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====== Quantitative phase analysis by the Direct-Derivation Method ======


Quantitative phase analysis by X-ray diffraction is a powerful method. The most widely used is quantification using the Rietveld methodology[1,2] via the Hill/Howard or Bish/Howard algorithm[3,4]. This was expanded by Scarlett & Madsen with the Partial Or No Known Crystal Structure (PONKCS) methodology[5], whereby the scattered intensity of an unknown phase was calibrated against a phase with a known crystal structure. More recently, quantification by the Direct-Derivation Methodology (DDM)[6-10] has been developed. Broadly summarised, the DDM approach uses the total integrated intensity of a phase, normalised by the elemental composition of that phase, to calculate the weight fraction of a particular phase, be it crystalline or amorphous.

The simplest implementation of DDM in TOPAS uses ''numerical_area'' to obtain the total integrated intensity, coupled with a user-provided elemental composition, to quantity given phases. These phases can be any combination of ''str'', ''hkl_Is'', ''xo_Is'', or ''d_Is''. For the non-''str'' phases, the peak intensities can be freely refining, or constrained by some scale factor. If there are number of individual ''xo_Is''/''d_Is'' peaks describing one phase, it is easiest to consolidate them all under a single ''xo_Is''/''d_Is'' phase. If you wish to implement are more complicated version, please consult the DDM literature[6-10].

Three macros are given below: ''DDM'', ''DDM_M_n2'', and ''DDM_a''. Any combination of these macros can be used in a single input file, with any combination of ''str'', ''hkl_Is'', ''xo_Is'', or ''d_Is'' phases. You are constrained to use only one DDM macro per phase

The first two arguments for all macros are number of the current phase, and the total number of phases. This is to allow for the correct summation of the masses for the calculation of the weight fractions. The phase number can be in any order, but must start from 1, and not skip any numbers. The current implementation is arbitrarily limited to a maximum of 10 phases, but this can be easily expanded. The last argument for all macros reports the weight percentage for that phase. 

For the ''DDM'' macro, the third argument is the chemical formula or estimated elemental composition for that particular phase. If the composition is known to be Al<sub>2</sub>O<sub>3</sub>, then the formula would be entered as “Al 2 + O 3”. If it were MgCO<sub>3</sub>.2.5H<sub>2</sub>O, then it could be entered as “Mg + C + O 3 + 2.5(H 2 + O)”, or “Mg + C + O 5.5 + H 5”. 

For the ''DDM_M_n2'' macro, the third and fourth arguments are the formula mass and number of square electrons, respectively. This allows you to explicitly enter the values calculated in the DDM macro. For the ''DDM_a'' macro, the third argument is ''a'', the ratio of formula mass to the number of square electrons. 

As an explicit side-effect, these macros also create the following parameters, where # represents the phase number as defined by the first argument. These can be used at will in further equations or macros.

| DDM_w_#      | Weight percentage of phase # | 
| DDM_m_#      | “Mass” of phase # | 
| DDM_m_total  | Total “mass” of all phases | 
| DDM_A_#      | Numerical area of phase # | 
| DDM_a_#      | M/n2 ratio of phase # | 
| DDM_n2_#     | Number of square electrons of phase # | 
| DDM_M_#      | Formula mass of phase # | 


Example input files are given below using the data from the IUCr CPD QPA RR, and are available from https://www.iucr.org/__data/iucr/powder/QARR/intro.htm

Contributor: Matthew Rowles. All mathematical derivations by Hideo Toraya.


