X-ray diffraction analysis of ultradisperse systems: The Debye formula

Problems of X-ray diffraction analysis of ultradisperse systems with the particle size up to 5 nm are discussed in the review. A method for calculating X-ray diffraction patterns using the Debye formula within the kinematic theory of X-ray scattering (Debye Function Analysis-DFA) is presented. The DFA method makes it possible to obtain information on the atomic structure, shape and size of nanoparticles, and verify hypotheses on the presence of deformations, stacking faults and other structural features of ultradisperse and nanostructured systems. The method is applicable for modeling the diffraction patterns of objects with an arbitrary (not necessarily crystal) structure. Applications of the method for examining the structure of various objects are discussed.     

Analysis of the electronic dipole polarizability of ions in cubic oxides,fluorides, and sulfides of alkaline earth elements

A new approach to calculating the electronic dipole polarizability of ions in crystals which is based on an analysis of the relationship between the electronic dipole polarizability of ion and its effective charge has been proposed. It is shown that applying this method to simple cubic oxides, fluorides, and sulfides of alkaline earth elements yields makes the calculation results consistent with the well-known data on the structure and type of bonds in these compounds.     

Coherence in the output spectrum of frequency shifted feedback lasers

We present a detailed theoretical analysis, using correlation functions, of the coherence properties of the output from a frequency shifted feedback (FSF) laser seeded simultaneously by an external seed laser and by spontaneous emission (SE). We show that the output of a FSF laser is a cyclostationary process, for which the second-order correlation function is not stationary, but periodic. However, a period-averaged correlation function can be used to analyze the optical spectrum. From the fourth-order correlation function of the output of a Michelson interferometer we obtain the essential characteristics of the radio-frequency (RF) spectrum, needed for describing the use of the FSF laser for optical-ranging metrology. We show that, even for a FSF laser seeded by SE, the RF spectrum comprises a sequence of doublets, whose separation gives directly a measure of the length difference between the interferometer arms. This doublet structure is a result of the correlation of interference terms of individual components of the cyclostationary stochastic process. It is not seen in the optical spectrum of the FSF laser but is observable in the RF spectrum. We analyze the competition between SE and continuous wave (CW) seeding to obtain an analytical expression for the ratio of power in the discrete CW signal to the background continuum spectrum from SE. We show that, unlike mode competition in conventional lasers, where there occurs exponential selectivity, here there is a balance between the two fields; the power in the fields is related linearly, rather than exponentially, to the control parameters.     

Calculation of effective charges of ions in displacive-type ferroelectrics

The procedure of calculating the effective charges of ions in ABO₃-type ferroelectrics is considered, which is based on the comparison of two experimentally determined quantities: spontaneous polarization in a crystal and the parameters of the tensor of an electric-field gradient at the quadrupolar nuclei of A ions calculated based on the classical electrostatic model. The determined effective charges of ions in an LiNbO₃ crystal are considered.     

The dynamics of asset lifetime under technological change

The variable lifetime of assets is analyzed in a serial replacement problem. Technological change impacts the maintenance cost and new asset cost. The optimal asset lifetime appears to be constant only when both costs decrease with the same rate. We identify cases when the technological change decreases or increases the optimal lifetime.     

Theoretical and experimental study of the transformation of 2-pyridone-5-amide into nitrile

Molecular and crystal structures of 2,4-dimethyl-6-oxo-1,6-dihydropyridine-3-carboxamide (1), 2,4-dimethyl-6-oxo-1,6-dihydropyridine-3-carbonitrile (2), and 2-chloro-4,6-dimethylniсotinonitrile (3), which are the products of sequential transformations, are studied by means of single crystal diffraction. The procedure for synthesizing each compound is described. All of the compounds are characterized using IR and ¹H NMR spectra. Possible reaction pathways are simulated using the density functional theory (DFT).