TEM
IN SITU STRAINING AND BULK STUDIES
OF THE SELECTION OF GLIDE SYSTEMS
IN FCC. CRYSTALS
ml r
'-r\\'' ^'J'-^Z^-^ K
TEM IN SITU STRAINING AND BULK STUDIES OF THE SELECTION OF GLIDE SYSTEMS IN F . C . C . SINGLE CRYSTALS
BIBLIOTHEEK TU Delft P 1641 1481
TEM 'IN SITU' STRAINING AND BULK STUDIES OF THE SELECTION OF GLIDE SYSTEMS IN F.C.C. SINGLE CRYSTALS
TER V E R K R I J G I N G V A N DE G R A A D V A N DOCTOR IN DE T E C H N I S C H E W E T E N S C H A P P E N A A N DE T E C H N I S C H E HOGESCHOOL D E L F T , OP G E Z A G V A N DE R E C T O R MAGNIFICUS PROF.IR.B.P.TH. V E L T M A N , VOOR E E N COMMISSIE A A N G E W E Z E N DOOR HET C O L L E G E V A N D E K A N E N T E V E R D E D I G E N OP WOENSDAG 21 JANUARI 1981 OM 16.00 UUR
PROEFSCHRIFT
DOOR
N A T U U R K U N D I G INGENIEUR
HENDRIK JAN KOLKMAN
G E B O R E N T E N U E N E N
DIT PROEFSCHRIFT KWAM TOT STAND ONDER LEIDING VAN
PROF. DR. IR. B. OKKERSE, PROMOTOR,
EN
Aan
Aan de v e l e n d i e aan de t o t s t a n d k o m i n g van d i t p r o e f s c h r i f t hebben b i j g e d r a g e n i s de s c h r i j v e r z i j n o p r e c h t e dank v e r s c h u l d i g d . Een a a n t a l b i j d r a g e n z i j met name genoemd. De werkzaamheden werden begonnen i n h e t L a b o r a t o r i u m v o o r M e t a a l k u n d e van de T e c h n i s c h e Hogeschool t e D e l f t . H i e r v e r v a a r d i g d e d r . i r . D. W e i n e r de koper é é n -k r i s t a l l e n , d i e door de heren L . A . J . van V e l z e n en J . F . van Lent met b e h u l p van Laue f o t o g r a f i e u i t g e r i c h t w e r d e n . Het v o n k v e r s p a n e n was i n handen van de heren P . K . J . Schrumpf en J . B . Hermsen. De e x p e r i m e n t e n werden mede u i t g e v o e r d d o o r C D . de Haan e n , t i j d e n s hun a f s t u d e e r p e r i o d e , door i r . J . J . S t a p e l , i r . J . van V o o r s t , i r . W.A.G. F r a n k e n en i r . H . F . C . Berckenkamp. B e i d e l a a t s t e n v e r r i c h t t e n ook een l i t e r a t u u r -s t u d i e i n h e t kader van hun k a n d i d a a t -s e x a m e n . Er werd g e b r u i k gemaakt van de door d r . i r . R. D e l h e z v e r v a a r d i g d e s t e r e o g r a f i s c h e p r o j e k t i e s . De heer J . C . M . J a c o b s e d r u k t e v e l e p l a t e n a f . Met P r o f . d r . i r . P. P e n n i n g werden een a a n t a l v r u c h t b a r e b e s p r e k i n g e n g e v o e r d .
Nadat de s c h r i j v e r i n d i e n s t was g e t r e d e n van h e t N a t i o n a a l L u c h t en R u i m t e v a a r t l a b o r a t o r i u m kon h e t p r o e f s c h r i f t worden v o l t o o i d mede i n door de nieuwe w e r k -g e v e r b e s c h i k b a a r -g e s t e l d e t i j d . P r o f . d r . R . J . H . W a n h i l l was z o v r i e n d e l i j k h e t m a n u s k r i p t k r i t i s c h door t e nemen. Het t i k w e r k , de t e k e n i n g e n en de f o t o ' s werden v e r z o r g d door r e s p . Mw. A . van d e r V e l d e , A . C . F . Hagedorn en K . J . M o s s e l .
CONTENTS L i s t o f p r i n c i p a l symbols and a b b r e v i a t i o n s 9 1 I n t r o d u c t i o n 1 1 -2 Review o f l i t e r a t u r e - 1 3 " 2.1 TEM/HVEM
in situ
s t r a i n i n g e x p e r i m e n t s -13-2.2 S c h m i d ' s law - 1 7 " 2.3 D e v i a t i o n s from S c h m i d ' s law in b . c . c . m e t a l s 2 1 -2.4 D e v i a t i o n s from S c h m i d ' s law i n f . c . c . m e t a l s -27-2.5 S u r f a c e e f f e c t s -36-3 E x p e r i m e n t a l p r o c e d u r e --36 -39-3.1 Scope o f t h e p r e s e n t work _3 9-3.2 General : Common a s p e c t s o f b u l k and
in situ
s t r a i n i n ge x p e r i m e n t s -3 9 -3.2.1 Geometry - 3 9 " 3 . 2 . 2 S i n g l e c r y s t a l s 4 3 -3 . 2 . -3 S u r f a c e damage -44-3.3 E x p e r i m e n t a l p r o c e d u r e f o r
in situ
i n v e s t i g a t i o n s 4 5 -3.3.1 P r e p a r a t i o n - 4 5 " 3-3-2 In situ s t r a i n i n g 3.4 E x p e r i m e n t a l p r o c e d u r e f o r b u l k c r y s t a l s 3.4.1 P r o d u c t i o n o f t e n s i l e specimens -50-3 . 4 . 2 The s t r a i n i n g e x p e r i m e n t s -5 2 3 . 4 . 3 P r e p a r a t i o n f o r t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y 5 2 -k Methods o f o b s e r v a t i o n 5 3 -4.1 D e t e r m i n a t i o n o f g l i d e systems by TEM - 5 3 " 4.2 D i m e n s i o n a l changes - 5 5 " 4 . 3 O r i e n t a t i o n change -58-4.4 D e t e r m i n a t i o n o f t h e g l i d e s h e a r s -62-5 E x p e r i m e n t a l r e s u l t s f o r thein situ
s t r a i n i n g e x p e r i m e n t s 5.1 I n t r o d u c t i o n -65-5.2 The i n i t i a l s i t u a t i o n -66-5.3 G l i d e d i s l o c a t i o n s -68-5.4 C r y s t a l l o g r a p h i c o r i e n t a t i o n changes -74-5.5 D e t e r m i n a t i o n o f the g l i d e s h e a r s -7 5 -5.6 D i m e n s i o n a l changes _7 9 -5.7 F r a c t u r e phenomena -80-75.8 D i s c u s s i o n 8 3 -6 B u l k e x p e r i m e n t s " 91" 6.1 I n t r o d u c t i o n - 9 1 " 6.2 TEM " 9 2 -6 . 3 The r e s u l t s o f o t h e r methods o f i n v e s t i g a t i o n ~93~ 6 . 4 C o n c l u s i o n s f o r the b u l k specimens " 9 ^ -7 D i s c u s s i o n " 9 9_ 7.1 Scope " 9 9 -7.2 G r i p e f f e c t s " 9 9 " 7.2.1 I n t r o d u c t i o n " 9 9 " 7 . 2 . 2 P l a s t i c h i n g e s " 9 9 " 7 . 2 . 3 E l a s t i c h i n g e s and o t h e r e l a s t i c c o n s i d e r a t i o n s -100-7 . 2 . 4 P r e s c r i b e d s t r a i n s -102-7 . 2 . 5 F i n a l remarks on g r i p e f f e c t s -104-7.3 Other e f f e c t s ~1 0 6~
7.4 The TEM
in situ
s t r a i n i n g e x p e r i m e n t s ^_ 1 n Q _ 7.5 The b u l k e x p e r i m e n t s 7.6 Recommendations f o r new e x p e r i m e n t s Summary -111 S a m e n v a t t i n g - 1 1 3 " -115-R e f e r e n c e s
LIST OF PRINCIPAL S Y M B O L S A N D A B B R E V I A T I O N S I, t h r o u g h VI : s p e c i f i c g l i d e d i r e c t i o n s A t h r o u g h D : s p e c i f i c g l i d e p l a n e norma 1 f o r f . c . c . m e t a l s ; f o r b . c . c . m e t a l s t h e r e v e r s e : g l i d e d i r e c t i o n , B u r g e r s v e c t o r ( i n g e n e r a l ) a b s o l u t e v a l u e o f b b . c . c . body c e n t e r e d c u b i c C . D . S . c o p l a n a r d o u b l e s l i p ( s e e s e c t i o n 2 . 3 ) i n t e r p l a n a r s p a c i n g f . c . c . f a c e c e n t e r e d c u b i c s h e a r modulus HVEM : h i g h v o l t a g e e l e c t r o n m i c r o s c o p e / m i c r o s c o p y ( s u b s c r i p t ) : r e f e r s t o s p e c i f i c g l i d e system kV k i l o V o l t d i s t a n c e between p i n n i n g p o i n t s : Schmid f a c t o r ; m = cosX cos6
T a y l o r f a c t o r ; M = I [y-i g l i de p i a n e normal ( s u b s c r i p t ) : r e f e r s t o t h e i n i t i a l s i t u a t i on ( s u b s c r i p t ) : r e f e r s t o t h e p r i m a r y g l i d e s y s t e m S.E. : s u r f a c e e f f e c t ( s e e s e c t i o n 2 . 3 ) specimen t h i c k n e s s
-9-TEM : t r a n s m i s s i o n e l e c t r o n m i c r o s c o p e / m i c r o s c o p y _u : d i s l o c a t i o n l i n e d i r e c t i o n w : specimen w i d t h x , y , z : c o o r d i n a t e s y s t e m w i t h r e s p e c t t o the s t r a i n i n g h o l d e r . z i s taken p a r a l l e l t o t h e d i r e c t i o n o f m o t i o n o f t h e movable g r i p ; x i s t a k e n p e r p e n d i c u l a r t o the p l a n e o f the g r i p s a : a n g l e between x q and [ 1 2 1] g : a n g l e between xQ and b_ y : g 1 i d e s h e a r e : s t r a i n a n g l e between n and z 3 — —o a n g l e between b and z 3 — —o d i s l o c a t i o n p a t h l e n g t h 0) : a n g l e between g l i d e l i n e and z^ s t r e s s r e s o l v e d s h e a r s t r e s s t : c r i t i c a l r e s o l v e d s h e a r s t r e s s c a n q l e between n and x —o
1 INTRODUCTION
P l a s t i c d e f o r m a t i o n o f m e t a l s i s due t o t h e g e n e r a t i o n and movement o f d i s l o c a t i o n s . So f a r , direct o b s e r v a t i o n o f t h e s e i m p o r t a n t phenomena i s o n l y p o s s i b l e by a p p l y i n g t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y (TEM).
