A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for TiSi2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA). The calculated values compare favorably with recent experimental results. An expression to calculate the bulk modulus along crystallographic axes of single crystals, using elastic constants, has been derived. From this the calculated linear bulk moduli are found to be in good agreement with the experiments. The shear modulus, Young’s modulus, and Poisson’s ratio for ideal polycrystalline TiSi2 are also calculated and compared with corresponding experimental values. The directional bulk modulus and the Young’s modulus for single crystal TiSi2 are estimated from the elastic constants obtained from LDA as well as GGA calculations and are compared with the experimental results. The shear anisotropic factors and anisotropy in the linear bulk modulus are obtained from the single crystal elastic constants. From the site and angular momentum decomposed density of states combined with a charge density analysis and the elastic anisotropies, the chemical bonding nature between the constituents in TiSi2 is analyzed. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as the integration of elastic wave velocities in different directions of the single crystal. The calculated elastic properties are found to be in good agreement with experimental values when the generalized gradient approximation is used for the exchange and correlation potential.

The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements

This paper reviews the crystal structure of compounds with the general formula AB 2 X 4 , which crystallize with the same atomic structure as the mineral spinel, MgAl 2 O 4 . Three degrees of freedom associated with the detailed atomic arrangements of spinels are considered here: (i) the lattice parameter, a; (ii) the anion parameter, u; and (iii) the cation inversion parameter, i. Oxide spinels are used as examples to explore the interrelationships between these parameters.

The five diit'erent elastic constants of all the hexagonal 4d transition metals {Y,Zr, Tc, and Ru) and the 5d transition metals Re and Os have been calculated by means of first-principles electronicstructure calculations using the full-potential linear mufBn-tin orbital method. The calculated data agree with the experimental values within 30+0. We demonstrate, using experimental data, that the hexagonal transition metals obey the Cauchy relations much better than the cubic ones. This is due to the fact that the shape of the density of states for the hexagonal materials retains its form to a larger extent, for all types of shears, than it does for the cubic metals. We introduce normalized elastic constants C" , =C';~. /B, where B is the bulk modulus, which show a regular behavior for the hexagonal transition metals, in contrast to the cubic transition metals, where large irregularities are observed. These regular as well as irregular behaviors are well reproduced by the full-potential calculations.

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