Cold Rolling Texture of Ni Based L12 Ordered Intermetallic Alloys

(1)

Cold Rolling Texture of Ni-Based L1

₂

Ordered Intermetallic Alloys

Yasuyuki Kaneno, Akira Takahashi

*

_{and Takayuki Takasugi}

Department of Materials Science, Graduate School of Engineering, Osaka Prefecture University, Sakai, 599-8531 Japan

Cold rolling textures of three kinds of Ni-based intermetallic alloys with L12ordered structure (i.e., Ni3(Si,Ti), Ni3Al, and Ni3Fe) were

investigated by the orientation distribution function (ODF). For comparison, the rolling texture of pure nickel with fcc disordered structure was also determined. The rolling textures of the 70% and 90% cold-rolled L12alloys as well as fcc nickel are composed of the-ﬁber ({011}h100i

(G){011}h211i(Bs)) and-ﬁber ({112}h111i(C){123}h634i(S){011}h211i(Bs)) components, but the {011}h211i(Bs) (and also the {011}h100i(G)) orientation is remarkable in the L12alloys while the {123}h634i(S) (and also the {112}h111i(C)) orientation is prominent in

fcc nickel. Moreover, the intensity of rolling texture in the L12alloys depended on materials (i.e., constituent elements). The observed rolling

texture of the L12ordered alloys was discussed in terms of cross slips of extended dislocations whose width was estimated by the energies of

stacking-fault-like defect (SFLD) (i.e., antiphase boundary (APB) in the case of L12ordered structure and stacking fault (SF) in the case of fcc

disordered structure). [doi:10.2320/matertrans.47.1485]

(Received December 8, 2005; Accepted April 7, 2006; Published June 15, 2006)

Keywords: intermetallic alloy, ordered alloy, deformation texture, cross slip, orientation distribution function

1. Introduction

There are many kinds of Ni3X type intermetallic ordered alloys. Among them, Ni3Al and Ni3(Si,Ti) ordered alloys

with L12 crystal structure, which is derived from A1 (fcc)

structure, have attracted considerable attention because these ordered alloys show a positive temperature dependence of

yield strength (i.e., high strength at elevated temperatures)

and also good properties in oxidizing and corrosive

atmo-sphere.1,2)In addition, by micro-3)and macro-alloying,2)both

the polycrystalline Ni3Al and Ni3(Si,Ti) alloys can be

plastically deformed in air at ambient temperature,3,4)

where-as most of intermetallic compounds suﬀer from a limited

ductility at ambient temperature. On the other hand, Ni3Fe

shows order (L12)disordered (fcc) transition at Tc¼

776K and the ordered Ni3Fe as well as the disordered one

exhibits a considerable tensile ductility at ambient

temper-ature.5)_{Therefore, microstructure control by}

thermomechan-ical processing is applicable to these deformable ordered alloys. Microstructural factors such as grain size, crystallo-graphic texture and grain boundary character, which notice-ably aﬀect material properties are substantially changed through the thermomechanical process. Previous studies on

deformation texture for Ni-based L12 ordered alloys have

been mostly focused on Ni3Al doped with boron,6–10)but few

studies for other Ni-based L12 ordered alloys have been

conducted so far.11) _{A comprehensive understanding for}

texture development during cold rolling of L12ordered alloys

is much needed not only in the scientiﬁc interest but also in the practical application of intermetallic compounds.

In the present study, polycrystalline Ni3Al, Ni3(Si,Ti) and

Ni3Fe ordered alloys with L12 structure, together with pure

nickel with fcc structure, were cold-rolled to 90% reduction. The cold rolling textures were investigated in terms of the ordered state and the constituent elements. Further, the

texture development during cold rolling of L12ordered alloys

was discussed in association with cross slips of extended

superlattice dislocations whose width was calculated by using the reported values of stacking-fault-like defect

(SFLD) energies (i.e., antiphase boundary (APB) energy in

the case of L12 ordered structure and stacking fault (SF)

energy in the case of fcc disordered structure).

