Einstein Model Research Articles

Manipulating electronic dynamics of 8-Pmmn borophene with surface optical phonons

In this work, the effects of surface optical (SO) phonons on the electronic spectrum of 8-Pmmn phase borophene have been investigated. To describe the analytical model we used a Fröhlich-type Hamiltonian on a borophene system within the continuum limit. Then, by following the analytical model with the Lee–Low–Pines variational approximation method, including two successive unitary transformations, the system Hamiltonian has been diagonalized. Our theoretical analysis indicates that SO absorption of the system strongly depends on the substrate-induced effects of the system. Moreover, it is observed that the polaronic energy gap decreases when increasing the internal distance between the 8-Pmmn borophene and the particular substrate. Also, the energy gap increases with increasing phonon energy (). In addition, the resulting bandgap induced by the electron–SO phonon interaction can be tuned by the associated interaction strengths of the substrate. Furthermore, taking lattice vibrations into account, the surface phonon specific heat of the system has been evaluated as a function of temperature. The specific heat becomes constant at high temperatures, as in the Einstein model. We specifically evaluated the contribution from the lattice vibrations on specific internal distances, z. The increase in the internal distance z causes the peak to shift to lower thermal energy.

Effects of quantum confinement on thermodynamic properties

Confined quantum systems can present anomalous behaviour. In particular, thermodynamic properties such as specific heat can show special features when the system is subject to spatial confinement described, for instance, by a harmonic potential. The energy eigenvalues of this confined system can be obtained from a variational approach by using, as trial functions, the solution of a particle in a box multiplied by a gaussian. For a strong confinement regime, the energy eigenvalues converge to the same values of the particle in the box and, for a weak confinement regime, the energy eigenvalues converge to the free harmonic oscillator. This behaviour reflects in the thermodynamics properties. In the curves of specific heat as a function of temperature, for instance, it is possible to identify two regions, one when the contribution of the harmonic oscillator is dominant and the other one where the contribution of the particle in a box becomes more relevant. These results indicate a phase transition of second-order close to the Einstein temperature.

Anomalous electronic properties in layered, disordered ZnVSb

New materials discovery is the driving force for progress in solid state physics and chemistry. Here we solve the crystal structure and comprehensively study physical properties of ZnVSb in the polycrystalline form. Synchrotron x-ray diffraction reveals that the compound attains a layered ZrSiS-type structure ($P4$/nmm, $a$ = 4.09021(2) \AA{}, $c$ = 6.42027(4) \AA{}). The unit cell is composed of a 2D vanadium network separated by Zn-Sb blocks that are slightly distorted from the ideal cubic arrangement. A considerable amount of vacancies were observed on the vanadium and antimony positions; the experimental composition is ${\mathrm{ZnV}}_{0.91}{\mathrm{Sb}}_{0.96}$. Low-temperature x-ray diffraction shows very subtle discontinuity in the lattice parameters around 175 K. Bonding V-V distance is below the critical separation of 2.97 \AA{} known from the literature, which allows for V-V orbital overlap and subsequent metallic conductivity. From ab initio calculations, we found that ZnVSb is a pseudogap material with an expected dominant vanadium contribution to the density of states at the Fermi level. The energy difference between the antiferromagnetic and nonordered magnetic configurations is rather small (0.34 eV/f.u.). X-ray photoelectron spectroscopy fully corroborates the results of the band structure calculations. Magnetic susceptibility uncovered that, in ZnVSb, itinerant charge carriers coexist with a small, localized magnetic moment of ca. 0.25 ${\ensuremath{\mu}}_{\mathrm{B}}$. The itinerant electrons arise from the ordered part of the vanadium lattice. Fractional localization, in turn, was attributed to V atoms neighboring vacancies, which hinder full V-V orbital overlap. Furthermore, the susceptibility and electrical resistivity showed a large hysteresis between 120 K and 160 K. The effect is not sensitive to magnetic fields up to 9 T. Curie-Weiss fitting revealed that the amount of itinerant charge carriers in ZnVSb drops with decreasing temperature below 160 K, which is accompanied by a concurrent rise in the localized magnetic moment. This observation together with the overall shape of the hysteresis in the resistivity allows for suggesting a plausible origin of the effect as a charge-transfer metal-insulator transition. Ab initio phonon calculations show the formation of a collective phonon mode at 2.8 THz (134 K). The experimental heat capacity reflected this feature by a boson peak with Einstein temperature of 116 K. Analysis of the heat capacity with both an ab initio perspective and Debye-Einstein model revealed a sizable anharmonic contribution to heat capacity, in line with disordered nature of the material. Further investigation of the electron and phonon properties for ZnVSb is likely to provide valuable insight into the relation between structural disorder and the physical properties of transition-metal-bearing compounds.

