Si — powder neutron TOF — Jorgensen-Von Dreele + size/strain¶

Verifies the isotropic microstructural size/strain broadening on top of the Jorgensen-Von Dreele pseudo-Voigt profile for a silicon time-of-flight powder pattern.

Refinement: the overall scale only; all other parameters are taken from the FullProf reference.

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='si')

structure.space_group.name_h_m = 'F d -3 m'  # FullProf Space group symbol
structure.space_group.coord_system_code = '2'

structure.cell.length_a = 5.431342  # FullProf a

structure.atom_sites.create(
    id='Si',  # FullProf Atom
    type_symbol='Si',  # FullProf Typ
    fract_x=0.125,  # FullProf X
    fract_y=0.125,  # FullProf Y
    fract_z=0.125,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=0.52448,  # FullProf Biso
)

project.structures.add(structure)

structure = StructureFactory.from_scratch(name='si') structure.space_group.name_h_m = 'F d -3 m' # FullProf Space group symbol structure.space_group.coord_system_code = '2' structure.cell.length_a = 5.431342 # FullProf a structure.atom_sites.create( id='Si', # FullProf Atom type_symbol='Si', # FullProf Typ fract_x=0.125, # FullProf X fract_y=0.125, # FullProf Y fract_z=0.125, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=0.52448, # FullProf Biso ) project.structures.add(structure)

Load the FullProf reference¶

In [5]:

FULLPROF_PROJECT_DIR = 'pd-neut-tof_si_jorgensen-von-dreele-size-strain'
FULLPROF_PRF_FILE = 'arg_si.prf'
FULLPROF_SUM_FILE = 'arg_si.sum'
FULLPROF_BAC_FILE = 'arg_si.bac'
FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_SUM_FILE)

FULLPROF_ZERO = -9.18766  # FullProf Zero
FULLPROF_SCALE = 0.6750847  # FullProf Scale
FULLPROF_TWOTHETA_BANK = 144.845  # FullProf 2ThetaBank
FULLPROF_DTT1 = 7476.91016  # FullProf Dtt1
FULLPROF_DTT2 = -1.54  # FullProf Dtt2
# FullProf Sigma-2/Sigma-1 carry the Gaussian size/strain; Gamma-2/Gamma-1
# carry the Lorentzian size/strain (raw coefficients).
FULLPROF_SIGMA_0 = 3.5544  # FullProf Sigma-0
FULLPROF_SIGMA_1 = 38.0419  # FullProf Sigma-1 = base 33.0419 + G-strain 5
FULLPROF_SIGMA_2 = 20.0  # FullProf Sigma-2 = G-size 20
FULLPROF_GAMMA_0 = 0.0  # FullProf Gamma-0
FULLPROF_GAMMA_1 = 3.5430  # FullProf Gamma-1 = base 2.5430 + L-strain 1
FULLPROF_GAMMA_2 = 2.0  # FullProf Gamma-2 = L-size 2
FULLPROF_ALPHA_0 = 0.0  # FullProf alph0
FULLPROF_ALPHA_1 = 0.597100  # FullProf alph1
FULLPROF_BETA_0 = 0.042210  # FullProf beta0
FULLPROF_BETA_1 = 0.009460  # FullProf beta1
FULLPROF_WDT = 8.2  # FullProf Wdt

# cryspy raw size/strain coefficients (additive to the base sigma/gamma)
SIZE_G = 20.0  # adds to sigma_2 (Gaussian size, d⁴)
STRAIN_G = 5.0  # adds to sigma_1 (Gaussian strain, d²)
SIZE_L = 2.0  # adds to gamma_2 (Lorentzian size, d²)
STRAIN_L = 1.0  # adds to gamma_1 (Lorentzian strain, d)

