Chapter 8 Symmetry Mode Refinements
The WO3 examples in this chapter and the data sets shown are given in various on line tutorials on John's webpages:
LaMnO3 symmetry mode refinement - Structural transformations. Directly refine symmetry-mode amplitudes rather than traditional atomic xyz coordinates of a distorted superstructure. Example based on simulated lab x-ray diffraction data from low-temperature orthorhombic LaMnO3. The symmetry modes are obtained using the ISODISTORT software.
P21/n room tempertaure WO3 example - Structural transformations. Directly refine symmetry-mode amplitudes rather than traditional atomic xyz coordinates of a distorted superstructure. Example based on laboratory x-ray diffraction data from room-temperature monoclinic WO3. The symmetry modes are obtained using the ISODISTORT software.
Room and high T refinements - Structural transformations. A more advanced symmetry-mode refinement example based on room-temperature WO3. Fit both neutron and X-ray data. Try to determine space-group symmetry at high temperature using ISODISTORT.
Exhaustive group-subgroup tree searching - By combining topas, ISODISTORT and some python scripts you can automatically search through different space group possibilities for samples which undergo symmetry-lowering phase transitions.
Using a GA to determine symmetry - This tutorial teaches you how to use a Genetic Algorithm with a P1 distortion mode model of a structure to decide which modes are actually important in fitting the data. This lets you simultaneously determine the space group and structure of a material. The tutorial uses WO3 as an example. See also the magnetic example below.
Chapter 8.5 Mg(H2O)6RbBr3 symmetry mode refinement
The data and cif files are linked in the single .zip file here.
The INP file is:
r_exp 3.66048948 r_exp_dash 5.71356407 r_wp 5.81321323 r_wp_dash 9.07369531 r_p 4.40883513 r_p_dash 7.43932786 weighted_Durbin_Watson 0.844563949 gof 1.58809724 iters 1000 continue_after_convergence xdd "RbBrMgBr2_6H2O_295K.raw" r_exp 3.66048948 r_exp_dash 5.71356407 r_wp 5.81321323 r_wp_dash 9.07369531 r_p 4.40883513 r_p_dash 7.43932786 weighted_Durbin_Watson 0.844563949 gof 1.58809724 range 1 ' do_errors bkg @ 349.66695` -169.568495` 131.058005` -63.3388818` 31.6250629` -18.4412314` 24.5858761` -38.5678066` 31.3723939` 3.263828` -15.0038769` -3.13862232` 4.42170131` 1.85545313` 2.01442939` -8.33280089` start_X 10 One_on_X(@, 6824.72452`) Zero_Error(@, 0.00286`) LP_Factor( 27.3) Rp 217.5 Rs 217.5 axial_conv filament_length 8 sample_length 8 receiving_slit_length 8 secondary_soller_angle @ 2.73398` axial_n_beta 20 Slit_Width( 0.1) lam ymin_on_ymax 0.0001 la 1 lo 1.540596 lh 0.401844 str CS_L(@, 802.58213`) CS_G(@, 818.88438`) Strain_G(@, 0.12267`) r_bragg 3.59543037 phase_name Structure MVW( 1781.925, 1311.261`, 96.228`) scale @ 8.50799312e-05` Phase_LAC_1_on_cm( 163.20756`) Phase_Density_g_on_cm3( 2.25657`) space_group C12/c1 a @ 9.641327` b @ 9.865327` c @ 13.786095` be @ 90.08790` '{{{mode definitions prm a1 -0.03398` min -2.00 max 2.00 'Pm-3m[0,1/2,0]X4-(0;0;a)[Br:d:dsp] Eu(a) prm a2 0.07955` min -2.00 max 2.00 'Pm-3m[0,1/2,0]X5-(0,0;0,0;a,-a)[Br:d:dsp] A2u(a) prm a3 -0.18402` min -2.00 max 2.00 'Pm-3m[0,1/2,0]X5-(0,0;0,0;a,-a)[Br:d:dsp] Eu(a) prm a4 0.03595` min -1.41 max 1.41 'Pm-3m[0,1/2,0]X5-(0,0;0,0;a,-a)[Rb:a:dsp] T1u(a) prm a5 0.34429` min -3.46 max 