18R martensite in FeMnAlC

Acta metall, mater. Vol. 43, No. 1, pp. 21 30, 1995

~

Pergamon

0956-7151(94)00233-9

Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0956-7151/94 $7.00 + 0.00

TRANSMISSION ELECTRON MICROSCOPY STUDIES OF THE CRYSTALLOGRAPHY OF B.C.C./18R MARTENSITE IN Fe-Mn-A1-C W. B. LEE1, F U - R O N G C H E N z, S. K. C H E N z, G. B. O L S O N 3 and C. M. WAN 1 LDepartment of Materials Science and Engineering, National Tsing Hua University, Taiwan, Republic of China, 2Materials Science Center, National Tsing Hua University, Taiwan, Republic of China and 3Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, U.S.A. (Received 12 November 1993; in revised form 18 May 1994)

A~tract--The 18R martensite phase was observed in the b.c.c, matrix of an Fe 25.8 wt% Mn-7.4 wt% A14).l 1 wt% C alloy, after cooling from high temperature. The crystal structure is determined from the selected area diffraction (SAD) and high resolution imaging techniques. The 18R martensite has an orthorhombic lattice with lattice constants a = 0.448 nm, b = 0.259 nm and c = 3.865 nm and is best described as an 18R(4~3 rather than an 18R(51-)3structure. [The expression of 18R(4~)3 and 18R(5T)3 comes from the combined notation of Ramsdell and Zhdanov [Nishiyama, Martensitic Transformation, p. 75 (1978)].] The stacking fault density relative to the 18R(4~)3 structure is determined from high resolution imaging to be 0.096. Martensite crystallographic parameters such as orientation relationship, habit plane, shape strain direction and magnitude of lattice invariant shear are calculated using the CRAB theory, in good agreement with experimental observations. The Burgers vector of anticoherency dislocations and the shape strain direction were confirmed using the two beam technique and computer image simulation. The observed interfacial dislocation structure and choice of lattice correspondence are discussed in terms of near-CSL concepts.

INTRODUCTION

These studies did not employ T E M experiments to determine carefully the martensitic crystallography such as habit plane, orientation relationship, shape deformation and magnitude of lattice invariant shear which can be compared with calculations from the established theory of martensitic crystallography [17, 19-22]. Furthermore, Kajiwara [22] showed the assumption of the f.c.c./b.c.c. Bain correspondence gives an unsatisfactory description for b.c.c, to 9R or 18R martensitic transformation. The structure of the martensite phase and martensitic crystallography are still not well characterized and understood in this alloy system. Therefore, the main purpose of this research is to apply T E M technique to investigate the crystal structure of the 18R martensite phase and the b.c.c./18R martensitic crystallography in this system, including the habit plane, orientation relationship, shape deformation and magnitude of the lattice invariant shear, and to compare these parameters with predictions of martensite crystallographic theory. Observed interfacial dislocation structure and choice of lattice correspondence will also be discussed in terms of near-CSL concepts from interfacial dislocation theory.

F e - M n - A l - b a s e d alloys are of interest for their good resistance to corrosion [1], oxidation [2, 3], stress corrosion cracking [4], and hydrogen embrittlement [4] as well as their good mechanical properties [5-7]. When an alloy was water-quenched from 1300°C, a b.c.c, to f.c.c, phase transformation was found [8, 9] and an 18R(51) 3 [10] martensite phase with a needle morphology was observed by light microscopy [11, 12]. More recent experiments suggested that this martensite phase has an 18R(4~)3 structure [13, 14]. The unit cells of the 18R(5])3 and 18R(4~)3 structures are depicted in Fig. 1. The 18R(5T)3 structure corresponds to single faulting after every 5th plane, while the 18R(42)3 structure corresponds to double faulting (or two-layer microtwinning) after every 4th plane. Both 18R martensites have an orthorhombic lattice. In the F e - M n - A 1 - C alloy system, a high stacking fault density is found within the 18R martensite phase. Basically, the martensite phase in this system is similar to the 9R martensite in C u - Z n [15, 16] or the 18R martensite in C u - Z n - A I [17]. Chen et al. [18] tried to use the inverse Bain distortion of b.c.c, to f.c.c, and the Burgers relationship of b.c.c, to h.c.p, to discuss the crystallography of the 18R martensite in an F e - M n - A I - C alloy. Chao et al. [13, 14] suggested that it is reasonable to interpret the b.c.c, to 18R martensitic transformation in this alloy in terms of the Bain correspondence and double shear model.

