ORIENTATION KELATION OF CRYSTAL LATTICES OF PHASES IN

TEXTURED POLYCRYSTALS

Z. A. Bryukhanova UDC 669.018.2-13-156:620.183

Some of the experimentally determinable characteristics of the martensitic transforma- tion are the orientation relations (OR) of the phases. The number of variants of OR that can be realized in a martensite transformation determines the number of orientations of marten- site formed in the austenite grain and affects the structure of the martensite packet [i].

The orientation relation of the crystal lattices of phases can usually be studied more easily on single crystals or in individual fairly large grains. In practice martensitic transformations frequently occur in pelycrystalline materials in which realization of the OR variants may be complicated by the influence of transformation processes in neighboring grains. This limits the possibility of the phenomena observe4 in single crystals being transferred directly to polycrystalline solids.

In polycrystalline aggregates martensitic transformations manifest themselves crystalio- graphically in changes in the textural characteristics of the end phase, the OR variants re- alized, and the form of the thermomechanical treatment (TMT). By virtue of this, the known OR between phases during martensitic transformations can be used to calculate the texture of the phase formed if the texture of the matrix phase is known and conversely, the correlation of the calculated preferred orientations with the experimental textural characteristics makes it possible to determine the realizable OR variants in each concrete alloy.

In this paper we calculate the characteristics of possible textures of martensite formed from textured austenite with the condition that the Kurdyumov-Zaks (K--Z) OR is realized and we analyze the possibilities of using them to ascertain the orientation relation of austenite and martensite for 13KhI8N7 steel.

For the initial textures we took the deformation and recrystallization textures for fcc metals [2] as well as the testures of austenite of 13KhI8N7 steel, which we obtained experi- mentally after various TMT regimes. All told, 30 initial orientations were analyzed.

Auxiliary constructions for solving the problem posed were carried out on the Wulff net. For instance to determine the characteristics of the texture of martensite formed from austenite wiah a (123) [iii] orientation, we proceed as follows. On the stereographic pro- jection of a cubic crystal with the (00]) plane in the center of the projection circle we mark the position of the (123) face and the [III] direction. Assuming that the KZ OR vari- ant (lll)y il (Oll)e and [i01]u II[IYI]a is realized in the 7 + a transformation, we turn the crystal so that the (iii)u plane comes out at the center of the projection (Fig. i). Then the entire a-cube turns about the AA' axis through an angle of 54.7 ~ The (123) plane and the [ili] direction occupy the positions marked in Fig. i. The [10~]y direction, lying in the (lll)a plane, comes out on the basic circle of the projection. Next we take the stereographic projection for the a-cube with the (011) plane at the center of the circle of projections. We combine the two stereographic projections of the y- and m-cubes so that the [i01]u and [iii]~ directions coincide. On the stereographic projection of the a-cube we mark the plane parallel to the (123)y plane and the direction parallel to [Iii]7 and we de- termine their indices. In Fig. 2 it is shown that with the condition that the indicated K--Z OR variant is realized, the (~ i0 5) plane of the martensite is positioned parallel to the (123) plan~_of the austenite while the [503] plane of the martensite is positioned par- allel to the [iii] direction of the austenite. That is to say, when the chosen OR variant is realized, the martensite texture (~ IO 5) [503] is formed from the (123) [[[i] texture of the austenite. Similar constructions were made for all the initial textures of austenite. In

Technological Institute of the Refrigeration Industry, Odessa. Translated from Izves- tiya Vysshykh Uchebnyh Zavedenii, Fizika, No. 3, pp. 85-88, March, 1983. Original article submitted February 23, 1982.

0038-5697/83/2603-0285507.50 �9 1983 Plenum Publishing Corporation 285

A

Fig. i Fig. 2

calculating the characteristics of the martensite texture we assumed equiprobable realization of all 24 variants of K--Z orientation relations, i.e., for each component of the austenite texture we obtained 24 possible variants of martensite texture. Table I gives* the marten- site textures formed from the (123) [Iii] textures of austenite.

