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Thermal evolution of the central region of a $0.9 \, M_\odot$ C/O white dwarf at the initial stage of the ion mixture crystallization is studied by numerically solving the heat equation on a fine spatial and temporal grid and by including a detailed treatment of the latent heat release. Formation of two spherical shells is observed. The outer one surrounds a region where crystallization has begun. The inner one bounds a fully solidified core which has exhausted its latent heat. The region between the shells is partially liquid and partially solid. It gradually emits the latent heat of crystallization and also it releases light elements (carbon) in the process of element redistribution, accompanying the mixture solidification. Assuming that all released light elements cross the outer shell, we have estimated their flux induced by the mixture crystallization. The resulting flux is not divergent and is much smaller than an estimate derived from the growth rate of the fully crystallized core., Comment: 4 pages, 3 figures, accepted in A&A

Crystallization of dense matter in neutron star crusts and white dwarf cores may be similar to epitaxial crystal growth in terrestrial laboratories. However in stellar crystals, the spacing between horizontal planes has to gradually increase with the outward movement of the crystallization front, tracing decrease of the electron density. This process produces Coulomb crystals with stretched rather than cubic elementary cells. We extend the analysis of the elastic and breaking properties of such crystals to the face-centered (fc) lattice. Shear deformations orthogonal to the stretch direction have been studied for 22 crystallographic shear planes. A common property for all these planes is a reduction and eventual nulling of the breaking shear strain with deviation from the unstretched configuration. The effective shear moduli for deformations orthogonal to the stretch direction have been calculated. It is possible that the epitaxial crystallization in compact stars results in a formation of large-scale crystallites or, at least, in growth of the whole crystallization front perpendicular to particular crystallographic planes. For fc structure growth orthogonal to the $\{111\}$ planes, we expect that, at any density, $\sim 5\%$ ($\sim 0.5\%$) of crystallite height is occupied by layers one (two) orders of magnitude weaker than the bulk of the crystallite. This may be important for realistic modeling of crustquakes on neutron stars., Comment: 8 pages, 2 figures, 2 tables, complete Table 1. Contributions to Plasma Physics in press: the special issue in memory of K. Golden and G. Kalman. This is the submitted version (practically the same as the accepted one)

Near-equilibrium bottom-up crystallization of fully-ionized neutron star crusts or white dwarf cores is considered. We argue that this process is similar to liquid-phase epitaxial (i.e. preserving order of previous layers) crystal growth or crystal pulling from melt in Earth laboratories whereby lateral positions of newly crystallizing ions are anchored by already solidified layers. Their vertical positions are set by charge neutrality. Consequently, interplane spacing of a growing crystal either gradually increases, tracing $n_\mathrm{e}$ decrease, as the crystallization front moves away from the stellar center, or decreases, tracing decrease of $\langle Z \rangle$, when the crystallization front crosses a boundary between layers of different compositions. This results in a formation of stretched Coulomb crystals, in contrast to the standard assumption of cubic crystal formation, which is based on energetics arguments but does not take into account growth kinetics. Overstretched crystals break, which limits the vertical sizes of growing crystallites. We study breaking shear strain and effective shear modulus of stretched matter and discuss possibility of macrocrystallite formation. The latter has interesting astrophysical implications, for instance, appearance of weak crustal layers, whose strength may increase by a few orders of magnitude upon breaking and refreezing at a late-time event. We also analyze interaction of adjacent Coulomb crystals, having different ion compositions, and estimate the strength of such interfaces., Comment: 11 pages, 4 figures, 1 table. Resubmitted to MNRAS after minor revision

Based on the linear mixing approach, we calculate the latent heat for crystallizing fully-ionized $^{12}$C/$^{16}$O and $^{16}$O/$^{20}$Ne mixtures in white dwarf (WD) cores for two different parametrizations of the corrections to the linear-mixing energies and with account of ion quantum effects. We report noticeable composition-dependent deviations of the excess entropy in both directions from the standard value of 0.77 per ion. Within the same framework, we evaluate the excess entropy and released or absorbed heat accompanying the exsolution process in solidified WD layers. The inclusion of this effect is shown to be important for reliable interpretation of WD cooling data. We also analyze the latent heat of crystallizing eutectic $^{12}$C/$^{22}$Ne mixture, where we find a qualitative dependence of both the phase diagram and the latent heat behaviour on ion quantum effects. This may be important for the model with $^{22}$Ne distillation in cooling C/O/$^{22}$Ne WD proposed as a solution for the ultramassive WD multi-Gyr cooling anomaly. Astrophysical implications of our findings for crystallizing WD are discussed., Comment: 5 pages, 2 figures. Letter to MNRAS, in press