EXPERIMENTALPROCEDURES The composition of Fe-25.8 wt% M n - 7 . 4 w t % AI-0.11 wt% C was chosen for this study. Specimens 100 × 10 x 2 mm 3 in size were cut from a cold-rolled 21

22

LEE et al.:

MARTENSITE IN Fe-Mn-AI~S

-0--O

q

bloc

c

,

c

o_.

2a/3

a a "0": atoms in the paper plane.

a

"0": atoms above or below the paper plane.

18R(4~)3 (a)

lSR(~)3 (b)

Fig. l. Unit cells of the 18R(4~)3 and the 18R(51)3 structures in the orthorhomhic lattice.

plate. After 1 h solution treatment at 1300°C in argon, the specimens were water quenched to room temperature. TEM specimens were thinned and ground mechanically to 0.15 mm and then punched into 3 mm diameter disks. Thin foils were perforated with a twin-jet polisher in a 6% HC104 and 94% CH3COOH solution operated at 15 V. Electron microscopy examinations were performed with a JEOL-

200CX STEM and a JEOL-4000EX TEM, each with a double-tilt specimen holder. An X-ray diffractometer with Cu target was used to determine the lattice constant of the b.c.c, parent phase. Because of the overlapping of X-ray peaks between f.c.c, and the 18R structures, the lattice constant of 18R martensite phase is determined from selected-area electron diffraction patterns.

Fig. 2. Light micrograph of specimen water-quenched from 1300°C.

(b)

~C

ISR(ST)3 I$R(42) 3 EXPERIMENT ~,Ia8

l,l,13 1,1~ u 7

u s u 8 l,IJ1

i,iJ8

Fig. 3. (a) Selected area diffraction pattern of martensite phase with [I]'0]ISRzone axis, (b) the bright field image of martensite phase, and (c) comparison of the experimental and the simulated diffraction spots at 9.5 nm thickness using multislice calculation. 23

24

LEE et al.: MARTENSITE IN Fe-Mn-AI~2 RESULTS AND DISCUSSION

try. Since the diffraction peaks of the 18R martensite and the y phase (f.c.c. structure) overlap, it is difficult Structure and lattice constant o f 18R martensite to deduce the lattice constants of the martensite phase Figure 2 is a light micrograph which shows the using the X-ray technique. The lattice constants of + ~ duplex structures in the F e - M n - A 1 - C alloy the 18R martensite phase are determined from a water-quenched from 1300°C to room temperature. composite diffraction pattern of the b.c.c, matrix and The ~ phase is a f.c.c, structure and the c~ phase is martensite phase shown in Fig. 4. The lattice constant b.c.c. As can be seen from Fig. 2, there is a needle-like of 18R phase is determined to be alsR =0.448 nm, martensite phase in the ~ grains. The b.c.c, phase is blsR = 0.259 nm, and c~sa = 3.865 nm from Fig. 4 with the Stable phase at high temperature. The crystal the reference of ab.c.c.. The lattice constants of 18R structure of the needle-like phase can be determined phase are very close to the ideal ratios alsa: b~sa: from the selected-area diffraction technique. Figure ClSR= V/~ : 1: 6V/-6 in a close-packed 18R orthorhom3(a) is a zone axis diffraction pattern of this phase. bic lattice. The zone axis of this diffraction pattern is The streaking in the diffraction pattern is due to the close to (111) b..... and is about 1° deviated from high density of stacking faults evident in the electron [1T0]~sa. From this pattern, we also know that the micrograph of Fig. 3(b). The zone axis of the diffrac- (T01)b..... plane and the (0, 0, 18)~8R plane make an tion pattern is determined to be [IT0]ISR. The struc- angle of about 5° and the (011)b ..... plane is nearly ture is orthorhombic. In order to confirm that the parallel to the 10-]'8)~Sa plane. It is clear that the crystal structure of the needle-like phase is the (0, 0, 18)~sa basal plane is the stacking fault plane. Figure 5(a) shows a high resolution image of b.c.c. 18R(5T)3 [11, 12] or the 18R(4~)3 [13, 14] structure, simulated diffraction patterns of thickness 9.5 nm for and martensite phases with the electron beam direc18R(5T)3 and 18R(4~)3 structures were calculated tion parallel to [I-i'0]lSR. The angular relationship using the program MacTempas [23] which is based on between the (T01)b.c.c plane and the (0, 0, 18)lSa plane the multislice method. Figure 3(c) shows the exper- can also be derived from this image. The trace of the imental and simulated diffraction spots of (T, i, 1--~)lSa average habit plane is close to (168)b ..... which can be to (I,T, 18)18a for the 18R(51) 3 and 18R(4~) 3 struc- estimated with the reference of the termination of the tures. It can be concluded easily that this martensite (0, 0, 18)lsa planes. Some of the (0, 0, 18)~8R planes of phase is closer to the 18R(4~) 3 rather than the the martensite shown in Fig. 5(b) are labeled in terms 18R(51)3 structure, because both of the positions and of stacking and shear sequences. The average stackthe relative intensities of 18R(5T)3 cannot fit with ing sequence for 282 close-packed (0, 0, 18)~SR planes in the same martensite phase is given in Table 1. those observed. The lattice constant a b..... of the b.c.c, matrix is Although the actual sequence is quasiperiodic, the determined to be 0.291 nm from X-ray diffractome- average stacking sequence is 18R(4.1915, 1.8085)3