2. Experimental

Raw materials used in this study were 99.9 mass% nickel, 99.999 mass% silicon, 99.9 mass% titanium, 99.99 mass% aluminum, 99.99 mass% iron and 99.5 mass% boron. A

Ni3(Si,Ti) alloy with a nominal composition of 79.0 at% Ni,

11.0 at% Si, 10.0 at% Ti and 50 mass.ppm B, a Ni3Al alloy

with a nominal composition of 76.0 at% Ni, 24.0 at% Al and

500 mass.ppm B, and a stoichiometric Ni3Fe alloy with a

nominal composition of 75.0 at% nickel and 25.0 at% Fe were prepared by arc melting in an argon gas atmosphere on a copper hearth using a non-consumable tungsten electrode. Homogenization heat treatment was conducted in a vacuum at 1323 K for 48 h for Ni3(Si,Ti) and Ni3Al, and at 1373 K for 48 h for Ni3Fe, followed by furnace cooling. Homogenized ingots were rolled at 573 K for Ni3(Si,Ti) and Ni3Al, and at room temperature for Ni3Fe, and then annealed at 1273 K for

5 h for Ni3(Si,Ti) and Ni3Al, and at 1023 K for 2 h for Ni3Fe,

respectively. This procedure was repeated several times until

a desired thickness (4{5mm) was obtained. To obtain

starting material, the rolled material was ﬁnally annealed at

1273 K for 5 h (Ni3(Si,Ti) and Ni3Al), and at 1023 K for 2 h

(Ni3Fe), respectively. Further, for Ni3Fe, the ordered

speci-men was prepared by annealing at 743 K for 30 days followed by furnace cooling. The degree of long-range order obtained in the ordered Ni3Fe specimen is assumed to be

approx-imately more than 0.9.12,13)_{For comparison, a fully-annealed}

commercially available pure nickel with purity of 99.7 mass% was also used. These starting materials were cold-rolled at room temperature to 70% and 90% reduction. Deformed microstructure in the longitudinal sections of specimens was observed by an optical microscope. Textures in a central layer along the thickness of a sheet were

measured by CuKradiation. Three incomplete pole ﬁgures,

(2)

{111}, {200} and {220} were measured up to a maximal tilt

angle of 75_{by the Schultz reﬂection method}14)_{and corrected}

with respect to defocusing error by using the randomly oriented powder sample. From these pole ﬁgures, the complete orientation distribution functions (ODFs) including odd terms for ghost correction were determined up to an

order of l¼22 by the iterative series expansion method,

using positivity conditions in pole ﬁgures and an ODF.15,16)

3. Results

The starting materials before cold rolling show a fully-recrystallized microstructure and have almost no preferential

orientation (i.e., random texture). Initial grain sizes of L12

ordered alloys are in the range of100{200mmwhile those

of fcc nickel are less than100mm. Figure 1 shows optical

micrographs of the longitudinal section of the 70% cold-rolled materials. Obviously, inhomogeneously deformed

microstructures are evolved in the Ni3(Si,Ti), Ni3Al and

Ni3Fe ordered alloys while homogeneously elongated grains

along rolling direction are developed in pure nickel. For

Ni3(Si,Ti), Ni3Al and Ni3Fe, shear bands are extensively

formed. These shear bands are mostly extended across several grains, and have been repeatedly observed in rolled

Ni3Al by other researchers.7,9,10) _{A similar feature of the}

deformed microstructures are observed in the 90% cold-rolled materials: the shear bands are more intensively formed in Ni3(Si,Ti), Ni3Al and Ni3Fe but not in pure nickel.

The’2sections of ODFs for the 70% and 90% cold-rolled

materials are given in Figs. 2 and 3, respectively. Some ideal orientations observed in the present materials are illustrated in Fig. 4. It is well known that rolling texture of

fcc materials is divided into two types,i.e. copper type(pure

metal type) andbrass type(alloy type), and also that nickel as

well as copper and aluminum typically show the copper type

rolling texture.17) The main features such as preferred

orientations and orientation spread in the rolling textures of

the L12 ordered alloys are basically similar to those for the

rolling texture of nickel, but the intensity of rolling textures is

signiﬁcantly lower in the L12 ordered alloys than in fcc

disordered nickel. Moreover, the intensity of the rolling

texture is diﬀerent among the L12 ordered alloys.

