auxiliary programs for diffraction experiments

Jiří Čapek^{1, a}, Zdenek Pala^{1, 2}

¹Department of Solid State Engineering, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague

²Institute of Plasma Physics, Academy of Sciences of the Czech Republic

^acapekjir@fjfi.cvut.cz

Because of recurring pleas of colleagues who are frequent users of X-ray diffraction results and who wanted to know the relevant volume of material which was irradiated, programs for calculation of penetration depth and linear absorption coefficients of crystalline phases were written in MatLab environment. In addition to it, we were often faced with oddly positioned Debye rings obtained in back reflection experiment. Debye rings’ convenient location on area, 2D, detector was, thus, achieved by repeatedly performing the experiments. That had led us to create a program which would visualize the outcome for selected experimental parameters.

Debye software was created as a visual aid for users doing the so called the back reflection experiment (or backscattering Debye-Scherrer experiment) [1]. It is a basic method for qualitative determination of real structure of materials. In materials only planes, which are oriented in the manner satisfying the Braggs’ law, can diffract. The diffracted radiation has a character of diffraction cones with the apex angle of 4θ. If this diffracted radiation impacts on a 2D detector, the so called Debye rings are detected. The user can make a model of the experiment upon changing the experimental parameters and also can check an expected result for untextured polycrystalline fine-grained materials. This is especially helpful for setting the right distance between the irradiated sample and 2D detector when the dimension of the detector is known. In Fig. 1, there is the result for standard alpha-ferrite steel in the distance of 50 mm from the detector when radiation from X-ray tube with chromium anode is used.

Figure 1. User interface of the debye software.	Figure 2. User interface of the absorption coefficient software.

Absorption coefficient software was created because it is de rigueur to know the values of linear absorption/attenuation coefficients when the penetration depth is to be calculated since it describes the reduction of an energy beam upon passing through a specific material [2]. For calculation of a linear absorption coefficient it is necessary to know the amount of each phase in material, densities and chemical formulas of the phases. In Fig. 2, there is the user interface of the program with the result of alpha-ferrite steel with oxidation layer (again for CrKα radiation). This constant is subsequently applied in the calculation of corresponding penetration depth as seen in Fig. 3.

X-ray penetration depth software was created because the users of XRD results must be informed about the volume of the material to which the results are relevant. Irradiated volume is given by irradiated surface, defined by experimental set-up and the inserted slits, multiplied by penetration depth. Most commonly, the penetration depth is represented by values of the so called effective penetration depth T^ef which defines the thickness of surface layer that gives rise to 63 % of diffracted intensity [1]. Hence, this software provides the opportunity to furnish users with T^ef values, or courses, for the given radiation penetrating the irradiated material. Final values generally depend on an incidence, a rebound angle and on an absorption coefficient. The user can choose between four types of experimental set-up. Except for standard Bragg-Brentano geometry and grazing incidence diffraction, courses of T^ef during residual-stress-aimed diffraction experiment for ω diffractometer can be visualized for all measured tilts and T^ef for ω-scans can be plotted as well [3]. User interface of this program is in Fig. 3 on the left while on the right; there is the result of T^ef course for linear absorption coefficient calculated above and Bragg-Brentano geometry.

Figure 3. User interface of the X-ray penetration depth software.

The programs are available for users who have at their disposal MatLab from http://electron.fjfi.cvut.cz/drupal/software-laborator-strukturni-rentgenografie.

1. I. Kraus, N. Ganev, Difrakční analýza mechanických napětí. Praha: ČVUT, 1995. ISBN 80-01-01366-9.

2. B. D. Cullity, S. R. Stock, Elements of X-ray Diffraction. New Jersey: Prentice Hall, 2001. ISBN 0-201-61091-4.

3. M. Birkholz, Thin Film Analysis by X-ray Scattering. Weinheim: WILEY-VCH, 2006. ISBN 978-3-527-31052-4.

This work was supported by the Grant Agency of the Czech Technical University in Prague, grant No. SGS13/219/OHK4/3T/14.