a centimeter resulted. This s t r i p was polished and tested i n the same manner as the b i c r y s t a l . Methods Used to Try to See S l i p Lines i n the Interior as Revealed by Further Electropolishing after Testing. (a) X-ray microscopy.  In this technique, devised by Berg *? and applied 1  20 to metals by Barrett,  a large area of the specimen surface i s bathed i n a  diverging beam of characteristic X-rays. The photographic plate must be placed within a few mms.  of the specimen surface (see F i g . 5).  Each point  on the plate represents a point on the surface, the plate being viewed, after development, on a metallograph.  In this way, inhomogeneities i n the structure  such as deformation bands, low angle boundaries and scratches can be shown up, (b)  Etching. Two etches were t r i e d .  The f i r s t , due to Lacombe and  Beaujard, -^ gives a very large number of small p i t s , which are believed to be 1  nucleated at least i n part by dislocations. HC1, 3% HF. ice.  The etch contains U6% HNO-j, 50%  I t must be kept around 0°C by surrounding the dish with melting  The second etch, due to Barrett and Levenson,  three parts HNO3, two parts HF., five parts H2O. pits.  21  has nine parts HC'l,  This develops much larger  For both etches the specimen i s immersed i n the solution for a few  seconds, (c) Precipitation of a second phase. Failure of the f i r s t two methods led to the adoption of a precipitation technique.  Age-hardening A l - k% kg  alloys were prepared i n the form of coarse-grained polycrystal s t r i p .  The  s t r i p was homogenised at 600°C, quenched, deformed, and aged at 200°C for 24 hours.  S i l v e r quenched i n solution precipitated out preferentially i n  s l i p bands. The surface had to be anodised before s l i p bands could be detected.  specimen Fig. 5  Schematic diagram for Berg-Barret X-ray microscopy.  Fig. 6.  .Orientation of the symmetric bicrystals.  - 14 -  Several attempts to etch up the precipitate i n the electropolished surface, removing the necessity for anodising, proved abortive. Perchloric acid-acetic acid electrolytes used i n electropolishing pure aluminum were unsuitable for the aluminum-silver a l l o y , and a 20% perchloric acid i n ethanol electrolyte at 40 V was used. This gave a high current, around SA, accompanied by rapid heating..  After 20-30 seconds the current was switched off and the solution  allowed to cool. I t was found that i f i n the f i n a l polish the voltage was s l i g h t l y reduced f o r a few seconds before the current was switched off a good anodised surface was given.  - 15 -  BICRYSTAL ORIENTATIONS  A s e r i e s of symmetric b i c r y s t a l s was grown based on a seed c r y s t a l w i t h a {100}  face upward and a <110>  axis along i t s length.  .Seeds f o r  the b i c r y s t a l s were prepared by t i l t i n g t h i s seed about i t s length axis by an angle 9 ( F i g . 6).  The two values of 9 f o r a b i c r y s t a l v a r i e d by up t o 3 ° .  At l e a s t three c r y s t a l s were tested f o r each o r i e n t a t i o n . was prepared, with 9 = 9 ° (see F i g . 7).  One t w i s t boundary  Single c r y s t a l s oriented f o r s i n g l e  TABLE 2. Orientation of the symmetric t i l t b i c r y s t a l s .  Orientation Difference Code A B C D E F G H  1 5 21 26 1/2 ' 39 75 92 113 150  (2 9°)  2  3  6 24  8 25  40 70 93  115 151  40 74 93 114 150  4  73 1L2  s l i p were prepared, and two series of b i c r y s t a l s grown from them.  In the  f i r s t , b i c r y s t a l Q 1, the preferred s l i p d i r e c t i o n s were p a r a l l e l to the boundary surface.  In the second, Q 2, the d i r e c t i o n s of easy s l i p l a y i n a  plane nearly p a r a l l e l t o the top surface of t h e b i c r y s t a l s (see F i g . 8).  - 1€  Fig. 8.  Orientation of the bicrystals Q 1, Q 2. The s l i p directions are shown.  -  - 17 RESULTS  Observations on Continuity. There i s no clear cut d e f i n i t i o n between no c o n t i n u i t y and c o n t i n u i t y . I t has been found convenient t o use the f o l l o w i n g terms of d e s c r i p t i o n • e x c e l l e n t * , *good*, ' f a i r ' , 'traces'.  I t i s hoped that w i t h the accompanying  micrographs a f a i r d e s c r i p t i o n of what was observed w i l l be accomplished. I t should be emphasized that some of the specimens v a r i e d over t h e i r length, g i v i n g c o n t i n u i t y at some places and not at others. cannot be wholly representative.  The p i c t u r e , t h e r e f o r e ,  Symmetric b i c r y s t a l s have two possible  of s l i p c o n t i n u i t y , s t r a i g h t or bent ( F i g s . 9-and-10).  sets  S t r a i g h t c o n t i n u i t y was  seen only once, and then f a i n t l y , i n the symmetric b i c r y s t a l s ( i n H 1, 2, 3). For b i c r y s t a l A, i t was not possible t o d i f f e r e n t i a t e between the two cases. Observations on bent s l i p are summarised i n Table 3  and micrographs 1 t o 7.  The series of pictures does not give a very t r u e representation.  Continuity  i n E was abundantly c l e a r e r than i n the other b i c r y s t a l s , and the s t r a i g h t c o n t i n u i t y i n H (Micros 11, 12) was c l e a r e r than could be shown. boundary b i c r y s t a l s and b i c r y s t a l s Q 1, Q 2 showed no c o n t i n u i t y .  The t w i s t Both  t r i c r y s t a l s showed good c o n t i n u i t y . TABLE 3 Observations on bent c o n t i n u i t y Code  A  ...B...... C D E F G H  Orientation d i f f e r e n c e 6  23  26 1/2  40 73 93 114 150  (20°)  1 Good Good Fair Good Excellent Good Fair Traces  2  3  Good Fair  Good Traces  Good Excellent Good Traces Traces  Good Excellent  -  -  -  Fair Traces  Fig. 1 0 . Standard cubic stereographic plot showing the stress axis for the symmetric t i l t bicrystals.  - 19 S l i p at the Boundaries (l)  Where s l i p i s continuous. When s l i p c o n t i n u i t y was examined i n d e t a i l , the f o l l o w i n g  i n t e r e s t i n g f a c e t s were revealed. (a)  In s e v e r a l cases examined there was  boundary where crossed (Micro 13).  a displacement  of the  This displacement was of the same order of  magnitude as the step height of a s l i p band. (b)  Inbent c o n t i n u i t y , the s l i p , band sometimes crossed the boundary  s t r a i g h t f o r a short way before j o i n i n g a s l i p band i n the second c r y s t a l (Micros 14, 15) •  Across the boundary s l i p bands sometimes became wavy f o r a  short distance (Micro (c)  Ogilvie  s t r a i g h t boundaries.  16). had s t a t e d that s l i p bands were continuous only over This i s not so (Micros 17, 18, 19).  