Figures 5(a) and (b) show texture index J18)₍_i.e._{, intensity}

of texture) for the 70% and 90% cold-rolled materials,

respectively. Texture indexJ, which is a single parameter to

characterize the intensity of texture, is deﬁned by the follows:

J¼

I

½fðgÞ2dg ð1Þ

Here, fðgÞ represents the orientation distribution function

(i.e., an orientation density) of the crystallites of a

poly-crystalline material. The texture indexJvaries between 1 in

the case of random orientation and1in the case of one or

more ideal single orientations.18)_{It is apparent from Fig. 5}

that the intensity of L12rolling textures decreases in the order

of Ni3(Si,Ti), Ni3Al and Ni3Fe, and also the discrepancy

among four materials becomes larger in 90% reduction than in 70% reduction.

The copper type rolling texture is known to be composed

of the-ﬁber that has orientation spread from the {011}h100i

(G) orientation to the {011}h211i (Bs) orientation, and

-ﬁber that runs from the {112}h111i(C) orientation, through

the {123}h634i (S) orientation, to the {011}h211i (Bs)

orientation.17)Figures 6 and 7 show the orientation density

along the - and -ﬁbers in the rolling textures for the (a)

70% and (b) 90% cold-rolled materials, respectively.

Gen-erally, the copper type rolling texture of the heavily (e.g.

more than 90% reduction) rolled metals and alloys consists of 100µm

100µm

(c)

RD ND

100µm

(b)

100µm

(a)

100µm

(d)

[image:2.595.118.485.72.334.2]

(3)

a weak -ﬁber and strong -ﬁber in which the S and C

orientations are stronger than the Bs orientation,19)as actually

observed in the 90% cold-rolled pure nickel (Fig. 7). For the 70% cold-rolled materials, the S and also C orientations are not so much developed compared with the Bs orientation

even in the case of nickel (Fig. 6b). For Ni3(Si,Ti) and Ni3Al,

the orientation distribution curves along the -ﬁber show a

peak at the Bs orientation and those along the-ﬁber show a

distinctive high orientation density from the G to Bs orientations, as clearly seen in Fig. 7. This result suggests that the texture transition from the copper type to brass type somewhat occurs in the Ni3(Si,Ti) and Ni3Al ordered alloys.

In the case of Ni3Fe, the trend for the - and -ﬁbers is

essentially the same as that for Ni3(Si,Ti) and Ni3Al though the orientation density in Ni3Fe is considerably low in comparison with that in Ni3(Si,Ti) and Ni3Al.

4. Discussion

The observed rolling textures of the cold-rolled Ni-based

L12 ordered alloys are composed of the - and -ﬁber

components. Basically, this textural feature is similar to that of fcc materials with medium or high stacking fault energy. In general, deformation texture is formed by crystal lattice rotation due to slip deformation. Slip system for L12-type

ordered structure is the same as that for fcc structure, i.e.

h101i{111}. Therefore, it is deduced that deformation texture

developed in L12ordered alloys is fundamentally the same as

that developed in fcc materials.

When comparing rolling textures of the L12ordered alloys

with those of fcc disordered nickel, intensity and main component of rolling textures are diﬀerent between them.

First, intensity of the rolling textures in the L12 ordered

alloys is low in comparison with that in the fcc disordered

nickel. Secondly, the Bs and also G orientations (i.e.,-ﬁber)

are prominent in the L12 ordered alloys while the S and C

orientations (i.e., a typical main component of the-ﬁber in

heavily rolled copper, aluminum and nickel, etc.) are marked in fcc nickel. The diﬀerence in the observed rolling textures

between the L12ordered and fcc disordered materials seems

Ni3(Si,Ti)

CR 70% Fmax=7.8

ϕ1

(a)

Levels: 1, 2, 3, 4, 5, 6, 7

Ni3Al

CR 70% Fmax=5.6

ϕ1

Φ

(b)

Levels: 1, 2, 3, 4, 5

Φ

Ni3Fe

CR 70% Fmax=2.9

ϕ1

(c)

Levels: 1, 2

Ni CR 70% Fmax=9.9

(d)

