Internal Standard

FelixDavis

Hi there,

I am trying to run an internal-standard refinement using NIST 676 (91.75% crystalline) alumina (14.951 wt%) mixed with Si powder (99.5%). However, after refinement, I’m getting an amorphous content of 0.85 wt%, which doesn’t seem correct. I’ve attached my code below.

Has anyone encountered a similar issue? It appears that my refinement may be underestimating the actual wt% of the internal standard.

Thanks

'-------------------------------------------------------------- 
'Input File for simple Rietveld Refinement 
'Replace any $, # or text after ---> as needed 
'Use Ta-> button to save/send to topas; Ta button to launch topas; run in topas with red arrow 
'-------------------------------------------------------------- 
r_wp  7.76512969 r_exp  2.08745748 r_p  5.7858612 r_wp_dash  13.9916875 r_p_dash  15.0171056 r_exp_dash  3.76130906 weighted_Durbin_Watson  0.124407268 gof  3.71989838
 
'-------------------------------------------------------------- 
'General information about refinement here 
'Remove commented lines as required 
'-------------------------------------------------------------- 
iters 100000 
chi2_convergence_criteria 0.001 
'do_errors 
 
'-------------------------------------------------------------- 
'Information on datafile etc here 
'Check that default weighting is appropriate for your data 
'-------------------------------------------------------------- 
xdd 14_Theta_2-Theta.xy 
	x_calculation_step = Yobs_dx_at(Xo); convolution_step 4 
 
			bkg @  1715.53667` -2175.29786`  911.585107` -326.099488` -151.956537`  176.590674` -179.927789`  130.912817` -152.355105` -29.3151637`
	'd5000 Bragg Brentano Sol-X Cu Ka1/a2 2 line emission 	
			Radius(150)
		Divergence( 1.24550168)
	  	axial_conv                    
		filament_length			  10
		sample_length				  24.00000
		receiving_slit_length     13
		primary_soller_angle	     5
		secondary_soller_angle    5

	Tube_Tails(, 0.00441278803, , -5, , 3.82772755, , 1.00003517e-05)

		lam
		ymin_on_ymax  0.0001
		la   0.01591 lo   1.5315264 lh  3.63805
		la   0.23547 lo   1.5406807 lh  0.00000
		la   0.01006 lo   1.5334719 lh  0.00148
		la   0.13463 lo   1.5445683 lh  0.00000
		la   0.00584 lo   1.5444958 lh  0.00000
		
	LP_Factor(!th2_monochromator, 0)
	CuKa2_analyt(0.0001)
	Zero_Error(zero, 0.0662749625`)
	Specimen_Displacement(height,-0.081285714`)
	Absorption(@, 500`_LIMIT_MIN_3)
		
		
	'--------------------------------------------------------------  
'Information on structure  
'Change recurring numbers in coordinates as required e.g. 0.3333 to =1/3;  
'--------------------------------------------------------------  
		str  
		phase_name "Corundum"  
		a a_corundum  4.761629` 
		b @ = a_corundum;:  4.761629` 
		c @  12.998705`
		al al_corundum  90.00113` 
		be @ = al_corundum;:  90.00113` 
		ga @  120.00772`
		volume  255.216`  
		space_group "R-3c"  
		site Al     x 0.00000       y 0.00000       z @  0.35337`			occ Al 1. 		beq @  0.72945` 		 min 0 
		site O      x @  0.30768`     y 0.00000       z 0.25000      	occ O	 1.         beq @  0.00000`_LIMIT_MIN_0 min 0 
		scale @  0.000643402757`                                                 
		r_bragg  4.63372857                                                   
		Phase_Density_g_on_cm3( 3.98040994`)  
		Spike_amount_in_specimen(14.951,91.75, 100`)  
macro Spike_amount_in_specimen(& std_wt_pct, & std_cryst, amor) 'or this goes in the spike phase str'  
{  
	'The spike phase str must be the first str in the xdd. This is because of how move_to works'  
	move_to xdd  
		local whole_specimen_total_std_addition_ = std_wt_pct;  
		local whole_specimen_cryst_std_addition_ = std_cryst whole_specimen_total_std_addition_ / 100;  
		local original_sample_amorphous_  100 : amor  
	move_to str  
		spiked_phase_measured_weight_percent = whole_specimen_cryst_std_addition_ ;  
}  
		LVol_FWHM_CS_G_L(1, 62.6324834`, 0.89, 62.55178`, @, 74.725196`,@, 627.064832`_LIMIT_MIN_0.3)  
		e0_from_Strain( 3.57919456e-07`, @, 0.000100000104`_LIMIT_MIN_0.0001, @, 0.0001`_LIMIT_MIN_0.0001) 
 
