INVESTIGATION OF PLANAR DEFECTS IN SHAPE MEMORY ALLOYS

Michail A. Baranov, Michail D. Starostenkov, Veronika V. Romanenko, Evgenya V. Chernyh, Evgenyi A. Dubov,

Абстракт

В настоящей работе методом компьютерного моделирования с использованием парных потенциалов Морза проведен анализ планарных дефектов консервативного типа в сверхструктурах B2, D019, D024, D03, L12 на основе ОЦК - решетки и ГПУ - решетки. Энергии образования антифазных границ (АФГ), сверхструктурных дефектов упаковки (СДУ), двойников рассчитаны в плоскостях {110}, {211}, {001}, {100} без релаксации и с учетом релаксации кристаллической решетки сплава. Сделано сравнение с экспериментальными данными. Кроме этого построены картины атомных смещений вблизи АФГ, СДУ, двойников, и осуществлен анализ поведения атомов в дефектном блоке кристалла. На основе анализа в исследуемых сплавах предложена классификация возможных планарных дефектов по типам атомных смещений вблизи них.

Abstract

In this paper it was carried out analysis of planar defects of conservative type in superstructures B2, D019, D024, D03, L12 on the basis of bcc-lattice and hcp-lattice by the method of computer simulation with using of Morse’s pair potentials. Energies of formation of antiphase boundaries (APB), superstructure fault defects (SFD), twins were calculated in planes {110}, {211}, {001}, {100} without relaxation and with relaxation of alloy crystal lattice. It was made a comparison with experimental data. Besides, the patterns of the atomic displacements were constructed near APB, SFD, twins. Analysis of atoms behavior in defect blockes was also made. On the basis of this analysis it was suggested classification of possible plane defects according to the types of atom displacements near them in all studied superstructures.

1. Introduction.

Ordered alloys are included in the class of compounds and they are located limited solid solutions and interstitial phases. Due to their original physico – mechanical properties, they are applied as constructional, electro - technical, magnetic, precisional, reactor materials in electrotechnics, machine-building, instrument-industry. Features of any ordered alloy are determined the type of its crystal lattice – superstructure- and set of defects, taking place in this alloy [1,2,3]. Besides, point and line defects, it is possible a formation of surface defects such as APBs and fault defects (FD) in ordered alloys.

Stability and localization are very important terms for energetic and configuration description of defects. Stability of defect is characterized by its ability to restore initial configuration after removing of external mechanical stresses. Localization of defect in crystal volume can be estimated by the sizes of region, were distortions, caused by defects, take place. If value of relaxation atomic displacements decreases up to zero, not approaching to boundaries of crystal block with defect, then corresponding defect can be considered as localized. Evidently, it is also stable, because it does not require applying of external mechanical stresses for preservation of its configuration.

2. Description of interatomic interactions in crystal.

As it was mentioned above, physico-mechanical properties of ordered alloys are determined by the presence of different defects, taking place in them. Therefore, study of energies of defect structures, patterns of atomic displacements near defects appears to be important. Helding of such investigations is possible as by experimental methods so by theoretical methods. When observing defects with the help of electron microscope complete picture of defect structures is not given, therefore, at present time the method of computer simulation is of considerable interest. Initial step of model construction is description of interatomic interactions in ordered alloys. For this proposes the row of Morse’s potential functions can be applied, such as pseudopotential functions, Morse’s function and its varieties, Mi - Grunaizen’s function, polynomial function, Finnis – Sinclair’s function and others [4,5,6]. Morse’s potentials were constructed for description of properties of alloys. Morse’s function is given as , and cutted off between third and forth coordination spheres. a , b , D – parameters of potential function, rij – radius of coordination sphere. The using of traditional approach to decision of problem of function interactions construction is introduction of the energy of crystal bond taking into account a cell as a sum of pair interatomic interactions at knots of the lattice [7].

3. State of crystal lattice near plane defects of conservative type.

It is well known, that in bcc-alloys the pencil sliding is realized along direction <111> [8]. Therefore, such systems of sliding as: р<111>{110}, р<111>{211}, р<210>{001}, р<010>{100} are possible in given superstructures, were р – vector of shift of hypocrystal. If р is divisible to parameter of alloy lattice, conservative APB will be formed, but when р is not divisible to parameter of alloy lattice fault defect will be observed. Let’s consider the formation of stable atomic configurations on the example of planar defects of conservative type in superstructures B2, D019, D024, D03, L12.

There are typical features, characterizing APBs in planes {211}. Atoms have only normal displacements to the plane of boundary because of the symmetry of superstructure B2. It is confirmed by investigation of APBs in two polar – orthogonal positions. All atoms of alloy displace along a normal to APBs. By the way, values of deformation is interchange.