In t h e v e r y f i r s t e x p e r i m e n t s o f H i r s c h e t a l . (1956) and Whelan e t a l . (1957) a l r e a d y e x i s t i n g d i s l o c a t i o n s were made t o move under t h e a c t i o n o f an i n t e n s e e l e c t r o n beam. T h i s movement was a s c r i b e d t o t h e t h e r m a l s t r e s s f i e l d s a s s o c i a t e d w i t h l o c a l h e a t i n g o f t h e s p o t under o b s e r v a t i o n ( G a l e a n d H a l e 1 9 6 1 ) . P a s h l e y and P r e s l a n d (1962) gave a b e t t e r e x p l a n a t i o n i n terms o f s t r e s s e s
c a u s e d by t h e c o n t a m i n a t i o n l a y e r w h i c h i s formed by t h e e l e c t r o n bombardment o f a d s o r b e d h y d r o c a r b o n m o l e c u l e s a t t h e s u r f a c e o f t h e s p e c i m e n . T h i s method i s s t i l l i n use ( C a r t e r 1977, Fuentes e t a l . 1 9 7 8 ) .
In t h e meantime, TEM s t r a i n i n g h o l d e r s were d e v e l o p e d b o t h f o r s i d e e n t r y ( W i l s d o r f e t a l . 1958) and t o p e n t r y g o n i o m e t e r s (Berghezan a n d Fourdeux 1 9 5 8 ) . S i n c e then many s o - c a l l e d
in situ
d e f o r m a t i o n e x p e r i m e n t s were p e r f o r m e d , a number o f them - s i n c e 1967 ( F u j i t a ) - a l s o w i t h h i g h v o l t a g e e l e c t r o n m i c r o s c o p y(HVEM). T h i s t y p e o f e x p e r i m e n t s i s summarized i n s e c t i o n 2 . 1 .
One m i g h t q u e s t i o n w h e t h e r i n
situ
d e f o r m a t i o n e x p e r i m e n t s a r e r e p r e s e n t a t i v e of b u l k b e h a v i o u r , s i n c e t h e specimens f o r TEM and HVEM ( u s u a l l y named f o i l s ) have t o be v e r y t h i n owing t o t h e heavy a b s o r p t i o n o f e l e c t r o n s i n t h e s p e c i m e n s .I n i t i a l l y t h e maximum p e n e t r a t i o n depth was e x p e c t e d t o v a r y a s t h e s q u a r e o f the e l e c t r o n v e l o c i t y ( H i r s c h 1 9 6 2 ) . T h i s i m p l i e d , because o f t h e r e l a t i v i s t i c c o r r e c t i o n o f t h e v e l o c i t y , t h a t a t 500 kV f o i l s c o u l d be o n l y 2 . 4 t i m e s t h i c k e r than a t 100 kV ( t h e maximum o p e r a t i n g v o l t a g e o f most t r a n s m i s s i o n e l e c t r o n m i c r o s c o p e s ) . However, h i g h e r i n c r e a s e s i n maximum o b s e r v a b l e t h i c k n e s s were found (Suguta e t a l . 1970, F u j i t a e t a l . 1 9 7 4 ) . A t y p i c a l v a l u e i s 0 . 3 um f o r Cu i n TEM o p e r a t i n g a t 100 k V , and 1 - 2 pm i n HVEM a t 500 kV ( F u j i t a 1 9 6 7 ) . The e x a c t v a l u e s d e p e n d , among o t h e r t h i n g s , on t h e p a r t i c u l a r d i f f r a c t i o n c o n d i t i o n s
(Humphreys e t a l . 1 9 7 1 ) .
Yet t h i s a d v a n t a g e o f HVEM cannot be f u l l y u t i l i z e d . When t h e a c c e l e r a t i n g v o l t a g e exceeds a t h r e s h o l d v a l u e , e . g . 197 kV f o r A l a n d 392 kV f o r Cu (Makin 1 9 6 8 ) , p r i m a r y knock-on damage ( t h e d i s p l a c e m e n t o f atoms) o c c u r s . T h i s
i n f l u e n c e s t h e d i s l o c a t i o n b e h a v i o u r d u r i n g
in situ
s t r a i n i n g e x p e r i m e n t s (Saka e t a l . 1975 a ) . T h u s , a t l e a s t f o r a number o f m a t e r i a l s ,in situ
s t r a i n i n g e x p e r i m e n t s have t o be c a r r i e d o u t on v e r y t h i n specimens and may n o t be t y p i c a l f o r b u l k b e h a v i o u r . Some a s p e c t s o f t h i s l i m i t e d t h i c k n e s s a r e d i s c u s s e d i n s e c t i o n s 2 . 2 t o 2 . 5-So f a r , h a r d l y any s y s t e m a t i c i n v e s t i g a t i o n c o n c e r n i n g t h e r e l a t i o n s between b u l k a n d HVEM/TEM
in situ
d e f o r m a t i o n e x p e r i m e n t s has been p e r f o r m e d ( s e e M a r t i n and K u b i n 1 9 7 9 ) . T h e r e f o r e i t was d e c i d e d t o c a r r y o u t a number o fin situ
s t r a i n i n g e x p e r i m e n t s a n d , f o r c o m p a r i s o n , some b u l k e x p e r i m e n t s . The c h o i c e o f-11-the m e t a l s , t h e o r i e n t a t i o n s o f t h e s i n g l e c r y s t a l s and -11-the p r e p a r a t i o n t e c h n i q u e s a r e d e a l t w i t h i n c h a p t e r 3 B e s i d e s the c o n v e n t i o n a l B u r g e r s v e c t o r d e t e r m i n a t
-ion o t h e r methods o f o b s e r v a t i o n a r e d e s c r i b e d i n c h a p t e r k. They c o n c e r n the c r y s t a l l o g r a p h i c o r i e n t a t i o n change and t h e d e t e r m i n a t i o n o f the g l i d e s h e a r s . E s p e c i a l l y the l a t t e r i s new i n t h i s f i e l d . The r e s u l t s o f the e x p e r i m e n t s a r e g i v e n f o r t h e f o i l specimens i n c h a p t e r 5 and f o r t h e b u l k specimens in c h a p t e r 6. F i n a l c o n c l u s i o n s a r e drawn i n c h a p t e r
7-REVIEW OF L I T E R A T U R E
2.1 TEM/HVEM IN SITU STRAINING EXPERIMENTS
T a b l e 2.1 l i s t s what i s t h o u g h t t o be most o f t h e
in situ
s t r a i n i n g TEM/HVEM e x p e r i m e n t s r e p o r t e d i n t h e l i t e r a t u r e . The p r e p a r a t i o n t e c h n i q u e s may a f f e c t t h e e x p e r i m e n t a l r e s u l t s . The f o l l o w i n g methods were u s e d :a) D i r e c t f o r m a t i o n o f t h i n f i l m s , by a-1) vacuum e v a p o r a t i o n , a-2) d e p o s i t i o n from s o l u t i o n . b) T h i n n i n g down from b u l k m a t e r i a l , by b-l) t h e "window t e c h n i q u e " , b-2) t h e " j e t - t e c h n i q u e " .
Table 2.1 Review of TEM/HVEM 'in situ' straining experiments on metals.
*
P reparat ion Refe rence S t a r t i Metal ng m a t e r i a l Fo rm F i n a l spec i men M i n . w i d t h x 1ength 1 n mm FI x t u r e kV
Dete rmi nat ion
g l i d e systems Remarks and key words P a s h l e y 1958
a-1 Mentor and P a s h l e y 1959 P a s h l e y I960
Au s i n g l e c r y s t •
(111} o r .
