Electron contribution to energy of alkali metals in the scheme of an embedded atom model

The behavior of the energy of molecular dynamics models of alkali metals constructed using the embedded atom potential at high temperatures is discussed. Pair potentials and embedding potentials for lithium, sodium, potassium, rubidium, and cesium are presented as uniform analytical expressions. If the parameters of the potential of the embedded atom model (EAM) are selected based on the known dependence of the density of liquid metal on temperature, then, as temperature approaches the critical one, the actual energy increases faster than the energy of the models in all cases. The thermal contribution of electron gas to the energy of metal is considered as the cause of the discrepancy. It is shown that it is possible to eliminate the discrepancy between energies of models and the actual metal at high temperatures, if the energy of thermal excitation of electrons is taken into consideration. The difference between the actual energy of metal and the energies of EAM for liquid Li, K, and Cs is almost equal to the contribution of the thermal energy of electrons. The thermal energy of electrons is taken into account in analysis of data obtained using shock compression.     

Molecular-dynamic simulation of the thermophysical properties of liquid uranium

The procedure for the calculation of the embedded atom model (EAM) potential, which involves the use of data on the structure of liquid metal in the vicinity of the melting temperature and of the results of impact tests, is applied to uranium. The use of the method of molecular dynamics and of the EAM potential produces good agreement with experiment as regards the structure, density, and potential energy of liquid metal at temperatures up to 5000 K, as well as along the shock adiabat up to pressures of ≈360 GPa. The thermodynamic properties of solid (bcc) and liquid uranium are determined at pressures up to 470 GPa and temperatures up to 12 000 K. The predicted value of bulk modulus of liquid at 1406 K is close to the actual value. The self-diffusion coefficient under isobaric heating increases with temperature by the power law with exponent of ≈2.103. The Stokes—Einstein relation is used to determine the dynamic viscosity at temperatures up to 6000 K. The obtained potential is not quite adequate for describing crystalline uranium under normal conditions. The melting temperature of uranium with EAM potential is equal to 1455 ± 2 K and somewhat higher than real. The melting temperature monotonically increases with pressure and reaches the value of 7342 K at 444 GPa. For obtaining agreement with experimental data for energy of uranium along the p = 0 isobar, it is assumed that an additional contribution to energy emerges at elevated temperatures, which is due to excitation of atomic electrons and leads to a high heat capacity: it may be as high as almost 100 kJ/mol at 5000 K. This contribution further causes a high heat capacity of highly compressed states of uranium.     

Optimal algorithm for constructing the embedded atom method potential for liquid metals

An optimal algorithm has been developed for calculating the embedding potential in the embedded atom method (EAM) with the aim of describing not only the temperature-dependent density of a liquid metal but also its energy up to its critical temperature. The algorithm is based on the unification of the form of the potential and calculation of its parameters from known density and energy data for the liquid metal. The basis of the algorithm is the use of least squares fitting of the pressure and energy in molecular dynamics simulations to data for a series of states of the liquid along an isobar. To describe liquid potassium, the pair contribution to the potential is represented by a power series in interparticle distance. Data on the properties of potassium at 343, 473, 723, 1000, 1500, 2000, and 2200 K were used. The embedding potential was expanded in terms of 1 − ρ, where ρ is the effective electron density in the EAM. In least squares fitting, fifteen equations were included: eight for the energy and seven for the pressure. The number of unknown coefficients was seven. Iterative calculations allow one to find optimal expansion coefficients and construct equilibrium models through molecular dynamics simulations. It is shown that the discrepancy in energy between simulations and the real metal at high temperatures can be eliminated by taking the electron excitation energy into consideration. The difference between the actual energy of a metal and the energy obtained in EAM simulations is very close to the contribution of the electron heat capacity.     