  - B. O. Loopstra and H. M. Rietveld, Acta Crystallographica B, 1969, 25, 787-791.
  - H. M. Rietveld, J. Appl. Crystallogr., 1969, 2, 65-71.
  - R. Hill and C. Howard, J. Appl. Crystallogr., 1987, 20, 467-474.
  - D. L. Bish and S. A. Howard, J. Appl. Crystallogr., 1988, 21, 86-91.
  - N. V. Y. Scarlett and I. C. Madsen, Powder Diffr., 2006, 21, 278-284.
  - H. Toraya, J. Appl. Crystallogr., 2016, 49, 1508-1516.
  - H. Toraya, J. Appl. Crystallogr., 2017, 50, 820-829.
  - H. Toraya, J. Appl. Crystallogr., 2018, 51, 446-455.
  - H. Toraya and K. Omote, J. Appl. Crystallogr., 2019, 52, 13-22.
  - H. Toraya, J. Appl. Crystallogr., 2019, 52, 520-531.


===== Macros =====

The main ''DDM'' macro:
<code topas>
macro DDM(m,n,chemical_formula,wt) {
	'formula masses'
	macro H  {   1.008 } macro He {   4.003 } macro Li {   6.941 } macro Be {   9.012 } macro B  {  10.811 }
	macro C  {  12.011 } macro N  {  14.007 } macro O  {  15.999 } macro F  {  18.998 } macro Ne {  20.18  }
	macro Na {  22.99  } macro Mg {  24.305 } macro Al {  26.982 } macro Si {  28.086 } macro P  {  30.974 }
	macro S  {  32.065 } macro Cl {  35.453 } macro Ar {  39.948 } macro K  {  39.098 } macro Ca {  40.078 }
	macro Sc {  44.956 } macro Ti {  47.867 } macro V  {  50.942 } macro Cr {  51.996 } macro Mn {  54.938 }
	macro Fe {  55.845 } macro Co {  58.933 } macro Ni {  58.693 } macro Cu {  63.546 } macro Zn {  65.39  }
	macro Ga {  69.723 } macro Ge {  72.64  } macro As {  74.922 } macro Se {  78.96  } macro Br {  79.904 }
	macro Kr {  83.8   } macro Rb {  85.468 } macro Sr {  87.62  } macro Y  {  88.906 } macro Zr {  91.224 }
	macro Nb {  92.906 } macro Mo {  95.94  } macro Tc {  98     } macro Ru { 101.07  } macro Rh { 102.906 }
	macro Pd { 106.42  } macro Ag { 107.868 } macro Cd { 112.411 } macro In { 114.818 } macro Sn { 118.71  }
	macro Sb { 121.76  } macro Te { 127.6   } macro I  { 126.905 } macro Xe { 131.293 } macro Cs { 132.906 }
	macro Ba { 137.327 } macro La { 138.906 } macro Ce { 140.116 } macro Pr { 140.908 } macro Nd { 144.24  }
	macro Pm { 145     } macro Sm { 150.36  } macro Eu { 151.964 } macro Gd { 157.25  } macro Tb { 158.925 }
	macro Dy { 162.5   } macro Ho { 164.93  } macro Er { 167.259 } macro Tm { 168.934 } macro Yb { 173.04  }
	macro Lu { 174.967 } macro Hf { 178.49  } macro Ta { 180.948 } macro W  { 183.84  } macro Re { 186.207 }
	macro Os { 190.23  } macro Ir { 192.217 } macro Pt { 195.078 } macro Au { 196.967 } macro Hg { 200.59  }
	macro Tl { 204.383 } macro Pb { 207.2   } macro Bi { 208.98  } macro Po { 209     } macro At { 210     }
	macro Rn { 222     } macro Fr { 223     } macro Ra { 226     } macro Ac { 227     } macro Th { 232.038 }
	macro Pa { 231.036 } macro U  { 238.029 }
	
	prm DDM_M_##m =chemical_formula; 'formula mass'
	#delete_macros { H  He Li Be B  C  N  O  F  Ne Na Mg Al Si P  S  Cl Ar K  Ca Sc Ti V  Cr Mn Fe Co Ni Cu Zn Ga 
	                 Ge As Se Br Kr Rb Sr Y  Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I  Xe Cs Ba La Ce Pr Nd Pm Sm 
	                 Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W  Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Th Pa U }
		
