playground:rietveld_refinement_of_structural_distortion-mode_amplitudes
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+ | ====== Rietveld refinement of structural distortion-mode amplitudes ====== | ||
+ | Branton J. Campbell< | ||
+ | |||
+ | |||
+ | |||
+ | //< | ||
+ | |||
+ | |||
+ | |||
+ | Email: [[..: | ||
+ | |||
+ | WWW ISODISPLACE: | ||
+ | |||
+ | WWW TOPAS: [[http:// | ||
+ | |||
+ | ===== Abstract ===== | ||
+ | |||
+ | For any crystal structure that can be viewed as a low-symmetry distortion of some higher-symmetry parent structure, one can represent the details of the distorted structure with a list of distortion-mode amplitudes rather than the traditional list of //xyz// atomic coordinates. | ||
+ | |||
+ | ===== 1.0 Introduction ===== | ||
+ | |||
+ | The details of a subtle superstructural distortion are often very difficult to extract from powder-diffraction data. The added structural complexity of the distorted structure is rarely compensated by the extra information in the low-symmetry powder pattern, which may include only limited peak broadening or splitting and a handful of weak superlattice reflections. | ||
+ | |||
+ | In this article, we demonstrate that identifying and refining a superstructural distortion can be dramatically simplified by new Rietveld-refinement capabilities that take full advantage of group-theoretical distortion-mode analysis. | ||
+ | |||
+ | ===== 2.0 The distortion-mode basis ===== | ||
+ | |||
+ | The free energy of any crystalline material can be expanded in terms of the order parameters of the irreducible representations of the parent space-group symmetry.**< | ||
+ | |||
+ | A superstructural distortion breaks some of the symmetries of the parent crystal structure. | ||
+ | |||
+ | Every superstructural distortion is associated with a //k//-point (or set of // | ||
+ | |||
+ | An order parameter of a multidimensional irrep can belong to any one of several different //order parameter directions// | ||
+ | |||
+ | While irreps and OPDs are purely mathematical abstractions, | ||
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+ | The traditional atomic-coordinate description of a given superstructure is entirely independent of any other structure that it may be related to. The distortion-mode description, | ||
+ | |||
+ | ===== 3.0 The WO3 phase diagram ===== | ||
+ | |||
+ | The structure of WO< | ||
+ | |||
+ | **Table 1:** // Summary of the ambient pressure WO< | ||
+ | |||
+ | | Temp. (°C) | //S.G.// | Supercell | Refs. | Tilts | // | ||
+ | | above 900 | // | ||
+ | | 790 to 900 | // | ||
+ | | 760 to 790 | // | ||
+ | | 400 to 760 | //Pbcn// | < | ||
+ | | 17 to 400 | // | ||
+ | | -40 to 17 | // | ||
+ | | below -40 | //Pc// | < | ||
+ | |||
+ | |||
+ | |||
+ | The most important distortion modes induced by < | ||
+ | |||
+ | An < | ||
+ | |||
+ | The group-subgroup relationships that exist among the distortion symmetries in Table 1 are as follows. | ||
+ | |||
+ | < | ||
+ | |||
+ | < | ||
+ | |||
+ | For any pair of structures that have a group-subgroup symmetry relationship, | ||
+ | |||
+ | In summary, the relatively small number of large-amplitude distortion modes for each phase emphasizes the importance of the distortion-mode basis. | ||
+ | |||
+ | ===== 4.0 Distortion-mode analysis of the P21/n phase of WO3 ===== | ||
+ | |||
+ | ==== 4.1 Mode decomposition ==== | ||
+ | |||
+ | WO< | ||
+ | |||
+ | To enter the cubic parent structure, follow the "Enter structure manually" | ||
+ | |||
+ | **Table 2:** //The P2< | ||
+ | |||
+ | | W1 | 0.2513(6) | 0.0277(7) | 0.2865(5) | O3 | 0.2821(4) | 0.2602(7) | 0.2870(4) | | ||
+ | | W2 | 0.2481(6) | 0.0342(6) | 0.7815(5) | O4 | 0.2107(4) | 0.2602(8) | 0.7310(4) | | ||
+ | | O1 | 0.0008(6) | 0.0366(8) | 0.2116(5) | O5 | 0.2859(6) | 0.0390(6) | 0.0065(5) | | ||
+ | | O2 | 0.9973(6) | 0.4632(8) | 0.2164(5) | O6 | 0.2849(6) | 0.4850(5) | 0.9922(4) | | ||
+ | |||
+ | |||
+ | |||
+ | ISODISPLACE provides four methods of generating distortions. | ||
+ | |||
+ | {{anewsletter5.0_jsoe_files: | ||
+ | |||
+ | {{anewsletter5.0_jsoe_files: | ||
+ | |||
+ | Most importantly, | ||
+ | |||
+ | A series of radio buttons near the top of the **Distortion** page provide several avenues of exploration. | ||
+ | |||
+ | From the distortion page, select "CIF file" and click " | ||
+ | |||
+ | ==== 4.2 Search restricted by space-group and basis ==== | ||