g 1 ued 100 f r a c t u r e phenomena
a-2 P r i c e 1961 a Cd s i n g l e c r y s t . 1 gl ued 100 - nonbasa1 g 1î de
a-2 P r i c e 1961 b Zn s i n g l e c r y s t . 1 gl ued 100 - twî nn ï ng
a-2 S r i v a s t a v a 1970 Pb s i n g l e c r y s t . 1 ? 100 +
Bauer et a l . 1972 L y l e s and W i 1 s d o r f 1975
Ag s i n g l e c r y s t . (0.1 - 1) x 1 gt ued 500 f r a c t u r e phenomena
b-l Berghezan and Fourdeux 1958; 1959
Al p o l y c r y s t a l 1 x 1| screwed 100
b- 1 W i l s o n and F o r s y t h I96I Al pot y c r y s ta 1 ? g 1 ued 100
-b-l v e s e l y 1968 a Mo s i ng1e c r y s t . 0.35 x 1 ? gi ued 100 + d e v i a t i o n s from S c h m i d ' s law
b-l Imura 1972, 1974 F e , F e - S i s ï n g l e c r y s t . 0.2 x 1 g l u e d 500 -b-l Imura 1972 Al s i n g l e c r y s t . 0.6 x 1.6 g 1 ued 500
-b-l Saka and Imura 1972 Fe-SÍ s i ng1e c r y s t • (0.3 - 0.7) x 2 gl ued 500 - d i s l . v e l o c i t y v e r s u s s t r e s s
b-l Saka et a l . 1973 Al s i n g l e c r y s t • 0.2 x 1 ? 7 400 - 1 s p e c , i r r a d i a t e d at h i g h e r kV ? Saka e t a l . 1975 a , b N! s i n g l e c r y s t . ? j 400 - J b e f o r e s t r a i n i n g
b-l Matsui et a l . 1974
Saka, Matsui e t a l . 1976 Mo s i n g l e c r y s t . 0.9 x 1.9 g 1 ued 1000- + d e v i a t i o n s from S c h m i d ' s law
Saka, Nöda and Imura 1976 800
b-2 w l t h o u t W i l s d o r f 1958 Al ,Fe p o l y c r y s t a l a p p r . 1.5 x 5.5 c1amped 100 -h o l e Wi I s d o r f e t a l . 1958
b-2 w i t h F u j i ta 1967 Al 5 i n g l e c r y s t . a p p r . 2 x 2 1 500
-h o l e ? o r : unknown
b-2 Furubayash i 1969 Fe-Si s i n g l e c r y s t . 2.5 x (4 o r l e s s ) screwed 500 + b-2 Ikeno and F u r u b a y a s h i 1972 Nb s i ng1e c r y s t • ? screwed 500 + ? b-2 Ohr and Narayan 198O s ta i
n-l e s s s t . s i ng 1 e c r y s t . 3 mm d i s c s deformed by b e n d i n g c1amped 200 + f r a c t u r e phenomenon ? Ruedl 1969 A l - A l p o l y c r y s t a l 1 x (3 o r l e s s ) 7 100 - v o i d f o r m a t i o n
? Louchet and Kubin 1975 Nb s i n g l e c r y s t . ? ? 800 + d e v i a t i o n s from S c h m i d ' s law
? L o u c h e t , Kubin and Vesely" 1979 Nb, Mo, n-Fe s î n g l e and p o l y c r y s t a l s ? ? ^800
b ( w i r e s ) T a b a t a e t a l . 1976 Al p o l y c r y s t a l s wi res , d 1 am. 5 I'm 7 2000 - s u r f a c e e f f e c t s See t e x t
In method a t h e w h o l e specimen a r e a may be t r a n s p a r e n t t o e l e c t r o n s . However, t h e s e specimens a r e n o t f u l l y r e p r e s e n t a t i v e o f normal b u l k m a t e r i a l . For example the d i s l o c a t i o n d e n s i t y o f specimens p r e p a r e d a c c o r d i n g t o method a-1 i s t o o
10 11 -2
h i g h (Menter and P a s h l e y 1 9 5 9 : 10 - 10 cm ) and o f specimens p r e p a r e d a c c o r d i n g t o method a-2 t o o low ( P r i c e 1961 a : 0) .
In method b1 a s h e e t o f metal i s l a c q u e r e d a t t h e c i r c u m f e r e n c e and e l e c t r o -
-13-p o l i s h e d . Because o f -13-p r e f e r e n t i a l a t t a c k a h o l e w i l l be formed near the window. The s h e e t i s r e l a c q u e r e d to c o v e r t h e h o l e , r e p o l i s h e d , and so o n . F i n a l l y , when t h e a r e a s u r r o u n d i n g the h o l e i s t h o u g h t t o be t h i n enough a specimen c o n t a i n i n g t h i s a r e a i s c u t out o f t h e s h e e t . Thus t h e specimen w i l l be t r a n s p a r e n t to e l e c t r o n s a t one edge o r , by a m o d i f i c a t i o n , a t b o t h edges (the " f i g u r e - o f - e i g h t " method as m e n t i o n e d by Saka and Imura 1 9 7 2 ) , but not i n the c e n t r e . D i s a d v a n t a g e s o f t h e method a r e the l a b o r i o u s p r o c e d u r e , t h e n o n - r e p r o d u c i b i 1 i t y and the r i s k o f m e c h a n i c a l damage.
In t h e " j e t - t e c h n i q u e " e l e c t r o l y t e s t r e a m s a r e d i r e c t e d to the c e n t r e o f the s p e c i m e n by means o f one o r two j e t s . P o l i s h i n g i s t e r m i n a t e d i m m e d i a t e l y upon p e r f o r a t i o n . The a r e a a d j a c e n t t o t h e h o l e i s t h i n enough f o r t r a n s m i s s i o n .
U n l i k e method b - 1 , t h i s method p r o d u c e s specimens t h a t a r e t r a n s p a r e n t t o e l e c t r o n s i n the c e n t r e , but not near the e d g e s . A d i s a d v a n t a g e o f t h i s method i s the
p o s s i b i l i t y o f s t r e s s c o n c e n t r a t i o n a r o u n d the h o l e ( F u r u b a y a s h i 1969)- W i l s d o r f (1958) o f t e n managed t o s t o p p o l i s h i n g j u s t b e f o r e p e r f o r a t i o n . He o b s e r v e d t h a t specimens t h a t d i d c o n t a i n a h o l e f r a c t u r e d w i t h o u t p r e c e d i n g d e f o r m a t i o n . It i s not c l e a r w h e t h e r t h e same e f f e c t has o c c u r r e d in o t h e r i n v e s t i g a t i o n s summarized
i n t a b l e 2 . 1 , s i n c e i n most c a s e s t h e f r a c t u r e s t r a i n was not g i v e n .
W i t h r e g a r d t o the s t a t e o f s t r e s s , the w i d t h t o l e n g t h r a t i o may be o f i m p o r t a n c e t o o . As can be seen i n t a b l e 2.1 t h e r e i s a l a c k o f e x a c t d a t a . The same h o l d s f o r o t h e r t o p i c s . O n l y L y l e s and W i l s d o r f (1975) s p e c i f i e d the number o f specimens i n v o l v e d i n t h e i r e x p e r i m e n t s .
Because o f the r i s k o f m e c h a n i c a l damage the mounting o f the specimens on the g r i p s i s o f i n t e r e s t ( t a b l e 2 . 1 ) . G l u e i n g i s p r o b a b l y the b e s t method.
E l e c t r o n d i f f r a c t i o n was used o n l y by P a s h l e y ( i 9 6 0 ) . L y l e s and W i l s d o r f (1975) used L a u e - p h o t o g r a p h y i n s t e a d o f s t r a i g h t f o r w a r d e l e c t r o n d i f f r a c t i o n to s t u d y the o r i e n t a t i o n change due to p l a s t i c d e f o r m a t i o n . V i d e o tape r e c o r d i n g , as used by t h e l a t t e r and many o t h e r a u t h o r s , e x c l u d e s e l e c t r o n d i f f r a c t i o n because a t e l e v i s i o n camera c a n n o t a c c e p t s p o t t y p a t t e r n s . In f a c t one has t o choose between d i s c o n t i n u o u s and c o n t i n u o u s s t r a i n i n g . C o n t i n u o u s s t r a i n i n g i s more r e a l i s t i c and e n a b l e s one t o s t u d y d i s l o c a t i o n v e l o c i t y (Saka and Imura 1 9 7 2 ) . On t h e o t h e r h a n d , c o n t i n u o u s s t r a i n i n g e x c l u d e s B u r g e r s v e c t o r d e t e r m i n a t i o n and the making o f d i f f r a c t i o n p a t t e r n s .
The main r e s u l t s o f the p a p e r s summarized in t a b l e 2.1 a r e :
Onset of plastio deformation
P a s h l e y (1960) c o n c l u d e d from d e c r e a s i n g d i s t a n c e s o f the s p o t s from the t r a n s m i t t e d beam i n t h e e l e c t r o n d i f f r a c t i o n p a t t e r n s t h a t h i s e v a p o r a t e d Au f i l m s deformed e l a s t i c a l l y up t o a b n o r m a l l y h i g h s t r a i n v a l u e s (1-1i%) . The Zn p l a t e l e t s o f P r i c e (1961 b) deformed by t w i n n i n g . In the o t h e r i n v e s t i g a t i o n s t h e s t r a i n i n g was a c c o m p l i s h e d by g l i d e .
t h a t i t i s d i f f i c u l t f o r a Frank-Read s o u r c e t o o p e r a t e i n a t h i n f o i l . T h i s was not s p e c i f i e d but may be u n d e r s t o o d as f o l l o w s . The c r i t i c a l s h e a r s t r e s s T c t o
a c t i v a t e a Frank-Read s o u r c e i s g i v e n by ( e . g . J o h n s o n and Ashby 1 9 6 8 ) :
Tc = Gb/L (1)
where L: d i s t a n c e between p i n n i n g p o i n t s
b: a b s o l u t e v a l u e o f t h e B u r g e r s v e c t o r b_ G: s h e a r modulus
For C u , w i t h T C = 10 N/m , b = 2.5 10 m and G = 43 1 0? N/m , L i s i n the
o r d e r o f 10 ym. T h i s i s to be compared w i t h the f o i l t h i c k n e s s i n the a r e a t a n s p a r e n t to e l e c t r o n s o f a t most 0 . 3 ym. Even f o r a r a t h e r o b l i q u e p l a n e a c l a s s i c a l Frank-Read s o u r c e w i l l be a l m o s t i m p o s s i b l e f o r f o i l s t h i n n e d down from b u l k m a t e r i a l , i . e . w i t h t h e L o f b u l k m a t e r i a l . T h i s i s a l s o t r u e f o r d o u b l e c r o s s - s l i p s o u r c e s ( K o e h l e r 1 9 5 2 ) .
F i s h e r (1952) p r o p o s e d t h e s i n g l e - e n d e d Frank-Read s o u r c e f o r s u r f a c e l a y e r s , w i t h o n l y one r e a l p i n n i n g p o i n t . Because o f image f o r c e s the second " p i n n i n g p o i n t " i s the m i r r o r image o f t h e i n t e r i o r p i n n i n g p o i n t a c r o s s the f r e e s u r f a c e . T h i s h a l v e s T c f o r the s u r f a c e l a y e r s as compared to the b u l k .
