First-principles calculations on structure and elasticity of wurtzite-type indium nitride under pressure
Introduction
Group-III nitrides have attracted considerable attention during the past decade due to their promising technological applications in the optoelectronic and electronic devices [1], [2], [3]. Indium nitride crystallizes as a hexagonal wurtzite structure under normal conditions [1], [2], [4], [5], [6], successful growth [7], [8] has also reported that InN grows in zincblende structure. Then, Serrano et al. [9], [10] confirmed that the ZB phase is indeed metastable using first-principles calculations. Theoretical studies based on total energy calculations [11], [12] clearly predicted the high pressure phase of InN is the rocksalt structure. It was confirmed experimentally [4], [13]. The subject of extensive elastic properties studies [14], [15], [16], [17], [18], [19] of InN has been fostered in recent years.
The elastic properties of a solid are important because they are closely related to various fundamental solid-state phenomena such as interatomic bonding, equations of state, and phonon spectra. Elastic properties are also linked thermodynamically with specific heat, thermal expansion, Debye temperature, and Grüneisen parameter. Most importantly, knowledge of the elastic constants is essential for many practical applications related to the mechanical properties of a solid: load deflection, thermoelastic stress, internal strain, sound velocities, and fracture toughness [20].
In 1979, Sheleg et al. [14] firstly reported the experimental elastic constants of wurtzite-type InN (w-InN) from the mean square displacements of the lattice atoms measured by X-ray diffraction. Since then, there have been several theoretical investigations on the elastic constants of w-InN at zero pressure [15], [16], [17], [18], [19]. In 1996, Kim et al. [15] presented a theoretical study of the elastic constants for the w-InN using the FP-LMTO and the tensor transformation method. Very shortly thereafter, Wright et al. [16] calculated the elastic constants of the w-InN from ab initio pseudopotentials and plane-wave method. Then, Chisholm et al. [18] and Marmalyuk et al. [17] studied the elastic constants of the w-InN utilizing empirical and theoretical approaches. Recently, Wang et al. [19] calculated the elastic constants of the w-InN applying a fundamental corresponding states relationship. However, to our knowledge, no other theoretical or experimental data of the w-InN under high pressure are yet reported.
Section snippets
Calculated details
In this work, the high pressure elastic properties of w-InN are investigated in detail. All calculations are performed based on the plane-wave pseudopotential density-function theory (DFT) [21]. Vanderbilt-type non-local ultrasoft pseudopotentials (USPP) [22] are employed to describe the electron–ion interactions. The effects of exchange–correlation interaction are treated with the local density approximation (LDA) of the Ceperley–Alder data as parameterized by Perdew–Zunger (CA–PZ) [23]. In
Results and discussion
In Table 3, we list the pressure dependencies of the calculated normalized primitive cell volume V/V0, and axial ratio c/a, elastic constants cij, the aggregate elastic modulus (B, G, E), and the Poisson’s ratio (ν) of the w-InN at zero temperature, where V0 is the zero pressure equilibrium primitive cell volume. According to our recent work [40], the phase transition pressure from the WZ to the RS occurs at 10.1 GPa for InN. For hexagonal crystals, the mechanical stability under isotropic
Conclusions
In summary, the lattice parameters, bulk modulus and its pressure derivative, the elastic properties of the w-InN are investigated by ab initio plane-wave pseudopotential density functional theory method. The pressure dependencies of the normalized primitive cell volume V/V0, the elastic constants cij, the aggregate elastic modulus (B, G, E), the Poisson’s ratio (ν), the compressional and shear wave velocities, and the Debye temperature ΘD are successfully obtained. The experimental values of
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