Levels: 1, 2, 3, 4, 5, 6, 7, 8, 9

ϕ1

Φ Φ

Fig. 2 ’2sectionsð’2¼0;5;. . .;90Þof the orientation distribution functions (ODFs) of 70% cold-rolled (a) Ni3(Si,Ti), (b) Ni3Al,

[image:3.595.149.449.72.495.2]

(4)

to be associated with the diﬃculty of octahedral cross slips from {111} to {111} planes. The diﬃculty or the easiness of octahedral cross slip is closely related to the width of extended dislocations; the larger the width of extended dislocation becomes, the harder the octahedral cross slip becomes. The width of the extended dislocations is inversely proportional to the energy of the stacking-fault-like defect

(i.e., antiphase boundary in the case of L12ordered structure

or stacking fault in the case of fcc disordered structure). Consequently, it is deduced that the octahedral cross slip becomes easier and then the deformation texture becomes more intense with increasing energy of the stacking-fault-like defect.

Here, let us estimate the width of extended dislocations. It

has been reported that the superlattice dislocation h110i in

Ni3(Si,Ti),20) Ni3Al1) and Ni3Fe21) is dissociated into two

1/2h110i dislocations bounded for the antiphase boundary

(APB), while the dislocation 1/2h110i in fcc nickel is

dissociated into two Shockley partials 1/6h211ibounded for

the stacking fault (SF). These dissociation manners of

dislocations are expressed by the following schemes;

ah110i ¼a=2h110i þAPBþa=2h110i

(for L12 structure) ð2Þ

a=2h110i ¼a=6h211i þSFþa=6h121i

(for fcc structure) ð3Þ

Here,a is lattice parameter. The width (w) of the extended

dislocation for the L12ordered alloys is given as follows:22)

w¼ Gb

2

h

2APB

cos2’þsin

2_’

1

ð4Þ

Similarly,wfor fcc materials is given as follows:23)

w¼ Gb

2

h

8SF

2

1 1

2

2cos 2’

ð5Þ

Here, Gis the shear modulus, bh is the Burgers vector for

super partial dislocation in the case of L12ordered alloys and

for Shockley partial dislocation in the case of fcc material,

APBis the antiphase boundary energy per unit area,SFis the

Ni3(Si,Ti)

CR 90% Fmax=12.7

ϕ1

(a)

Levels: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12

Ni3Al

CR 90% Fmax=11.5

ϕ1

(b)

Levels: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Φ Φ

Ni3Fe

CR 90% Fmax=6.1

ϕ1

(c)

Levels: 1, 2, 3, 4, 5, 6

(d)

Levels: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12,14, 16

ϕ1

Ni CR 90% Fmax=18.2

Φ Φ

Fig. 3 ’2sectionsð’2¼0;5;. . .;90Þof the orientation distribution functions (ODFs) of 90% cold-rolled (a) Ni3(Si,Ti), (b) Ni3Al,

[image:4.595.149.449.73.494.2]

(5)

stacking fault energy per unit area,’is the angle between the dislocation and the Burgers vector of the perfect dislocation

(’¼0_{in the case of screw dislocations and}_’_¼₉₀ _{in the}

case of edge dislocations),is the Poisson’s ratio (¼1=3

was used in the present calculation). The lattice parameters

(a) of Ni3(Si,Ti), Ni3Al Ni3Fe and nickel are 0.3552,24)

0.3572,25) _0.355026) _{and 0.3524 nm,}27) _{respectively.} _b

h is

given as a=pffiffiffi2 for the L12 alloys anda=

ffiffiffi

6

p

for fcc nickel,

respectively. The shear modulus (G) of Ni3(Si,Ti), Ni3Al

Ni3Fe and nickel has been reported as 84.7, 77.0, 79.2 and

86.5 GPa, respectively.28) _{Also, the values of}

APB for

Ni3(Si,Ti), Ni3Al and Ni3Fe have been reported to be 215

(35),29)_{180 (}₂₀₎30)_{and 133 (}₈₎21)_mJ/m2_{, respectively,}

while the value of SF for nickel has been reported to be

Fig. 4 Some ideal orientations in Euler angle space. 1 2 3 4 5 6 7

Ni Ni3Al Ni3(Si,Ti)

Ni3Fe

Texture index,

J

1 2 3 4

Ni Ni3Al Ni3(Si,Ti)

Ni3Fe

Texture index,

J

(a)

(b)

Fig. 5 Texture index J18) _{for the (a) 70% and (b) 90% cold-rolled} materials.

