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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:

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 will be 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)

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