3.46 'Pm-3m[0,0,0]GM1+(a)[O:f:dsp] A1(a) prm a6 0.01730` min -2.45 max 2.45 'Pm-3m[0,0,0]GM3+(a,0)[O:f:dsp] A1(a) prm a7 2.36162` min -2.83 max 2.83 'Pm-3m[0,0,0]GM4+(a,-a,0)[O:f:dsp] E(a) prm a8 0.15038` min -2.83 max 2.83 'Pm-3m[0,0,0]GM5+(a,b,b)[O:f:dsp] E(a) prm a9 0.02173` min -2.83 max 2.83 'Pm-3m[0,0,0]GM5+(a,b,b)[O:f:dsp] E(b) prm a10 -1.61762` min -2.83 max 2.83 'Pm-3m[0,1/2,0]X1-(0;0;a)[O:f:dsp] E(a) prm a11 0.07180` min -2.83 max 2.83 'Pm-3m[0,1/2,0]X4-(0;0;a)[O:f:dsp] A1(a) prm a12 0.17458` min -2.83 max 2.83 'Pm-3m[0,1/2,0]X5-(0,0;0,0;a,-a)[O:f:dsp] E_1(a) prm a13 0.33838` min -2.00 max 2.00 'Pm-3m[0,1/2,0]X5-(0,0;0,0;a,-a)[O:f:dsp] E_2(a) '}}} '{{{mode-amplitude to delta transformation prm Br_1_dx = +0.03601*a2 + 0.03601*a3;: -0.00376` prm Br_1_dy = -0.03601*a2 + 0.03601*a3;: -0.00949` prm Br_1_dz = -0.03601*a1;: 0.00122` prm Rb_1_dy = +0.07203*a4;: 0.00259` prm O_1_dx = +0.02079*a5 + 0.01470*a6 + 0.02547*a8 + 0.02547*a10 - 0.02547*a11;: -0.03179` prm O_1_dy = -0.02079*a5 - 0.01470*a6 + 0.02547*a8 + 0.02547*a10 + 0.02547*a11;: -0.04295` prm O_1_dz = +0.01801*a7 + 0.01801*a9 + 0.02547*a12;: 0.04737` prm O_2_dx = +0.02079*a5 + 0.01470*a6 + 0.02547*a8 - 0.02547*a10 + 0.02547*a11;: 0.05427` prm O_2_dy = -0.02079*a5 - 0.01470*a6 + 0.02547*a8 - 0.02547*a10 - 0.02547*a11;: 0.03579` prm O_2_dz = +0.01801*a7 + 0.01801*a9 - 0.02547*a12;: 0.03848` prm O_3_dx = -0.03601*a7 + 0.03601*a9;: -0.08426` prm O_3_dy = -0.05093*a13;: -0.01723` prm O_3_dz = +0.02079*a5 - 0.02940*a6;: 0.00665` '}}} '{{{distorted parameters prm !Mg_1_x = 0;: 0.00000 prm !Mg_1_y = 1/2;: 0.50000 prm !Mg_1_z = 0;: 0.00000 prm Br_1_x = 3/4 + Br_1_dx;: 0.74624` prm Br_1_y = 1/4 + Br_1_dy;: 0.24051` prm Br_1_z = 3/4 + Br_1_dz;: 0.75122` prm !Br_2_x = 0;: 0.00000 prm !Br_2_y = 0;: 0.00000 prm !Br_2_z = 0;: 0.00000 prm !Rb_1_x = 0;: 0.00000 prm Rb_1_y = 0 + Rb_1_dy;: 0.00259` prm !Rb_1_z = 1/4;: 0.25000 prm O_1_x = 0.35500 + O_1_dx;: 0.32321` prm O_1_y = 0.14500 + O_1_dy;: 0.10205` prm O_1_z = 0 + O_1_dz;: 0.04737` prm O_2_x = 0.35500 + O_2_dx;: 0.40927` prm O_2_y = 0.14500 + O_2_dy;: 0.18079` prm O_2_z = 1/2 + O_2_dz;: 0.53848` prm O_3_x = 1/2 + O_3_dx;: 0.41574` prm O_3_y = 0 + O_3_dy;: -0.01723` prm O_3_z = 0.85500 + O_3_dz;: 0.86165` '}}} '{{{mode-dependent sites site Mg_1 x = Mg_1_x; y = Mg_1_y; z = Mg_1_z; occ Mg 1 beq bm 2.19023` site Rb_1 x = Rb_1_x; y = Rb_1_y; z = Rb_1_z; occ Rb 1 beq =bm; site Br_1 x = Br_1_x; y = Br_1_y; z = Br_1_z; occ Br 1 beq bbr 1.67475` site Br_2 x = Br_2_x; y = Br_2_y; z = Br_2_z; occ Br 1 beq =bbr; site O_1 x = O_1_x; y = O_1_y; z = O_1_z; occ O 1 beq bo 0.07538` site O_2 x = O_2_x; y = O_2_y; z = O_2_z; occ O 1 beq =bo; site O_3 x = O_3_x; y = O_3_y; z = O_3_z; occ O 1 beq =bo; '}}} view_structure Out_CIF_STR(RbBrMgBr2_6H2O_295K_DM.cif) Create_2Th_Ip_file(RbBrMgBr2_6H2O_295K_DM.pks) xdd_out RbBrMgBr2_6H2O_295K_DM.prf load out_record out_fmt out_eqn { " %11.5f " = X; " %11.5f " = Yobs; " %11.5f " = Ycalc; " %11.5f\n" = Yobs-Ycalc; } str Strain_G(, 0.17437_0.00430) r_bragg 1.72210317 phase_name Structure MVW( 661.487, 327.428, 3.772`) scale @ 3.59815094e-05` space_group Fm-3m Phase_LAC_1_on_cm( 323.72600) Phase_Density_g_on_cm3( 3.35472) Cubic( 6.89242_0.00010) site Rb1 num_posns 4 x 0 y 0 z 0 occ Rb+1 1 beq !B6 2_LIMIT_MIN_-10 site Br1 num_posns 4 x 0.5 y 0.5 z 0.5 occ Br-1 1 beq =B6; : 2.00000 Create_2Th_Ip_file(RbBr_295K_DM.pks)