45 60 75 90

0 2 4 6 8 10 12

Euler angle, ϕ2/deg.

{112}<111> (C) {123}<634> (S) {011}<211> (Bs)

Orientation density,

f

(

g

)

β-fiber

Ni

Ni3(Si,Ti)

Ni3Al

Ni3Fe

0 15 30 45 60 75 90

0 2 4 6 8 10 12

α-fiber Ni

Ni3(Si,Ti)

Ni3Al

Ni3Fe

{011}<100> (G) {011}<211> (Bs) {011}<011>

f

(

g

)

(a) (b)

[image:5.595.70.269.69.325.2] [image:5.595.327.528.79.362.2] [image:5.595.130.469.503.772.2]

(6)

128 mJ/m2.31)By using these values, the width of extended dislocations can be calculated from equations (4) and (5). The results are summarized in Table 1. It is apparent from Table 1 that the width of both screw and edge dislocations is

signiﬁcantly larger in the L12 ordered alloys than in fcc

disordered nickel. Also, it should be noted that the width of extended dislocations of the present Ni-based intermetallic alloys is considerably smaller than that of copper with

medium SF (80mJ/m2)31) in which width of extended

dislocations is estimated to be 1:1nm for screw

disloca-tions and 3:0nm for edge dislocations, respectively.32)

Actually, using by a transmission electron microscope (TEM), these widely extended (or dissociated) dislocations

have been observed e.g. for Ni3(Si,Ti),30) _Ni3Al33) _and

Ni3Fe34) deformed at low temperature. Furthermore, the

width of extended (screw) dislocations increases in the order of Ni (0.835 nm), Ni3(Si,Ti) (3.69 nm), Ni3Al (4.34 nm) and Ni3Fe (6.40 nm). This result is consistent well with the order of the intensity of the observed rolling textures (Fig. 5). As mentioned above, octahedral cross slips become more

diﬃcult with increasing width of the extended dislocations.

As a result, the development of the -ﬁber texture is

suppressed and alternatively the Bs (and G) orientation (the

-ﬁber texture) remains as a main component of rolling

textures in the L12 ordered alloys. Moreover, these

dis-sociated superlattice dislocation bounded for the APB may lead to unusual (and various) crystal lattice rotation in the

L12 ordered structure diﬀerent from that in fcc disordered

materials, resulting in weak deformation texture. It appears that such unusual crystal lattice rotation is a unique phenomenon in ordered intermetallic alloys in which widely extended superlattice dislocations are operated. Strictly describing, here, superlattice dislocations introduced in

ordered Ni3Fe show a four-fold dissociation scheme,21)_i.e._,

ah101i ¼a=6h211i þCSFþa=6h112i þAPB

þa=6h211i þCSFþa=6h112i

ðCSF: complex stacking faultÞ:

It is therefore considered that cross slips hardly occur and at the same time unusual (unexpected) crystal rotation occurs in this case.

The texture transition from the copper-type to brass-type

has been often related to deformation twins,35–37) _{as have}

been observed in -brass with a low stacking energy.

Concerning this point, TEM observations have been made so far and consequently, no deformation twins have been

observed for the 90% cold-rolled Ni3(Si,Ti)38) _{and for the}

cold-rolled Ni3Al.39)As far as the present authors know, there

are no previous works reporting the deformation twins activated in Ni3X type ordered alloys deformed at low temperature. Therefore, an idea that the deformation twin is closely associated with the formation of the texture in L12-type Ni3X ordered alloys is excluded from the realistic

45 60 75 90

0 2 4 6 8 10 12 14 16 18

{112}<111> (C) {123}<634> (S) {011}<211> (Bs)

f

(

g

)

β-fiber

Ni

Ni3(Si,Ti)

Ni3Al

Ni3Fe

0 15 30 45 60 75 90

0 2 4 6 8 10 12 14 16 18

α-fiber Ni

Ni3(Si,Ti)

Ni3Al

Ni3Fe

{011}<100> (G) {011}<211> (Bs) {011}<011>

f

(

g

)

(a) (b)

[image:6.595.130.468.66.340.2]

Fig. 7 Orientation densityfðgÞof orientations along the (a)-ﬁber and (b)-ﬁber for the 90% cold-rolled materials.