Further, the  o r i e n t a t i o n conditions he s t i p u l a t e d were not followed here. (d) 70°  S l i p bands can t u r n through q u i t e sharp angles, up to n e a r l y  (see, f o r example, Micro 20). "(2)  Where there i s no c o n t i n u i t y . (a)  The s l i p bands o f t e n faded out near t o the boundary, g i v i n g  way to wavy s l i p or a g e n e r a l l y 'rumpled' surface (see Micros 21, 22, (b)  23).  The s l i p bands tended to run along p a r a l l e l t o the boundary  when held up there (Micros 23, 24, 25), o c c a s i o n a l l y crossing before so doing (Micro 25). (c) ' In b i c r y s t a l s G (~110°) the s l i p d i r e c t i o n was very n e a r l y p a r a l l e l t o the p o l i s h e d surface, making the observation of s l i p bands difficult. (Micro 26).  A wide region of very wavy s l i p occurred along the boundary  - 20  -  S t r e s s - S t r a i n Curves The Hounsfield tensometer gave a d i r e c t load-extension curve.  The  e a r l y parts of the curve, up t o around 30 l b s load, were found t o be highlyvariable.  E l e c t r i c a l strain-gauge measurements showed that up t o t h i s load  there was no appreciable extension of the specimen, and i t was assumed that any extension shown was caused by t a k i n g up s l a c k at the g r i p s .  With few  exceptions the load-extension curves were l i n e a r above 30 l b s . load; i t was b e l i e v e d t h a t the slope i n t h i s region i n d i c a t e d a true work-hardening of the bicrystalso  Values were found from t h i s slope f o r extensions at 125 l b s ,  load over a 3 cm. l e n g t h , t h i s being a measure of the inverse slope of the curve,,  Results were not of great p r e c i s i o n , due t o ( l ) bending stresses  introduced, (2)  inaccuracies i n the load measuring device, and (3)  rather  crude estimates of c r o s s - s e c t i o n a l area and distance between the g r i p s .  It  i s however f e l t that the values, obtained were consistent enough to be significant.  A p l o t i s made i n F i g . 11.  The b i c r y s t a l s E, which showed the  -best c o n t i n u i t y , appear to be more e a s i l y deformed than the b i c r y s t a l s D and 12 F.  Aust and Chen  gave values of the work hardening slope s t e a d i l y i n c r e a s -  ing from 0 - 9 0 ° m i s o r i e n t a t i o n . Observations on Thin P o l y c r y s t a l S t r i p No c o r r e l a t i o n could be found between the s l i p band spacing on opposite faces of the s t r i p . present oh a  I t was noted, however, t h a t where c o n t i n u i t y was  boundary, s l i p was a l s o continuous over the same boundary i n  the other face when not obscured by secondary s l i p (Micros 27, 28). S l i p Below the Surface. (1)  X-ray Microscopy  0  The method proved i n s u f f i c i e n t l y s e n s i t i v e t o  r e v e a l c l e a r l y the s l i p band c o n t i n u i t y , although s l i p bands could be detected.  Extension at 125 l b s . load over a 3 cm. gauge length (units of 0.01 m.m.) 30 i  »'o~> less reliable values  i \  25  M  \  20  L \"  15  /  10 o  o  o o  —I  1  -I  10  20  30  1  -J  40 50  -4  1  1  -l  1  1  _ l  l  i  i  |  i  |  60 70- 80 - 90 100 -110- 120 130 140 150 160 170 180  "J:.  .Orientation.difference (2.©)...for the bicrystals.  Fig. 11  Work hardening slopes i n the symmetric bicrystals.  ' ^  _ 22 More suited to t h i s technique would be the examination of sub-boundaries or deformation (2)  bands.  Etching.  In no case were s l i p l i n e s revealed.  Wyon and Marchin,  i n an extensive research into the etching of d i s l o c a t i o n s i n high p u r i t y aluminum, noted that »»it was t h i s method.* *  never found possible to reveal s l i p markings by  Their f i n d i n g s can only be echoed.  The etch-pit patterns are of interest i n t h e i r own  right.  Micros  29.. and 30 show the effect of the Lacombe and Beaujard etch on a b i c r y s t a l with a -(111} plane very nearly p a r a l l e l to the surface, annealed, a f t e r growth, at 600°C  f o r several days.  Micro 29 shows the surface a f t e r severe attack and  Micro 30 reveals the dark patches to be overlapping etch p i t s . cant conclusions may be drawn.  Two  signifi-  F i r s t , the boundary suffers very l i t t l e  p r e f e r e n t i a l attack, and second, there i s no sign of polygonisation or c e l l structure.  The e l e c t r o p o l i s h has apparently removed completely any surface  deformation. Micros 31, 32,  and 33 were taken from etched surfaces of crystals  electropolished (Subsequent to deformation. along s l i p bands.  In none do the etch p i t s a l i g n  Micro 31 i l l u s t r a t e s the difference i n size between etch  p i t s given by the two etches.  The large t r i a n g u l a r p i t s were given by Barrett  and Levenson's etch and the small ones by Lacombe and Beaujard s, T  Micro  32  i l l u s t r a t e s the very perfect e q u i l a t e r a l triangle p i t s given by Lacombe and Beaujard»s etch on a { i l l } surface, and Micro 33 shows the square p i t s given by t h i s etch on a c r y s t a l near to the cube o r i e n t a t i o n . {111} etched within a few seconds whereas {100}  surfaces were  surfaces needed the order of a  minute,  (3)  Aj ~ Id Ag A l l o y -Stpjp.  Pictures of the anodised surfaces taken  under p o l a r i s e d l i g h t are shown i n Micros 34,  35,  36 and 37.  They show c l e a r l y  - 23  -  that s l i p band c o n t i n u i t y can be present i n the i n t e r i o r as w e l l as on the surface.  There i s of course no guarantee that the Same follows f o r h i g h - p u r i t y  aluminum with no s i l v e r a d d i t i o n , but there i s no reason f o r there to be difference i n deformation mechanisms.  any  The surface appearance of specimens of  the A l - U% Ag a l l o y e l e c t r o p o l i s h e d and p u l l e d i s i d e n t i c a l with that of the pure aluminum.  The  frequency of c o n t i n u i t y i n the i n t e r i o r of a p o l y c r y s t a l i s  not markedly d i f f e r e n t from that on the  surface.  S l i p C o n t i n u i t y i n Annealed B i c r y s t a l s . Two  b i c r y s t a l s , B3 and E4, were annealed at 600°C f o r several days  before t e s t i n g .  No very s i g n i f i c a n t d i f f e r e n c e i n s l i p behaviour was  although b i c r y s t a l B3 d i d show poorer c o n t i n u i t y than B l or  noted,  B2.  S l i p Continuity Observed on Anodised Surfaces. A few b i c r y s t a l s and p o l y c r y s t a l s were anodised before deformation. No d i f f e r e n c e i n s l i p c o n t i n u i t y c h a r a c t e r i s t i c s could be detected.  - 24 -  DISCUSSION 1.  The S l i p Systems Active i n the Symmetric T i l t Bicrystals. At room temperature aluminum s l i p s i n <110> directions on £lll}  planes.  There are four s l i p planes, (111), (111), (111) and ( i l l ) , each with  three possible s l i p directions, making twelve s l i p systems per crystal. The choice of crystals with a <110> stress axis greatly simplifies the picture. A cubic stereogram i s given i n F i g . 11.  S l i p planes ( T i l ) , (111) are p a r a l l e l  to the applied stress, and having no shear stress component across them w i l l not give s l i p .  S l i p direction [llti] (or \j-10~] ) i s perpendicular to the applied  stress and therefore inoperative. The s l i p systems reduce to:  "; For  (111)  LlOl] ,  (111)  [Oil], [lOl]  symmetric bicrystals  Loll]  obtained by a rotation of the standard seed  about i t s IJLlQj axis, superscripts1 and 2 w i l l be used to represent s l i p elements i n crystals 1, 2.  It i s easily seen that (111) and ( i l l ) , (or 1  2  (111) and (Hl)^) w i l l intersect the top surface i n p a r a l l e l l i n e s , 2  whereas  (111) and (111) , or (ill)" and ( i l l ) , w i l l intersect i n lines at an angle, 1  1-  2  2  giving a herring-bone structure (see F i g . 9).  The twist boundary w i l l of  course give s l i p bands normal to the length axis, and the b i c r y s t a l Q oriented for single s l i p w i l l give bands p a r a l l e l i n the two crystals but inclined to the length axis. 2.  S l i p i n the Interior. The A l - 4$ Ag alloys show conclusively that s l i p band continuity  i s not just a surface effect, but that s l i p bands j o i n at the boundary throughout the metal.  Further, were i t simply a surface effect, a specimen  with an anodised surface might possibly behave d i f f e r e n t l y from an electro-  - 25 polished one, but no such d i f f e r e n c e was observed. something of a problem.  This conclusion poses  Unless the a c t i v e s l i p planes i n neighbouring c r y s t a l s  i n t e r s e c t i n a l i n e i n the boundary, d i s l o c a t i o n s cannot pass d i r e c t l y from one c r y s t a l t o the other.  Consider the s i t u a t i o n depicted i n F i g . 12.  The  d i s l o c a t i o n must take on a stepped form i n order to l i e completely on s l i p planes i n c r y s t a l 2 and keep i t s c o n t i n u i t y w i t h the s l i p plane i n c r y s t a l 1. On moving out i n t o c r y s t a l 2 the steps are presumably removed by g l i d i n g out of the d i s l o c a t i o n .  Were t h i s not so s l i p would, t o an observer, be t a k i n g place  on a non-octahedral plane. 3.  No record of such an observation i s known.  S l i p Band C o n t i n u i t y and Work Hardening. The t e n s i l e t e s t s i n d i c a t e ( F i g . 10) that the b i c r y s t a l s E, where s l i p  band c o n t i n u i t y was very marked, showed r a t h e r l e s s work hardening than expected. I t appears, t h e r e f o r e , that s l i p band c o n t i n u i t y i s a t r u e s t r e s s - r e l a x a t i o n , but too much credence should not be placed on t h i s .  The s c a t t e r i n r e s u l t s shows  that more r e l i a b l e data, t a k i n g a greater number of t e s t s per example and u s i n g a more s e n s i t i v e machine, should be obtained before a d e t a i l e d t h e o r e t i c a l 12  explanation i s j u s t i f i e d .  I t should be noted that Chen and Aust  tested no  b i c r y s t a l s w i t h m i s o r i e n t a t i o n between 55° and 85°, and would t h e r e f o r e have missed a minimum i n work hardening slope at around 70°.• The observations of Urie and Wain-'-''' t i e i n w i t h the data presented here. 4.  Possible Mechanisms f o r S l i p Band C o n t i n u i t y. There are two basic mechanisms t h a t could account f o r the observed  continuity.  E i t h e r the d i s l o c a t i o n s p i l e up against the boundary and t h e i r  s t r e s s f i e l d s a c t i v a t e d i s l o c a t i o n sources i n the next c r y s t a l , or the d i s l o c a t i o n s i n some way pass r i g h t through the boundary. theory w i l l be treated f i r s t .  The source a c t i v a t i o n  - 26  ^/dislocation coming from crystal 1  Fig. 12.  Formation of a stepped dislocation i n crystal 2 when a dislocation crosses from crystal 1. The plane of the diagram i s the boundary plane. The dotted l i n e represents the dislocation i n crystal 2.  /  /  Fig. 15.  As Fig..12, where steps i n the dislocation i n crystal 2 j o i n neighbouring s l i p planes.  -  - 27 (a)  A t h e o r e t i c a l treatment of d i s l o c a t i o n source a c t i v a t i o n across a boundary. When M d i s l o c a t i o n s with Burgers vector b p i l e up against a  boundary under an applied shear s t r e s s , they possess a s t r e s s f i e l d ahead of the p i l e - u p with a value equivalent t o that of a s i n g l e d i s l o c a t i o n of Burgers  •  23  vector M b at the centre of g r a v i t y of the p i l e - u p . s t r e s s concentration at the head of a s l i p band. shear i n the s l i p plane of c r y s t a l 1.  There i s therefore a  This s t r e s s w i l l be pure  I f the c r y s t a l l a t t i c e i s assumed  e l a s t i c a l l y i s o t r o p i c , and i n aluminum t h i s should lead t o no serious inaccurac i e s , the s t r e s s i n c r y s t a l 2 ahead of the s l i p plane i n c r y s t a l 1 w i l l also be pure shear.  For a given shear s t r e s s T a c t i n g ahead of a s l i p system of  c r y s t a l 1 i n c r y s t a l 2, shear stresses NT a c t i n g on each of the four s l i p systems of c r y s t a l 2 can be found, where N i s a geometrical f a c t o r .  The shear  s t r e s s from the applied t e n s i l e load w i l l be the same on a l l eight s l i p systems (four per c r y s t a l ) .  A method t o c a l c u l a t e N i s given i n Appendix 2.  !  If  continuous s l i p i s caused by d i s l o c a t i o n source a c t i v a t i o n , high values of N between any two s l i p systems i n the two c r y s t a l s should lead t o observed s l i p 1 2 continuity. systems  N-value s between s l i p systems i n ( i l l ) and ( i l l ) and between  ( i l l ) and ( i l l ) have been c a l c u l a t e d f o r symmetric c r y s t a l s with  misorientations from 0 - 180°j high values f o r the f i r s t should lead t o bent c o n t i n u i t y and high values f o r the second t o s t r a i g h t c o n t i n u i t y .  P l o t s are  given i n F i g s . 