The third generation Calphad description of Al–C including revisions of pure Al and C

New descriptions of pure Al and liquid C were developed and used to describe the Al–C system for the third generation of Calphad databases. The stable phases of the elements are described with a single expression for the entire temperature range. The expression is based on the Einstein model and an important parameter is therefore the Einstein temperature. For the metastable phases, the difference in entropy between stable and metastable phases is used to calculate the Einstein temperature for the metastable allotrope. In this way we avoid breaking the third law of thermodynamics, which would be the consequence if the SGTE lattice stabilities were used. The liquid-amorphous phase for the pure substances and for the binary is described with the two-state model. For the pure substances, we introduce a zero-point entropy that is related to the entropy of melting. The heat capacity of the liquid of the pure substances approaches 3R at high temperatures if the electronic contribution is subtracted. The Al–C system has one stable carbide, Al4C3, which is described with a model equivalent to that used for the solid unary phases but with two Einstein functions. In Al–C, the FCC phase is stable and its metastable end-member, Al1C1, is described with a new model, here called the hybrid model, as it combines the Einstein model (giving the harmonic contribution) and the Neumann–Kopp relationship (adding the additional contributions) to describe the heat capacity. Its Einstein temperature is estimated and its formation energy is obtained from DFT calculations. The total energy of the end-members of the metastable phases BCC(Al1C3) and HCP(Al1C0.5) is calculated with DFT and their Einstein temperatures are estimated using the mass-effect model. The Al–C system was chosen because it is a simple system without magnetism and the results show that the proposed models can reproduce experimental information well. When only one temperature range is used to describe the solid phases, they may be re-stabilized at high temperatures and the recently presented equal-entropy criterion (EEC) is used to exclude solid phases with higher entropy than the liquid.

Understanding water slippage through carbon nanotubes.

It is a formidable challenge to understand water slippage through carbon nanotubes (CNTs), despite its great significance in fundamental research and technology. Herein, we propose an effective scheme to describe water slippage properties by extending two friction models - the phononic friction model and Einstein's diffusion model, both relying on the potential corrugation of water slippage. Our scheme effectively captures the tube-size effect on the viscosity and slippage of water molecules through CNTs. It also identifies the experimentally reported size-dependent transition from continuum to sub-continuum flow and further reveals that this transition is likely to be determined by the hydrogen bond instead of the structural transition or entropic change. Besides, the size-dependence of slip lengths is found to be controllable by temperature. Our methods are thus expected to be a useful basis for further studies on substance transport under confinement.

Phase space of multi-fluid universe in F(T)-gravity and some enhancements for the oscillating interaction model

Recently, a Friedmann–Robertson–Walker universe filled with various cosmological fluids has been considered by Odintsov et al. (Phys Rev D 96:044022, 2017) from phase space vantage point where various expressions for the Equation-of-State (EoS) parameter were studied. Since these types of EoS parameters are generative of appreciable results in the Hilbert–Einstein model, hence we intend to investigate all the cases in a homogeneous F(T)-gravity (T is the torsion) through phase space analysis in precise detail. In short, three viable models of interaction between dark matter and dark energy, including usual-type, power-law type, and oscillating type, are investigated comprehensively. It is indicated that the power-law interaction in the related dynamical systems should be of increasing nature with time to get more critical points. Due to the failure of the oscillating model of Odintsov et al. (2017) in F(T)-gravity, four modified models are suggested and examined in both F(T) and Hilbert–Einstein models. As to be seen, the modified models not only are generative of critical points equivalent to that of Odintsov et al. (2017), but also give rise to further critical points covering crucial stages of the evolution of the universe. In the context of these four models, such as the old one, at early times the interactions are negligible and they commence to grow as the cosmic time approaches the late-time in which the unification of early inflation and late acceleration is obtained. Using an indirect method, it is shown that the oscillating models have substantial roles in transitions between eras.

