Beta-Phase stability and martensitic nucleation in hume-rothery alloys
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I.
INTRODUCTION
A number of noble metal based beta-phase alloys undergo a martensitic transformation either on cooling or under the influence of an external applied stress. The strain energy term for the formation of a martensite nucleus depends on the transformation strain amplitude and on the corresponding elastic constants. The strain energy term will thus be affected by the second and third order elastic constants of the beta- and the martensite phase. One of the elastic constants of the beta phase, the C'-constant, is low and decreases with decreasing temperature but does not vanish at the transformation temperature. Due to anharmonicity the C'-constant changes with strain if a homogeneous strain is applied to the lattice. Depending on the orientation of the shear plane with respect to the applied strain, C ' softens, increases, or is not affected. If the applied strain is increased, a point may be reached at which the softened C'-constant becomes zero, and the lattice is then mechanically unstable. It has been shown that this critical strain amplitude to make some bcc lattices mechanically unstable is small.~ Because the critical amplitude is small and because such strain amplitudes are encountered in the vicinity of lattice defects, Gu6nin and Gobin have considered the martensitic nucleation in terms of a localized lattice instability 2 and have shown that such critical strains are realized around some specific lattice defects. They have calculated the effect of shear strains existing around dislocations on the mechanical stability and have shown, for example, that a screw dislocation with Burgers vector b = a[01i-] generates a region of several nanometers around the dislocations where the critical shear strain is attained. The influence of an external applied stress superimposed on the local regions of strain has not been analyzed. In the present paper the mechanical stability of the beta phase will be studied in more detail using some new experimental data concerning the second and third order elastic constants and their temperature dependence. 3 Those new BERT VERLINDEN, Research Assistant, and LUC DELAEY, Professor, are with the Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, de Croylaan 2, B3030 Heverlee, Belgium. This paper is based on a presentation made in the symposium "Pretransformation Behavior Related to Displacive Transformations in Alloys" presented at the 1986 annual AIME meeting in New Orleans, March 2-6, 1986, under the auspices of the ASM-MSD Structures Committee. METALLURGICAL TRANSACTIONS A
data allow calculation of the influence of an external applied stress on the elastic constants in different directions with respect to the direction of applied stress. The mechanical stability of the strained regions that exist around lattice defects will be calculated taking into account the stressinduced modification of the elastic constants. These calculations lead to a full description of the elastic properties and mechanical stability of the beta phase at the
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