Table of Contents
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 Al2O3, then the formula would be entered as “Al 2 + O 3”. If it were MgCO3.2.5H2O, 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:
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' }
The DDM_M_n2
macro:
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' }
The DDM_a
macro:
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' }
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.
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
This second input file provides an example usage with hkl_Is
phases where the intensities of the individual reflections are allowed to freely refine.
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` } '}}}'