Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn

This review is dedicated to the analysis of the hexagonal-to-orthorhombic transition into Ti₃Sn. The place of martensitic transformation into broader category of displacive (diffusionless) transformations is shown from the point of view of a transformation strain associated with the transition. The...

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Дата:	2014
Автор:	Ivanova, O.I.
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Опубліковано:	Інститут проблем матеріалознавства ім. І.М. Францевича НАН України 2014
Назва видання:	Электронная микроскопия и прочность материалов
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Цитувати:	Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn / O.I. Ivanova // Электронная микроскопия и прочность материалов: Сб. научн . тр. — К.: ІПМ НАН України, 2014. — Вип. 20. — С. 83-92. — Бібліогр.: 25 назв. — рос.

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spelling	irk-123456789-1142852017-03-06T03:02:30Z Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn Ivanova, O.I. This review is dedicated to the analysis of the hexagonal-to-orthorhombic transition into Ti₃Sn. The place of martensitic transformation into broader category of displacive (diffusionless) transformations is shown from the point of view of a transformation strain associated with the transition. The transformation strain regarded to the transformation into Ti₃Sn was analyzed and the displacive shear-dominant (martensitic) origin of this transition was shown. The latter part of the work is dedicated to the comparison of the volume change and transformation temperature in Ti₃Sn with those into other materials undergoing martensitic transformation. Огляд присвячений аналізу перетворення із гексагональної в орторомбічну фазу в Ti₃Sn. Показано місце мартенситного перетворення в ширшій категорії бездифузійних перетворень з точки зору деформації перетворення. Деформація перетворення в Ti₃Sn проаналізована і зсувний (мартенситний) характер перетворення проілюстровано. Порівняно зміни об’єму та температури перетворення в Ti₃Sn з такими в інших матеріалах, що зазнають мартенситного перетворення. Обзор посвящен анализу превращения из гексагональной в орторомбическую фазу в Ti₃Sn. Показано место мартенситного превращения в более широкой категории бездиффузионных превращений с точки зрения деформации превращения. Деформация превращения в Ti₃Sn проанализирована и сдвиговый (мартенситный) характер превращения показан. Проведено сравнение изменения объема и температуры превращения в Ti₃Sn с этими характеристиками в других материалах, претерпевающих мартенситное превращение. 2014 Article Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn / O.I. Ivanova // Электронная микроскопия и прочность материалов: Сб. научн . тр. — К.: ІПМ НАН України, 2014. — Вип. 20. — С. 83-92. — Бібліогр.: 25 назв. — рос. XXXX-0048 http://dspace.nbuv.gov.ua/handle/123456789/114285 669.01:669.296.017.12 en Электронная микроскопия и прочность материалов Інститут проблем матеріалознавства ім. І.М. Францевича НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	This review is dedicated to the analysis of the hexagonal-to-orthorhombic transition into Ti₃Sn. The place of martensitic transformation into broader category of displacive (diffusionless) transformations is shown from the point of view of a transformation strain associated with the transition. The transformation strain regarded to the transformation into Ti₃Sn was analyzed and the displacive shear-dominant (martensitic) origin of this transition was shown. The latter part of the work is dedicated to the comparison of the volume change and transformation temperature in Ti₃Sn with those into other materials undergoing martensitic transformation.
format	Article
author	Ivanova, O.I.
spellingShingle	Ivanova, O.I. Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn Электронная микроскопия и прочность материалов
author_facet	Ivanova, O.I.
author_sort	Ivanova, O.I.
title	Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn
title_short	Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn
title_full	Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn
title_fullStr	Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn
title_full_unstemmed	Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn
title_sort	analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in ti₃sn
publisher	Інститут проблем матеріалознавства ім. І.М. Францевича НАН України
publishDate	2014
url	http://dspace.nbuv.gov.ua/handle/123456789/114285
citation_txt	Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn / O.I. Ivanova // Электронная микроскопия и прочность материалов: Сб. научн . тр. — К.: ІПМ НАН України, 2014. — Вип. 20. — С. 83-92. — Бібліогр.: 25 назв. — рос.
