No abstract

536.421.1 In terms of the concepts of heterogeneous nucleation and the related driving wave process, a version of the dynamic theory of the formation of martensite crystals is stated in which the wave process initiates the fastest transformation of close-packed {111} γ atomic planes of a parent fcc phase into {110} α planes of a bcc phase. The lattice parameter ratio and the orientations of habit planes are analytically related with the elastic properties of the γ -phase. Quantitative estimation performed with the use of elastic moduli for an iron-nickel alloy yields habitus orientations close to {10 3 7} γ . An experiment is proposed to verify the theoretical predictions. A new pattern of the short-wave correction that finishes the fcc-bcc rearrangement is set forth.The growth of crystals in the (γ-α) fcc-bcc martensitic transformation is a fast process with strongly pronounced indications of the first-order transition. The nucleation is heterogeneous and the growth is controlled by a driving wave process (DWP). Recall [1, 2] that a DWP which forms a plate-shaped region bounded with habit planes (HP's), carries nearly plane and nearly homogeneous threshold deformation (of the tension-compression type) on the mesoscopic scale (of the order of the crystal thickness). As a result, the HP appears to be an invariant (or slightly distorted) plane. The wave normals n 1 and n 2 of the wave beams that describe, respectively, tensile deformation (ε 1 > 0) and compressive deformation (ε 2 < 0) in the superposition region are collinear to the eigenvectors ξ i (i = 1, 2) of the deformation tensor of the elastic field of a defect in the nucleation region (DWP inherits the information on the directions of ξ i ): n 1 || ξ 1 , n 2 || ξ 2 , n 1 ⊥ n 2 | n i | = | ξ i | = ||ξ⊥|||ξ|1.(1)These processes are sketched in Fig. 1. It can easily be shown [1−3] that the normal N w to a habitus plane that is related to the propagation of a driving wave is set by the kinematic relation N w || n 2 ± n 1 ae, ae = 2where v 1 and v 2 are the moduluses of the wave velocity. On the other hand, for a tension-compression deformation the normals to invariant planes are given by

For a model electronic spectrum of a bcc crystal, characteristic s-surfaces are found that separate, in the quasimomentum space, pairs of electronic states potentially active in the generation of elastic waves at the stage of growth of a martensite crystal. Numerical estimation of the fraction of active electronic states (R eff /R) is performed for the energy range ∆ = 0.2 eV near the Fermi level. The ratio R eff /R is calculated as a function of the parameter ratio for the interaction between the nearest and the second neighbors for both bcc and fcc lattices.In the wave model of the growth of a martensite crystal [1] of the fcc-bcc (γ-α) type, the central part is played by the mechanism by which the waves of displacement of atoms by nonequilibrium 3d-electrons are generated. The key parameter is the number of pairs of inversely occupied electronic states which are able to effectively participate in the generation of phonons, R eff . The nonequilibrium character of the electronic subsystem in the interphase region at the stage of crystal growth under reconstructive martensitic transformations is set mainly by the chemical potential gradient ∇µ (we designate its direction by e). The pairs of electronic states potentially active in the generation of displacement waves possess the opposite signs of the nonequilibrium components ∆f of the Fermi electron distribution function. In the quasi-momentum space, these pairs of states are separated by s-surfaces on which the quantity ∆f proportional to the scalar product (v, ∇µ), where v is the group velocity of the electrons, vanishes.If the sections of the s-surfaces whose energies of states, ε, are in an acceptable (of the order of 0.1 eV) range of values of the deviations ∆ from the Fermi level µ are considerable in area, the number of pairs of inversely occupied electronic states able to effectively participate in the generation of phonons, R eff , will be great, and this will ensure the fulfillment of the condition for wave generationwhere σ 0 ~ (v, ∇µ) is the initial inverted population of states and σ th is their threshold inverted population.Clearly, for a known analytic form of the law of electron dispersion, ε(k), it is possible to determine the field of velocities v(k) = ∇ε k and then to find the s-surfaces that separate pairs of inversely occupied electronic states in the k-space. The goal of this work is to construct the s-surfaces typical of the tight-binding approximation for bcc crystals and to calculate the areas ∆S of sections of the s-surfaces (note that R eff ~ ∆S) for various values of µ and parameters of the interaction between the nearest and the second neighbors for both bcc and fcc lattices for a fixed electron energy range, ∆ ≈ 0.2 eV, near the Fermi level.