Cylindrical image plate diffractometer – orienting and indexing of large compact samples in reflection mode

 

Z. Matěj1, J. Šmilauerová1, J. Pospíšil1, T. Brunátová1, P. Harcuba1, V. Holý1, R. Kužel1

 

1Faculty of Mathematics and Physics, Charles University in Prague,
Ke Karlovu 5, 121 16 Praha 2, Czech Republic

 

matej@karlov.mff.cuni.cz

 

Introduction

Rigaku RAPID II installed in the X-ray lab at MFF UK [1] is a versatile diffractometer proposing diverse options for material analysis by X-rays. It is equipped with a three-axis goniometer and a large curved image plate (IP) detector. The instrument can be routinely utilised for single crystal structure solution as well as for powder diffraction. Residual stress or texture studies were also reported [2]. The aim of this contribution is a discussion of possibilities and limitations of this instrument, which is not as common as the Bragg-Brentano or parallel beam diffractometers. Its unique advantage, that large parts of the reciprocal space are explored simultaneously, is illustrated on an example application of the analysis of (coherent) inclusion nanoparticles in Ti-alloys.

 

Figure 1. Rigaku R-Axis Rapid II diffractometer with image plate system.

Figure 2. Florescent target mounted in the sample position. During a typical experiment two goniometer axes are set to fixed positions (omega = 210°, psi = 55°) and the sample is spinning/oscillating around the axis (phi) perpendicular to the sample surface.

Diffractometer, large samples and reflection geometry

The diffractometer is depicted in Fig. 1. Its standard applications include analysis of small (~ 0.01-1 mm) single crystal samples or powders filled in glass/capton capillaries. These experiments can be done directly in transmission geometry and the advantage of the large cylindrical IP detector to capture a wide range (~ 200°) of scattering angles is fully utilised. Contrary, for large (~ 10 mm) compact samples of a “coin” size and thickness, which are of main interest here, the reflection geometry is the only reasonable option. A typical experiment is depicted in Fig. 2. The sample surface is roughly aligned to be perpendicular to the (phi) spin axis. Other two goniometer axes (omega, psi) are set to general fixed positions. A quick (20-30 min) “survey” experiment can be done with sample (phi) spinning or a series of pictures can be acquired with crystal oscillating in small (phi) intervals during an “overnight” experiment.

 

Figure 3. Analysis of Debye rings from the NIST standard Si powder sample for calibration of beam and sample displacement instrumental corrections. Diffracted intensity in the bottom right corner of the IP is shadowed by the goniometer head.

Reference samples

In order to understand the diffraction geometry in detail and test the accuracy of the experiment the NIST standard Si powder sample and a high quality defect free Si wafer were measured under conditions described above. The analysis of the Debye rings from the powder sample is illustrated in Fig. 3. In the first step diffracted intensity at several (beta) positions on the rings was fitted with Cu-Kalpha doublet profiles. The refined experimental 2Theta positions were then compared with that calculated for the nominal lattice parameter and including zero-beam and sample displacement [3] corrections. This difference was smaller than ~ 0.05° on all the Debye rings. If in addition the lattice parameter was refined, the discrepancy from the nominal value was about ±0.001 Å. For single crystal data the accuracy reached was slightly worth. About 15-40 diffraction maxima were analysed. The differences in 2Theta positions were practically same ~ ±0.05° and the (beta) positions on the rings were predicted with ~ 0.1° error. Unfortunately the discrepancy in the lattice parameter was ±0.003 Å for the single crystal experiments.

 

Figure 4. A preliminary analysis of the quick “survey” measurement of the LCB beta-Ti alloy single crystal using the Rigaku 2DP software. Simulated green Debye rings are related to the (bcc) beta-Ti matrix phase. Contrary red lines come from the minor omega-Ti nanoparticles. The lattices of both phases are coherent hence some beta-Ti green rings are overlapped with red rings of (hexagonal) omega-Ti.

Orienting and indexing of single crystals of LCB Ti-alloy

Indexing of LCB beta-Ti alloy [4] is a challenging problem. The single crystals consist of a metastable bcc beta-Ti matrix and of a large fraction of (coherent) inclusion nanoparticles of hexagonal-Ti. The samples were analysed also by pole figures (PF) measurements and reciprocal space mapping in [5].

A preliminary analysis of the quick “survey” experiment using the Rigaku 2DP software is depicted in Fig. 4. Diffraction maxima from two different crystal systems (bcc beta-Ti matrix and inclusion of hexagonal omega-Ti phase) are simply identified. A large part of the reciprocal space is examined in this rapid experiment. This is an advantage especially if we consider that e.g. for PF measurements the line (2Theta) position must be known a priory. The longer “overnight” experiments brilliantly simplify the orientation and indexing procedures and enhance signal from weak diffraction maxima. An image from such a measurement is depicted in Fig. 5. Finally it was indexed by the beta-Ti matrix and four families of omega-Ti inclusions [5].

 

Figure 5. Possible indexing of an image taken in the oscillation mode. Intensity maxima can be indexed by (bcc) beta-Ti matrix (blue circles) and by 4 families (subindexes A, B, C, D) [5] of (hexagonal) omega-Ti (cyan crosses).

 

References

1.    R. Kužel, Rigaku R-Axis Rapid II at MFF UK: http://www.xray.cz/kfkl-osa/eng/rapid/ (Jul 23, 2013).

2.    M. Gelfi, E. Bontempi, R. Roberti, L.E. Depero, Acta Mat., 52, (2004), 583.

3.    N. V. Y. Scarlett, M. R. Rowles, K. S. Wallwork, I. C. Madsen, J. Appl. Crystallogr., 44, (2011), 60-64.

4.    J. Šmilauerová, J. Pospíšil, J. Cryst. Growth, (2013), submitted.

5.    V. Holý, J. Šmilauerová, J. Stráský, J. Pospíšil, M. Janeček, Mat. Struct. Chem. Bio. Phys. Tech., 20, (2013), a contribution in these proceedings.

 

Acknowledgements.

This work has been supported by the Grant Agency of the Czech Republic (project no. P108/11/1539) and within the Charles University Research Center “Physics of Condensed Matter and Functional Materials” (no. UNCE 204023/2012).