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Elastic constants and their derived properties of various cubic Heusler compounds were calculated using the first-principles density functional theory. To begin with, Cu2MnAl is used as a case study to explain the interpretation of the basic quantities and compare them with experiments. The main part of the work focuses on Co-2-based compounds that are Co2MnM with the main group elements M = Al, Ga, In, Si, Ge, Sn, Pb, Sb, Bi, and Co2TM with the main group elements Al or Si, and the 3d transition metals T = Sc, Ti, V, Cr, Mn, and Fe. It is found that many properties of Heusler compounds correlate to the mass or nuclear charge Z of the main group element. Additional representation and compact simplification of the elastic data is useful to investigate and compare their influence on crystal stability and physical properties. Here, Blackman's and Every's diagrams are used to compare the elastic properties of the materials, whereas Pugh's and Poisson's ratios are used to analyze the relationship between interatomic bonding and physical properties. It is found that Pugh's criterion on brittleness needs to be revised whereas Christensen's criterion describes the ductile-brittle transition of Heusler compounds very well. The calculated elastic properties give hint on a metallic bonding with an intermediate brittleness for the studied Heusler compounds. The universal anisotropy of the stable compounds has values in the range of 0.57 < A(U) < 2.73. The compounds with higher A(U) values are found close to the middle of the transition metal series. In particular, Co2ScAl with A(U) = 0.01 is predicted to be an isotropic material that comes closest to an ideal Cauchy solid as compared to the remaining Co-2-based compounds. Apart from the elastic constants and moduli, the sound velocities, Debye temperatures, and hardness are predicted and discussed for the studied systems. The calculated slowness surfaces for sound waves reflect the degree of anisotropy of the compounds. (c) 2018 Author(s).
