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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.

A type-VII clathrate with a Eu2+ guest embedded into a Ni–P covalent framework, EuNi2P4, was synthesized by a standard two-stage ampoule synthesis and confirmed to crystallize in the orthorhombic space group Fddd with unit cell parameters a = 5.1829(1) A, b = 9.4765(1) A, and c = 18.9900(1) A. A general technique for studying the lattice and magnetic properties of REE containing compounds is proposed. The temperature and field dependences of electrical resistivity ρ(T,H), magnetization M(T,H), magnetic susceptibility χ(T,H), heat capacity Cp(T), and unit cell parameters a(T), b(T), c(T), and volume V(T) were experimentally studied and analyzed at different pressures in the temperature range of 2–300 K. A cascade of anomalies in the studied dependences was identified and attributed to the magnetic phase transformation and peculiar lattice contributions at temperatures below 20 K. As a result of comparison with an isostructural clathrate SrNi2P4, the parameters of the magnetic and lattice contributions were determined. It is characteristic that the phase transition from the paramagnetic to the magnetically ordered state is not reflected in the temperature changes of the lattice parameters due to weak bonds between guest europium atoms and the Ni–P host matrix. We have constructed a tentative H–T phase diagram based on the M(T) and M(H) data, which includes 6 different phases. It is established that the anomalous lattice contribution to the clathrate heat capacity CTLS(T) appears due to the effect of two-level systems (TLS) in the Eu2+ subsystem on the thermodynamic properties of EuNi2P4. The values of TLS parameters as well as the parameters of the magnetic subsystem of the clathrate were determined.

Heat capacity CP(T) and lattice parameters a(T), b(T) and c(T) of LuB44Si3.5 borosilicide are experimentally studied as a function of temperature in the range of 2-300 K. The results are compared with those of pseudo-isostructural LuB50 boride. At the lowest temperatures, it is shown that the CP(T) dependence of borosilicide changes linearly with temperature. This is attributed to the effect of glass-like behaviour of the heat capacity due to the disorder in the sublattice of non-metals. The presence of defects in the B-Si sublattice and the irregular form of the cages in the B-Si matrix, which are occupied by Lu3+ ions, lead to the formation of two-level systems (TLS) in the Lu3+ subsystem. The TLS make a characteristic bell-like low-temperature contribution to the heat capacity of borosilicide. We show that there is a wide temperature range (5-150 K) of negative thermal expansion of borosilicide, which is attributed to the influence of quasi-independent vibrations of Lu3+ ions in the cages of the borosilicide crystal structure.

A sample of lutetium carboboride LuB2C was synthesized from a mixture of lutetium hydride, boron and carbon by annealing in argon. The temperature dependence of the heat capacity Cp(T) (2-300 K) and lattice parameters a(T), b(T), and c(T) (5-300 K) of the carboboride was experimentally determined. The experimental values of the heat capacity were fitted with the approximation Cp(T) = aT + ΣCD + CE + CTLS(T). Here the first term is the electronic contribution, the second is the sum of the Debye components, the third is the Einstein contribution, and the fourth is the contribution to the heat capacity due to the vibrations of the two-level systems which are formed in the Lu-subsystem due to the asymmetry of the B-C atomic arrangement around the Lu3+-ions and, as a consequence, the possible transition of the lutetium atoms between spatially close, but energetically non-equivalent positions. A strong anisotropy of the thermal expansion of the carboboride was revealed. Along the c axis the coefficient of thermal expansion monotonically increases; in the basal plane, the expansion is practically not observed. The temperature dependence of the unit cell volume Vu(T) has been analyzed in the Debye-Einstein approximation taking into account the electronic contribution and effect of two-level systems. The values of the Gruneisen parameters corresponding to different modes of the phonon spectrum of the carboboride have been determined. The frequencies of the lattice vibrations, determined in a Raman scattering experiment, are in satisfactory agreement with the parameters obtained from Cp(T) using the Debye-Einstein approximation. Using ab initio band theory methods and an exchange-correlation functional in the PBE form in the VASP package, it was established that the total energies of these two crystal structures differ by no more than 0.01 eV f.u.-1. Calculations of the thermodynamic properties of LuB2C yielded similar results for orthorhombic and tetragonal phases of the carboboride.