13 and 14. A l l s l i p systems being equally favoured, i t i s assumed that each i s capable of g i v i n g r i s e t o pile-ups at the boundary.  I t i s seen that the best  bent c o n t i n u i t y would be expected at around 40° m i s o r i e n t a t i o n , and good s t r a i g h t c o n t i n u i t y around 130°. Comparison of F i g s . 13 and 14 with Table 3 shows there to be l i t t l e c o r r e l a t i o n between these p r e d i c t i o n s and the observed continuity.  For example, b i c r y s t a l B w i t h m i s o r i e n t a t i o n 23° should give b e t t e r  N  Orientation difference (26) Fig. 13.  Values of N f o r bent continuity.  0  10  20  30  40  50  oO  70 80 90 100 110 Orientation difference (20)  120  130  140  150  Io~6  170  .180  1 Fig. 14.  Values of N for straight continuity.  w  o  1  - 30 c o n t i n u i t y than b i c r y s t a l E w i t h 7 3 ° ; the opposite i s observed.  The d i s l o c a t i o n  source a c t i v a t i o n idea appears i n v a l i d . , •(b)  An examination of the possible movement o f d i s l o c a t i o n s through the boundary. I f d i s l o c a t i o n s are t o pass through the boundary, three c r i t e r i a  would appear to be c o n t r o l l i n g ; 1)  the edge or screw character of the dislocations„  2)  the nature of the boundary.  3)  the angle 0 through which the d i s l o c a t i o n must t u r n at the boundary (see F i g . 12),  which i s the angle between the l i n e s of  i n t e r s e c t i o n of the a c t i v e s l i p planes i n the two c r y s t a l s w i t h the boundary plane.  0 w i l l i n future be r e f e r r e d t o as  "the angle of d i s l o c a t i o n t w i s t " at the boundary. Consider f i r s t the symmetric t i l t b i c r y s t a l s . bent c o n t i n u i t y at a misorientation  angle around 7 0 ° , and (2)  c o n t i n u i t y only i n b i c r y s t a l s H w i t h m i s o r i e n t a t i o n clearly.  They showed ( l ) best straight  150°, and then not very  For bent c o n t i n u i t y , the angle of d i s l o c a t i o n t w i s t i s zero.  It i s  i n s t r u c t i v e t o investigate the nature of the d i s l o c a t i o n s approaching the boundary.  Table 4 gives the angle a between the s l i p d i r e c t i o n and the  boundary plane.  Small values f o r a mean that the s l i p d i r e c t i o n i s nearly  p a r a l l e l t o the boundary plane, i . e . the d i s l o c a t i o n s coming up t o the boundary are screw d i s l o c a t i o n s .  Comparison of Tables 3 and 4 i n d i c a t e t h a t , except f o r  the low angle boundary b i c r y s t a l A, good s l i p band c o n t i n u i t y corresponds t o low values f o r  Screw d i s l o c a t i o n s appear able t o traverse the boundary  better than edges.  - 31 Table 4. The angle a between s l i p direction and the boundary plane f o r the symmetric t i l t boundary.  a°  Misorientations 0  30  10  20 23 (Bicrystal B) 30 50  70 90 110 114 130 150  26  22  20  17 8 0 8 17 19 26 34  30 34 38 40 42 49 55 59 63  58 54  For c r i t e r i o n 3)> values of the angle of dislocation twist at the boundary 0 have been read from a stereographic plot. The results are given i n Table 5. Table 5 Angle of dislocation twist 0 (for straight continuity only i n the symmetric t i l t b i c r y s t a l s ) . Symmetric t i l t bicrystals orientation difference 0 24 40  60 80 100 120 140 150 18° twist boundary b i c r y s t a l b i c r y s t a l Ql »» Q2 t r i c r y s t a l 1 (13°) tt (39°) 2  0° 70 68 66 62 54 48 38 28 20 18 78 38 1 3  The symmetric bicrystals H (misorientation 150°) showed some slight  i  - 32 s t r a i g h t c o n t i n u i t y , whereas the t w i s t boundary b i c r y s t a l showed none. • c r i t i c a l 0-value f o r continuous s l i p between 15°  and 20°  -  A  would appear l i k e l y  The remarkably small 0-values i n the t r i c r y s t a l s should be noted. T r i c r y s t a l 2,  where the outside c r y s t a l s , t i l t e d 39°,  have s l i p  nearly p a r a l l e l to the boundary, showed e x c e p t i o n a l l y good c o n t i n u i t y , rather b e t t e r than t r i c r y s t a l 1.  I t compared w e l l with b i c r y s t a l E, where the seeds  had nearly the same o r i e n t a t i o n s as the outside c r y s t a l s of t r i c r y s t a l 2„ excellent c o n t i n u i t y i n b i c r y s t a l E i s not, therefore, actuated by p e c u l i a r i t y i n i t s boundary m i s o r i e n t a t i o n of 74°,  The  any  but simply by the screw  character of the d i s l o c a t i o n s coming up against the boundary.  Bicrystal. Ql  also has s l i p d i r e c t i o n p a r a l l e l to the boundary, but c o n t i n u i t y of the  slip  bands i s prevented by a high angle of d i s l o c a t i o n t w i s t . 5.  T h e o r e t i c a l Considerations on the E f f e c t on Continuity of the Angle of D i s l o c a t i o n Twist (0) at the Boundary. I t has been shown that to pass, through a boundary with a t w i s t  element a ; d i s l o c a t i o n must take on a stepped form ( F i g . 12).  What w i l l happen  to such a d i s l o c a t i o n when i t expands i n t o the s l i p planes of c r y s t a l 2? long segments w i l l probably bow out under the applied shear s t r e s s , and short segments w i l l act as drags on the movement. consider how  The the  I t i s of i n t e r e s t to  strong t h i s drag w i l l be.  The s i t u a t i o n i s analogous to that f o r the movement of a jogged dislocation.  Annealed aluminum w i l l have the order of 10  per square centimeter.  - 10  dislocations  When one centimeter length of a d i s l o c a t i o n moves one  centimeter forward, i t must pick up 10^  - 10^  25  I f 0 i s as before the angle of  a where a i s the l a t t i c e parameter.  • .. d i s l o c a t i o n t w i s t at the boundary, and the  jogs, i . e . one jog per 2 1/2  step3  -  produced j o i n neighbouring  - 33 s l i p planes, then the distance d between these steps w i l l be given approximatel y by d =  (see F i g . 15 and Appendix 3 ) o  a  2 sin  0  When 0 = 5 °  d = 8a  0 » 1.0°  d = 4a  0-20°  d = 2a  I t can r e a d i l y be seen that the number of jogs produced i n a d i s l o c a t i o n when passing through a low angle boundary w i l l not be much greater than the number i t would pick up i n a normal s l i p process i n annealed metal. are (see  In general, jogs  thought not t o produce a large dragging force on d i s l o c a t i o n s i n aluminum^ f o r example A. Seeger, " G l i d e and Work Hardening i n M e t a l s " , Lake  P l a c i d Conference, 1956, p„243)o  In many cases they can g l i d e along e a s i l y  with the r e s t o f the d i s l o c a t i o n , o r can mutually a n n i h i l a t e . I t i s possible t h a t s l i p c o n t i n u i t y can be prevented by the extra energy needed t o give a stepped d i s l o c a t i o n r a t h e r than by d i f f i c u l t y i n moving such a d i s l o c a t i o n once formed.  