No abstract

Abstractions which occupy the tetrahedral (8a) sites in normal spinel move to the octahedral (16d) sites in inverse spinel while half of the smaller Al 3+ ions move in the opposite direction. The extent of this move is measured by the disorder or inversion parameter, I (the fraction of tetrahedral sites occupied by the Al ions; I = 0 for normal spinel and I = 1 for inverse spinel). Previous studies suggest that the lattice constant of spinel can decrease as the disorder parameter increases to better accommodate the Ni ions. In situ neutron diffraction studies performed by us indicate that this process is also occurring during the reduction of NiAl 2 O 4 to Ni and Al 2 O 3 . It is possible that the compressive residual stresses generated during reduction play a role in the structural evolution of NiAl 2 O 4 .To systematically investigate the effect of pressure on the structure of NiAl 2 O 4 , x-ray diffraction studies at the X17 beamline of the National Synchrotron Light Source were performed. The pressure (up to 35 GPa) was applied via a diamond anvil cell and the experiments were conducted using a polychromatic x-ray beam. By comparing the relative intensities of certain spinel reflections that are sensitive to cationic disorder, a trend toward inverse spinel as a function of pressure was observed. The results are presented in comparison to previous studies on this material.

This work describes a detector‐fixed method in which X‐ray photons are collected on different points of the sensitive area of the detector without movement of the detector and which is suitable for measuring a single‐crystal orientation using (ω, ϕ) rotations. This method was used to determine the orientation of a silicon wafer whose (100) plane makes a small angle (misorientation angle) with the surface. ω scans of the 400 reflection were measured as a function of ϕwhile χ and 2θ were fixed at 0 and 69°, respectively.

The method described in this paper improves the old methods of crystal orientation, applies new parametric equations for crystallography, and increases the precision and accuracy of measurements. The method applies to inorganic and organic crystals. A breakthrough in crystal orientation happened about 25 years ago when two equations dependent on the Bragg angle and an arbitrary direction in the crystal were developed. Unfortunately, they were analytically insolvable and their unique solution was found numerically. Finding the numerical solution of crystal orientation is challenging from a mathematical point of view. In these conditions the numerical solution was found using the Newton method. The Newton method required a specific programming that limits the full benefit of the method in the laboratory. In recent years, a new numerical technique called GRG (generalized reduced gradient), which can be run on many inexpensive computers, was found to be a good fit for these equations. The solutions that can be found with the GRG method are now completed with additional parametric equations; they are easy to use with computers in many laboratories. In this way, parametrization of nonlinear equations for X-ray crystal orientation determines the positions of a reference surface of the single crystal relative to its crystallographic system and to a goniometer setting with two perpendicular axes of rotation. This approach was successfully validated and checked for different Si wafers with (111) and (004) orientation. The paper shows an innovative approach through the parametric equations in conjunction with exact solutions found with a GRG subroutine. The results of the method demonstrate the potential for new applications in industry and research.

The methods for X‐ray crystal orientation are rapidly evolving towards versatility, fewer goniometry measurements, automation, high accuracy and precision. One method that attracts a lot of attention is energy‐dispersive X‐ray diffraction (EDXRD) which is based on detecting reflections from crystallographic planes in a crystal at fixed angles of a parallel polychromatic X‐ray incident beam. In theory, an EDXRD peak can move in a diffraction pattern as a function of a crystallographic plane d‐spacing and its orientation relative to a fixed direction in space can change also. This is equivalent to the possibility of measuring the orientation of single crystals. The article provides a modeling for the EDXRD method whose main feature is the nonmoving crystal in the sense of traditional goniometry where the angle measurements of diffracting planes are a must. The article defines the equation of orientation for the method and shows the derivation in great detail. It is shown that the exact solutions of the equations can be obtained using the generalized reduced gradient method, a mathematical subroutine that is implemented in Excel software. The significance and scientific impact of the work are discussed along with the validated tested results.