Thermoelectric power of mixed electronic-ionic conductors III. Case of calcium titanate

The primary purpose of the present work is the determination of the thermopower component related to electronic charge carriers for undoped calcium titanate. The second purpose of this work is establishment of the relationship between this thermopower component and the electronic component of electrical conductivity. An essential part of the present study includes the determination of the thermopower components corresponding to different charge carriers (electrons, electron holes and ions). The determination procedures are based on the following three models:

Symmetrical model. This model assumes consistency between thermopower and electrical conuctivity in terms of the n-p transition (this model assumes that minimum of electrical conductivity corresponds to the electronic component of the thermopower equal zero). It was shown that this model does not apply for CaTiO₃.

The Heikes model. This model is based on Heikes formula and also hopping mechanism of the transport of electrons. It was shown that thermopower of CaTiO₃ cannot be described by this model and, consequently, thermopower vs. electrical conductivity cannot be considered within the Jonker formalism.

General model. This model is based on a general thermopower equation for mixed conductors without any simplifying assumptions. Application of this model indicates that the electronic component of thermopower is not consistent with the minimum of electrical conductivity.

     

Electrochemical studies on lead iodide

The total d.c. electrical conductivity of undoped PbI₂ was measured as a function of iodine potential in the region 150–300°C to determine the nature of charge carriers in PbI₂. Results indicate that PbI₂ is an ionic conductor with electron holes as the minority carriers in this temperature range. Electrical polarization experiments were also performed to determine the electron hole conductivity and concentrations, mobilities and chemical diffusion coefficients of electron holes in undoped PbI₂ between 150 and 300°C.     

Thermoelectric power of mixed electronic-ionic conductors II. Case of titanium dioxide

The purpose of the present work is the determination of the thermopower components corresponding to different charge carriers (electrons, electron holes and ions) for TiO₂ and the use of these data for evaluation of the effect of symmetry between these two properties. The procedure of the determination of these components was based on the following two approximations:

The first approximation is based on a symmetrical model assuming a consistency between thermopower and electrical conductivity within the n-p transition (minimum of electronic component of the electrical conductivity corresponds to zero value of the electronic component of thermopower).

The second approximation is based on the apparent asymmetry between thermopower and electrical conductivity within the n-p transition as determined from the first approximation.

The analysis, based on the data of the electronic components of thermopower and electrical conductivity for TiO₂ single crystal, results in the band gap (using the Jonker formalism). The determined band gap is equal to 2.77 eV and 2.57 eV at the first and the second approximations, respectively, while the band gap determined from the experimentally measured data is equal 3.35 eV. These values are consistent with the band gap determined from the data of electrical conductivity corresponding to the n-p transition point (E_g=3.16 eV) and for the data measured experimentally and those free of the ionic conductivity component (E_g=2.79 eV). The obtained results indicate that thermopower and electrical conductivity most likely exhibit the effect of symmetry.     

Electrical conductivity and dielectric constant of A-type Nd2O3

The measurements of electrical conductivity (σ) from 300 to 1200 K and dielectric constant (ε′) from 4·2 to 1200 K of A-type Nd₂O₂ pellets are reported here. Electrical conductivity (σ) data can be explained in terms of impurity. The dielectric constant (ε′) increases slowly up to 500 K as is expected for ionic solids. The increase ofε′ becomes much faster above 500 K, which is attributed to space charge polarization of thermally generated charge carriers.     

Ionic conduction and effect of cation doping in Tl<Subscript>4</Subscript>HgI<Subscript>6</Subscript>

The ionic conduction properties of undoped and doped Tl₄HgI₆ were investigated using electrical conductivity, dielectrics, differential scanning calorimetry, and X-ray diffraction techniques. The heavy Tl⁺-ions diffusion was activated at high temperature, whereas low conductivity at the lower temperature suggested electronic contribution in undoped Tl₄HgI₆. The partial replacement of heavy Tl⁺ ion by suitable cations (Ag⁺ and Cu⁺) enhanced the conductivity by several orders of magnitude, whereas diminution in conductivity results with increasing dopants’ concentration in Tl₄HgI₆. These results can be interpreted in terms of a lattice contraction and vacancy–vacancy interaction (leading to the cluster formation), respectively. The dielectric values of undoped Tl₄HgI₆ system gradually increasing with temperature, followed by a sharp change, were observed around 385 K and can be explained on the basis of increasing number of space charge polarization and ions jump orientation effects. The activation energy of undoped and doped Tl₄HgI₆ systems were calculated, and it was found that ionic conductivity activation energy for 5 mol% of cation dopants is much lower than that of undoped one, and also 10 mol% doped Tl₄HgI₆ systems.     