An a n a l y s i s o f energy changes when a  d i s l o c a t i o n becomes stepped has been c a r r i e d out i n Appendix 3o  Insufficient  information about the l o c a t i o n o f the s l i p sources make i t impossible t o calculate a maximum 0-value above which s l i p c o n t i n u i t y would become i m p o s s i b l e I t i s , however, q u i t e c l e ^ r t h a t applied forces can supply s u f f i c i e n t energy to give steps i n the d i s l o c a t i o n .  Step formation can be eliminated as a  mechanism f o r preventing s l i p c o n t i n u i t y unless the s l i p sources are very near (less than 0,1 inches) from the boundary. E l a s t i c i n t e r a c t i o n s between t h e s t r a i n f i e l d s of the moving s l i p d i s l o c a t i o n s and the d i s l o c a t i o n s i n the boundary are l i k e l y t o give stronger 2L  blocking. valueso  Dehlinger  has shown t h a t such i n t e r a c t i o n s can assume large  The problem cannot be solved u n t i l exact models o f boundary s t r u c t u r e  0  - 34 have been developed. T h e o r e t i c a l Estimation of the Frequency of Continuous S l i p Across Boundaries i n a P o l y c r y s t a l . Observations on p o l y c r y s t a l aluminum show t h a t s l i p bands are continuous across a few percent of the g r a i n boundaries.  What p r o p o r t i o n  would be crossed i f the maximum angle of d i s l o c a t i o n t w i s t 0 i s taken, as  15°?  Suppose t h a t there i s only one s l i p plane a c t i v e i n each c r y s t a l near the boundary.  Then the problem i s a very simple one.  Take the i n t e r s e c t i o n of  the s l i p plane i n c r y s t a l 1 w i t h the bojjndary as a f i x e d a r b i t r a r y l i n e .  In  a random aggregate, the s l i p plane from c r y s t a l 2 i s e q u a l l y l i k e l y , to cut the boundary i n any l i n e .  The p r o b a b i l i t y f o r a favourable r e l a t i v e o r i e n t a -  t i o n of the two grains i s (see F i g . 16) -29. = 1. 180 o plane a c t i v e the proportion w i l l r i s e .  With more than one  slip  I t has, t h e r e f o r e , been demonstrated  that i t i s not unreasonable t o suppose t h a t t h i s c o n d i t i o n must be s a t i s f i e d before c o n t i n u i t y can occur. 7.. Further Evidence f o r the Transparency of C r y s t a l Boundaries t o Screw Dislocations. Screw d i s l o c a t i o n s can e a s i l y change t h e i r plane of . s l i p . Consequently, s t r a i g h t s l i p bands give way t o wavy bands when s l i p i s c a r r i e d out by the movement of d i s l o c a t i o n s w i t h n e a r l y pure screw character. Micro 16.  Examine  I t w i l l be observed that the prominent s l i p band i n the lower  c r y s t a l i s s t r a i g h t as f a r as the boundary.  Once across the boundary i t peters  out i n t o a wavy s l i p t r a c e before j o i n i n g a s l i p band i n the second c r y s t a l . The s l i p across the boundary i s not always wavy, as can be seen from Micros 15, 17j but t h i s need cause no discrepancy i n the argument t h a t only screws ^ penetrate.  A screw d i s l o c a t i o n w i l l change i t s s l i p plane only i f some b a r r i e r  - 36  -  to motion i n the s l i p plane i s encountered, such as a second a c t i v e s l i p system near the boundary,, Micros 21,  22,  23,  and 24 i l l u s t r a t e the prevalence of wavy s l i p  i n the boundary region, even when there i s no c o n t i n u i t y .  In a l l these  p i c t u r e s the d i s l o c a t i o n s approaching the boundary w i l l be of nearly pure screw o r i e n t a t i o n , but s i m i l a r observations have been made on other b i c r y s t a l s . Micro 23 makes i t q u i t e c l e a r that the d i s l o c a t i o n s do not reach the boundary before being held up and so caused t o cross s l i p .  As soon as the s l i p bands  reach the region of double s l i p near the boundary, short wavy l i n e s s t a r t t o branch out.  At the boundary there i s a very large obstacle t o s l i p , and screw  d i s l o c a t i o n s escape from the s l i p plane i n large numbers g i v i n g r i s e t o the short region of s l i p along the boundary seen i n Micros 23,  24,  and 25.  In  Micro 25 one of these s l i p bands p a r a l l e l t o the a x i s of s t r e s s occurs across the  boundary from i t s generating s l i p band. Micro 26 shows the e f f e c t of the boundary,in the case where the  s l i p d i r e c t i o n i s n e a r l y p a r a l l e l t o the polished surface. observed over q u i t e a wide region around the boundary.  Wavy s l i p i s  The s l i p bands.seen  on a s i n g l e c r y s t a l of such a specimen would be caused by d i s l o c a t i o n s of n e a r l y screw o r i e n t a t i o n .  S l i p f a r from the boundary takes the normal form  of closely-spaced bands, and i t can be assumed t h a t , t o get wavy s l i p , d i s l o c a t i o n s of pure screw o r i e n t a t i o n are needed.  In b i c r y s t a l s of type Q2  there i s a very large s i z e e f f e c t and a large amount of double s l i p w i l l be present at the boundary.  This accounts f o r the wide regions over which screw  d i s l o c a t i o n s are released by c r o s s - s l i p . Perhaps the best evidence f o r the generation of screw d i s l o c a t i o n s at boundaries comes from Micro 20,  where the s l i p bands bend round t o j o i n  s l i p bands i n the neighbouring c r y s t a l a f t e r passing through the boundary.  The d i s l o c a t i o n s causing these bent s l i p bands cannot l i e on one s l i p plane, and must therefore be screw d i s l o c a t i o n s . To sum up, the properties of d i s l o c a t i o n s show that the movement of screw d i s l o c a t i o n s w i l l lead to wavy s l i p .  This i s supported by the a v a i l a b l e  evidence and there i s no reason t o doubt i t s v a l i d i t y .  Observations of wavy  and bent s l i p a t the boundary support the view that those d i s l o c a t i o n s penetrating the boundary are pure screws. 8.  Reasons Why Screw D i s l o c a t i o n s should Pass More E a s i l y Through Grain Boundaries than do Edges or Mixed D i s l o c a t i o n s . For a low angle t i l t boundary the p o s i t i o n i s f a i r l y c l e a r (see F i g .  17).  An edge or mixed d i s l o c a t i o n coming down i t s s l i p plane towards the  boundary w i l l enter the s t r a i n f i e l d of the boundary d i s l o c a t i o n s .  