Thermal expansion study of ordered and disordered Fe3Al: An effective approach for the determination of vibrational entropy

Physical properties of {Ti,Zr,Hf}2Ni2Sn compounds

Physical properties, i.e. electrical resistivity (4.2-800 K), Seebeck coefficient (300-800 K), specific heat (2-110 K), Vickers hardness and elastic moduli (RT), have been defined for single-phase compounds with slightly nonstoichiometric compositions: Ti_2.13Ni₂Sn_0.87, Zr_2.025Ni₂Sn_0.975, and Hf_2.055Ni₂Sn_0.945. From X-ray single crystal and TEM analyses, Ti_2+xNi₂Sn_1-x, x ∼ 0.13(1), is isotypic with the U₂Pt₂Sn-type (space group P4₂/mnm, ternary ordered version of the Zr₃Al₂-type), also adopted by the homologous compounds with Zr and Hf. For all three polycrystalline compounds (relative densities >95%) the electrical resistivity of the samples is metallic-like with dominant scattering from static defects mainly conditioned by off-stoichiometry. Analyses of the specific heat curves C_pvs. T and C_p/T vs. T² reveal Sommerfeld coefficients of γ_Ti2Ni2Sn = 14.3(3) mJ mol^-1 K^-2, γ_Zr2Ni2Sn = 10(1) mJ mol^-1 K^-2, γ_Hf2Ni2Sn = 9.1(5) mJ mol^-1 K^-2 and low-temperature Debye-temperatures: θLTD = 373(7)K, 357(14)K and 318(10)K. Einstein temperatures were in the range of 130-155 K. Rather low Seebeck coefficients (<15 μV K^-1), power factors (pf < 0.07 mW mK^-2) and an estimated thermal conductivity of λ < 148 mW cm^-1 K^-1 yield thermoelectric figures of merit ZT < 0.007 at ∼800 K. Whereas for polycrystalline Zr₂Ni₂Sn elastic properties were determined by resonant ultrasound spectroscopy (RUS): E = 171 GPa, ν = 0.31, G = 65.5 GPa, and B = 147 GPa, the accelerated mechanical property mapping (XPM) mode was used to map the hardness and elastic moduli of T₂Ni₂Sn. Above 180 K, Zr₂Ni₂Sn reveals a quasi-linear expansion with CTE = 15.4 × 10^-6 K^-1. The calculated density of states is similar for all three compounds and confirms a metallic type of conductivity. The isosurface of elf shows a spherical shape for Ti/Zr/Hf atoms and indicates their ionic character, while the [Ni₂Sn]^n- sublattice reflects localizations around the Ni and Sn atoms with a large somewhat diffuse charge density between the closest Ni atoms.

The specific features of phononic and magnetic subsystems of type-VII clathrate EuNi2P4

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) Å, b = 9.4765(1) Å, and c = 18.9900(1) Å. 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.

Crystal lattice disorder and characteristic features of the low-temperature thermal properties of higher borides

Heat capacity C_P(T) and lattice parameters a(T), b(T) and c(T) of LuB₄₄Si_3.5 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 C_P(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.

Thermodynamic properties and lattice dynamics investigation of LuB2C: experiment and ab initio calculations

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.

Effect of the cation sublattice composition of tin-based type-I clathrates on their low-temperature thermal properties

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.

Boron-phil and boron-phob structure units in novel borides Ni3Zn2B and Ni2ZnB: experiment and first principles calculations

The crystal structures of two novel borides in the Ni-Zn-B system, τ₅-Ni₃Zn₂B and τ₆-Ni₂ZnB, were determined by single crystal X-ray diffraction (XRSC) in combination with selected area electron diffraction in a transmission electron microscope (SAED-TEM) and electron probe microanalysis (EPMA). Both compounds crystallize in unique structure types (space group C2/m, a = 1.68942(8) nm, b = 0.26332(1) nm, c = 0.61904(3) nm, β = 111.164(2)°, R_F = 0.0219 for Ni₃Zn₂B, and space group C2/m, a = 0.95296(7) nm, b = 0.28371(2) nm, c = 0.59989(1) nm, β = 93.009(4)°, R_F = 0.0163 for Ni₂ZnB). Both compounds have similar building blocks: two triangular prisms centered by boron atoms are arranged along the c-axis separated by Zn layers, which form empty octahedra connecting the boron centered polyhedra. Consistent with the (Ni+Zn)/B ratio, isolated boron atoms are found in τ₅-Ni₃Zn₂B, while B-B pairs exist in τ₆-Ni₂ZnB. The crystal structure of Ni₂ZnB is closely related to that of τ₄-Ni₃ZnB₂, i.e. Ni₂ZnB can be formed by removing the nearly planar nickel layer in Ni₃ZnB₂ and shifting the origin of the unit cell to the center of the B-B pair. The electrical resistivity and specific heat of τ₅-Ni₃Zn₂B reveal the metallic behavior of this compound with an anomaly at low temperature, possibly arising from a Kondo-type interaction. Further analysis on the lattice contribution of the specific heat reveals similarity with τ₄-Ni₃ZnB₂ with some indications of lattice softening in τ₅-Ni₃Zn₂B, which could be related to the increasing metal content and the absence of B-B bonding in τ₅-Ni₃Zn₂B. For the newly found phases, τ₅-Ni₃Zn₂B and τ₆-Ni₂ZnB as well as for τ₃-Ni₂₁Zn₂B₂₀ and τ₄-Ni₃ZnB₂ density functional theory (DFT) calculations were performed by means of the Vienna Ab initio Simulation Package (VASP). Total energies and forces were minimized in order to determine the fully relaxed structural parameters, which agree very well with experiment. Energies of formations in the range of -25.2 to -26.9 kJ mol^-1 were calculated and bulk moduli in the range of 179.7 to 248.9 GPa were derived showing hardening by increasing the B concentration. Charge transfer is discussed in terms of Bader charges resulting in electronic transfer from Zn to the system and electronic charge gain by B. Ni charge contributions vary significantly with crystallographic position depending on B located in the neighbourhood. The electronic structure is presented in terms of densities of states, band structures and contour plots revealing Ni-B and Ni-Zn bonding features.