Fig. 4. Composite diffraction pattern of b.c.c, matrix and martensite phase with [IT0]ISRzone axis or near [-i-lT]b.c.c.zone axis. Subscript "b" refers to the b.c.c, lattice and "m" refers to the 18R(4~a structure in orthorhombic axis.

ATOMICstacking

(b) ATOMIC LAYER

38 37 36 35 34 33 32 31 3O 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 ,g

stacking sequence

shear sequence --

2

4

6

4

"

74 73 72 71 I:_l 69 70 I 68 67 66 ~

;

shear ~uenee

112

111 110 : 109 108 106 107 105 104 103 lo2 lOl 100 99 98 97

58 59 57 i 56 55 54 53 52

95 96

T

51 M

ss

3

49 48 i 47 46 45 44 43 ~ 42 41 40 39

86 ~ 83 82 81 80 79 78 77 76

3

3 :i ~ ~ 3

1

75

63 62 61 ~ 60

8

6

stacking ATOMICsequencez~_ LAYER

shear sequence

LAYER sequence 115 114

]

3

6

4

94 93 92

i-

~

3

89

50

87 4

lnm Fig. 5. (a) High resolution image of b.c.c, and martensitephases and (b) the stackingsequence over I15 atomic stacking layers under magnification.Line segments "--" represents the stacking faults. 25

26

LEE et al.: MARTENSITE IN Fe-Mn-A1-C Table 1. Stackingsequence of martensitephase in Fe-Mn-AI~2 alloy Stacking sequence Stacking event Stacking probability (%)

6~ 3 6

5~ 7 13

4~ 12 22

Total atomic layer Average stacking sequence

4"i" 7 13

33" 1 2

3~ 7 13

3"1" 11 20

2"i5 9

1T 1 2

282 layers (60.6 nm) 18R (4.1915, 1.8085)3

which is very close to 18R(4~)3. The martensite phase can, therefore, be regarded as an 18R(4~)3 structure with a stacking fault density equal to 0.096. This stacking fault density is calculated from the number of extra (0, 0, 18)18R stacking faults relative to the perfect 18R(4~)3 structure. This representation will be discussed further. Theoretical calculation o f martensitic crystallography for b.c.c, to 18R(42) s F r o m the above analyses of the diffraction pattern and the high resolution image, the crystal structure of martensite in the F e - M n - A 1 - C alloy can be described as an 18R(4~)3 structure rather than an 18R(5-f)3 structure. The crystallography for the 18R(4)-) 3 martensite is therefore discussed in this section. The martensitic crystallography for the 18R(5~3 structure will be compared and discussed in the next section. It is well known that the theory of martensitic transformation crystallography is based on the assumption that there should be no average distortion

at the matrix/martensite interface (i.e. at the habit plane). From this basic condition, crystallographic features such as habit plane, orientation relationship, shape deformation and the magnitude of the lattice invariant shear can be calculated. Kajiwara applied the Suzuki method to calculate the martensitic crystallography of b.c.c, to 9R(2-i')3 structure in C u - Z n or Cu-A1 alloys [22]. Chen and Olson [16] applied the CRAB [24] theory to calculate the martensitic crystallography for a Cu-Zn alloy and similar results to Kajiwara's were obtained. In this paper, the CRAB theory is applied to calculate the martensitic crystallography for b.c.c./18R martensite in the F e - M n A1-C alloy, to compare with the crystallography obtained from TEM. In the previous section, the 18R(4~) 3 close-packed structure was conveniently expressed as an orthorhombic lattice with c-axis perpendicular to the close-packed plane and lattice constant ratio alsR:blsR: C18R close to x/~: 1: 6x/~. The lattice deformation of b.c.c, to 9R martensite was first proposed

