Structure refinement from precession electron diffraction data

 

M. Klementová, L. Palatinus

 

Department of Structure Analysis, Institute of Physics of the AS CR, Cukrovarnická 10,

162 00 Prague, Czech Republic

klemari@fzu.cz

 

Electron microscopy, spectroscopy and diffraction are indispensable tools for the characterization of nanocrystalline materials. Within an electron microscope, electron diffraction remains the most accurate and versatile method of obtaining accurate structural information at the atomic level. Consequently there have been many attempts to use it as a quantitative tool [1- 4]. However, in many cases fully quantitative analyses proved difficult because of the complications due to dynamical diffraction. There has recently been a resurgence of interest in quantitative analysis of high-energy electron diffraction data due to the introduction of the precession electron diffraction (PED) technique [5]. Key to this was the demonstration by Gjønnes and collaborators that PED data could be used within direct methods rather well, and also used at least partially to refine a structure [6]. While it was apparent from the early days that PED remained somewhat dynamical and needed a full calculation for quantitative results [7], numerous groups have reported reasonable results with approximate kinematical refinements [e.g., 8-9].

The purpose of this presentation is to demonstrate that the PED data can be used successfully for accurate structure refinement, yielding results that are comparable to an equivalent refinement against x-ray or neutron diffraction data. We provide results on three different materials and several data sets measured with three different microscopes. The three refined structures range from a simple structure of silicon to the relatively complex structures of orthopyroxene (Mg,Fe)2Si2O6 (10 independent atoms, VUC = 843 A3) and gallium-indium tin oxide (Ga,In)2SnO5 (17 independent atoms, VUC = 392 A3). The thickness of the samples varies from 30 nm to 110 nm. We analyse the sensitivity of the results to the choice of the parameters of the algorithm. The differences between full dynamical refinement, a simplified two-beam dynamical refinement [10] and the refinement in kinematical approximation are analysed, and the results are compared with refinement against non-precessed electron diffraction data.

For all three samples the method yielded stable refinements with acceptable refined parameters and reasonable figures of merit, which were in all cases much smaller than the corresponding figures of merit obtained with kinematical refinement. In particular, the full dynamical treatment allowed for the refinement of atom occupancies at mixed crystallographic sites – an impossible achievement with kinematical approximation. We have also compared the refinement against PED data with the refinement against non-precessed data (Tab. 1).

Table 1.  Refinement results on two silicon samples with different thickness. On each sample four data sets with different precession angle were collected. R2 and R1 are the unweighted residual values calculated on intensities and amplitudes, respectively, t is refined thickness and Uiso is the refined isotropic displacement parameter of the Si atom. Refinement was performed against diffraction data from [110] zone axis.

 

 

prec. angle

R2 [%]

R1 [%]

t [nm]

Uiso[Å2]

Sample 1

j=0°

12.40

15.77

41.5(6)

0.0143(23)

 

j=1°

10.80

7.10

36.7(7)

0.0106(14)

 

j=2°

6.00

3.66

39.9(7)

0.0090(11)

 

j=3°

5.88

4.63

35.2(8)

0.0039(14)

Sample 2

j=0°

8.88

18.82

104.9(2)

0.0053(3)

 

j=1°

12.70

9.04

107.3(16)

0.0054(19)

 

j=2°

6.55

4.31

113.2(9)

0.0054(10)

 

j=3°

3.82

2.52

116.6(8)

0.0033(7)

 

References

1.          J.M. Cowley, Acta Cryst., 6, (1953), 516.

2.          B.K. Vainshtein, Structure analysis by electron diffraction, Pergamon Press. 1964.

3.          J.C.H. Spence & J.M. Zuo, Electron microdiffraction, Springer. 1992.

4.          D.L. Dorset, Biochim. Biophys. Acta, 424, (1976), 396.

5.          R. Vincent & P.A. Midgley, Ultramicroscopy, 53, (1993), 271.

6.          K. Gjonnes, Ultramicroscopy, 69, (1997), 1.

7.          C.S. Own, A.K. Subramanian, L.D. Marks, Microsc. Microanal., 10, (2004), 96.

8.          E. Mugnaioli, T. Gorelik, U. Kolb, Ultramicroscopy, 109, (2009), 758.

9.          M. Gemmi, H. Klein, A. Rageau, P. Strobel, F. Le Cras, Acta Cryst., B66, (2010), 60.

10.      W. Sinkler, C.S. Own, L.D. Marks, Ultramicroscopy, 107, (2007), 543.