crystod-xrd

crystod-xrd#

Powder X-ray diffraction patterns: the Bragg peaks of the structure in a POSCAR, with their Miller indices, multiplicities, d spacings, 2θ positions and relative intensities, written as a text table and drawn as a broadened pattern.

I want to …

command

compute the pattern for Cu Kα (Kα1 + Kα2)

crystod-xrd -c POSCAR

use a single, monochromatic line

crystod-xrd -c POSCAR --xraytype CuKa1

use another anode

crystod-xrd -c POSCAR --xraytype MoKa

draw Gaussian instead of Lorentzian peaks

... --peak-profile gaussian

restrict the angular window

... --two-theta 5 60

try it without a structure file

crystod-xrd --example ScF3

36. Powder X-ray diffraction patterns#

Example directory: example/36_xrd_pattern (testsuite section 36)

The intensities are computed with the XRDCalculator of pymatgen: atomic scattering factors, the Lorentz-polarization factor and the multiplicity of each family of planes, for the structure exactly as given in the POSCAR (no symmetrization, no thermal factors).

crystod-xrd -c example/test_POSCARs/221_PPOSCAR_ScF3

 * Structure *
 221_PPOSCAR_ScF3: ScF3, Pm-3m

 * Radiation *
 CuKa: CuKa1 = 1.5405929 A, CuKa2 = 1.5444274 A  (Ka1 : Ka2 = 2 : 1)

 * Bragg peaks (36) in 10 - 120 deg *
    h   k   l  mult       d (A)  2theta (deg)  intensity  line
    1   0   0     6    4.069590       21.8217    100.000  CuKa1
    1   0   0     6    4.069590       21.8766     50.000  CuKa2
    1   1   0    12    2.877635       31.0530     11.215  CuKa1
    1   1   0    12    2.877635       31.1322      5.606  CuKa2
    ...
    3   0   0     6    1.356530       69.1999     13.937  CuKa1   + (2 2 1) x24
    3   0   0     6    1.356530       69.3968      6.964  CuKa2   + (2 2 1) x24
    ...

Peak table written to: XRD_221_PPOSCAR_ScF3_CuKa.txt
Pattern (lorentzian profile, width 0.1 deg) written to: XRD_221_PPOSCAR_ScF3_CuKa.pdf

Families of planes with the same d spacing, such as the cubic (3 0 0) and (2 2 1), contribute to one peak; the first family is listed in the columns and the others after the line name.

_images/xrd_ScF3_CuKa.png

The pattern of ScF3 for the Cu Kα doublet with Lorentzian peaks (the default). The tick marks under the curve are the Bragg positions; the Kα1/Kα2 splitting grows with the angle and is resolved above about 60°.#

The radiation (--xraytype)#

A doublet (CuKa, the default, and AgKa, MoKa, CoKa, FeKa, CrKa) superposes the Kα1 and Kα2 patterns with the 2:1 intensity ratio of the two lines. This is what a laboratory diffractometer without a Kα2 monochromator records: every reflection appears twice, the Kα2 partner at half the intensity and slightly higher angle. A single line gives the monochromatic pattern. The names are case-insensitive.

name

wavelength (Å)

name

wavelength (Å)

CuKa1

1.5405929

CoKa1

1.788996

CuKa2

1.5444274

CoKa2

1.792835

CuKb

1.392234

FeKa1

1.936041

MoKa1

0.70931715

FeKa2

1.939973

MoKa2

0.713607

CrKa1

2.289726

AgKa1

0.55942178

CrKa2

2.293651

AgKa2

0.5638131

The wavelengths are those of the RIETAN-FP manual (F. Izumi and K. Momma).

The drawn pattern (--peak-profile, --width)#

Every peak is broadened into a profile of unit area scaled by its intensity, so the integrated intensity of a peak does not depend on the profile:

  • lorentzian (default): (w/π) / ((2θ − 2θ₀)² + w²), w the half width at half maximum;

  • gaussian: exp(−(2θ − 2θ₀)² / 2w²) / (w √(2π)), w the standard deviation.

--width sets w in degrees (default 0.1). The profile only shapes the figure; the peak table is the same for both.

Outputs and other options#

option

effect

--two-theta MIN MAX

the window of the peak list and the plot (default 10 120)

--min-intensity PERCENT

drop reflections weaker than this (default 0: every reflection is kept, including the very weak ones pymatgen would hide below 0.1 %)

-o PREFIX

write PREFIX.txt and PREFIX.pdf (default XRD_{cell file}_{xraytype})

--show

also open the pattern in a matplotlib window

--tolerance

symmetry tolerance of the printed space-group symbol (default 0.01 Å)

The text table is comma-separated, one reflection per line: h, k, l, multiplicity, d, two_theta, intensity, line, families, with the structure, the radiation and the wavelengths in the header.

From Python#

from crystod import xrd

structure = xrd.load_structure("POSCAR")
pattern = xrd.compute_xrd_pattern(structure, "CuKa", (10, 120))
for peak in pattern.peaks[:4]:
    print(peak.hkl, round(peak.two_theta, 3), round(peak.intensity, 2), peak.line)
two_theta, intensity = xrd.smear_pattern(pattern, "lorentzian", width=0.1)

The full list of functions is on the crystod.xrd page of the API reference.

Citation

The intensities come from pymatgen: S. P. Ong et al., “Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis”, Comput. Mater. Sci. 68, 314-319 (2013).