Dulong-Petit Value Research Articles

Structural, elastic, electronic, thermal, and phononic properties of yttrium carbide: First-principles calculations

In this paper, structural, electronic, elastic, phononic, and thermal properties of YC in both rock-salt (B1) and CsCl (B2) phases are studied. Calculations have been performed by using QUANTUM-ESPRESSO/PWSCF computational package which is based on density functional theory (DFT) and pseudo-potential method. Local density approximation (LDA) and generalized gradient approximation (GGA) have been used for modeling the exchange and correlation effects. According to the total energy diagram versus unit cell volume, the YC compound in the B1 phase is more stable than that of the B2 phase at ambient pressure. The computed elastic parameters indicated that the B2 phase did not satisfy the mechanical stability conditions at ambient pressure and is considered to be an unstable phase of the YC structure.The analysis of the enthalpy versus pressure diagram predicts that the structural phase transition from the B1 phase to the B2 phase occurs at pressures 51 GPa and 71.5 GPa, for various LDA and GGA approximations, respectively. Based on the phonon dispersion curves at ambient pressure, the B1 phase of the YC compound is dynamically stable, while at high pressure, the YC compound in the B2 phase has shown stability. Using calculated elastic constants, the small amount of Zener anisotropy factor A shows a strongly anisotropic nature of the YC structure. The higher amount of the calculated Poisson's ratio (~0.40) than that of the corresponding critical value (~0.33) together with the positive values of Cauchy pressure within the LDA and GGA approximations present the ductility and metallic behavior of the YC compound in the B1 phase. The band structure and total density of states calculations also verify the metallic behavior of the YC compound in the stable B1 phase. From PDOS calculations, overlapping the 4d orbital of the Y atom and 2p orbital of the C atom near the Fermi level indicates that these orbitals have significant contributions to the bonding between the Y and C atoms. This bonding is substantiated by the corresponding electron density distribution. The thermodynamic calculations indicated that the heat capacity increases regularly and continuously with the increase in temperature T, toward the classical Dulong-Petit value of 6R for the bulk structure of the YC compound with two atoms in the primitive cell. It can also be predicted for the YC compound that the smaller lattice parameter within the LDA approximation compared to the GGA approximation causes stiffness increases, followed by an increase in the Debye temperature. The increasing trend of entropy versus temperature indicates the endothermic behavior of the YC compound.

High-Temperature Specific Heat of Al–Cu–Ru Icosahedral Quasicrystals and 1/1 Crystal Approximants

We report the results of specific heat measurements for Al–Cu–Ru icosahedral quasicrystals (i-QCs) and 1/1 crystal approximants (1/1-CAs) in the temperature range from 350 to 1250 K. The i-QCs and 1/1-CAs showed a marked upward deviation of the specific heat from the value of Dulong-Petit’s law above 600 K, reaching approximately 1.5 times the value at 1100 K. In addition, some i-QCs showed a large broad peak in the specific heat at approximately 1200 K. The origin of these excessive specific heat values above the Dulong-Petit value is discussed considering the high-dimensional nature of the structural order in the QCs and CAs.

Lone-Electron-Pair Micelles Strengthen Bond Anharmonicity in MnPb16Sb14S38 Complex Sulfosalt Leading to Ultralow Thermal Conductivity

Designing crystalline solids in which intrinsically and extremely low lattice thermal conductivity mainly arises from their unique bonding nature rather than structure complexity and/or atomic disorder could promote thermal energy manipulation and utilization for applications ranging from thermoelectric energy conversion to thermal barrier coatings. Here, we report an extremely low lattice thermal conductivity of ∼0.34 W m-1 K-1 at 300 K in the new complex sulfosalt MnPb16Sb14S38. We attribute the ultralow lattice thermal conductivity to a synergistic combination of scattering mechanisms involving (1) strong bond anharmonicity in various structural building units, owing to the presence of stereoactive lone-electron-pair (LEP) micelles and (2) phonon scattering at the interfaces between building units of increasing size and complexity. Remarkably, low-temperature heat capacity measurement revealed a Cp value of 0.206 J g-1 K-1 at T > 300 K, which is 22% lower than the Dulong-Petit value (0.274 J g-1 K-1). Further analysis of the Cp data and sound velocity (ν = 1834 m s-1) measurement yielded Debye temperature values of 161 and 187 K, respectively. The resulting Grüneisen parameter, γ = 1.65, further supports strong bond anharmonicity as the dominant mechanism responsible for the observed extremely low lattice thermal conductivity.

