Jason Larkin | Carnegie Mellon University (original) (raw)
Papers by Jason Larkin
We predict the properties of the propagating and nonpropagating vibrational modes in amorphous si... more We predict the properties of the propagating and nonpropagating vibrational modes in amorphous silica (a-SiO 2 ) and amorphous silicon (a-Si) and, from them, thermal conductivity accumulation functions. The calculations are performed using molecular dynamics simulations, lattice dynamics calculations, and theoretical models. For a-SiO 2 , the propagating modes contribute negligibly to thermal conductivity (6%), in agreement with the thermal conductivity accumulation measured by Regner et al. [Nat. Commun. 4, 1640]. For a-Si, propagating modes with mean-free paths up to 1 μm contribute 40% of the total thermal conductivity. The predicted contribution to thermal conductivity from nonpropagating modes and the total thermal conductivity for a-Si are in agreement with the measurements of Regner et al. The accumulation in the measurements, however, takes place over a narrower band of mean-free paths (100 nm-1 μm) than that predicted (10 nm-1 μm).
The strain-dependent phonon properties and thermal conductivities of a soft system [Lennard-Jones... more The strain-dependent phonon properties and thermal conductivities of a soft system [Lennard-Jones (LJ) argon] and a stiff system (silicon modeled using first-principles calculations) are predicted using lattice dynamics calculations and the Boltzmann transport equation. As is commonly assumed for materials under isotropic strain, the thermal conductivity of LJ argon decreases monotonically as the system moves from compression into tension. The reduction in thermal conductivity is attributed to decreases in both the phonon lifetimes and group velocities. The thermal conductivity of silicon, however, is constant in compression and only begins to decrease once the system is put in tension. The silicon lifetimes show an anomalous behavior, whereby they increase as the system moves from compression into tension, which is explained by examining the potential energy surface felt by an atom. The results emphasize the need to separately consider the harmonic and anharmonic effects of strain on material stiffness, phonon properties, and thermal conductivity.
Molecular dynamics simulations and lattice dynamics calculations are used to study the vi-bration... more Molecular dynamics simulations and lattice dynamics calculations are used to study the vi-brational modes and thermal transport in Lennard-Jones superlattices with perfect and mixed interfaces. The secondary periodicity of the superlattices leads to a vibrational spectrum (i.e., dispersion relation) that is distinct from the bulk spectra of the constituent materials. The mode eigenvectors of the perfect superlattices are found to be good representations of the majority of the modes in the mixed superlattices for up to 20% interfacial mixing, allowing for extraction of phonon frequencies and lifetimes. Using the frequencies and lifetimes, the in-plane and cross-plane thermal conductivities are predicted using a solution of the Boltzmann transport equation (BTE), with agreement found with predictions from the Green-Kubo method for the perfect superlattices. For the mixed superlattices, the Green-Kubo and BTE predictions agree for the cross-plane direction , where thermal conductivity is dominated by low-frequency modes whose eigenvectors are not affected by the mixing. For the in-plane direction, mid-frequencies modes that contribute to thermal transport are disrupted by the mixing, leading to an underprediction of thermal conductivity by the BTE. The results highlight the importance of using a dispersion relation that includes the secondary periodicity when predicting the thermal conductivity of perfect and/or short period superlattices.
The virtual crystal (VC) approximation for mass disorder is evaluated by examining two model allo... more The virtual crystal (VC) approximation for mass disorder is evaluated by examining two model alloy systems: Lennard-Jones argon and Stillinger-Weber silicon. In both material systems, the perfect crystal is alloyed with a heavier mass species up to equal concentration. The analysis is performed using molecular dynamics simulations and lattice dynamics calculations. Mode frequencies and lifetimes are first calculated by treating the disorder explicitly and under the VC approximation, with differences found in the high-concentration alloys at high frequencies. Notably, the lifetimes of high-frequency modes are underpredicted using the VC approximation, a result we attribute to the neglect of higher-order terms in the model used to include point-defect scattering. The mode properties are then used to predict thermal conductivity under the VC approximation. For the Lennard-Jones alloys, where high-frequency modes make a significant contribution to thermal conductivity, the high-frequency lifetime underprediction leads to an underprediction of thermal conductivity compared to predictions from the Green-Kubo method, where no assumptions about the thermal transport are required. Based on observations of a minimum mode diffusivity, we propose a correction that brings the VC approximation thermal conductivities into better agreement with the Green-Kubo values. For the Stillinger-Weber alloys, where the thermal conductivity is dominated by low-frequency modes, the high-frequency lifetime underprediction does not affect the thermal conductivity prediction and reasonable agreement is found with the Green-Kubo values.
The objective of this chapter is to describe how equilibrium molecular dynamics simulations (with... more The objective of this chapter is to describe how equilibrium molecular dynamics simulations (with the help of harmonic lattice dynamics calculations) can be used to predict phonon properties and thermal conductivity using normal mode decomposition. The molecular dynamics and lattice dynamics methods are reviewed and the normal mode decomposition technique is described in detail. The application of normal mode decomposition is demonstrated through case studies on crystalline, alloy, and amorphous Lennard-Jones phases. Notable works that used normal mode decomposition are presented and the future of molecular dynamics simulations in phonon transport modeling is discussed.