		corrected_weight_percent  13.7175425`
		
'-------------------------------------------------------------- 
'Information on structure 
'Change recurring numbers in coordinates as required e.g. 0.3333 to =1/3; 
'-------------------------------------------------------------- 
	str 
		phase_name "Silicon" 
		space_group "Fd-3m" 
		al lpa1  89.93390`
		be lpa1  89.93390`
		ga lpa1  89.93390`
		a lpa3  5.428861`
		b lpa3  5.428861`
		c lpa3  5.428861`
		volume  160.002` 
		site Si     x 0.00000       y 0.00000       z 0.00000      occ Si 1.0			
 
		scale @  0.0173959439`
		r_bragg  6.64228406
		'TCHZ_Peak_Type(pku, 0.0101157625,pkv, -0.000257764491,pkw, -0.00138941474,!pkz, 0.0000,pkx, 0.0136644513_LIMIT_MIN_0.0001, pky, 0.0001_LIMIT_MIN_0.0001) 
		Phase_Density_g_on_cm3( 2.33182682`) 
				macro Original_WP1(result) 'this goes in every non-spike str in the xdd'  
		{  
		local orig_wt_ = 100 Get(corrected_weight_percent) / (100 - whole_specimen_total_std_addition_); :  result  
		existing_prm original_sample_amorphous_ -= orig_wt_;  
		}   

		 
		LVol_FWHM_CS_G_L(1, 38.8431269`, 0.89, 54.2485004`, @, 10000`_LIMIT_MIN_0.3,@, 60.9056953`)   
		e0_from_Strain( 0.00101313676`, @, 0.000100000009`_LIMIT_MIN_0.0001, @, 0.464538094`) 
		
		corrected_weight_percent  85.3973065`
		
		weight_percent_amorphous  0.885151012`

rowlesmr

If you're using my spike phase macros, you don't want to look at the built-in weight fraction keywords.

try this:

      
'-------------------------------------------------------------- 
'Input File for simple Rietveld Refinement 
'Replace any $, # or text after ---> as needed 
'Use Ta-> button to save/send to topas; Ta button to launch topas; run in topas with red arrow 
'-------------------------------------------------------------- 
r_wp  7.76512969 r_exp  2.08745748 r_p  5.7858612 r_wp_dash  13.9916875 r_p_dash  15.0171056 r_exp_dash  3.76130906 weighted_Durbin_Watson  0.124407268 gof  3.71989838
 
'-------------------------------------------------------------- 
'General information about refinement here 
'Remove commented lines as required 
'-------------------------------------------------------------- 
iters 100000 
chi2_convergence_criteria 0.001 
'do_errors 
 


macro Spike_amount_in_specimen(& std_wt_pct, & std_cryst, amor) 'or this goes in the spike phase str'  
{  
	'The spike phase str must be the first str in the xdd. This is because of how move_to works'  
	move_to xdd  
		local whole_specimen_total_std_addition_ = std_wt_pct;  
		local whole_specimen_cryst_std_addition_ = std_cryst whole_specimen_total_std_addition_ / 100;  
		local original_sample_amorphous_  100 : amor  
	move_to str  
		spiked_phase_measured_weight_percent = whole_specimen_cryst_std_addition_ ;  
}  

macro Original_WP(result) 'this goes in every non-spike str in the xdd'  
{  
	local orig_wt_ = 100 Get(corrected_weight_percent) / (100 - whole_specimen_total_std_addition_); :  result  
	existing_prm original_sample_amorphous_ -= orig_wt_;  
}   



'-------------------------------------------------------------- 
'Information on datafile etc here 
'Check that default weighting is appropriate for your data 
'-------------------------------------------------------------- 
xdd 14_Theta_2-Theta.xy 
	x_calculation_step = Yobs_dx_at(Xo); convolution_step 4 
 
			bkg @  1715.53667` -2175.29786`  911.585107` -326.099488` -151.956537`  176.590674` -179.927789`  130.912817` -152.355105` -29.3151637`
	'd5000 Bragg Brentano Sol-X Cu Ka1/a2 2 line emission 	
			Radius(150)
		Divergence( 1.24550168)
	  	axial_conv                    
		filament_length			  10
		sample_length				  24.00000
		receiving_slit_length     13
		primary_soller_angle	     5
		secondary_soller_angle    5

