Settling the matter of the role of vibrations in the stability of high-entropy carbides

Abstract

High-entropy ceramics are attracting significant interest due to their exceptional chemical stability and physical properties. While configurational entropy descriptors have been successfully implemented to predict their formation and even to discover new materials, the contribution of vibrations to their stability has been contentious. This work unravels the issue by computationally integrating disorder parameterization, phonon modeling, and thermodynamic characterization. Three recently synthesized carbides are used as a testbed: (HfNbTaTiV)C, (HfNbTaTiW)C, and (HfNbTaTiZr)C. It is found that vibrational contributions should not be neglected when precursors or decomposition products have different nearest-neighbor environments from the high-entropy carbide.

Along the road to crystal structure prediction (CSP) of pharmaceutical-like molecules

“…E vib ( T ) is the total (thermal and zero-point) vibrational energy. At ambient pressure, the pV term is usually negligible, reducing the Helmholtz free energy formula to F ( T ) = E latt + F vib ( T ) − TS conf , with the vibrational contributions defined by eqn (3)–(6): 103 where g ( ω ) is the phonon density of states as a function of frequency ω , ħ is the reduced Planck constant, and k B is the Boltzmann constant. 104 At 0 K, both the S vib ( T ) and the thermal vibrational energy contribution vanish, and the only remaining term is the zero-point vibrational energy, E ZPVE , defined as: E ZPVE is largely dictated by high-energy internal vibrations, whereas both S vib ( T ) and the thermal contributions to E vib are dominated by excitations of low-energy lattice vibrations (external modes).…”

aflow++: a C++ framework for autonomous materials design

“…[VASP_FORCE_OPTION]CONVERT_UNIT_CELL=SPRIM which also takes SCONV (aflow++ conventional representation), NIGGLI (Niggli standard form [74,75]), MINK (Minkowski-reduced lattice), INCELL (moving atoms inside the inequivalent unit cell), COMPACT (moving atoms to reduce distance between them and expose bonds), WS (Wigner-Seitz cell), CART/FRAC (Cartesian/direct coordinates), PRES (no modification of input structure). The aflow++ standard conventional representation has been useful for phonon calculations (via finite-displacement), achieving more spherical supercells that include more full coordination shells while keeping cell sizes as small as possible (see Section VII B) [41].…”

“…The aflow++ Automatic Phonon Library (APL) calculates phonon modes in the harmonic approximation by diagonalizing the dynamical matrix D (q) [41]:…”

“…aflow-POCC has been validated for a number of systems and properties [8,10,31,41,150], including electronic, magnetic, thermodynamic, and thermomechanical properties. It has also been demonstrated that the accuracy improves with larger supercell sizes [31], providing better sampling and capturing longer-range effects.…”

“…Descriptors are feasibly-calculated quantities based on microscopic features that offer predictive power of macroscopic properties of the material [33]. Their development and application remain at the heart of aflow++, particularly for the prediction of thermodynamic stability/synthesizability [34], electronic [35][36][37], and thermomechanical [38][39][40][41][42][43][44] properties.…”