[001

[i0~]bcc

[100118R(~)3

[100~RCST)s

"0": atoms in the paperplane. "O": atoms above or belowthe paperplane.

Ca)

Co)

(~)

Fig. 6. Schematic lattice deformation of the b.c.c, to 18R structure. (a) b.c.c, lattice viewed from [0T0]b..... direction, (b) 18R(4~ 3 lattice viewed from [010]tga(4~)3 direction, and (c) 18R(5-1")3 lattice viewed from [010]~SR(ST)3 direction. Solid lines express the corresponding atom positions after the b.c.c, lattice transformed (shear) into the 18R lattice. Dash lines represent the 18R lattice cell.

LEE et al.:

by Nishiyama and Kajiwara [25]. Using a similar lattice deformation for b.c.c./18R martensitic transformation, the vector ab.¢.c.[-i-0T], ab.c.¢.[0]'0], and ab.c.~.[T'O,0, 8] in the b.c.c, phase are transformed into alsR[100], blsR[010], and ClSR[001] in the 18R martensite phase. The relation is depicted in Fig. 6(b) for b.c.c, to 18R(4~)3 and in Fig. 6(c) for b.c.c, to 18R(5]-)3 martensitic transformation. F r o m Fig. 6(b) the lattice correspondence matrix 18RCb.c.¢.for b.c.c./18R(4~)3 used in martensite crystallographic theory can be expressed as

I]

=

lsRCb .....

w 18R

v

LW/b.cx.

0 -1

-

Table 2. Theoretical relationship between planes or directions in F e - M n - A I - C alloy during martensitic transformation B.c.c.

18R(4]~)3

Calculated angle (deg.)

(01 l) (ll0)

(1-i-8) 0-T~)

0.35° 5.42°

(I01)

(~0~

6.24 °

001)

(0018)

5.53°

0"10) (0TI)

(1 T 10) 0"18)

7.04 ° 13.9 °

fliT]

llTOl

0.98°

I l l 11

[iT0I

12.23 °

lift]

[19-1l

0.55°

[Till

['i'-~1]

10.38 °

(1)

where [u v W]b..... and [u v W]lsR are the vectors of the b.c.c, and 18R structures, respectively, and

18R Cb.c.c. : ~

27

MARTENSITE IN Fe-Mn-AI-C

18 0

Based on the stacking of close packed planes, we assume the lattice invariant shear direction is [10 lib..... (or [T00hSR) and the plane of lattice invariant strain is (T01)b..... [or (001)~SR]. The lattice invariant shear corresponds to a set of anticoherency dislocations at the martensite interface [26]. Figure 7 are the bright field images of interfacial dislocations using the diffraction conditions g = (10T)b...... g = (110)b.c.c and g = (0]']')b...... respectively. The spacing of the interfacial dislocations is measured to be 7.3 ___2 nm. The interfacial dislocations are out of contrast in the diffraction condition g = (10T)b.~.~' shown in Fig. 7(a). By applying the g . b rule, the Burgers vector of interface dislocation may thus be the same as the assumed lattice invariant shear direction [101]b.c.~.. Using the lattice correspondence ~SRCb..... and the lattice invariant shear as an input for the calculation of CRAB martensitic crystallography, the final lattice deformation matrix ~sRSb..... and the crystallography of martensite can be obtained. They are given as follows

[:]

= 18RSb .....

w 18R

Iul

(2)

/)

Lw_lb.~.c.

where lsRSb.c.c.=

1.0195625

--0.0141548

0.1581624 1.1508770

--0.8855700 -- 0.1091620

--10.01558] --0.91809 / • 8.74663_]

(3) Equation (2) gives the relationship between the directions of b.c.c, and 18R martensite. The relationship between planes (h k l)b ..... and (h k l)18R can then be expressed as (hkl)b.¢.c. = ~ ( h k l ) l s R

[

-7.6817830 x [-0.3194280 L - 1.0147577

1.191652 -20.016720 -0.093018

-8.6711532] -2.4673860 / . 0.8861901J

(4)

Fig. 7. Interface dislocation images using (a) g = (10l-)b ...... (b) g = (110)b...... and (c)g = (0]-i')b..... respectively.