The c o n c e p t o f F i s h e r a p p l i e d t o t h i n f o i l s e n a b l e s s o u r c e s t o o p e r a t e , but a t h i g h e r s t r e s s e s than the d o u b l e - e n d e d Frank-Read s o u r c e s i n the b u l k , s i n c e L
i s r e p l a c e d by a l i n e a r measure somewhat l a r g e r than h a l f the f o i l t h i c k n e s s . For specimens w i t h a n o n - u n i f o r m t h i c k n e s s l i k e the b-2 t y p e o f specimen such s o u r c e s a r e t h e r e f o r e to be e x p e c t e d i n t h e t h i c k e r a r e a s .
S i n g l e - e n d e d Frank-Read s o u r c e s were a c t u a l l y o b s e r v e d by Imura (1972) i n Fe, by C a r t e r (1977) in Cu-10 at.% Al and by L o u c h e t , K u b i n and V e s e l y (1979) in s e v e r a l b . c . c . m e t a l s . However, d i s l o c a t i o n s were a l s o r e p o r t e d to be
g e n e r a t e d a t t h e edges ( F u j i t a 1967, S r i v a s t a v a 1970) a n d , f o r p o l y c r y s t a l s , i n the g r a i n - b o u n d a r i e s ( F u j i t a 1967, W i l s d o r f 1 9 5 8 ) . P r i c e (1961 a) found i n i n i t i a l l y d i s l o c a t i o n f r e e Cd p l a t e l e t s t h a t d i s l o c a t i o n s were formed a l o n g the l i n e where the specimen was g l u e d to the s t r a i n i n g d e v i c e and a g a i n a t the e d g e s . In most papers m e n t i o n e d i n t a b l e 2.1 the o r i g i n o f the d i s l o c a t i o n s i s not r e v e a 1 e d .
Continuation of glide
Loops and d i p o l e s l e f t b e h i n d by j o g s i n moving d i s l o c a t i o n s were o b s e r v e d in Cd by P r i c e (1961 a) and i n Fe-Si and Nb by F u r u b a y a s h i (1969) and Ikeno and F u r u b a y a s h i ( 1 9 7 2 ) . D i p o l e s and m u l t i p o l e s due to the mutual t r a p p i n g o f groups o f edge d i s l o c a t i o n s o f o p p o s i t e s i g n , w h i c h i s a common f e a t u r e o f g l i d e i n b u l k f . c . c . m e t a l s ( e . g . Mughrabi 1971 a ) , were not r e p o r t e d . Imura (1972) found c e l l f o r m a t i o n i n A l . R e c e n t l y L o u c h e t , Kubin and V e s e l y (1979) s t u d i e d the
-15-d e f o r m a t i o n o f b . c . c . m e t a l s a t low t e m p e r a t u r e s .
The o f t e n o b s e r v e d d e v i a t i o n s from S c h m i d ' s law w i l l be t r e a t e d s e p a r a t e l y ( s e c t i o n s 2 . 3 and 2 . 4 ) .
Fracture
A c c o r d i n g t o Saka and Imura (1972) and Imura (1972) the s t r e s s - s t r a i n c u r v e s o f Fe-Si f o i l and b u l k specimens a r e c o m p a r a b l e when the a c t i v e B u r g e r s v e c t o r
i s p a r a l l e l to the g l i d e l i n e . However t h e f r a c t u r e s t r a i n o f f o i l specimens was much lower when t h e a c t i v e B u r g e r s v e c t o r was about p e r p e n d i c u l a r t o the
g l i de l i n e .
W i l s d o r f ( 1 9 5 8 ) , P a s h l e y (1958, 1960) and Menter and P a s h l e y ( 1 9 5 9 ) , Imura (1974) and L y l e s and W i l s d o r f (1975) a l l o b s e r v e d the same f r a c t u r e phenomena. T h i s i s
r e m a r k a b l e because t h e s e a u t h o r s used b . c . c . and f . c . c . specimens made by
c o m p l e t e l y d i f f e r e n t m e t h o d s , v i z . t h i n n e d down from the b u l k and e v a p o r a t e d and grown from s o l u t i o n (see t a b l e 2 . 1 ) . The o b s e r v a t i o n s w e r e : a c r a c k i s formed a t one o f the edges o f the specimen and s t a r t s to p r o p a g a t e . The a c t u a l c r a c k i s p r e c e d e d by l o c a l t h i n n i n g o f the specimen and the f o r m a t i o n o f t r a p e z o i d a l h o l e s . In f . c . c . {111} f o i l s the edges o f t h e h o l e s a r e p a r a l l e l t o <110> d i r e c t i o n s ( L y l e s and W i l s d o r f 1 9 7 5 ) . The h o l e i n i t i a t i o n i s due t o c l e a v a g e . However, the f a i l u r e o f the r e m a i n i n g b r i d g e s a c r o s s the c r a c k i s a c c o m p l i s h e d by g l i d e . A c c o r d i n g t o L y l e s (1971) the b e h a v i o u r j u s t d e s c r i b e d i s r e p r e s e n t a t i v e o f e l o n g a t i o n r a t e s o f 10 ^ - 10 ** m/s ( c o r r e s p o n d i n g t o s t r a i n i n g r a t e s o f — 3 — 2 — 1 —8 1 0 - 1 0 s in L y l e s1 c a s e ) . For the s l o w e r e l o n g a t i o n r a t e o f 10 m/s ( i . e . a s t r a i n i n g r a t e o f 10 ^ s L y l e s1 s p e c i m e n s f a i l e d by e x c e s s i v e s h e a r i n a n a r r o w s l i p z o n e , w i t h o u t f o r m a t i o n o f c r a c k s o r h o l e s .
A c c o r d i n g t o L y l e s (1971) the t y p e s o f f r a c t u r e phenomena a r e o n l y dependent on the e l o n g a t i o n r a t e , not on the t h i c k n e s s . However, B e e v e r s and Honeycombe
(1962) t e s t e d pure A l and Cu b u l k s i n g l e c r y s t a l s o f c i r c u l a r and s q u a r e c r o s s s e c t i o n under c o n d i t i o n s ( s t r a i n i n g r a t e 10 - 10 s ) f o r w h i c h the e l o n g a t i o n r a t e s must have e x c e e d e d 10 m/s, and y e t the c r y s t a l s f a i l e d by e x c e s s i v e
s h e a r , i n c o n t r a s t t o the h i g h e l o n g a t i o n r a t e specimens o f L y l e s .
Ohr and Narayan (1980) were the f i r s t to d e t e r m i n e the n a t u r e o f the p l a s t i c zone i n f r o n t o f a s h e a r c r a c k . It was found to c o n s i s t o f a p i l e - u p o f screw d i s l o c a t i o n s ; the c r a c k o p e n i n g d i s p l a c e m e n t c o r r e s p o n d e d to the sum o f the B u r g e r s v e c t o r s o f the d i s l o c a t i o n s i n the p i l e - u p . It i s not c l e a r why Ohr and Narayan were a b l e t o make t h e s e o b s e r v a t i o n s d u r i n g TEM
in situ
s t r a i n i n g e x p e r i m e n t s , whereas o t h e r a u t h o r s were n o t .* The g l i d e l i n e i s the i n t e r s e c t i o n o f the g l i d e p l a n e and the p l a n e o f t h e f o i 1 .
2.2 SCHMID'S LAW
At e l e v a t e d t e m p e r a t u r e s ( e . g . f o r Al > 540 K and f o r Cu > 1270 K) f . c . c . m e t a l s s h e a r e x c l u s i v e l y on {110} p l a n e s and i n <110> d i r e c t i o n s (Le H a z i f e t a l . 1 9 7 3 ) . At lower t e m p e r a t u r e s , i n c l u d i n g room t e m p e r a t u r e (Al < 350 K;
Cu < 820 K ) , the o n l y g l i d e p l a n e s a r e {111} p l a n e s and the o n l y g l i d e d i r e c t i o n s a r e a g a i n <110> d i r e c t i o n s . As t h e r e a r e f o u r {111} p l a n e s each c o n t a i n i n g t h r e e <110> d i r e c t i o n s t h e r e a r e t w e l v e p o s s i b l e and c r y s t a 1 l o g r a p h i c a 1 1 y e q u i v a l e n t g l i d e systems a t room t e m p e r a t u r e .
In b . c . c . c r y s t a l s the s l i p d i r e c t i o n s a r e w e l l e s t a b l i s h e d as <111>
d i r e c t i o n s * * , whereas the g l i d e p l a n e s a r e {110} p l a n e s ( j u s t the r e v e r s e o f the s i t u a t i o n f o r f . c . c . c r y s t a l s ) . However, {112} and {113} p l a n e s may a l s o be g l i d e p l a n e s , so t h a t t h e r e a r e
at least
t w e l v e g l i d e systems a v a i l a b l e f o r b . c . c . m e t a l s .The c h o i c e between the g l i d e systems i s g o v e r n e d by the Schmid o r C r i t i c a l R e s o l v e d Shear S t r e s s law (Schmid 1925) w h i c h s t a t e s (Schmid and Boas 1 9 5 0 ) : " G l i d e a l w a y s o c c u r s a l o n g t h e s y s t e m s u b j e c t e d t o maximum s h e a r s t r e s s . . . . A c r i t i c a l v a l u e o f the r e s o l v e d s h e a r s t r e s s is r e q u i r e d f o r the i n i t i a t i o n o f g l i d e on a s u b s t a n t i a l s c a l e " . The b a s i s o f S c h m i d ' s law i s e m p i r i c a l . The law was e s t a b l i s h e d in 1925, i . e . some t i m e b e f o r e d i s l o c a t i o n t h e o r i e s were
d e v e l o p e d . These t h e o r i e s accommodate S c h m i d ' s law when, f o r e x a m p l e , Frank-Read s o u r c e s (see s e c t i o n 2.1) b e g i n t o o p e r a t e f o r r e s o l v e d s h e a r s t r e s s e s h i g h e r than a c r i t i c a l r e s o l v e d s h e a r s t r e s s T .
c
In the c a s e o f u n i a x i a l t e n s i o n , w h i c h i s the u s u a l mode o f t e n s i l e t e s t i n g o f s i n g l e c r y s t a l s , the r e s o l v e d s h e a r s t r e s s x on a p a r t i c u l a r g l i d e system i s g i v e n b y :
x = a c o s A c o s e = ma (2) where a : the a p p l i e d t e n s i l e s t r e s s in the a x i a l d i r e c t i o n
A: the a n g l e between the s l i p d i r e c t i o n o r B u r g e r s v e c t o r b and the tens i 1 e a x i s
6: the a n g l e between n, t h e normal to the g l i d e p l a n e , and the t e n s i l e ax i s
m = c o s A c o s 6 i s known as t h e " S c h m i d f a c t o r " .