Evaluation of Temperature and Germanium Concentration Dependence of EXAFS Oscillations in Si-Rich Silicon Germanium Thin Films

1. Background and purpose Silicon germanium (SiGe) has higher mobility and lower thermal conductivity than pure Si, and it is expected as a next-generation electronic and thermoelectric device material. Understanding of carrier scattering and phonon transport is important for controlling the thermal conductivity, which involves the thermal vibration of atoms, in electronic and thermoelectric devices. However, there has been no report evaluating the influence of the Ge closest ligand in SiGe thin film on thermal vibration. The dependence on Ge concentration and temperature has not been clarified yet. In this study, we evaluated the relationship between the local lattice vibration between Ge and the ligand in the SiGe thin film and the Ge concentration by XAFS (X-ray Absorption Fine Structure) measurement, and estimated the Einstein temperature (T E) that characterizes phonons. 2. Experimental method Si0.847Ge0.153 and Si0.703Ge0.297 were epitaxially grown on Si (001) substrates, and the thicknesses of these films were 33 and 38 nm, respectively [1]. We measured the XAFS of Ge-K absorption edge for the SiGe films by fluorescence XAFS measurement at BL14B2 in SPring-8. We also measured the Ge powder as a reference sample by transmission XAFS measurement. While the measurement, we controlled the sample temperature between 10 - 300 K or 300 - 600 K using a refrigerator or a heating stage, respectively. 3. Results and Discussion The Debye-Waller factor is expressed by Eq. (1) [2], and the amount of change in the Debye-Waller factor from the value at 10 K (ΔDWF) can be expressed by Eq. (2). Here, σ(T) is a Debye-Waller factor, T is an absolute temperature, A is a constant, and T E is the Einstein temperature. σ 2(T) = Acoth(T E / 2T), (1)Δσ 2(T) = A[coth(T E / 2T) – coth{T E / (2 × 10)}], (2)Figure 1 shows the relationship between the amount of change in the Debye-Waller factor (ΔDWF) based on the value at 10 K and temperature for Ge and SiGe. The solid and dashed lines exhibit the calculation using Eq.(1) with the obtained T E shown in Fig.2. From Fig. 1, the ΔDWF of SiGe is likely to change with temperature less than that of Ge, which suggests that the state of lattice vibration has been changed due to the alloy.It has been reported by Kosemura et al. that the coefficient of phonon sensitivity to strain in SiGe slightly change with Ge concentration[1], which indicates that the lattice strain in SiGe thin film affects phonons little. This is consistent with the fact that the two SiGe thin films with different Ge concentrations showed almost the same ΔDWFs as shown in Fig. 1.Figure 2 shows the relationship between T E and Ge concentration obtained from Eq. (2). From Fig. 2, it can be seen T E decreases as Ge concentration increases, then it is considered that the DWF in SiGe is more likely to be thermally excited as the Ge concentration increases. Moreover, since the estimated T Es depended on the Ge concentration, it was suggested that the thermal conductivity of SiGe thin film could be controlled by the Ge concentration.

Theoretical investigation of thermal disorder in CuCo alloys

In this work, we investigate thermal disorder in intermetallic CuCo alloys by extending the anharmonic correlated Einstein model in extended X-ray absorption fine structure (EXAFS) theory. The expressions of bond-stretching force constants, Einstein frequency and temperature, the atomic mean-square relative displacement characterizing the EXAFS Debye–Waller factor have been derived in terms of Morse potential parameters. We perform numerical calculations for CuCo alloys up to temperature 800 K to study the temperature effects on these thermodynamic quantities. Our research shows that Co–Co bonds are stiffer than Cu–Cu bonds. This leads to the atomic mean-square relative displacement curve of CuCo alloys is lower than the one of Cu metal, but higher than the one of bulk Co. The increasing of Co concentration in CuCo alloys will make the increasing of thermal disorder in the alloy system. Moreover, the dynamic disorder caused by thermal lattice vibrations gives significant contribution to the EXAFS Debye–Waller factor at high temperature.

