An analytical formula is obtained from first principles describing the temperature dependence of the elastic modulus of borides, carbides, oxides, nitrides, composites, metals (both simple and transitional), as well as high-entropy alloys (HEAs).

With increasing temperature, the level of mechanical properties that characterize the strength of the material decreases and the level of plastic properties increases. The energy of the interatomic bonds and the compound’s melting point temperature determine the physical properties of the material at high temperatures. Therefore, alloys based on refractory metals soften less with increasing temperature than alloys with lower melting point and cohesive energy.

One of the main requirements for modern materials, products of which are used in extreme operating conditions, is their performance at high temperatures. This explains the interest in studying the temperature-dependent changes in the properties of these materials.

Elastic characteristics are not structurally sensitive like strength, which means that the elastic modulus, calculated from first principles, are characteristics of both, ideal and real (i.e, with defects) materials. Therefore, the role of theoretical methods for calculating the elastic modulus is extremely high.

Direct calculation of the elasticity modulus at different temperatures is a rather difficult task, especially for composites and alloys, because of the complexity of system’s energy thermal part accounting.

To identify the dependence of the mechanical characteristics on temperature, it’s necessary to be able to calculate the energy values of the material’s electron–ion system at different temperatures. In the framework of the pseudopotentials method, this means finding the change in the volume of the unit cells of crystals at non-zero temperatures, i.e. to obtain an explicit dependence of the total energy on the lattice parameters or volume at a nonzero temperature [1].

The elastic characteristics represent the second derivatives of the energy of the electron–ion system by the lattice parameter.

The work explores: linear elastic modulus (Young's modulus) of metals (simple and transitional), metallic equiatomic high-entropy alloys (HEAs), covalent and ionic-covalent crystals, carbides, borides (C, BN, AlN, SiC, B6O, AlB6, HfB, MeB2, LaB6, etc.) and eutectic composites in a wide range of temperatures.

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