	Tube_Tails(, 0.00441278803, , -5, , 3.82772755, , 1.00003517e-05)

		lam
		ymin_on_ymax  0.0001
		la   0.01591 lo   1.5315264 lh  3.63805
		la   0.23547 lo   1.5406807 lh  0.00000
		la   0.01006 lo   1.5334719 lh  0.00148
		la   0.13463 lo   1.5445683 lh  0.00000
		la   0.00584 lo   1.5444958 lh  0.00000
		
	LP_Factor(!th2_monochromator, 0)
	CuKa2_analyt(0.0001)
	Zero_Error(zero, 0.0662749625`)
	Specimen_Displacement(height,-0.081285714`)
	Absorption(@, 500`_LIMIT_MIN_3)
		
		
	'--------------------------------------------------------------  
'Information on structure  
'Change recurring numbers in coordinates as required e.g. 0.3333 to =1/3;  
'--------------------------------------------------------------  
		str  
		phase_name "Corundum"  
		a a_corundum  4.761629` 
		b @ = a_corundum;:  4.761629` 
		c @  12.998705`
		al al_corundum  90.00113` 
		be @ = al_corundum;:  90.00113` 
		ga @  120.00772`
		volume  255.216`  
		space_group "R-3c"  
		site Al     x 0.00000       y 0.00000       z @  0.35337`			occ Al 1. 		beq @  0.72945` 		 min 0 
		site O      x @  0.30768`     y 0.00000       z 0.25000      	occ O	 1.         beq @  0.00000`_LIMIT_MIN_0 min 0 
		scale @  0.000643402757`                                                 
		r_bragg  4.63372857                                                   
		Phase_Density_g_on_cm3( 3.98040994`)  
		LVol_FWHM_CS_G_L(1, 62.6324834`, 0.89, 62.55178`, @, 74.725196`,@, 627.064832`_LIMIT_MIN_0.3)  
		e0_from_Strain( 3.57919456e-07`, @, 0.000100000104`_LIMIT_MIN_0.0001, @, 0.0001`_LIMIT_MIN_0.0001) 
		
		Spike_amount_in_specimen(14.951,91.75, 100`)  
 
		
'-------------------------------------------------------------- 
'Information on structure 
'Change recurring numbers in coordinates as required e.g. 0.3333 to =1/3; 
'-------------------------------------------------------------- 
	str 
		phase_name "Silicon" 
		space_group "Fd-3m" 
		al lpa1  89.93390`
		be lpa1  89.93390`
		ga lpa1  89.93390`
		a lpa3  5.428861`
		b lpa3  5.428861`
		c lpa3  5.428861`
		volume  160.002` 
		site Si     x 0.00000       y 0.00000       z 0.00000      occ Si 1.0			
 
		scale @  0.0173959439`
		r_bragg  6.64228406
		'TCHZ_Peak_Type(pku, 0.0101157625,pkv, -0.000257764491,pkw, -0.00138941474,!pkz, 0.0000,pkx, 0.0136644513_LIMIT_MIN_0.0001, pky, 0.0001_LIMIT_MIN_0.0001) 
		Phase_Density_g_on_cm3( 2.33182682`) 

		 
		LVol_FWHM_CS_G_L(1, 38.8431269`, 0.89, 54.2485004`, @, 10000`_LIMIT_MIN_0.3,@, 60.9056953`)   
		e0_from_Strain( 0.00101313676`, @, 0.000100000009`_LIMIT_MIN_0.0001, @, 0.464538094`) 
		
		Original_WP(0)

FelixDavis

Thank you for the quick response. Yest that was what I was using. But now I ran the refinement using the code you just provided, but the amorphous phase still calculates to only 0.93 wt%, which is unexpectedly low. I suspect the program is still underestimating the NIST 676 (corundum), leading to an inaccurate amorphous phase quantification. I am certain that my internal standard alone contains more than 0.93 wt% amorphous material—even before accounting for the Si.

rowlesmr

Do you mean that you're getting something like

Spike_amount_in_specimen(14.951,91.75, 0.93`)

The amorphous content indicated there is the amorphous material in the original specimen, before you added the internal std.

