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.

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)