We predict the properties of the propagating and nonpropagating vibrational modes in amorphous si... more We predict the properties of the propagating and nonpropagating vibrational modes in amorphous silica (a-SiO 2 ) and amorphous silicon (a-Si) and, from them, thermal conductivity accumulation functions. The calculations are performed using molecular dynamics simulations, lattice dynamics calculations, and theoretical models. For a-SiO 2 , the propagating modes contribute negligibly to thermal conductivity (6%), in agreement with the thermal conductivity accumulation measured by Regner et al. [Nat. Commun. 4, 1640]. For a-Si, propagating modes with mean-free paths up to 1 μm contribute 40% of the total thermal conductivity. The predicted contribution to thermal conductivity from nonpropagating modes and the total thermal conductivity for a-Si are in agreement with the measurements of Regner et al. The accumulation in the measurements, however, takes place over a narrower band of mean-free paths (100 nm-1 μm) than that predicted (10 nm-1 μm).
The strain-dependent phonon properties and thermal conductivities of a soft system [Lennard-Jones... more The strain-dependent phonon properties and thermal conductivities of a soft system [Lennard-Jones (LJ) argon] and a stiff system (silicon modeled using first-principles calculations) are predicted using lattice dynamics calculations and the Boltzmann transport equation. As is commonly assumed for materials under isotropic strain, the thermal conductivity of LJ argon decreases monotonically as the system moves from compression into tension. The reduction in thermal conductivity is attributed to decreases in both the phonon lifetimes and group velocities. The thermal conductivity of silicon, however, is constant in compression and only begins to decrease once the system is put in tension. The silicon lifetimes show an anomalous behavior, whereby they increase as the system moves from compression into tension, which is explained by examining the potential energy surface felt by an atom. The results emphasize the need to separately consider the harmonic and anharmonic effects of strain on material stiffness, phonon properties, and thermal conductivity.
Molecular dynamics simulations and lattice dynamics calculations are used to study the vi-bration... more Molecular dynamics simulations and lattice dynamics calculations are used to study the vi-brational modes and thermal transport in Lennard-Jones superlattices with perfect and mixed interfaces. The secondary periodicity of the superlattices leads to a vibrational spectrum (i.e., dispersion relation) that is distinct from the bulk spectra of the constituent materials. The mode eigenvectors of the perfect superlattices are found to be good representations of the majority of the modes in the mixed superlattices for up to 20% interfacial mixing, allowing for extraction of phonon frequencies and lifetimes. Using the frequencies and lifetimes, the in-plane and cross-plane thermal conductivities are predicted using a solution of the Boltzmann transport equation (BTE), with agreement found with predictions from the Green-Kubo method for the perfect superlattices. For the mixed superlattices, the Green-Kubo and BTE predictions agree for the cross-plane direction , where thermal conductivity is dominated by low-frequency modes whose eigenvectors are not affected by the mixing. For the in-plane direction, mid-frequencies modes that contribute to thermal transport are disrupted by the mixing, leading to an underprediction of thermal conductivity by the BTE. The results highlight the importance of using a dispersion relation that includes the secondary periodicity when predicting the thermal conductivity of perfect and/or short period superlattices.
The virtual crystal (VC) approximation for mass disorder is evaluated by examining two model allo... more The virtual crystal (VC) approximation for mass disorder is evaluated by examining two model alloy systems: Lennard-Jones argon and Stillinger-Weber silicon. In both material systems, the perfect crystal is alloyed with a heavier mass species up to equal concentration. The analysis is performed using molecular dynamics simulations and lattice dynamics calculations. Mode frequencies and lifetimes are first calculated by treating the disorder explicitly and under the VC approximation, with differences found in the high-concentration alloys at high frequencies. Notably, the lifetimes of high-frequency modes are underpredicted using the VC approximation, a result we attribute to the neglect of higher-order terms in the model used to include point-defect scattering. The mode properties are then used to predict thermal conductivity under the VC approximation. For the Lennard-Jones alloys, where high-frequency modes make a significant contribution to thermal conductivity, the high-frequency lifetime underprediction leads to an underprediction of thermal conductivity compared to predictions from the Green-Kubo method, where no assumptions about the thermal transport are required. Based on observations of a minimum mode diffusivity, we propose a correction that brings the VC approximation thermal conductivities into better agreement with the Green-Kubo values. For the Stillinger-Weber alloys, where the thermal conductivity is dominated by low-frequency modes, the high-frequency lifetime underprediction does not affect the thermal conductivity prediction and reasonable agreement is found with the Green-Kubo values.
The objective of this chapter is to describe how equilibrium molecular dynamics simulations (with... more The objective of this chapter is to describe how equilibrium molecular dynamics simulations (with the help of harmonic lattice dynamics calculations) can be used to predict phonon properties and thermal conductivity using normal mode decomposition. The molecular dynamics and lattice dynamics methods are reviewed and the normal mode decomposition technique is described in detail. The application of normal mode decomposition is demonstrated through case studies on crystalline, alloy, and amorphous Lennard-Jones phases. Notable works that used normal mode decomposition are presented and the future of molecular dynamics simulations in phonon transport modeling is discussed.