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====== 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:
[[http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_isoriet.htm|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.
[[http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_isoriet_wo3_simple.htm|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.
[[http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_isoriet_wo3_advanced.htm|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.
[[http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_exhaustive_symmetry.htm|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.
[[http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_GA_wo3.htm|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 [[http://community.dur.ac.uk/john.evans/topas_book/mgh2o6rbbr3_symmetry_modes.zip|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)