A Critical Study of the Elastic Properties and Stability of Heusler Compounds: Phase Change and Tetragonal <i>X<sub>2</sub>YZ</i> Compounds

Abstract

In the present work, the elastic constants and derived properties of tetragonal Heusler compounds were calculated using the high accuracy of the full-potential linearized augmented plane wave (FPLAPW) method. To find the criteria required for an accurate calculation, the consequences of increasing the numbers of k-points and plane waves on the convergence of the calculated elastic constants were explored. Once accurate elastic constants were calculated, elastic anisotropies, sound velocities, Debye temperatures, malleability, and other measurable physical properties were determined for the studied systems. The elastic properties suggested metallic bonding with intermediate malleability, between brittle and ductile, for the studied Heusler compounds. To address the effect of off-stoichiometry on the mechanical properties, the virtual crystal approximation (VCA) was used to calculate the elastic constants. The results indicated that an extreme correlation exists between the anisotropy ratio and the stoichiometry of the Heusler compounds, especially in the case of Ni 2 MnGa. Metastable cubic Ni 2 MnGa exhibits a very high anisotropy (≈28) and hypothetical cubic Rh 2 FeSn violates the Born-Huang stability criteria in the L2 1 structure. The bulk moduli of the investigated tetragonal compounds do not vary much (≈130 ··· 190 GPa). The averaged values of the other elastic moduli are also rather similar, however, rather large differences are found for the elastic anisotropies of the compounds. These are reflected in very different spatial distributions of Young's moduli when comparing the different compounds. The slowness surfaces of the compounds also differ considerably even though the average sound velocities are in the same order of magnitude (3.2 ··· 3.6 km/s). The results demonstrate the importance of the elastic properties not only for purely tetragonal Heusler compounds but also for phase change materials that exhibit magnetic shape memory or magnetocaloric effects.

Half-metallicity in new Heusler alloys Mn2ScZ (Z = Si, Ge, Sn)

“…The details about the type of strains applied are given in ref. 84. The symmetry of the cubic crystal reduces the total number of independent elastic constants into 3 i.e.…”

“…The Pugh's ratio (B/G) with a critical value of 1.75 (ref. 84) predicts their ductile with ionic type of bonding. One can also determine the type of atomic bonding by calculating C P with large negative value for directional covalent bonding whereas a positive value for non-directional metallic bonding and all the materials are found to show non-directional metallic bonding in the present study.…”

A theoretical analysis of elastic and optical properties of half Heusler MCoSb (M=Ti, Zr and Hf)

“…One of the method to ensure the stability of a structure through theoretical calculations is to check its mechanical stability which according to Born [8] is a necessary condition for thermodynamic and structural stability. Thus, the role of elastic constants is important to determine the mechanical stability in order to further verify the stability criterion and the order parameter of a structure [9]. Very few experimental and theoretical works are available on the investigation of elastic properties of these compounds.…”

Structural, Elastic, Electronic and Magnetic Properties of MnNbZ (Z=As, Sb) and FeNbZ (Z=Sn, Pb) Semi-Heusler Alloys

“…give very close results to each other indicates that the calculations are correct, which are clearly shown in table(1) and(2). The Young's modulus and Poisson's ratio used to investigate the hardness of polycrystalline materials were calculated using the following formulas,45 …”

“…The bulk modulus (B) and the isotropic shear modulus (G) has been calculated using the Voigt-Reuss and Hill approximation. 44,45 Using C ij elastic constants, they can be calculated as: The fact that the bulk modulus calculated from the optimization and the elastic properties greater than these values, the material is ductile, otherwise, it is brittle. 47 Cauchy pressure (C 12 -C 44 ) can be defined as the angular character with atomic bonding, the negative value for directional covalent bonding whereas positive value for non-directional metallic bonding.…”