(a) Explicitly disordered alloy supercell of silicon and “heavy” silicon ( direction into the page). 50 (b) Equivalent VC supercell with one averaged mass. The sphere size represents increasing mass only, no bond disorder is considered. The 8-atom conventional cubic unit cell is shown in(b).
Vibrational DOS for LJ alloys calculated using the VC approximation and an explicitly disordered supercell (labeled Gamma) for concentrations of (a) 0.05, (b) 0.15, and (c) 0.5. VC and Gamma show similar low-frequency behavior for all concentrations. For increasing concentrations, the frequencies of both VC and Gamma decrease, while the high frequency DOS for Gamma spreads and reaches to a higher maximum frequency because of the explicit disorder. The supercells are of size (6912 atoms).
Left and right panels: The structure factor for longitudinal (SL ) and transverse (ST ) polarizations along high-symmetry directions of the mass disordered LJ argon supercells ( , c = 0.05, 0.5). Center panels: The VC predicted dispersion curves (solid lines) agree well with the locations of the peaks in SL and ST (data points). The wavenumber axis in the center panel is normalized by the maximum value of the wavenumber in the given direction.
Lifetimes predicted using VC-NMD and Gamma-NMD from MD simulations of (a) perfect LJ argon and (b)–(d) mass-disordered LJ alloys for . and scalings are observed at low to mid frequencies. For both VC-NMD and Gamma-NMD, most mode lifetimes are greater than the Ioffe-Regel limit of . 74 While there is more scatter in the Gamma-NMD data (see Sec. ??? ), the lifetime magnitudes and trends agree well, an important consideration when comparing the VC-NMD and VC-ALD lifetimes in Fig. 5(a) .
(a) Predicted lifetimes using VC-NMD and VC-ALD for LJ argon (T = 10 K, , and c = 0.05). (b) Mode diffusivities compared to the high-scatter limit, DHS [Eq. (18) ], and IR limit, DIR [Eq. (19) ]. VC-NMD and VC-ALD predict a large number of high-frequency modes with . (c) Thermal conductivity frequency spectrum, which peaks at high frequency, in contrast to SW silicon [(Fig. 8(c) ].
AF theory predictions of disordered mode diffusivities for LJ argon alloy and amorphous phases. The amorphous phase is well-described by a mode-independent diffusivity DHS [Eq. (18) ]. The system size for the alloy is (6912 atoms), and the amorphous phase has 6912 atoms.
Thermal conductivity predictions for LJ argon and alloys at T = 10 K using the VC-NMD, VC-ALD, and GK methods. The high-scatter thermal conductivity prediction kHS [Eq. (3) ] and the high-scatter adjusted VC-NMD* and VC-ALD* are also plotted.
(a) Predicted lifetimes using VC-NMD and VC-ALD for SW silicon (T = 300 K, , and c = 0.05). (b) Mode diffusivities compared to the high-scatter limit, DHS [Eq. (18) ], and the IR limit, DIR [Eq. (19) ]. VC-NMD and VC-ALD predict a large number of high-frequency modes with , as seen in the LJ argon alloys [Fig. 5(b) ]. (c) Thermal conductivity frequency spectra, which peak at low frequency, in contrast to LJ argon [Fig. 5(c) ].
Thermal conductivity predictions for SW silicon and alloys at a temperature of 300 K using the VC-ALD and GK methods. The high-scatter thermal conductivity prediction kHS is also plotted. The adjusted VC-ALD* is not shown since it differs by less than one percent compared to VC-ALD.
The normal mode kinetic energy, , of two modes (A and B) at wavevector [0.25 0 0] calculated using VC-NMD for a mass disordered LJ FCC supercell ( and c = 0.5) is shown in the main figure. The VC dispersion-predicted peaks are labeled by . The inset shows the same mode's energy [kinetic (KE) and total (TE)] autocorrelation functions. Note the additional oscillation effects in the KE and TE autocorrelation functions for Mode B, which are due to the two peaks in . A mode lifetime can be extracted unambiguously using the integral of the TE autocorrelation function [Eq. (11) in Sec. ??? ].
Thermal conductivity predictions using the VC-NMD, VC-ALD, and GK methods. For LJ argon alloys, the bulk extrapolation is used for all three methods. For SW silicon alloys, only VC-ALD and GK can be used to extrapolate a bulk thermal conductivity (see Sec. IV ). For VC-NMD and GK, the uncertainties are estimated by omitting independent simulations from the ensemble averaging (see Sec. II C ). For VC-ALD, the uncertainties are estimated by omitting extrapolation points used for Eq. (21) .
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