Thermoelectric study of the phase transitions in cerium at ultrahigh pressures from 0 to 20 GPa

The pressure dependences of the thermoelectric power S of Ce samples were measured at pressures P from 0 to 20 GPa in a synthetic diamond cell. The dependence of S on P was found to be nonmonotonic both in the region of transitions from the fcc (γ) phase to the modified fcc (α) phase followed by the transition to the body-centered monoclinic (α″) and the tetragonal (ε) phases at pressures of about 1, 5–6, and 12–15 GPa, respectively, and in the stability region of these phases. The thermoelectric power sign was found to be positive for all high-pressure Ce phases. The found S(P) dependence was compared with the published computational data on the electronic structure of the cerium phases. Cerium was taken as an example to demonstrate the advantage of the thermoelectric studies over other methods of investigation of phase transitions.     

Die charakteristische Thermokraft der Grenzflächenatome

For a single-band conductor where two or more scattering mechanisms are present, each giving rise to a characteristic thermoelectric powerS _n and a electrical resistivity? _n the resultant thermoelectric powerS is given, as a first approximation, by\(S = \sum\limits_n {\varrho _n S_n /\varrho } \). Denoting withS ₀ the characteristic thermoelectric power due to the scattering of the conduction electrons by the boundary atoms, and withS _i and? _i the resultant thermoelectric power and electrical resistivity arising from all other scattering mechanisms, one may writeS=S ₀+? _i(S _i?S ₀)/?. The thermoelectric powerS and the electrical resistivity? of thin layers of potassium, evaporated in a vacuum ～5·10^?9 Torr on a glass substrate at 90° K temperature, were measured at different thicknesses. The variation ofS as a function of 1/? verifies the above mentioned relation. Thus, the thermoelectric power, characteristic for the scattering by potassium boundary atoms can be determined.     

Phase transitions investigation in ZnTe by thermoelectric power measurements at high pressure

The pressure-induced phase transitions were studied in ZnTe by the thermoelectric power (S) technique. For the high-pressure trigonal phase P3₁21 cinnabar the large thermopower values S≈+400 correspond to semiconductor hole conductivity. During a transition into the orthorhombic structure Cmcm the value of S dropped by 40-50 times indicating metallic hole conductivity, like in the high pressure phases of other chalcogenides of II Group (HgSe, HgTe, CdTe) with Cmcm structure. In a transient region between the trigonal and orthorhombic phase (especially under decreasing pressure) a novel phase has been observed with a negative value of S. By analogy with other Zn and Cd chalcogenides whose NaCl phases have an electron type of conductivity the phase observed may have a NaCl structure.     

New promising bulk thermoelectrics: intermetallics,pnictides and chalcogenides

The need of alternative “green” energy sources has recently renewed the interest in thermoelectric (TE) materials, which can directly convert heat to electricity or, conversely, electric current to cooling. The thermoelectric performance of a material can be estimated by the so-called figure of merit, zT = σ α ² T/λ (α the Seebeck coefficient, σ α ² the power factor, σ and λ the electrical and thermal conductivity, respectively), that depends only on the material. In the middle 1990s the “phonon glass and electron crystal” concept was developed, which, together with a better understanding of the parameters that affect zT and the use of new synthesis methods and characterization techniques, has led to the discovery of improved bulk thermoelectric materials that start being implemented in applications. During last decades, special focus has been made on skutterudites, clathrates, half-Heusler alloys, Si_1?x Ge _x-, Bi₂Te_3- and PbTe-based materials. However, many other materials, in particular based on intermetallics, pnictides, chalcogenides, oxides, etc. are now emerging as potential advanced bulk thermoelectrics. Herein we discuss the current understanding in this field, with special emphasis on the strategies to reduce the lattice part of the thermal conductivity and maximize the power factor, and review those new potential thermoelectric bulk materials, in particular based on intermetallics, pnictides and chalcogenides. A final chapter, discussing different shaping techniques leading to bulk materials (eventually from nanostructured TE materials), is also included.     