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

FULLPROF_PROJECT_DIR = 'pd-neut-tof_si_jorgensen-von-dreele-size-strain' FULLPROF_PRF_FILE = 'arg_si.prf' FULLPROF_SUM_FILE = 'arg_si.sum' FULLPROF_BAC_FILE = 'arg_si.bac' FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_SUM_FILE) FULLPROF_ZERO = -9.18766 # FullProf Zero FULLPROF_SCALE = 0.6750847 # FullProf Scale FULLPROF_TWOTHETA_BANK = 144.845 # FullProf 2ThetaBank FULLPROF_DTT1 = 7476.91016 # FullProf Dtt1 FULLPROF_DTT2 = -1.54 # FullProf Dtt2 # FullProf Sigma-2/Sigma-1 carry the Gaussian size/strain; Gamma-2/Gamma-1 # carry the Lorentzian size/strain (raw coefficients). FULLPROF_SIGMA_0 = 3.5544 # FullProf Sigma-0 FULLPROF_SIGMA_1 = 38.0419 # FullProf Sigma-1 = base 33.0419 + G-strain 5 FULLPROF_SIGMA_2 = 20.0 # FullProf Sigma-2 = G-size 20 FULLPROF_GAMMA_0 = 0.0 # FullProf Gamma-0 FULLPROF_GAMMA_1 = 3.5430 # FullProf Gamma-1 = base 2.5430 + L-strain 1 FULLPROF_GAMMA_2 = 2.0 # FullProf Gamma-2 = L-size 2 FULLPROF_ALPHA_0 = 0.0 # FullProf alph0 FULLPROF_ALPHA_1 = 0.597100 # FullProf alph1 FULLPROF_BETA_0 = 0.042210 # FullProf beta0 FULLPROF_BETA_1 = 0.009460 # FullProf beta1 FULLPROF_WDT = 8.2 # FullProf Wdt # cryspy raw size/strain coefficients (additive to the base sigma/gamma) SIZE_G = 20.0 # adds to sigma_2 (Gaussian size, d⁴) STRAIN_G = 5.0 # adds to sigma_1 (Gaussian strain, d²) SIZE_L = 2.0 # adds to gamma_2 (Lorentzian size, d²) STRAIN_L = 1.0 # adds to gamma_1 (Lorentzian strain, d) 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='si',
    sample_form='powder',
    beam_mode='time-of-flight',
    radiation_probe='neutron',
    scattering_type='bragg',
)
verify.set_reference_as_measured(experiment, x, calc_fullprof)

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

experiment.instrument.setup_twotheta_bank = FULLPROF_TWOTHETA_BANK
experiment.instrument.calib_d_to_tof_offset = FULLPROF_ZERO
experiment.instrument.calib_d_to_tof_linear = FULLPROF_DTT1
experiment.instrument.calib_d_to_tof_quadratic = FULLPROF_DTT2

experiment.peak.type = 'jorgensen-von-dreele'
# Base broadening (size/strain are supplied separately as additive terms)
experiment.peak.broad_gauss_sigma_0 = FULLPROF_SIGMA_0
experiment.peak.broad_gauss_sigma_1 = FULLPROF_SIGMA_1 - STRAIN_G
experiment.peak.broad_gauss_sigma_2 = FULLPROF_SIGMA_2 - SIZE_G
experiment.peak.broad_lorentz_gamma_0 = FULLPROF_GAMMA_0
experiment.peak.broad_lorentz_gamma_1 = FULLPROF_GAMMA_1 - STRAIN_L
experiment.peak.broad_lorentz_gamma_2 = FULLPROF_GAMMA_2 - SIZE_L
# Microstructural size/strain components
experiment.peak.broad_gauss_size_g = SIZE_G
experiment.peak.broad_gauss_strain_g = STRAIN_G
experiment.peak.broad_lorentz_size_l = SIZE_L
experiment.peak.broad_lorentz_strain_l = STRAIN_L
experiment.peak.rise_alpha_0 = FULLPROF_ALPHA_0
experiment.peak.rise_alpha_1 = FULLPROF_ALPHA_1
experiment.peak.decay_beta_0 = FULLPROF_BETA_0
experiment.peak.decay_beta_1 = FULLPROF_BETA_1

experiment.excluded_regions.create(id='1', start=0, end=5000)
experiment.excluded_regions.create(id='2', start=10000, end=100000)

experiment.peak.cutoff_fwhm = FULLPROF_WDT

project.experiments.add(experiment)