FelixDavis

Hi Matt,
Thank you for your prompt response. I ran the latest code you provided, but the calculated amorphous content in my sample (for both Si and corundum) is only 0.93%, as shown below. I’m confident the actual amorphous fraction is significantly higher—likely in the 8–9% range. I would greatly appreciate any help in resolving this issue.
Thanks.

'-------------------------------------------------------------- 
'Input File for simple Rietveld Refinement 
'Replace any $, # or text after ---> as needed 
'Use Ta-> button to save/send to topas; Ta button to launch topas; run in topas with red arrow 
'-------------------------------------------------------------- 
r_wp  7.7620454 r_exp  2.08745748 r_p  5.78438102 r_wp_dash  13.9882358 r_p_dash  15.0170736 r_exp_dash  3.76187536 weighted_Durbin_Watson  0.1243267 gof  3.71842085
 
'-------------------------------------------------------------- 
'General information about refinement here 
'Remove commented lines as required 
'-------------------------------------------------------------- 
iters 100000 
chi2_convergence_criteria 0.001 
'do_errors 
 


macro Spike_amount_in_specimen(& std_wt_pct, & std_cryst, amor) 'or this goes in the spike phase str'  
{  
	'The spike phase str must be the first str in the xdd. This is because of how move_to works'  
	move_to xdd  
		local whole_specimen_total_std_addition_ = std_wt_pct;  
		local whole_specimen_cryst_std_addition_ = std_cryst whole_specimen_total_std_addition_ / 100;  
		local original_sample_amorphous_  100 : amor  
	move_to str  
		spiked_phase_measured_weight_percent = whole_specimen_cryst_std_addition_ ;  
}  

macro Original_WP(result) 'this goes in every non-spike str in the xdd'  
{  
	local orig_wt_ = 100 Get(corrected_weight_percent) / (100 - whole_specimen_total_std_addition_); :  result  
	existing_prm original_sample_amorphous_ -= orig_wt_;  
}   



'-------------------------------------------------------------- 
'Information on datafile etc here 
'Check that default weighting is appropriate for your data 
'-------------------------------------------------------------- 
xdd 14_Theta_2-Theta.xy 
	x_calculation_step = Yobs_dx_at(Xo); convolution_step 4 
 
			bkg @  1715.76859` -2175.21427`  911.25799` -326.204739` -151.973343`  176.550846` -179.810994`  130.95562` -152.622763` -29.3059147`
	'd5000 Bragg Brentano Sol-X Cu Ka1/a2 2 line emission 	
			Radius(150)
		Divergence( 1.24550168)
	  	axial_conv                    
		filament_length			  10
		sample_length				  24.00000
		receiving_slit_length     13
		primary_soller_angle	     5
		secondary_soller_angle    5

	Tube_Tails(, 0.00441278803, , -5, , 3.82772755, , 1.00003517e-05)

		lam
		ymin_on_ymax  0.0001
		la   0.01591 lo   1.5315264 lh  3.63805
		la   0.23547 lo   1.5406807 lh  0.00000
		la   0.01006 lo   1.5334719 lh  0.00148
		la   0.13463 lo   1.5445683 lh  0.00000
		la   0.00584 lo   1.5444958 lh  0.00000
		
	LP_Factor(!th2_monochromator, 0)
	CuKa2_analyt(0.0001)
	Zero_Error(zero, 0.0662763397`)
	Specimen_Displacement(height,-0.081294602`)
	Absorption(@, 500`_LIMIT_MIN_3)
		
		
	'--------------------------------------------------------------  
'Information on structure  
'Change recurring numbers in coordinates as required e.g. 0.3333 to =1/3;  
'--------------------------------------------------------------  
		str  
		phase_name "Corundum"  
		a a_corundum  4.761625` 
		b @ = a_corundum;:  4.761625` 
		c @  12.998701`
		al al_corundum  90.00111` 
		be @ = al_corundum;:  90.00111` 
		ga @  120.00768`
		volume  255.216`  
		space_group "R-3c"  
		site Al     x 0.00000       y 0.00000       z @  0.35335`			occ Al 1. 		beq @  0.72991` 		 min 0 
		site O      x @  0.30774`     y 0.00000       z 0.25000      	occ O	 1.         beq @  0.00000`_LIMIT_MIN_0 min 0 
		scale @  0.00064345098`                                                 
		r_bragg  4.62462292                                                   
		Phase_Density_g_on_cm3( 3.98041613`)  
		LVol_FWHM_CS_G_L(1, 62.7903312`, 0.89, 62.7137821`, @, 74.9260027`,@, 627.769776`_LIMIT_MIN_0.3)  
		e0_from_Strain( 3.57919252e-07`, @, 0.000100000002`_LIMIT_MIN_0.0001, @, 0.0001`_LIMIT_MIN_0.0001) 
		