series	Электронная микроскопия и прочность материалов
work_keys_str_mv	AT ivanovaoi analysisofthetransformationstrainassociatedwiththehexagonaltoorthorhombictransitioninti3sn
first_indexed	2025-07-08T07:13:36Z
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fulltext	84 UDC 669.01:669.296.017.12 Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti3Sn Ivanova Olga Frantsevich institute for problems of Material Science, Kyiv, e-mail: iv4103@gmail.com This review is dedicated to the analysis of the hexagonal-to-orthorhombic transition into Ti3Sn. The place of martensitic transformation into broader category of displacive (diffusionless) transformations is shown from the point of view of a transformation strain associated with the transition. The transformation strain regarded to the transformation into Ti3Sn was analyzed and the displacive shear-dominant (martensitic) origin of this transition was shown. The latter part of the work is dedicated to the comparison of the volume change and transformation temperature in Ti3Sn with those into other materials undergoing martensitic transformation. Keywords: martensitic transformation, transformation strain, shape memory alloys. Introduction Intermetallic compound Ti3Sn and some Ti3Sn-based alloys were reported to exhibit high damping capacity in the frequency range 0,10—10 Hz [1, 2] and unusual mechanical properties such as low Young’s modulus and good room temperature plasticity [3—5]. Such properties in conjunction with strength and high melting temperature are of interest for materials for aerospace components operating under vibration and extremely difficult environment. According to [1, 2] the origin for high damping and unusual mechanical behaviour is a phase transformation occurring in the intermetallic compound Ti3Sn at about 350 K which is accompanied by a peak of damping capacity and a reduction of Young’s modulus. According to [6] the room temperature Ti3Sn has orthorhombic Cmcm structure (space group № 63, lattice parameters a = 0,585 nm, b = 1,034 nm, c = 0,475 nm) and undergoes a phase transformation to the hexagonal DO19 structure (space group № 194, lattice parameters a = 0,5938 nm, c = 0,4749 nm) under heating. Microstructural observations by TEM have revealed self- accommodated twinned microstructure with compound (110) twins in room-temperature single-phase Ti3Sn [2—6]. For the phase transition into Ti3Sn the ratio between transformation temperature and melting temperature 18,0 K1943 K343 melt trans == T T is low enough to suggest the diffusionless nature of the transition. A 85 formation of specific twinned self-accommodated microstructure [3— 6] points to its martensitic origin. Most of them undergoes diffusion- displacive transition and several intermetallic compound doesn’t undergo any transformation. Ni3Sn and Fe3Mg were reported to exhibit martensitic transformation, but these two © Ivanova Olga, 2014 compounds have ordered cubic DO3 or L12 high-temperature phase which transforms into hexagonal phase [7]. However the Ti3Sn compound crystallizes into hexagonal close-packed DO19 superlattice from the melt. It is unusual for the case of martensitic transformations because the high-temperature phase is mostly cubic. Into our previous work [6] it is shown that hexagonal lattice transforms to an orthorhombic Cmcm structure in Ti3Sn. Carrying out analysis of the transformation strain we aimed to show the martensitic (displacive) origin of the transition, and compare it with martensitic transformations into other alloys and intermetallic compounds. Classifications of diffusionless phase transitions Buerger in 1951 have made a classification of phase transformations into solid state based on the mechanism of the transition and on the structural relations between parent and product phases. According to this classification [8] phase transformation can be divided on reconstructive, displacive and order/disorder transformations. During reconstructive transition chemical bonds are broken and new bonds formed. In this case the space group symmetries of parent and product phases are unrelated. Reconstructive transformations are quite abrupt and have no order parameter. These transformations are of first order thermodynamic character, they occur by nucleation and growth, show thermal hysteresis; parent and product phases coexist at equilibrium. Displacive transitions involve the distortion of bonds. In this case of