Thermal Conductivity of Carbon Aerogels as a Function of Pyrolysis Temperature

Amorphous carbon samples with a total porosity of about 85% were synthesized via pyrolysis of sol–gel derived resin precursors. Since the pores in the samples investigated have dimensions of a few tens of nanometers only, the gaseous contribution to the thermal conductivity is largely suppressed at ambient pressure. Values for the total thermal conductivity as low as 0.054 W·m⁻¹·K⁻¹ at 300°C are detected. However, the pyrolysis temperature has a great impact on the contribution of the solid backbone to the total thermal conductivity. From the same precursor a series of samples was prepared via pyrolysis at temperatures ranging from 800 to 2500°C. The thermal conductivity of this series of carbons at 300°cC under vacuum increases by a factor of about 8 if the pyrolysis temperature is shifted from 800 to 2500°C. To elucidate the reason for this strong increase, the infrared radiative properties, the electrical conductivity, the macroscopic density, the microcrystallite size, the sound velocity, and the inner surface of the samples were determined. Evaluation of the experimental data yields only a negligible contribution from radiative heat transfer and electronic transport to the total thermal conductivity. The main part of the increasing thermal conductivity therefore has to be attributed to an increasing phonon mean free path in the carbons prepared at higher pyrolysis temperatures. However, the phonon mean free path does not match directly the in-plane microcrystallite size of the amorphous carbon. Rather, the in-plane microcrystallite size represents an upper limit for the phonon mean free path. Hence, the limiting factor for the heat transport via phonons has to be defects swithin the carbon microcrystallites which are partially cured at higher temperatures.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Architecture of thermal barrier coatings produced by electron beam-physical vapor deposition (EB-PVD)

Extremely high temperatures and severe atmospheric conditions in the hot section of aircraft engines during operation result in degradation and structural failures of turbine components. Replacing these components is very expensive. Thermal barrier coatings (TBC) composed of ZrO₂-8wt%Y₂O₃(8YSZ) applied by Electron Beam-Physical Vapor Deposition (EB-PVD) to turbine components offer excellent properties for thermal protection and resistance against oxidation - induced erosion and corrosion. However, the life of turbine components is still limited due to premature failure of the TBC. It is hypothesized that the life of the coated components can be extended by lowering the thermal conductivity of the TBC by creating multiple non-distinct or distinct interfaces and alloy additions such as Nb-oxide which will result in a reduction in the thermal conductivity and oxygen transport through the coating. This paper presents the microstructural results of standard 8YSZ, layered 8YSZ, Nb-oxide alloyed 8YSZ and functionally graded 8YSZ with Nb-oxide deposited by EB-PVD. TBC samples were examined by various methods including scanning electron microscopy (SEM), high-resolution optical microscopy (OM), X-ray diffraction (XRD), and thermal cycling tests. The preliminary results strongly suggest that multiple interfaced TBC exhibits better oxidation resistant properties as compared to standard and alloyed TBC.     

Numerical Analysis of Heat Transport Behavior in the Ferromagnetic Metallic State of La0.80Ca0.20MnO3 Manganites

The lattice contribution to the thermal conductivity (κ_ph) in La_0.80Ca_0.20 MnO₃ manganites is discussed within the Debye-type relaxation rate approximation in terms of the acoustic phonon frequency and relaxation time. The theory is formulated when heat transfer is limited by the scattering of phonons from defects, grain boundaries, charge carriers, and phonons. The lattice thermal conductivity dominates in La–Ca–MnO manganites and is an artifact of strong phonon-impurity and -phonon scattering mechanisms in the ferromagnetic metallic state. The electronic contribution to the thermal conductivity (κ_e) is estimated following the Wiedemann–Franz law. This estimate sets an upper bound on κ_e, and in the vicinity of the Curie temperature (240 K) κ_e is about 1% of total heat transfer of manganites. Another important contribution in the metallic phase should come from spin waves (κ_m). It is noticed that κ_m increases with a T² dependence on the temperature. These channels for heat transfer are algebraically added and κ_tot develops a broad peak at about 55 K, before falling off at lower temperatures. The behavior of the thermal conductivity in manganites is determined by competition among the several operating scattering mechanisms for the heat carriers and a balance between electron, magnon, and phonon contributions. The numerical analysis of heat transfer in the ferromagnetic metallic phase of manganites shows similar results as those revealed from experiments.      