		Spike_amount_in_specimen(14.951,91.75,-0.354741189`)  
 
		
'-------------------------------------------------------------- 
'Information on structure 
'Change recurring numbers in coordinates as required e.g. 0.3333 to =1/3; 
'-------------------------------------------------------------- 
	str 
		phase_name "Silicon" 
		space_group "Fd-3m" 
		al lpa1  89.93392`
		be lpa1  89.93392`
		ga lpa1  89.93392`
		a lpa3  5.428861`
		b lpa3  5.428861`
		c lpa3  5.428861`
		volume  160.002` 
		site Si     x 0.00000       y 0.00000       z 0.00000      occ Si 1.0			
 
		scale @  0.0173877255`
		r_bragg  6.64759647
		'TCHZ_Peak_Type(pku, 0.0101157625,pkv, -0.000257764491,pkw, -0.00138941474,!pkz, 0.0000,pkx, 0.0136644513_LIMIT_MIN_0.0001, pky, 0.0001_LIMIT_MIN_0.0001) 
		Phase_Density_g_on_cm3( 2.33182666`) 

		 
		LVol_FWHM_CS_G_L(1, 38.9205721`, 0.89, 54.3565712`, @, 10000`_LIMIT_MIN_0.3,@, 61.0269501`)   
		e0_from_Strain( 0.00101126007`, @, 0.0001`_LIMIT_MIN_0.0001, @, 0.463677419`) 
		
		Original_WP( 100.354741`)  
		
		weight_percent_amorphous  0.931753666`

rowlesmr

I’m confident the actual amorphous fraction is significantly higher—likely in the 8–9% range.

Why are you confident? what are you basing this on? Just want to make sure we aren't talking at cross-purposes.

rowlesmr

weight_percent_amorphous 0.931753666`

No. Don't use this.

Look only at

Spike_amount_in_specimen(14.951,91.75,-0.354741189`)  
'                                      ^^^^^^^^^^^^ this is the amorphous amount in the original specimen before std addition

and

 Original_WP( 100.354741`)

This is telling you that you have -0.35 wt% amorphous present in your original specimen, before adding the internal std.

Have a look at do_errors to see if this is within error of zero, which it probably is within the overall error of this technique. Check that all of your intensity corrections are doing the right thing. Are thermal parameters sensible?

rowlesmr

Why are you refining Si cubic angle?
Why are you refining the corundum angles?

They are all fixed by symmetry!

Don't refine thermals.

Can you post your data?

For corundum, try the Maslen etal structure:

	str
		phase_name "Corundum_syn_04_005_4213_icdd"
		Hexagonal( 4.7540, 12.9820)
		scale @  0.0006
		space_group "R-3c"
		site Al1 num_posns 0 x 0.0     y 0.0 z 0.35228 occ Al 1.0 beq 0.18397
		site O2  num_posns 0 x 0.69401 y 0.0 z 0.25    occ O  1.0 beq 0.21003

for silicon, try this str:

	str
		phase_name "Silicon_51688_icsd"
		scale @  0.017
		Cubic( 5.43053)
		space_group "F d -3 m S"
		site Si1 num_posns 0 x 0. y 0. z 0. occ Si 1. beq 0.54

FelixDavis

Thank you for your response. When I initially left the parameters untouched, the refinement significantly underestimated the internal standard. I only obtain a closer estimate when those parameters are adjusted. Please see the attached code with your suggested refinements, it's still heavily underestimating the internal standard.