* A c c o r d i n g t o K a r n t h a l e r (1978) g l i d e on {001} p l a n e s a t room t e m p e r a t u r e i s p o s s i b l e in N i , Cu and A g .
** However, Hale and Henderson Brown (1968) found 94 : 5 : 1 f o r the r a t i o o f d i s l o c a t i o n s w i t h B u r g e r s v e c t o r s £a<111>, a<100> and a<110> (see a l s o F r a n c e and L o r e t t o 1 9 6 8 ) .
-17-100
100
Fig. 2.1 '(001) stenographic projection.
This figure shows the notation used by Schmid and Boas (1950) for f.c.c. crystals. In this case A — D are the poles of the glide planes and I — VI are the poles of the glide directions. For b.c.c. crystals A — D are the glide directions, whereas I — VI are possible glide planes. The glide plane is quoted first, so the primary system is denoted as BIV for f.c.c. crystals, and as IVB for b.c.c. crystals.
In each triangle the system with the highest Schmid factor m is given for f.c.c. crystals; for b.c.c. crystals the capitals and Roman numerals can be transposed as long as glide on only 110 planes is concerned.
V
The p o s i t i o n o f t h e t e n s i l e a x i s w i t h r e s p e c t t o t h e g l i d e p l a n e normals and g l i d e d i r e c t i o n s i s c o n v e n i e n t l y r e p r e s e n t e d by a s t e r e o g r a p h i c p r o j e c t i o n . F i g u r e 2.1 g i v e s t h e o r i g i n a l n o t a t i o n a d o p t e d by Schmid and Boas. Though M i l l e r
Table 2.2 Relationship between some notations.
M i l l e r î n d ï c e s ïn
(001) p r o j e c t i o n Schmid and Boas C o n v e n t i o n o f ( f o r f . c . c . c r y s t a l s o n l y ) O t h e r customary terms T i l A c r i t i c a l plane*^ i l l B p r i m a r y p l a n e TTl C c o n j u g a t e p l a n e 1T1 D c r o s s - s t î p p l a n e 011 1 O i l 1 1 101 III" c r i t i c a l s l i p d i r e c t i o n T o i IV p r i m a r y s l i p d i r e c t i o n T i o V c o n j u g a t e s l i p d i r e c t i o n 110 VI In German: u n e r w a r t e t e G l e i t e b e n e . i n d i c e s a r e o f t e n u s e d , they g i v e r i s e t o m i s t a k e s i n w r i t t e n and e s p e c i a l l y spoken l a n g u a g e . T h e r e f o r e t h r o u g h o u t t h i s t h e s i s t h e c o n v e n t i o n o f f i g u r e 2.1 w i l l be u s e d . T h i s c o n v e n t i o n was meant f o r f . c . c . c r y s t a l s ; n e v e r t h e l e s s i t can be used f o r b . c . c . c r y s t a l s as l o n g as g l i d e on {110} p l a n e s i s c o n s i d e r e d .
T a b l e 2.2 g i v e s t h e r e l a t i o n s h i p w i t h t h e M i l l e r i n d i c e s . Some o t h e r n o t a t i o n s , w h i c h a r e i n f a c t u n n e c e s s a r y , have been p r o p o s e d , see f o r i n s t a n c e B i s h o p and
H i l l ( 1 9 5 1 ) , D i e h l e t a l . (1954) and Mader e t a l . ( 1 9 6 3 ) .
The 24 t r i a n g l e s i n f i g u r e 2.1 a r e c r y s t a l l o g r a p h i c a l l y i d e n t i c a l .
C u s t o m a r i l y , t h e o r i e n t a t i o n o f the t e n s i l e a x i s o f a c u b i c c r y s t a l i s s p e c i f i e d by p l o t t i n g t h e p o l e o f the t e n s i l e a x i s i n t h e t r i a n g l e 001 A I, t h e s o -c a l l e d s t a n d a r d s t e r e o g r a p h i -c t r i a n g l e . U n f o r t u n a t e l y , i n some papers o t h e r t r i a n g l e s a r e u s e d , e . g . M a t s u i e t a l . (1974) and S a k a , Noda and Imura (1976) (both q u o t e d i n t a b l e 2 . 1 ) . More s e r i o u s i s t h e f a c t t h a t i n a number o f p a p e r s t h e r e i s no s t e r e o g r a p h i c p r o j e c t i o n a t a l l , b u t o n l y a p e r s p e c t i v e d r a w i n g o f t h e s p e c i m e n , i n c l u d i n g some g l i d e p l a n e s and g l i d e d i r e c t i o n s ; examples among the papers quoted i n t a b l e 2.1 a r e Ikeno and F u r u b a y a s h i (1972) and Saka and Imura ( 1 9 7 2 ) . F u r t h e r m o r e i t i s a r a t h e r t e d i o u s p r o c e d u r e t o deduce t h e e x a c t o r i e n t a t i o n s from t h e d a t a g i v e n by Wu and Smoluchowski (1950) ( t o be d i s c u s s e d
i n s e c t ion 2 . 4 ) .
For f l a t specimens n o t o n l y t h e o r i e n t a t i o n o f t h e t e n s i l e a x i s b u t a l s o the o r i e n t a t i o n o f t h e normal t o t h e l a r g e s t f a c e may be o f i m p o r t a n c e . The p o s i t i o n o f t h i s normal can be p l o t t e d i n a p r o j e c t i o n l i k e f i g u r e 2 . 1 . A good a l t e r n a t i v e i s t o use a s t e r e o g r a p h i c p r o j e c t i o n w i t h t h e normal t o t h e l a r g e s t f a c e , i n s t e a d o f ( 0 0 1 ) , i n t h e c e n t r e and t h e t e n s i l e a x i s on the o u t e r c i r c l e ( e . g . S a k a , Noda and Imura 1 9 7 6 ) .
R e t u r n i n g t o f i g u r e 2 . 1 : In each t r i a n g l e t h e g l i d e s y s t e m w i t h t h e h i g h e s t Schmid f a c t o r m i s i n d i c a t e d . Thus when t h e t e n s i l e a x i s i s chosen i n the
s t a n d a r d t r i a n g l e , BIV i s t h e a c t i v e s y s t e m a c c o r d i n g t o S c h m i d ' s l a w , i r r e s p e c t i v e o f t h e e x a c t l o c a t i o n o f the t e n s i l e a x i s w i t h i n the s t a n d a r d
t r i a n g l e . N e v e r t h e l e s s the v a l u e o f nig|y v a r i e s t h r o u g h o u t t h e s t a n d a r d t r i a n g l e . * * See t h e p l o t s o f D i e h l e t a l . (1954).
-19-The minimum i s 0 . 2 7 f o r t h e [111] c o r n e r , where nig|y = mc j e t c . ( s e e f i g u r e 2 . 1 ) .
The upper l i m i t i s 0 - 5 0 ; t h e c o r r e s p o n d i n g t e n s i l e a x i s o r i e n t a t i o n i s o f i r r a t i o n a l M i l l e r i n d i c e s :
- i + £/6, -g/6, i + ^ / 6
and i s i n d i c a t e d i n f i g u r e 2 . 1 . The m's o f t h e o t h e r systems f o r t h e ™g|y = 0 . 5 0 o r i e n t a t i o n a r e g i v e n i n t a b l e 2 . 3
-Table 2.3 Schmid factors m for w g / y - 0.50 orientation (see figure 2.1). System AI I AI I I AVI B I I BV CI CI I I CV Dl D1V DVI
m 0.29 0.47 0.18 0.25 0.25 0.32 0.20 0.12 0.22 0.17 0.05
There i s some c o n f u s i o n w i t h r e s p e c t t o S c h m i d ' s l a w . Kuhlmann-Wi1sdorf (1978) f o r m u l a t e d S c h m i d ' s law as f o l l o w s : " T h e r e s o l v e d s h e a r s t r e s s r e q u i r e d t o d e f o r m a c r y s t a l i n g l i d e i s i n d e p e n d e n t o f t h e magnitude and d i r e c t i o n o f the normal s t r e s s a c t i n g on t h e s l i p p l a n e " . However, Kuhlmann-Wi1sdorf showed t h e o r e t i c a l l y t h a t t h e normal s t r e s s does have a ( s m a l l ) i n f l u e n c e , and speaks i n t h i s c o n n e c t i o n o f d e v i a t i o n s from S c h m i d ' s l a w . Lucke and Lange (1952) a p p a r e n t l y a r e o f o p i n i o n t h a t S c h m i d ' s law s t a t e s t h a t f o r a p a r t i c u l a r metal the c u r v e s o f r e s o l v e d s h e a r s t r e s s v e r s u s g l i d e s h e a r f o r s i n g l e
c r y s t a l s a r e a l l t h e same, i r r e s p e c t i v e o f o r i e n t a t i o n . But a c c o r d i n g t o S c h m i d ' s law as q u o t e d e a r l i e r t h i s i s o n l y t r u e f o r t h e i n t e r c e p t i o n w i t h t h e r e s o l v e d s h e a r s t r e s s a x i s . And even t h i s needs c o r r e c t i o n : D i e h l (1956 a) showed t h a t , a t l e a s t f o r C u , T c does depend on o r i e n t a t i o n . Moreover Johnson e t a l . (1968)
found t h a t t h e t o t a l amout o f s e c o n d a r y s l i p ( i . e . s l i p on o t h e r systems than the p r i m a r y one) i s about 50 % a t t h e o n s e t o f p l a s t i c d e f o r m a t i o n (see a l s o s e c t i o n 7 . 5 ) .
