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The state variables include a combination of three displacement parameters and three stress parameters.
During a refinement, atoms are initially modelled using isotropic displacement parameters and later using a 3×3 tensor describing an anisotropic probability density function (PDF).
A nonlinear regression analysis was done on the maximum stress and total displacement parameters and equations were defined as a function of the RCE design parameters.
In this formulation, all displacement parameters and the warping function are defined at the centroid axis and also thickness-curvature effects and Wagner effect are accurately taken into account.
The explicit expressions for displacement parameters are then derived using the displacement state vector consisting of 14 displacement parameters, and the exact stiffness matrix is determined using the force deformation relations.
Next systems of linear algebraic equations with non-symmetric matrices are constructed by introducing 14 displacement parameters and transforming the fourth-order simultaneous differential equations into the first-order simultaneous equations.
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In equation (1), the crystallographic parameters [ i.e. atomic positions, atomic displacement parameters (ADPs) and chemical occupancy in routine refinements] that each component of and depends upon will be collectively denoted as the vector and we can therefore denote those dependencies with the compact notations and.
Furthermore, the C1-type model is in general less accurate as displacement parameters ∂w∂x and ∂w∂y are not completely independent.
In particular, the refinement guidelines include strategies to refine the host framework, locate guests and determine occupancies, discussion of the proper use of geometric and anisotropic displacement parameter restraints and constraints, and whether to perform solvent squeezing/masking.
Based on the experimental X-ray synchrotron powder diffraction data, the unit-cell dimensions and positional and displacement parameters of atoms in the Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 structures between RT and 1173 K were derived by full-profile Rietveld refinement technique.
In the refinement procedure, the unit cell dimensions and positional and displacement parameters of atoms were refined together with background and peak profile parameters and correction of absorption and instrumental zero shift.
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