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The formation of intermediate phase in martensite transformation of FeMnC and FeMnCrC steel
Scripta METALLURGICA
Vol. I0, pp. 1011-1014, 1976 Printed in the United States
Pergamon Press, Inc.
THE FORMATION OF INTERMEDIATE PHASE IN MARTENSITE TRANSFORMATION OF Fe-Mn-C AND Fe-Mn-Cr-C STEEL
R y u i c h i r o Oshima, Hirozumi Azuma and F r a n c i s c o E i i c h i F u j i t a Department o f M a t e r i a l P h y s i c s , F a c u l t y o f E n g i n e e r i n g S c i e n c e , Osaka U n i v e r s i t y , Toyonaka, Osaka 560, Japan
(Received August i0, 1976)
INTRODUCTION One o f t h e p r e s e n t a u t h o r s (FEF) and o t h e r s (1-4) i n v e s t i g a t e d t h e Fe 57 M6ssbauer s p e c t r a o f t h e low t e m p e r a t u r e m a r t e n s i t e p h a s e o f F e - l - v l . 8 w t % C , Fe-6wt%Ni-l.8wt%C and Fe-Swt%Mn-l.6wt%C s t e e l , and c o n c l u d e d t h a t (1) carbon atoms occupy t h e t e t r a - and o c t a h e d r a l i n t e r s t i c e s w i t h equal p o p u l a t i o n s i n t h e f r e s h l y formed m a r t e n s i t e a t low t e m p e r a t u r e s and (2) t h e t e t r a h e d r a l interstitial carbon atoms jump t o t h e o c t a h e d r a l s i t e s d u r i n g t h e t e m p e r i n g t o room t e m p e r a t u r e . It is clear that the tetrahedral interstitial carbon atoms o f m a r t e u s i t e can n o t be i n t r o d u c e d by t h e d i r e c t s h e a r mechanism o f m a r t e n s i t e t r a n s f o r m a t i o n p r o p o s e d by Kurdjumov and Sachs (5) and Nishiyama ( 6 ) . F u j i t a has r e c e n t l y p r o p o s e d a new t h e o r y o f m a r t e n s i t e t r a n s f o r m a t i o n o f f e r r o u s a l l o y s ( 7 , 8 ) , a c c o r d i n R t o which t h e a u s t e n i t e l a t t i c e t r a n s f o r m s f i r s t t o an i n t e r m e d i a t e s i x l a y e r s t r u c t u r e by s h u f f l i n R o f f c c l a t t i c e on (111) p l a n e s alonR [112] d i r e c t i o n and t h e n t o t h e u l t i m a t e bcc m a r t e n s i t e by h a l f d i s l o c a t i o n t y p e s h e a r i n g a l o n g e v e r y two p l a n e s o f t h e same k i n d and in t h e same d i r e c t i o n and t h e t e t r a - and o c t a h e d r a l s i t e occupancy o f carbon i s accounted for. In a d d i t i o n , Oshima and Wayman (9) found e x t r a d i f f r a c t i o n s p o t s i n t r a n s m i s s i o n 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 o b t a i n e d from a s - f o r m e d m a r t e n s i t e o f Fe-Mn-C and Fe-Mn-Cr-C a l l o y s a t low t e m p e r a t u r e s , and s u g g e s t e d a r e g u l a r p e r i o d i c s t r u c t u r e w i t h a p e r i o d i c i t y o f s i x {011} i n t e r p l a n a r d i s t a n c e s i n t h e f r e s h l y formed m a r t e n s i t e . In t h e p r e s e n t work, t h e F u j i t a ' s s i x l a y e r s t r u c t u r e i s t h o u g h t t o be c o n n e c f e d w i t h t h e e x t r a d i f f r a c t i o n s p o t s o b s e r v e d i n f r e s h l y formed m a r t e n s i t e o f Fe-Mn-C and Fe-Mn-Cr-C s t e e l , and t h e s t r u c t u r e f a c t o r s o f t h e model a r e c a l c u l a t e d and compared w i t h t h e o b s e r v e d i n t e n s i t i e s and p o s i t i o n s o f t h e e x t r a s p o t s . The o b s e r v e d d i f f r a c t i o n p a t t e r n s a r e t o l e r a b l y e x p l a i n e d by t h e s i x l a y e r model. Some d i s a g r e e m e n t s between t h e c a l c u l a t e d and e x p e r i m e n t a l r e s u l t s a r e i n t e r p r e t e d by m o d i f y i n g t h e s t a c k i n g o f t h e s i x l a y e r s t r u c t u r e t o r e l e a s e t h e t i g h t n e s s o f t h e atomic a r r a n g e m e n t s i n t h e s t r u c t u r e and m u l t i p l e r e f l e c t i o n e f f e c t . In c o n n e c t i o n w i t h t h e f o r m a t i o n o f new s i x l a y e r s t r u c t u r e , c u r r e n t s u b j e c t s c o n c e r n i n g t h e p o s i t i o n o f c a r b o n atoms i n f r e s h l y formed m a r t e n s i t e a r e a l s o d i s c u s s e d . EXPERIMENTAL Fe-5.5wt%Mn=lwt%C, Fe=6wt%Mn-lwt%C and Fe-3wt%Mn-3wt%Cr-lwt%C a l l o y s a r e u s e d f o r t h i s s t u d y Disc s p e c i m e n s punched from about 0.4mm t h i c k s h e e t s o f t h e s e m a t e r i a l s a r e s e a l e d i n e v a c u a t e d q u a r t z c a p s u l e s , and a u s t e n i t i z e d a t 1200°C f o r 1 h r p r i o r t o w a t e r q u e n c h i n g . All specimens a r e c o m p l e t e l y a u s t e n i t i c a f t e r q u e n c h i n g , and t h e y a r e c h e m i c a l l y and e l e c t r o l y t i c a l l y t h i n n e d . The s p e c i m e n s a r e t r a n s f o r m e d t o m a r t e n s i t e by c o o l i n g on a c o l d s t a g e o f H i t a c h i HU-11A e l e c t r o n microscope. RESULTS AND DISCUSSION In t h e f r e s h l y formed m a r t e n s i t e o f a l l o f t h e above m e n t i o n e d a l l o y s , e x t r a s p o t s a s s o c i a t e d w i t h t h e normal b c t ( b c c ) m a r t e n s i t e a r e found i n t r a n s m i s s i o n 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 a k e n a t -140°C. The e x t r a s p o t s a r e o b s e r v e d i n v a r i o u s r e c i p r o c a l l a t t i c e p l a n e o f bcc m a r t e n s i t e as shown i n F i g . 