Table 1 Calculated width of extended dislocations for Ni3(Si,Ti), Ni3Al,

Ni3Fe and nickel. Values of lattice parameter (a), the Burgers vector (bh),

shear modulus (G), stacking fault energy (SF) and antiphase boundary energy (APB) quote from the literatures.

Ni3Fe Ni3Al Ni3(Si,Ti) Ni

a(nm) 0.355224Þ _0.357225Þ _0.355026Þ _0.352427Þ

bh(nm) 0.2512 0.2526 0.2510 0.1439

G(GPa) 84.728Þ _77.028Þ _79.228Þ _86.528Þ

SF(mJ/m2) — — — 12831Þ

APB(mJ/m2) 13321Þ 18030Þ 21529Þ — w(screw,’¼0_{) (nm)} _6.40 _4.34 _3.69 _0.835

[image:6.595.46.291.428.528.2]

(7)

explanation. On the other hand, inhomogeneous deformation such as shear banding may result in a weak deformation texture. It has been reported that grains formed by shear bands have widely spread grain orientations, resulting in a weak cube recrystallization textures for polycrystalline fcc

copper.40) _{However, to furthermore clarify the rolling}

textures in the L12 ordered alloys, more extensive studies,

particularly on the deformed microstructures, are required.

5. Conclusion

Polycrystalline Ni3(Si,Ti), Ni3Al, and Ni3Fe alloys with

L12 ordered structure, together with pure nickel with fcc

disordered structure, were cold-rolled up to 90% reduction and then rolling textures were determined. The rolling texture

of the 70% and 90% cold-rolled L12alloys was composed of

the - and-ﬁber components similar to that of fcc nickel,

but the {011}h211i (Bs) (and also the {011}h100i (G))

orientation is remarkable in the L12 alloys while the

{123}h634i (S) orientation is prominent in fcc nickel

Moreover, the intensity of rolling texture in the L12 alloys

depended on materials (i.e., constituent elements): the

intensity of the rolling texture increases in the order of nickel, Ni3(Si,Ti), Ni3Al and Ni3Fe. These results can be interpreted by consideration of cross slips for superlattice dislocations and ordinary dislocation whose width are estimated by energies of stacking-fault-like defect (SFLD)

(i.e., antiphase boundary (APB) in the case of L12 ordered

structure and stacking fault (SF) in the case of fcc disordered structure).

Acknowledgements

This work was supported in part by the Grant-in-aid for Scientiﬁc Research from the Ministry of Education, Culture, Sports and Technology, Japan.

REFERENCES

1) N. S. Stoloﬀ and C. T. Liu:Physical Metallurgy and Processing of Intermetallic Compounds, edited by N. S. Stoloﬀ and V. K. Sikka (Chapman & Hall, New York, N.Y., 1996) pp. 159–211.

2) T. Takasugi, M. Nagashima and O. Izumi: Acta Metall. Mater. 38

(1990) 747–755.

3) K. Aoki and O. Izumi: J. Japan Inst. Met.43(1979) 1190–1196. 4) T. Takasugi, S. Rikukawa and S. Hanada: Acta Metal. Mater.40(1992)

1895–1906.

5) H. Sakurai, H. Makita, S. Hanada and O. Izumi:Proc. of Recrystal-lization ’90, edited by T. Chandra (The Minerals, Metals and Materials Society, Warrendale, PA, 1990) pp. 623–628.

6) G. Gottstein, G. P. Nagpal and W. Kim: Mater. Sci. Eng.A108(1989) 165–179.

7) J. Ball and G. Gottstein: Intermetallics1(1993) 171–185.