*Özışık, Hacı ( Aksaray, Yazar ) *Deligöz, Engin ( Aksaray, Yazar ), The characteristics of the electronic and phonon subsystems of lanthanum tetraboride (LaB4) studied using first-principles calculations. The calculated lattice parameters, as well as the positions of atomic, are satisfactorily consistent with the experimental data. The partial densities of states, band structure, Fermi surface, phonon dispersion curve of LaB4 are calculated and analysed. The reliability of the calculation results is confirmed by a satisfactory agreement between the calculated thermodynamic parameters of LaB4 (temperature changes in heat capacity, entropy, Gruneisen parameter and volume modulus) with experimental data.

The specific heat, thermal expansion and magnetic properties of polycrystalline sample of nonstoichiometric dysprosium boride DyB 50 , that was synthesized by boron-thermal reduction of the metal from its oxide in vacuum, were studied at 2–300 K. The measurements revealed a heat capacity and magnetic susceptibility anomalies at about T N ≈ 6.3 K, caused by the transition to an antiferromagnetic state. The anomalies of studied properties of DyB 50 at higher temperatures have been ascribed to the influence of crystal electric field (CEF). The scheme of CEF-splitting of Dy 3+ ion ground level in boride has been proposed.

We performed an experimental study on thermal properties of the Sn18In6As21.5I8 clathrate by measuring temperature dependencies of its heat capacity (2-300 K) and thermal expansion (5-300 K). By comparing the results with those published previously for Sn-based clathrates Sn24P19.2I8, Sn20Zn4P20.8I8, and Sn17Zn7P22I8, we established that partial replacement of tin and phosphorus by heavier indium and arsenic, respectively, leads to lowering vibration frequencies in both host and guest substructures. Deviation of the observed thermal properties at low temperatures from those predicted by the Einstein-Debye model is caused by the Schottky-like contribution of two-level systems to heat capacity and thermal expansion. These systems form owing to transitions of guest atoms in non-spherical 24-vertex cages between stationary states with close energies.

A holmium boride HoB50 polycrystalline sample was synthesised by boron-thermal reduction from the elements at high temperature. The temperature dependencies of the heat capacity Ср(Т) and the unit cell parameters a(T), b(T), c(T) of holmium boride were determined experimentally in the temperature range 2–300 K. In terms of Cp(T) dependence, smooth anomalies were revealed at TС1 max ≈ 6.5 K and TС2 max ≈ 30 K; the first of these is caused by an antiferromagnetic transition and the second by the influence of the crystalline electric field (CEF). The high-temperature anomaly in the heat capacity of the boride is satisfactorily reproduced due to a simplified scheme for CEF-splitting of the ground state of the Ho3+ ions. The dependencies a(T), b(T), c(T) of holmium boride clearly show a pronounced anisotropy of thermal expansion. The anomalies in the temperature changes of the HoB50 unit cell volume at elevated temperatures are analysed within the CEF model described above.

The heat capacity C v (T) and unit cell volume V(T) temperature dependencies of lutetium borides LuB 2 and LuB 4 in the region of 2–300 К were analysed in the Debye-Einstein approximation. The characteristic temperatures of the Debye and Einstein components of boride heat capacity and thermal expansion were found. The anomalous contribution to the borides’ thermal characteristics was revealed. This contribution was attributed to the influence of two-level systems (TLS), formed in the subsystem of lutetium ions due to asymmetry in the way they are surrounded by the boron atoms in the boride crystal structure. The TLS influence is revealed on heat capacity temperature dependencies by the Schottky-type maxima at T max LuB2 =13.8 K, T max LuB4 =22.7 K, as well as by the negative contribution to the borides’ thermal expansion. The borides’ Gruneisen parameters corresponding to the heat capacity and thermal expansion TLS anomalies are negative, and amount to several 10 s of units.