It w i l l  pass through the boundary under a minimum applied s t r e s s when i t s s l i p plane b i s e c t s the space d between neighbouring boundary d i s l o c a t i o n s . between such d i s l o c a t i o n s i s given by: sin 0 =  where  a . 2d  J2  a = l a t t i c e parameter 2 6=  boundary  misorientation  The number of s l i p planes c u t t i n g the boundary i n distance n =  =  d,  d distance between the s l i p planes JJ a  d I  =  1/4 JT sin 6  For m i s o r i e n t a t i o n 2 9 = 5°  10°  15°  20°  n = 14  7.2  4.7  3.6  The  distance  - 38 For low angle boundaries, 5° or below, most d i s l o c a t i o n s w i l l penetrate the boundary,, Consider now the s i t u a t i o n f o r a screw d i s l o c a t i o n . e a s i l y change i t s s l i p plane.  This can  The easiest path through the boundary w i l l be  i n e f f e c t a v a l l e y i n the energy f i e l d set up by reactions between the stress f i e l d s of the moving screw and the boundary d i s l o c a t i o n s ; the d i s l o c a t i o n w i l l follow t h i s valley.  A screw d i s l o c a t i o n w i l l therefore always be i n a  favourable s l i p plane t o penetrate the boundary. For boundaries w i t h misorientation i s no longer s a t i s f a c t o r y .  above 20° the d i s l o c a t i o n model  A model f o r g r a i n boundary s t r u c t u r e used f r e q u e n t l y 25  i s Mott's suggested ' i s l a n d s ' of good f i t i n a 'sea' of bad f i t . model s i m i l a r arguments t o those j u s t put forward can be applied.  To t h i s The i s l a n d s  of perfect l a t t i c e w i l l be easy t o penetrate, and the screw d i s l o c a t i o n s seek them out.  The i s l a n d must be large enough to allow a stable loop o f  d i s l o c a t i o n t o b e l l y out through i t .  Having no way f o r estimating the diameter  of the islands w i t h a s u f f i c i e n t degree of accuracy t h i s condition tested.  will  cannot be  The mechanism envisaged i s that a screw d i s l o c a t i o n moves up t o the  boundary and positions i t s e l f t o be across the diameter o f s e v e r a l of the i s l a n d s of perfect f i t .  At such points i t w i l l pass i n t o the next c r y s t a l and  spread out on the s l i p plane, g i v i n g a segmented s l i p band.  This i s perhaps  connected with the observation that where c o n t i n u i t y i s good the s l i p bands near the boundary tend to be wide* 9.  Conclusions (a)  S l i p band c o n t i n u i t y i s a true bulk e f f e c t and i s not confined  1  to the surface. (b)  Work hardening appears t o be lowered by good s l i p band c o n t i n u i t y .  - 39 (c)  D i s l o c a t i o n source a c t i v a t i o n theory i s incompatible with  the r e s u l t s obtained here. (d)  Factors favouring c o n t i n u i t y are: 1)  a low angle boundary  2)  a small angle of d i s l o c a t i o n t w i s t at the boundary, a l i m i t i n g value of 0 max = 15 - 20° being i n d i c a t e d .  3)  s l i p d i r e c t i o n nearly p a r a l l e l t o the boundary, i . e . screw d i s l o c a t i o n s pushed  (e)  at the boundary.  Detailed metallographic study of deformation markings at  the boundary support the idea that screw d i s l o c a t i o n s are released by crosss l i p near the boundary and that screw d i s l o c a t i o n s pass through the boundary.  - 40 APPENDIX I  Electropolishing Large Areas of Aluminum* Introduction There are many descriptions i n the l i t e r a t u r e *  of electropolishes  f o r aluminum. Most of these refer to procedures f o r the preparation of specimens with small surface area f o r micrographic examination. Electropolishing large areas presents much greater problems i n heat dissipation and electrolyte-flow. Experimental d e t a i l s . The following polishing solutions were t r i e d : Alcoa bright dip (chemical polish) Perchloric acid-ethyl alcohol mixtures, A phosphoric acid electrolyte 1 part n i t r i c acid to four parts methyl alcohol, 15$ perchloric acid i n acetic acid. Most electropolishes are effective only i n a restricted temperature range, usually below 20°C. E f f i c i e n t cooling i s therefore essential. For these aluminum polishes, surrounding the bath with ice was  generally  ineffective (5 amps at 50 volts puts i n enough energy to melt 12 grams of ice per second). In practice,the most successful arrangement u t i l i s e d a stainless steel beaker as cathode, surrounded by cold running water, the l i q u i d i n the beaker being s t i r r e d .  A glass beaker and aluminum cathode were sometimes  used where cooling was less c r i t i c a l .  - 41 Results.' Electrolyte  Current  Temperature  Density  90-110°C  Alcoa b r i g h t d i p  70$ orthophosphoric27, 28 2.5$ water 26.51% " c a r b i t o l " 1% HF  6.3-0.5 amps/cm^  20-70°C  20$ p e r c h l o r i c acid i n ethyl alcohol  0.5-1.0 amps/cm  10-18°C  not  1 part HNC|  9  4 parts CH 0H  critical  15$ p e r c h l o r i c i n acetic acid  '2 0.1-0.3 amps/cm.  Good general surfaces w i t h p i t t e d areas, striations vertical i n bath. Rather inconsistent. Some p i t t i n g . Tendency to get white deposit on the surface.  Quite good i n some cases. Greater C.D., b e t t e r p o l i s h . See next s e c t i o n for details.  10-20°C  Good at low m a g n i f i c a t i o n Some roughness shown up at x600 m a g n i f i c a t i o n and above.  14-20°C.  Good. Slower a c t i n g than the previous e l e c t r o l y t e s  0.5-0.7 amps/cm  3  Q u a l i t y of F i n i s h  Perchloric acid-ethyl alcohol solutions. These are the most widely used e l e c t r o p o l i s h e s on aluminum. large surfaces, however, they have c e r t a i n disadvantages.  For '  The best p o l i s h i s  obtained at high current d e n s i t i e s , but t h i s i s accompanied by r a p i d heating of the s o l u t i o n .  With the present arrangement, runs are l i m i t e d t o 30-45  seconds.(this a p p l i e s also t o the HN0 -CH 0H e l e c t r o l y t e ) . 3  5  A f u r t h e r drawback  i s a black deposit that f r e q u e n t l y forms over part of th*e surface, under which there i s no p o l i s h .  This happens most f r e q u e n t l y i n s o l u t i o n s with 20$  strength (S.G. 1.25)  perchloric acid.  A s o l u t i o n with concentrated (60$)  p e r c h l o r i c never gave the deposit, but areas of severe p i t t i n g developed. I n both s o l u t i o n s the trouble was minimised by obtaining a smooth f l o w o f  - 42 e l e c t r o l y t e past the surface, but r e s u l t s were f a r from consistent. 