parent and product phases show group/subgroup relations. Low- symmetry phase approaches the transition to higher symmetry-phase continuously. Order parameter exists and measures a ‘distance’ of the low-symmetry to the high-symmetry structure. These transitions can be of second or weak first order and are characterized by vanishing or small latent heat, volume jump and thermal hysteresis. During order/disorder transitions the structural difference between phases is related to the different chemical occupation of the same crystallographic sites. These transitions have second order character and show vanishing enthalpy and volume changes. Phase transformations which involve long range diffusion are regarded as reconstructive rather than displacive. However some transformations requiring diffusion also have displacive character; 86 they are called "diffusional-displacive transformations" to emphasize their mixed characteristics; sometimes the term "nonferrous bainites" is used for them [9]. Displacive transformations involve atom’s displacement within unit cell and long range diffusion is not required. Cohen et al. in 1979 proposed a classification scheme that identifies a class of displacive transformations. According to his classification [9], martensitic transformation is a subclass of broader category of displacive transformation and is defined as a shear- dominant, lattice-distortive, diffusionless transformation occurring by nucleation and growth. This classification scheme is reproduced on fig. 1. The first subdivision is made between “shuffle transformations”, in which kinetic and morphology are dominating by shuffle displacements, and “lattice-distortive transformations” which are driven by lattice-distortive strain energy. A shuffle is a coordinated movement of atoms that alters the symmetry or Diffusionless/displacive phase transformations Shuffle displacements Interfacial energy Shuffle transformation Kinetic and morphology are dominated by shuffle displacements TiZr alloys (β→ω) SrTiO3 (ferroelastic) Lattice-distortive displacements Strain energy energy Lattice-distortive transformation Kinetic and morphology are dominated by homogeneneous lattice-distortive deformation dilatational component Deviatoric component Dilatation dominant No undistorted line Sn (bct→dc) Ce (fcc →fcc’) Deviatoric dominant undistorted line vibrational displacements driving energy Latice-distortive displacements strain energy Quasimartensitic Occurring continuously Nb-Ru (fcc →fcc’) Mn-Ni (antiferomagnetic) Martensitic Occurring by nucleation and growth Fe-based alloys, Ni-Ti, Cu-based Diffusionless/displacive phase transformations Shuffle displacements Interfacial energy Shuffle transformation Kinetic and morphology are dominated by shuffle displacements TiZr alloys (β→ω) SrTiO3 (ferroelastic) Lattice-distortive displacements Strain energy energy Lattice-distortive transformation Kinetic and morphology are dominated by homogeneneous lattice-distortive deformation dilatational component Deviatoric component Dilatation dominant No undistorted line Sn (bct→dc) Ce (fcc →fcc’) Deviatoric dominant undistorted line vibrational displacements driving energy Latice-distortive displacements strain energy Quasimartensitic Occurring continuously Nb-Ru (fcc →fcc’) Mn-Ni (antiferomagnetic) Martensitic Occurring by nucleation and growth Fe-based alloys, Ni-Ti, Cu-based Fig. 1. Classification scheme of diffusionless/displacive phase transformation proposed by Cohen et al. [9]. structure of the crystal and rearranges the atom positions within a unit cell. In the case of lattice-distortive transformations the kinetic 87 and morphology are dominated by homogeneous lattice-distortive deformation; that is a homogeneous strain that transforms the lattice of parent phase into a lattice of product phase. A further subdivision was made between “dilatation-dominant” and “deviatoric- dominant” transformations according to the relative magnitudes of the two components of the homogeneous lattice deformation, i. e., the dilatational and the deviatoric (shear) components. The next subdivision is made between martensitic transformation, occurring by nucleation and growth and quasimartensitic transformation occurring continuously according to the relative magnitudes of the lattice-distortive displacements and lattice vibrational displacements. Martensitic transformation requires heterogeneous nucleation and passes through