Isotopic effects in Debye-Waller factor and in EXAFS studied based on anharmonic correlated Einstein model

Isotopic effects in Debye-Waller factor and in extended X-ray absorption fine structure (EXAFS) have been studied. The studies are succeeded based on anharmonic correlated Einstein model for isotopes derived for providing analytical expressions of cumulants containing isotopic effects and for application of these cumulants to EXAFS of isotopes. Advantageous development here is creation of a method giving not only the isotopic effects but also the considered quantities only from second cumulant. The model is simplified by using one-dimension with taking many-body effects into account based on including nearest neighbor contributions to vibrations between absorber and backscatterer isotopic atoms. Morse potential is assumed to describe single-pair isotopic atomic interaction. Isotopic effects evidenced in cumulants, EXAFS spectra and their Fourier transform magnitudes of Ni isotopes calculated by present theory are found to be in good similarity to those obtained in experimental results of 70Ge and 76Ge.

Thermophysical systematics of Ni3In and Ni3Sn compounds: Ab initio database and interrelations

The subject of the paper is the use of density-functional-theory methods to determine the zero-kelvin cohesive and elastic properties, as well as the vibrational contribution to the thermal properties of the Ni3X (X = In,Sn) compounds, which are interesting in the field of lead-free soldering materials. The phases are stable at low temperatures in the DO19 (hP8) structure, and at high pressures in the cubic L12 (cP4) structure. In the current work, the T = 0 K energy-volume relations given by the VASP are combined with phonon calculations using the PHONOPY code to develop a quasi-harmonic-approximation account of the vibrational contribution to the thermal properties. The resulting ab initio database is used to: i) analyze trends in the composition dependence of the cohesive energy, the bulk modulus, the elastic constants, the engineering elastic moduli and three Debye temperatures; ii) test some rather general, as well as various material-dependent correlations between these properties; and, iii) test with the present compounds the theory-based interrelations between cohesive and vibrational properties previously established in studies of the transition metals and of a large class of related Cu-X and Ni-X (X = In,Sn) compounds. In particular, the cohesive energy of the present elements and compounds is shown to correlate with an entropy-based characteristic energy, and with the vibrational contribution to the thermal expansion coefficient evaluated at the Einstein temperature.

Studies on thermophysical property variations of graphene nanoparticle suspended ethylene glycol/water

The objective of the study is to determine the thermophysical property variations (such as viscosity, density, specific heat capacity and thermal conductivity) of graphene suspended base fluid (ethylene glycol (EG)/water (W)), with respect to graphene nanoparticle concentration and hot fluid inlet temperature. Graphene nanoparticle concentrations (0.2, 0.4, 0.6, 0.8 and 1 vol.%) and the base fluid of 30:70 vol.% of EG: Water is prepared initially. The impact of graphene nanoparticle addition on base fluids based on experimentation in the commercial plate heat exchanger was studied. In this experiment, the hot fluid inlet temperature was varied at 55, 65 and 75 ?C. The experimental results of thermophysical properties were compared with the selected models proposed in the literature. Einstein (1956), Kitano (1981) and Bachelor models (1977) have been used to consider the effect of viscosity. The measured density and specific heat capacity were validated with Pak and Cho and Xuan models, respectively. To consider the effect of thermal conductivity, three different models (Maxwell (1954), Vajjah (2010) and Sahoo (2012)) have been used. Study revealed that the thermophysical properties of base fluid significantly affect the graphene nanoparticle suspension.

Evaluation of Temperature and Germanium Concentration Dependence of EXAFS Oscillations in Si-Rich Silicon Germanium Thin Films

We measured the influence of the germanium (Ge) nearest neighbor atom on the lattice vibration of silicon germanium (SiGe) thin films on silicon substrate, which is expected as a material for next-generation electronic and thermoelectric devices, by x-ray absorption fine structure measurement. The amount of changes in the Debye-Waller factor (Δσ 2) of each sample were estimated from the obtained extended x-ray absorption fine structure spectra, and it was experimentally clarified that the lattice vibration of the SiGe films were different from that of Ge. On the other hand, it is considered that the lattice vibration of the SiGe films were suppressed by the compressive strain, since Δσ 2 have hardly changed with the Ge concentration. The Einstein temperature estimated from Δσ 2 decreased with increasing Ge concentration, suggesting that the thermal conductivity of SiGe film can be controlled by Ge concentration.

Generalized uncertainty principle corrections on atomic excitation

In this paper, we investigate the effect of minimal length on Einstein model of a gas of two-level atoms in thermal equilibrium with blackbody radiation at temperature T. We reformulate the classical Hamiltonian describing the interaction of atomic electrons with the electromagnetic field of blackbody radiation by employing Kempf Algebra to obtain the Hamiltonian with a minimal length. In the electric dipole approximation, we obtain the modified transition rate relations, and modified Einstein coefficients for broadband excitation. We utilize the modified quantities to obtain the modified cross-section in the resonant laser excitation. We deduce the upper bounds for the deformation parameter and minimal length.