Temperature-Dependent Thermal Boundary Conductance at Al/Al<Subscript>2</Subscript>O<Subscript>3</Subscript> and Pt/Al<Subscript>2</Subscript>O<Subscript>3</Subscript> interfaces

With the ever-decreasing size of microelectronic devices, growing applications of superlattices, and development of nanotechnology, thermal resistances of interfaces are becoming increasingly central to thermal management. Although there has been much success in understanding thermal boundary conductance at low temperatures, the current models applied at temperatures more common in device operation are not adequate due to our current limited understanding of phonon transport channels. In this study, the scattering processes in Al and Pt films on Al₂O₃ substrates are examined by transient thermoreflectance testing at high temperatures. At high temperatures, traditional models predict the thermal boundary conductance to be relatively constant in these systems due to assumptions about phonon elastic scattering. Experiments, however, show an increase in the conductance indicating potential inelastic phonon processes.     

Impact compression of alkali metals: Computer-aided simulation

This article describes a method for calculation of the potential of the embedded atom model (EAM), suitable for calculation of the properties of alkali metals in highly compressed states. For the first time, sequential consideration of the thermal energy and thermal pressure of collective electrons has been introduced into the EAM flowchart. The parameters of the EAM potential have been calculated, which make it possible to obtain good agreement in terms of pressure and energy for five alkali metals under impact compression. The properties of the molecular dynamic models of alkali metals at 300 and 0 K are compared with the data of static compression. The agreement between them is sufficient up to pressures of 15–20 GPa, and at higher compression rates divergences become significant. A lack of experimental data makes it impossible to understand whether the reason for these divergences is incomplete adequacy of the EAM potential or systematic errors contained in the experimental data in the range of high pressures. The proposed potentials make it possible to calculate the thermodynamic, structural, and diffusion properties of alkali metals in highly compressed states at temperatures up to 20000–30000 K.     

Thermal Conductivity of Small Nickel Particles

The thermal conductivity of nanoscale nickel particles due to phonon heat transfer is extrapolated from thin film results calculated using nonequilibrium molecular dynamics (NEMD). The electronic contribution to the thermal conductivity is deduced from the electrical conductivity using the Wiedemann–Franz law. Based on the relaxation time approximation, the electrical conductivity is calculated with the Kubo linear-response formalism. At the average temperature of T=300 K, which is lower than the Debye temperature Θ_D=450 K, the results show that in a particle size range of 1.408–10.56 nm, the calculated thermal conductivity decreases almost linearly with decreasing particle size, exhibiting a remarkable reduction compared with the bulk value. The phonon mean free path is estimated, and the size effect on the thermal conductivity is attributed to the reduction of the phonon mean free path according to the kinetic theory.     

Embedded atom method potentials for alkali metals

The embedded atom method potentials calculated earlier for liquid lithium, sodium, potassium, rubidium, and cesium and presented in the form of tables are corrected and represented in a unified analytical form. When the parameters of the potential are adjusted using the known temperature dependence of the melt density along the melting line of the metal, the actual energy rises more rapidly than the simulated energy as the critical point is approached. The likely reason for the discrepancy is the thermal contribution of the electron gas to the energy of the metal. The discrepancy between the simulated energy and the actual energy of the metal at high temperatures can be considerably reduced by taking into consideration the thermal excitation energy of the electrons.     

Application of the embedded atom model to liquid metals: Liquid lithium

The procedure for the calculation of the embedded atom model (EAM) potential for liquid metal, which involves the use of diffraction data on the structure of material in the vicinity of the melting point, is applied to lithium. In fitting the parameters of EAM potential, use is made of data on the structure of lithium at 463, 523, and 868 K, as well as on the thermodynamic properties of lithium at temperatures up to 3400 K. The use of the method of molecular dynamics (MD) and of the EAM potential enables one to obtain good agreement with experiment as regards the structure, density, and potential energy of liquid metal at temperatures up to 3000 K, as well as along the shock adiabat up to pressures of ～260 GPa. The predicted value of bulk modulus at 463 K is close to the actual value. The self-diffusion coefficients under isobaric heating increase with temperature by the power law with exponent of 1.7182. The obtained potential is inadequate for describing crystalline lithium. The predicted melting temperature of lithium with EAM potential is 428 ± 2 K and is close to real temperature.     