Heat Capacity of Decagonal and Icosahedral Quasicrystalline Phases at High Temperatures

The paper deals with the calculations of heat capacity of quasicrystalline decagonal Al69Co21Ni10 and icosahedral Al63Cu25Fe12 quasicrystalline phases of Al–Co–Ni and Al–Cu–Fe alloys, respectively. According to the Gruneisen law, heat capacity is an energy characteristic, which reflects the phases’ resistance to failure. For calculations of the heat capacity, structure of quasicrystalline phases is considered in the model representation of anisotropic crystals. As a result, it is found that the heat capacity of quasicrystalline phases at high temperatures is the excessive one, i.e. it exceeds the Dulong-Petit value. Therefore, quasicrystalline phases at high temperatures are more stable, than the crystalline phase. For the decagonal quasicrystalline phase, heat capacity is more than 3R in the temperature range of ~480–1500 К, and for the icosahedral quasicrystalline phase – in the temperature range of ~380–1120 К. It follows that decagonal phases remain stable at high temperatures at which the icosahedral phases are destroyed.

The importance of the Debye bosons (sound waves) for the lattice dynamics of solids

For a number of materials with cubic lattice structure the dispersion relations of the Debye bosons (sound waves) and of the acoustic phonons along [ζ 0 0] direction have been analyzed quantitatively. When all phonon modes are excited, that is, for temperatures of larger than the Debye temperature the dispersion of the mass-less Debye bosons exhibits a pronounced non-linearity, which is explained by interactions with the phonon background. For the exponent x in the dispersion relation ~qx of the Debye bosons, the rational values of x=1/4, 1/3, 1/2, 2/3 and 3/4 could be established firmly. The discrete values of x show that there are distinct modes of interaction with the phonons only. It is furthermore shown that for many materials the dispersion of the acoustic phonons along [ζ 0 0] direction follows a perfect sine function of wave vector, which is known to be the dispersion of the linear atomic chain. This dispersion is unlikely to be the intrinsic behavior of three-dimensional solids. It is argued that the sine-function is induced by the Debye boson-phonon interaction. Quantitative analyses of the temperature dependence of the heat capacity show that the heat capacity can be described accurately over a large temperature range by the expression cp=c0-B‧T-ε. The constants c0 and B are material specific and define the absolute value of the heat capacity. However, for the exponent ε the same rational value occurs for materials with different chemical compositions and lattice structures. The temperature dependence of the heat capacity therefore exhibits universality. This universality must be considered as a non-intrinsic dynamic property of the atomistic phonon system, arising from the Debye boson-phonon interaction. The discrete modes of boson-phonon interaction are essential for the observed universality classes of the heat capacity. Safely identified values for ε are ε=1, 5/4 and 4/3. The fit values for c0 are generally larger than the theoretical Dulong-Petit value. Universal exponents are identified also in the temperature dependence of the coefficient of the linear thermal expansion, α(T). Since the universality in α(T) holds for the same thermal energies (temperatures) as for the ~qx functions in the dispersion of the Debye bosons it can be concluded that the Debye bosons also determine the temperature dependence of α(T). Our results show that the dynamics of the atomic lattice is modified for all temperatures by the Debye bosons. Atomistic models restricting on inter-atomic interactions therefore are neither sufficient to explain the phonon dispersion relations nor the detailed temperature dependence of the heat capacity.

Anharmonicities in the temperature-dependent bending rigidity of BC3 monolayer

The present work investigated the temperature-dependent thermodynamic and structural characteristics of graphene-like monolayer boron carbide (g-BC3) using classical molecular dynamics simulations. Herein, we mainly focused on the temperature dependence of mean square displacement of thermally stimulated ripples and bending rigidity of g-BC3. We observed that at high temperatures, the specific heat capacity at constant volume exhibits a significant increase beyond the limit of Dulong-Petit value due to the presence of anharmonicity in the g-BC3. Besides, the linear thermal expansion coefficient is found to be negative owing to the excitation of low-frequency bending vibrations in the out-of-plane orientation. Studies reveal that the out-of-plane of height fluctuations and bending rigidity are fully dependent on temperature and are described using the continuum theory of membranes. Moreover, the study on the height fluctuation and correlation shows variation from the estimation of the harmonic theory of membranes as a consequence of the anharmonic features of g-BC3. We believe that our study will provide a notable contribution to numerous applications of g-BC3 including nanoelectromechanical (NEMS) devices to become a reality.