1 . They a r e t h e s a t e l l i t e s i n a < l l 0 > d i r e c t i o n o f normal bcc m a r t e n s i t e n e a r each f u n d a m e n t a l s p o t , and d i s t r i b u t e d a t 1/6 i n t e r v a l s a l o n g t h e < l l 0 > d i r e c t i o n . In some c a s e s t h e i n t e r v a l s and d i r e c t i o n s o f t h e e x t r a s p o t s s l i g h t l y d e v i a t e from 1/6 and < l l 0 > respectively. The second o r d e r s a t e l l i t e r e f l e c t i o n s a r e a l s o o b s e r v e d w i t h lower i n t e n s i t i e s t h a n t h e f i r s t o n e s . A l l e x t r a s p o t s d i s a p p e a r around =80°C when t h e specimen i s h e a t e d t o room ]011
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temperature. They do n o t r e a p p e a r when t h e specimen i s c o o l e d a g a i n . T h i s means t h a t t h e e x t r a s p o t s a r e corresponding to the formation of an i r r e v e r s i b l e i n t e r m e d i a t e s t r u c ture. S i n c e t h e F u j i t a ' s new t h e o r y p r e d i c t s an i n t e r m e d i a t e s i x l a y e r s t r u c t u r e t o form on t h e way from a u s t e n i t e t o m a r t e n s i t e , t h e observed extra diffraction spots in a s - f o r m e d m a r t e n s i t e a t low t e m p e r a t u r e s a r e t h o u g h t t o a r i s e from the six layer structure. Hence, the structure factors of the six l a y e r model a r e c a l c u l a t e d and compared with the observed intensities and p o s i t i o n s o f t h e e x t r a s p o t s . F i g . 2 shows a u n i t c e l l o f t h e s i x l a y e r model. In t h i s f i g u r e c r y s t a l l o g r a p h i c r e l a t i o n between t h e FIG. 1 s i x l a y e r s t r u c t u r e l a t t i c e and t h e bcc l a t t i c e i s a l s o i n d i c a t e d . Diffraction patterns obtained The u n i t c e l l h a s s i x atoms a t from f r e s h l y formed m a r t e n s i t e (0,0,0), ( 5 / 6 , 5 / 6 , 1 / 6 ) , (2/6,2/6, a t low t e m p e r a t u r e s . 2/6), (I/6,1/6,3/6), (4/6,4/6,4/6) and (3/6,3/6,5/6). With this unit cell, the structure factors can be written as: SHK L = Z f.exp{2wi(l.H + m.K + n.L)} f {1 + exp~l(SH+SK+L) + exl~3i(2H+2K+2L) + e x ~
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FIG. 2 Unit c e l l o f six l a y e r structure and lattice correspondence for the six layer structure to bcc. (H+K+3L)
+ exp~(4H+4K+4L) + exF~xit3H+3K+SL)~,''~ where f is the atomic scattering factor of iron or manganese, and H, K and L are the r e f l e c t i n g indices. Table I l i s t s the results of various (HKL) intensity calculations. Since the extra diffraction spots a r e always found with bcc martensite spots, the Miller indices (hkl) referred to bcc martensite are also shown in this table. The transformation of the Miller indices from TABLE 1 Calculated Intensities for Six Layer Structure I
HKL
I
h
k
1
5HKL/2f2
HKL
h
k
1
SHKL/2f2
HKL
h
k
1
SHKL/2f2
4.5 0 13.5
043 044 045 046 051 052 053 054 055 056 061 062 063 064 065 066
15/6 16/6 17/6 3 16/6 17/6 3 1916
4 4 4 ~ § 5 ~ 5
916 8/6 7/6 1 14/6 13/6 2 1116
20/6
g lO/6
21/6 1916 20•6 21/6 2216 2316
§ 9/6 61716 6 16/6 61516 6 14/6 6 13/6
0 0 13.5 0 4.5 0 0 13.5 0 0 0 0 0 0 0
6
18.0
I
01 0 0201 030 O40 050 060 001 OO2 003 0O4 0O5 006
0 1 0 1 0 1
3/6 1 916 2 15/6
3/6
1 3 916 4 2 S 15/6
3
&
3
1/6 2/6
0 0
i/6 3/6
3/6
o
_~/6
4/6 5/6 1 4/6 5/6 1 7/6
0 0 0 1 i i i
416
g/6
0 0 0 0 0 18.0
0 0 0 0 0 18.0
2/6 1/6 0 1/6
0 13.5 0 0
015 016 021 022 023 024 025 026 031 032 033 034 035 036 041 042
8/6
1
916 7/6
i 3/6 2 5/6
2/6
8/6
2
4/6 '
9/6 2 3/6 i 10/6 2 2/6 . 1116 2 1 / 6 ; 2 2 0 I 10/6 3 8 / 6 ' 11/6 3 7/6 I 2 3 11 13/6 S 5/6 , 14/6 3 4/61 15/6 3 3 / 6 I 13/6 4 11/6 [ 1416 4 1016 I
0
0 4.5 0 0 0 0 0 0 0 0 0 4.5
4
2
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t h o s e o f (HKL) t o t h o s e o f (hkl) i s r e a d i l y o b t a i n e d by u s i n g t h e l a t t i c e c o r r e s p o n d e n c e as shown i n F i g . 2 , that is,
h=~(SH+3K+L), k= H - L
and
I=~(3H+SK-L).
