TEV—A Program for the Determination of the Thermal Expansion Tensor from Diffraction Data

Abstract

TEV (Thermal Expansion Visualizing) is a user-friendly program for the calculation of the thermal expansion tensor αij from diffraction data. Unit cell parameters determined from temperature dependent data collections can be provided as input. An intuitive graphical user interface enables fitting of the evolution of individual lattice parameters to polynomials up to fifth order. Alternatively, polynomial representations obtained from other fitting programs or from the literature can be entered. The polynomials and their derivatives are employed for the calculation of the tensor components of αij in the infinitesimal limit. The tensor components, eigenvalues, eigenvectors and their angles with the crystallographic axes can be evaluated for individual temperatures or for temperature ranges. Values of the tensor in directions parallel to either [uvw]'s of the crystal lattice or vectors (hkl) of reciprocal space can be calculated. Finally, the 3-D representation surface for the second rank tensor and pre-or user-defined 2-D sections can be plotted and saved in a bitmap format. TEV is written in JAVA. The distribution contains an EXE-file for Windows users and a system independent JAR-file for running the software under Linux and Mac OS X. The program can be downloaded from the following

Nanoindentation, High-Temperature Behavior, and Crystallographic/Spectroscopic Characterization of the High-Refractive-Index Materials TiTa2O7 and TiNb2O7

“…The quality of the fitting can be described numerically by the coefficient of determination R 2 : where a i is the observed value for component i, âthe calculated value for component i, a ̅ i the mean, and n the number of different temperatures. 20 The thermal expansion of a monoclinic crystal can be expressed by a second rank tensor of the form where α 13 = α 31 . This tensor refers to an orthogonalized coordinate system {e 1 , e 2 , e 3 }.…”

Donor‐unsupported Phosphanylmethanides Li[CH2PR2] (R = tBu, Ph) – Crystal Structure of Li[CH2PtBu2] Solved by XRPD and DFT‐D Calculations

“…For Li[CH 2 P t Bu 2 ], we find a volume decrease of about 10 % for every calculated structure. To evaluate this effect, thermal expansion studies were carried out using the program TEV,27 treating the unit cell parameters with a linear model 35. The thermal expansion along the crystallographic b axis (0.0014 Å per K) is more than three times greater than along the other axes ( a : 0.0004 Å per K; c : 0.0004 Å per K).…”

“…An example parameter file for the calculations with fixed and free unit cell parameters is deposited in the Supporting Information. The RMSCD (root mean square cartesian displacement) parameters were calculated as suggested by van de Streek et al27…”

Li2Ca2Si2O7: Structural, spectroscopic and computational studies on a sorosilicate

“…A continuous behaviour is obvious. For processing these data the TEV software [34] has been employed. First, the evolution of the two lattice parameters a and c was fitted to polynomials of different orders.…”