30 f o l l o w i n g explanation has been put forward.  The  Turbulence at the surface leads  to l o c a l overheating, and the f o l l o w i n g reactions: C10^~ > CI" + 0 C H 0H+ 0 — * 2 C + 3 H 0 2  5  2  With the strongest a c i d , the carbon deposit i s f u r t h e r o x i d i s e d t o CO, COj l e a v i n g a p i t t e d area.  This suggestion i s backed by the f o l l o w i n g  observations: (1)  A l o r A l oxide can act as a strong c a t a l y s t f o r such reactions.  (2)  The HNO^ CH^OH e l e c t r o l y t e can give a s i m i l a r deposit d f allowed  to overheat. (3)  At the same C D . , the specimen cheats up very much f a s t e r i n the  e l e c t r o l y t e with the 60$ p e r c h l o r i c than i n that with the 20$ p e r c h l o r i c .  This  i s a t t r i b u t e d t o heat evolved a t the specimen surface while the carbon i s oxidised o f f . An e l e c t r o p o l i s h f o r r a p i d removal o f metal When i t i s desired t o remove l a y e r s o f aluminum several microns t h i c k , e.g. t o remove surface working, a 15$ p e r c h l o r i c a c i d i n e t h y l a l c o h o l s o l u t i o n i s recommended. Temperature must be kept below 20°C f o r a p o l i s h . There must be no s t i r r i n g . Summary^ For e l e c t r o p o l i s h i n g large areas of aluminum, the most consistent o f the s o l u t i o n s t r i e d i s 15$ p e r c h l o r i c a c i d i n a c e t i c a c i d . a c t i o n i s slow, needing 1-1 1/2 hours f o r a good f i n i s h . delineated by t h i n l i n e s .  The p o l i s h i n g Grain boundaries are  - 43 APPENDIX I I The Shear Stresses Acting on S l i p Planes Ahead of a Pile-up of D i s l o c a t i o n s . The mathematics of the procedure t o be described were developed by o, 32 A.E. Love- - , i t has been applied to s l i p i n metals i n a paper by Davis et a l . 3  1  The b a s i c equation i s s P i = PN = P[(ei.ei  x li.li )  (e, . l i x e i . l j ) ] ,  where P i i s the shear stress on s l i p systems i , caused by an a p p l i e d shear s t r e s s P on s l i p systems.1.  The vectors are u n i t v e c t o r s , such that t h e i r  dot products are cosines. e i , ei  are normal to t h e s l i p planes _ i ,  li, li  are s l i p d i r e c t i o n s .  Values of N are derived, w i t h N =[cos(angle between s l i p plane normals) x cos(angle between s l i p directions}) +  (cos(angle between normal  to s l i p p l a n e l and s l i p d i r e c t i o n i ) x . cos(angle between normal t o plane i and s l i p d i r e c t i o n ! )J. For  each b i c r y s t a l , a stereogram i s p l o t t e d g i v i n g the s l i p planes  ;and d i r e c t i o n s f o r both c r y s t a l s .  Angles between a l l a c t i v e s l i p d i r e c t i o n s  and s l i p plane normals are read o f f from the stereogram.  For each s l i p  system i n c r y s t a l 1, N-values are found f o r a l l the s l i p systems 'in c r y s t a l 2. I f s l i p band c o n t i n u i t y i s caused by s l i p source a c t i v a t i o n across the boundary, high N-values should lead t o good c o n t i n u i t y .  F i g s . 13 and 14 show  N-values f o r symmetric b i c r y s t a l s w i t h m i s o r i e n t a t i o n from 0° t o 180°. Each c r y s t a l has 12 s l i p systems. would have t o be c a l c u l a t e d . however,  In the general case 144 N-values  The b i c r y s t a l s grown f o r t h i s i n v e s t i g a t i o n ,  had c r y s t a l s w i t h t h e i r <110> axes p a r a l l e l t o the s t r e s s a x i s ,  and the applied stress w i l l give appreciable shear stresses only on two s l i p  - 44 planes per c r y s t a l , each plane having two p o s s i b l e s l i p d i r e c t i o n s .  There  are therefore only four s l i p systems per c r y s t a l t h a t need be considered, g r e a t l y reducing the labour involved.  - 45 APPENDIX I I I  An A n a l y s i s of the Energy Considerations i n the Formation o f a Stepped D i s l o c a t i o n at a Twist Boundary, Data f o r aluminum: shear modulus c r i t i c a l shear s t r e s s £  0  =  2.7 x 10 gms/cm.  =  5 x 103  gms/cm.  2  energy f o r a j o g i n an edge d i s l o c a t i o n — 0.4 e.v. energy f o r a j o g i n a screw d i s l o c a t i o n =  2/3 x .4 e.v.  l a t t i c e parameter a,  2.5 A  =  A low angle t w i s t boundary can be represented by d i s l o c a t i o n s w i t h screw components.  When a s l i p d i s l o c a t i o n moves through such a boundary i t  w i l l receive jogs where i t cuts the boundary d i s l o c a t i o n s ; the screw component of these d i s l o c a t i o n s w i l l lead t o those parts of the jogs that l i e i n the boundary plane.  For s i m p l i c i t y , assume t h a t the jogs are e q u a l l y  spaced along the s l i p d i s l o c a t i o n and perpendicular t o i t s l i n e .  Jogs w i l l  form that have a minimum energy, and those that j o i n the s l i p planes i n t h e shortest l i n e s w i l l be favoured.  There are four s l i p planes i n aluminum,  and there w i l l , except i n s p e c i a l cases, be three possible jog d i r e c t i o n s . An angle f a i r l y near t o 90° between jog l i n e s and the d i s l o c a t i o n l i n e i s therefore l i k e l y .  (The boundary grown had a {l00} boundary plane; the  d i s l o c a t i o n l i n e and t h e jogs w i l l therefore be e x a c t l y perpendicular). On t h i s model (see F i g , 15),  a = d sin 0 d  =  a {2 s i n  0  46 •for  0=  5°  d = 8 a  0  =10°  d =  0  =15°  d = 2.7 a  0  = 20°  d = 2 a  0  = 25°  d =  0 = 30°  4  a  1.7a  d = 1.4 a  V a r i a t i o n s from 90° i n the angle between s l i p d i r e c t i o n and j o g w i l l have l i t t l e e f f e c t on d u n t i l d becomes greater than 2 a (e.g. i f t h i s angle i s 70°, at 0=20  d = 1.98  a).  I t i s desirable to c a l c u l a t e the shear s t r e s s e s needed to give the: jog d e n s i t i e s i n d i c a t e d . must be considered.  To do t h i s the microscopic d e t a i l s of the process-  The mechanism envisaged i s i l l u s t r a t e d i n F i g . 18..  Increase i n energy i n the formation of each step i n a d i s l o c a t i o n with Burger's vector b i s given .bys. A E = the energy f o r a j o g - /Ah* for  0 = 20°,/*b  2  d(l< - cos 0.)  d ( l - cos 0) =/ib d 2  0.06  = 0.06  e.v.  This i s n e g l i g i b l e compared t o the energy f o r a jog (•—0.4 e;.v.,) i n theaccuracy of these c a l c u l a t i o n s . . For a l l 0-values considered,. A'E='0.4. e.v. Work done by the d i s l o c a t i o n i n forming each jog. =  force x distance  = 1/2 force x d s i n 0 ;  = 1/2-6b dwhere  d sin.0 r  £~ = shear stress at the d i s l o c a t i o n = N 60  - kl  s l i p dislocation boundary  F i g . 