Related papers: X-ray phase determination by the principle of mini…
A new method of the phase determination in X-ray crystallography is proposed. The method is based on the so-called "minimum charge" principle, recently suggested by Elser. The electron density function $\rho$ is sought in the form…
The core theme of X-ray crystallography is reconstructing the electron density distribution of crystals under the constraints of observed diffraction data. Nevertheless, the reconstruction of electron density distribution by straightforward…
A new method for identifying crystalline phases in X-ray diffraction data has been proposed, which is especially useful for the study of multiphase materials (more than eight - ten phases) with a relatively low content (less than 1 - 3…
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual Fourier-space formulations of atomicity. The new algorithm implements atomicity constraints in real-space, as well as…
A method for estimating the relative content of crystalline phases of a multiphase sample, based on probabilistic analysis of the intensities of the diffraction pattern reflexes, has been developed. The method is based on the introduction…
Quantitative phase analysis is one of the major applications of X-ray powder diffraction. The essential principle of quantitative phase analysis is that the diffraction intensity of a component phase in a mixture is proportional to its…
Standard X-ray crystallography methods use free-atom models to calculate mean unit cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a…
How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a…
In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
The values of the signal-to-noise ratio are determined, at which the method of processing X-ray diffraction data reveals reflections with intensity less than the noise component of the background. The possibilities of the method are…
We study the nucleation of nearly-hard charged colloidal particles. We use Monte Carlo simulations in combination with free-energy calculations to accurately predict the phase diagrams of these particles and map them via the freezing…
In a standard method of determining electron density for soft X-ray (SXR) flare kernels it is necessary to assume what is the extension of a kernel along the line of sight. This is a source of significant uncertainty of the obtained…
The amorphous propagation of microstructures during the electrochemical charging of a battery is the main reason for the capacity decay and short circuit. The charge distribution across the micro-structure is the result of both local and…
The structural complexity and instability of many interference phase microscopy methods are the major obstacles toward high-precision phase measurement. In this vein, improving more efficient configurations as well as proposing new methods…
We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of…
Phase separation in charged systems may involve the replacement of critical points by microphase separated states, or charge-density-wave states. A density functional theory for highly charged colloids at low ionic strength is developed to…
The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that representing instead the $\mathit{logarithm}$ of the density…
We consider the estimation of the global mode of a density under some decay rate condition around the global mode. We show that the maximum of a histogram, with proper choice of bandwidth, achieves the minimax rate that we establish for the…
Ionic crystals, such as solid electrolytes and complex oxides, are central to modern technologies for energy storage, sensing, actuation, and other functional applications. An important fundamental issue in the atomic and quantum-scale…