Investigation of thermophysical properties of aqueous magnesium ferrite nanofluids

Highly stable aqueous nanofluids of magnesium ferrite (MgFe2O4) have been synthesized in various concentrations through a two-step method. Their thermophysical properties are analyzed by studying viscosity and thermal conductivity with respect to the concentration and temperature. The structural analysis of MgFe2O4 nanoparticles reveals their cubic spinel structure, whereas transmission electron microscopy (TEM) analysis confirms the spherical morphology. The magnetic studies of MgFe2O4 nanoparticles show the superparamagnetic behavior. The MgFe2O4 nanofluid exhibits non-Newtonian shear thinning behavior. The viscosity values are fitted with Einstein, Wang, and Chen models. The effective thermal conductivity data of MgFe2O4 nanofluids is compared with Hamilton-Crosser model. The enhancements in viscosity and thermal conductivity with respect to concentration and temperature are investigated. A quantitative comparison of enhancement coefficients of viscosity and thermal conductivity is made to understand the heat transfer performance of MgFe2O4 nanofluids. From the enhancement ratio, it is proved that the prepared MgFe2O4 nanofluids have enhanced heat transfer efficiency.

EXAFS investigation of the local structure in URu2−xFexSi2 : Evidence for distortions below 100 K

X-ray absorption measurements at the U ${L}_{\mathrm{III}}$, Ru $K$, and Fe $K$ edges are reported for the hidden order (HO) material ${\mathrm{URu}}_{2\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Si}}_{2}$ ($x=0$, 0.05, 0.08, 0.10, 0.12, 0.15, and 0.20) as a function of $x$ and temperature $T$. When Fe is substituted for Ru, the local structure about Fe shrinks slightly and the first neighbor Fe-Si bond length decreases by $\ensuremath{\approx}0.05\phantom{\rule{0.16em}{0ex}}\AA{}$. More importantly excess disorder is observed below 80--100 K (the coherence temperature ${T}^{*}$) in plots of the Debye-Waller factor ${\ensuremath{\sigma}}^{2}$ ($\ensuremath{\sigma}$ is the width of the pair distribution function); at low $T$ the data deviate from the usual Einstein or correlated-Debye model plots. This excess disorder is most prominent for the Ru-Si bond, and ${\ensuremath{\sigma}}^{2}$ actually increases below 80 K. These results suggest a local orthorhombic distortion with ${B}_{1g}$-like symmetry that develops below 80--100 K. A model that describes these local distortions is presented, and discussed in terms of other measurements that indicate a breaking of fourfold symmetry at low $T$. In addition, the square root of the difference between ${\ensuremath{\sigma}}^{2}(T)$ for the Ru-Si pair and a Debye fit to these data serves as an order parameter for this orthorhombic distortion, in the temperature range below 100 K. This quantity is a length related to $a\text{\ensuremath{-}}b$, the difference between the $a$ and $b$ lattice constants in the orthorhombic phase, and provides a connection between this distortion and ${T}^{*}$. X-ray absorption near edge structure (XANES) measurements also show that there are no changes in the edge positions down to 0.1 eV for any edge as a function of $x$, for $T$ in the HO regime.

Temperature dependence of EXAFS spectra of BCC crystals analyzed based on classical anharmonic correlated Einstein model

In this work, the temperature dependence of extended X-ray absorption fine structure (EXAFS) of the body-centered cubic crystals was investigated based on the anharmonic correlated Einstein model using the classical statistical theory. The oscillation of the anharmonic EXAFS spectra presented in terms of the cumulant expansion up to the fourth order. Here, the thermodynamic parameters of a system are derived from an anharmonic effective potential that has taken into account the influence of all nearest neighbors of absorbing and backscattering atoms. Analytical expressions of the first four EXAFS cumulants are obtained in simple forms of temperature or parallel mean-square relative displacement. The numerical results for crystalline molybdenum in the temperature range from 0 to 900 K are found to be in good agreement with those obtained using the other theoretical methods and experiments at various temperatures. The analytical results for the contributions of the cumulants to the amplitude reduction and phase shift of the EXAFS oscillation discover the role and meaning of high-order cumulants in analyzing the temperature dependence of the EXAFS spectra.