So S c h m i d ' s law s h o u l d be f o r m u l a t e d as f o l l o w s : " A t t h e o n s e t o f p l a s t i c d e f o r m a t i o n g l i d e on a s u b s t a n t i a l s c a l e o c c u r s a l o n g t h e s y s t e m s u b j e c t e d t o maximum s h e a r s t r e s s " . In t h i s r e s p e c t d e v i a t i o n s from S c h m i d ' s law o r anomalous g l i d e , t o be d i s c u s s e d i n t h e next s e c t i o n s , mean t h a t t h e s e l e c t i o n o f g l i d e s y s t e m s a t t h e o n s e t o f p l a s t i c d e f o r m a t i o n i s not governed by the r e s o l v e d s h e a r s t r e s s e s a l o n e .
2.3 DEVIATIONS F R O M SCHMID'S LAW IN B.C.C. M E T A L S
R e c e n t l y many papers were p u b l i s h e d c o n c e r n i n g d e v i a t i o n s from S c h m i d ' s law in b . c . c . m e t a l s . These d e v i a t i o n s a r e u s u a l l y r e f e r r e d t o as anomalous g l i d e . The s i t u a t i o n i s f a i r l y c l e a r a t t h e moment and c a n be summarized as f o l l o w s . D e v i a t i o n s from S c h m i d ' s law a r e o b s e r v e d i n :
a) The group Va metals Nb, V and T a . Anomalous g l i d e o n l y o c c u r s here a t low t e m p e r a t u r e s and i n h i g h - p u r i t y s i n g l e c r y s t a l s ( B r e s s e r s and C r e t e n 1977) not o r i e n t e d near t h e A-I t i e l i n e i n t h e s t a n d a r d s t e r e o g r a p h i c t r i a n g l e ( C r e t e n e t a l . 1 9 7 7 ) . W i t h o u t e x c e p t i o n t h e anomalous systems a r e IIA and M B , t h e p r i m a r y s y s t e m b e i n g IVB.
As r e g a r d s (HVEM)
in situ
s t r a i n i n g , o n l y L o u c h e t and K u b i n (1975) d e m o n s t r a t e d anomalous g l i d e f o r group Va m e t a l s by such an e x p e r i m e n t , namely on Nb (see f i gure 2 . 2 ) .b) The group VI metals W and Mo. E s p e c i a l l y Mo has been t h e s u b j e c t o f
i n v e s t i g a t i o n s w i t h both b u l k specimens ( V e s e l y 1968 b) and t h i n f o i l s f o r TEM ( V e s e l y 1968 a) and HVEM (Matsui e t a l . 1 9 7 4 ; S a k a , M a t s u i e t a l . 1 9 7 6 ; S a k a , Noda and Imura 1976)
in situ
o b s e r v a t i o n s (see a l s o f i g u r e 2 . 2 ) . I I A - I I B anomalous g l i d e i s a g a i n o f t e n o b s e r v e d ; b u t t h e o c c u r r e n c e o f o t h e r s y s t e m s , d e p e n d i n g on t h e o r i e n t a t i o n o f t h e s u r f a c e , has a l s o been r e p o r t e d . Anomalous g l i d e i s o b s e r v e d i n Mo a t room t e m p e r a t u r e . It i s s u p p r e s s e d at h i g h e r s t r a i n s ( V e s e l y 1968 b, T a y l o r 1 9 7 4 ) , b u t not by a l l o y i n g ( J e f f c o a t e t a l . 1 9 7 6 ) . These f a c t s a r e i n d i r e c t c o n t r a s t t o t h e b e h a v i o u r o f group Va m e t a l s .Two n o n - c o n t r a d i c t o r y e x p l a n a t i o n s have been o f f e r e d by a group o f J a p a n e s e i n v e s t i g a t o r s , namely:
a) The s o - c a l l e d c o - p l a n a r d o u b l e s l i p ( C . D . S . ) mechanism f o r both group Va and group VI m e t a l s (Matsui and Kimura 1974 b; M a t s u i and Kimura 1 9 7 5 ; S a k a , M a t s u i e t a l . 1 9 7 6 ; S a k a , Noda and Imura 1 9 7 6 ) .
b) The s o - c a l l e d s u r f a c e e f f e c t ( S . E . ) mechanism f o r group VI m e t a l s (Matsui and Kimura 1973, M a t s u i and Kimura 1974 a , M a t s u i e t a l . 1 9 7 4 ) .
In b . c . c . m e t a l s edge d i s l o c a t i o n s have much h i g h e r m o b i l i t y than screws and move w e l l below t h e y i e l d s t r e s s ( e . g . Low and Guard 1959, Saka and Imura
1972, L o u c h e t e t a l . 1 9 7 9 ) . T h i s p l a y s an i m p o r t a n t r o l e i n both t h e C . D . S . and S.E. mechanisms, t o be d i s c u s s e d b e l o w .
The S.E. mechanism i s c l o s e l y r e l a t e d t o t h e t h e o r y o f Lohne (1974) f o r
-21-f.a.c. metals,
though t h i s r e l a t i o n s h i p was not noted by Lohne. In both t h e o r i e s a s c r e w d i s l o c a t i o n e m e r g i n g a t a f r e e s u r f a c e i s c o n s i d e r e d . When the B u r g e r s v e c t o r i s not a t r i g h t a n g l e s to t h e s u r f a c e the end segment w i l l be d e f l e c t e d by t h e image f o r c e s t o a p o s i t i o n more p e r p e n d i c u l a r t o the s u r f a c e . In t h i s way t h e l e n g t h o f the end segment i s reduced but the l i n e e n e r g y per u n i t l e n g t h i s i n c r e a s e d owing t o t h e change o f c h a r a c t e r o f the end segment. In the e q u i l i b r i u m p o s i t i o n the t o t a l e n e r g y ( l i n e l e n g t h x l i n e e n e r g y / u n i t l e n g t h ) i s m i n i m a l .The o r i g i n a l screw d i s l o c a t i o n has two ( f . c . c . ) o r t h r e e o r more ( b . c . c . ) p o s s i b l e g l i d e p l a n e s . The end segment o f mixed c h a r a c t e r w i l l choose the
e n e r g e t i c a l l y most f a v o u r a b l e p l a n e . In g e n e r a l t h i s i s the g l i d e p l a n e t h a t i s as n e a r l y p e r p e n d i c u l a r t o the s u r f a c e as p o s s i b l e . T h i s l a t t e r g l i d e p l a n e i s not n e c e s s a r i l y the g l i d e p l a n e c o r r e s p o n d i n g to the l a r g e s t Schmid f a c t o r .
~k
M a t s u i and Kimura (1973) and Lohne (1974) u t i l i z e d i f f e r e n t s i m p l i f i e d models and d i f f e r e n t methods o f c a l c u l a t i o n , but i t i s c o n c l u d e d i n both p a p e r s t h a t a d e f l e c t i o n o f the end segment w i l l o c c u r . T h i s e f f e c t was a c t u a l l y
o b s e r v e d i n f . c . c . m e t a l s (Lohne 1973) and a c c o r d i n g to M a t s u i e t a l . (1974) in b . c . c . m e t a l s t o o ( f i g u r e 6 in t h e i r p a p e r ) . M a t s u i and Kimura (1973) c o n s i d e r 500 - 1000 b, i . e . i n t h e i r c a s e 0.09 - 0 . 1 8 urn, as a r e a s o n a b l e e s t i m a t e f o r
t h e l e n g t h o f t h e d e f l e c t e d segment. On the o t h e r hand Lohne (1974) found 100 ym by X - r a y t o p o g r a p h y . If t h i s l a t t e r f i g u r e a l s o h o l d s f o r b . c . c . m e t a l s the d e f l e c t i o n near the s u r f a c e cannot be seen by HVEM/TEM, s i n c e the specimen t h i c k n e s s i s such t h a t d i s l o c a t i o n s i n the t h i n a r e a s w o u l d be d e f l e c t e d a l o n g t h e i r w h o l e l e n g t h .
In b o t h t h e o r i e s the i n f l u e n c e o f an o x i d e l a y e r i s i g n o r e d . However, an o x i d e l a y e r w i t h a h i g h e r s h e a r modulus than t h a t o f t h e p a r e n t metal w i l l r e p e l
d i s l o c a t i o n s . As l o n g as t h i n o x i d e l a y e r s a r e c o n c e r n e d t h i s e f f e c t can be n e g l e c t e d , but i t c a n n o t be n e g l e c t e d f o r t h i c k l a y e r s (Head 1 9 5 3 ) . In t h i s way the absence o f the S.E. mechanism f o r group Va m e t a l s was e x p l a i n e d by S a k a , Noda, and Imura (1976) and M a t s u i and Kimura ( 1 9 7 3 ) . Owing to the p r e p a r a t i o n method t h e s e m e t a l s s h o u l d p o s s e s s a t h i c k o x i d e l a y e r .
M a t s u i and Kimura (1973) c o n s i d e r the mixed end segments o f screw d i s l o c a t i o n s i n b . c . c . c r y s t a l s as k i n k s , i n t r o d u c e d by the s u r f a c e but a b l e to p r o p a g a t e
a l o n g the s c r e w . In t h i s way t h e s c r e w under c o n s i d e r a t i o n w i l l s t a r t to move a t a s t r e s s c o n s i d e r a b l y lower than the c r i t i c a l s h e a r s t r e s s to move a pure s c r e w . The m o t i o n t a k e s p l a c e i n the g l i d e p l a n e in w h i c h the end segments a r e d e f l e c t e d a n d , as m e n t i o n e d b e f o r e , t h i s does not n e c e s s a r i l y c o r r e s p o n d t o the g l i d e
s y s t e m w i t h t h e h i g h e s t s h e a r s t r e s s . I n s t e a d , a c c o r d i n g to M a t s u i e t a l . ( 1 9 7 4 ) , the s e l e c t i o n r u l e s f o r the g l i d e systems a r e :
M a t s u i and Kimura (1973) announced t h a t a more g e n e r a l c a s e w o u l d be p r e s e n t e d l a t e r . No such paper has come t o the a u t h o r ' s a t t e n t i o n .
a) The r e s o l v e d s h e a r s t r e s s s h o u l d be l a r g e enough t o move mixed d i s l o c a t i o n s . b) The a n g l e between the g l i d e p l a n e and the ( l o c a l ) * s u r f a c e s h o u l d be near 90° c) The a n g l e between the B u r g e r s v e c t o r and t h e ( l o c a l ) * g l i d e l i n e d i r e c t i o n
s h o u l d be l e s s than about 6 5 ° .