F i g . S shows a r e c i p r o c a l l a t t i c e f o r a bcc c r y s t a l t o which t h e p o i n t s due t o t h e i n t e r m e d i a t e s i x l a y e r s t r u c t u r e a r e added. The c a l c u l a t e d 1/6 and 1/3 e x t r a s p o t s a p p e a r o n l y one s i d e o f each bcc s p o t s , w h i l e t h e o b s e r v e d e x t r a s p o t s a r e on b o t h s i d e s o f each s p o t a l o n g one ( 1 1 0 ) d i r e c t i o n as s e e n in F i g . 1 . When t h e m u l t i p l e r e f l e c t i o n e f f e c t and t h e o c c u r r e n c e o f t h e s h u f f l i n g i n t h e o t h e r • BCC nor.~l reflection 0 normal "~ d i r e c t i o n from p l a c e t o p l a c e a r e t a k e n i n t o c o n s x d e r a 0 I/6 spot~ 6 laYer reflectlofl t l o n , t h i s disagreement is e a s i l y e x p l a i n e d . Another o I/3 spot J disagreement is that the observed extra spots distribute FIG. 3 a t n o t e x a c t l y 1/6 b u t 1 / 5 . 5 , ~ 1 / 6 i n t e r v a l s a l o n g t h e <110> d i r e c t i o n . As t o t h e o r i g i n o f t h i s d e v i a t i o n , two R e c i p r o c a l lattice f o r bcc possibilities a r e c o n s i d e r e d . The f i r s t one i s due t o t h e c r y s t a l t o which p o i n t s due s t a c k i n g f a u l t , but no s t r e a k s a r e o b s e r v e d a l o n g t h e to six layer structure are <110~ d i r e c t i o n o f e x t r a s p o t s and, t h e r e f o r e , t h i s p o s s i added. b i l i t y i s n o t i m p o r t a n t . The second i s due t o a s m a l l modulatxon o f t h e s i x l a y e r l a t t i c e t o r e l e a s e t h e t i g h t n e s s in t h e atomic a r r a n g e m e n t s i n i t ( 7 ) . M o d i f i c a t i o n by p a r t i a l displacements o f atoms a l o n g t h e {110} l a y e r s w i l l g i v e r i s e t o t h e e x t r a s p o t s w i t h t h e i n t e r v a l s o f r e c i p r o c a l o f n o n - i n t e g e r s as a r e o b s e r v e d , w h i l e t h o s e normal t o t h e l a y e r s w i l l p r o d u c e t h e t h i r d o r d e r 1/6 r e f l e c t i o n s o r t h e 1/2 e x t r a s p o t s which do n o t a p p e a r i n t h e c a l c u l a t i o n w i t h no m o d i f i c a t i o n . A dark f i e l d m i c r o g r a p h u s i n g a f u n d a m e n t a l s p o t and an a s s o c i a t e d e x t r a s p o t shows a v e r y f i n e s t r i a t e d s t r u c t u r e o f t h e o r d e r o f 30 A and no o t h e r d e f e c t c o n t r a s t as s e e n i n F i g . 4 . Although t h e d i r e c t i o n o f t h e s t r i a t i o n s i s a l m o s t normal t o t h a t o f t h e e x t r a s p o t s , t h e y do n o t run s t r a i g h t b u t z i g z a g . This f a c t c o r r e s p o n d s t o t h e exp e r i m e n t a l r e s u l t t h a t t h e d i r e c t i o n o f e x t r a s p o t s sometimes d e v i a t e s from an e x a c t <011> d i r e c tion. The p r e s e n t r e s u l t s s t r o n g l y s u g g e s t t h a t t h e atomic p r o c e s s o f t h e f c c - b c c m a r t e n s i t e t r a n s f o r m a t i o n o f Fe-Mn-C and Fe-Mn-Cr-C s t e e l p a s s e s t h r o u g h t h e new i n t e r m e d i a t e s i x l a y e r s t r u c t u r e , i n c o n t r a s t w i t h t h e d i r e c t s h e a r mechanism o f m a r t e n s i t e t r a n s f o r m a t i o n p r o p o s e d by Kurdjumov and Sachs or Nishiyama. In t h e e x i s t i n g s t a t e o f t h i n g s , i t seems t o be t h e most i m p o r t a n t t o d i s c u s s w h e t h e r carbon atoms occupy b o t h t e t r a - and o c t a h e d r a l i n t e r s t i t i a l s i t e s in the v i r g i n s t a t e of m a r t e n s i t e . Lysak e t a l . (10,11) f i r s t r e p o r t e d t h a t an u n e x p e c t e d l y low t e t r a g o n a l i t y a p p e a r e d i n f r e s h l y formed m a r t e n s i t e o f manganese and rhenium s t e e l a t low t e m p e r a t u r e s and t h e a x i a l r a t i o app r o a c h e d t h e e x p e c t e d v a l u e on h e a t i n g t o room t e m p e r a t u r e . Kurdjumov e t a l . (12) o b t a i n e d t h e same r e s u l t and s u g g e s t e d t h a t carbon atoms occupy n o t o n l y one o f t h r e e s u b l a t t i c e s o f o c t a hedral interstitial s i t e s i n h e r i t e d from a u s t e n i t e , Oz, but a l s o g e t i n t o t h e o t h e r two s u b l a t t i c e s Ox, z., xn t h e a s - f o r m e d m a r t e n s i t e a t low t e m p e r a t u r e s . Roytbourd and K h a c h a t u r i a n (13) p r o p o s e d an (011) t w i n n i n g mechanism t o r e a c h t h i s c o n f i g u r a t i o n . E n t i n e t a l . (14) c a r r i e d out t h e n e u t r o n s p e c t r o s c o p y o f a s - f o r m e d m a r t e n s i t e o f Fe-8at%Ni-6.7at%C a t 80°K. They compared t h e purely nuclear intensities of martensite reflections with those calculated for various models to determine the positions of carbon atoms. They concluded that about 80% of carbon atoms occupy
TABLE 2 Calculated Intensities for Various Carbon Configurations Carbon Positions
IFC200)I2+IF(020)I 2 FIG.
4
Dark field m i c r o g r a p h t a k e n from a f u n d a m e n t a l and an a s s o c i a t e d e x t r a s p o t .
