Order-Disorder Transitions in A_2BC Ternary Alloys with the Plane Square or the Body-Centered Cubic Lattice

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The statistics of the ternary alloy A_2BC in the plane square or the b.c.c. lattice is investigated with the same schematic model as used in the usual theories on binary alloys. The calculation is made at the level of the Bragg-Williams approximation. The behaviours of the system are determined by two quantities v_1=V_<CA>/V_<BC> and v_2=V_<AB>/V_<BC> and by the sign of V_<BC>, where V_<ij>=(ε_<ii> +ε_<jj>)/2-ε_<ij>・(i and j stand for A. B or C; ε_<ij> is the interaction energy between i- and j-atoms.) Four types of ordered states can appear: A(BC) type, (AB)(AC) type and other two intermediate types. They are all partly ordered states in which the Heusler type is not included, for only two sublattices can be distinguished under the present assumption. Which type appears is determined by v_1, v_2 values. The transition is always of the second kind. The contours of the transition temperature on the v_1-v_2 plane are parabolas, and those of the peak value of the specific heat are a pencil of the half infinite straight lines with the center at (3/4, 3/4). The latter contours have the maximum when V_<BC>=0, that is, when the system reduces to the AB binary alloy. The segregation temperatures are calculated, without taking the ordering effect into account, in order to show that the order-disorder transition cannot realize at least for some v_1, v_2 values, being covered by segregation.
社団法人日本物理学会の論文
1954-08-25