Effect of charge scattering anisotropy on the thermoelectric properties of the (Bi,Sb)<Subscript>2</Subscript>(Te,Se,S)<Subscript>3</Subscript> solid solutions

An analysis is made of the thermoelectric and galvanomagnetic properties of solid solutions based on bismuth and antimony chalcogenides (Bi,Sb)₂(Te,Se,S)₃ with n-and p-type conductivities and different substitutions in the Bi₂Te₃ sublattices. It is shown that the thermoelectric efficiency Z is observed to increase in compositions with a low carrier scattering anisotropy in the reflection plane. The relaxation time tensor component τ ₃₃ along the trigonal direction perpendicular to the crystal growth axis is found to decrease as compared to the components along the binary (τ ₁₁) and bisector (τ ₂₂) directions.     

Thermoelectric properties of high-pressure silicon phases

The thermo emf in Czochralski-grown silicon single crystals (Cz-Si) was experimentally studied in a range of pressures up to 20 GPa. The pressure dependences revealed phase transitions in the metallic phase of silicon, which passed from tetragonal to orthorhombic and then to hexagonal lattice. The high-pressure silicon phases, as well as the metallic high-pressure phases in A_NB_8?N semiconductors, possess conductivity of the hole type. As the pressure decreases, the emf behavior reveals transitions to the metastable phases Si-XII and Si-III. Preliminary thermobaric treatment of the samples at a pressure of up to 1.5 GPa and a temperature of T=50–650°C influences the thermoelectric properties of Cz-Si at high pressures.     

Thermophysical studies of the phase transitions in (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>NbOF<Subscript>6</Subscript> crystals

The thermophysical properties of oxyfluoride (NH₄)₃NbOF₆ were studied in detail over wide ranges of temperatures and pressures. At atmospheric pressure, a sequence of four structural phase transitions was established with the following changes in entropy: ΔS ₁ = Rln 2.7, δS ₂ = Rln38.3, ΔS ₃ = 0.08R, and ΔS ₄ = 0.17R. An external hydrostatic pressure was found to narrow the region of existence of the initial cubic phase. A triple point was detected in the p-T diagram; at a pressure above 0.07 GPa, the transition between the tetragonal and monoclinic phases occurs through a distorted high-pressure phase.     

Thermo-and galvanomagnetic properties of lead chalcogenides at high pressures up to 20 GPa

The Nernst-Ettingshausen (NE) effect in the initial NaCl and high-pressure GeS phases was studied at a high pressure P for n-PdTe, p-PbSe, and p-PbS to estimate the mobility µ and the charge-carrier scattering parameter r. It was found that the transverse and longitudinal NE effects in PbTe and PbSe increase with pressure, indicating the transition to the gapless state near P≈3 GPa. The sign of the transverse NE effect changes because of the change in the electron scattering mechanism in the GeS phase. The experimentally observed weakening of the NE and magnetoresistance effects at high P gives evidence for the indirect energy gap E_g in the high pressure phases with GeS structure.     

Phase transition in CdHfO<Subscript>3</Subscript>

The phase transition from an orthorhombic phase (space group Pnma) to a rhombohedral phase (space group R3m) of the CdHfO₃ hafnate is investigated using methods of structural analysis. It is shown that crystal lattices of both phases contain polar structural units (octahedra, cubooctahedra). On this basis, it is assumed that the orthorhombic and rhombohedral phases of the CdHfO₃ compound are the antiferroelectric and ferroelectric phases, respectively.     

String order and degenerate entanglement spectrum of S = 1 / 2 and S = 1 Heisenberg bond-alternating chains

Generalized string orders and entanglement spectrum of S = 1/2 and S = 1 Heisenberg bond-alternating chains have been investigated by the infinite time-evolving block decimation (iTEBD) method. Generalized string order parameters with appropriate θ are capable of distinguishing all the topological phases. Central charges c ? 1 and critical exponents β ?1/12 indicate all the topological QPTs belong to the Gaussian universality class. Interestingly, odd- and even-fold degeneracies of the entanglement spectrum are observed. Even-fold (doubly) degenerate entanglement spectra and the typical two-fold degenerate lowest-lying level are found to exist in both the spin-1/2 dimer and the S = 1 Haldane phases. However, odd-fold degenerate entanglement spectra with three-fold degenerate lowest-lying level are observed in both the S = 1 dimer and the S = 2 Haldane phase. The degeneracy of the lowest-lying entanglement spectrum level, which can be understood by entanglement spectra in the dimer limit (J ₁ = 0), is adopted to estimate the lowest boundary of the bipartite entanglement. The entanglement spectrum and the generalized string orders are valuable for uncovering the underlying features of these symmetry-protect topological (SPT) states. Similar entanglement spectrum shows that the S = 1 (S = 2) Haldane phase is essentially the same as the S = 1/2 (S = 1) dimer phase.     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