F r o m equations (3) and (4), the relationship between some important planes and directions can be obtained and are shown in Table 2. F r o m Table 2, it can be seen that []-l]-]b..... is approximately parallel to

28

LEE

.

.

.

.

.

.

.

et al.:

MARTENSITE IN Fe-Mn-AI-C

.

Fig. 8. Diffraction contrast fringes using (a) g = (ll0)b..... and (b) g = (01-i]b...... respectively.

[1To]tsR and (011) b..... approximately parallel to (TT8)~srt. This is consistent with the experimental orientation relationship from Fig. 4. This orientation relationship is also similar to those in Cu-Zn and Cu-A1 alloys [25]. They are [1T1]b.cc.[I[T10]gR and (01 l)b.c.c. II(114)9 a .

From the CRAB crystallography calculation, the magnitude of lattice invariant shear g is 0.0144 corresponding to a predicted anticoherency dislocation spacing of 10.6nm which is within the measurement error of the observed dislocation spacing in Fig. 7. The calculated shape strain direction is [0.0891, -0.7207, 0.6875]b ..... with a shape strain magnitude of 0.2522. The shape strain direction can be determined experimentally using the two-beam technique at the tip of the martensite together with computer image simulation [16]. Figure 8(a) and (b) are two bright field images of the martensite tip recorded from g = (ll0)b ..... and (01T)b...... respectively. The average spacing of the fringe depends on the absolute magnitude of g . R0 [16]. The R0 is a shear displacement vector. Since the martensite tip is tapering, the martensite thickness and therefore the total displacement vary. As depicted in Fig. 9(a), the total displacement R can be expressed as nR0, where n is the martensite thickness in number of (011)b ..... lattice plane. The fringe contrast in the martensite tip can be called displacement variation contrast. This contrast can be simulated using the scattering matrix method and is depicted in Fig. 9(b). From the computer simulation, it can be seen that the smaller value of Ig "R01 gives a wider spacing of the displacement variation fringes. The contrast behavior of the bright field images in Fig. 8 is consistent with a displacement vector close to the predicted shape strain direction. The solution of habit plane from the calculation of martensitic crystallography is (1, 6.303, 7.7119)b ..... which is very close to that determined from experiment. The crystallographic information is summarized in a stereographic projection shown in Fig. 10.

+ i?

W=0.1

nl R W=I.0

g ' R 0 = 1/8

(a)

g-R0 = 2/8

g.R0 = 3/8

Co)

Fig. 9. (a) Assumed tapering martensite plate in the tip and (b) computer simulated displacement variation contrast. "W" is the excitation error.

29

LEE et al.: MARTENSITE IN Fe-Mn-A142

~00~,

0 1 ° ) b ~ (1 lO)b

(o,ots)m. (]'Ol)b

[~]-l]b

['-[~i] b

habit plane h'ace

(0tl~,

(oT%

•

[011]b

fO'OJm

[%oL ,(o1%

(168)b q'("]25")m

t~ooL/

o?J. .

~,

e /

/

/ (110~/ trace

~

/ (10%

m : 18R(42)3 martensite b : bcc

Fig. 10. Stereographic projection of b.c.c, to 18R(4~)3 martensitic transformation.

The (0, 0, 18)18Rbasal plane trace and the habit plane trace are shown as well as the Burgers vector of the anticoherency dislocations and the shape strain direction. Comparison of martensitic crystallography for different martensite structures Based on Fig. 6(c), the ab.c.c.[TOT], ab.c.c.[010], and ab.¢.c.[11, 0, 7] vectors in the b.c.c, parent phase transform into alsR[100], blsR[010], and ClSR[001] of the 18R(5T)3 martensite phase. Assuming the same lattice invariant shear for a b.c.c, to 18R(5])3 martensitic

transformation, the martensitic crystallography can also be computed using the CRAB theory. The comparison of martensitic crystallography for b.c.c./ 18R(4~)3 and b.c.c./18R(5]') 3 martensite is given in Table 3. It can be seen that the b.c.c./18R(5])3 martensite yields the same habit plane and shape strain direction as the b.c.c./18R(4~)3 martensite. However, the magnitude of lattice invariant shear for 18R(5]')3 martensite is 0.0968 compared to 0.0144 for the 18R(4~)3 structure. The relation of martensite crystallographic theory to the coincidence-site lattice (CSL) theory originally