[F(O02) I ~
Oz
0.8 0z+0.20x,y
15.9 -=2.00 7.95
]F(211) I2+IF(121)I ~
7.06
[F (112) [ 2
7.95
=0.89
15.9
0.5 0z+0.5 Tx,y,z 14.2
=2.00 7.95 7.80 6.93
=2.00 7.10
=1.13
8.29 7.19
-1.15
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10,
No.ll
one o f t h e o c t a h e d r a l i n t e r s t i t i a r s u b l a t t i c e s and no more t h a n 20% o f c a r b o n atoms go i n t o t h e other types of sublattices. Although detailed experimental conditions are not fully available from t h e i r p a p e r , t h e s c a t t e r e d i n t e n s i t i e s f o r v a r i o u s c o n f i g u r a t i o n s o f c a r b o n atoms a r e r e e x amined, and i t i s found t h a t t h e O and T h a l f and h a l f c o n f i g u r a t i o n i s a l s o p o s s i b l e t o i n t e r pret the observed intensity. T a b l e 2 i s t h e c a l c u l a t e d r e s u l t s , which g i v e a l m o s t same i n t e n s i t i e s f o r 80%0z+20%Ox, Y and 50%Oz+50%Tx v z. T h i s means t h a t t h e n e u t r o n d i f f r a c t i o n s t u d y a g r e e s w i t h t h e t h e o r e t i c a l p r e d i c t i o n 6 ~ ' t h e e q u a l o c c u p a n c i e s o f c a r b o n atoms i n t e t r a - and octahedral interstitial s i t e s i n f r e s h l y formed m a r t e n s i t e as w e l l as t h e MUssbauer e f f e c t s t u d y . The low t e t r a g o n a l i t y o f f r e s h l y formed m a r t e n s i t e o f manganese and r h e n i u m s t e e l i s a l s o exp l a i n e d by t h e h a l f and h a l f occupancy o f t e t r a - and o c t a h e d r a l i n t e r s t i t i a l s i t e s by c a r b o n i n t h e v i r g i n s t a t e o f low t e m p e r a t u r e m a r t e n s i t e as Lysak e t a l . p r o p o s e d and F u j i t a e t a l . c a l c u l a t e d ( 1 5 ) . The c a r b o n atoms i n t h e t e t r a h e d r a l i n t e r s t i t i a l s i t e s move t o o c t a h e d r a l i n t e r stitial s i t e s , Oz, d u r i n g t e m p e r i n g i n c r e a s i n g t h e a x i a l r a t i o and c h a n g i n g t h e H ~ s s b a u e r p a t t e r n s and e l e c t r i c a l r e s i s t i v i t i e s ( 1 5 ) . Lysak and N i k o l i n (16) o b s e r v e d an i n t e r m e d i a t e 18 l a y e r s t r u c t u r e i n t h e p r o c e s s o f m a r t e n s i t e t r a n s f o r m a t i o n i n Fe-btn-C s t e e l and c o n c l u d e d t h a t t h e t e t r a hedral interstitial c a r b o n p o s i t i o n s a r e a t t r i b u t e d t o m a r t e n s i t e f o r m a t i o n by way o f such an i n t e r m e d i a t e p h a s e . However, t h e 18 l a y e r s t r u c t u r e i s q u i t e d i f f e r e n t from t h e i n t e r m e d i a t e s i x l a y e r s t r u c t u r e r e p o r t e d i n t h e p r e s e n t p a p e r . While t h e 18 l a y e r s t r u c t u r e i s a long p e r i o d stacking order structure of close-packed plane of the fcc lattice, the present six layer structure is naturally assignable to the structure of bcc stacking order. CONCLUSIONS An i r r e v e r s i b l e i n t e r m e d i a t e p h a s e p r o d u c i n g e x t r a d i f f r a c t i o n s p o t s i s examined i n f r e s h l y formed m a r t e n s i t e o f Fe-5.5wt%Mn-lwt%C, Fe-6wt%Mn-lwt%C and Fe-Swt%Mn-3wt%Cr-lwt%C s t e e l a t low temperatures. The c r y s t a l s t r u c t u r e i s a n a l y z e d on t h e b a s i s o f t h e F u j i t a ' s s i x l a y e r model o f t h e i n t e r m e d i a t e s t r u c t u r e i n f c c - b c c m a r t e n s i t e t r a n s f o r m a t i o n , and t h e o b s e r v e d d i f f r a c t i o n patterns are well explained. C o e x i s t e n c e o f t h e i n t e r m e d i a t e s t r u c t u r e w i t h f i n e domains o f t h e o r d e r o f 50 A w i t h normal m a r t e n s i t e i s found by t h e d a r k f i e l d e l e c t r o n m i c r o s c o p y . It is strongly suggested that the atomic process of the fcc-bcc martensite transformation of t h e s e s t e e l s i s t h r o u g h a new i n t e r m e d i a t e s i x l a y e r s t r u c t u r e . In c o n n e c t i o n w i t h t h e i n t e r m e d i a t e p h a s e f o r m a t i o n , t h e s u b j e c t o f t h e p o s i t i o n o f c a r b o n atoms i n t h e v i r g i n s t a t e o f m a r t e n s i t e a t low t e m p e r a t u r e i s d i s c u s s e d . The r e s u l t s o f t h e n e u t r o n s p e c t r o s c o p y by E n t i n e t a l . a r e r e e x a m i n e d , and i t i s found t h a t t h e p r e s e n t a n a l y s i s i s c o n s i s t e n t w i t h t h e F u j i t a ' s mechanism. ACKNOWLEDGMENTS The a u t h o r s a r e g r a t e f u l t o Prof.M.Oka and Mr.H.Okamoto o f T o t t o r i U n i v e r s t y f o r t h e i r k i n d h e l p t o t a k e t h e dark f i e l d m i c r o g r a p h o f F i g . 4 . They a r e i n d e b t e d t o Prof.C.M.Wayman o f U n i v e r s i t y of I l l i n o i s f o r providing s h e e t s of specimen material. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
H. Ino, T . M o r i y a , F . E . F u j i t a and Y.Maeda, J . Phys. Soc. J a p a n 22, 346 ( 1 9 6 7 ) . F . E . F u j i t a , T . M o r i y a and H . I n o , P r o c e e d i n g s ICSTIS, S e c t i o n 6, 1273 (1971). C . S h i g a , M.Kimura and F . E . F u j i t a , J . J a p a n I n s t . M e t a l s 58, 1037 (1974). F . E . F u j i t a and C . S h i g a , F i r s t JIM Symposium, Kobe (1976). ( P r o c e e d i n g s i n p r e s s ) . G.V.Kurdjumov and G . S a c h s , Z. Phys. 64, 325 (1950). Z . N i s h i y a m a , S c i . Rep. Tohoku Univ. 23, 657 (1954). F . E . F u j i t a , J . J a p a n I n s t . M e t a l s 59, 1082 (1975). F . E . F u j i t a , F i r s t JIM Symposium, Kobe (1976). ( P r o c e e d i n g s i n p r e s s ) . R.Oshima and C.M.Wayman, S c r i p t a Met. 8, 223 (1974). L . I . L y s a k , Ya.N.Vovk and Y u . M . P o l i s h c h u k , F i z . m e t a l , m e t a l l o v e d . 23, 898 (1967). L . I . L y s a k and L.O.Andrushchuk, F i z . m e t a l , m e t a l l o v e d . 28, 348 (1969). Y u . L . A l ' S h e v s k i j and G.V.Kurdjumov, F i z . m e t a l , m e t a l l o v e d . 25, 172 (1968). A . L . R o y t b o u r d and A . G . K h a c h a t u r i a n , F i z . m e t a l , m e t a l l o v e d . 30, 1189 ( 1 9 7 0 ) . I . R . E n t i n , Y.A.Somenkov and S . S h . S h i l ' s h t e i n , Doklady Akad. Nauk S . S . S . R . 206, 1096 ( 1 9 7 2 ) . C . S h i g a , F . E . F u j i t a and M.Kimura, J . J a p a n I n s t . M e t a l s 39, 1205 (1975). L . I . L y s a k and B . I . N i k o l i n , F i z . m e t a l , m e t a l l o v e d . 20, 547 ( 1 9 6 5 ) .