Analysis of the calculated data shows that the existence of an orientation relation be- tween the lattices of the y- and s-phases should result in specific textures, unlike the de- formation textures of bcc metals and alloys, being formed in the bcc phase. With the condi- tion that the realization of all K--Z OR variants during the martensitic transformation is equiprobable, according to the data obtained, we observe a marked weakening of the texture (transition to a multicomponent texture). In cases when the values of some of the indices i, k, I and u, v, w in the initial textures coincide or are zero we obtain a set of crystal- !ographically equivalent textures, i.e., a smaller number of martensite textures correspond to the realization of the 24 OR variants. For instance, 12 independent martensite textures correspond to the (112) [ii~] austenite orientation, six independent martensite textures correspond to the (001) [i~0] orientation, while the number of independent martensite tex- tures decreases to three for the (001) [I00] orientation.

From the data obtained it also follows that if a smaller number of OR variants (not all 24) are realized during the y + y transformation, then a smaller number of components of the martensite texture should be observed. Thus, depending on the OR variants realized, the type of martensite texture and the degree of its dissipation will change.

We studied the influence of hot deformation on the formation of cooling martensite and deformation martensite in 13KhlSN7 steel. After austenitization at I050-II00~ the steel specimens were subjected to hot rolling followed by air cooling in order to obtain cooling martensite. Deformation martensite was obtained by cold rolling previously hot-rolled steel. The degree of deformation was 50-70%. In the steel after both forms of treatment, besides cooling martensite and deformation martensite a fair amount of residual austenite was pre- served, which made it possible to study the textures of austenite and martensite simultane- ously on one and the same specimen.

The pole figures (PF) determined for the {lll}y and {200}~ planes showed that the hot rolling Jextures of a~stenite are multicomponent: the (iii) [ii~], (iii) [011], (001) Ill0], (001) [210], (011) [011], and (416) [302] orientations are among the strong ones. There also are weak components inherent to the cold roiling textures of fcc metals.

The cold rolling texture of previously hot-rolled steel is characterized by the (001) [ll0], (011) [0~i], (112) [ill], and (123) []-ll] orientations. Components with the (IIi) plane in the rolling plane are veryweak.

Analysis of the PF determined for {ii0}~ and {200}~ gave the following results. The texture of cooling martensite is characterized by strong components with the (011) ~ane in common and the [3~i], [~il], [~il], [2ii], [0~I], [i00], [f3~], [2~3], [Iil], and [iii] di- rections. Also among the strong components are (001) [~0], [410], and (ii0) ([i0) [iil], [ill] and the (982), (982) [~3] [2~3] and (112) [Iil], as well as (112) [~65i and (338) [~3] that are the latter.

*The complete table of transformation textures for all the initial austenite orientations is not given because of its unwieldiness.

286

TABLE i. Martensite Textures Formed from (123) [1[I] Austenite Texture During Realization of 24 Variants of Kurdyumov--Zaks Orientation Relations

' No. of OR KZ orientation relatt~ Martcn~ite T e x n l r ~ s

'v'ari~t

l

2

4

5

7

8

IO

I I

I2

13

I4

I5

I6

r7

2O

2I

22

23

24

Orl III

o~I III

oi! III

Oil Ill

Oll Ill

Cll III

on l~i

011 ill

oI~ ~

oli I[~

on ~k Oil lil

oli I i I

o l i Iil

OlI II~

o~I ~

0!7 IIi

Cl! I I i

i [ r iOI

H~ o~ l~I lOl

!II II0

i [ : ~0~

ri~ Yo:

H~ Ho

"~l Oil

II! 011

r k :fo I~I 70~

TT !!I 0~

~o s so3 .... 487 514

5 :m o~z

~o s 5[4 355 ~o3

9 o n ~4 ~z2 o~z 0 i 0 5 0 3

~24 o~i ~fg~

3O5

IO0

325

6f65

512

13~

755

2II

g03

503

5I~

5T4 Oil'

0Tr

011 [

Ig8 0If

The texture of deformation martensite contains basic components with a common (012) plane or one close to it as well as the [051] direction or one close to it. Orientations close to (512) [151] are distinct. Orientations inherent to cooling martensite with the (011) plane in the rolling plane become weaker. Unlike the texture of cooling martensite the PF of deformation have the texture maxima (iii) [150] and (iii) [~51], inherent to the deformation textures of bb metals, as strong components.