Phase diagrams of fully ionized binary ionic mixtures are considered within the framework of the linear mixing formalism taking into account recent advances in understanding quantum one-component plasma thermodynamics. We have followed a transformation of azeotropic phase diagrams into peritectic and eutectic types with increase of the charge ratio. For solid $^{12}$C/$^{16}$O and $^{16}$O/$^{20}$Ne mixtures, we have found extensive miscibility gaps. Their appearance seems to be a robust feature of the theory. The gaps evolve naturally into two-solid regions of eutectic phase diagrams at higher $Z_2/Z_1$. They do not depend on thermodynamic fit extensions beyond their applicability limits. The gaps are sensitive to binary mixture composition and physics, being strongly different for C/O and O/Ne mixtures and for the three variants of corrections to linear-mixing solid-state energies available in the literature. When matter cools to its miscibility gap temperature, the exsolution process takes place. It results in a separation of heavier and lighter solid solutions. This may represent a significant reservoir of gravitational energy and should be included in future white dwarf (WD) cooling simulations. Ion quantum effects mostly resulted in moderate modifications, however, for certain $Z_2/Z_1$, these effects can produce qualitative restructuring of the phase diagram. This may be important for the model with $^{22}$Ne distillation in cooling C/O/Ne WD proposed as a solution for the ultramassive WD cooling anomaly., Comment: 13 pages, 8 figures, accepted in MNRAS

Using path-integral Monte Carlo (PIMC) simulations, we have calculated energy of a crystal composed of atomic nuclei and uniform incompressible electron background in the temperature and density range, covering fully ionized layers of compact stellar objects, white dwarfs and neutron stars, including the high-density regime, where ion quantization is important. We have approximated the results by convenient analytic formulae, which allowed us to integrate and differentiate the energy with respect to temperature and density to obtain various thermodynamic functions such as Helmholtz free energy, specific heat, pressure, entropy etc. In particular, we have demonstrated, that the total crystal specific heat can exceed the well-known harmonic lattice contribution by a factor of 1.5 due to anharmonic effects. By combining our results with the PIMC thermodynamics of a quantum Coulomb liquid, updated in the present work, we were able to determine density dependences of such melting parameters as the Coulomb coupling strength at melting, latent heat, and a specific heat jump. Our results are necessary for realistic modelling of thermal evolution of compact degenerate stars., Comment: 17 pages, 17 figures, 4 tables, accepted to MNRAS

A reliable description of nuclear fusion reactions in inner layers of white dwarfs and envelopes of neutron stars is important for realistic modelling of a wide range of observable astrophysical phenomena from accreting neutron stars to type Ia supernovae. We study the problem of screening of the Coulomb barrier impeding the reactions, by a plasma surrounding the fusing nuclei. Numerical calculations of the screening factor are performed from the first principles with the aid of quantum-mechanical path integrals in the model of a one-component plasma of atomic nuclei for temperatures and densities typical for dense liquid layers of compact degenerate stars. We do not rely on various quasiclassic approximations widely used in the literature, such as factoring-out the tunneling process, tunneling in an average spherically symmetric mean-force potential, usage of classic free energies and pair correlation functions, linear mixing rule and so on. In general, a good agreement with earlier results from the thermonuclear limit to $\Gamma \sim 100$ is found. For a very strongly coupled liquid $100 \lesssim \Gamma \leq 175$, a deviation from currently used parametrisations of the reaction rates is discovered and approximated by a simple analytic expression. The developed method of nuclear reaction rate calculations with account of plasma screening can be extended to ion mixtures and crystallised phases of stellar matter., Comment: 8 pages, 6 figures, accepted to MNRAS

We present an accurate analytic approximation for the energy of a quantum one-component Coulomb liquid of ions in a uniform electron background which has been recently calculated from first principles (Baiko 2019). The approximation enables us to develop in an analytic form a complete thermodynamic description of quantum ions in a practically important range of mass densities at temperatures above crystallization. We show that ionic quantum effects in liquid cores of white dwarfs (WDs) affect heat capacity, cooling, thermal compressibility, pulsation frequencies and radii of sufficiently cold WDs, especially with relatively massive helium and carbon cores., Comment: 19 pages, 6 figures; submitted 5 weeks ago