Chemical diffusion in calcium titanate

This work reports the gas/solid equilibration kinetics for the O₂/CaTiO₃ system. The electrical conductivity measurement was applied for monitoring the kinetics in the ranges of temperature 973-1323 K and oxygen partial pressure 10 Pa-72 kPa. It was found that the gas/solid equilibration kinetics for the polycrystalline CaTiO₃ specimen in the above experimental conditions is determined by bulk diffusion rather than by grain boundary conditions. The obtained data of the electrical conductivity vs. time were used for the determination of the chemical diffusion coefficient as a function of temperature at low and high p(O₂), respectively:

(1)     

Proton and native-ion conductivities in Y2O3 at high temperatures

The ionic conductivity of hot-pressed samples of undoped Y₂O₃ has been studied by the emf-method in atmospheres of controlled oxygen and water-vapor pressures. The variation in the ionic conductivity was studied as a function of time (7 months at 1200°C), temperature (600–1300°C), water-vapor pressure (3–1400 Pa), and oxygen pressure (10⁻¹⁰ −10⁵ Pa). The overall conductivity can be divided into contributions from electronic carriers (mainly electron holes), native ionic defects, and hydrogen defects. The transport of charged hydrogen species is dominated by migration of “free” protons. The hydrogen-ion conductivity is detectable under all conditions and becomes the dominant ionic-conductivity contribution at high water-vapor pressures and low temperatures. The ionic contributions are discussed in terms of grain-boundary and bulk transport properties. Native-ion and proton-diffusion coefficients in yttria are estimated. Equations for the emf of oxide specimens containing charged hydrogen defects have been derived.     

Concentration and lifetime of nonequilibrium charge carriers in CsI and NaCl subjected to x-ray irradiation

The temperature dependence of radiation-induced conductivity was studied in the range of 80–300 K in alkali halide CsI and NaCl crystals subjected to pulsed x-ray irradiation. It is shown that an increase in electrical conductivity with increasing temperature is satisfactorily accounted for by the thermal separation of electrons and holes with common origins. The concentration and lifetime of conducting electrons, as well as the spatial distribution and the probability of thermal separation of nonequilibrium charge carriers in the common-origin electron-hole pairs after thermalization were estimated. The possible effect of the two commonorigin holes generated in the Auger process on the enhancement of recombination rate of electrons is discussed.     

Effect of gamma irradiation on transport of charge carriers in Cu nanowires

In this paper, we report the effect of gamma ray photons on the electrical conductivity of 100 nm Cu nanowires prepared by the technique of electrodeposition using track-etched membranes. Different fluences of photons have been used to observe the effect and in each case of post-irradiation, electrical conductivity is found to increase in a linear manner with increase in applied potential difference; however the rate of increase of conductivity is different in different cases of radiation fluence. Grain boundary scattering is of significance for the post-irradiation parabolic nature of the I–V characteristics (IVC), which are of a linear pattern following Ohm’s law before irradiation. Increase or decrease in the number of charge carriers during their transport through the nanowires is the result of two competitive processes—specular and diffusive scattering of charge carriers (electrons) from grain boundaries, which are itself a region of high resistance rather than inter-grain regions. The results have been discussed in light of the Mayadas and Shatzkes (MS) model with a slight modification for irradiated nanowires.     

Temperature and concentration dependences of the electrical resistivity for alloys of plutonium with americium under normal conditions

The temperature and concentration dependences of the electrical resistivity for alloys of americium with plutonium are analyzed in terms of the multiband conductivity model for binary disordered substitution-type alloys. For the case of high temperatures (T > Θ_D, Θ_D is the Debye temperature), a system of self-consistent equations of the coherent potential approximation has been derived for the scattering of conduction electrons by impurities and phonons without any constraints on the interaction intensity. The definitions of the shift and broadening operator for a single-electron level are used to show qualitatively and quantitatively that the pattern of the temperature dependence of the electrical resistivity for alloys is determined by the balance between the coherent and incoherent contributions to the electron-phonon scattering and that the interference conduction electron scattering mechanism can be the main cause of the negative temperature coefficient of resistivity observed in some alloys involving actinides. It is shown that the great values of the observed resistivity may be attributable to interband transitions of charge carriers and renormalization of their effective mass through strong s-d band hybridization. The concentration and temperature dependences of the resistivity for alloys of plutonium and americium calculated in terms of the derived conductivity model are compared with the available experimental data.     

