PbSO₄ — powder neutron CW — Bérar-Baldinozzi asymmetry¶

Verifies the empirical Bérar-Baldinozzi asymmetry workflow for anglesite. The page fits cryspy asymmetry parameters because FullProf and cryspy use different coefficient conventions.

In [2]:

import easydiffraction as edi
from easydiffraction import ExperimentFactory
from easydiffraction import StructureFactory
from easydiffraction.analysis import verification as verify

import easydiffraction as edi from easydiffraction import ExperimentFactory from easydiffraction import StructureFactory from easydiffraction.analysis import verification as verify

Build the project¶

In [3]:

project = edi.Project()

project = edi.Project()

Define the structure¶

In [4]:

structure = StructureFactory.from_scratch(name='pbso4')

structure.space_group.name_h_m = 'P n m a'  # FullProf Space group symbol

structure.cell.length_a = 8.479506  # FullProf a
structure.cell.length_b = 5.397256  # FullProf b
structure.cell.length_c = 6.958973  # FullProf c

structure.atom_sites.create(
    id='Pb',  # FullProf Atom
    type_symbol='Pb',  # FullProf Typ
    fract_x=0.18752,  # FullProf X
    fract_y=0.25,  # FullProf Y
    fract_z=0.16705,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=1.39017,  # FullProf Biso
)
structure.atom_sites.create(
    id='S',  # FullProf Atom
    type_symbol='S',  # FullProf Typ
    fract_x=0.06549,  # FullProf X
    fract_y=0.25,  # FullProf Y
    fract_z=0.68373,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=0.39270,  # FullProf Biso
)
structure.atom_sites.create(
    id='O1',  # FullProf Atom
    type_symbol='O',  # FullProf Typ
    fract_x=0.90816,  # FullProf X
    fract_y=0.25,  # FullProf Y
    fract_z=0.59544,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=1.99307,  # FullProf Biso
)
structure.atom_sites.create(
    id='O2',  # FullProf Atom
    type_symbol='O',  # FullProf Typ
    fract_x=0.19355,  # FullProf X
    fract_y=0.25,  # FullProf Y
    fract_z=0.54331,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=1.47771,  # FullProf Biso
)
structure.atom_sites.create(
    id='O3',  # FullProf Atom
    type_symbol='O',  # FullProf Typ
    fract_x=0.08109,  # FullProf X
    fract_y=0.02727,  # FullProf Y
    fract_z=0.80869,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=1.30007,  # FullProf Biso
)

project.structures.add(structure)

structure = StructureFactory.from_scratch(name='pbso4') structure.space_group.name_h_m = 'P n m a' # FullProf Space group symbol structure.cell.length_a = 8.479506 # FullProf a structure.cell.length_b = 5.397256 # FullProf b structure.cell.length_c = 6.958973 # FullProf c structure.atom_sites.create( id='Pb', # FullProf Atom type_symbol='Pb', # FullProf Typ fract_x=0.18752, # FullProf X fract_y=0.25, # FullProf Y fract_z=0.16705, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=1.39017, # FullProf Biso ) structure.atom_sites.create( id='S', # FullProf Atom type_symbol='S', # FullProf Typ fract_x=0.06549, # FullProf X fract_y=0.25, # FullProf Y fract_z=0.68373, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=0.39270, # FullProf Biso ) structure.atom_sites.create( id='O1', # FullProf Atom type_symbol='O', # FullProf Typ fract_x=0.90816, # FullProf X fract_y=0.25, # FullProf Y fract_z=0.59544, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=1.99307, # FullProf Biso ) structure.atom_sites.create( id='O2', # FullProf Atom type_symbol='O', # FullProf Typ fract_x=0.19355, # FullProf X fract_y=0.25, # FullProf Y fract_z=0.54331, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=1.47771, # FullProf Biso ) structure.atom_sites.create( id='O3', # FullProf Atom type_symbol='O', # FullProf Typ fract_x=0.08109, # FullProf X fract_y=0.02727, # FullProf Y fract_z=0.80869, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=1.30007, # FullProf Biso ) project.structures.add(structure)