A theoretical investigation of structural,mechanical, electronic and thermoelectric properties of orthorhombic CH<Subscript>3</Subscript>NH<Subscript>3</Subscript>PbI<Subscript>3</Subscript>

The structural, mechanical, electronic and thermoelectric properties of the low temperature orthorhombic perovskite phase of CH₃NH₃PbI₃ have been investigated using density functional theory (DFT). Elastic parameters bulk modulus B, Young’s modulus E, shear modulus G, Poisson’s ratio ν and anisotropy value A have been calculated by the Voigt–Reuss–Hill averaging scheme. Phonon dispersions of the structure were investigated using a finite displacement method. The relaxed system is dynamically stable, and the equilibrium elastic constants satisfy all the mechanical stability criteria for orthorhombic crystals, showing stability against the influence of external forces. The lattice thermal conductivity was calculated within the single-mode relaxation-time approximation of the Boltzmann equation from first-principles anharmonic lattice dynamics calculations. Our results show that lattice thermal conductivity is anisotropic, and the corresponding lattice thermal conductivity at 150 K was found to be 0.189, 0.138, and 0.530 Wm^?1K^?1 in the a, b, and c directions. Electronic structure calculations demonstrate that this compound has a DFT direct band gap at the gamma point of about 1.57 eV. The electronic transport properties have been calculated by solving the semiclassical Boltzmann transport equation on top of DFT calculations, within the constant relaxation time approximation. The Seebeck coefficient S is almost constant from 50 to 150 K. At temperatures 100 and 150 K, the maximal figure of merit is found to be 0.06 and 0.122 in the direction of the c-axis, respectively.     

Converting heat to electricity by a graphene stripe with heavy chiral fermions

A conversion of thermal energy into electricity is considered in the electricallypolarized graphene stripes with zigzag edges where the heavy chiral fermion (HCF) statesare formed. The stripes are characterized by a high electric conductance G _e and by a significantSeebeck coefficient S. The electric current in the stripes is induced due toa non-equilibrium thermal injection of “hot” electrons. This thermoelectric generationprocess might be utilized for building of thermoelectric generators with an exceptionallyhigh figure of merit ZδT ?1 and with an appreciable electric power densities ~1 MW/cm².     

Effect of chromium and tellurium impurities on the thermoelectric parameters of galena

Concentration dependences of the Seebeck coefficient, resistivity, and thermal conductivity of thermoelectric PbS crystals with chromium (0 < x ≤ 0.01) and tellurium (0 < y ≤ 0.03) impurities are examined in the temperature region of 300–800 K. It is shown that the introduction of chromium increases the number of free electrons in PbCr _x S _1–x crystals and reduces the Seebeck coefficient. However, an increase in the concentration of tellurium in PbCr _x S _1–x–y Te _y alloys raises the Seebeck coefficient while simultaneously reducing the thermal conductivity. As a result, the thermoelectric efficiency of PbCr _x S _1–x–y Te _y crystals increases. The reasons for the observed effects are discussed.     

Structural phase transitions and the equation of state of SnTe at high pressures up to 2 mbar

Synchrotron X-ray diffraction studies of the structure of SnTe have been performed at room temperature and high pressures under the conditions of quasihydrostatic compression up to 193.5 GPa created in diamond anvil cells. Two structural phase transitions have been detected at P ≈ 3 and 23 GPa. The first phase transition is accompanied by a stepwise decrease in the volume of the unit cell by 4% because of the orthorhombic distortion of the initial SnTe-B1 cubic structure of the NaCl type. It has been found that two intermediate rhombic phases of SnTe with the space groups Cmcm and Pnma coexist in the pressure range of 3–23 GPa. The second phase transition at 23 GPa occurs from the intermediate rhombic modification to the SnTe-B2 cubic phase with the CsCl structure type. This phase transition is accompanied by an abrupt decrease in the volume of the unit cell by 8%. The pressure dependence of the volumes per formula unit at room temperature has been determined.     

