Impact of Exchange-Correlation Functionals on Predictions of Phonon Hydrodynamics: A Study of Fluorides, Chlorides, and Hydrides

TL;DR

The study investigates how exchange-correlation functionals influence predictions of phonon hydrodynamics in fluorides, chlorides, and hydrides by combining density functional theory with perturbation theory and an iterative Boltzmann transport equation. Phonon transport regimes are identified using Guyer’s criterion, with average scattering rates guiding the ballistic, hydrodynamic, and diffusive windows; second-sound predictions are explored for several compounds. The authors find that the choice of functional (PBE, PBESOL, LDA) significantly affects lattice constants, LO–TO splittings, and thermal transport, yielding wide hydrodynamic windows for LDA and notable variations across materials, including novel hydrodynamics predictions for LiH, NaH, KH, KF, NaCl, and KCl. Isotope scattering can substantially alter the hydrodynamic windows in Li-containing compounds, and meta-GGA/hybrid functionals tend to produce results that lie between PBE and PBESOL, underscoring the nontrivial impact of XC selection on phonon-mediated heat transport and its experimental observability.

Abstract

We employ density functional theory calculations to examine the effect of various exchange-correlation (XC) functionals, including the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE), the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBESOL), and the local density approximation (LDA), on the electrical, mechanical, and thermal properties of sodium fluoride (NaF), lithium fluoride (LiF), potassium fluoride (KF), sodium chloride (NaCl), potassium chloride (KCl), lithium hydride (LiH), sodium hydride (NaH), and potassium hydride (KH). The lattice thermal conductivity is computed based on an iterative solution of the Boltzmann transport equation (BTE). Based on Guyer's criterion and direct solutions to the linearized BTE, we determine the ballistic, phonon hydrodynamics and diffusive regimes as function of length scale and temperature. In addition to confirming previous predictions of phonon hydrodynamics in NaF and LiF, we report novel predictions of phonon hydrodynamics in NaH, LiH, KH, KF, NaCl and KCl. The impact of isotopes on the calculated lattice thermal conductivity and phonon hydrodynamics windows is also reported. The impact of Meta-GGA and hybrid functionals is also discussed. We find that the selection of a functional impacts the prediction of thermal conductivity and the window for observation of phonon hydrodynamics.

Figures (7)

• Figure 1: Unit cell of NaCl cubic crystal. Blue spheres denote Na atoms; gray spheres denote Cl atoms.
• Figure 2: Calculated phonon dispersion and phonon density of states for: (a) NaF, black circles are the measured data from Ref. buyers1967lattice. (b) LiF, black circles are the measured data from Ref. dolling1968lattice. (c) KF, black circles are the measured data from Ref. buhrer1970lattice. (d) NaCl, black circles are the measured data from Ref. schmunk1970lattice. (e) KCl, black circles are the measured data from Ref. copley1969lattice. (f) LiH, black circles are the measured data from Ref. verble1968lattice. (g) NaH. (h) KH. Calculations were done with PBE (black), PBESOL (red), and LDA (blue).
• Figure 3: Calculated lattice thermal conductivity for: (a) NaF. (b) LiF. (c) KF. (d) NaCl. (e) KCl. (f) LiH. (g) NaH. (h) KH. Calculations were done with PBE (black solid line), PBESOL (red solid line), and LDA (blue solid line). Calculations also show the effect of the isotopes on the thermal conductivity: PBE (black circles), PBESOL (red circles), and LDA (blue circles). Experimental data: Ref. smirnov1845thermal (orange circles), Ref. petrov1974temperature (gray triangles), Ref. walker1963thermal (pink squares), Ref. petrov1976behaviour (orange triangle), Ref. vetrano1957batelle (pink triangles), Ref. slack1973nonmetallic (orange squares). Theoretical data: Ref. gheribi2016formulation (purple diamonds), Ref. lindsay2016isotope (pink diamonds), Ref. liang2018lattice (green pentagons), Ref. singh2003effects (purple squares), Ref. yang2017thermal (purple pentagons).
• Figure 4: Phonon hydrodynamics windows for NaF at $L$ = 8.3 mm. Calculations were done with PBE (black dashed lines), PBESOL (red dashed lines), and LDA (blue dashed lines). Double arrow lines show the hydrodynamics range for each functional. The experimental value (Ref. jackson1970second) is shown as a dashed vertical orange line.
• Figure 5: Thermal transport regimes (phonon hydrodynamics regime, ballistic regime, and diffusive regime) for: (a) NaF. (b) LiF. (c) KF. (d) NaCl. (e) KCl. (f) LiH. (g) NaH. (h) KH. Double arrow lines show the window of phonon hydrodynamics for each functional. PBE (black dashed lines), PBESOL (red dashed lines), and LDA (blue dashed lines).