Load the FullProf reference¶

In [5]:

FULLPROF_PROJECT_DIR = 'pd-neut-cwl_pbso4_beba-asymmetry'
FULLPROF_PRF_FILE = 'pbso4.prf'
FULLPROF_SUM_FILE = 'pbso4.sum'
FULLPROF_BAC_FILE = 'pbso4.bac'
FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_SUM_FILE)

FULLPROF_ZERO = -0.08424  # FullProf Zero
FULLPROF_SCALE = 1.463815  # FullProf Scale
FULLPROF_WAVELENGTH = 1.912000  # FullProf Lambda
FULLPROF_U = 0.153402  # FullProf U
FULLPROF_V = -0.453103  # FullProf V
FULLPROF_W = 0.419409  # FullProf W
FULLPROF_X = 0.0  # FullProf X
FULLPROF_Y = 0.086818  # FullProf Y
FULLPROF_WDT = 30.0  # FullProf Wdt
FULLPROF_ASY_1 = 0.29465  # FullProf Asy1
FULLPROF_ASY_2 = 0.02261  # FullProf Asy2
FULLPROF_ASY_3 = -0.10961  # FullProf Asy3
FULLPROF_ASY_4 = 0.04941  # FullProf Asy4

x, calc_fullprof = verify.load_fullprof_calc_profile(
    FULLPROF_PROJECT_DIR,
    FULLPROF_PRF_FILE,
    FULLPROF_BAC_FILE,
    FULLPROF_ZERO,
)

FULLPROF_PROJECT_DIR = 'pd-neut-cwl_pbso4_beba-asymmetry' FULLPROF_PRF_FILE = 'pbso4.prf' FULLPROF_SUM_FILE = 'pbso4.sum' FULLPROF_BAC_FILE = 'pbso4.bac' FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_SUM_FILE) FULLPROF_ZERO = -0.08424 # FullProf Zero FULLPROF_SCALE = 1.463815 # FullProf Scale FULLPROF_WAVELENGTH = 1.912000 # FullProf Lambda FULLPROF_U = 0.153402 # FullProf U FULLPROF_V = -0.453103 # FullProf V FULLPROF_W = 0.419409 # FullProf W FULLPROF_X = 0.0 # FullProf X FULLPROF_Y = 0.086818 # FullProf Y FULLPROF_WDT = 30.0 # FullProf Wdt FULLPROF_ASY_1 = 0.29465 # FullProf Asy1 FULLPROF_ASY_2 = 0.02261 # FullProf Asy2 FULLPROF_ASY_3 = -0.10961 # FullProf Asy3 FULLPROF_ASY_4 = 0.04941 # FullProf Asy4 x, calc_fullprof = verify.load_fullprof_calc_profile( FULLPROF_PROJECT_DIR, FULLPROF_PRF_FILE, FULLPROF_BAC_FILE, FULLPROF_ZERO, )

Create the experiment¶

In [6]:

experiment = ExperimentFactory.from_scratch(
    name='pbso4',
    sample_form='powder',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
    scattering_type='bragg',
)
verify.set_reference_as_measured(experiment, x, calc_fullprof)

experiment.linked_structures.create(structure_id='pbso4', scale=FULLPROF_SCALE)

experiment.instrument.setup_wavelength = FULLPROF_WAVELENGTH
experiment.instrument.calib_twotheta_offset = FULLPROF_ZERO

experiment.peak.type = 'pseudo-voigt'
experiment.peak.broad_gauss_u = FULLPROF_U
experiment.peak.broad_gauss_v = FULLPROF_V
experiment.peak.broad_gauss_w = FULLPROF_W
experiment.peak.broad_lorentz_x = FULLPROF_X
experiment.peak.broad_lorentz_y = FULLPROF_Y

experiment.peak.cutoff_fwhm = FULLPROF_WDT

project.experiments.add(experiment)