	'square electrons'
	macro  H  { ( 1^2) } macro  He { ( 2^2) } macro  Li { ( 3^2) } macro  Be { ( 4^2) } macro  B  { (5^2) }
	macro  C  { ( 6^2) } macro  N  { ( 7^2) } macro  O  { ( 8^2) } macro  F  { ( 9^2) } macro  Ne { (10^2) }
	macro  Na { (11^2) } macro  Mg { (12^2) } macro  Al { (13^2) } macro  Si { (14^2) } macro  P  { (15^2) }
	macro  S  { (16^2) } macro  Cl { (17^2) } macro  Ar { (18^2) } macro  K  { (19^2) } macro  Ca { (20^2) }
	macro  Sc { (21^2) } macro  Ti { (22^2) } macro  V  { (23^2) } macro  Cr { (24^2) } macro  Mn { (25^2) }
	macro  Fe { (26^2) } macro  Co { (27^2) } macro  Ni { (28^2) } macro  Cu { (29^2) } macro  Zn { (30^2) }
	macro  Ga { (31^2) } macro  Ge { (32^2) } macro  As { (33^2) } macro  Se { (34^2) } macro  Br { (35^2) }
	macro  Kr { (36^2) } macro  Rb { (37^2) } macro  Sr { (38^2) } macro  Y  { (39^2) } macro  Zr { (40^2) }
	macro  Nb { (41^2) } macro  Mo { (42^2) } macro  Tc { (43^2) } macro  Ru { (44^2) } macro  Rh { (45^2) }
	macro  Pd { (46^2) } macro  Ag { (47^2) } macro  Cd { (48^2) } macro  In { (49^2) } macro  Sn { (50^2) }
	macro  Sb { (51^2) } macro  Te { (52^2) } macro  I  { (53^2) } macro  Xe { (54^2) } macro  Cs { (55^2) }
	macro  Ba { (56^2) } macro  La { (57^2) } macro  Ce { (58^2) } macro  Pr { (59^2) } macro  Nd { (60^2) }
	macro  Pm { (61^2) } macro  Sm { (62^2) } macro  Eu { (63^2) } macro  Gd { (64^2) } macro  Tb { (65^2) }
	macro  Dy { (66^2) } macro  Ho { (67^2) } macro  Er { (68^2) } macro  Tm { (69^2) } macro  Yb { (70^2) }
	macro  Lu { (71^2) } macro  Hf { (72^2) } macro  Ta { (73^2) } macro  W  { (74^2) } macro  Re { (75^2) }
	macro  Os { (76^2) } macro  Ir { (77^2) } macro  Pt { (78^2) } macro  Au { (79^2) } macro  Hg { (80^2) }
	macro  Tl { (81^2) } macro  Pb { (82^2) } macro  Bi { (83^2) } macro  Po { (84^2) } macro  At { (85^2) }
	macro  Rn { (86^2) } macro  Fr { (87^2) } macro  Ra { (88^2) } macro  Ac { (89^2) } macro  Th { (90^2) }
	macro  Pa { (91^2) } macro  U  { (92^2) }
	
	prm DDM_n2_##m = chemical_formula ; 'square electrons'
	#delete_macros { H  He Li Be B  C  N  O  F  Ne Na Mg Al Si P  S  Cl Ar K  Ca Sc Ti V  Cr Mn Fe Co Ni Cu Zn Ga 
	                 Ge As Se Br Kr Rb Sr Y  Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I  Xe Cs Ba La Ce Pr Nd Pm Sm 
	                 Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W  Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Th Pa U }
	
	prm DDM_a_##m = DDM_M_##m / DDM_n2_##m; 'mass per square electron'
	prm DDM_A_##m = Get(numerical_area); 'numerical area of phase'
	prm DDM_m_##m = DDM_a_##m DDM_A_##m; ' "mass" of this phase'
	
