The newly developed GSAS-II software is a general purpose package for data reduction, structure solution and structure refinement that can be used with both single-crystal and powder diffraction data from both neutron and X-ray sources, including laboratory and synchrotron sources, collected on both two- and one-dimensional detectors. It is intended that GSAS-II will eventually replace both the GSAS and the EXPGUI packages, as well as many other utilities. GSAS-II is open source and is written largely in object-oriented Python but offers speeds comparable to compiled code because of its reliance on the Python NumPy and SciPy packages for computation. It runs on all common computer platforms and offers highly integrated graphics, both for a user interface and for interpretation of parameters. The package can be applied to all stages of crystallographic analysis for constant-wavelength X-ray and neutron data. Plans for considerable additional development are discussed.

GSAS-II: the genesis of a modern open-source all purpose crystallography software package

During the past decade, computer simulations based on a quantum-mechanical description of the interactions between electrons and between electrons and atomic nuclei have developed an increasingly important impact on solid-state physics and chemistry and on materials science—promoting not only a deeper understanding, but also the possibility to contribute significantly to materials design for future technologies. This development is based on two important columns: (i) The improved description of electronic many-body effects within density-functional theory (DFT) and the upcoming post-DFT methods. (ii) The implementation of the new functionals and many-body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures. In this review, I discuss the implementation of various DFT functionals [local-density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, hybrid functional mixing DFT, and exact (Hartree-Fock) exchange] and post-DFT approaches [DFT + U for strong electronic correlations in narrow bands, many-body perturbation theory (GW) for quasiparticle spectra, dynamical correlation effects via the adiabatic-connection fluctuation-dissipation theorem (AC-FDT)] in the Vienna ab initio simulation package VASP. VASP is a plane-wave all-electron code using the projector-augmented wave method to describe the electron-core interaction. The code uses fast iterative techniques for the diagonalization of the DFT Hamiltonian and allows to perform total-energy calculations and structural optimizations for systems with thousands of atoms and ab initio molecular dynamics simulations for ensembles with a few hundred atoms extending over several tens of ps. Applications in many different areas (structure and phase stability, mechanical and dynamical properties, liquids, glasses and quasicrystals, magnetism and magnetic nanostructures, semiconductors and insulators, surfaces, interfaces and thin films, chemical reactions, and catalysis) are reviewed. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008

Ab-initio simulations of materials using VASP: Density-functional theory and beyond.

The aim of this critical review is to provide a broad but digestible overview of mechanochemical synthesis, i.e. reactions conducted by grinding solid reactants together with no or minimal solvent. Although mechanochemistry has historically been a sideline approach to synthesis it may soon move into the mainstream because it is increasingly apparent that it can be practical, and even advantageous, and because of the opportunities it provides for developing more sustainable methods. Concentrating on recent advances, this article covers industrial aspects, inorganic materials, organic synthesis, cocrystallisation, pharmaceutical aspects, metal complexes (including metal–organic frameworks), supramolecular aspects and characterization methods. The historical development, mechanistic aspects, limitations and opportunities are also discussed (314 references).

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Mechanochemistry: opportunities for new and cleaner synthesis

A set of general guidelines for structure refinement using the Rietveld (whole-profile) method has been formulated by the International Union of Crystallography Commission on Powder Diffraction. The practical rather than the theoretical aspects of each step in a typical Rietveld refinement are discussed with a view to guiding newcomers in the field. The focus is on X-ray powder diffraction data collected on a laboratory instrument, but features specific to data from neutron (both constant-wavelength and time-of-flight) and synchrotron radiation sources are also addressed. The topics covered include (i) data collection, (ii) background contribution, (iii) peak-shape function, (iv) refinement of profile parameters, (v) Fourier analysis with powder diffraction data, (vi) refinement of structural parameters, (vii) use of geometric restraints, (viii) calculation of e.s.d.'s, (ix) interpretation of R values and (x) some common problems and possible solutions.

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Rietveld refinement guidelines

Residual stress is that which remains in a body that is stationary and at equilibrium with its surroundings. It can be very detrimental to the performance of a material or the life of a component. Alternatively, beneficial residual stresses can be introduced deliberately. Residual stresses are more difficult to predict than the in-service stresses on which they superimpose. For this reason, it is important to have reliable methods for the measurement of these stresses and to understand the level of information they can provide. In this paper, which is the first part of a two part overview, the effect of residual stresses on fatigue lifetimes and structural integrity are first summarised, followed by the definition and measurement of residual stresses. Different types of stress are characterised according to the characteristic length scale over which they self-equilibrate. By comparing this length to the gauge volume of each technique, the capability of a range of techniques is assessed. In the sec...