Vectors of atomic displacements near APBs are located in planes (0-11) in superstructures B2, D03 (fig. 1). “Even” and “odd” planes (0-11) are observed, which can be combined each other by reformations of symmetry even with the presence of microdeformations, obtained at lattice relaxation. It leads to considerable splitting of planes, parallel to APB, into subplanes. For instance, in superstructure B2 there are two subplanes, in D03 – four. In superstructures B2, D03 there is only one direction of shift - <-111> - normal to the plane of figure 1. Atoms of Al have the largest displacements, when atoms of Fe remain almost non-moved.

Energies of formation of conservative type APBs are given in table 1. Results of computer experiment correlate with theoretical calculations very well.

a)

b)

Fig. 1. Atomic configurations and patterns of microdeformations near APBs р<-111>(211) in alloys Fe3Al(D03) (р=а/2; а/4) – a), FeAl(B2) - b). atoms of Al – whit circles, atoms of Fe – gray (at corresponding patterns) – black. Scale of atomic displacements а) - 25:1, b) - 10.

Table 1.

Energies of formation of conservative type APBs in bcc and hcp alloys

      Energies of APBs, mJ/m2

Superstructure

Plane

Vector of shift

Starting

Equilibrium

В2

D03

 

 

D019

 

L12

(110)

(211)

(110)

(211)

(001)

(100)

(110)

(211)

а0/2<-111>

а0/2<-111>

а/4<-111>

а/2<-111>

а/4<-111>

а/2<-111>

а/4<210>

а/2<210>

а/2<010>

а/4<-111>

а/2<-111>

а/4<-111>

400

300

100

5

250

10

152

139

473

600

8

190

50

100

20

3

200

7

50

38

296

220

5

150

Atomic configurations, forming in the result of lattice relaxation near FD а0/6<-111>(211) and а0/6<-111>(211) in alloy Fe3Al, have essential differences. In the first case (fig. 2) a tendention to reconstruction of the ideal lattice is observed. The structure, different from ideal, forms in the second case (fig. 3).

Fig. 2. Equilibrium configuration of FD -а0/6<-111>(211) in alloy Fe3Al. Atoms of Fe – gray circles кружки, atoms of Al – whit. Orientation: (0-11) – plane of pattern; <211> - to the right, <-111> - down. Scale of atomic displacements 4:1.

Fig. 3. Equilibrium configuration of FD а0/6<-111>(211) in alloy Fe3Al. Atoms of Fe – gray circles кружки, atoms of Al – whit. Orientation: (0-11) - plane of pattern; <211> - to the right, <-111> - down. Scale of atomic displacements 10:1.

This difference is found in the case of rectangles forming by atomic projections at plane (0-11) perpendicular to defect plane, for example their transformation into trapezoids. The trapezoids situated on plane of FD form hexagons, touching by foundations. In this case the displacement of admixture atoms can be advantageous. This effect can be interpreted as formation of narrow phase stripe with a symmetry lower than symmetry of initial lattice, but the defect appears to be the origin of this phase. Above mentioned distortions disappear with the increasing of the distance from defect plane. This effects can be found in all the studied alloys. Shift components of atomic displacements vectors are not observed at the investigation of atomic configurations of FD (211) in plane (-111). Thus, basic directions of lattice relaxation near FD ± а0/6<-111>(211) are <211>- normal to FD and <-111> - (shift direction). Investigation of stable atomic configuration of FD а0/6<-111>(110) in plane (-110) shows, that each plane displaces as a whole without splitting and deformation near defect. Energies of FD formation are approximately equal to energy of APB formation in the studied superstructures. Shift twins can exist only in plane (211) in bcc crystal. Patterns of atomic configurations and microdeformations near twins in studied alloys are given in figure 4. According to classical semi – empirical model, value of relaxation displacements is considered to be insignificant. Deformation of lattice occupies several planes and decreases up to zero in the limits of model block. By the way, the considerable splitting of planes (211) is observed only in the nearest sphere of twining plane.

а)

 

 

б)

Fig. 4. Atomic configurations and patterns of microdeformations near twins (211) in alloys Fe3Al(D03) - a), FeAl(B2) - b). Atoms of Al – whit circles (at corresponding patterns), atoms of Fe - gray. Scale of atomic displacements - 15:1.

Vectors of atomic displacements in each hypocrystal are oriented along <100> advantageously. Patterns of atomic displacements in the studied alloys are similar with patterns of displacements in Fe3Al. But the splitting, observed in these alloys, is different from splitting in Fe3Al. It is obtained, that the energies of twins formation are approximately equal to energies of APB and FD.

Taking into account the results of simulation three groups of defects can be obtained, according to the types of atomic displacements near them:

Theoretically possible amount of defect classes in all the studied superstructures was obtained by combination of all defects into one class, having splittings and shift deformations of planes. Six classes of defects in superstructures B2 and C11b and nine classes of defects in superstructures D03, L21, B32 were found.

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