Anisotropic Thermal Boundary Resistance across 2D Black Phosphorus: Experiment and Atomistic Modeling of Interfacial Energy Transport

Interfacial thermal boundary resistance (TBR) plays a critical role in near‐junction thermal management of modern electronics. In particular, TBR can dominate heat dissipation and has become increasingly important due to the continuous emergence of novel nanomaterials with promising electronic and thermal applications. A highly anisotropic TBR across a prototype 2D material, i.e., black phosphorus, is reported through a crystal‐orientation‐dependent interfacial transport study. The measurements show that the metal–semiconductor TBR of the cross‐plane interfaces is 241% and 327% as high as that of the armchair and zigzag direction‐oriented interfaces, respectively. Atomistic ab initio calculations are conducted to analyze the anisotropic and temperature‐dependent TBR using density functional theory (DFT)‐derived full phonon dispersion relation and molecular dynamics simulation. The measurement and modeling work reveals that such a highly anisotropic TBR can be attributed to the intrinsic band structure and phonon spectral transmission. Furthermore, it is shown that phonon hopping between different branches is important to modulate the interfacial transport process but with directional preferences. A critical fundamental understanding of interfacial thermal transport and TBR–structure relationships is provided, which may open up new opportunities in developing advanced thermal management technology through the rational control over nanostructures and interfaces.     

Computer simulation of liquid zinc

An embedded atom model potential for zinc has been developed, which makes it possible to calculate liquid zinc properties both under normal pressure and in strongly compressed states using the molecular dynamics method. In order to calculate the potential, the data on density, energy, and compressibility of liquid zinc and the data on shock compression of zinc were used. Pair contribution to the potential and the embedding potential are represented by analytical functions. Liquid zinc properties are calculated at temperatures up to 1500 K. The values of energy, bulk compression modulus, and self-diffusion coefficient, as well as pair correlation functions at T < 1000 K, agree well with the experiment. The electron contribution to the thermal capacity at those temperatures is not high. Zinc models are constructed for densities up to 15.86 g/cm³ and pressures up to 773 GPa. Zinc models melt in the case of shock compression at compression rates of V/V ₀ < 0.7 and temperatures above 1900 K. A significant contribution of electron excitation energy to the zinc energy is observed at temperatures above 20000 K. The estimated average surplus thermal capacity of electrons at 30000–50000 K is ∼12 J/mole K. Discrepancies between the molecular dynamic calculation and the Gruneisen model at low temperatures are relatively low; however, they rise as temperature increases. A series of zinc nanocluster models with magic sizes of 55 and 147 atoms is constructed. The clusters have an amorphous structure with slightly lower energy than that of icosahedral or cuboctahedral configuration, after cooling from 600 to 10 K. The surface energy of zinc at T = 0 calculated based on the dependence of energy of clusters on size is 1.3 J/m².     

Phonon Dispersion in the Fcc Metals Ca, Sr and Yb

Within the harmonic approximation and adiabatic approximation, the expressions of atomic force constants have been derived. Phonon dispersion curves along four major symmetry directions and four off-symmetry directions have been simulated for alkaline-earth metals Ca, Sr and the rare-earth metal Yb by combining the modified analytic embedded atom method with the theory of lattice dynamics. The simulated phonon dispersion curves for the fcc metals Ca, Sr and Yb along four major symmetry directions have been compared to the corresponding experimental data. The results show that the simulated results are general consistent with available experimental results, with a maximum deviation of approximately 14?%. The simulated phonon frequencies of the fcc metals Ca, Sr and Yb lay a significant foundation for guiding and judging relative experiment results, especially for the phonon dispersion relation along off-symmetry directions.     

Computer simulation of aluminum in the high-pressure range

A technique is developed for constructing crystalline aluminum models with the potential of the embedded atom model (EAM) obtained earlier in [1] and corrected for describing strongly compressed states. This technique was applied for aluminum in the range of high pressures created by strong shock waves. Using the method of molecular dynamics (MD) and EAM potential, it is possible to achieve good agreement with experiment as far as the structure, density, and energy of the metal along the shock adiabat up to a pressure of ∼260 GPa and temperature of ∼11500 K are concerned. Several models have been constructed in the high-pressure range at absolute zero temperature, and the adequacy of the Grüneisen model has been evaluated. Models for liquid aluminum have been constructed at temperatures up to 800 K, and the parameters of the critical point (∼7050 K, density of 0.675 ± 0.034 g/cm³, pressure of 0.325 ± 0.02 GPa, Z = pV/RT = 0.22 ± 0.03) have been determined.     