Novel aspects of charge and lattice dynamics in the hole-doped manganite La0.67Sr0.33MnO3

Previous infrared studies on the hole-doped manganite La_0.67Sr_0.33MnO₃ (LSMO) have analysed its charge dynamics in terms of one type of charge carrier despite evidence of both electron and hole Fermi surfaces. Here, we investigate the charge dynamics of an LSMO film with infrared and optical spectroscopy in order to provide a complete picture of metallic conduction. In the ferromagnetic metallic phase, the low-frequency optical conductivity is best explained by a two-carrier model comprising electrons and holes. The number densities, effective masses and relaxation response of the delocalized electrons and holes are quantified. We discover that only one-third of the doped charges are coherent and contribute to the dc transport. Metallic LSMO cannot be classified as a bad metal at low temperatures because the mean free path of the coherent, mobile charge carriers exceeds the Ioffe–Regel–Mott limit. The incoherent spectral response of the doped charges manifests itself as a broad mid-infrared feature. We also report the first observation of splitting of an infrared-active phonon due to local Jahn–Teller distortion in the vicinity of the thermally driven transition to the nonmetallic, paramagnetic phase in LSMO. This demonstrates that infrared spectroscopy is capable of detecting the presence of local lattice distortions in correlated electron systems.     

Electrical conduction in manganese tungstate

The a.c. and d.c. electrical conductivity and thermoelectric power of a single crystal of MnWO₄ are reported in the temperature range 300–1200 K. It has been found that the dominant charge carriers are holes over the entire temperature range studied. A break in the log σ-($\text{1}\text{T}$) curve occurs around 600 K. The activation energies below and above this break temperature have been estimated as 0.53 and 0.57 eV. The charge carrier mobilities have also been estimated. The data have been analysed using the polaronic concept of electrical conduction.     

Quasi-one dimensional electrical conductivity and thermoelectric power studies on a discotic liquid crystal

We have studied the electrical conductivity of well aligned samples of hexahexylthiotriphenylene (HHTT) in the pure as well as doped states. The dopant used was a small concentration (0.62 mole %) of the electron acceptor trinitrofluorenone (TNF). In the columnar phases, doping causes the AC(1 kHz) conductivity along the columnar axis (σ _‖) to increase by a factor of 10⁷ or more relative to that in undoped samples; σ _‖ attains a value of 10⁻²S/m, which was the maximum measurable limit of our experimental set up. On the other hand, in the isotropic phase doping makes hardly any difference to the conductivity. The frequency dependence of the conductivity has been investigated. The DC conductivity of doped samples exhibits an enormous anisotropy, σ _‖/σ _⊥ ≥ 10¹⁰, which is 7 orders higher than that reported for any liquid crystalline system, and, to our knowledge, the largest observed in an organic conductor. We also report the first thermoelectric power studies on these ‘molecular wires’. The sign of the thermoelectric power is in conformity with the expected nature of the charge carriers, namely, holes.     

Impurity band in SnBi<Subscript>4</Subscript>Se<Subscript>7</Subscript>: thermoelectric power and electrical resistivity measurements

Thermoelectric power and electrical resistivity measurements on polycrystalline samples of Bi₂Se₃ and stoichiometric ternary compound in the quasi-binary system SnSe–Bi₂Se₃ in the temperature range of 90–420 K are presented and explained assuming the existence of an impurity band. The variation of the electron concentration with temperature above 300 K is explained in terms of the thermal activation of a shallow donor, by using a single conduction band model. The density of states effective mass m ^*=0.15m ₀ of the electrons, the activation energy of the donors, their concentration, and the compensation ratio are estimated. The temperature dependence of the electron mobility in conduction band is analyzed by taking into account the scattering of the charge carriers by acoustic phonon, optical phonon, and polar optical phonon as well as by alloy and ionized impurity modes. On the other hand, by considering the two-band model with electrons in both the conduction and impurity bands, the change in the electrical resistivity with temperature between 420 and 90 K is explained.     