Dynamics of the crystal structure of tin-based type-I clathrates with different degrees of disorder in their cationic frameworks

The temperature dependencies of heat capacity, C_P(T), and cubic unit cell parameter, a(T), were experimentally obtained in the range of 2-300 K for the compounds Sn₂₄P_19.2I₈, Sn₂₀Zn₄P_20.8I₈, 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.

Structural irregularities and peculiarities of low-temperature thermal properties of Sn24P19.4Br8 clathrate

Temperature changes of the heat capacity and unit cell parameters of Sn₂₄P_19.4Br₈ 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.

Ba-filled Ni-Sb-Sn based skutterudites with anomalously high lattice thermal conductivity

Novel filled skutterudites BayNi4Sb12-xSnx (ymax = 0.93) have been prepared by arc melting followed by annealing at 250, 350 and 450 °C up to 30 days in vacuum-sealed quartz vials. Extension of the homogeneity region, solidus temperatures and structural investigations were performed for the skutterudite phase in the ternary Ni-Sn-Sb and in the quaternary Ba-Ni-Sb-Sn systems. Phase equilibria in the Ni-Sn-Sb system at 450 °C were established by means of Electron Probe Microanalysis (EPMA) and X-ray Powder Diffraction (XPD). With rather small cages Ni4(Sb,Sn)12, the Ba-Ni-Sn-Sb skutterudite system is perfectly suited to study the influence of filler atoms on the phonon thermal conductivity. Single-phase samples with the composition Ni4Sb8.2Sn3.8, Ba0.42Ni4Sb8.2Sn3.8 and Ba0.92Ni4Sb6.7Sn5.3 were used to measure their physical properties, i.e. temperature dependent electrical resistivity, Seebeck coefficient and thermal conductivity. The resistivity data demonstrate a crossover from metallic to semiconducting behaviour. The corresponding gap width was extracted from the maxima in the Seebeck coefficient data as a function of temperature. Single crystal X-ray structure analyses at 100, 200 and 300 K revealed the thermal expansion coefficients as well as Einstein and Debye temperatures for Ba0.73Ni4Sb8.1Sn3.9 and Ba0.95Ni4Sb6.1Sn5.9. These data were in accordance with the Debye temperatures obtained from the specific heat (4.4 K < T < 140 K) and Mössbauer spectroscopy (10 K < T < 290 K). Rather small atom displacement parameters for the Ba filler atoms indicate a severe reduction in the "rattling behaviour" consistent with the high levels of lattice thermal conductivity. The elastic moduli, collected from Resonant Ultrasonic Spectroscopy ranged from 100 GPa for Ni4Sb8.2Sn3.8 to 116 GPa for Ba0.92Ni4Sb6.7Sn5.3. The thermal expansion coefficients were 11.8 × 10(-6) K(-1) for Ni4Sb8.2Sn3.8 and 13.8 × 10(-6) K(-1) for Ba0.92Ni4Sb6.7Sn5.3. The room temperature Vickers hardness values vary within the range from 2.6 GPa to 4.7 GPa. Severe plastic deformation via high-pressure torsion was used to introduce nanostructuring; however, the physical properties before and after HPT showed no significant effect on the materials thermoelectric behaviour.

Changes in microstructure and physical properties of skutterudites after severe plastic deformation

Although electrical resistivity after HPT of DD_0.68Fe₃CoSb₁₂ is higher, the lower thermal conductivity overcompensates resulting in a 20% higher ZT.