Using Metropolis method to compute path integrals, the energy of quantum strongly-coupled Coulomb liquid ($1 \leq \Gamma \leq 175$) composed of distinguishable atomic nuclei and uniform incompressible electron background is calculated from first principles. The range of considered temperatures and densities represents fully-ionized layers of white dwarfs and neutron stars. In particular, the results allow one to determine reliably the heat capacity of ions in dense fluid stellar matter, which is a crucial ingredient for modelling thermal evolution of compact degenerate stars., Comment: 6 pages, 3 figures, accepted to MNRAS

The strength of neutron star crust is crucial for modelling magnetar flares, pulsar glitches and gravitational wave emission. We aim to shed some light on this problem by analysing uniaxial stretch deformation (elongation and contraction) of perfect body-centered cubic Coulomb crystals, paying special attention to the inherent anisotropy of this process. Our analysis is based on the semi-analytical approach of Baiko and Kozhberov (2017), which, for any uniform deformation, allows one to calculate, in fully non-linear regime, critical deformation parameters beyond which the lattice loses its dynamic stability. We determine critical strain, pressure anisotropy and deformation energy for any stretch direction with respect to the crystallographic axes. These quantities are shown to be strongly anisotropic: they vary by a factor of almost 10 depending on the orientation of the deformation axis. For polycrystalline crust, we argue that the maximum strain for the stretch deformation sustainable elastically is 0.04. It is lower than the breaking strain of 0.1 obtained in molecular dynamic simulations of a shear deformation by Horowitz and Kadau (2009). The maximum pressure anisotropy of polycrystalline matter is estimated to be in the range from 0.005 to 0.014 $nZ^2e^2/a$, where $n$ is the ion number density, $Ze$ is the ion charge, and $a$ is the ion-sphere radius. We discuss possible mechanisms of plastic motion and formation of large crystallites in neutron star crust as well as analyse energy release associated with breaking of such crystallites in the context of magnetic field evolution and magnetar flaring activity., Comment: 7 pages, 6 figures, accepted to MNRAS

Although crystallized neutron star crust is responsible for many fascinating observational phenomena, its actual microscopic structure in tremendous gravitational and magnetic fields is not understood. Here we show that in a non-uniform magnetic field, three-dimensional ionic Coulomb crystals comprising the crust may stretch or shrink while their electrostatic pressure becomes anisotropic. The pressure depends non-linearly on the magnitude of the stretch, so that a continuous magnetic field evolution may result in an abrupt crystal elongation or contraction. This may provide a trigger for magnetar activity. A phonon mode instability is revealed, which sets the limits of magnetic field variation beyond which the crystal is destroyed. These limits sometimes correspond to surprisingly large deformations. It is not known what happens to crust matter subject to a pressure anisotropy exceeding these limits. We hypothesize that the ion system then possesses a long-range order only in one or two dimensions, that is becomes a liquid crystal., Comment: 12 pages; submitted

Corrections to elastic moduli, including the effective shear modulus, of a solid neutron star crust due to electron screening are calculated. At any given mass density, the crust is modelled as a body-centred cubic Coulomb crystal of fully ionized atomic nuclei of a single type with a polarizable charge-compensating electron background. Motion of the nuclei is neglected. The electron polarization is described by a simple Thomas-Fermi model of exponential electron screening. The results of numerical calculations are fitted by convenient analytic formulae. They should be used for precise neutron star oscillation modelling, a rapidly developing branch of stellar seismology., Comment: 6 pages

We study electrical and thermal conductivities of degenerate electrons emitting and absorbing phonons in a strongly magnetized crystalline neutron star crust. We take into account modification of the phonon spectrum of a Coulomb solid of ions caused by a strong magnetic field. Boltzmann transport equation is solved using a generalized variational method. The ensuing three-dimensional integrals over the transferred momenta are evaluated by two different numerical techniques, the Monte-Carlo method and a regular integration over the first Brillouin zone. The results of the two numerical approaches are shown to be in a good agreement. An appreciable growth of electrical and thermal resistivities is reported at quantum and intermediate temperatures $T \lesssim 0.1 T_{\rm p}$ ($T_{\rm p}$ is the ion plasma temperature) in a wide range of chemical compositions and mass densities of matter even for moderately magnetized crystals $\omega_{\rm B} \sim \omega_{\rm p}$ ($\omega_{\rm B}$ and $\omega_{\rm p}$ are the ion cyclotron and plasma frequencies). This effect is due to an appearance of a soft ($\omega \propto k^2$) phonon mode in the magnetized ion Coulomb crystal, which turns out to be easier to excite than acoustic phonons characteristic of the field-free case. These results are important for modelling magneto-thermal evolution of neutron stars., Comment: accepted to MNRAS