In a l a t e r paper M a t s u i and Kimura (1975) s t a t e t h a t the a n g l e between the B u r g e r s v e c t o r and the t e n s i l e a x i s s h o u l d be s m a l l . However, i n t h i s way c o n d i t i o n s b) and c) can be f u l f i l l e d but not c o n d i t i o n a ) .
A p a r t from t h e
propagation
mechanism d e s c r i b e d a b o v e , M a t s u i and Kimura (1973) a l s o p r o p o s e d amultiplication
mechanism, based on t h e d e f l e c t i o n near the s u r f a c e . No e x p e r i m e n t a l p r o o f was g i v e n .V e s e l y (1968 a) i s r e s p o n s i b l e f o r a n o t h e r
propagation
m o d e l . It r e s e m b l e s the S.E. mechanism and i s s i m i l a r l y s u p p o r t e d by the o b s e r v a t i o n o f g l i d e systems d u r i n gin situ
s t r a i n i n g TEM e x p e r i m e n t s . V e s e l y ' s s t a r t i n g - p o i n t s a r e :a) For e n e r g y reasons the d i s l o c a t i o n s s h o u l d a r r a n g e t h e m s e l v e s p e r p e n d i c u l a r to the g l i d e l i n e s . Thus w i t h r e s p e c t t o the d i s l o c a t i o n l i n e e n e r g y V e s e l y o n l y t a k e s the d i s l o c a t i o n l e n g t h i n t o a c c o u n t , not the c h a r a c t e r , and no d e f l e c t i o n near the s u r f a c e s i s i n v o l v e d .
b) Edge d i s l o c a t i o n s a r e p r e f e r r e d because o f the l o w e r m o b i l i t y o f screw d i s -l o c a t i o n s .
Combining t h e s e two s t a t e m e n t s i t i s found t h a t the B u r g e r s v e c t o r ( s ) o f t h e a c t i v a t e d d i s l o c a t i o n s w i l l be a l m o s t p a r a l l e l to t h e s u r f a c e . Now the s e l e c t i o n
r u l e s o f V e s e l y a r e as f o l l o w s :
a) For each B u r g e r s v e c t o r t h e p l a n e w h i c h i s most n e a r l y p e r p e n d i c u l a r t o the f o i l p l a n e i s s e l e c t e d ; in t h i s way f o u r g l i d e systems a r e o b t a i n e d .
b) The " a c t i v i t y " o f a p a r t i c u l a r s e l e c t e d s y s t e m i s p r o p o r t i o n a l to
V = m s i n 3 (3) where (3 i s the a n g l e between the f o i l normal and the B u r g e r s v e c t o r .
C o n s e q u e n t l y the g l i d e s y s t e m t h a t i s p r e f e r e n t i a l l y a c t i v a t e d has a l a r g e Schmid f a c t o r and a B u r g e r s v e c t o r t h a t i s a p p r o x i m a t e l y p a r a l l e l t o the f o i l p l a n e .
* The term " l o c a l " c o v e r s t h e p o s s i b i l i t y o f specimens b e i n g c y l i n d r i c a l i n s t e a d o f f l a t .
-23-Of c o u r s e e q . (3) s h o u l d not be r e g a r d e d as an e x a c t f o r m u l a . There seems to be no r e a s o n why the 6-dependence o f V s h o u l d be e x p r e s s e d as s i n g and n o t , f o r
2
i n s t a n c e , as s i n g. N e v e r t h e l e s s , the c r i t e r i o n o f V e s e l y has the v i r t u e o f b e i n g unambiguous, u n l i k e the s e l e c t i o n r u l e s o f M a t s u i e t a l . A p a r t from t h i s t h e r e i s l i t t l e d i f f e r e n c e between t h e two s e t s o f s e l e c t i o n r u l e s :
In b o t h c a s e s a l a r g e Schmid f a c t o r , a g l i d e p l a n e a l m o s t p e r p e n d i c u l a r t o the s u r f a c e and a B u r g e r s v e c t o r a l m o s t p a r a l l e l to the s u r f a c e a r e s t r o n g l y p r e f e r r e d . The J a p a n e s e a u t h o r s q u o t e V e s e l y ' s work but t h e y do not g i v e a r e a s o n why t h e i r c r i t e r i o n s h o u l d r e p l a c e V e s e l y ' s c r i t e r i o n .
M a t s u i e t a l . (1974) made an i n t e r e s t i n g p o i n t w i t h r e g a r d to p o s s i b l e d i f f e r e n c e s between t h e b e h a v i o u r o f f o i l s and c y l i n d r i c a l metal c r y s t a l s . In a t h i n f o i l the a n g u l a r r e l a t i o n s between a d i s l o c a t i o n and the s u r f a c e a r e the same a t both e m e r g i n g p o i n t s o f a d i s l o c a t i o n . G e n e r a l l y t h i s i s not t h e c a s e i n a c y l i n d r i c a l c r y s t a l . In o t h e r words the c o n d i t i o n s o f the c r i t e r i a o f V e s e l y and M a t s u i e t a l . a r e not e q u a l l y f u l f i l l e d a t both e m e r g i n g p o i n t s o f a s t r a i g h t d i s l o c a t i o n i n a c y l i n d r i c a l c r y s t a l . An i n t e r m e d i a t e c a s e are c r y s t a l s w i t h a s q u a r e c r o s s s e c t i o n . M a t s u i e t a l . made t h i s remark w i t h s p e c i a l r e g a r d to t h e i r m u l t i p l i c a t i o n mechanism. On the o t h e r hand V e s e l y , who a c t u a l l y p e r f o r m e d b u l k e x p e r i m e n t s (1968 b) b e s i d e s
in situ
s t r a i n i n g TEM e x p e r i m e n t s , i s o fo p i n i o n t h a t the s o u r c e s on n o n - p r i m a r y s l i p a r e p r e s e n t i n a t h i n s u r f a c e l a y e r . The term C.D.S. mechanism was i n t r o d u c e d by M a t s u i and Kimura ( 1 9 7 5 ) . In the same i s s u e o f the same j o u r n a l a s i m i l a r t h e o r y was d e v e l o p e d by L o u c h e t and K u b i n ( 1 9 7 5 ) .
The main d i f f e r e n c e between t h e s e t h e o r i e s c o n c e r n s t h e o n s e t o f anomalous g l i d e . In the C . D . S . mechanism o f M a t s u i and Kimura the n e c e s s a r y A and B d i s -l o c a t i o n s a r e t h o u g h t t o be g e n e r a t e d by the S.E. mechanism, because o f the s m a l l a n g l e between the A and B B u r g e r s v e c t o r s and the t e n s i l e a x i s ( f i g u r e 2.1) The s t a r t i n g - p o i n t o f Louchet and K u b i n i s t h a t IVB and I M A a r e the g l i d e
systems w i t h the l a r g e s t Schmid f a c t o r s ( t a b l e 2 . 3 ) . T h e r e f o r e , i n the p r e p l a s t i c r e g i o n IVB and M I A edge d i s l o c a t i o n s p r o p a g a t e t h r o u g h the c r y s t a l , l e a v i n g B and A screws b e h i n d . When the r e s o l v e d s h e a r s t r e s s on the p r i m a r y s y s t e m reaches the m a c r o p l a s t i c l i m i t the B screws s t a r t t o move i n t h e i r normal IV p l a n e . In d o i n g so t h e y meet t h e s t i l l s e s s i l e A d i s l o c a t i o n s t h a t i n t e r s e c t the IV p l a n e .
In both p a p e r s two t y p e s o f i n t e r a c t i o n between t h e B and A d i s l o c a t i o n s were c o n s i d e r e d . In t h e c a s e o f a t t r a c t i v e i n t e r a c t i o n , i . e . d i s l o c a t i o n s w i t h
l i k e s i g n , an a [ 1 0 0 ] j u n c t i o n d i s l o c a t i o n i s f o r m e d . The t h r e e B u r g e r s v e c t o r s i n v o l v e d have I I as a common g l i d e p l a n e ( f i g u r e 2 . 1 ) . T h e r e f o r e a p l a n a r and i n p r i n c i p l e g l i s s i l e n e t w o r k c o n s i s t i n g o f A , B and a [ 1 0 0 ] screw d i s l o c a t i o n s i s b u i l t up in the II p l a n e . Such networks were a c t u a l l y o b s e r v e d d u r i n g HVEM in
situ
s t r a i n i n g e x p e r i m e n t s . L o u c h e t and K u b i n (1975) o b s e r v e d s e s s i l e networksg l i s s i l e n e t w o r k s in Mo.
A c c o r d i n g to L o u c h e t and Kubin t h e s e s s i l e I M A screw d i s l o c a t i o n s a c t as s t r o n g f o r e s t d i s l o c a t i o n s f o r the p r i m a r y IVB s c r e w d i s l o c a t i o n s i n t h e c a s e o f r e p u l s i v e i n t e r a c t i o n . The o n l y way f o r the p r i m a r y d i s l o c a t i o n s t o a v o i d t h e s e f o r e s t d i s l o c a t i o n s i s to c r o s s - s l i p to t h e II p l a n e and t o move p a r a l l e l t o them. C o n s e q u e n t l y MB i s e x p e c t e d i n s t e a d o f IVB.