	'calculating total weight of all phases so I can calculate weight fraction'
	'  currently limited to only 10 phases, but can be easily extended.'
	#m_if m == 1;
		#m_if     n == 1; prm DDM_m_total = DDM_m_1;
		#m_elseif n == 2; prm DDM_m_total = DDM_m_1+DDM_m_2;
		#m_elseif n == 3; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3;
		#m_elseif n == 4; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4;
		#m_elseif n == 5; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5;
		#m_elseif n == 6; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6;
		#m_elseif n == 7; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7;
		#m_elseif n == 8; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7+DDM_m_8;
		#m_elseif n == 9; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7+DDM_m_8+DDM_m_9;
		#m_elseif n ==10; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7+DDM_m_8+DDM_m_9+DDM_m_10;
		#m_endif
	#m_endif
	
	prm DDM_w_##m = 100 DDM_m_##m / DDM_m_total; : wt 'weight percentage'
}
</code>


The ''DDM_M_n2'' macro:
<code topas>
macro DDM_M_n2(m,n,M,n2,wt) {

	prm DDM_M_##m = M; 'formula mass'
	prm DDM_n2_##m = n2; 'square electrons'
	prm DDM_a_##m = DDM_M_##m / DDM_n2_##m; 'mass per square electron'
	prm DDM_A_##m = Get(numerical_area); 'numerical area of phase'
	prm DDM_m_##m = DDM_a_##m DDM_A_##m; ' "mass" of this phase'
	
	'calculating total weight of all phases so I can calculate weight fraction'
	'  currently limited to only 10 phases, but can be easily extended.'
	#m_if m == 1;
		#m_if     n == 1; prm DDM_m_total = DDM_m_1;
		#m_elseif n == 2; prm DDM_m_total = DDM_m_1+DDM_m_2;
		#m_elseif n == 3; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3;
		#m_elseif n == 4; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4;
		#m_elseif n == 5; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5;
		#m_elseif n == 6; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6;
		#m_elseif n == 7; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7;
		#m_elseif n == 8; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7+DDM_m_8;
		#m_elseif n == 9; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7+DDM_m_8+DDM_m_9;
		#m_elseif n ==10; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7+DDM_m_8+DDM_m_9+DDM_m_10;
		#m_endif
	#m_endif
	
	prm DDM_w_##m = 100 DDM_m_##m / DDM_m_total; : wt 'weight percentage'
}
</code>


The ''DDM_a'' macro:
<code topas>
macro DDM_a(m,n,alpha,wt) {

	prm DDM_a_##m = alpha; 'mass per square electron'
	prm DDM_A_##m = Get(numerical_area); 'numerical area of phase'
	prm DDM_m_##m = DDM_a_##m DDM_A_##m; ' "mass" of this phase'
	
	'calculating total weight of all phases so I can calculate weight fraction'
	'  currently limited to only 10 phases, but can be easily extended.'
	#m_if m == 1;
		#m_if     n == 1; prm DDM_m_total = DDM_m_1;
		#m_elseif n == 2; prm DDM_m_total = DDM_m_1+DDM_m_2;
		#m_elseif n == 3; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3;
		#m_elseif n == 4; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4;
		#m_elseif n == 5; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5;
		#m_elseif n == 6; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6;
		#m_elseif n == 7; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7;
		#m_elseif n == 8; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7+DDM_m_8;
		#m_elseif n == 9; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7+DDM_m_8+DDM_m_9;
		#m_elseif n ==10; prm DDM_m_total = DDM_m_1+DDM_m_2+DDM_m_3+DDM_m_4+DDM_m_5+DDM_m_6+DDM_m_7+DDM_m_8+DDM_m_9+DDM_m_10;
		#m_endif
	#m_endif
	
	prm DDM_w_##m = 100 DDM_m_##m / DDM_m_total; : wt 'weight fraction'
}
</code>


===== Example input files =====

This first input file provides an example usage with ''str'' phases. It also allows for a comparison in quantification values between the DD and Hill/Howard methods.
<code topas>
xdd "cpd-1g.raw"
	r_exp  9.0848375 r_exp_dash  9.20330023
	r_wp  11.2186846 r_wp_dash  11.3649719
	r_p  8.24844865 r_p_dash  8.55083901
	weighted_Durbin_Watson  1.3712468 gof  1.23488006
	
	bkg bg -0.255565762`  29.2852008` -12.8972512`  9.24105796` -3.46070069`  0.332234403`
	One_on_X(oneonx, 1177.41963`)

