High Compression‐Induced Conductivity in a Layered Cu–Br Perovskite

We show that the onset pressure for appreciable conductivity in layered copper‐halide perovskites can decrease by ca. 50 GPa upon replacement of Cl with Br. Layered Cu–Cl perovskites require pressures >50 GPa to show a conductivity of 10^?4 S cm^?1, whereas here a Cu–Br congener, (EA)₂CuBr₄ (EA=ethylammonium), exhibits conductivity as high as 2×10^?3 S cm^?1 at only 2.6 GPa, and 0.17 S cm^?1 at 59 GPa. Substitution of higher‐energy Br 4p for Cl 3p orbitals lowers the charge‐transfer band gap of the perovskite by 0.9 eV. This 1.7 eV band gap decreases to 0.3 eV at 65 GPa. High‐pressure X‐ray diffraction, optical absorption, and transport measurements, and density functional theory calculations allow us to track compression‐induced structural and electronic changes. The notable enhancement of the Br perovskite's electronic response to pressure may be attributed to more diffuse Br valence orbitals relative to Cl orbitals. This work brings the compression‐induced conductivity of Cu‐halide perovskites to more technologically accessible pressures.     

Expanded Analogs of Three-Dimensional Lead-Halide Hybrid Perovskites

Replacing the Pb−X octahedral building unit of A^IPbX₃ perovskites (X=halide) with a pair of edge-sharing Pb−X octahedra affords the expanded perovskite analogs: A^IIPb₂X₆. We report seven members of this new family of materials. In 3D hybrid perovskites, orbitals from the organic molecules do not participate in the band edges. In contrast, the more spacious inorganic sublattice of the expanded analogs accommodates larger pyrazinium-based cations with low-lying π* orbitals that form the conduction band, substantially decreasing the band gap of the expanded lattice. The molecular nature of the conduction band allows us to electronically dope the materials by reducing the organic molecules. By synthesizing derivatives with A^II=pyridinium and ammonium, we can isolate the contributions of the pyrazinium-based orbitals in the band gap transition of A^IIPb₂X₆. The organic-molecule-based conduction band and the inorganic-ion-based valence band provide an unusual electronic platform with localized states for electrons and more disperse bands for holes upon optical or thermal excitation.     

Cooperative Carbon Dioxide Adsorption in Alcoholamine- and Alkoxyalkylamine-Functionalized Metal–Organic Frameworks

A series of structurally diverse alcoholamine- and alkoxyalkylamine-functionalized variants of the metal–organic framework Mg₂(dobpdc) are shown to adsorb CO₂ selectively via cooperative chain-forming mechanisms. Solid-state NMR spectra and optimized structures obtained from van der Waals-corrected density functional theory calculations indicate that the adsorption profiles can be attributed to the formation of carbamic acid or ammonium carbamate chains that are stabilized by hydrogen bonding interactions within the framework pores. These findings significantly expand the scope of chemical functionalities that can be utilized to design cooperative CO₂ adsorbents, providing further means of optimizing these powerful materials for energy-efficient CO₂ separations.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

Pressure amorphization through displacive disorder

After classifying amorphous materials according to their topology, we review a recently proposed theory of pressure amorphization (PA) that arises from some degree of displacive disorder while retaining a crystalline topology. That theory is based on the notion that one or more branches of the phonon spectrum become soft and flat with increasing pressure and is illustrated by a simple model that possesses the range of features displayed by many of the materials which undergo PA with displacive disorder. We report the results of Langevin simulations of the simple model which show how the probability of amorphization increases with the number of unit cells in the system and support our theory. We comment on how to generalize the model for the study of real systems. Received 29 march 2002     

Low-energy linear structures in dense oxygen: implications for the epsilon phase

Using density functional theory implemented within the generalized gradient approximation, a new nonmagnetic insulating ground state of solid oxygen is proposed and found to be energetically favored at pressures corresponding to the epsilon phase. The newly predicted static ground state is composed of linear herringbone-type chains of O2 molecules and has Cmcm symmetry (with an alternative monoclinic cell). Importantly, this phase supports IR-active zone-center phonons, and their computed frequencies are found to be in broad agreement with recent infrared absorption experiments.