Ab initio Structure Determination with Powder Diffraction Data

Ab initio structure determination with powder diffraction data is non-trivial and non-routine process. The knowledge of crystal structure is important for patent protection, understanding of properties, phase quantification and other purposes. However, in many cases a single crystal of a new compound of interest is not available for structure determination. Newly synthesized compounds or minerals are often available only as a fine powder. When there are no single crystals available for single crystal diffraction and no isostructural compounds for Rietveld refinement, it may be possible to solve the structure using only powder data by so called ab initio methods.

Standard report (even though there is no such thing as an "ab initio structure determination with powder diffraction"! ) of ab initio structure refinement includes the following:

Sample preparation for diffraction experiment
Experimental conditions
Diffraction raw data file in original and ASCII formats
Final Rietveld plot
Table of crystallographic data
Coordinates of atoms and isotropic thermal displacement factors
Figure - asymmetric unit with atoms labeling scheme
Figure - ball-stick and polyhedral representation of the structure

EXAMPLE OF STANDARD REPORT

Ab initio structure determination Report

1. Sample Preparation:

One gram of dry sample was hand-pulverized and 1μm fraction separated with a microsieve was used for data collection.

2. Experimental Conditions:

Part of pulverized sample was top-loaded into the standard glass sample holder (18mm height and 0.8 mm depth), and compacted with a class slide. Data collection was performed using horizontal goniometer Rigaku DMAX-B powder diffractometer with diffracted beam graphite monochromator. Slits DS=1º, SS=1º, RS=0.15º. Two theta angular range=5-80º, Step size=0.05º, Step time=5 sec.

3. Diffraction data file

Diffraction data file in Binary (Z000111.raw), ASCII (A000111.raw) and MS Excel (X,Y) formats are in CD

4. Final Rietveld plot

5. Conditions of X-ray data collection and Refinement for A2B3C4X12 in Space group P2₁22

Data collection

Diffractometer, geometry

Radiation

2θ range

Step scan

Time per step

Siemens D5000, Bragg-Brentano

Co Ka

10-120

0.02

20 sec.

Structure determination

Indexing

Pattern decomposition

Structure solution

Program ABC

Le Bail algorithm, Program XYX

Direct methods, Program UVW

Results of Rietveld refinement

Cell parameters

Volume, Z

Independent Reflection/parameters refined

η (pseudo-Voigt)

Zero point

Half-width parameters (U,V,W)

Asymmetry parameters

Background polynomial parameters

a=1.234(5), b=2.345(6), c=3.456(7)

123.23(2), 3

469/45

0.82

-0.0023

0.109 -0.089 0.024

0.151(3), 0.002(1)

a, b, c, d, e, f

Reliability factors

For points with Bragg contribution

Structure reliability factors

R_p=11.2 R_wp 13.2 R_exp=9.5 χ²=1.6

R_B=4.56, R_F=5.14

6. Coordinates of atoms and isotropic thermal displacement factors

Atom x y z U(eq) [Ang²]

A1 0.45249(12) 0.23430(4) 0.16901(6) 0.0193(3)

A2 -0.09360(10) 0.25795(5) 0.16846(6) 0.0185(3)

A3 0.18270(11) 0.25286(4) -0.10130(6) 0.0179(3)

B1 0.0568(8) 0.1962(3) -0.0290(4) 0.0264(19)

B2 0.3040(8) 0.3057(3) -0.0139(4) 0.0194(19)

B3 0.0030(8) 0.3181(3) 0.0920(5) 0.0250(19)

B4 0.0123(8) 0.2922(3) -0.1905(4) 0.0221(18)

C1 0.3114(8) 0.2997(3) 0.1911(5) 0.0267(19)

C2 0.3656(8) 0.2209(3) -0.1886(4) 0.0236(18)

C3 0.3523(8) 0.1751(3) 0.0869(4) 0.0214(17)

X1 -0.3248(7) 0.2482(3) 0.1000(4) 0.0283(18)

X2 0.1002(9) 0.1015(2) 0.0667(4) 0.0206(17)

X3 0.2496(9) 0.3942(3) 0.0971(4) 0.0216(17)

X4 0.0407(9) 0.1901(3) 0.1781(5) 0.0240(19)

7. Figure - asymmetric unit with atoms labeling scheme

8. Figure - ball-stick and polyhedral representation of the structure