Table 3. Theoretical comparisonof 18R(4~)3 and 18R(51)3 martensite structures in Fe Mn-AI-C alloy Structure type 18R(4'2)3 18R(5T)3 Habit plane ( 1, 6.303,7.712)b.c.c" (1, 6.303,7.712)b Direction of shape s t r a i n [0.089,-0.721,0.688lb.cc. [0.089,-0.721, 0.688]b.c.c Magnitude of shape strain 0.2522 0.2522 Magnitude of lattice invariant shear (g) 0.0144 -0.0968 1.009 0.014 0.01] [ 0.953 0.014 0.067] Lattice deformation matrix ]-0.019 0.886 -0.139[ [-0.011 0.886 -0.148/ [_ 0.026 0.109 1.125J I_-0.038 0.109 1.189J .....

AM 4 3 / 1 ~

30

LEE et al.: MARTENSITE IN Fe-Mn-A1-C

developed for grain boundaries has been discussed by Balluffi and Olson [27]. When a system is near several possible CSL conditions, the choice of CSL reference (or "secondary correspondence" [27]) will determine the exact description of interface as "secondary" dislocation arrays. The 18R(4~)3 and 18R(5T)3 structures depicted in Fig. 6 represent perfectly periodic CSL reference lattices, each of which can be derived by periodic faulting of a simple 3R structure. Exact invariant plane condition described by CRAB theory can not be met by these perfectly periodic structures. Hence actual structure observed in Fig. 5 and summarized in Table 1 is quasiperiodic with an irrational total fault density as demanded by calculations of Table 3. The distribution of faults summarized in Table 1 shows comparable frequencies of single and double faults, and so this aspect of structure does not discriminate between the 18R(4~)3 and 18R(51)3 structures as the better reference state. As overall fault density represented by the average (4.1915, 1.8085)3 structure is closer to the (4~)3 structure, the latter gives a "secondary" dislocation description which is in best agreement with the diffraction contrast images. This then corresponds to the best "nearCSL" description of martensite interfacial structure and associated internal substructure.

CONCLUSIONS The lattice constants of the 18R martensite in the Fe-25.8 wt% M n - 7 . 4 wt% A1-0.11 wt% C alloy are determined to be a~8R= 0.448 rim, b~8a = 0.259 nm, and ClSR= 3.865 nm. The crystal structure determined from the SAD and high resolution imaging techniques can be best described as an 18R(4~)3 rather than an 18R(5T)3 structure. The stacking fault density relative to 18R(4~)3 martensite is determined from high resolution imaging to be 0.096. The martensite crystallographic parameters such as orientation relationship, habit plane, shape strain direction and magnitude of lattice invariant shear have been calculated using the CRAB crystallographic theory. The predicted orientation relationship of b.c.c./18R(4~3 is near (011)b.e.c.//(TT8)IgR and 0-1"l-]b.~.c.//[1T0]~sR. The habit plane is (1, 6.303, 7.7119)b ..... and the shape strain direction is [0.0891, - 0 . 7 2 0 7 , 0.6875]b ..... with the magnitude of 0.2522. The Burgers vector of anticoherency dislocations and the shape strain direction were confirmed using the two beam technique and computer image simulation. The calculated magnitude of lattice invariant shear g = 0 . 0 1 4 4 agrees well with an observed anticoherency dislocation spacing. Overall, the calculated crystallography fits very well with the experimental observation by TEM. It is concluded that the 18R(4~)3 structure is the best representation of

the martensite structure as a near-CSL reference state. Acknowledgements--The authors would like to acknowledge the support from Materials Science Center. S.K.C. and W.B.L. gratefully thank the financial support by the National Science Council of R.O.C. under grant No. NSC810405-E-007-53 I. F.R.C. thanks the support by the National Science Council of R.O.C. under grant No. NSC82-0208-M007-166. GBO appreciates the support from NSF under grant 8820116. The support of Mrs H. T. Chiu in maintaining JEOL-4000EX TEM is also appreciated. REFERENCES

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