Free energy, internal energy, and specific heat for each of the three phonon spectrum branches of a magnetized Coulomb crystal with body-centered cubic lattice are calculated by numerical integration over the Brillouin zone in the range of magnetic fields $B$ and temperatures $T$, such that $0 \le \omega_{\rm B}/\omega_{\rm p}\le 10^3$ and $10^{-4} \le T/T_{\rm p} \le 10^4$. In this case, $\omega_{\rm B}$ is the ion cyclotron frequency, $\omega_{\rm p}$ and $T_{\rm p}$ are the ion plasma frequency and plasma temperature, respectively. The results of numerical calculations are approximated by simple analytical formulas. For illustration, these formulas are used to analyze the behavior of the heat capacity in the crust of a neutron star with strong magnetic field. Thermodynamic functions of magnetized neutron star crust are needed for modeling various observational phenomena in magnetars and high magnetic field pulsars., Comment: 11 pages, 9 figures; accepted to MNRAS

Shear modulus of solid neutron star crust is calculated by thermodynamic perturbation theory taking into account ion motion. At given density the crust is modelled as a body-centered cubic Coulomb crystal of fully ionized atomic nuclei of one type with the uniform charge-compensating electron background. Classic and quantum regimes of ion motion are considered. The calculations in the classic temperature range agree well with previous Monte Carlo simulations. At these temperatures the shear modulus is given by the sum of a positive contribution due to the static lattice and a negative $\propto T$ contribution due to the ion motion. The quantum calculations are performed for the first time. The main result is that at low temperatures the contribution to the shear modulus due to the ion motion saturates at a constant value, associated with zero-point ion vibrations. Such behavior is qualitatively similar to the zero-point ion motion contribution to the crystal energy. The quantum effects may be important for lighter elements at higher densities, where the ion plasma temperature is not entirely negligible compared to the typical Coulomb ion interaction energy. The results of numerical calculations are approximated by convenient fitting formulae. They should be used for precise neutron star oscillation modelling, a rapidly developing branch of stellar seismology., Comment: 10 pages, 3 figures, accepted to MNRAS

The body-centered cubic Coulomb crystal of ions in the presence of a uniform magnetic field is studied using the rigid electron background approximation. The phonon mode spectra are calculated for a wide range of magnetic field strengths and for several orientations of the field in the crystal. The phonon spectra are used to calculate the phonon contribution to the crystal energy, entropy, specific heat, Debye-Waller factor of ions, and the rms ion displacements from the lattice nodes for a broad range of densities, temperatures, chemical compositions, and magnetic fields. Strong magnetic field dramatically alters the properties of quantum crystals. The phonon specific heat increases by many orders of magnitude. The ion displacements from their equilibrium positions become strongly anisotropic. The results can be relevant for dusty plasmas, ion plasmas in Penning traps, and especially for the crust of magnetars (neutron stars with superstrong magnetic fields $B \gtrsim 10^{14}$ G). The effect of the magnetic field on ion displacements in a strongly magnetized neutron star crust can suppress the nuclear reaction rates and make them extremely sensitive to the magnetic field direction., Comment: 25 pages, 8 figures; accepted to Phys. Rev. E

Phonon frequency moments and thermodynamic functions (electrostatic and vibrational parts of the free energy, internal energy, and heat capacity) are calculated for bcc and fcc Coulomb crystals in the harmonic approximation with a fractional accuracy within one part on 10^5. Temperature dependence of thermodynamic functions is fitted by analytic formulas with an accuracy of a few parts in 10^5. The static-lattice (Madelung) part of the free energy is calculated with an accuracy about 10^{-12}. The Madelung constant and frequency moments of hcp crystals are also computed., Comment: 5 pages, 2 tables, RevTeX3. Scheduled to November 2001 issue of Phys. Rev. E

