Abstract
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 Co2-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<AU<2.73. The compounds with higher AU values are found close to the middle of the transition metal series. In particular, Co2ScAl with AU=0.01 is predicted to be an isotropic material that comes closest to an ideal Cauchy solid as compared to the remaining Co2-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.
Highlights
There is a broad interest in Heusler compounds owing to the multitude of different thermal, electrical, magnetic, and transport properties that are realized in a rather simple crystalline structure
The main part of the work focuses on Co2-based compounds that are Co2MnM with the main group elements M 1⁄4 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 1⁄4 Sc, Ti, V, Cr, Mn, and Fe
We developed our own routines and used them to determine the elastic constants and to analyze them in detail
Summary
There is a broad interest in Heusler compounds owing to the multitude of different thermal, electrical, magnetic, and transport properties that are realized in a rather simple crystalline structure. According to Born, a necessary condition for the thermodynamic stability of a crystal lattice is that the crystals have to be mechanically stable against arbitrary (small) homogeneous deformations This is the main concept of elastic constants. Elastic constants provide important information concerning the strength of materials and often act as stability criteria or order parameters in the study of the problem of structural transformations.6–8 Further physical properties, such as hardness, velocity of sound, Debye temperature, and melting point are related to the elastic constants.. The information is an essential requirement for industrial applications and for fundamental research Examples of the latter case are the superconducting and heavy fermion systems, in which a drastic change of elastic constants and related properties has been obtained upon phase transition.. The results for the elastic properties of tetragonal and phase change materials that exhibit magnetic shape memory and magnetocaloric effects are published elsewhere. Some basic calculational aspects, including the convergence of the method, are found in Ref. 21
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