Techniques of synthesis of RE diborides (RB 2 ) are developed (R=Tb, Dy, Ho, Er, Lu). Temperature dependence of magnetisation, a heat capacity, a lattice parameters of diborides in the range of 2–300 K are measured. According to joint calorimetric and X-ray research the analysis of a phonon component of a heat capacity and thermal expansion of RE-diborides is carried out by Debye-Einstein's models, the parameters of the model are determined. The change of magnetisation of the ferromagnetic RB 2 compounds with growth of temperature caused by violation of ordering in the system of the atomic magnetic moments is compared with the change of entropy of a magnetic subsystem calculated from calorimetric data. Analytical expansion for calculation of a magnetic component of a heat capacity by RB 2 magnetisation data at the temperatures of 2–300 K is obtained.

Specific heat and thermal expansion in LuB50 and TbB50 borides at 2–300 K were experimentally studied. In both compounds, for a large range of low temperatures a negative thermal expansion caused by defects in the crystal lattice was observed. The effect of the crystal electric field on the thermal characteristics of TbB50 was observed as a Schottky anomaly in the temperature dependence of the heat capacity and as an additional negative contribution to the thermal expansion. The analysis of the heat capacity data suggests that the ground state of the ion Tb3+ is a quasi-quintet, consisting of close-located singlet and two doublets. The phase transition of TbB50 to the antiferromagnetic state appears as a very weak broad anomaly in the temperature dependence of the heat capacity; within the scattering of the experimental data, it is not visible in the temperature dependence of the unit cell volume.

Heat capacity and lattice parameters of cerium tetraboride were experimentally determined at 2 – 300 K. An anomalously large contribution of free electrons to the heat capacity was influenced by Fermi liquid state in the cerium boride. The parameters of Einstein and Debye contributions to CeB 4 heat capacity, as well as free electron gas contribution and Schottky heat capacity have been determined. A negative thermal expansion (NTE) of CeB 4 was found (5–25 K). We were not able to explain the NTE by the influence of intermediate valence of cerium ions. The NTE was attributed to the influence of the crystal electric field (CEF) on Ce 3+ ions.

The temperature dependencies of heat capacity, CP(T), and cubic unit cell parameter, a(T), were experimentally obtained in the range of 2-300 K for the compounds Sn24P19.2I8, Sn20Zn4P20.8I8, and Sn17Zn7P22I8, which belong to a family of type-I clathrates. The experimental data were analyzed in the frames of the Debye-Einstein approximation, further accounting for the contributions of positional disorder in the clathrate frameworks as well as those of defect modes arising from the distribution of guest atoms over unequal in energy but close in space positions inside the framework cages. By fitting the experimental data, the Debye and Einstein characteristic temperatures describing the dynamics of the framework and guest atoms, respectively, were obtained. Their analysis revealed peculiar dependencies of the characteristic temperatures upon the number of substituted zinc atoms and the concentration of vacancies in the framework, which are discussed in this paper.

Temperature changes of the heat capacity and unit cell parameters of Sn24P19.4Br8 clathrate were experimentally determined in the temperature range of 2 to 300 K. The data obtained were analyzed using Debye–Einstein approximation and taking into account the impact of both disorder in the host matrix and the presence of vacancies in the framework. Anomalous negative contribution to the thermal expansion was revealed and related to the defect mode influence on the clathrate thermal properties as a result of vibrations of two-level systems (TLS). The guest atoms that have the opportunity to occupy spatially close yet energetically non-equivalent positions in the asymmetric environment of the host matrix atoms play a principal role in the TLS formation. The results are compared with those previously obtained for semiclathrate Ge31P15Se8.

