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give the phenomenological Weiss model a quantummechanical basis and to provide an itinerant electron interpretation. They used an ordered Fe3Ni structure to simulate the Invar alloy and found that the ferromagnetic ground state has its equilibrium at a larger volume than the nonmagnetic state which lies slightly higher in energy. Recent high-precision calculations' verified the existence of an additional low-moment state leading to a magnetovolume instability. On the basis of these results 47 8706 1993 The American Physical Society 47 FIRST-PRINCIPLES CALCULATIONS OF THE INSTABILITY. . . 8707the Invar effect is explained by the specific temperature evolution of the LM and HM states which are assumed to merge at high temperatures. However, the nature of the mixing of these states remains unclear.In spite of its simplicity, the model has proven to be very successful. Moruzzi" has shown that the gradual transition from the high-volume (HM) to the low-volume (LM) state with increasing temperature can be accounted for by combining total-energy-band calculations with the Debye-Gruneisen theory. In his formulation the temperature evolution of the free energy is governed by volumedependent quantities, the rigid-lattice total energy E( V) and the volume dependence of the Debye temperature O=OO(Vo/V)r, where V is the volume and Vo is the rigid-lattice equilibrium volume. By choosing a different set of thermal parameters ( VO, OO, and y) for the HM and LM branches of ordered Fe3Ni, Moruzzi observed that Invar behavior requires that the HM solution defines the ground state at low temperatures, while the LM solution leads to the ground state at high temperatures. This theory qualitatively explains the anomalous temperature dependence of the thermal expansion, bulk modulus, magnetization, high-field susceptibility, and the different pressure dependencies of the lattice constant at different temperatures of Invar.A different microscopic investigation was undertaken by Johnson et al. ' ' They used a self-consistent KKR-CPA study of the Fe-Ni system for different volumes and investigated the competition between bonding and magnetism. More recently they used a mean-field statistical mechanics approach at finite temperatures which uses the accurate KKR-CPA energy for the configurationally averaged energy as input. With increasing Fe content, the theory predicts a crossover in the Invar region from the HM state to a state of magnetic dis-