a two-phase mixture of parent and product phases; it is a first order diffusionless phase transformation. In the case of quasimartenstic transformations these two displacements are comparable. In this case a nucleation is not required since domains of product phase appear simultaneously throughout the material by continuous strain modulation. The “martensitic transformations” are therefore the displacive and shear-dominant phase transformations where the lattice- distortive strain is large enough to dominate the kinetics and the morphology of the transformation. These transformations are characterizes by existence of invariant line which remains unchanged during transformation. The homogeneous lattice-distortive strain can be represented by a matrix according to y = S x, where the strain S deforms the lattice vector x into a lattice vector y. This strain is homogeneous because it transforms straight lines into other straight lines. A spherical body of the parent phase will thus be transformed into another sphere or into an ellipsoidal body. The actual shape of the ellipsoid depends on the deformation along the three principal axes. The ellipsoid obtained after a pure shear intersects the original sphere; hence a set of vectors exist, whose lengths remain unchanged. The initial and the isotropically dilated spheres have no intersection and it is therefore not possible to find a vector whose length has not been changed by the transformation. An undistorted line can only result from a homogeneous lattice deformation if the deviatoric or shear component sufficiently exceeds the dilatational component. Bilby and Christian [10] stated that for an undistorted line to exist after homogenous deformation, that one of the principal distortions must be greater than unity, one must be less than unity and one must be equal to unity. Fig. 2 shows one section of the sphere which represents a unit sphere of parent phase and a section of ellipsoid which represents a 88 product phase. The ellipsoid has a unity principal distortion along y axis, greater that unity distortion along x axis, less then unity distortion along z axes. The invariant line of contact between sphere and ellipsoid can be find; it is A’OB’ line. The plane A’OB’ is a plane of zero distortion and represents a habit plane into crystal lattice. Thus during martensitic transformation the transformation strain exist and displays the volume change that accompanies the transition. This differs martensitic from shuffle transformation. Shear-dominant nature of martensitic transformation requires the existence of invariant line which leads to the necessary condition that one of principal strains must be greater than unity, one must be less than unity and one must be equal to unity. This differs martensitic transformation from dilatational transformation. Into latter case all principal Fig. 2. Bain distortion with one strain of zero, one greater than zero and one less than zero [10]. strains higher or smaller then unity. Quasimartensitic and martensitic transitions can be distinguished by the magnitude of volume change, latent heat or thermal hysteresis. Transformation into Ti3Sn As reported into [6], Ti3Sn high temperature hexagonal DO19 (P63/mmc, space group #194) phase transforms to orthorhombic Cmcm (space group #63) phase. These structures obey group- subgroup relations thus transition from P63/mmc to Cmcm structure can be displacive. Below we analyze the lattice transformation strain in order to show the existence of invariant line and to show its shear- dominant origin. The defined orthorhombic lattice of Ti3Sn can be viewed as a distorted hexagonal phase with a relation between lattice parameters: аorto ≈ аhех, borto ≈ ≈ √3ahex, corto ≈ chex. Based on the dimensions of orthorhombic and hexagonal structures, a crystallographic relation between these phases can be suggested. A schematic of the crystal structures of the orthorhombic and 89 hexagonal phases and their lattice correspondences are shown in fig. 3, a. Therefore the orientation relationships between orthorhombic and hexagonal phases become (110)orto\|\|(100)hex, <001>orto\|\|<001>hex. The transition from hexagonal to orthorhombic phase is accompanied by a shortening of 1,5% along x axis and an elongation of 0,5% along y axis (into orthorhombic basis) leading to the total transformation strain about 990,0 100 0005,10 00985,0 det 00 0 3 0 00 detdet hex ortho hex ortho