8) C. Escher, S. Neves and G. Gottstein: Acta Mater.46(1998) 441–450. 9) S. G. Chowdhury, R. K. Ray and A. K. Jena: Mater. Sci. Eng.A277

(2000) 1–10.

10) B. Bhattacharya and R. K. Ray: Metall. Mater. Trans.31A(2000) 3011–3021.

11) Y. Kaneno, I. Nakaaki and T. Takasugi: Intermetallics10(2002) 693– 700.

12) D. G. Morris, G. T. Brown, R. C. Piller and R. E. Smallman: Acta Metal.24(1976) 21–28.

13) T. Takasugi, T. Eguchi, M. Yoshida and O. Izumi: J. Japan Inst. Met.53

(1989) 34–41.

14) L. G. Schulz: J. Appl. Phys.29(1949) 1030–1033.

15) M. Dahms and H. J. Bunge: J. Appl. Crys.22(1989) 439–447. 16) H. Inoue and N. Inakazu: J. Jpn. Inst. Metals58(1989) 892–898. 17) F. J. Humphreys and M. Hatherly: Recrystallization and Related

Annealing Phenomena(Elsevier Science, Oxford, U.K., 1995) pp. 44– 49.

18) H. J. Bunge: Texture Analysis in Materials Science (Butterworth, London, U.K., 1982) p. 88.

19) J. Hirsch and K. Lu¨cke: Acta Metall.11(1988) 2863–2882. 20) M. Yoshida and T. Takasugi: Phil. Mag.A65(1992) 41–52. 21) A. Korner and H. P. Karnthaler: Phil. Mag.A52(1985) 29–38. 22) N. S. Stoloﬀ:Strengthening Methods in Crystals, edited by A. Kelly

and R. B. Nicholson (Elsevier Publishing Company, LTD, Amsterdam, Holland, 1971) p. 206.

23) L. E. Murr: Interfacial Phenomena in Metals and Alloys (Addison-Wesley Publishing Company, Reading, Mass., 1975) p. 144. 24) T. Takasugi, O. Shindo, O. Izumi and M. Hirabayashi: Acta Metal.

Mater.38(1990) 739–745.

25) N. Masahashi, T. Takasugi and O. Izumi: Acta Metall.36(1988) 1815– 1822.

26) T. Takasugi, T. Eguchi. M. Yoshida and O. Izumi: J. Japan Inst. Met.53

(1989) 34–41.

27) Selected Powder Diﬀraction Data for Metal and Alloys, edited by S. Weissmann (JCPDS International Centre for Diﬀraction Data, Swarthmore, PA, 1978) p. 91.

28) H. Yasuda, T. Takasugi and M. Koiwa: Acta Metal. Mater.40(1992) 381–387.

29) K. J. Hemker and M. J. Mills: Phil. Mag.A68(1993) 305–324. 30) M. Yoshida and T. Takasugi:Strength of Materials, ed. by H. Okikawa,

K. Maruyama, S. Takeuchi and M. Yamaguchi (Japan Institute of Metals, Sendai, Japan, 1994) pp. 357–360.

31) L. E. Murr: Interfacial Phenomena in Metals and Alloys (Addison-Wesley Publishing Company, Reading, Mass., 1975) p. 146. 32) A. Seeger and G. Scho¨ck: Acta Metall.1(1953) 519–530.

33) P. Veyssiere and J. Douin: Intermetallic Compounds, ed. by J. H. Westbrook and R. L. Fleischer (John Wiley and Sons, New York, 1995) p. 519.

34) A. Korner: Acta Metal.33(1985) 1399–1406. 35) V. G. Wassermann: Z. Metallk.54(1963) 61–65.

36) H. Hu, R. S. Cline and S. R. Goodman: Recrystallization, Grain Growth and Textures, (American Society for Metals, Metals Park, Ohio, 1965) pp. 295–367.

37) J. Hirsch, K. Lu¨cke and M. Hatherly: Acta Metall.36(1988) 2905– 2927.

38) Y. Kaneno and T. Takasugi: unpublished work.

39) K. Kishida, M. Demura and T. Hirano: Mater. Res. Soc. Symp. Proc.

842(2005) 85–91.