Thermoelectric power of mixed electronic-ionic conductors I. Basic equations

The present work considers thermopower of oxide materials within n-p transition regime. Specifically, basic equations describing the effect of thermocell reactions on both ionic and electronic component of thermoelectric power are derived. The proposed formalism considers the impact of gas/solid reactions on the relationship between thermopower and electrochemical potential within a system involving a metal oxide of nonstoichiometric composition and a metal (such as Pt) that is applied as a measuring electrode. The derived theoretical model allows the determination of the thermopower components corresponding to different charge carriers, including ions, electrons and electron holes, for metal oxides. The proposed model may be used for derivation of defect chemistry models based on thermopower data that are free of the ionic component.     

Effect of vanadium doping on the electrical properties of Bi12GeO20 crystals

A study is reported of the temperature dependences of the dc and ac electrical conductivities, as well as of I–V characteristics of pure and vanadium-doped germanosillenite crystals. It has been established that the charge carriers in Bi₁₂GeO₂₀ are electrons and holes. Doping with vanadium gives rise to a strong dependence of the conductivity and its activation energy on the dopant concentration. Within the model, the results explain the hopping-charge transfer in doped, closely compensated semiconductors.     

Magnetic semiconductors

As far as the electrical conductivity is concerned, solids are usually classified as metals, semiconductors, or insulators. In metals the concentration of the charge carriers responsible for the electrical conductivity is large, whereas in semiconductors and insulators the carrier concentration is much smaller. The distinction between semiconductors and insulators is based on a difference in the nature of the conductivity. For semiconductors the charge carriers (electrons or holes) occupy the states of energy bands; these states are not Iocalized on particular atoms, but spread throughout the entire crystal. In such a situation the mobility of the carriers can be quite high and would, in fact, be infinite in a rigid periodic lattice; in this model the thermal motion of the atoms induces a scattering of the carriers and thus limits the conductivity to finite values. The classical examples of semiconductors are the elements Si and Ge and compounds such as GaAs, InSb, CdTe, ZnS, etc.     

Excitation of intrinsic defects in ionic crystals by high-power optical and electron beams

The efficiency of excitation and recharging of intrinsic defects by hot charge carriers has been investigated in ionic crystals acted on by high-power optical and electron beams. The interaction cross sections of hot electrons and holes with intrinsic lattice sites and F _n -type defects (n=1,2) are shown to be commensurate. It is also shown that the potential of the intracrystalline field in the vicinity of F and F ₂ centers is nearly regular. Fiz. Tverd. Tela (St. Petersburg) 40, 1030–1035 (June 1998)     

Electrical properties of TiO<Subscript>2</Subscript>: equilibrium vs dynamic electrical conductivity

The present work reports semiconducting properties of high purity TiO₂ determined in the gas/solid equilibrium, as well as during controlled heating and cooling in the range 300–1,273 K. The activation energy of the electrical conductivity is considered in terms of the activation enthalpy of the formation of ionic defects and the activation enthalpy of the mobility of electronic defects. These data, determined from the dynamic electrical conductivity experiments, are compared to the electrical conductivity data determined in equilibrium. It is shown that only the equilibrium electrical conductivity data for high-purity TiO₂ are well defined. It is shown that the activation energy of the electrical conductivity determined in equilibrium differs substantially from that for the dynamic electrical conductivity data during cooling and heating. It is concluded that the formation enthalpy term determined from the dynamic conductivity data is determined by the heating/cooling rate rather than materials’ properties.     

Electrical properties and proton conduction of gadolinium doped ceria

The electrical properties and proton conduction of Gd_0.1Ce_0.9O_1.95 (10GCO) were investigated via impedance spectroscopy in different atmospheres and various gas concentration cells. In oxygen atmosphere, GCO is nearly a pure oxygen ionic conductor, while in hydrogen GCO behaves as a mixed conductor of oxygen ions, electrons and protons. Depending on the temperature, the total conductivity is usually enhanced by one to two orders of magnitude in hydrogen than in air/oxygen due to mixed conduction. By examining ionic transport properties of oxygen ions and protons using gas concentration cells we have discovered that the ionic transport properties depend largely on the gas atmospheres and change from one type to the other. Proton conduction generally exists in GCOs, and becomes significant in hydrogen atmospheres, which normally results in a contribution between 5 to 10 % of the total conductivity for 10 GCO. A maximum value of 17 % of the contribution by protons has been observed. The reduction of Ce⁴⁺ to Ce³⁺ of the sample in reduced atmospheres causes the formation of additional oxygen vacancies and electrons, associated also with the creation of protons. All these charge carriers are responsible for the electrical and transport properties of the investigated GCO materials. Paper presented at the 5th Euroconference on Solid State Ionics, Benalmádena, Spain, Sept. 13–20, 1998.