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Total-energy band calculations, including an antiferromagnetic extension of the fixed-spinmoment procedure, are used to study magnetovolume effects in bulk fcc iron and maganese. By constraining these systems to have a fixed tota1 magnetic moment in a single-atom fcc unit cell, we find magnetovolume instabilities in the form of first-order transitions from nonmagnetic to ferromagnetic behavior. Constraining the moments to have fixed values in a CuAu unit ce11 of two atoms to allow for antiferromagnetic (and field-induced ferrimagnetic) order alters these instabilities and yields second-order transitions from nonmagnetic to antiferromagnetic behavior at volumes coincident with the equilibrium volumes for both metals.

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Paths of tetragonal states between two phases of a material, such as bcc and fcc, are called Bain paths. Two simple Bain paths can be defined in terms of special imposed stresses, one of which applies directly to strained epitaxial films. Each path goes far into the range of nonlinear elasticity and reaches a range of structural parameters in which the structure is inherently unstable. In this Letter we identify and analyze the general properties of these paths by density functional theory. Special examples include vanadium, cobalt, and copper, and the epitaxial path is used to identify an epitaxial film as related uniquely to a bulk phase. [S0031-9007(97)03190-6] PACS numbers: 64.70. Kb, 61.50.Ks, 62.20.Dc Pseudomorphic epitaxy of a cubic or tetragonal (001) film typically results in a strained tetragonal structure. If the stresses on the tetragonal state vanish and also the state corresponds to a local minimum of energy with respect to tetragonal deformations, the structure will be called a tetragonal phase. Such a phase will be stable or metastable, depending on whether it has the lowest energy compared to other minima. Frequently metals have two tetragonal phases; sometimes both are cubic, e.g., bcc and fcc Na and Rb [1,2]; sometimes one is cubic and the other phase is tetragonal, e.g., Ti and V [2,3]. They can, of course, also have phases with other structures; e.g., Ti also has a hcp phase.Many paths can go from one tetragonal phase to the other. If the geometries along such a path have tetragonal symmetry and if they connect bcc and fcc phases, the paths have been called Bain paths [4]. A purpose of the present work is to define and discuss a particular Bain path which will be called the epitaxial Bain path (EBP). The EBP is produced by isotropic stress or strain in the (001) plane of tetragonal phases accompanied by vanishing stress perpendicular to the plane, such as pseudomorphic epitaxy produces on an (001) cubic or tetragonal film. Epitaxy provides a valuable means of stabilizing metastable phases and of putting phases under very large strains, both tensile and compressive in the plane of the epitaxy. The EBP of a material identifies the phase that has been strained, checks quantitatively the elastic behavior, which can be highly nonlinear, and predicts which phase of the material will form on a given substrate. Thus, in order to understand the properties of epitaxial films and new materials, the knowledge of the EBP is indispensable.A different Bain path has long been discussed, particularly by Milstein [1], in which uniaxial stress is applied to a tetragonal state along the ͓001͔ axis accompanied by zero stress in the (001) plane; this path is conveniently called the uniaxial Bain path (UBP). We compare the two paths, EBP and UBP, which are both physically realizable. We show that both have the same lowest possible maximum energy or barrier energy of all Bain paths between the two tetragonal phases. However, the EBP has a special value in relating strained tetragonal structures produced by epita...

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It is shown that the theory of elasticity under hydrostatic pressure p at zero temperature is unified and simplified by the use of the Gibbs free energy G, rather than the energy E. The minima of G, but not of E, give the equilibrium structure; the second derivatives of G, but not of E, with respect to strains at the equilibrium structure give the zero-temperature elastic constants; the stability of a phase at p is then determined by the same Born stability conditions used at p = 0 when applied to the elastic constants from G. Examples are noted of mistakes due to use of E rather than G.

First-principles total-energy band calculations using the fixed-spin-moment procedure are used to study the volume dependence of the magnetic behavior for fcc Rh and Pd. We calculate the total energy, the magnetic moment, and the spin-polarized l-decomposed electron occupancy from below the equilibrium volume to the free-atom limit, and show the magnetic susceptibility in the nonmagnetic range. We find that both metals are nonmagnetic at zero pressure, but undergo first-order transitions from nonmagnetic to magnetic behavior at expanded volumes. In both cases, the onset of magnetic behavior is accompanied by magnetic moments that exceed the Hund's-rule atomic limit. With increasing volume, we find a depletion of s and p states and a corresponding increase of d states with an approach to the 4d and 4d ' free-atom configurations for Rh and Pd, respectively.