The results obtained experimentally were compared with calculated textures. As it turned out, the experimental characteristics of the textures of cooling martensite and defor- mation martensite contain maxima that correspond to the phase transition of strong textural components of austenite and are in accord with those calculated only for certain K--Z OR. During the formation of cooling martensite textural transformations occur within the first six K--Z OR. The formation of deformation martensite corresponds to the preferred realiza- tion of only two OR variants (Nos. 3 and 4). The last four OR variants correspond to the appearance of weaker orientations, i.e., participate in the transformation to a lesser ex- tent. The data obtained are in agreement with the published data from investigations on single crystals and individual grains of large-grain specimens. It is often pointed out that all of the possible orientational variants are not always realized during martensitic trans- fromations. Thus, Vovk [3] observed the realization of four OR variants during the forma- tion of deformation martensite and concluded that the orientation of the deformation marten- site is identical with the orientation of cooling martensite in the steel he studied. Dur- ing the deformation of austenite only the number of OR variants realized decreases.

The number of OR variants realized is determined by various factors. These may include elastic _• arising in d~e material, untransformed portions of the old phase, and various lattice imperfections [4]. ~en defo~ation martensite and cooling martensite are formed

287

from hot-rolled austenite, the orientational influence of the texture of the initial phase can be an additional factor prohibiting certain OR variants.

Hence, this method of analyzing the textures of austenite and martensite enables those OR variants that are realized in one specific material or other to be chosen from the di- versity of such variants.

LITERATURE CITED

1. 2.

3. 4.

V. M. Schastlivtsev, Fiz. Met. Metalloved., 33, No. 2, 326-334 (1972). G. Wasserman and I. Greven, Textures of Metallic Materials [Russian translation], Metallurgiya, Moscow (1969). Ya. N. Vovk, in: Metal Physics [in Russian], Naukova Dumka, Kiev (1974), p. 54, 63-66. V. D. Sadovskii and I. P. Sorokin, in: Structure and Properties of Textured Metals and Alloys [in Russian], Nauka, Moscow (1969), pp. 171-174.

LOCAL GROUND STATE DENSITY IN METAL--DIELECTRIC--SEMICONDUCTOR STRUCTURES

D. I. Sheka, A. M. Voskoboinikov, and V. I. Strikha

UDC 621.315.592

States localized at the boundary of a metal--semiconductor contact and the charge concen- trated in these states determine the operation of such a junction as a solid-state micro- electronics element to a significant degree: these factors are responsible for formation of the space-charge region potential barrier, define additional current channels, etc.

The usual situation in such a junction is one where an intermediate layer exists in the contact (for example, optimal solar cell characteristics are realized when the intermediate layer has a finite thickness [i]). However, the nature of surface states in such a three- layer structure and the dependence of their characteristics on layer parameters has remained

practically unstudied.

In the present study we will consider a MOS structure containing as its intermediate layer a plane-parallel dielectric layer of thickness d. We shall be concerned with station- ary states* unrelated to disruption of the problem's translational symmetry along the boun- dary, and corresponding to damping solutions in the semiconductor region z > 0.

The corresponding general solution for a specified energy value in the semiinfinite semiconductor can be constructed using a procedure of analytical continuation of the disper- sion law E(~) and eigenfunctions of an infinite crystal into the forbidden energy region

[3, 4] :

'~s ~ A;,e q~zu~, (r) e iz~ . . . . . = . .. . ( 1 ) k

H e r e r = (Ox, Py ; z ) ; ~ = ( ~ x , X y ; i q ) ; q a r e r o o t s o f t h e e q u a t i o n c ( i q , ) = E.

*Quasistationary solutions of an analogous problem were considered in [2]; the complex energy method was used, which does not permit description of the case of small intermediate layer thickness (d ~ 0), and moreover, does not provide information on states whose local density

decreases rapidly with growth in d.

T. G. Shevchenko Kiev State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 89-93, March, 1983. Original article submitted Auzust 23,

1982.

288 0038-5697/83/2603-0288507.50 �9 1983 Plenum Publishing Corporation