On The Theory of Isotope-effect in the d-wave Superconductors

The isotope-effect in a two-dimensional model of the d-wave phonon-exchange superconductor is studied. It is shown that the mean-field critical temperature, the Berezinskii–Kosterlitz–Thouless critical temperature and the superconducting gap strongly depend on the phonon frequency only in some range of the model parameters. These dependencies have different from the BCS theory forms. A qualitative comparison of the results with experimental data on some high-temperature superconductors is made. In particular, it is shown that the isotope-effect is significant in the case of strong electron–phonon coupling, when the phonon frequency is small compared to the free electron bandwidth.     

Factors affecting the magnitudes and anisotropies of the thermal and electrical conductivities of poly(l-lactic) acid composites with carbon fibers of various sizes

Investigation of the thermal and electrical conductivities of poly(l-lactic acid) composites containing carbon fibers (CFs) of various sizes has revealed that the thermal conductivity depends largely on the length of the CFs in the composites and that the electrical conductivity depends largely on the aspect ratio of the CFs. These different dependencies are due to the effect of the number of interfaces between the CFs in a percolation network formed in the composites, where electron transport is enhanced but phonon thermal conduction is limited by phonon scattering at the interfaces between the CFs. The anisotropy of each conductivity is also influenced by the length of the CFs, which could determine the alignment of the CFs in the molded composites.     

Relevance of the Phonon-Coupling Mode on the Superconducting Pairing Interaction of La<Subscript>2−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>CuO<Subscript>4</Subscript>

Despite the intensive efforts for determining the mechanism that causes high-temperature superconductivity in copper oxide materials (cuprates), no consensus on the pairing mechanism has been reached. Recent advances in angle-resolved photoemission spectroscopies (ARPES) have suggested that a sizeable electron–phonon coupling exists as the principal cause for kinks in the dispersion relations (energy versus wavevector) of the electronic states. Here, we report on a systematic study of the influence of the electron–phonon-coupling parameter “λ” in the electronic quasiparticle dispersions along the nodal direction for La_2−x Sr _x CuO₄, covering the entire doping range over which the electron transport properties vary from insulating (0≲x≲0.03) to superconducting (0.05≲x≲0.25) and eventually non-superconducting metal (x>0.25). This includes our recently introduced theoretical model to adjust the experimental data on the fermionic band dispersion. The coupling constant λ, calculated consistently with the nodal kink dispersions, reproduces the observed critical temperatures T _c , the gap ratio 2Δ ₀/k _B T _c , and other parameters which have been studied from several equations. Our results suggest that, at least in La_2−x Sr _x CuO₄, electron–phonon coupling is the most relevant boson-coupling mode to influence the electron dynamics, and must therefore be included in any microscopic theory of superconductivity.     

Linking Interfacial Bonding and Thermal Conductivity in Molecularly-Confined Polymer-Glass Nanocomposites with Ultra-High Interfacial Density

Thermal transport in polymer nanocomposites becomes dependent on the interfacial thermal conductance due to the ultra-high density of the internal interfaces when the polymer and filler domains are intimately mixed at the nanoscale. However, there is a lack of experimental measurements that can link the thermal conductance across the interfaces to the chemistry and bonding between the polymer molecules and the glass surface. Characterizing the thermal properties of amorphous composites are a particular challenge as their low intrinsic thermal conductivity leads to poor measurement sensitivity of the interfacial thermal conductance. To address this issue here, polymers are confined in porous organosilicates with high interfacial densities, stable composite structure, and varying surface chemistries. The thermal conductivities and fracture energies of the composites are measured with frequency dependent time-domain thermoreflectance (TDTR) and thin-film fracture testing, respectively. Effective medium theory (EMT) along with finite element analysis (FEA) is then used to uniquely extract the thermal boundary conductance (TBC) from the measured thermal conductivity of the composites. Changes in TBC are then linked to the hydrogen bonding between the polymer and organosilicate as quantified by Fourier-transform infrared (FTIR) and X-ray photoelectron (XPS) spectroscopy. This platform for analysis is a new paradigm in the experimental investigation of heat flow across constituent domains.