Heat capacity Ср(Т) and thermal expansion V(T) of the Ge31P15Se8 semiclathrate were studied in the temperature range of 2–300 K. It is shown that the total heat capacity takes remarkably high values at low temperatures, exceeding 1 J mol−1 K−1, owing to a glass-like contribution arisen from irregularities in the structure of the clathrate framework. A Schottky-like term is subtracted and attributed to asymmetry of the guest atom environment inside the distorted polyhedral cages of the framework. At temperatures below 30 K, a negative thermal expansion was found possibly caused by guest atomic transitions between energetically non-equivalent states within distorted cages of the framework. Values of the Debye and Einstein terms (θD = 560 K, θE1 = 130 K, and θE2 = 95 K) of the thermal characteristics of Ge31P15Se8 are related to concerted and localized vibrations of different fragments of the semiclathrate crystal structure.

The thermal conductivity of a ZnWO4 single crystal in the principal crystallographic directions has been studied experimentally in the temperature range of 50–573 K, and the heat capacity of the single crystal has been measured in the range of 81–301 K.

We experimentally study the heat capacity and thermal expansion of thulium boride (TmB50) at temperatures of 2–300 K. The wide temperature range (2–180 K) of boride negative expansion was revealed. We found the anomalies in C(T) heat capacity temperature dependence, attributed to the Schottky contribution (i.e. the influence of the crystal electric field: CEF), as well as the magnetic phase transition. CEF-splitting of the f-levels of the Tm3+ ion was described by the Schottky function of heat capacity with a quasi-quartet in the ground state. Excited multiplets are separated from the ground state by energy gaps δ1 = 100 K, and δ2 ≈ 350 K. The heat capacity maximum at Tmax ≈ 2.4 K may be attributed to the possible magnetic transition in TmB50. Other possible causes of the low-temperature maximum of C(T) dependence are the nonspherical surroundings of rare earth atoms due to the boron atoms in the crystal lattice of the boride and the emergence of two-level systems, as well as the splitting of the ground multiplet due to local magnetic fields of the neighboring ions of thulium. Anomalies in heat capacity are mapped with the thermal expansion features of boride. It is found that the TmB50 thermal expansion characteristic features are due to the influence of the CEF, as well as the asymmetry of the spatial arrangement of boron atoms around the rare earth atoms in the crystal lattice of RB50. The Gruneisen parameters, corresponding to the excitation of different multiplets of CEF-splitting, were determined. A satisfactory accordance between the experimental and estimated temperature dependencies of the boride thermal expansion coefficient was achieved.

A homogeneous powder sample of EuCu2P2 was synthesized from the elements by a two-step high-temperature ampule technique. X-ray powder diffraction analysis have shown that the compound belongs to the ThCr2Si2 structure type and features copper deficiency. The study of temperature changes of heat capacity, Cp(T) (2–300 K), and unit cell parameters, a(T) and c(T) and volume Vu(T) (5–300 K), revealed a pronounced anomaly at about TСmах = 44 K evidencing the phase transition to the ferromagnetic state. Detailed analyses of the extracted excess (magnetic) components of EuCu2P2 thermodynamic characteristics, Cm(T) and ΔVm(T), have been performed using the Debye-Einstein and mean field theory approaches. We have found that the anomalous nature of Cm(T) and ΔVm(T) at T