	Specimen_Displacement(sd, -0.03253`)
	LP_Factor(26.4)
	Rp 173
	Rs 173
	axial_conv 
		filament_length  12
		sample_length  15
		receiving_slit_length  12
		primary_soller_angle  4.6
		secondary_soller_angle  4.6
		axial_n_beta  30
	Slit_Width( 0.3)
	Divergence( 1)
	lam
		ymin_on_ymax  0.0001
		la  0.0159 lo  1.534753 lh  3.6854
		la  0.5791 lo  1.540596 lh  0.437
		la  0.0762 lo  1.541058 lh  0.6
		la  0.2417 lo  1.54441 lh  0.52
		la  0.0871 lo  1.544721 lh  0.62

	start_X 7
	finish_X 147.5
	

	str 
		phase_name "Cor"
		
		DDM(1,3,Al 2 + O 3, 29.78243`)
		MVW( 611.768, 254.824`, 33.746`)
		
		scale sc_cor  0.000356672539`
		LVol_FWHM_CS_G_L( 1, 136.44164`, 0.89, 164.17169`,@, 298.29820`,@, 308.33263`)
		e0_from_Strain( 0.00005`,@, 0.00010`_LIMIT_MIN_0.0001,@, 0.02152`)
		space_group "R_-3_C"
		Trigonal(acor  4.759054` min 4.7 max 4.8, ccor  12.991775` min 12.95 max 13.05)
		site Al num_posns  12 x  0 y  0 z  0.35218 occ Al+3  1 beq  0.2259
		site O num_posns  18 x  0.30603 y  0 z  0.25 occ O-2  1 beq  0.2367
	
	str 
		phase_name "Flu"
		
		DDM(2,3,Ca + F 2, 34.10413`)
		MVW( 312.299, 163.118`, 33.433`)

		scale sc_flu  0.00108136708`
		LVol_FWHM_CS_G_L( 1, 597.30690`, 0.89, 835.04027`,,,csL_flu, 938.24749`)
		e0_from_Strain( 0.00014`,,,strL_flu, 0.06547`)
		space_group "F_M_-3_M"
		Cubic(acell_flu  5.463878` min 5.4 max 5.5)
		site Ca num_posns  4 x  0 y  0 z  0 occ Ca+2  1 beq  0.25
		site F num_posns  8 x  0.25 y  0.25 z  0.25 occ F-1  1 beq  0.5
	
	str
		phase_name "Zin"
		
		DDM(3,3,Zn + O, 36.11344`)
		MVW( 162.817, 47.616`, 32.821`)

		scale sc_zin  0.00697540954`
		LVol_FWHM_CS_G_L( 1, 147.83204`, 0.89, 206.67049`,,,csL_zin, 232.21403`)
		space_group "P_63_M_C"
		Hexagonal(acell_zin  3.249678` min 3.2 max 3.3, ccell_zin  5.206440` min 4.8 max 5.5)		
		site Zn num_posns  2 x =1/3; y =2/3; z  0    occ Zn+2  1 beq  0.25
		site O  num_posns  2 x =1/3; y =2/3; z =3/8; occ O-2   1 beq  0.5
</code>


This second input file provides an example usage with ''hkl_Is'' phases where the intensities of the individual reflections are allowed to freely refine.
<code topas>

xdd "cpd-1g.raw"
	r_exp  9.0145123 r_exp_dash  9.43912697
	r_wp  10.1211 r_wp_dash  10.5978387
	r_p  7.07515051 r_p_dash  7.56235889
	weighted_Durbin_Watson  1.67803374 gof  1.12275624
	
	bkg bg  3.98842635`  23.0525098` -10.8652563`  5.46953231` -2.6256097` -1.10572562`
	One_on_X(oneonx, 1034.34459`)