The diffusive thermal conductivity of neutrons in dense matter [$\rho \sim (1 - 8) \times 10^{14}$ g cm$^{-3}$] of neutron star cores is calculated. The contribution from neutron--neutron and neutron--proton collisions is taken into account. We use the transition probabilities calculated for symmetric dense nucleon matter on the basis of the Dirac--Brueckner approach to the in-medium effects and the Bonn model of bare nucleon--nucleon interaction. The diffusive thermal conductivity of neutrons in the presence of neutron and proton superfluidities is analyzed in a microscopic manner; the effects of superfluidity are shown to be significant. The low temperature behavior of the thermal conductivity appears to be extremely sensitive to the relation between critical temperatures of neutrons and protons. The results are fitted by simple analytic expressions. In combination with the formulae for the electron and muon thermal conductivities, obtained earlier, the present expressions provide a realistic description of the full diffusive thermal conductivity in the neutron star cores for normal and various superfluid phases., Comment: 13 pages, 4 figures, accepted to AA

We analyze cooling of neutron stars, assuming the presence of localized protons in the densest region of their cores. Choosing a single threshold density for proton localization and adjusting neutron star mass, we reproduce the observational data on effective surface temperatures of Vela and PSR 0656+14, with or without an accreted hydrogen envelope. However, the presence of a tiny hydrogen envelope is mandatory, in this model, for reproducing the Geminga data., Comment: 5 pages, 3 figures, latex, uses aa.cls, to be published in Astronomy and Astrophysics

The dynamic structure factor ${\tilde S}({\bf k},\omega)$ and the two-particle distribution function $g({\bf r},t)$ of ions in a Coulomb crystal are obtained in a closed analytic form using the harmonic lattice (HL) approximation which takes into account all processes of multi-phonon excitation and absorption. The static radial two-particle distribution function $g(r)$ is calculated for classical ($T \gtrsim \hbar \omega_p$, where $\omega_p$ is the ion plasma frequency) and quantum ($T \ll \hbar \omega_p$) body-centered cubic (bcc) crystals. The results for the classical crystal are in a very good agreement with extensive Monte Carlo (MC) calculations at $1.5 \lesssim r/a \lesssim 7$, where $a$ is the ion-sphere radius. The HL Coulomb energy is calculated for classical and quantum bcc and face-centered cubic crystals, and anharmonic corrections are discussed. The inelastic part of the HL static structure factor $S''(k)$, averaged over orientations of wave-vector {\bf k}, is shown to contain pronounced singularities at Bragg diffraction positions. The type of the singularities is different in classical and quantum cases. The HL method can serve as a useful tool complementary to MC and other numerical methods., Comment: 8 pages, 3 figures; accepted to Phys. Rev. E

As pointed out by Kutschera and W{\'o}jcik, very low concentration of protons combined with a specific density dependence of effective neutron-proton interaction could lead to a localization of ``proton impurities'' in neutron medium at densities exceeding four times normal nuclear matter density. We study consequences of the localization of protons for transport processes in dense neutron star cores, assuming random distribution of proton impurities. Kinetic equations, relevant for the transport of charge, heat and momentum, are solved using variational method. Localization of protons removes a T^{-2} factor from the transport coefficients, which leads, at lower temperatures, to a strong decrease of thermal conductivity, electrical conductivity and shear viscosity of neutron star matter, as compared to the standard case, where protons form a Fermi liquid. Due to the localization of protons a number of conventional neutrino emission processes (including modified URCA process) become inoperative in neutron star cores. On the other hand, the energy loss rate from neutrino-antineutrino pair bremsstrahlung due to electron and neutron scattering off (localized) protons, will have a specific T^6 dependence, which could modify the cooling of the neutron star core, as compared to the standard case. Possible astrophysical implications of the localization of protons for neutron star evolution and dynamics are discussed., Comment: 27 pages, no figures, uses appb.sty (included)

New calculations of the thermal and electrical electron conductivities are performed for a broad range of physical parameters typical for envelopes of neutron stars and cores of white dwarfs. We consider stellar matter composed of astrophysically important chemical elements from H to Fe in the density range from 10^2-10^4 g/ccm up to 10^7-10^{10} g/ccm, where atoms are fully ionized and electrons are strongly degenerate. We have used modified ion structure factors suggested in physics/9811052. In the ion liquid, these modifications take into account, in an approximate way, instantaneous electron-band structures that reduce the electron-ion scattering rate. In crystallized matter, the new structure factors include multi-phonon processes important at temperatures not very much lower than the melting temperature T_m. The transport coefficients obtained differ significantly from those derived earlier in the important temperature range T_m/5 < T < 5 T_m. The results of our numerical calculations are fitted by analytical expressions convenient for astrophysical applications., Comment: 10 pages, 7 figures, LaTeX using aa.cls and epsf.sty. Corrected typos in Eq.(16) (v2) and in Eq.(A3) (v3)