hex ortho = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ = c c a b a a U which corresponds to reduction of crystal lattice volume of about 1%. Principal strains of the pure lattice dilatation can be deducted as a difference between calculated transformation strains and unit matrix and equal to e1 = –0,015, e2 = 0,005, e3 = 0. This evidences that the strain ellipsoid of orthorhombic phase is contracted along x axis, dilated along y axis and not a b Fig. 3. Lattice correspondence between orthorhombic and hexagonal phases (a) [6]; a sphere of the hexagonal phase and dilated ellipsoid of orthorhombic phase (b). Undistorted invariant plane can be found as an intersection between the ellipsoid and the sphere (AB and A’B’ circles). altered along z direction compared to the strain sphere of the hexagonal phase. fig. 3, b shows a sphere representing the hexagonal phase and an ellipsoid of orthorhombic phase which is contracted on e1 = –0,015 (1,5%) along x axis, dilated on e2 = 0,005 (0,5%) along y axis and not altered along z axes. Therefore, an undistorted invariant plane can be found as an intersection between dilated ellipsoid of orthorhombic phase and initial sphere of hexagonal phase (AB and A’B’ circles). The presence of an invariant plane indicates that this orthorhombic-to-hexagonal transition is lattice-distortive and shear-dominant, and thus martensitic transformation according to the definition given by Cohen et al [9]. The transformation strain matrix correspondent to 90 hexagonal-to-orthorhombic transition in Ti3Sn has λ2 = 1 which points to good geometrical compatibility [11—13] between parent and product phases and might explain small thermal hysteresis measured into previous works [14]. The volume change and transformation strain associated with the hexagonal-to-orthorhombic transition into Ti3Sn are deducted and this transition can be compared with those into other materials. Table 1 shows volume changes, transformation and melting temperatures for some alloys and intermetallic compounds undergoing martensitic transformation. Crystal structures of parent phases of the SMAs are either of ordered cubic superlattice (B2) or disordered cubic (fcc) lattice, as seen in the table 2. Product phase have low-symmetry orthorhombic or monoclinic lattice. It is seen from table 1 and fig. 4 that alloys with lower Ms have negative volume change while into materials with higher transformation temperature parent B2 phase is denser then martensite. Shape memory materials can be distinguished on low- (if Ms < 400 K) and high-temperature (if Ms > 400 K) ones [22]. Ti3Sn having Ms = 343 K belongs to low-temperature materials. As it seen from fig. 1 the volume change associated with the transition in Ti3Sn is negative and quite big compared to other low-temperature SMA. Ms/Tm ratio is a measure of interplay between diffusion processes and martensitic transformation. Into high-temperature SMA diffusion processes T a b l e 1. Volume changes, transformation and melting temperatures for some alloys undergoing martensitic transformation Composition, % (at.) VP, 10-3 nm VM, 10-3 nm ∆V/VM, % Ms, K Tm, K [15] Ms/Tm Ti—49,8Ni 13,7035 13,6573 –0,34 330 [16] 1313 0,24 AuCd 18,3303 18,2177 –0,62 325 [17] 629 0,52 Ag—45Cd 18,1982 17,9047 –1,64 199 [18] 740 0,27 Ti49,5Ni40,5Cu10 13,9091 13,9119 0,02 400 [17] Ti—4Mo 17,3389 17,4777 0,79 780 [19] 3146 0,25 Ti—20Nb 17,7254 17,6805 –0,25 493 [20] 2846 0,17 Ti—24Nb 17,7358 17,7249 –0,06 338 [20] 2766 0,12 Zr—49,9Cu 17,5311 17,6094 0,45 413 [21] 1461 0,28 Ti3Sn 18,1269 17,9577 –0,94 343 [1] 1943 0,18 VP , VM — volume per atom for parent and martensitic phase; — volume change during martensitic transformation. T a b l e 2. Crystal structures of parent and martensitic phases of the alloys listed into table 1 [15] %100× − =∆ M PM V VVV 91 of internal stress relaxation inhibit the shape recovery if Ms/Tm is high [23, 24]. Into materials with low-temperature martensitic transformation the interplay between diffusion processes of point defects rearrangement might lead to twinning pseudoelasticity [25]. Twinning pseudoelasticity i. e. strain recovery below transformation temperature was observed into AuCd, In—Tl, some Cu-based alloys and was not found into Ni—Ti [25]. For Ti3Sn this ratio is 0,18 (table 1) meaning that diffusion processes are not expected to deteriorate mechanical effects associated with martensitic transformation. Although twinning