Vol. I0, pp. 1011-1014, 1976 Printed in the United States
Pergamon Press, Inc.
THE FORMATION OF INTERMEDIATE PHASE IN MARTENSITE TRANSFORMATION OF Fe-Mn-C AND Fe-Mn-Cr-C STEEL
R y u i c h i r o Oshima, Hirozumi Azuma and F r a n c i s c o E i i c h i F u j i t a Department o f M a t e r i a l P h y s i c s , F a c u l t y o f E n g i n e e r i n g S c i e n c e , Osaka U n i v e r s i t y , Toyonaka, Osaka 560, Japan
(Received August i0, 1976)
INTRODUCTION One o f t h e p r e s e n t a u t h o r s (FEF) and o t h e r s (1-4) i n v e s t i g a t e d t h e Fe 57 M6ssbauer s p e c t r a o f t h e low t e m p e r a t u r e m a r t e n s i t e p h a s e o f F e - l - v l . 8 w t % C , Fe-6wt%Ni-l.8wt%C and Fe-Swt%Mn-l.6wt%C s t e e l , and c o n c l u d e d t h a t (1) carbon atoms occupy t h e t e t r a - and o c t a h e d r a l i n t e r s t i c e s w i t h equal p o p u l a t i o n s i n t h e f r e s h l y formed m a r t e n s i t e a t low t e m p e r a t u r e s and (2) t h e t e t r a h e d r a l interstitial carbon atoms jump t o t h e o c t a h e d r a l s i t e s d u r i n g t h e t e m p e r i n g t o room t e m p e r a t u r e . It is clear that the tetrahedral interstitial carbon atoms o f m a r t e u s i t e can n o t be i n t r o d u c e d by t h e d i r e c t s h e a r mechanism o f m a r t e n s i t e t r a n s f o r m a t i o n p r o p o s e d by Kurdjumov and Sachs (5) and Nishiyama ( 6 ) . F u j i t a has r e c e n t l y p r o p o s e d a new t h e o r y o f m a r t e n s i t e t r a n s f o r m a t i o n o f f e r r o u s a l l o y s ( 7 , 8 ) , a c c o r d i n R t o which t h e a u s t e n i t e l a t t i c e t r a n s f o r m s f i r s t t o an i n t e r m e d i a t e s i x l a y e r s t r u c t u r e by s h u f f l i n R o f f c c l a t t i c e on (111) p l a n e s alonR [112] d i r e c t i o n and t h e n t o t h e u l t i m a t e bcc m a r t e n s i t e by h a l f d i s l o c a t i o n t y p e s h e a r i n g a l o n g e v e r y two p l a n e s o f t h e same k i n d and in t h e same d i r e c t i o n and t h e t e t r a - and o c t a h e d r a l s i t e occupancy o f carbon i s accounted for. In a d d i t i o n , Oshima and Wayman (9) found e x t r a d i f f r a c t i o n s p o t s i n t r a n s m i s s i o n 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 o b t a i n e d from a s - f o r m e d m a r t e n s i t e o f Fe-Mn-C and Fe-Mn-Cr-C a l l o y s a t low t e m p e r a t u r e s , and s u g g e s t e d a r e g u l a r p e r i o d i c s t r u c t u r e w i t h a p e r i o d i c i t y o f s i x {011} i n t e r p l a n a r d i s t a n c e s i n t h e f r e s h l y formed m a r t e n s i t e . In t h e p r e s e n t work, t h e F u j i t a ' s s i x l a y e r s t r u c t u r e i s t h o u g h t t o be c o n n e c f e d w i t h t h e e x t r a d i f f r a c t i o n s p o t s o b s e r v e d i n f r e s h l y formed m a r t e n s i t e o f Fe-Mn-C and Fe-Mn-Cr-C s t e e l , and t h e s t r u c t u r e f a c t o r s o f t h e model a r e c a l c u l a t e d and compared w i t h t h e o b s e r v e d i n t e n s i t i e s and p o s i t i o n s o f t h e e x t r a s p o t s . The o b s e r v e d d i f f r a c t i o n p a t t e r n s a r e t o l e r a b l y e x p l a i n e d by t h e s i x l a y e r model. Some d i s a g r e e m e n t s between t h e c a l c u l a t e d and e x p e r i m e n t a l r e s u l t s a r e i n t e r p r e t e d by m o d i f y i n g t h e s t a c k i n g o f t h e s i x l a y e r s t r u c t u r e t o r e l e a s e t h e t i g h t n e s s o f t h e atomic a r r a n g e m e n t s i n t h e s t r u c t u r e and m u l t i p l e r e f l e c t i o n e f f e c t . In c o n n e c t i o n w i t h t h e f o r m a t i o n o f new s i x l a y e r s t r u c t u r e , c u r r e n t s u b j e c t s c o n c e r n i n g t h e p o s i t i o n o f c a r b o n atoms i n f r e s h l y formed m a r t e n s i t e a r e a l s o d i s c u s s e d . EXPERIMENTAL Fe-5.5wt%Mn=lwt%C, Fe=6wt%Mn-lwt%C and Fe-3wt%Mn-3wt%Cr-lwt%C a l l o y s a r e u s e d f o r t h i s s t u d y Disc s p e c i m e n s punched from about 0.4mm t h i c k s h e e t s o f t h e s e m a t e r i a l s a r e s e a l e d i n e v a c u a t e d q u a r t z c a p s u l e s , and a u s t e n i t i z e d a t 1200°C f o r 1 h r p r i o r t o w a t e r q u e n c h i n g . All specimens a r e c o m p l e t e l y a u s t e n i t i c a f t e r q u e n c h i n g , and t h e y a r e c h e m i c a l l y and e l e c t r o l y t i c a l l y t h i n n e d . The s p e c i m e n s a r e t r a n s f o r m e d t o m a r t e n s i t e by c o o l i n g on a c o l d s t a g e o f H i t a c h i HU-11A e l e c t r o n microscope. RESULTS AND DISCUSSION In t h e f r e s h l y formed m a r t e n s i t e o f a l l o f t h e above m e n t i o n e d a l l o y s , e x t r a s p o t s a s s o c i a t e d w i t h t h e normal b c t ( b c c ) m a r t e n s i t e a r e found i n t r a n s m i s s i o n 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 a k e n a t -140°C. The e x t r a s p o t s a r e o b s e r v e d i n v a r i o u s r e c i p r o c a l l a t t i c e p l a n e o f bcc m a r t e n s i t e as shown i n F i g . 