	Specimen_Displacement(sd, -0.03317`)
	LP_Factor(26.4)
	Rp 173
	Rs 173
	axial_conv 
		filament_length  12
		sample_length  15
		receiving_slit_length  12
		primary_soller_angle  4.6
		secondary_soller_angle  4.6
		axial_n_beta  30
	Slit_Width( 0.3)
	Divergence( 1)
	lam
		ymin_on_ymax  0.0001
		la  0.0159 lo  1.534753 lh  3.6854
		la  0.5791 lo  1.540596 lh  0.437
		la  0.0762 lo  1.541058 lh  0.6
		la  0.2417 lo  1.54441 lh  0.52
		la  0.0871 lo  1.544721 lh  0.62

	start_X 7
	finish_X 147.5
	

	hkl_Is 
		phase_name "Cor"
		
		DDM(1,3,Al 2 + O 3, 30.72756`)
				
		LVol_FWHM_CS_G_L( 1, 155.73193`, 0.89, 194.67508`,@, 409.73464`_LIMIT_MIN_0.3,@, 312.46150`)
		e0_from_Strain( 0.00007`,@, 0.01272`_LIMIT_MIN_0.0001,@, 0.02604`)
		Trigonal(acor  4.758979` min 4.7 max 4.8, ccor  12.991822` min 12.95 max 13.05)
		space_group "R_-3_C"
		load hkl_m_d_th2 I '{{{'
		{
			   1   0  -2   6    3.480061      25.57622     cor_pk01     4.62293`
			   1   0   4   6    2.551003      35.15059     cor_pk02     15.07662`
			   2  -1   0   6    2.379489      37.77658     cor_pk03     7.07115`
			   0   0   6   2    2.165304      41.67834     cor_pk04     0.24150`
			   2  -1   3  12    2.085423      43.35385     cor_pk05     26.14997`
			   2   0   2   6    1.964232      46.17824     cor_pk06     0.39908`
			   2   0  -4   6    1.740030      52.55157     cor_pk07     18.72297`
			   2  -1   6  12    1.601481      57.50031     cor_pk08     48.57334`
			   3  -1   1  12    1.546663      59.74063     cor_pk09     1.53223`
			   3  -1  -2  12    1.514796      61.13008     cor_pk10     1.97109`
			   1   0  -8   6    1.510913      61.30407     cor_pk11   4.58544`
			   3  -1   4  12    1.404555      66.51853     cor_pk12   23.15010`
			   3   0   0   6    1.373799      68.20935     cor_pk13   37.10533`
			   3  -1  -5  12    1.336042      70.41682     cor_pk14   0.87001`
			   2   0   8   6    1.275501      74.30201     cor_pk15   1.32460`
			   1   0  10   6    1.239077      76.87650     cor_pk16   16.80035`
			   2  -1   9  12    1.234182      77.23768     cor_pk17   7.05237`
			   3  -1   7  12    1.193174      80.41941     cor_pk18   0.45131`
			   4  -2   0   6    1.189745      80.69896     cor_pk19   5.30595`
			   3   0   6   6    1.160020      83.21720     cor_pk20   0.15832`
			   3   0  -6   6    1.160020      83.21720     cor_pk21     0.15832`
			   4  -2   3  12    1.147238      84.35617     cor_pk22     4.61975`
			   4  -1  -1  12    1.138671      85.13973     cor_pk23     0.00003`
			   4  -1   2  12    1.125773      86.35160     cor_pk24     4.00388`
			   3  -1  -8  12    1.124177      86.50439     cor_pk25     3.20760`