The e x p l a n a t i o n o f M a t s u i and Kimura (1975) i s t h a t the r e p u l s i n g d i s -l o c a t i o n s i n t r o d u c e k i n k s i n each o t h e r . C a -l c u -l a t i o n shows t h a t t h e s e k i n k s a r e s i t u a t e d i n II; hence b o t h d i s l o c a t i o n s can e a s i l y move i n t h a t p l a n e . Thus the mixed k i n k s run a l o n g t h e screws as was t h e c a s e f o r the S . E . mechanism.
C o n s e q u e n t l y b o t h M B and M A a r e t o be e x p e c t e d .
R e c e n t l y , G a r r a t t - R e e d and T a y l o r (1980) p u b l i s h e d the r e s u l t s o f an
i n v e s t i g a t i o n on b u l k Nb s i n g l e c r y s t a l s deformed i n t e n s i o n a t low t e m p e r a t u r e s . For c r y s t a l s w i t h d i f f e r e n t l y o r i e n t e d t e n s i l e axes g l i d e l i n e bands c o r r e s p o n d i n g to d i f f e r e n t g l i d e p l a n e s were found by o p t i c a l m i c r o s c o p y . The t y p e o f s l i p band was found to be p r e d i c t e d by the f a c t o r
m' = cose cosA^ cosA2 (4) where the s u b s c r i p t s 1 and 2 r e f e r to the two B u r g e r s v e c t o r s in a p a r t i c u l a r
g l i d e p l a n e , the o t h e r symbols were d e f i n e d i m m e d i a t e l y f o l l o w i n g e q . ( 2 ) . From e q . (4) i t f o l l o w s t h a t b o t h g l i d e systems o f a p a i r o f a c t i v a t e d c o - p l a n a r systems s h o u l d have a c o n s i d e r a b l e Schmid f a c t o r . For c r y s t a l s w i t h t h e i r t e n s i l e axes o r i e n t e d i n t h e c e n t r e o f the s t a n d a r d t r i a n g l e i t was found i n p a r t i c u l a r t h a t t h e r e were more II and l e s s V s l i p l i n e b a n d s . TEM i n v e s t i g a t i o n o f t h e s e c r y s t a l s r e v e a l e d d i s l o c a t i o n and d e b r i s bands p a r a l l e l to the II, IV and V p l a n e s , m o s t l y bounded by t w i s t w a l l s . The predominance o f the II bands o b s e r v e d by o p t i c a l m i c r o s c o p y was not c o n f i r m e d by the TEM work and t h i s remains u n -e x p l a i n -e d by G a r r a t t - R -e -e d and T a y l o r . Th-e t w i s t w a l l s p a r a l l -e l to t h -e II p l a n -e were composed o f A and B screw d i s l o c a t i o n s . T h i s c o r r e s p o n d s to the o b s e r v a t i o n s o f L o u c h e t and K u b i n ( 1 9 7 5 ) , S a k a , M a t s u i e t a l . (1976) and S a k a , Noda and Imura
( 1 9 7 6 ) , c i t e d a b o v e , e x c e p t t h a t G a r r a t t - R e e d and T a y l o r d i d not o b s e r v e j u n c t i o n d i s l o c a t i o n s . In f i g u r e 2.2 t h e r e s u l t s o f the
in situ
s t r a i n i n g e x p e r i m e n t s on b . c . c . m e t a l s a r e g i v e n i n r e l a t i o n s h i p to the o r i e n t a t i o n o f the f o i l n o r m a l . V e s e l y ' s f o i l normal o r i e n t a t i o n " b " and M a t s u i ' s o r i e n t a t i o n a r e c l o s e t o g e t h e r . If i t i s t a k e n i n t o a c c o u n t t h a t V e s e l y ' s r e s u l t s a r e g i v e n i n o r d e r o f i m p o r t a n c e and t h a t the p l a n e s (123) and (2T3) a r e n e a r l y p a r a l l e l , the r e s u l t s f o r t h e s e o r i e n t a t i o n s a r e r a t h e r c o n s i s t e n t . * The C . D . S . mechanism i s not o b s e r v e d h e r e . * M a t s u i and Kimura (1974 a) s t a t e t h a t M a t s u i e t a l . (1974) o b s e r v e d {112} and{123} s y s t e m s , but t h i s i s i n c o r r e c t .
-25-100
100
Fig. 2.2 Anomalous glide during 'in situ'straining experiments on b.c.c. metals. + Vesely 1968, orientation a and b Mo
V Matsui et al. 1974 Mo
O Kubin and Lounchet 1975 Nb i Saka, Matsui et al. 1976 i
I Saka, Noda and Imura 1976 >
The tensile axes are plotted in the standard triangle. The observed glide systems are plotted near the foil normals.
\
T h i s i s u n d o u b t l y because from t h e n e c e s s a r y B u r g e r s v e c t o r s A and B o n l y A i s a c t i v a t e d ; t h i s may be u n d e r s t o o d by V e s e l y ' s c r i t e r i o n , s i n c e B i s f a r from b e i n g p a r a l l e l t o t h e s u r f a c e .
V e s e l y ' s f o i l normal o r i e n t a t i o n " a " and t h e f o i l normal o r i e n t a t i o n o f Saka e t a l . a r e c l o s e t o g e t h e r t o o . F o r t h e s e o r i e n t a t i o n s B i s ( a l m o s t ) p a r a l l e l to t h e s u r f a c e . T h e r e f o r e t h e p r i m a r y s y s t e m IVB i s f a v o u r e d a c c o r d i n g t o V e s e l y ' s c r i t e r i o n . Less f a v o u r a b l e a r e ( 3 2 1 ) A , o r o t h e r g l i d e systems w i t h t h e i r g l i d e p l a n e i n t h e n e i g h b o u r h o o d o f ( 3 2 1 ) , l i k e V I , a n d IC. The r e s u l t s o f V e s e l y and Saka e t a l . a r e r a t h e r s i m i l a r t h e n . An e x c e p t i o n i s t h a t V e s e l y d i d n o t o b s e r v e t h e C . D . S . systems M B a n d M A . T h i s i s r e m a r k a b l e because t h e n e c e s s a r y d i s l o c a t i o n s w i t h B u r g e r s v e c t o r s A and B were a v a i l a b l e . In both c a s e s Mo was s t u d i e d , by TEM by V e s e l y and by HVEM by Saka e t a l . P o s s i b l y t h e d i m e n s i o n s o f t h e network i n t h e anomalous p l a n e , w h i c h was more n e a r l y p a r a l l e l to t h e f o i l i n t h e specimens o f Saka e t a l . , d i t n o t f i t i n t o t h e l i m i t e d
t h i c k n e s s o f t h e t h i n a r e a s i n V e s e l y ' s s p e c i m e n s .
F u r t h e r m o r e , M a t s u i and Kimura (197^ a) e x p l a i n e d why i n g e n e r a l anomalous c o - p l a n a r d o u b l e s l i p m i g h t n o t be o b s e r v e d i n t h i n f o i l s . G r i p e f f e c t s a r e n o r m a l l y m i n i m i z e d by a c t i v a t i o n o f two c o - p l a n a r s y s t e m s , b u t i n t h i n f o i l s the g r i p e f f e c t s may a l s o be accommodated e l a s t i c a l l y . The r e a s o n i n g i s i n t e r e s t i n g a n d w i l l be t r e a t e d i n s e c t i o n 7 . 2 . 5 . Now V e s e l y ' s specimens were somewhat more s l e n d e r than t h o s e o f Saka e t a l . ( s e e t a b l e 2 . 1 ) . Hence g r i p e f f e c t s were p o s s i b l y l e s s i m p o r t a n t and c o - p l a n a r d o u b l e s l i p n o t r e q u i r e d .
The o r i e n t a t i o n o f t h e specimens t e s t e d by L o u c h e t a n d K u b i n , w i t h t h e anomalous p l a n e (and hence both A and B) p a r a l l e l t o t h e f o i l , seems t o be v e r y f a v o u r a b l e f o r t h e C . D . S . mechanism d e s p i t e t h e low r e s o l v e d s h e a r s t r e s s e s f o r the anomalous s y s t e m s . D i s l o c a t i o n s w i t h t h e p r e v i o u s l y m e n t i o n e d B u r g e r s v e c t o r s c o u l d a l s o be a c t i v a t e d e i t h e r by t h e S . E . mechanism o r a c c o r d i n g t o V e s e l y ' s c r i t e r i o n .
2.4 DEVIATIONS FROM SCHMID'S LAW IN F.C.C. M E T A L S
B e f o r e d i s c u s s i n g papers c o n c e r n i n g d e v i a t i o n s from S c h m i d ' s law i n f . c . c . m e t a l s , some d i f f e r e n c e s between b . c . c . and f . c . c . m e t a l s w i l l be c o n s i d e r e d . a) The geometry o f f . c . c . a n d b . c . c . metal c r y s t a l s i s d i f f e r e n t . In b . c . c .
m e t a l s each B u r g e r s v e c t o r has t h r e e g l i d e p l a n e s , and even more when ( 1 1 2 ) and {113} p l a n e s a r e i n v o l v e d . On t h e o t h e r hand t h e r e a r e o n l y two g l i d e p l a n e s a v a i l a b l e f o r each B u r g e r s v e c t o r i n a f . c . c . c r y s t a l . As a consequence c e r t a i n c o n d i t i o n s m e n t i o n e d i n t h e p r e c e d i n g s e c t i o n , e . g . t h e n e a r l y
p e r p e n d i c u l a r p o s i t i o n o f a g l i d e p l a n e w i t h r e s p e c t t o t h e s u r f a c e , a r e e a s i e r f u l f i l l e d i n b . c . c . c r y s t a l s .
b) There a r e some i n d i c a t i o n s t h a t i n f . c . c . m e t a l s t h e v e l o c i t y o f edge d i s -l o c a t i o n s i s g r e a t e r than t h a t o f screw d i s -l o c a t i o n s ( B e c k e r and Haasen 1 9 5 3 , Haasen and Siems 1 9 5 7 , Young and S h e r r i l l 1 9 7 6 ) , as i s t h e c a s e f o r b . c . c .