1 . They a r e t h e s a t e l l i t e s i n a < l l 0 > d i r e c t i o n o f normal bcc m a r t e n s i t e n e a r each f u n d a m e n t a l s p o t , and d i s t r i b u t e d a t 1/6 i n t e r v a l s a l o n g t h e < l l 0 > d i r e c t i o n . In some c a s e s t h e i n t e r v a l s and d i r e c t i o n s o f t h e e x t r a s p o t s s l i g h t l y d e v i a t e from 1/6 and < l l 0 > respectively. The second o r d e r s a t e l l i t e r e f l e c t i o n s a r e a l s o o b s e r v e d w i t h lower i n t e n s i t i e s t h a n t h e f i r s t o n e s . A l l e x t r a s p o t s d i s a p p e a r around =80°C when t h e specimen i s h e a t e d t o room ]011
1012
INTERMEDIATE
PHASE
IN M A R T E N S I T E
TRANSFORMATION
temperature. They do n o t r e a p p e a r when t h e specimen i s c o o l e d a g a i n . T h i s means t h a t t h e e x t r a s p o t s a r e corresponding to the formation of an i r r e v e r s i b l e i n t e r m e d i a t e s t r u c ture. S i n c e t h e F u j i t a ' s new t h e o r y p r e d i c t s an i n t e r m e d i a t e s i x l a y e r s t r u c t u r e t o form on t h e way from a u s t e n i t e t o m a r t e n s i t e , t h e observed extra diffraction spots in a s - f o r m e d m a r t e n s i t e a t low t e m p e r a t u r e s a r e t h o u g h t t o a r i s e from the six layer structure. Hence, the structure factors of the six l a y e r model a r e c a l c u l a t e d and compared with the observed intensities and p o s i t i o n s o f t h e e x t r a s p o t s . F i g . 2 shows a u n i t c e l l o f t h e s i x l a y e r model. In t h i s f i g u r e c r y s t a l l o g r a p h i c r e l a t i o n between t h e FIG. 1 s i x l a y e r s t r u c t u r e l a t t i c e and t h e bcc l a t t i c e i s a l s o i n d i c a t e d . Diffraction patterns obtained The u n i t c e l l h a s s i x atoms a t from f r e s h l y formed m a r t e n s i t e (0,0,0), ( 5 / 6 , 5 / 6 , 1 / 6 ) , (2/6,2/6, a t low t e m p e r a t u r e s . 2/6), (I/6,1/6,3/6), (4/6,4/6,4/6) and (3/6,3/6,5/6). With this unit cell, the structure factors can be written as: SHK L = Z f.exp{2wi(l.H + m.K + n.L)} f {1 + exp~l(SH+SK+L) + exl~3i(2H+2K+2L) + e x ~
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FIG. 2 Unit c e l l o f six l a y e r structure and lattice correspondence for the six layer structure to bcc. (H+K+3L)
+ exp~(4H+4K+4L) + exF~xit3H+3K+SL)~,''~ where f is the atomic scattering factor of iron or manganese, and H, K and L are the r e f l e c t i n g indices. Table I l i s t s the results of various (HKL) intensity calculations. Since the extra diffraction spots a r e always found with bcc martensite spots, the Miller indices (hkl) referred to bcc martensite are also shown in this table. The transformation of the Miller indices from TABLE 1 Calculated Intensities for Six Layer Structure I
HKL
I
h
k
1
5HKL/2f2
HKL
h
k
1
SHKL/2f2
HKL
h
k
1
SHKL/2f2
4.5 0 13.5
043 044 045 046 051 052 053 054 055 056 061 062 063 064 065 066
15/6 16/6 17/6 3 16/6 17/6 3 1916
4 4 4 ~ § 5 ~ 5
916 8/6 7/6 1 14/6 13/6 2 1116
20/6
g lO/6
21/6 1916 20•6 21/6 2216 2316
§ 9/6 61716 6 16/6 61516 6 14/6 6 13/6
0 0 13.5 0 4.5 0 0 13.5 0 0 0 0 0 0 0
6
18.0
I
01 0 0201 030 O40 050 060 001 OO2 003 0O4 0O5 006
0 1 0 1 0 1
3/6 1 916 2 15/6
3/6
1 3 916 4 2 S 15/6
3
&
3
1/6 2/6
0 0
i/6 3/6
3/6
o
_~/6
4/6 5/6 1 4/6 5/6 1 7/6
0 0 0 1 i i i
416
g/6
0 0 0 0 0 18.0
0 0 0 0 0 18.0
2/6 1/6 0 1/6
0 13.5 0 0
015 016 021 022 023 024 025 026 031 032 033 034 035 036 041 042
8/6
1
916 7/6
i 3/6 2 5/6
2/6
8/6
2
4/6 '
9/6 2 3/6 i 10/6 2 2/6 . 1116 2 1 / 6 ; 2 2 0 I 10/6 3 8 / 6 ' 11/6 3 7/6 I 2 3 11 13/6 S 5/6 , 14/6 3 4/61 15/6 3 3 / 6 I 13/6 4 11/6 [ 1416 4 1016 I
0
0 4.5 0 0 0 0 0 0 0 0 0 4.5
4
2
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I013
t h o s e o f (HKL) t o t h o s e o f (hkl) i s r e a d i l y o b t a i n e d by u s i n g t h e l a t t i c e c o r r e s p o n d e n c e as shown i n F i g . 2 , that is,
h=~(SH+3K+L), k= H - L
and
I=~(3H+SK-L).
