XRD简介(英文).doc

Optical related technology
X-ray Diffraction

Abstract: X-ray diffraction (XRD) technology is widely used in materials characterization. Identify chemistry constituents of the product, analyze the space group, lattice parameter and etc. In this article, I will introduce the principle of XRD including the diffractometer and simple application with the XRD pattern.

Introduction
1. X-ray is a kind of electromagnetic radiation generated by the inner electron transition. Its wavelength ranging from 0.01 to 10nm. X-ray photons with a short wavelength (below 0.2nm) have the energies above 5keV. Therefore comes the penetrating ability [1]. Moreover, X-ray interact with matter and project the matter’s information in X-ray diffraction pattern. As result, X-ray are widely used to image the inside of the object and is thought highly in the field medical radiography and material characterization.
2. X-ray diffraction is an interaction between X-ray and matter. Consider the material as lattice as show at figure 1. Consider the situation as what we had learned-the Rayleigh scattering. In some direction, we can detect the interference of two narrow X-ray beams, and constructive interference meet the optical path difference:
2dsinθ=nλ (n=0,1,2…).
Kwon as the Bragg’s law. d is the distance between two particles, θis the angle between incident X-ray and lattice plane, λ is the wavelength of X-ray. We can learn from the equation that the constructive inter only happen in some particular angle since the wavelength and the distance (consider as the grating constant) are fixed for one material, and for the three dimensional world we have three constant marked as (h k l) to describe the space group. Nevertheless, is hard to directly detect the 3D pattern, instead, we introduce the spherical projection pattern and develop some mathematical translation to restructure the 3D condition shows at figure 2. We can learn the direction and distance from the spherical coordinate. Let’s go over the procedure of XRD. First we shot a X-ray to the sample and get its diffraction pattern and read the information from the 2D pattern[2].
3. X-ray Diffractometer is high integration optical apparatus shows at figure 3. The X-ray source usually chooses Cu as target material applying hot electrons which accelerated by high voltage and generate X-ray [3]. Sample platform and detector link together and rotate along the horizontal spherical center axis. We can also have the sample platform and detector fixed and rotate the X-ray gun. We introduce the concept of resolution to evaluate the quality of the X-ray Diffractometer. A strong and stable X-ray generator is necessary. The other condition is the minimum angle which the machine can stable rotate. The resolution usually plays an important role in quantifying analysis such as determine the doping ratio by measure the XRD peak offset.

Simple analysis with XRD pattern
Assume we have got our XRD pattern file, we can import them into XRD analysis software “jade” shows at figure 4. As we already talk about that XRD can identify the space group of the crystal material. If we get the standard XRD pattern (verified by other method). We can compare our XRD pattern to the standard pattern (PDF) and see whether the diffraction peak match. In figure 4, I take the Lead sulfur (PbS) as an example. The mountain like curve is the XRD pattern we detect from the X-ray Diffractometer, x axis is 2θ/degree and the y axis represent the intensity; Vertical line is PDF, it marks the position and intensity of the standard diffraction pattern of PbS. So we can read the crystal parameter from the PDF information: space group Fm-3m (No.225), the size of the cell is 5.9362*5.95362*5.9362<90*90*90>we can know the shape of PbS cell is almost cube. But we still need SEM and TEM technology to precise determine, recall the XRD characterization procedure, we only learn the information from PDF. If you have a deeper look on the XRD pattern in figure 4, the XRD pattern peak unitary slightly offset to the left against the PDF’s. It suggests the PbS sample has a smaller size than the PDF’s standard size. We can calculate the exact size by applying mathematics but I won’t go that further.
Conclusion and expectation
In this article, we discussed the principle of X-ray, X-ray Diffraction, X-ray Diffractometer and X-ray diffraction pattern. It turns out the XRD technology is so convenient to image the inside of the matter. But we also see the shortcoming of this technique: 3D to 2D projection lose some information and fail to detect the absorption information. I suggest having more detector in different position to improve the accuracy and tunable X-ray source to determine the absorption of the material.

Reference
[1] https://en.wikipedia.org/wiki/X-ray
[2] <晶体学基础> 秦善
[3] X衍射以及其应用简介—陶琨（清华大学）