+ | |||
+ | Now return to the main ISODISPLACE page and assume that we don't yet know the details of the distorted structure, but see evidence from the diffraction data for a 2´2´2 supercell with space group // | ||
+ | |||
+ | ==== 4.3 The general method (specify k-points, irreps, OPDs) ==== | ||
+ | |||
+ | Return again to the main ISODISPLACE page and assume that you already know which // | ||
+ | |||
+ | ==== 4.4 Filtered search over special k-points ==== | ||
+ | |||
+ | A special //k//-point search allows one to conveniently explore any distortion symmetry that can be generated by a single irrep at a special //k//-point of symmetry. | ||
+ | |||
+ | In summary, ISODISPLACE provides several different methods of generating distortion symmetries: (1) a filtered search over special // | ||
+ | |||
+ | ===== 5.0 Distortion-mode refinements ===== | ||
+ | |||
+ | We now proceed to illustrate a distortion-mode refinement using laboratory X-ray data collected on a sample of predominantly monoclinic WO< | ||
+ | |||
+ | Distortion-mode refinements can be performed in a straightforward fashion using the menus/ | ||
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+ | * **Select Data File**: allows you to browse for one of a number of TOPAS-supported data file formats (.raw files, .xy, .xye, .rd, etc) and writes corresponding lines to the .inp file. | ||
+ | * **Instrument/ | ||
+ | * http:// | ||
+ | * **®****TA**: | ||
+ | |||
+ | These “four clicks” will set up a command file containing everything needed for a sensible default Rietveld refinement. | ||
+ | |||
+ | {{anewsletter5.0_jsoe_files: | ||
+ | |||
+ | This straightforward process produces a .inp file in which each mode amplitude is set up as a refinable parameter labelled //a1// -- //an// for brevity (though the full mode label is listed alongside). | ||
+ | |||
+ | prm W_1_dy = + 0.125*a1 -- 0.125*a2;: -0.00308 | ||
+ | |||
+ | where the number after the colon indicates the derived value and is updated on refinement. | ||
+ | |||
+ | site W1 Y = ideal_W_1_y + W_1_dy; | ||
+ | |||
+ | where ideal_W1_yis the fractional coordinate of W1 in the current cell setting appropriate for the high-symmetry structure. | ||
+ | |||
+ | {{anewsletter5.0_jsoe_files: | ||
+ | |||
+ | \\ {{anewsletter5.0_jsoe_files: | ||
+ | |||
+ | //< | ||
+ | |||
+ | Figure 7c gives an indication of how sensitive laboratory X-ray data are to the distortion modes involving oxygen -- note that the W:O ratio of scattering powers is 83< | ||
+ | |||
+ | ===== 6.0 Conclusions ===== | ||
+ | |||
+ | The internet-based ISODISPLACE software tool allows one to generate and interactively visualize almost any superstructural distortion, and to save the result in a CIF file that contains two complete structural descriptions: | ||
+ | |||
+ | ===== Acknowledgements ===== | ||
+ | |||
+ | We acknowledge Alan Coelho for the development of the TOPAS Academic software package. | ||
+ | |||
+ | ===== References ===== | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | [1] L. D. Landau and E. M. Lifshitz, // | ||
+ | |||
+ | [2] B. J. Campbell, H. T. Stokes, D. E. Tanner and D. M. Hatch, // | ||
+ | |||
+ | [3] H. T. Stokes and D. M. Hatch, //Isotropy subgroups of the 230 crystallographic space groups//, (World Scientific, Singapore, 1987). | ||
+ | |||
+ | [4] C. J. Bradley and A. P. Cracknell, //The mathematical theory of symmetry in solids//, (Oxford, Clarendon Press, 1972). | ||
+ | |||
+ | [5] H. T. Stokes, D. M. Hatch and J. D. Wells, // | ||
+ | |||
+ | [6] C. J. Howard, V. Luca and K. S. Knight, // | ||
+ | |||
+ | [7] T. Vogt, P. M. Woodward and B. A. Hunter, //The high-temperature phases of WO< | ||
+ | |||
+ | [8] P. M. Woodward, A. W. Sleight and T. Vogt, //Structure refinement of triclinic tungsten trioxide//, J. Phys. Chem. Solids **56**, 1305-15 (1995). | ||
+ | |||
+ | [9] R. Diehl, G. Brandt and E. Salje, // | ||
+ | |||
+ | [10] E. K. H. Salje, S. Rehmann, F. Pobell, D. Morris, K. S. Knight, T. Herrmannsdorfer and M. T. Dove, //Crystal structure and paramagnetic behaviour of epsilon WO< | ||
+ | |||
+ | [11] A. M. Glazer, //The classification of tilted octahedra in perovskites//, | ||
+ | |||
+ | [12] C. J. Howard and H. T. Stokes, // | ||
+ | |||
+ | |||
+ | |||
+ |
playground/rietveld_refinement_of_structural_distortion-mode_amplitudes.txt · Last modified: 2022/11/03 15:08 by 127.0.0.1