Melting Line of Graphite.

A thin plate of highly oriented pyrolytic graphite (HOPG) with the hexagonal axis (c axis) perpendicular to its surface was sandwiched between two plates of the window material and heated by an electric current pulse. The quasistatic heating process has been affected, in which the graphite sample undergoes thermal expansion only along the c axis and is melted at a pressure of 0.3-2GPa. The set of thermodynamic quantities characterizing completely the thermodynamic states of the sample in such a process (specific volume, enthalpy, temperature, and pressure) as well as the electrical resistivity, were measured with an uncertainty <5%. It has been found that under the above pressures the HOPG melts at the temperatures of 6.3 to 6.7kK, which are substantially higher than the literature values derived from indirect measurements. The jumps in the volume, resistivity and enthalpy of carbon on melting have been determined as well as values of the isochoric heat capacity and the sound velocity of the graphite and liquid carbon. The heat capacities in the vicinity of the melting line turned out to be close to the Dulong-Petit value while the sound velocity of liquid carbon clearly demonstrates an increase with volume indicating a change from the planar sp^{2} to tetrahedral sp^{3} covalent bonding.

Temperature dependence of decagonal quasicrystals heat capacity

The heat capacity of decagonal quasicrystals of the Al–Co–Cu or Al–Co–Ni alloys was calculated at the temperatures of 600, 700, and 900 K in this work. The expression for the heat capacity of the quasicrystals was obtained based on the Debye model. For the quasicrystals, the linear “excessive” heat capacity is observed in the range of temperatures between 400 to 600 К which means the deviation from the 3R Dulong-Petit value. The heat capacity at a temperature of 900 К is about 28.4 J/mol К which is higher than the Dulong-Petit value (~ 25 J/mol К). The “excessive” heat capacity relates to the peculiarities in the decagonal quasicrystal anisotropy. These crystals are quasiperiodic in the x and y directions, and periodic in the z direction. As a result, there is a difference in the dispersive laws in the different directions. The Debye temperature values have essential influence on the temperature dependencies of the heat capacity of the decagonal quasicrystals. Thus, the higher the Debye temperature and the larger “excessive” heat capacity, the more stable are considered the quasicrystals exposed to the temperature effects.

Bizarre behavior of heat capacity in crystals due to interplay between two types of anharmonicities.

The heat capacity of classical crystals is determined by the Dulong-Petit value CV ≃ D (where D is the spatial dimension) for softly interacting particles and has the gas-like value CV ≃ D/2 in the hard-sphere limit, while deviations are governed by the effects of anharmonicity. Soft- and hard-sphere interactions, which are associated with the enthalpy and entropy of crystals, are specifically anharmonic owing to violation of a linear relation between particle displacements and corresponding restoring forces. Here, we show that the interplay between these two types of anharmonicities unexpectedly induces two possible types of heat capacity anomalies. We studied thermodynamics, pair correlations, and collective excitations in 2D and 3D crystals of particles with a limited range of soft repulsions to prove the effect of interplay between the enthalpy and entropy types of anharmonicities. The observed anomalies are triggered by the density of the crystal, changing the interaction regime in the zero-temperature limit, and can provide about 10% excess of the heat capacity above the Dulong-Petit value. Our results facilitate understanding effects of complex anharmonicity in molecular and complex crystals and demonstrate the possibility of new effects due to the interplay between different types of anharmonicities.