Ferroelectric phase transition in orthorhombic CdTiO<Subscript>3</Subscript>: First-principles studies

Parameters of the crystal structure and phonon spectra for orthorhombic cadmium titanate with space group Pbnm and its two possible ferroelectrically distorted phases (with space groups Pbn2₁ and Pb2₁ m) were calculated from first principles within the density functional theory. The obtained structural parameters and frequencies of Raman- and infrared-active modes are in good agreement with available experimental data for the Pbnm phase. Expansion of the total energy in a Taylor series of two order parameters showed that the ground state of the system corresponds to the Pbn2₁ structure into which the Pbnm phase transforms through a second-order phase transition without intermediate phases. A substantial discrepancy between calculated and experimentally observed lattice distortions and spontaneous polarization in the polar phase was explained by quantum fluctuations, as well as by existence of twins and competing long-period structures.     

Correlation of the molecular structure of discotic nematic liquid crystals with their orientational order and specific features of the nematic-isotropic phase transition

The orientational order parameter S of molecules in high-temperature discotic nematic liquid-crystal phases of triphenylene derivatives is investigated as a function of the length of side flexible molecular chains at different temperatures. It is established that the orientational order parameters S in the range of the transition from the nematic phase to the isotropic liquid phase (the N _D -I transition) are smaller than those predicted from the molecular-statistical theory and computer simulation. It is shown that the N _D -I transition is close to both the isolated Landau point and the tricritical point (regardless of the chemical structure of the molecules and the anisotropy of dispersion intermolecular interactions). Consistent explanations are offered for a number of experimental findings, such as the anomalously small changes in the enthalpy and entropy upon the N _D -I transition (as compared to those revealed upon the N-I transition in calamitic nematic liquid crystals), the anomalously strong response of the isotropic phase of discotic nematic liquid crystals to external fields (thermodynamically conjugate to the order parameter S) and the long relaxation times of this response, and the formation of cybotactic discotic molecular clusters in the isotropic phase in the vicinity of the N _D -I transition.     

Layer stacking dependence on thermoelectric properties of massive Dirac fermions in bilayer graphene

We numerically study the thermoelectric transport in AB- and AA-stacked bilayer graphene in the presence of a strong magnetic field and disorder. In the AB-stacked case, we find that the thermoelectric conductivities display different asymptotic behaviors, depending on the ratio between the temperature and the width of the disorder-broadened Landau levels (LLs), similar to those of monolayer graphene. In the high temperature regime, the transverse thermoelectric conductivity α _xy saturates to a universal value 5.54k _B e/h at the center of each LL, and displays a linear temperature dependence at low temperatures. The calculated Nernst signal has a peak with a height of the order of k _B /e, and the thermopower changes sign at the central LL. We attribute this unique behavior to the coexistence of particle and hole LLs. In the AA-stacked bilayer case, it is found that the thermoelectric transport properties are consistent with the behavior of a band insulator. The obtained results demonstrate the sensitivity of the thermoelectric conductivity to the band gap near the Dirac point.     

Prebreakdown excitation of crystals at double multiphoton resonance: I. Probabilities of interband transitions

Expressions for the probabilities of l-photon transitions (for arbitrary l) between the upper valence band v and lower conduction band c at two-photon resonance on the adjacent transition between the band c and the upper conduction band c ₁ are obtained by means of the S transformation of the electron-photon Hamiltonian. The effects of electron band spectrum transformation and photon reemission are taken into account.     

Metal-insulator transition in whiskers of the NbS<Subscript>3</Subscript> quasi-one-dimensional conductor under pressure

The effect of pressure on the conduction of the NbS₃ quasi-one-dimensional conductor is studied. A pressure-induced insulator-metal transition is observed. The transition is accompanied by an increase in conductivity by six orders of magnitude at room temperature. Under pressures of 3–4 GPa, an additional phase transition appears in the temperature dependences of resistance. This transition manifests itself in an increase in the local conduction activation energy. The quantity dln(R)/d(1/T) reaches its maximum under pressures of 4–5 GPa, and the temperature position of the maximum of dln(R)/d(1/T) depends on the pressure as T* ≈ 7.5P + 202 K.