We report on the optical and charge transport properties of novel alkali metal chalcogenides, Cs2Hg6S7 and Cs2Cd3Te4, pertaining to their use in radiation detection. Optical absorption, photoconductivity, and gamma ray response measurements for undoped crystals were measured. The band gap energies of the Cs2Hg6S7 and Cs2Cd3Te4 compounds are 1.63 eV and 2.45 eV, respectively. The mobility-lifetime products for charge carriers are of the order of ~10-3 cm2/V for electrons and ~10-4 cm2/V for holes. Detectors fabricated from the ternary compound Cs2Hg6S7 shows well-resolved spectroscopic features at room temperature in response to ϒ -rays at 122 keV from a 57 Co source, indicating its potential as a radiation detector.

We address the issue of decreasing band-gap with increasing atomic number, inherent in semiconducting materials, by introducing a concept we call dimensional reduction. The concept leads to semiconductor compounds containing high atomic number elements and simultaneously exhibiting a large band gap and high mass density suggesting that dimensional reduction can be successfully employed in developing new γ-ray detecting materials. As an example we discuss the compound Cs2Hg6S7 that exhibits a band-gap of 1.65eV and mobility-lifetime products comparable to those of optimized Cd0.9Zn0.1Te.

We report the physical characterization and thermoelectric properties of (Pb0.95Sn0.05Te)0.92(PbS)0.08 containing excess Pb and Sb prepared using the matrix encapsulation technique. Samples of (Pb0.95Sn0.05Te)0.92(PbS)0.08 : Pb 0.5 - 4 at. % rapidly quenched from the melt show microscale Pb inclusions that increase the thermal conductivity while slightly increasing the power factor, compared to (Pb0.95Sn0.05Te)0.92(PbS)0.08. Samples of (Pb0.95Sn0.05Te)0.92(PbS)0.08 : Pb 0.5%, Sb 2% prepared using the same technique show microscale Sb and Pb inclusions that upon heating cause rapid PbS and Sb segregation from the PbTe matrix. This behavior significantly alters the microstructure and degrades the transport properties of the material.

Sufficient conditions are given on a Banach space $X$ which ensure that $\ell_{\infty}$ embeds in ${\mathcal L}\, (X)$, the space of all bounded linear operators on $X$. A basic sequence $(e_n)$ is said to be quasisubsymmetric if for any two increasing sequences $(k_n)$ and $(\ell_n)$ of positive integers with $k_n \leq \ell_n$ for all $n$, $(e_{k_n})$ dominates $(e_{\ell_n})$. If a Banach space $X$ has a seminormalized quasisubsymmetric basis then $\ell_{\infty}$ embeds in ${\mathcal L}\, (X)$.

A hereditarily indecomposable asymptotic $\ell_2$ Banach space is constructed. The existence of such a space answers a question of B. Maurey and verifies a conjecture of W. T. Gowers.

We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space $X$ . In particular we give an example of a reflexive $X$ so that all spreading models of $X$ contain ${{\ell }_{1}}$ but none of them is isomorphic to ${{\ell }_{1}}$ . We also prove that for any countable set $C$ of spreading models generated by weakly null sequences there is a spreading model generated by a weakly null sequence which dominates each element of $C$ . In certain cases this ensures that $X$ admits, for each $\alpha \,<\,{{\omega }_{1}}$ , a spreading model ${{\left( \tilde{x}_{i}^{\left( \alpha\right)} \right)}_{i}}$ such that if $\alpha \,<\,\beta $ then ${{\left( \tilde{x}_{i}^{\left( \alpha\right)} \right)}_{i}}$ is dominated by (and not equivalent to) ${{\left( \tilde{x}_{i}^{\left( \beta\right)} \right)}_{i}}$ . Some applications of these ideas are used to give sufficient conditions on a Banach space for the existence of a subspace and an operator defined on the subspace, which is not a compact perturbation of a multiple of the inclusion map.

Novel quaternary compounds AgPbmSbTem+2 (LAST-m) with different m values have been synthesized recently and some of these compounds show promising thermoelectric properties at high temperatures. The two end members of the series, PbTe (m=∞) and AgSbTe2 (m=0), are also known to be good thermoelectrics. In this paper, we discuss the results of ab initio electronic structure calculations for these two end members and for LAST-2 and LAST-14 to see how the electronic structure near the chemical potential μ evolves with m. Whereas PbTe and LAST-14 are narrow band gap semiconductors, the other two compounds show pseudo-gap structure. Even in the absence of a true gap, the rapidly varying density of states (DOS) near μ may be conducive to large Seebeck coefficient in LAST-2 and AgSbTe2.

High efficiency thermoelectric modules are of great interest for power generation applications where hot side temperatures of approximately 800K exist. The fabrication of such modules requires a multidisciplinary effort for the optimization of the material compositions, the engineering of the module systems, modeling and fabrication of the devices, and constant feedback from characterization. Pb-Sb-Ag-Te (LAST) and Pb-Sb-Ag-Sn-Te (LASTT) compounds are among the best known materials for this temperature range. Modeling of these materials and possible cascaded structures shows efficiencies of 14% can be achieved for low resistance contacts. Using antimony we have achieved contact resistivities less than 20 µΩ·cm2. Here we give a detailed presentation on the procedures used in the fabrication of thermoelectric generators based on these new materials. We also present the characterization systems and measurements on these generators.

A strictly singular non-compact operator on the Gowers and Maurey space GM is constructed.

We give new examples of weak Hilbert spaces.