'-------------------------------------------------------------- 
'Input File for simple Rietveld Refinement 
'Replace any $, # or text after ---> as needed 
'Use Ta-> button to save/send to topas; Ta button to launch topas; run in topas with red arrow 
'-------------------------------------------------------------- 
r_wp  8.897997 r_exp  2.09080223 r_p  6.12657569 r_wp_dash  16.0843288 r_p_dash  15.9725056 r_exp_dash  3.77940681 weighted_Durbin_Watson  0.11685438 gof  4.25578129
 
'-------------------------------------------------------------- 
'General information about refinement here 
'Remove commented lines as required 
'-------------------------------------------------------------- 
iters 100000 
chi2_convergence_criteria 0.001 
'do_errors 
 


macro Spike_amount_in_specimen(& std_wt_pct, & std_cryst, amor) 'or this goes in the spike phase str'  
{  
	'The spike phase str must be the first str in the xdd. This is because of how move_to works'  
	move_to xdd  
		local whole_specimen_total_std_addition_ = std_wt_pct;  
		local whole_specimen_cryst_std_addition_ = std_cryst whole_specimen_total_std_addition_ / 100;  
		local original_sample_amorphous_  100 : amor  
	move_to str  
		spiked_phase_measured_weight_percent = whole_specimen_cryst_std_addition_ ;  
}  

macro Original_WP(result) 'this goes in every non-spike str in the xdd'  
{  
	local orig_wt_ = 100 Get(corrected_weight_percent) / (100 - whole_specimen_total_std_addition_); :  result  
	existing_prm original_sample_amorphous_ -= orig_wt_;  
}   



'-------------------------------------------------------------- 
'Information on datafile etc here 
'Check that default weighting is appropriate for your data 
'-------------------------------------------------------------- 
xdd 14_Theta_2-Theta.xy 
	x_calculation_step = Yobs_dx_at(Xo); convolution_step 4 
 
			bkg @  1723.29044` -2157.08604`  922.282297` -317.508237` -142.610469`  191.541622` -170.52811`  139.625737` -146.405206` -23.9539791`
	'd5000 Bragg Brentano Sol-X Cu Ka1/a2 2 line emission 	
			Radius(150)
		Divergence( 1.24550168)
	  	axial_conv                    
		filament_length			  10
		sample_length				  24.00000
		receiving_slit_length     13
		primary_soller_angle	     5
		secondary_soller_angle    5

	Tube_Tails(, 0.00441278803, , -5, , 3.82772755, , 1.00003517e-05)

		lam
		ymin_on_ymax  0.0001
		la   0.01591 lo   1.5315264 lh  3.63805
		la   0.23547 lo   1.5406807 lh  0.00000
		la   0.01006 lo   1.5334719 lh  0.00148
		la   0.13463 lo   1.5445683 lh  0.00000
		la   0.00584 lo   1.5444958 lh  0.00000
		
	LP_Factor(!th2_monochromator, 0)
	CuKa2_analyt(0.0001)
	Zero_Error(zero, 0.0572562898`)
	Specimen_Displacement(height,-0.0695557713`)
	Absorption(@, 88.9740927`)
		
		
	'--------------------------------------------------------------  
'Information on structure  
'Change recurring numbers in coordinates as required e.g. 0.3333 to =1/3;  
'--------------------------------------------------------------  
	str
		phase_name "Corundum_syn_04_005_4213_icdd"
		Hexagonal( 4.7540, 12.9820)
		scale @  0.0006
		space_group "R-3c"
		site Al1 num_posns  12 x 0.0     y 0.0 z 0.35228 occ Al 1.0 beq 0.18397
		site O2  num_posns  18 x 0.69401 y 0.0 z 0.25    occ O  1.0 beq 0.21003
		scale @  0.000558599733`                                                
		r_bragg  6.50711263                                                   
		Phase_Density_g_on_cm3( 3.99802325)  
		LVol_FWHM_CS_G_L(1, 68.3868747`, 0.89, 66.8580409`, @, 77.800765`,@, 1154.00493`_LIMIT_MIN_0.3)  
		e0_from_Strain( 0.000625268616`, @, 0.285475748`, @, 0.0019255574`_LIMIT_MIN_0.0001) 
		
		Spike_amount_in_specimen(14.951,91.75,-23.2725516`)  
 
		
'-------------------------------------------------------------- 
'Information on structure 
'Change recurring numbers in coordinates as required e.g. 0.3333 to =1/3; 
'-------------------------------------------------------------- 
	str
		phase_name "Silicon_51688_icsd"
		scale @  0.017
		Cubic( 5.43053)
		space_group "F d -3 m S"
		site Si1 num_posns  8 x 0. y 0. z 0. occ Si 1. beq 0.54	
 
		scale @  0.0184432865`
		r_bragg  4.56410384
		'TCHZ_Peak_Type(pku, 0.0101157625,pkv, -0.000257764491,pkw, -0.00138941474,!pkz, 0.0000,pkx, 0.0136644513_LIMIT_MIN_0.0001, pky, 0.0001_LIMIT_MIN_0.0001) 
		Phase_Density_g_on_cm3( 2.32967259) 