Electronic band structure of (111) SrRuO3 thin films: An angle-resolved photoemission spectroscopy study

We studied the electronic band structure of pulsed laser deposition (PLD) grown (111)-oriented SrRuO$_3$ (SRO) thin films using \textit{in situ} angle-resolved photoemission spectroscopy (ARPES) technique. We observed previously unreported, light bands with a renormalized quasiparticle effective mass of about 0.8$m_{e}$. The electron-phonon coupling underlying this mass renormalization yields a characteristic "kink" in the band dispersion. The self-energy analysis using the Einstein model suggests five optical phonon modes covering an energy range 44 to 90 meV contribute to the coupling. Besides, we show that the quasiparticle spectral intensity at the Fermi level is considerably suppressed, and two prominent peaks appear in the valance band spectrum at binding energies of 0.8 eV and 1.4 eV, respectively. We discuss the possible implications of these observations. Overall, our work demonstrates that high-quality thin films of oxides with large spin-orbit coupling can be grown along the polar (111) orientation by the PLD technique, enabling \textit{in situ} electronic band structure study. This could allow for characterizing the thickness-dependent evolution of band structure of (111) heterostructures$-$a prerequisite for exploring possible topological quantum states in the bilayer limit.

Structural instability and poorly defined phase transitions in rare-earth dodecaborides RB12 (R=Ho-Lu) at intermediate temperatures

The single-crystal structures of YbB12, TmB12, and LuB12 were studied in the temperature range of 88–293 K, those of HoB12 and ErB12 – in the range of 88–500 K using high-resolution X-ray diffraction data in order to correlate the structure changes with the changes in the physical properties of the dodecaborides under study. The lattice deformations caused by the cooperative Jahn – Teller effect were studied. A method is proposed for approximating the temperature dependences of atomic displacement parameters (ADPs) from lattice sites using the extended Debye or Einstein models. The break points in the temperature dependences of ADPs in combination with nonmonotonic changes in the lattice parameters near the critical temperatures Tc indicate phase transformations revealed from diffraction data. The lattice instability and the rearrangement of the phonon spectrum near Tc are accompanied by the observed changes in the physical characteristics. A sensitive structural diagnostic tool was created to detect implicit phase transitions, quantum critical points and quantum instabilities of various nature that lead to the appearance of anomalies in the physical properties of crystals.

Schrödinger and Planck oscillators: not quite the same physics for a modified Einstein solid

In the statistical mechanics of quantum harmonic oscillators, the zero-point energy can either be included (Schrödinger oscillators) or omitted (Planck oscillators). For the usual results, the type of oscillator makes no difference but, looking more closely, it turns out that including or not this energy is not without consequences. A simple model is introduced that we called the modified Einstein solid (MES). In this model the frequency of the oscillators change with the volume of the solid, and this change is characterized by a certain value of the Grüneisen parameter. The specific heat is the same as in the standard Einstein model, but the pressure, equation of state and bulk modulus can be evaluated in the MES. Using Planck oscillators, the pressure shows an anomalous behavior in terms of the volume, and the bulk modulus becomes negative for certain temperature and volume values, which is physically incorrect. When Schrödinger oscillators are used, the bulk modulus is always positive. Therefore, the different behavior of both types of oscillators indicates that only Schrödinger oscillators lead to correct results.

Structural Disorder and Heat Capacity of a Solid Solution between Cadmium and Strontium Fluorides

The heat capacity Cp(T) of cadmium fluoride, strontium fluoride, and the Cd0.5Sr0.5F2 solid solution has been studied experimentally (2–300 K). We have detected deviations ΔCp(T) of the Cp(T) data from additivity. The low-temperature (2–50 K), positive deviations ΔCp(T) have been tentatively attributed to the effect of two-level systems associated with the glasslike character of the low-temperature thermal properties of the solution due to disorder in the Cd–Sr sublattice. The high-temperature (100–300 K), negative deviations ΔCp(T) are caused by the effect of anharmonicity of lattice vibrations, whose increasing role is also associated with the disordered arrangement of atoms in the crystal lattice upon formation of the solution. The Cp(T) data for the solution of the system studied have been analyzed in the Debye–Einstein model. We have determined model parameters: characteristic temperatures Θi and the fractions of different contributions, ai, to total thermal characteristics of the substances studied.