Thermal conductivity of Al–Gd–TM glass-forming alloys

Thermal diffusivity, specific heat capacity and thermal conductivity of Al86Gd6TM8 (TM = Cu, Ni, Co, Fe, Mn, Cr, Ti, Zr, Mo, Ta) glass-forming alloys in the temperature range of 300–880 K were determined by laser flash method. The temperatures of endothermic and exothermic reactions of the alloys were determined by differential scanning calorimetry method. The alloys were prepared by conventional arc-melting technique under helium atmosphere. All the alloys studied exhibit strong supercooling of the liquidus temperatures up to 80 K, which indicates their good glass-forming ability. The specific heat capacity of the alloys achieves the Dulong–Petit's value in the temperature range of 350–550 K except Al86Cr8Gd6 and Al86Zr8Gd6 compositions. The values of both thermal diffusivity and thermal conductivity of the alloy studied are significantly lower than those for pure aluminum. It is found that embedding 14% (mole fraction) of transition elements (Gd+TM) in the aluminum matrix leads to significant decrease in the absolute magnitudes of both thermal diffusivity and thermal conductivity in crystalline state. The thermal conductivity of glass-forming Al86Gd6TM8 alloys is strongly affected by directed chemical bonding between alloy components.

Prediction of a large number of electron pockets near the band edges in type-VIII clathrate Si46 and its physical properties from first principles

The material design of type-VIII clathrate Si46 is presented based on first principles. The structural, electronic, elastic, vibrational, and thermodynamic properties of this hypothetical material are presented. Our results predict that type-VIII clathrate Si46 is an indirect semiconductor with a bandgap of 1.24 eV. The band structure revealed an interestingly large number of electron pockets near both conduction and valance band edges. Such a large density of states near the band edges, which is higher than that of the best thermoelectric materials discovered so far, can result in a large thermoelectric power factor (>0.004 W m−1 K−2) making it a promising candidate for thermoelectric applications. The elastic properties as well as the vibrational modes and the phonon state densities of this material were also calculated. Our calculations predict that the heat capacity at constant volume (isochoric) of this clathrate increases smoothly with temperature and approaches the Dulong–Petit value near room temperature. The electronic band structure shows a large number of valleys closely packed around the valance band edge, which is rare among the known semiconducting materials. These valleys can contribute to transport at high temperature resulting in a possibly high performance (ZT > 1.5) p-type thermoelectric material.

Electronic, elastic, vibrational, and thermodynamic properties of type-VIII clathrates Ba8Ga16Sn30 and Ba8Al16Sn30 by first principles

We present the results of studying electronic, elastic, vibrational, and thermodynamic properties of type-VIII clathrates Ba8Ga16Sn30 Ba8Al16Sn30 calculated from a first-principles approach. The calculations utilize the generalized gradient approximation to density functional theory. The results indicate that the Ba8Ga16Sn30 and Ba8Al16Sn30 are indirect semiconductors with fundamental band gaps of 160 meV and 315 meV, respectively. It was also found that the stiffness of Al containing type-VIII clathrate does not show any significant change against the uniform pressure, shearing, and linear strains. The phonon spectrum and the phonon state densities of these compounds as well as the Raman and infrared active modes were further calculated and the effects of replacing the Ga with Al atoms on the properties of interest were discussed. The calculated elastic, vibrational, and thermodynamic properties along with Raman and IR spectra are reported for the first time. The identification of the Raman and infrared active modes will be especially useful for the experimental characterizations of these compounds. Our calculations show that the heat capacities of these clathrates increase smoothly with temperature and approach the Dulong-Petit value at about room temperature, which agrees with the existing experimental data.

Single-Ion Heat Capacities, Cp(298)ion, of Solids: with a Novel Route to Heat-Capacity Estimation of Complex Anions