pseudoelasticity is not expected Parent phase Martensitic phase Composition, % (at.) Space group Lattice parameters, nm Space group Lattice parameters, nm Ti—49,8Ni B2 a = 0,3015 B19' a = 0,2889, b = 0,4120, c = 0,4622, β = 96,8o AuCd B2 a = 0,3322 B19 a = 0,4766, b = = 0,3151, c = 0,4859 Ag—45Cd Cubic a = 0,3314 Orthorho mbic a = 0,30968, b = 0,48651, c = 0,47536 49,5Ti— 40,5Ni— 10Cu B2 a = 0,303 [16] B19 a = 0,2881, b = 0,4279, c = 0,4514 [16] Ti—4Mo β a = 0,3261 [19] α'' a = 0,3012, b = 0,4983, c = 0,4658 [19] Ti—20Nb β a = 0,328505 [20] α'' a = 0,31257, b = 0,48704, c = 0,46456 [20] Ti—24Nb β a = 0,328569 [20] α'' a = 0,31785, b = 0,4812, c = 0,46355 [20] Zr—49,9Cu B2 a =0,3273 [22] B19' a = 0,3237, b = 0,4138, c = 0,5449, β = 105,19о [22] Ti3Sn DO19 a = 0,5938, c = 0,4749 [6] Orthorho mbic a = 0,585, b = 1,034, c = 0,475 [6] 92 for Ti3Sn because of low Ms/Tm, the strain recovery below transformation temperature was observed in the non-stoichiometric Ti75.5Sn24.5 [5]. Fig. 4. Transformation temperature Ms versus volume change accompanied martensitic transformation according to table 1. Summary The transformation strain matrix associated with orthorhombic to hexagonal in Ti3Sn contains eigenvalues λ1<0, λ2 = 1, λ3>0 and corresponds to the volume change of about 1% (det U = 0,99). These imply that the transformation is lattice-distortive and shear dominant, i. e. martensitic. The condition λ2 = 1 points to good geometrical compatibility between parent and product. The volume change accompanied the transition in Ti3Sn is negative and quite big compared to other low-temperature SMA. 1. Vdovychenko O. V. Dynamic mechanical behavior of intermetallide Ti3Sn / [ O. V. Vdovychenko, M. V. Bulanova, Yu. V. Fartushna, A. A. Shcheretsky] // Scripta Mater. — 2010. — 62. — P. 758—761. 2. Wong C. R. Low frequency damping and ultrasonic attenuation in Ti3Sn-based alloys / C. R. Wong, R. L. Fleischer // J. Mater. Res. — 1994. — 9, No. 6. — P. 1441—1448. 3. Окунь И. Ю. Аномальная пластичность в интерметаллиде Ti3Sn / [И. Ю. Окунь, А. В. Котко, С. А. Фирстов и др.] // Электронная микроскопия и прочность материалов. — К. : Ин-т пробл. материаловедения НАН Украины. — 2007. — Вып. 14. — С. 12—20. 4. Буланова М. В. Фазовый состав, структура и механические свойства богатых титаном сплавов системы Ti—Dy—Sn / [М. В. Буланова, Ю. Н. Подрезов, Ю. В. Фартушная, А. Н. Рафал] // Доп. Нацiональної академiї наук України. — 2007. — № 6. — C. 95—104. 5. Ivanova O. Room temperature strain recovery into non- stoichiometric intermetallic compound Ti3Sn / [O. Ivanova, A. R. 93 Yavari, K. Georgarakis, Yu. Podrezov] // J. Alloys.Compd. — 2014. — 617. — P. 34. 6. Ivanova O. In situ X-Ray diffraction study of the phase transformation in the non stoichiometric intermetallic compound Ti3Sn / [O. Ivanova, M. Karpets, A. R. Yavari et al.] // Ibid. — 2014. — 582. — P. 360. 7. Ghosh G. 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Ren // Ibid. — 2001. — 312. — P. 207. Аналіз деформації перетворення, пов’язаної з перетворенням з гексагональної в орторомбічну фазу в Ti3Sn О. М. Іванова Огляд присвячений аналізу перетворення із гексагональної в орторомбічну фазу в Ti3Sn. Показано місце мартенситного перетворення в ширшій категорії бездифузійних перетворень з точки зору деформації перетворення. Деформація перетворення в Ti3Sn проаналізована і зсувний (мартенситний) характер перетворення проілюстровано. Порівняно зміни об’єму та температури перетворення в Ti3Sn з такими в інших матеріалах, що зазнають мартенситного перетворення. Ключові слова: мартенситне перетворення, деформація перетворення, сплави з ефектом пам’яті форми. Анализ деформации превращения, связанной с превращением из гексагональной в орторомбическую фазу в Ti3Sn О. М. Иванова Обзор посвящен анализу превращения из гексагональной в орторомбическую фазу в Ti3Sn. Показано место мартенситного превращения в более широкой категории бездиффузионных превращений с точки зрения деформации превращения. Деформация превращения в Ti3Sn проанализирована и сдвиговый (мартенситный) характер превращения показан. Проведено сравнение изменения объема и температуры превращения в Ti3Sn с этими характеристиками в других материалах, претерпевающих мартенситное превращение. Ключевые слова: мартенситное превращение, деформация превращения, сплавы с эффектом памяти формы.

Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn

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