F i g . S shows a r e c i p r o c a l l a t t i c e f o r a bcc c r y s t a l t o which t h e p o i n t s due t o t h e i n t e r m e d i a t e s i x l a y e r s t r u c t u r e a r e added. The c a l c u l a t e d 1/6 and 1/3 e x t r a s p o t s a p p e a r o n l y one s i d e o f each bcc s p o t s , w h i l e t h e o b s e r v e d e x t r a s p o t s a r e on b o t h s i d e s o f each s p o t a l o n g one ( 1 1 0 ) d i r e c t i o n as s e e n in F i g . 1 . When t h e m u l t i p l e r e f l e c t i o n e f f e c t and t h e o c c u r r e n c e o f t h e s h u f f l i n g i n t h e o t h e r • BCC nor.~l reflection 0 normal "~ d i r e c t i o n from p l a c e t o p l a c e a r e t a k e n i n t o c o n s x d e r a 0 I/6 spot~ 6 laYer reflectlofl t l o n , t h i s disagreement is e a s i l y e x p l a i n e d . Another o I/3 spot J disagreement is that the observed extra spots distribute FIG. 3 a t n o t e x a c t l y 1/6 b u t 1 / 5 . 5 , ~ 1 / 6 i n t e r v a l s a l o n g t h e <110> d i r e c t i o n . As t o t h e o r i g i n o f t h i s d e v i a t i o n , two R e c i p r o c a l lattice f o r bcc possibilities a r e c o n s i d e r e d . The f i r s t one i s due t o t h e c r y s t a l t o which p o i n t s due s t a c k i n g f a u l t , but no s t r e a k s a r e o b s e r v e d a l o n g t h e to six layer structure are <110~ d i r e c t i o n o f e x t r a s p o t s and, t h e r e f o r e , t h i s p o s s i added. b i l i t y i s n o t i m p o r t a n t . The second i s due t o a s m a l l modulatxon o f t h e s i x l a y e r l a t t i c e t o r e l e a s e t h e t i g h t n e s s in t h e atomic a r r a n g e m e n t s i n i t ( 7 ) . M o d i f i c a t i o n by p a r t i a l displacements o f atoms a l o n g t h e {110} l a y e r s w i l l g i v e r i s e t o t h e e x t r a s p o t s w i t h t h e i n t e r v a l s o f r e c i p r o c a l o f n o n - i n t e g e r s as a r e o b s e r v e d , w h i l e t h o s e normal t o t h e l a y e r s w i l l p r o d u c e t h e t h i r d o r d e r 1/6 r e f l e c t i o n s o r t h e 1/2 e x t r a s p o t s which do n o t a p p e a r i n t h e c a l c u l a t i o n w i t h no m o d i f i c a t i o n . A dark f i e l d m i c r o g r a p h u s i n g a f u n d a m e n t a l s p o t and an a s s o c i a t e d e x t r a s p o t shows a v e r y f i n e s t r i a t e d s t r u c t u r e o f t h e o r d e r o f 30 A and no o t h e r d e f e c t c o n t r a s t as s e e n i n F i g . 4 . Although t h e d i r e c t i o n o f t h e s t r i a t i o n s i s a l m o s t normal t o t h a t o f t h e e x t r a s p o t s , t h e y do n o t run s t r a i g h t b u t z i g z a g . This f a c t c o r r e s p o n d s t o t h e exp e r i m e n t a l r e s u l t t h a t t h e d i r e c t i o n o f e x t r a s p o t s sometimes d e v i a t e s from an e x a c t <011> d i r e c tion. The p r e s e n t r e s u l t s s t r o n g l y s u g g e s t t h a t t h e atomic p r o c e s s o f t h e f c c - b c c m a r t e n s i t e t r a n s f o r m a t i o n o f Fe-Mn-C and Fe-Mn-Cr-C s t e e l p a s s e s t h r o u g h t h e new i n t e r m e d i a t e s i x l a y e r s t r u c t u r e , i n c o n t r a s t w i t h t h e d i r e c t s h e a r mechanism o f m a r t e n s i t e t r a n s f o r m a t i o n p r o p o s e d by Kurdjumov and Sachs or Nishiyama. In t h e e x i s t i n g s t a t e o f t h i n g s , i t seems t o be t h e most i m p o r t a n t t o d i s c u s s w h e t h e r carbon atoms occupy b o t h t e t r a - and o c t a h e d r a l i n t e r s t i t i a l s i t e s in the v i r g i n s t a t e of m a r t e n s i t e . Lysak e t a l . (10,11) f i r s t r e p o r t e d t h a t an u n e x p e c t e d l y low t e t r a g o n a l i t y a p p e a r e d i n f r e s h l y formed m a r t e n s i t e o f manganese and rhenium s t e e l a t low t e m p e r a t u r e s and t h e a x i a l r a t i o app r o a c h e d t h e e x p e c t e d v a l u e on h e a t i n g t o room t e m p e r a t u r e . Kurdjumov e t a l . (12) o b t a i n e d t h e same r e s u l t and s u g g e s t e d t h a t carbon atoms occupy n o t o n l y one o f t h r e e s u b l a t t i c e s o f o c t a hedral interstitial s i t e s i n h e r i t e d from a u s t e n i t e , Oz, but a l s o g e t i n t o t h e o t h e r two s u b l a t t i c e s Ox, z., xn t h e a s - f o r m e d m a r t e n s i t e a t low t e m p e r a t u r e s . Roytbourd and K h a c h a t u r i a n (13) p r o p o s e d an (011) t w i n n i n g mechanism t o r e a c h t h i s c o n f i g u r a t i o n . E n t i n e t a l . (14) c a r r i e d out t h e n e u t r o n s p e c t r o s c o p y o f a s - f o r m e d m a r t e n s i t e o f Fe-8at%Ni-6.7at%C a t 80°K. They compared t h e purely nuclear intensities of martensite reflections with those calculated for various models to determine the positions of carbon atoms. They concluded that about 80% of carbon atoms occupy
TABLE 2 Calculated Intensities for Various Carbon Configurations Carbon Positions
IFC200)I2+IF(020)I 2 FIG.