Single-ion heat capacities, C(p)(298)(ion), are additive values for the estimation of room-temperature (298 K) heat capacities of ionic solids. They may be used for inferring the heat capacities of ionic solids for which values are unavailable and for checking reported values, thus complementing our independent method of estimation from formula unit volumes (termed volume-based thermodynamics, VBT). Analysis of the reported heat-capacity data presented here provides a new self-consistent set of heat capacities for both cations and anions that is compatible (and thus may be combined) with an extensive set developed by Spencer. The addition of a large range of silicate species permits the estimation of the heat capacities of many silicate minerals. The single-ion heat capacities of individual silicate anions are observed to be strictly proportional to the total number of atoms (Si plus O), n, contained within the silicate anion complex itself (e.g., for the anion Si(2)O(7)(2-), n = 9, for SiO(4)(2-), n = 5), C(p)(silicate anion)/J K(-1) mol(-1) = 13.8n, in a new rule that is an extension of the Neumann-Kopp relationship. The same linear relationship applies to other homologous anion series (for example, oxygenated heavy-metal anion complexes such as niobates, bismuthates, and tantalates), although with a different proportionality constant. A similar proportionality, C(p)(complex anion)/J K(-1) mol(-1) ≈ 17.5n, which may be regarded as a convenient "rule of thumb", also applies, although less strictly, to complex anions in general. The proportionality constants reflect the rigidity of the complex anion, being always less than the Dulong-Petit value of 25 J K(-1) mol(-1). An emergent feature of our VBT and single-ion approaches to an estimation of the thermodynamic properties is the identification of anomalies in measured values, as is illustrated in this paper.

&lt;i&gt;Ab Initio&lt;/i&gt; Study of the Phonon Frequency, Electrical and Thermal Properties of TiN

With a motivation to understand microscopic aspects of TiN relevant to the electronic structure, phonon and thermal properties of transition metal nitride TiN superlattices, we determine its electronic structure, phonon spectra and thermal properties using first-principles calculations based on density functional theory with a generalized gradient approximation of the exchange correlation energy. We find that the electronic bands crossed by EF are half occupied, TiN has the ability of taking part in chemical reactions and also has the surface activity; A large gap in its phonon spectra, anomalies in the phonon dispersion of metallic TiN, manifested as dips in acoustic branches, but it do not contain soft modes in any direction; The specific heat (Cv) of TiN rises rapidly at low temperatures, the Cv values of the material, is identical to the Dulong-Petit value at high temperatures. Under the quasi-harmonic approximation (QHA), the thermal expansion, specific heat and bulk modulus B(T) are obtained, and the B(T) decreases along with the increase of temperature.

Phason dynamics in one-dimensional lattices

In quasicrystals, the phason degree of freedom and the inherent anharmonic potentials lead to complex dynamics which cannot be described by the usual phonon modes of motion. We have constructed simple one-dimensional model systems, the dynamic Fibonacci chain (DFC) and approximants thereof. They allow us to study the dynamics of periodic and quasiperiodic structures with anharmonic double well interactions both by analytical calculations and by molecular dynamics simulations. We found soliton modes like breathers and kink solitons and we were able to obtain closed analytical solutions for special cases, which are in good agreement with our simulations. Calculation of the specific heat shows an increase above the Dulong-Petit value, which is due to the anharmonicity of the potential and not caused by the phason degree of freedom.

Structure, Heat Capacity, and High-Temperature Thermal Properties of Yb14Mn1−xAlxSb11

A series of compounds, Yb_(14)Mn_(1−x)Al_xSb_11 with (0 < x < 1), was prepared via Sn flux and the structures investigated. Single-crystal X-ray diffraction reveals that the volume of the unit cell increases with increasing Al content. Bond-distance changes are less than 2% and the increase in volume of the unit cell is associated with the decreasing distortion of the tetrahedron with increasing Al content. The specific heat, C_p, was measured from 300 to 1100 K. The measured C_p for these compounds is 19% higher than the Dulong-Petit value at the peak zT temperature (1223 K). These measured values permit a recalculation of thermal conductivity, revealing an extremely low lattice thermal conductivity of approximately 0.3−0.4 W/(m K) at 1223 K. The maximum zT of Yb_(14)Mn(1−x)Al_xSb_11 is approximately 0.8 and 1.1 for the x = 0 and x = 0.6 compositions, respectively.

First-principles calculations of the vibrational and thermal properties of the type-I clathratesBa8Ga16SixGe30−xandSr8Ga16SixGe30−x