18.  (a)  Formation of one step.  (b)  Dislocation with the f u l l number of jogs.  The passage of a dislocation through a boundary.  -  - 48 with  N= number of d i s l o c a t i o n s i n a p i l e - u p tending to push the d i s l o c a t i o n through the boundary.  Now equating energy needed to cause the stepped d i s l o c a t i o n with the work done "n i t s formation, A.E  60  -_1 2  N a d  2  sin  0  vT  .4 x 1.6 x 1 0 * = N x 50 x 10 12  6  x 2.5  3  x 10~ x K 24  sin 0  2  ergs  2/T where d»Ka now  N = 2.3 x 1 0 K sin 0 3  2  for  0=  25 ,  K = 1.7  N = 1.9 x 10  3  0 =  20 ,  K = 2  N  3  0=  10 ,  K = 4  N = 0.85 x 1 0  1.7 x 1 0  3  These values are probably r e l i a b l e t o ±50$. The number of d i s l o c a t i o n s expected i n a p i l e - u p under shear s t r e s s 6 3 i s given by  23 N a TT L 60  where  L = the length  Thus  N = 3.2 x 10%,  for  . L = 1 cm. L = 1_ cm. 10  Again, accuracy i s probably about  of the p i l e - u p .  N = 3.2 x 1 0  4  N = 3.2 x 1 0  3  ±50$.  When a stress s u f f i c i e n t t o give s l i p l i n e s i s a p p l i e d , pile-ups  - 49 of these orders w i l l form at the boundary.  Comparison w i t h the N-values  needed t o give steps i n a d i s l o c a t i o n l i n e , , show that a l l s l i p sources d i s t a n t 1/10 cm. or more from the boundary w i l l be able to give these steps. . A f a c t o r not yet mentioned i s the p o s s i b i l i t y of thermal f l u c t u a t i o n s a c t i v a t i n g the formation of the steps. have t o push enough of the d i s l o c a t i o n expand out i n t o the second c r y s t a l .  The a c t i v a t i o n would presumably  through the boundary t o enable i t t o  The c r i t i c a l radius f o r a d i s l o c a t i o n  i n aluminum i s of the order 10~3 - 10"^ cms.; therefore have t o be a c t i v a t e d simultaneously.  a l a r g e number of steps would I t i s u n l i k e l y that thermal  a c t i v a t i o n i s a s i g n i f i c a n t f a c t o r at room temperature.  - 50 BIBLIOGRAPHY  1.  R. Von M i s e s ,  Z. Agnew.U, Mech., 8, 161, 1928.  2.  G. Taylor, "Strains i n a C r y s t a l l i n e Aggregate", from "Deformation and Flow of Solids"? I n t e r n a t i o n a l Union of T h e o r e t i c a l and Applied Mechanics! Colloquium, Madrid, 1955.  3.  J . Bishop and R. H i l l , P h i l . Mag. '£2, 414, 1298, 1951.  4.  B. J a o u l , J . Mech. Phys. S o l i d s , j>, 2, 1957.  5.  A. Kochendorfer, " P l a s t i s c h e Eigenschaften Von K r i s t a l ] e n " , Springer 1941.  6.  D. McLean, "Grain Boundaries i n Metals", Oxford 1957.  7.  D.W.  8.  T. Kawada, J . Phys. Soc. of Japan, 6, 363, 485, 1951.  9.  J . J , GiLman, Acta Met. 1, 426, 1953.  Bainbridge, C.H. L i and E.H. Edwards, Acta Met. 2, 322, 1954.  10.  B. Chalmers, Proc. Roy. Soc. A "162. 120, 1937.  11.  R. Clark and B. Chalmers, Acta Met. 2, 80, 1954.  12.  K.T. Aust and N.K. Chen, Acta Met, 2, 632, 1954.  13.  R.L, F l e i s c h e r and B. Chalmers, Acta Met,, 6,- 265, 1958  14.  G.J. O g i l v i e , J . I n s t . Metals 81, 491, 1952-53.  15.  P. Lacombe and L. Beaujard, J . I n s t . Metals 74., 1, 1948.  16.  J . J . Gilman, Trans. A.I.M.E., 212, 783, 1958.  17.  V.M, Urie and H.L. Wain, J . I n s t . Metals, 81, 153, 1952.  18.  T. Kawada, J . Phys. Soc. of Japan 7, 240, 1952.  19.  W. Berg, Z. K r i s t . 8£, 286, 1934. Naturwissenschaften 19., 391, 1931.  20.  C.S. B a r r e t t , Trans. A.I.M.E. l 6 l , 15, 1945.  21.  C.S. Barrett and L.H. Levenson, Trans. A.I.M.E., 13J7, 76, 1940.  22.  G. Wyon and J.W, Marchin, P h i l . Mag, 46, 1120, 1955.  23.  A.H, C o t t r e l l , "Dislocations and P l a s t i c Flow i n C r y s t a l s " , Oxford 1952, pp. 106, 107  24.  U, Dehlinger, Solvay Conference, 415, 1951.  25.  N.F. Mott, Proc. Phys. Soc. 60, 391, 1948,  .  - 51 BIBLIOGRAPHY (continued) 26o  P.A, Jaquet, M e t a l l u r g i c a l Reviews, 1, 157,  27.  E.C. Pearson, G. Marchand, and R.H. Hay, Canadian Mining and M e t a l l u r g i c a l B u l l e t i n , 45_, 598,  1956.  1952.  28.  A. Hone and E.C. Pearson, Metal Progress, j>3_, 363,  29.  G„E. P e l l i s s i e r , H. Markus and R.F. Mehl, Metal Progress 3.8, 554,  30.  D.R. Wiles, P r i v a t e communication.  31.  A.E. Love, "A T r e a t i s e on the Mathematical Theory of E l a s t i c i t y " , Cambridge U n i v e r s i t y Press, 1927. R.S. Davis, R.L. F l e i s c h e r , J.D. Livingstone and B. Chalmers, Journal of Metals, 7, 136, 1957.  32. 33.  1948. 1940.  A. Seeger, "Report of a Conference on Defects i n C r y s t a l l i n e S o l i d s " , P h y s i c a l Society of London, p. 391, 1955.  MICROGRAPHS (The background pattern seen i n some of these p i c t u r e s was caused 1/ interference effects w i t h i n the metallograph, l a t e r corrected). Bent C o n t i n u i t y i n Symmetric T i l t B i c r y s t a l s . Mag: xlOO.  I  A Micro 1. B i c r y s t a l A. 29 = 6°  Micro 2. B i c r y s t a l B 29 23°  / BCrystal i  26 r  C  Micro 6. B i c r y s t a l F 29 = 93°  - 57 -  Non-Continuity Across an 18° Twist Boundary-  Micro 9.  Mag: xlOO  Micro 10. Mag: xlOO  - 59 Straight Continuity i n B i c r y s t a l H  Micro.12.  Mag:  x200  Micro 15.  Same as Micro 14 Mag: x200  - 62 -  S l i p Band Becoming Wavy A f t e r Crossing the Boundary  Micro 16„  B i c r y s t a l E2 Mag: x200  - 63 S l i p Bands Continuous Through Bent Boundaries  Micro 17.  Polycrystal s t r i p Mags xlOO  Micro 18.  Polycrystal s t r i p . MagsxlOO  - 64 -  S l i p Bands Bent at the Boundary  Micro 20.  Polycrystal strip Mag;  x200  - 66 Wavy S l i p Near the Boundary  Micro 22.  Bicrystal Ql Mags xlOO  -  S l i p Band Segments P a r a l l e l to the Boundary  K i c r o 23.  3icrystal Ql -lagtxlOO  Micro 2U.  B i c r y s t a l E2 Mag: xlOO  67  -  Micro 25.  B i c r y s t a l E2 Mag; xlOO  Micro 26.  Mags x30  - 70 -  The Same Boundary Viewed from Opposite Faces of Thin S t r i p  Micro 28.  Mag: xlOO  Micro 30.  As Micro 29 Mag: x2,000  Micro 31.  Etched consecutively i n Lacombe and Beaujard's, and i n B a r r e t t and Levenson's reagents. Mag; xlOO.  Micro 32.  Etched i n Barrett and Levenson's reagent. Surface near £lll} o r i e n t a t i o n . Mag; xlOO.  -  Micro 33.  As Micro 32, but surface near $100}orientation. Mags xlOO.  73-  S l i p Band C o n t i n u i t y i n the I n t e r i o r at A l - k% Ag A l l o y s as Revealed by E l e c t r o p o l i s h i n g . Viewed on an anodised surface under p o l a r i s e d l i g h t , Mag; xlOO.  Micro 34.  g r a i n boundary Micro 35.  Micro 36.  grain  Micro 37.  

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