Melvin Cutler

Thermoelectric behaviour of molten Tl[sbnd]Te alloys at compositions approaching pure thallium

Abstract In the composition range 70 to 100 atomic % thallium, the phase diagram of Tl[sbnd]Te has a region with two immiscible phases below 600°c, corresponding to the separation of a metallic and a liquid semiconductor phase. We have made measurements of the electrical resistivity p ancl the Seebeck coefficient S at temperatures up to 850°c in the range in which the two liquid phases are mutually soluble in orcler to study the transition between metallic and semiconductor behaviour. As the concentration of tellurium is increased, p and the magnitude of S increase, and their temperature coefficients change from weakly positive values typical of metals to weakly negative values typical of liquid semiconductors with low resistivity. We find that the transport behaviour can be accounted for very well by a model which treats the alloy as a solution containing Tl2Te molecules plus metallic TI atoms. As Te is added to Tl2 electrons are removed from the conduction band, and scattering centres due to Tl2Te are a...

The thermoelectric behaviour of disordered systems

Abstract A very general approach is used to derive formulae for the thermopower and the electronic thermal conductivity in terms of the electrical conductivity taken as a function of energy [sgrave](E). It depends on two assumptions: (1) the electrical conductivity can be properly considered to be the sum of processes at specific energies, justifying the expression [sgrave](E), and (2) each electron carries with it an energy E when it moves. The resulting formulae are particularly useful for disordered systems, where the transport mechanisms are poorly understood, and for which different modes of behaviour may occur at different energies, such as hopping in localized states or diffusive motion in extended states.

Acceptor band transport in SeTe liquid semiconductor alloys

Abstract The behavior of the electrical conductivity σ and thermopower S of alloys with 50 to 70 At.% Se has been analyzed in terms of a two band model corresponding to transport in the valence band and in a narrow acceptor band. Detailed quantitative information is obtained for the parameters describing the acceptor band. The effects of oxygen impurities on the results are examined, and the relation to the metal transition are discussed.

The metal-semiconductor transition in thallium-rich liquid Tl-Te alloys

Abstract Evidence that liquid T1xTe1-x alloys in the composition range ⅔ > × > 1 are pseudobinary mixtures Tl+Tl2Te prompts the examination of the implications of this molecular structure for the change in the electronic structure as the composition is changed continuously from a typical metal T1 to a typical liquid semiconductor T12Te. By ignoring the mixing of states, a first approximation is derived from a superposition of tight-binding bands due to the two constituents T1 and T12Te. The relative energies of the bands due to the two constituents are strongly affected by charge transfer between them. When the semiconductor constituent has a small band gap and a large high-frequency dielectric constant as in T12Te, the conduction-band edge of the semiconductor drops below the Fermi energy when the metal concentration is still large. This is in contrast to the case of a metal dissolved in a wide band gap semiconductor such as argon, where the conduction band of the metal simply narrows and becomes an impu...

Threefold bonding of tellurium in liquid semiconductor alloys

Abstract Bond orbital considerations show that a third covalent band in tellurium is unstable unless the concentration of threefold bonded (3F) tellurium atoms is smaller than the concentration of dangling bonds. At low hole concentrations, the formation of 3F atoms is inhibited further because of non-linear screening of their positive charge, which results in a large electrostatic energy. Consequently 3F bonding becomes important only in liquids whose electrical conductivity is higher than an estimated value ≈1500 Ω −1 cm −1 .

Transport at the mobility edge in liquid semiconductors

Abstract Thermoelectric transport at the mobility edge is interpreted in terms of a variable conductivity at the mobility edge σ c , assuming that R in Motts formula σ c = 610/R is the distance between negatively charged centers. This leads to information about the concentration c − of negative charges as well as the distance e Fl of the Fermi energy from the mobility edge. Applying this model to new Se x Te 1−x data, we find that c − has an activation energy ∼ 0.25 eV when x>0.4, and increases more rapidly with T at x = 0.40. There is a change in d e Fl / dT at e Fl ⋟ 0.08 eV . probably caused by holes becoming the dominant positively charged species.

Simple Model for Cohesion in Metals

A simple model for the binding energy of metals has been examined. The electrostatic energy for the ion—electron interaction is calculated classically, assuming a uniform density of valence electrons within a Wigner—Seitz sphere but outside a spherical core of arbitrary radius rc. rc is determined by matching the equilibrium volume to the experimental value. Several expressions are examined for the kinetic energy and for the energy due to the electron—electron interaction, and the results are compared with experimental data for alkali metals. It is found that the best results are obtained if the presence of the core is ignored completely in computing the energy of the electron—electron interaction. One then obtains not only good agreement for the binding energy (ΔE≲0.01 Ry), but also values for the compressibility which are typically within 10% of experimental values. The empirical values of rc are comparable with the ionic radii. The pressure—volume curves agree with experiment to a degree comparable wit...

The semiconductor-to-metal transition in liquid SeTe alloys: II. Thermodynamic behavior

Abstract Density and heat capacity data indicate a molecular transformation from a low temperature (L) to a high temperature (H) form involving groups of ∼10 atoms. A model proposed in earlier work, in which thermal generation of ion pairs, mostly directly bonded (D p centers), causes the L to H transition, leads naturally to clustering of D p units at alternate sites on a chain. An Ising lattice model has been used to fit the experimental heat capacity curves. Comparison with density results indicates that the H form contains nearly equal numbers of neutral atoms and D p units, as well as an appreciable fraction of other kinds of bond defect atoms.

A Monte Carlo method for determining the equilibrium distribution of ring structures in covalent alloys

A Monte Carlo method has been used to calculate from the bond parameters the entropy Sr and enthalpy Er of formation of a ring molecule. This involves the usual method of determining the fraction of configurations of an m-atom chain which are consistent with formation of another bond to create an m-atom ring. The novel feature is the calculation of a ring closure partition function from the strain energy of the ring-forming bond. This makes it possible to take into account the elasticity of the bonds and removes an arbitrary element inherent in previous approaches to this problem. A study is made of ring formation in selenium and sulfur. It is found that in small rings, the results are less sensitive to the bond geometry than what is suggested by rigid bond models, and that the requirement that atoms do not overlap has a strong effect. The application of the method to the study of ring structures in network-forming covalent alloys is discussed.

The Thermal Conductivity of Liquid Semiconductors

Transport equations are presented in a form appropriate for considering ambipolar transport in liquid semiconductors. This is done by making use of Fermi-Dirac integrals to allow for near-degeneracy, and using a formulation which does not assume two separate bands. The theory is applied to published data for liquid Sb2Se3.