Experimental investigation of heat capacity, CP, unit cell parameter, a, as well as the ESR absorption for a clathrate-like compound Eu7Cu44As23 has been performed in the temperature range of 2–300 K. The CP(T) function exhibits a sharp maximum at the temperature of ferromagnetic ordering, Tc ≈ 17 K, whereas the a(T) shows no anomaly at this temperature. This unusual behavior is governed by the clathrate-like structure of Eu7Cu44As23, where Eu2+ guest cations residing in oversized cavities of the host framework order ferromagnetically imposing no influence on the framework dynamics. The analysis of maximum of the Cp(T) function at 2–20 K allows determining the exchange integral, J, which is a characteristic of the magnetic interaction Eu2+ – Eu2+: J ≈ 0.27 K The analysis of the temperature dependencies of heat capacity, CP(T), and unit cell volume, V(T), in the frames of the Debye-Einstein model enabled determining characteristic temperatures of host and guest subsystems. Along with this, the contribution of two-level systems into thermodynamic properties of Eu7Cu44As23 was evaluated and related to the possibility of guest Eu2+ cations to occupy nonequivalent positions inside the cages of the host framework. The ESR of Eu2+ in Eu7Cu44As23 was studied at 5–300 K. The intensity of the ESR signal shows a sharp drop at low temperatures, which confirms the ferromagnetic character of the magnetic phase transition in Eu7Cu44As23. The experimental ESR spectrum was approximated by two Dyson lines, L1 and L2, which correspond to two g-factors: g1 = 2.081 ± 0,030 and g2 = 2,094 ± 0,016. The increase in L1 linewidth with temperature at 75–275 K is d(ΔH1)/dT = 0.027 G/K. These values of g-factors and d(ΔH1)/dT are derived the exchange integrals of the interaction of the Eu2+ local moment with conduction electrons J1* = 0.241 eV and J1** = 0.252 eV accordingly. For L2 J2* = 0.255 eV. Value J2** ≈ 0.26 eV is valid in 100–130 K interval only. The change of ΔH2(T) slope at higher temperatures may be due to crystal field effect.

The temperature changes in the heat capacity Cp(T) and lattice parameters a(T) of solid solutions of CaxSr1-x F2 are experimentally studied at temperatures of 2–300 K for x = 0, 0.25, 0.5, 0.75 and 1. Deviations from the Kopp-Neumann rule (Vegard's rule) in the values of Cp(T) and a(T) for these solutions are identified. The experimental dependencies of Cp(T) and a(T) for end-member crystals and their solid solutions are analysed using the Debye-Einstein model, taking into account the effects of anharmonicity of lattice vibrations at elevated temperatures, and the parameters of this approximation are determined. An anomalous arrangement of the curves for Cp(T) and a(T) is revealed for these solutions, relative to the corresponding dependence for end-member crystals. Despite cationic substitution taking place during the formation of solid solutions of the system under study, restructuring of the crystal structure mainly affects the nature of the oscillations of the anion sublattice. Most affected by the anharmonicity are the Einstein modes, corresponding to the vibrations of the F− ions, and the coupled vibrations of two different fluorine sublattices.

Heat capacity, thermal expansion, and magnetization of ytterbium boride $\mathrm{Yb}{\mathrm{B}}_{50}$ were studied at temperatures 0.6--300 K, 5--300 K, and 2--300 K, respectively. We revealed two smooth peaks at about 4.0 and 60 K in the temperature dependence of the heat capacity. A comparison with the heat capacity of the diamagnetic isostructural boride $\mathrm{Lu}{\mathrm{B}}_{50}$ shows that these anomalies can be attributed to excitations in the ytterbium sublattice (Schottky anomalies). A scheme for splitting of the ground $^{2}F_{7/2}$ multiplet of $\mathrm{Y}{\mathrm{b}}^{3+}$ ions in the crystal field is proposed. Reliability of the proposed crystal-field energies of the $\mathrm{Y}{\mathrm{b}}^{3+}$ ions is confirmed by the analysis of temperature dependencies of magnetic susceptibility and magnetization in applied magnetic fields up to 55 kOe. A clear anisotropy of the thermal expansion and a negative expansion within a wide temperature range (40--185 K) were observed. Assuming that this anomaly of the thermal expansion in higher borides is caused by the specific thermal evolution of a crystal lattice observed earlier, in particular, in $\mathrm{Lu}{\mathrm{B}}_{50}$, and the interaction of rare-earth ions with lattice strains, we have determined phenomenological Gr\"uneisen parameters which characterize effects due to thermal transitions of $\mathrm{Y}{\mathrm{b}}^{3+}$ ions between the ground and excited states. A phase transition of $\mathrm{Yb}{\mathrm{B}}_{50}$ to any magnetically ordered state was not observed down to the lowest temperatures of experiments.