		 
		LVol_FWHM_CS_G_L(1, 36.5026914`, 0.89, 50.9824428`, @, 10000`_LIMIT_MIN_0.3,@, 57.2411294`)   
		e0_from_Strain( 0.000994357588`, @, 0.0001`_LIMIT_MIN_0.0001, @, 0.455925715`) 
		
		Original_WP( 123.272552`)

johnsoevans

Can I make a couple of more philisophical points? My personal view is that: (1) Rietveld is hard; (2) Quant Rietveld is harder; (3) Quant Rietveld is even harder if you want to get the correct answer.

There are lots of potential pitfalls with both data collection and data analysis if you need accurate and precise quant analysis. I'd strongly recommend reading some of the specialist literature. The Chapter in the Billinge/Dinnebier text book by Madsen/Scarlett is one place to start. Any reports on the Reynolds Cup will also show how careful you need to be.

The second point is that TOPAS (particularly in launch mode) is deliberately designed to give the user power and flexibility via built in macros, user-defined macros, etc. As such, it doesn't automatically apply some of the checks or constraints you'd find in other packages. e.g. it let you refine angles for Si because you asked it to. That's nearly always a bad idea, unless you've got a specific scientific reason for wanting to. The flexibiltiy means that it's crucial that you know exactly what each macro in the INP file is doing, and know whether it is sensible/applicable for your experiment. Introducing any parameter you don't understand is dangerous.

You can look in tech ref, or topas.inc, or the topas wiki for this information. Or the Rietveld text that Robert, Andreas and I wrote discusses a lot of the more comment macros, with citations back to the original literature.

For example, in your file I noticed you have the source emission defined twice: once via the lam commands with what looks like the CuKa5 description that's suitable for fundamental parameters, then again with CuKa2_analyt(), which is for use with the TCHZ function. You also refine height and zero together, which are highly (infinitely?) correlated.

In case it helps there are some notes on the wiki that contain some of the common "Rietveld crimes": https://https://topas.awh.durham.ac.uk/lib/exe/fetch.php?media=evans_ln1_david_ln1.pdf

Just for readabiltiy, you can put your INP file text in posts as code (use the </> icon) which will make them more readable. I think it just puts triple quotes around things. If you just paste flarum will often mess up the formatting.

FelixDavis

Thank you for your help. I collected a new set of XRD data for Si and corundum (15.07 wt%) using the structure file you provided. However, when I applied the LVol_FWHM_CS_G_L macro to determine crystallite size, the refined corundum phase fraction dropped to approximately 11 wt%, which is not physically reasonable.

I tested multiple refinement strategies, but in all cases the internal standard was underestimated by more than 4 wt%. In contrast, when I used the TCHZ peak-shape model without incorporating the line emission profile and tube-tail correction, the refined corundum content increased to 14.76 wt%, which is much closer to the expected value, though still underestimated.

I have included the relevant refinement code below and would appreciate any insight into why the use of LVol_FWHM_CS_G_L leads to this discrepancy. I have performed many Rietveld refinements and have successfully quantified both lab-made and commercial materials using multiple software packages, so this behavior is unexpected. My motivation for using TOPAS in this case is to extract reliable crystallite sizes, which I have been cross-validating with TEM. While the crystallite sizes appear reasonable, the phase quantification deviates significantly.

Most concerning is that the refinement yields a negative amorphous content, despite the corundum standard being 91.75% crystalline. This should be a straightforward two-phase quantification problem, yet I am clearly missing something. Any guidance would be greatly appreciated.
`'--------------------------------------------------------------
'Input File for simple Rietveld Refinement
'Replace any $, # or text after ---> as needed
'Use Ta-> button to save/send to topas; Ta button to launch topas; run in topas with red arrow
'--------------------------------------------------------------
r_wp 12.6902722 r_exp 2.17923184 r_p 8.65647629 r_wp_dash 21.4948058 r_p_dash 20.1402727 r_exp_dash 3.6911868 weighted_Durbin_Watson 0.0707012697 gof 5.8232777

