Lattice Dynamics and Thermochemistry of Solid‐State Materials from First‐Principles Quantum‐Chemical Calculations

Abstract

Within the last decade, the prediction of the thermodynamic properties of solid‐state materials based on first‐principles quantum‐chemical methods has matured to a degree that allows for quantitative applications in real‐world scenarios. The key ingredient for modeling the thermodynamic potentials and their temperature dependence is given by the accurate simulation of lattice dynamics as described by the phonon model. On the basis of the electronic as well as phononic energies (plus other energetic contributions, if needed), macroscopic thermodynamic potentials such as the Gibbs free energy are accessible via the quasi‐harmonic approximation for any given solid‐state material, at least in principle.

Melting Behavior of Alkaline-Earth Metal Carbodiimides and Their Thermochemistry from First-Principles

“…Phonon computations were conducted using the program PHONOPY based on the Hellmann–Feynman forces calculated using VASP. The supercells for the force calculations were set up by multiplying the unit cells in each direction such that the lattice parameters of the supercells were well above 10 Å. Thermodynamic potentials were obtained in the framework of the quasi-harmonic approximation. , The calculations were conducted for the crystal structures of all of the alkaline-earth metal carbodiimides, alkaline-earth metals, graphite, and crystalline nitrogen. ,,,− …”

“…Going beyond pure electronic energies at 0 K and reaching finite T , the Gibbs energies of the crystalline compounds at high temperatures were obtained by the quasi-harmonic approximation in the standard procedure. , The Gibbs free energy of gaseous nitrogen was constructed by summing up the electronic total energy E 0 , the vibrational zero-point Helmholtz free energy A ph,0 calculated for crystalline α-nitrogen, literature values of the sublimation enthalpy ΔH sub , the entropy S , and the heat capacity C p ( T ) of gaseous nitrogen. , The following equation was employed, as in a previous publication The Gibbs energies for the decomposition reaction are plotted in Figure . The point of ΔG r = 0 indicates the temperature where the spontaneous decomposition of the alkaline-earth metal carbodiimide occurs.…”

Examination of a Structural Preference in Quaternary Alkali-Metal (A) Rare-Earth (R) Copper Tellurides by Combining Experimental and Quantum-chemical Means

“…An inspection of the phonon band structure for the “K 3 Er 4 Cu 5 Te 10 ” type-III-based model (Figure S7) reveals the presence of negative values of the phonon frequencies, while such imaginary wavenumbers, which typically , point to a dynamic instability of a given solid-state material, are not evident in the phonon band structure of the type-I-fashioned “K 3 Er 4 Cu 5 Te 10 ” model (Figure S6). An additional analysis of the Fermi level characteristics for both “K 3 Er 4 Cu 5 Te 10 ” models points to situations that are frequently ,, regarded as electronically favorable states because the Fermi levels of both “K 3 Er 4 Cu 5 Te 10 ” models are located within band gaps (Figure ).…”

Identifying the Origins of Vacancies in the Crystal Structures of Rock Salt-type Chalcogenide Superconductors

“…The enthalpies of formation at zero temperature were calculated based on the total (electronic ground state) energies because the pressure-dependent zero-temperature enthalpy, i.e., H el ( p ) = E el ( V ( p )) + pV ( p ), approaches E el as the pressure vanishes. 46,47 In this context, it should also be mentioned that this approach could be used since E el approximates the internal energy at zero temperature. 47 Thus, the enthalpies of formation of MS (M = Sc, Y, Zr, Lu), M 31 S 32 (M = Sc, Y, Lu), and Zr 29 S 32 were computed by subtracting the sum of the total energies of all constituting elements from the total energy of the respective sulfideandfor p = 0 bar and T = 0 K. Notably, the enthalpy of formation of the zirconium-deficient sulfide has been calculated based on total energies of Zr 29 S 32 and 29 zirconium atoms.…”

“…46,47 In this context, it should also be mentioned that this approach could be used since E el approximates the internal energy at zero temperature. 47 Thus, the enthalpies of formation of MS (M = Sc, Y, Zr, Lu), M 31 S 32 (M = Sc, Y, Lu), and Zr 29 S 32 were computed by subtracting the sum of the total energies of all constituting elements from the total energy of the respective sulfideandfor p = 0 bar and T = 0 K. Notably, the enthalpy of formation of the zirconium-deficient sulfide has been calculated based on total energies of Zr 29 S 32 and 29 zirconium atoms. A comparison of the enthalpies of formation for all sulfides reveals negative values of Δ H f for all materials such that the formations of these compounds tend to be preferred.…”