The effect of the magnetic field on the energy loss rate in the direct Urca reactions is studied. The general expression for the neutrino emissivity at arbitrary magnetic field B is derived. The main emphasis is laid on a case, in which the field is not superstrong, and charged reacting particles (e and p) populate many Landau levels. The magnetic field keeps the process operative if Delta k / k_{Fn} < N_{Fp}^{-2/3} (N_{Fp} is the number of the Landau levels populated by protons and Delta k = k_{Fn}-k_{Fp}-k_{Fe}), that is beyond the well-known switch-on limit in the absence of the field, Delta k < 0. Cooling of magnetized neutron stars with strong neutron superfluid in the outer cores and nonsuperfluid inner cores is simulated. The magnetic field near the stellar center speeds up the cooling if the stellar mass M is slightly less than the minimum mass M_c at which the direct Urca reaction becomes allowed for B=0. If B=3x10^{16} G the affected mass range is M_c-M < 0.1M_c, while for B=3x10^{15} G the range is M_c-M < 0.015M_c. This may influence a theoretical interpretation of the observed thermal radiation as illustrated for the Geminga pulsar. The case of superstrong magnetic fields (B>10^{18} G), such that e and p populate only the lowest Landau levels is briefly outlined., Comment: 10 pages, 5 figures, uses l-aa.sty. To be published in Astronomy and Astrophysics

The dynamical structure factor of a Coulomb crystal of ions is calculated at arbitrary temperature below the melting point taking into account multi-phonon processes in the harmonic approximation. In a strongly coupled Coulomb ion liquid, the static structure factor is split into two parts, a Bragg-diffraction-like one, describing incipient long-range order structures, and an inelastic part corresponding to thermal ion density fluctuations. It is assumed that the diffractionlike scattering does not lead to the electron relaxation in the liquid phase. This assumption, together with the inclusion of multi-phonon processes in the crystalline phase, eliminates large discontinuities of the transport coefficients (jumps of the thermal and electric conductivities, as well as shear viscosity, reported previously) at a melting point., Comment: 4 pages, 2 figures, REVTeX using epsf.sty. Phys. Rev. Lett., in press

Thermal and electric conductivities of relativistic degenerate electrons are calculated for the case when electrons scatter by phonons in Coulomb crystals made of spherical finite--size nuclei at densities $10^{11}$~g/cm$^3 < \rho < 10^{14}$~g/cm$^3$, corresponding to the inner crust of a neutron star. In combination with the results of the previous article (for lower $\rho$), simple unified fits are obtained which describe the kinetic coefficients in the range $10^3$~g/cm$^3 < \rho < 10^{14}$~g/cm$^3$, for matter with arbitrary nuclear composition. The results are valid for studying thermal evolution of neutron stars and evolution of their magnetic fields. The difference between the kinetic coefficients in the neutron star crust composed of ground state and accreted matters is analyzed. Thermal drift of the magnetic field in the neutron star crust is discussed., Comment: 16 pages, 6 eps-files of figures, accepted for publication in Astronomy Letters (Pisma v Astronomicheskii Zhurnal)

Thermal and electric conductivities are calculated for degenerate electrons scattered by phonons in a crystal made of atomic nuclei. The exact phonon spectrum and the Debye--Waller factor are taken into account. Monte Carlo calculations are performed for body-centered cubic (bcc) crystals made of C, O, Ne, Mg, Si, S, Ca, and Fe nuclei in the density range from $10^3$ to $10^{11}$ g cm$^{-3}$ at temperatures lower than the melting temperature but higher than the temperature at which the Umklapp processes begin to be "frozen out". A simplified method of calculation is proposed, which makes it possible to describe the results in terms of simple analytic expressions, to extend these expressions to any species of nucleus, and to consider face-centered cubic (fcc) crystals. The kinetic coefficients are shown to depend tangibly on the lattice type. The results are applicable to studies of heat transfer and evolution of the magnetic field in the cores of white dwarfs and in the crusts of neutron stars. The thermal drift of the magnetic field in the crust of a neutron star is discussed., Comment: 20 pages, 4 eps-files of figures