experiment = ExperimentFactory.from_scratch( name='si', sample_form='powder', beam_mode='time-of-flight', radiation_probe='neutron', scattering_type='bragg', ) verify.set_reference_as_measured(experiment, x, calc_fullprof) experiment.linked_structures.create(structure_id='si', scale=FULLPROF_SCALE) experiment.instrument.setup_twotheta_bank = FULLPROF_TWOTHETA_BANK experiment.instrument.calib_d_to_tof_offset = FULLPROF_ZERO experiment.instrument.calib_d_to_tof_linear = FULLPROF_DTT1 experiment.instrument.calib_d_to_tof_quadratic = FULLPROF_DTT2 experiment.peak.type = 'jorgensen-von-dreele' # Base broadening (size/strain are supplied separately as additive terms) experiment.peak.broad_gauss_sigma_0 = FULLPROF_SIGMA_0 experiment.peak.broad_gauss_sigma_1 = FULLPROF_SIGMA_1 - STRAIN_G experiment.peak.broad_gauss_sigma_2 = FULLPROF_SIGMA_2 - SIZE_G experiment.peak.broad_lorentz_gamma_0 = FULLPROF_GAMMA_0 experiment.peak.broad_lorentz_gamma_1 = FULLPROF_GAMMA_1 - STRAIN_L experiment.peak.broad_lorentz_gamma_2 = FULLPROF_GAMMA_2 - SIZE_L # Microstructural size/strain components experiment.peak.broad_gauss_size_g = SIZE_G experiment.peak.broad_gauss_strain_g = STRAIN_G experiment.peak.broad_lorentz_size_l = SIZE_L experiment.peak.broad_lorentz_strain_l = STRAIN_L experiment.peak.rise_alpha_0 = FULLPROF_ALPHA_0 experiment.peak.rise_alpha_1 = FULLPROF_ALPHA_1 experiment.peak.decay_beta_0 = FULLPROF_BETA_0 experiment.peak.decay_beta_1 = FULLPROF_BETA_1 experiment.excluded_regions.create(id='1', start=0, end=5000) experiment.excluded_regions.create(id='2', start=10000, end=100000) experiment.peak.cutoff_fwhm = FULLPROF_WDT project.experiments.add(experiment)

⚠️ Switching peak profile type adds these settings with defaults:                                                                 
   • broad_lorentz_gamma_0=0.0                                                                                                    
   • broad_lorentz_gamma_1=0.0                                                                                                    
   • broad_lorentz_gamma_2=0.0                                                                                                    
   • broad_lorentz_size_l=0.0                                                                                                     
   • broad_lorentz_strain_l=0.0                                                                                                   

Peak profile type for experiment 'si' changed to

jorgensen-von-dreele

edi-cryspy VS FullProf¶

In [7]:

experiment.calculator.type = 'cryspy'

experiment.linked_structures['si'].scale = FULLPROF_SCALE

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

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

experiment.calculator.type = 'cryspy' experiment.linked_structures['si'].scale = FULLPROF_SCALE project.analysis.calculate() calc_ed_cryspy = experiment.data.intensity_calc LABEL_ED_CRYSPY = verify.engine_label('cryspy') project.display.pattern_comparison( 'si', reference=calc_fullprof, candidate=calc_ed_cryspy, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY, )

Calculator for experiment 'si' already set to

cryspy

Loading plot…

Fit edi-cryspy to FullProf¶

In [8]:

experiment.linked_structures['si'].scale.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(
    'si',
    reference=calc_fullprof,
    candidate=calc_ed_cryspy_refined,
    reference_label=FULLPROF_LABEL,
    candidate_label=LABEL_ED_CRYSPY_REFINED,
)

experiment.linked_structures['si'].scale.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( 'si', reference=calc_fullprof, candidate=calc_ed_cryspy_refined, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY_REFINED, )

Standard fitting

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

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.05	92538.77
2	5	0.30	74130.98	19.9% ↓
3	7	0.42	43433.34	41.4% ↓
4	9	0.52	6509.82	85.0% ↓
5	11	0.63	1.34	100.0% ↓
6	14	0.81	1.34

🏆 Best goodness-of-fit (reduced χ²) is 1.34 at iteration 11

✅ 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)	0.81
4	🔁 Iterations	11
5	📏 Goodness-of-fit (reduced χ²)	1.34
6	📏 R-factor (Rf, %)	0.84
7	📏 R-factor squared (Rf², %)	0.38
8	📏 Weighted R-factor (wR, %)	0.38

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	si	linked_structure	si	scale		0.6751	643.7919	0.0776	95264.61 % ↑

• 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¶

With the cryspy TOF size/strain wiring and Jorgensen-Von Dreele fix (cryspy issue #49), the refined cryspy pattern now agrees with FullProf.

In [9]:

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

verify.assert_patterns_agree( [ ( f'{LABEL_ED_CRYSPY_REFINED} vs {FULLPROF_LABEL}', verify.restrict_to_included(experiment, 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	0.38	✅
2		Max deviation (%)	< 6	0.23	✅
3		Area ratio	0.99 to 1.01	1.0042	✅
4		Shape correlation	> 0.999	1.0000	✅

Out[9]:

True