			   2   0 -10   6    1.099000      88.99978     cor_pk26     8.93622`
			   0   0  12   2    1.082652      90.71286     cor_pk27     2.26102`
			   4  -1  -4  12    1.078244      91.18820     cor_pk28     9.92676`
			   4  -1   5  12    1.046300      94.81934     cor_pk29     0.00009`
			   4  -2   6  12    1.042712      95.24925     cor_pk30     34.94990`
			   4   0  -2   6    1.017628      98.39293     cor_pk31     3.73943`
			   3  -1  10  12    0.997724     101.07760     cor_pk32   18.03021`
			   2  -1  12  12    0.985444     102.82864     cor_pk33   1.28018`
			   4   0   4   6    0.982116     103.31656     cor_pk34   3.84701`
			   4  -1  -7  12    0.973287     104.64056     cor_pk35   0.12173`
			   5  -2   1  12    0.943019     109.53989     cor_pk36   1.12322`
			   3  -1 -11  12    0.941144     109.86383     cor_pk37   0.46183`
			   5  -2  -2  12    0.935654     110.82749     cor_pk38   0.27050`
			   4  -1   8  12    0.934736     110.99074     cor_pk39   5.14339`
			   4  -2   9  12    0.918103     114.07151     cor_pk40   3.65067`
			   5  -2   4  12    0.907828     116.09914     cor_pk41   16.45021`
			   1   0 -14   6    0.905322     116.60968     cor_pk42   6.39990`
			   5  -1   0  12    0.899362     117.85022     cor_pk43   8.84487`
			   5  -2  -5  12    0.888515     120.21215     cor_pk44   0.54551`
			   5  -1   3  12    0.880574     122.03515     cor_pk45   2.25026`
			   5  -1  -3  12    0.880574     122.03515     cor_pk46   2.25026`
			   4   0  -8   6    0.870015     124.59776     cor_pk47   3.15392`
			   4  -1 -10  12    0.858187     127.68554     cor_pk48   17.21667`
			   3   0  12   6    0.850334     129.88323     cor_pk49   3.77955`
			   3   0 -12   6    0.850334     129.88323     cor_pk50   3.77955`
			   2   0  14   6    0.846148     131.10984     cor_pk51   7.40862`
			   5  -2   7  12    0.842487     132.21724     cor_pk52   0.82661`
			   3  -1  13  12    0.841149     132.63040     cor_pk53   0.13019`
			   5  -1   6  12    0.830568     136.07696     cor_pk54   13.25630`
			   5  -1  -6  12    0.830568     136.07696     cor_pk55   13.25630`
			   4  -1  11  12    0.821380     139.37393     cor_pk56   1.14600`
			   5   0   2   6    0.817722     140.78189     cor_pk57   0.65254`
			   5  -2  -8  12    0.817110     141.02369     cor_pk58   1.16832`
			   2  -1  15  12    0.813882     142.32912     cor_pk59   4.13251`
			   4   0  10   6    0.807287     145.17719     cor_pk60   10.55744`
			   4  -2  12  12    0.800740     148.30093     cor_pk61   0.00048`
			   5   0  -4   6    0.798952     149.21733     cor_pk62   96.08941`
		}
'}}}'
	
