Statistical Thermodynamics of Binary Solid Solutions with Anisotropic Distribution of Atoms
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A statistical-thermodynamical treatment of the anisotropic distribution of atoms in solid solutions, which is responsible for an additional magnetic anisotropy induced by annealing under externally applied magnetic field or stress in ferromagnetic alloys as well as for the internal friction of the α-brass type, is developed in connection with ordinary order-disorder and precipitation phenomena. In order to describe the degree of anisotropic distribution of atoms, we introduce, at first, anisotropic short-range order parameters, σ_κ's, each of which is defined for each nearest-neighbor direction, k. Then, a tensor, Γ, characterizing the short-range atomic configuration involving anisotropic distribution of atoms is defined in terms of σ_κ's. The diagonal sum of Γ is proportional to the value of Bethe's short-range order parameter relative to that at complete disorder and its deviator part describes the anisotropic distribution of nearest-neighbor atom pairs. It is shown that the interaction energy of atomic configuration with directional force (stress or force associated with magnetic interaction of ferromagnetic atoms) can be expressed generally in terms of Γ. The configurational entropy of atoms is evaluated by Takagi's method. Long-range and anisotropic short-range order parameters and hence Γ are calculated for body-centered cubic alloys in which the degree of anisotropic distribution of atoms is small as in actual cases. Thus, the behavior of the anisotropic distribution of atoms as dependent on the temperature, atomic concentration, and direction of applied force is clarified ; in particular the way of abrupt diminution of the anisotropic distribution of atoms with the superlattice formation is indicated. It is also shown that the magnetic anisotropy induced by the anisotropic distribution of atoms has an orthorhombic symmetry and the three anisotropy constants are proportional to the principal values of the deviator part of Γ. Agreement with experimental results on magnetically annealed iron-cobalt alloys is found satisfactory.
- 東北大学の論文
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