We have performed density-functional calculations of the vibrational and thermal properties of some of the type-I semiconductor clathrate ``alloys'' ${\text{Ba}}_{8}{\text{Ga}}_{16}{\text{Si}}_{x}{\text{Ge}}_{30\ensuremath{-}x}$ and ${\text{Sr}}_{8}{\text{Ga}}_{16}{\text{Si}}_{x}{\text{Ge}}_{30\ensuremath{-}x}$ as a function of Si composition $x$. We find that the guest-atoms Ba and Sr produce localized vibrational modes lying below $80\text{ }{\text{cm}}^{\ensuremath{-}1}$, which tend to reduce the acoustic bandwidth of the host material. Our results also predict an upshift in the flat optic modes of the host framework as the Si content of the lattice increases and that the guest-atom-associated Einstein temperature in these materials varies with $x$. Our calculated isotropic atomic displacement parameters as functions of temperature for the guest Ba and Sr atoms in these clathrates predict that Sr has a larger isotropic displacement parameter than Ba, thus suggesting that Sr should be more efficient than Ba in suppressing the thermal conductivity. We have also calculated the temperature dependences of the vibrational contributions to the specific heat, the entropy, and the Helmholtz free energy in these materials. We find that the heat capacities of these clathrates increase smoothly with temperature and approach the Dulong-Petit value at around room temperature. As expected, we also find that in these materials, there is also a slight $x$ dependence of the heat capacity, free energy, and vibrational entropy.

Thermodynamic analysis of light-actinide elements

The thermophysical properties of the alpha phases of the light actinide elements Th, U, Np and Pu were analysed. For each of the analysed elements, the Gibbs free-energy was modelled by an explicit function of temperature T and pressure P over the whole relevant T– P range, in a manner compatible with the CALPHAD (Calculation of Alloy Phase Diagrams) method. Several adjustable model-parameters were fitted to available experimental results. The model is based on a new semi-empirical equation of state, which interpolates with Thomas–Fermi type models for the volume and with the Dulong–Petit value for the heat capacity, at extreme pressures.

Superfluidity below 20 K in condensed excitons

In the condensed excitonic phase of intermediate valent TmSe 0.45Te 0.55 the heat conductivity and the thermal diffusivity have been obtained between 300 and 1.5 K and between ambient pressure and 17 kbar (1.7 GPa), as a first experiment of its kind. Pressure and temperature are used to navigate in three different phases of the material, the intermediate valent semiconducting phase, the condensed excitonic phase and the intermediate valent metallic phase. In the condensed excitonic phase the heat conductivity λ increases strongly below about 20 K, suggesting a superfluid phase for the lowest temperatures. In a solid under equilibrium conditions this has never been seen before. Also the thermal diffusivity a strongly increases below 20 K, giving evidence for second sound. The quotient λ/ ρa represents the specific heat, which thus can be calculated, for the first time as a function of pressure and for a large temperature range. When entering the condensed excitonic phase under pressure and from high temperatures (100–250 K), the Dulong–Petit value of the specific heat drops precipitously to about half its value. Also this phenomenon is unprecedented. In addition the longitudinal sound velocity has been measured under pressure and as a function of temperature. Entering the excitonic phase the sound velocity drastically increases by about a factor 2.

Possibility of a superfluid phase in a Bose condensed excitonic state

In the condensed excitonic phase of intermediate valent ${\mathrm{TmSe}}_{0.45}{\mathrm{Te}}_{0.55}$ the thermodynamic properties have been measured. The heat conductivity and the thermal diffusivity have been obtained between 300 K and 1.5 K and between ambient pressure and 17 kbar (1.7 GPa), as a first experiment of its kind. Pressure and temperature are used to navigate in three different phases of the material, the intermediate valent semiconducting phase, the condensed excitonic phase, and the intermediate valent metallic phase. In the condensed excitonic phase the heat conductivity \ensuremath{\lambda} increases strongly below about 20 K, suggesting a superfluid phase for the lowest temperatures. In a solid under equilibrium conditions this has never been seen before. Also the thermal diffusivity $a$ strongly increases below 20 K, giving evidence for second sound. The quotient $\ensuremath{\lambda}/\ensuremath{\rho}a$ represents the specific heat, which thus can be calculated, for the first time as a function of pressure. When entering the condensed excitonic phase under pressure and from high temperatures (100 K--250 K), the Dulong-Petit value of the specific heat drops precipitously to about half its value. Also this phenomenon is unprecedented. The entropy has been calculated from the heat capacity and the Debye temperature has been obtained as a function of pressure. In addition the longitudinal sound velocity has been measured under pressure and as a function of temperature. Entering the excitonic phase the sound velocity drastically increases by about a factor 2.