experiment = ExperimentFactory.from_scratch( name='pbso4', sample_form='powder', beam_mode='constant wavelength', radiation_probe='neutron', scattering_type='bragg', ) verify.set_reference_as_measured(experiment, x, calc_fullprof) experiment.linked_structures.create(structure_id='pbso4', scale=FULLPROF_SCALE) experiment.instrument.setup_wavelength = FULLPROF_WAVELENGTH experiment.instrument.calib_twotheta_offset = FULLPROF_ZERO experiment.peak.type = 'pseudo-voigt' experiment.peak.broad_gauss_u = FULLPROF_U experiment.peak.broad_gauss_v = FULLPROF_V experiment.peak.broad_gauss_w = FULLPROF_W experiment.peak.broad_lorentz_x = FULLPROF_X experiment.peak.broad_lorentz_y = FULLPROF_Y experiment.peak.cutoff_fwhm = FULLPROF_WDT project.experiments.add(experiment)

Peak profile type for experiment 'pbso4' changed to

pseudo-voigt

edi-cryspy VS FullProf¶

In [7]:

experiment.peak.type = 'pseudo-voigt + berar-baldinozzi asymmetry'
experiment.peak.broad_gauss_u = FULLPROF_U
experiment.peak.broad_gauss_v = FULLPROF_V
experiment.peak.broad_gauss_w = FULLPROF_W
experiment.peak.broad_lorentz_x = FULLPROF_X
experiment.peak.broad_lorentz_y = FULLPROF_Y
experiment.peak.asym_beba_a0 = FULLPROF_ASY_1
experiment.peak.asym_beba_b0 = FULLPROF_ASY_2
experiment.peak.asym_beba_a1 = FULLPROF_ASY_3
experiment.peak.asym_beba_b1 = FULLPROF_ASY_4

experiment.calculator.type = 'cryspy'

project.analysis.calculate()
calc_ed_cryspy = experiment.data.intensity_calc
LABEL_ED_CRYSPY = verify.engine_label('cryspy')

project.display.pattern_comparison(
    'pbso4',
    reference=calc_fullprof,
    candidate=calc_ed_cryspy,
    reference_label=FULLPROF_LABEL,
    candidate_label=LABEL_ED_CRYSPY,
)

experiment.peak.type = 'pseudo-voigt + berar-baldinozzi asymmetry' experiment.peak.broad_gauss_u = FULLPROF_U experiment.peak.broad_gauss_v = FULLPROF_V experiment.peak.broad_gauss_w = FULLPROF_W experiment.peak.broad_lorentz_x = FULLPROF_X experiment.peak.broad_lorentz_y = FULLPROF_Y experiment.peak.asym_beba_a0 = FULLPROF_ASY_1 experiment.peak.asym_beba_b0 = FULLPROF_ASY_2 experiment.peak.asym_beba_a1 = FULLPROF_ASY_3 experiment.peak.asym_beba_b1 = FULLPROF_ASY_4 experiment.calculator.type = 'cryspy' project.analysis.calculate() calc_ed_cryspy = experiment.data.intensity_calc LABEL_ED_CRYSPY = verify.engine_label('cryspy') project.display.pattern_comparison( 'pbso4', reference=calc_fullprof, candidate=calc_ed_cryspy, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY, )

⚠️ Switching peak profile type adds these settings with defaults:                                                                 
   • asym_beba_a0=0.0                                                                                                             
   • asym_beba_a1=0.0                                                                                                             
   • asym_beba_b0=0.0                                                                                                             
   • asym_beba_b1=0.0                                                                                                             

⚠️ Switching peak profile type resets these settings to defaults:                                                                 
   • broad_gauss_u: 0.153402 -> 0.01                                                                                              
   • broad_gauss_v: -0.453103 -> -0.01                                                                                            
   • broad_gauss_w: 0.419409 -> 0.02                                                                                              
   • broad_lorentz_y: 0.086818 -> 0.0                                                                                             
   • cutoff_fwhm: 30.0 -> 0.0                                                                                                     

Peak profile type for experiment 'pbso4' changed to

pseudo-voigt + berar-baldinozzi asymmetry

Calculator for experiment 'pbso4' already set to

cryspy

Loading plot…

Fit edi-cryspy to FullProf¶

In [8]:

# cryspy and FullProf implement the Berar-Baldinozzi asymmetry with
# different conventions, so the FullProf coefficients do not transfer
# 1-to-1. Freeing cryspy's own coefficients recovers the FullProf
# profile, confirming the structure and the symmetric profile are
# correct.
experiment.calculator.type = 'cryspy'

experiment.peak.asym_beba_a0.free = True
experiment.peak.asym_beba_b0.free = True
experiment.peak.asym_beba_a1.free = True
experiment.peak.asym_beba_b1.free = True

project.analysis.fit()
project.display.fit.results()

project.analysis.calculate()
calc_ed_cryspy_refined = experiment.data.intensity_calc
LABEL_ED_CRYSPY_REFINED = verify.engine_label('cryspy', note='refined')

project.display.pattern_comparison(
    'pbso4',
    reference=calc_fullprof,
    candidate=calc_ed_cryspy_refined,
    reference_label=FULLPROF_LABEL,
    candidate_label=LABEL_ED_CRYSPY_REFINED,
)

# cryspy and FullProf implement the Berar-Baldinozzi asymmetry with # different conventions, so the FullProf coefficients do not transfer # 1-to-1. Freeing cryspy's own coefficients recovers the FullProf # profile, confirming the structure and the symmetric profile are # correct. experiment.calculator.type = 'cryspy' experiment.peak.asym_beba_a0.free = True experiment.peak.asym_beba_b0.free = True experiment.peak.asym_beba_a1.free = True experiment.peak.asym_beba_b1.free = True project.analysis.fit() project.display.fit.results() project.analysis.calculate() calc_ed_cryspy_refined = experiment.data.intensity_calc LABEL_ED_CRYSPY_REFINED = verify.engine_label('cryspy', note='refined') project.display.pattern_comparison( 'pbso4', reference=calc_fullprof, candidate=calc_ed_cryspy_refined, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY_REFINED, )

Calculator for experiment 'pbso4' already set to

cryspy

Standard fitting

📋 Using experiment 🔬 'pbso4' for 'single' fitting

🚀 Starting fit process with 'lmfit (leastsq)'...

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.12	3247.87
2	8	1.13	7.69	99.8% ↓
3	14	1.82	7.69

🏆 Best goodness-of-fit (reduced χ²) is 7.69 at iteration 8

✅ Fitting complete.

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	1.82
4	🔁 Iterations	11
5	📏 Goodness-of-fit (reduced χ²)	7.69
6	📏 R-factor (Rf, %)	0.70
7	📏 R-factor squared (Rf², %)	0.93
8	📏 Weighted R-factor (wR, %)	0.93

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	pbso4	peak		asym_beba_a0		0.2947	-0.3645	0.0028	223.70 % ↓
2	pbso4	peak		asym_beba_b0		0.0226	-0.0236	0.0005	204.17 % ↓
3	pbso4	peak		asym_beba_a1		-0.1096	0.0288	0.0065	126.30 % ↓
4	pbso4	peak		asym_beba_b1		0.0494	-0.0378	0.0012	176.57 % ↓

• start = parameter value before refinement
• value = refined value from least-squares minimization
• s.u. = standard uncertainty (one sigma), from the covariance matrix
• change = relative change from start, in %; ↑ = increase, ↓ = decrease

Loading plot…

Agreement check¶

In [9]:

verify.assert_patterns_agree([
    (f'{LABEL_ED_CRYSPY_REFINED} vs {FULLPROF_LABEL}', calc_fullprof, calc_ed_cryspy_refined),
])

verify.assert_patterns_agree([ (f'{LABEL_ED_CRYSPY_REFINED} vs {FULLPROF_LABEL}', calc_fullprof, calc_ed_cryspy_refined), ])

	Comparison	Metric	Expected	Actual	OK
1	edi 0.19.0 (cryspy 0.12.1, refined) vs FullProf 8.40	Profile diff (%)	< 2.5	0.93	✅
2		Max deviation (%)	< 6	5.58	✅
3		Area ratio	0.99 to 1.01	1.0041	✅
4		Shape correlation	> 0.999	0.9999	✅

Out[9]:

True