4
Dark field m i c r o g r a p h t a k e n from a f u n d a m e n t a l and an a s s o c i a t e d e x t r a s p o t .
[F(O02) I ~
Oz
0.8 0z+0.20x,y
15.9 -=2.00 7.95
]F(211) I2+IF(121)I ~
7.06
[F (112) [ 2
7.95
=0.89
15.9
0.5 0z+0.5 Tx,y,z 14.2
=2.00 7.95 7.80 6.93
=2.00 7.10
=1.13
8.29 7.19
-1.15
1014
INTERMEDIATE PHASE IN MARTENSITE ~RANSFORMATION
Vol.
10,
No.ll
one o f t h e o c t a h e d r a l i n t e r s t i t i a r s u b l a t t i c e s and no more t h a n 20% o f c a r b o n atoms go i n t o t h e other types of sublattices. Although detailed experimental conditions are not fully available from t h e i r p a p e r , t h e s c a t t e r e d i n t e n s i t i e s f o r v a r i o u s c o n f i g u r a t i o n s o f c a r b o n atoms a r e r e e x amined, and i t i s found t h a t t h e O and T h a l f and h a l f c o n f i g u r a t i o n i s a l s o p o s s i b l e t o i n t e r pret the observed intensity. T a b l e 2 i s t h e c a l c u l a t e d r e s u l t s , which g i v e a l m o s t same i n t e n s i t i e s f o r 80%0z+20%Ox, Y and 50%Oz+50%Tx v z. T h i s means t h a t t h e n e u t r o n d i f f r a c t i o n s t u d y a g r e e s w i t h t h e t h e o r e t i c a l p r e d i c t i o n 6 ~ ' t h e e q u a l o c c u p a n c i e s o f c a r b o n atoms i n t e t r a - and octahedral interstitial s i t e s i n f r e s h l y formed m a r t e n s i t e as w e l l as t h e MUssbauer e f f e c t s t u d y . The low t e t r a g o n a l i t y o f f r e s h l y formed m a r t e n s i t e o f manganese and r h e n i u m s t e e l i s a l s o exp l a i n e d by t h e h a l f and h a l f occupancy o f t e t r a - and o c t a h e d r a l i n t e r s t i t i a l s i t e s by c a r b o n i n t h e v i r g i n s t a t e o f low t e m p e r a t u r e m a r t e n s i t e as Lysak e t a l . p r o p o s e d and F u j i t a e t a l . c a l c u l a t e d ( 1 5 ) . The c a r b o n atoms i n t h e t e t r a h e d r a l i n t e r s t i t i a l s i t e s move t o o c t a h e d r a l i n t e r stitial s i t e s , Oz, d u r i n g t e m p e r i n g i n c r e a s i n g t h e a x i a l r a t i o and c h a n g i n g t h e H ~ s s b a u e r p a t t e r n s and e l e c t r i c a l r e s i s t i v i t i e s ( 1 5 ) . Lysak and N i k o l i n (16) o b s e r v e d an i n t e r m e d i a t e 18 l a y e r s t r u c t u r e i n t h e p r o c e s s o f m a r t e n s i t e t r a n s f o r m a t i o n i n Fe-btn-C s t e e l and c o n c l u d e d t h a t t h e t e t r a hedral interstitial c a r b o n p o s i t i o n s a r e a t t r i b u t e d t o m a r t e n s i t e f o r m a t i o n by way o f such an i n t e r m e d i a t e p h a s e . However, t h e 18 l a y e r s t r u c t u r e i s q u i t e d i f f e r e n t from t h e i n t e r m e d i a t e s i x l a y e r s t r u c t u r e r e p o r t e d i n t h e p r e s e n t p a p e r . While t h e 18 l a y e r s t r u c t u r e i s a long p e r i o d stacking order structure of close-packed plane of the fcc lattice, the present six layer structure is naturally assignable to the structure of bcc stacking order. CONCLUSIONS An i r r e v e r s i b l e i n t e r m e d i a t e p h a s e p r o d u c i n g e x t r a d i f f r a c t i o n s p o t s i s examined i n f r e s h l y formed m a r t e n s i t e o f Fe-5.5wt%Mn-lwt%C, Fe-6wt%Mn-lwt%C and Fe-Swt%Mn-3wt%Cr-lwt%C s t e e l a t low temperatures. The c r y s t a l s t r u c t u r e i s a n a l y z e d on t h e b a s i s o f t h e F u j i t a ' s s i x l a y e r model o f t h e i n t e r m e d i a t e s t r u c t u r e i n f c c - b c c m a r t e n s i t e t r a n s f o r m a t i o n , and t h e o b s e r v e d d i f f r a c t i o n patterns are well explained. C o e x i s t e n c e o f t h e i n t e r m e d i a t e s t r u c t u r e w i t h f i n e domains o f t h e o r d e r o f 50 A w i t h normal m a r t e n s i t e i s found by t h e d a r k f i e l d e l e c t r o n m i c r o s c o p y . It is strongly suggested that the atomic process of the fcc-bcc martensite transformation of t h e s e s t e e l s i s t h r o u g h a new i n t e r m e d i a t e s i x l a y e r s t r u c t u r e . In c o n n e c t i o n w i t h t h e i n t e r m e d i a t e p h a s e f o r m a t i o n , t h e s u b j e c t o f t h e p o s i t i o n o f c a r b o n atoms i n t h e v i r g i n s t a t e o f m a r t e n s i t e a t low t e m p e r a t u r e i s d i s c u s s e d . The r e s u l t s o f t h e n e u t r o n s p e c t r o s c o p y by E n t i n e t a l . a r e r e e x a m i n e d , and i t i s found t h a t t h e p r e s e n t a n a l y s i s i s c o n s i s t e n t w i t h t h e F u j i t a ' s mechanism. ACKNOWLEDGMENTS The a u t h o r s a r e g r a t e f u l t o Prof.M.Oka and Mr.H.Okamoto o f T o t t o r i U n i v e r s t y f o r t h e i r k i n d h e l p t o t a k e t h e dark f i e l d m i c r o g r a p h o f F i g . 4 . They a r e i n d e b t e d t o Prof.C.M.Wayman o f U n i v e r s i t y of I l l i n o i s f o r providing s h e e t s of specimen material. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
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