	hkl_Is 
		phase_name "Flu"
		
		DDM(2,3,Ca + F 2, 33.55659`)

		LVol_FWHM_CS_G_L( 1, 401.22091`, 0.89, 560.91034`,,,csL_flu, 630.23634`)
		e0_from_Strain( 0.00012`,,,strL_flu, 0.05406`)
		space_group "F_M_-3_M"
		Cubic(acell_flu  5.463929` min 5.4 max 5.5)
		load hkl_m_d_th2 I '{{{'
		{
			   1   1   1   8    3.154601      28.26704     flu_pk01  36.45299`
			   2   0   0   6    2.731964      32.75415     flu_pk02     0.31637`
			   2   2   0  12    1.931790      46.99989     flu_pk03  124.65238`
			   3   1   1  24    1.647436      55.75383     flu_pk04   57.94099`
			   2   2   2   8    1.577300      58.46633     flu_pk05     0.72057`
			   4   0   0   6    1.365982      68.65398     flu_pk06   35.19172`
			   3   3   1  24    1.253511      75.83298     flu_pk07   35.80714`
			   4   2   0  24    1.221772      78.17054     flu_pk08    2.66242`
			   4   2   2  24    1.115320      87.36351     flu_pk09   85.44234`
			   3   3   3   8    1.051534      94.20073     flu_pk10    18.88074`
			   5   1   1  24    1.051534      94.20073     flu_pk11    18.88074`
			   4   4   0  12    0.965895     105.78338    flu_pk12   33.13100`
			   5   3   1  48    0.923573     113.03237    flu_pk13   43.74909`
			   4   4   2  24    0.910655     115.53112    flu_pk14    2.43207`
			   6   0   0   6    0.910655     115.53112    flu_pk15    2.43207`
			   6   2   0  24    0.863923     126.15710    flu_pk16   51.00086`
			   5   3   3  24    0.833241     135.17404    flu_pk17   18.13935`
			   6   2   2  24    0.823718     138.50396    flu_pk18    0.07424`
		}
'}}}'
	
	hkl_Is
		phase_name "Zin"
		
		DDM(3,3,Zn + O, 35.71585`)

		LVol_FWHM_CS_G_L( 1, 153.44741`, 0.89, 214.52081`,,,csL_zin, 241.03462`)
		space_group "P_63_M_C"
		Hexagonal(acell_zin  3.249654` min 3.2 max 3.3, ccell_zin  5.206477` min 4.8 max 5.5)		
		load hkl_m_d_th2 I '{{{'
		{
			   1   0   0   6    2.814283      31.77033     zin_pk01    39.73252`
			   0   0   2   2    2.603238      34.42302     zin_pk02    34.06743`
			   1   0   1  12    2.475749      36.25558     zin_pk03    90.33878`
			   1   0   2  12    1.911027      47.54182     zin_pk04    36.41711`
			   2  -1   0   6    1.624827      56.59893     zin_pk05    84.16870`
			   1   0   3  12    1.477196      62.86040     zin_pk06    95.37484`
			   2   0   0   6    1.407141      66.38045     zin_pk07    19.07228`
			   2  -1   2  12    1.378373      67.95203     zin_pk08    97.28395`
			   2   0   1  12    1.358404      69.09109     zin_pk09    48.05522`
			   0   0   4   2    1.301619      72.56967     zin_pk10    8.33230`
			   2   0   2  12    1.237874      76.96489     zin_pk11    18.93243`
			   1   0   4  12    1.181383      81.38980     zin_pk12     9.95841`
			   2   0   3  12    1.093010      89.61862     zin_pk13     52.41764`
			   3  -1   0  12    1.063699      92.79956     zin_pk14     19.38349`
			   3  -1   1  24    1.042171      95.31438     zin_pk15     45.99950`
			   2  -1   4  12    1.015858      98.62448     zin_pk16     31.46827`
			   3  -1   2  24    0.984671     102.94147     zin_pk17   22.71564`
			   1   0   5  12    0.976590     104.14012     zin_pk18   42.08322`
			   2   0   4  12    0.955513     107.44513     zin_pk19  6.87601`
			   3   0   0   6    0.938094     110.39628     zin_pk20  28.25685`
			   3   0   1  12    0.923228     113.09704     zin_pk21  2.26790`
			   3  -1   3  24    0.906909     116.28570     zin_pk22  67.06570`
			   3   0   2  12    0.882541     121.57570     zin_pk23  36.39947`
			   0   0   6   2    0.867746     125.17121     zin_pk24  4.42764`
			   2   0   5  12    0.837034     133.93149     zin_pk25  26.70439`
			   1   0   6  12    0.829223     136.54012     zin_pk26  5.85450`
			   3   0   3  12    0.825250     137.94623     zin_pk27  0.44415`
			   3  -1   4  24    0.823649     138.52944     zin_pk28  12.54989`
			   4  -2   0   6    0.812413     142.94096     zin_pk29  18.42862`
		}
'}}}'
</code>