Computational Physics
(S. L. Qiu and F. Mari)
Funded by the NSF



In this project, we set out to find the stable and metastable phases of a crystal. Metastable phases of a material of given composition are essentially new materials, which may have properties very different from the ground state phase. Much effort has been made to find the metastable phases of a material by applying pressure, changing temperature, and by varying concentrations of components. The growing interest in finding such new materials makes theoretical studies of metastable phases particularly important, both to indicate where experimentalists should look and to verify any observed phases. We propose to reduce the search for the ground state and metastable phases of an arbitrary crystal at any pressure to a computationally feasible problem. The first-principles computation can be shown to be a search for the minimum of a calculable free energy function G as a function of the structural parameters in a space of a moderate number of dimensions—6 for a pure Bravais lattice, 9 for structures with two atoms in the unit cell, etc. The computation requires that we find the minimum in a moderate number of steps starting from an assumed structure. A key to finding the minima is to test the positive definiteness of the quadratic terms of an expansion of G in strains around the assumed structure. If that quadratic form in the strains is positive definite, which is easily tested by finding if the eigenvalues of the coefficient matrix of the quadratic form are all positive, there is a clear efficient path to the minimum. If an eigenvalue is negative, there is a clear path to a new state with a positive eigenvalue using the eigenvector of that negative eigenvalue.

This procedure has been tested in various special cases, especially for crystals of tetragonal symmetry and the operations seem easily generalizable to arbitrary symmetry. A number of new metastable phases of tetragonal and hcp structures have been found by this procedure.

There may be a vast number of undiscovered metastable phases when all symmetries are considered, when several atoms in the unit cell are allowed and when a large range of pressures is studied. We plan to do calculations on metals systematically (especially 3d, 4d and 5d metals) looking for metastable phases up to high pressure. We expect that the predictions of new metastable phases from our proposed calculations will stimulate more experimental research for new materials. Also our calculations will provide new insights into the phase stability of the metastable phases, since quantitative values of G will be found.

All our calculations on metastable phases of tetragonal and hcp structures were carried out with WIEN2k code in parallel mode using the computational resources BOCA4 Beowulf at the College of Science. It usually takes from several months to a year to finish calculations of a single element such as hcp Fe, Zn and Cd in a structure space of two dimensions. Basically, in WIEN2k, parallelization is achieved by a master with multiple slaves. It is achieved on the k-point level by distributing subsets of the k-mesh to different processors and subsequent summation of the results. All the distribution work is done by the master and all the slaves used in the calculations communicate with the master all the time and the final results will be stored in the master. Traffic is going back and forth between the server and the nodes. The synchronization of the nodes is extremely sensitive to the parallel executions, otherwise the calculation will be crashed.

Since a structure space of 6 dimensions or 9 dimensions is used in the proposed project, more powerful computers, preferably ones with shared-memory to reduce communication and synchronization overhead among master and slave, are demanded. We plan to port our code to the global shared memory platform and execute the code on the SGI supercluster.