Negative thermal expansion of Cu2O studied by quasi-harmonic approximation and cubic force-constant method

Abstract

Cubic cuprous oxide, Cu 2 O, is characterized by a peculiar structural response to temperature: it shows a relatively large negative thermal expansion below 250 K, then followed by a positive thermal expansion at higher temperatures. The two branches of its thermal expansion (negative and positive) are almost perfectly symmetric at low temperatures, with the minimum of its lattice parameter at about 250 K and with the lattice parameter at 500 K almost coinciding with that at 0 K. We perform lattice-dynamical quantum-mechanical calculations to investigate the thermal expansion of Cu 2 O. Phonon mode-specific Grüneisen parameters are computed, which allows us to identify different spectral regions of atomic vibrations responsible for the two distinct regimes of thermal expansion. Two different computational approaches are explored, their results compared, and their numerical aspects critically assessed: a well-established method based on the quasiharmonic approximation, where harmonic frequencies are computed at different lattice volumes, and an alternative approach, where quadratic and cubic interatomic force-constants are computed at a single volume. The latter scheme has only recently become computationally feasible in the context of lattice thermal conductivity simulations. When proper numerical parameters are used (phonon sampling, tolerances, etc.), the two approaches are here shown to provide a very consistent description, yet at a rather different computational cost. All of the experimentally observed features of the complex thermal expansion of Cu 2 O are correctly reproduced up to 500 K, with a slight overall underestimation of the volume contraction.

Thermal expansion and phonon anharmonicity of cuprite studied by inelastic neutron scattering and ab initio calculations

“…5(a) and 5(c) at different temperatures. These Grüneisen parameters are in good agreement with prior QH calculations and experimental results [59]. The plots are color-coded, so the Grüneisen parameters for each mode correspond to the same color mode in the dispersions in Figs.…”

“…Authors of previous studies of cuprite showed the success of QH theory for predicting thermal expansion [59,[61][62][63][64], and some studies included results on phonon dynamics [61,62,65]. We find similar success with QH theory for thermal expansion and with AH theory.…”

“…4. For cuprite, Grüneisen parameters from sTDEP and QH calculations are essentially the same [59]. In the QH approximation, phonon shifts follow the q dependence of the Grüneisen parameters shown in Fig.…”

Evolutionary Algorithm‐Based Crystal Structure Prediction for Copper(I) Fluoride

“…[35,36] For a3 dm etal such as Cu, the use of hybrid DFT over GGA or GGA + U is expected to increase the accuracy of the predictions. [37][38][39][40][41][42][43] All-electron, Gaussian-type triple-z-valence + polarization (TZVP) and split-valence + polarization (SVP) basis sets based on Karlsruhe def2 basis sets were used within the crystal structure predictions (a list with of all used basis sets is provided as SI). [44] Cu I ions are expected to show weak "cuprophilic" d 10 -d 10 interactions, [45][46][47][48] which were taken into account in the USPEX search using Grimme's D3 dispersion correction with zero-damping (ZD).…”

Thermoelasticity of Flexible Organic Crystals from Quasi-harmonic Lattice Dynamics: The Case of Copper(II) Acetylacetonate

“…While calculations based on the density functional theory (DFT) have proved reliable in the prediction of many static properties of materials in the last decades, the effective inclusion of thermal effects still represents a challenge to state-of-the-art DFT methodologies, particularly so when one needs to go beyond the usual harmonic approximation in the description of the lattice dynamics. − For instance, this is the case when (i) cubic interatomic force constants are needed to compute phonon lifetimes and the thermal lattice conductivity and (ii) the free energy dependence on volume and strain is needed to determine thermal expansion and thermoelasticity. While the former class of physical properties above requires the explicit evaluation of anharmonic terms of the nuclear potential, − the latter has often been tackled within the so-called quasi-harmonic approximation (QHA), as long as inorganic solids were considered. − …”