The experimental temperature dependence of thulium tetraboride specific heat C p (T) and other heat capacity data for other RE-tetraborides were investigated in the 2–300 K temperature interval. Anomalies of C p (T) dependence of TmB 4 at T N1 = 9.6 K and T N2 = 11.4 K due to the antiferromagnetic ordering have been revealed. The ground state of the ion Tm 3+ was confirmed as a doublet. The diffuse anomaly of C p (T) is attributed to the Schottky contribution to the specific heat of the tetraboride, which is caused by the influence of the crystal electric field (CEF). The presence of the residual (zero-point) entropy S 0 of the magnetic moments system of Tm 3+ ions, due to frustration of the Shastry-Sutherland lattice, is detected. As a measure of the frustration of the system, a new characteristic of frustrated systems, the entropy frustration figure of merit, the value of which depends on the zero-point entropy of the system, is introduced: f S = S 0 /ΔS m max , where ΔS m max is the maximum value of entropy change of the boride magnetic subsystem. For TmB 4 and tetraborides of Gd, Tb, Dy, Ho, and Er, f s values determined from thermal measurements, and f = Ө c-w /T N ( Ө c-w denotes the Curie-Weiss temperature; T N is Neel temperature), calculated according to the magnetic measurement data, are practically identical.

The $$\hbox {Ca}_{9}\hbox {RE}(\hbox {VO}_{4})_{7}$$ (RE $$=$$ La, Nd, Gd) and $$\hbox {Ca}_{10}\hbox {M}(\hbox {VO}_{4})_{7}$$ (M $$=$$ Li, Na, K) single crystals have been grown by the Czochralski method. The binary vanadates are isostructural to “whitlockite” mineral (rhombohedral symmetry, R3c space group). Their thermal conductivity has been investigated in the range 50 K–300 K parallel to the c axis. For $$\hbox {Ca}_{9}\hbox {Gd}(\hbox {VO}_{4})_{7}$$ crystals, the thermal conductivity has been investigated in the range 300 K–550 K also. Additionally, for the $$\hbox {Ca}_{10}\hbox {M}(\hbox {VO}_{4})_{7}$$ (M $$=$$ Li, Na, K) crystals the heat capacity has been studied in the temperature range 80 K–300 K. The character of the temperature dependence of thermal conductivity is close to that of glasses. The possible reasons of the observed features of the thermal conductivity have been analyzed. Raman spectra of $$\hbox {Ca}_{10}\hbox {M}(\hbox {VO}_{4})_{7}$$ (M $$=$$ Li, Na, K) crystals have been measured and discussed. The spectral lines were broad and similar to polycrystalline or amorphous solids. These crystals are expected to be suitable for application as efficient nonlinear optic and laser materials.

The temperature dependences of heat capacity, C p (T) , and lattice parameters, a(T) , b(T) , c(T) , of ErB 50 in the temperature range of 2–300 K were experimentally studied. Two features in C p (T) were observed: a maximum at T m1 = 3.12 K, that is associated with a magnetic ordering (transition to an antiferromagnetic state), and a broad anomaly at about T m2 = 27 K that is due to the effects of the crystal electric field (CEF) on the boride heat capacity. Based on these data a scheme of splitting of Er 3+ ions f-levels by the crystal field was suggested. Comparison of the temperature dependence of unit cell volume V(T) for ErB 50 with the literature data for LuB 50 revealed an excess contribution into the thermal expansion of erbium boride at low temperatures. It was determined that this contribution is due to the CEF effects on ErB 50 thermal expansion.