'--------------------------------------------------------------
'General information about refinement here
'Remove commented lines as required
'--------------------------------------------------------------
iters 100000
chi2_convergence_criteria 0.001
'do_errors

macro Spike_amount_in_specimen(& std_wt_pct, & std_cryst, amor) 'or this goes in the spike phase str'
{
'The spike phase str must be the first str in the xdd. This is because of how move_to works'
move_to xdd
local whole_specimen_total_std_addition_ = std_wt_pct;
local whole_specimen_cryst_std_addition_ = std_cryst whole_specimen_total_std_addition_ / 100;
local original_sample_amorphous_ 100 : amor
move_to str
spiked_phase_measured_weight_percent = whole_specimen_cryst_std_addition_ ;
}

macro Original_WP(result) 'this goes in every non-spike str in the xdd'
{
local orig_wt_ = 100 Get(corrected_weight_percent) / (100 - whole_specimen_total_std_addition); : result
existing_prm original_sample_amorphous -= orig_wt_;
}

'--------------------------------------------------------------
'Information on datafile etc here
'Check that default weighting is appropriate for your data
'--------------------------------------------------------------
xdd "15p07 Corudum- Si-12-9-25_Theta_2-Theta.xy"
x_calculation_step = Yobs_dx_at(Xo); convolution_step 4
bkg @ 1502.85822-1872.28488 845.21646-370.634564 26.417075613.9522265
Simple_Axial_Model(axial, 8.96116089`)

'd5000 Bragg Brentano Sol-X Cu Ka1/a2 2 line emission 
LP_Factor(!th2_monochromator, 0) 
CuKa2_analyt(0.0001) 
Zero_Error(zero, 0.0565282371`)

'--------------------------------------------------------------
'Information on structure
'Change recurring numbers in coordinates as required e.g. 0.3333 to =1/3;
'--------------------------------------------------------------
str
phase_name "Corundum_syn_04_005_4213_icdd"
Hexagonal( 4.7540, 12.9820)
scale @ 0.00103927873space_group "R-3c" site Al1 num_posns 12 x 0.0 y 0.0 z 0.35228 occ Al 1.0 beq 0.18397 site O2 num_posns 18 x 0.69401 y 0.0 z 0.25 occ O 1.0 beq 0.21003 TCHZ_Peak_Type(pku, 0.00883343669,pkv, -0.00525732096,pkw, 0.000738160499,!pkz, 0.0000,pkx, 0.267953478, pky, 0.233425741)
Phase_Density_g_on_cm3( 3.99802325)
Spike_amount_in_specimen(16.1234,91.75,-1.81886822`)

	 
	 
 
 
str
	phase_name "Silicon_51688_icsd"
	scale @  0.0259189096`
	Cubic( 5.43053)
	space_group "F d -3 m S"
	site Si1 num_posns  8 x 0. y 0. z 0. occ Si 1. beq 0.54
	TCHZ_Peak_Type(pku, 0.00883343669`,pkv, -0.00525732096`,pkw,  0.000738160499`,!pkz, 0.0000,pkx, 0.267953478`, pky, 0.233425741`) 
	Phase_Density_g_on_cm3( 2.32967259)
	Original_WP( 101.818868`)  `

rowlesmr

What is your instrument setup? how did you prepare the specimen? what does your data look like?

johnsoevans

It also looks like you have the same peak shape for both strs, whereas I guess they're different when you're including size/strain contributions. If you have a different TCHZ for each phase do the %'s change?

FelixDavis

I believe that only a single TCHZ function can be applied to either structure. While the use of TCHZ slightly improves the estimation of corundum compared to the size–strain contribution, it still underestimates the corundum content, which in turn leads to an inaccurate estimation of the amorphous phase. I used other software packages which show that I have 7% to 8% amorphous phase. I am also using Rigaku Miniflex.

johnsoevans

Make the parameter names different so values aren’t equated: pku1 and pku2 etc.

FelixDavis

Thanks so much John. It worked and the results are very close to what I estimated with the other software. But why I wasn't able to use LVol_FWHM_CS_G_L and e0_from_Strain to get similar results like the TCHZ method.

johnsoevans

I'm glad it's working. TCHZ is, of course, a different peak shape model to the size/strain methods but it would be a bit surprising if the results weren't reasonably consistent between the two methods. One thing you could do is output the calculated pattern from the TCHZ fit and use it as an "experimental" data set and try and fit it with the size/strain model. You'd then have a known model to test, without any potential experimental artefacts.