Crystal Geometry and Mechanisms of Phase Transformation in Crystallins Solids

Lieberman, D.S.

doi:10.2172/12511877

Cited by 7 publications

(3 citation statements)

References 21 publications

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“…(Brief summary of the crystallographic theory; see [47], [25], [7], and [3] for the version given here.) After substituting for B using (3), the equation (λB…”

Section: Theoretical Methodsmentioning

confidence: 99%

Energy barriers and hysteresis in martensitic phase transformations

2009

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Abstract. We report results from a systematic program of changing composition of alloys in the system TiNiX, X= Cu, Pt, Pd, Au, to pursue certain special lattice parameters that have been identified previously with low hysteresis. We achieve λ 2 = 1, where λ 2 is the middle eigenvalue of the transformation strain matrix, for alloys with X = Pt, Pd, Au. In all cases there is a sharp drop of the graph of hysteresis vs. composition at the composition where λ 2 = 1. When the size of the hysteresis is replotted vs. λ 2 we obtain an universal graph for these alloys, which also agrees with trends in an earlier combinatorial study of alloys in the system TiNiCu. Motivated by these experimental results, we present a new theory for the size of the hysteresis based on the growth from a small scale of fully developed austenite martensite needles. In this theory the energy of the transition layer plays a critical role. New methods for calculation the optimal layer are developed that rely on Γ-convergence arguments, the small parameter being |λ 2 − 1|. The limiting energy of the transition layer is found to be governed by a nonstandard linear elasticity problem. Overall, the results point to a simple systematic method of achieving low hysteresis and a high degree of reversibility in transforming materials.

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“…(Brief summary of the crystallographic theory; see [47], [25], [7], and [3] for the version given here.) After substituting for B using (3), the equation (λB…”

Section: Theoretical Methodsmentioning

confidence: 99%

Energy barriers and hysteresis in martensitic phase transformations

2009

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“…Line grande hyst6r6se de temp6rature existe entre les temp6ratures de d6but de transformation A S au chauffage et Ms au refroidissement (environ 300 degr6s, de nickel en poids, au chauffage (As, Af) et au refroidissement (Ms, Mr), d'apr6s [2], avec des vitesses moyennes de 5 ~ 9 rain -1 et des alliages pr6alablement homog6n6is6s 1 heure h 1050 ~ Sur le plan fondamental, l'&ude des transformations martensitiques a 6t6 consacr6e jusqu'ici principalement aux aspects cristallographiques, ph6no-m6nologiques et morphologiques [3][4][5]. Dans le domaine des compositions d'alliages que nous avons 6tudi6es, de 20 h 31 pour cent de nickel en poids, la morphologie de la martensite ~' obtenue par refroidissement de l'aust6nite diff6re suivant la teneur en nickel: entre 20 et 29 pour cent de nickel, la martensite apparaR sous forme de lattes, au-delh de 29 pour cent, elle pr6sente un aspect aciculaire, comparable ~t celui des aciers Fe-C.…”

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Etalonnage calorimetrique d'un microanalyseur thermique differentiel entre — 180 et 950 ‡C. application a la determination experimentale de l'enthalpie des transformations structurales α′→γ et γ→α′ dans les alliages fer-nickel

Harmelin

Chappuis

Lehr

1979

Journal of Thermal Analysis

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Thermal effects of the ~' --+ )) structure transformation during heating and that of --~ ~' during cooling (martensitic transformation) were determined in a series of highpurity iron-nickel alloys containing 20--31 per cent nickel with a differential thermal microanalyzer used as microcalorimeter.The calorimetric calibration of the DTA apparatus was carried out in the range from --180 ~ up to 950 ~ on the basis of solid-solid or solid-liquid phase transformations of 18 mineral or organic compounds selected as standards.The transformation enthalpies of the thermal effects were calculated from the correlation Tf Tf [AH]rs = M/m[Q]T~ Tfwhere M: mole mass of the alloy; m: sample mass; [Q]T~: thermal effect measured between the initial and final temperatures of the transformation. While the nickel content increases from 20 up to 31 percent, the enthalpy of the martensitic transformation AH~, decreases from 820 to 310 cal 9 mole -1 for cooling, and the enthalpy of the reverse transformation AH~,~ for heating decreases from 480 to 330 cal 9 mole-L L'existence d'une relation de proportionnalit6 entre l'effet thermique 1i6 au changement de phase d'un 6chantillon et l'aire du pic d'analyse thermique diff6-rentielle qui lui est associ6 prdsente un int6rat consid6rable sur le plan exp6ri-mental car elle permet l'6tude thermodynamique in situ des phases hors d'6quilibre qui apparaissent au cours du refroidissement continu ou se transforment au chauffage.C'est le cas des alliages fer-nickeI qui subissent une transformation structurale spontan6e au cours du refroidissement de la phase stable 5. haute temp6rature, de structure cubique 5. faces centr6es, l'aust6nite 7. Cette transformation, d6sign6e sous le nom de transformation martensitique, s'effectue par un d6placement coop6ratif de tous les atomes du r6seau cristallin, de type cisaillement [1 ]. Elle donne naissance h une phase m6tastable de structure cubique centr6e, la martensite c~'. Lots d'un nouveau chauffage, la transformation inverse ct' ~ ~ se produit.L'une des caract6ristiques de ces transformations est de s'effectuer dans un large domaine de temp6rature (une centaine de degr6s) d6fini par: 11".i.. Thermal Anal. 16, 1979

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“…Many significant changes in material properties are consequent upon the formation of martensitic phases: for example, the transformations to phases of high hardness in iron-base alloys, and the switch between semiconductor and metallic conductor in some oxides (Lieberman,[1]). When cooled, the homogeneous austenite phase switches to the twinned martensite.…”

Section: §1 Introductionmentioning

confidence: 99%

A model for twinning

Maddocks

Parry

1986

J Elasticity

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The modelling of twins in crystals with strain gradient theories provides interesting problems both in thermodynamics and in the calculus of variations. Here, Dunn and Serrin's thermomechanical theory of interstitial working is used to obtain a variational principle that governs the equilibria of materials with non-convex Helmholtz free energy. In some geometries, this principle reduces to a novel calculus of variations problem; an example is described in which symmetry-related uniform equilibrium states can be connected by nonconstant extremals which realise local minima of the free energy. Certain implications of different definitions of local minima are also discussed.

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Crystal Geometry and Mechanisms of Phase Transformation in Crystallins Solids

Cited by 7 publications

References 21 publications

Energy barriers and hysteresis in martensitic phase transformations

Energy barriers and hysteresis in martensitic phase transformations

Etalonnage calorimetrique d'un microanalyseur thermique differentiel entre — 180 et 950 ‡C. application a la determination experimentale de l'enthalpie des transformations structurales α′→γ et γ→α′ dans les alliages fer-nickel

A model for twinning

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