Residual stress. Part 1 – Measurement techniques

The mathematical functions necessary for Rietveld refinement of time-of-flight neutron powder diffraction patterns from spallation sources are developed and a computer program for least-squares analysis is described. The results of Rietveld refinements of nickel and a low-carbon steel are described and discussed. The method fully exploits the high resolution (Δd/d ~ 0.3 ~ 0.5%) available with powder diffractometers currently in operation on these sources and examples are given of precise determination of atom coordinates, thermal parameters, lattice parameters and the detection of small strains.

Rietveld Refinement with Spallation Neutron Powder Diffraction Data

A generalized spherical-harmonic description of the texture for polycrystalline materials has been implemented in a multiple-phase/multiple-data-set Rietveld refinement code. It has been tested using two sets of neutron time-of-flight data taken from a standard calcite sample previously used for a round-robin study [Wenk (1991). J. Appl. Cryst. 24, 920–927] and has been shown to give similar texture results as those obtained from individual pole figures. Simultaneous refinement of the calcite crystal structure including anisotropic thermal parameters gives results essentially identical to a recent single-crystal X-ray study.

Quantitative texture analysis by Rietveld refinement

Macrostrain variations in engineering components are frequently examined using neutron diffraction, at both reactors and pulsed sources. It is desirable to minimize the sampling volume in order to maximize the spatial resolution, although this increases the required measurement time. At reactors, macrostrain behavior is inferred from a single lattice reflection (deemed to be representative of the bulk response). At a pulsed source, a complete diffraction pattern is recorded and accordingly it is natural to fit the entire diffraction spectra using a Rietveld [J. Appl. Cryst. 2, 65 (1969)] refinement. This means that an idealized crystal structure is fit to the measured distorted crystal structure, which includes deviation of the measured lattice reflections from the ideal due to elastoplastic strain anisotropies, which are dependent on the particular lattice reflection (hkl) considered. We show that elastic macrostrains calculated from lattice parameter changes in Rietveld refinements (without accounting for hkl dependent anisotropies) are almost identical to the bulk elastic response and are comparable to the response obtained from a single lattice reflection typically used by practitioners at a steady state source. Moreover good refinements on the complete pattern are obtained with short measurement times compared to what is required for good statistics for single reflections. By incorporating a description of the elastic strain anisotropy expected in cubic materials into the Rietveld code, an empirical prediction of plastic strain history is possible. The validity of these arguments is demonstrated by analysis of a uniaxial tensile load test and a reanalysis of previously reported data taken on a deformed stainless steel ring. The plastic strain predictions compare favorably with a finite element model.

Use of Rietveld refinement for elastic macrostrain determination and for evaluation of plastic strain history from diffraction spectra

The structure of kaolinite (non-hydrogen atoms only) from Keokuk, Iowa, was refined in space group C1 using CuKa X-ray powder diffraction data and Rietveld refinement techniques (Rwp = 12.3%). A distance least-squares (DLS) model for the initial atomic coordinates avoided a false minimum and unrealistic results characteristic of previous Rietveld refinements of kaolinite. All Keokuk samples ex- amined contain small amounts of dickite. The profile of the mixture was calculated using a fixed set of dickite atomic parameters and by constraining the dickite profile parameters to those refined for kaolinite. Results indicate that the individual kaolinite layer is very similar to the dickite layer; bond distances, which are similar to dickite and nacrite, are: Si-O, 1.60"1.63 A; Al-O, 1.87-1.97 ~. The tetrahedral rotation angle is 6.9 ~ compared with 7.3 ~ for dickite and 7.4 ~ for nacrite. Previous Rictveld refinements apparently suffered from poor preferred orientation models, failure to consider the presence of dickite as a second phase, and, most importantly, refinement to a false-minimum structure. The conclusions based on the earlier refinements must therefore be r+evaluated, especially regarding the kaolinite space group and hydrogen positions. Existing X-ray and electron diffraction and spectroscopic data support the presence of C-centering in kaolinite.

R. B. Von Dreele

Papers

Rietveld refinement guidelines

Rietveld Refinement with Spallation Neutron Powder Diffraction Data

Quantitative texture analysis by Rietveld refinement

Use of Rietveld refinement for elastic macrostrain determination and for evaluation of plastic strain history from diffraction spectra

Rietveld Refinement of Non-Hydrogen Atomic Positions in Kaolinite