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   󰁆󰁯󰁲󰁴󰁧󰁥󰁳󰁣󰁨󰁲󰁩󰁴󰁴󰁥󰁮󰁥 󰁐󰁲󰁡󰁫󰁴󰁩󰁫󰁵󰁭 󰁉󰁉󰁉 󰁐󰁨󰁡󰁳󰁥 󰁴󰁲󰁡󰁮󰁳󰁩󰁴󰁩󰁯󰁮󰁳 󰁩󰁮 󰁮󰁡󰁮󰁯󰁭󰁡󰁴󰁥󰁲󰁩󰁡󰁬󰁳 󰁐󰁡󰁲󰁴 󰀲 󰁔󰁷󰁯󰀭󰁤󰁩󰁭󰁥󰁮󰁳󰁩󰁯󰁮󰁡󰁬 󰁘󰀭󰁲󰁡󰁹 󰁤󰁩󰁦󰁦󰁲󰁡󰁣󰁴󰁩󰁯󰁮 󰀨󰁘󰁒󰁄 󰀲  󰀩 󰀭 󰁂󰁲󰁵󰁫󰁥󰁲 󰁄󰀸 󰀫 󰁇󰁁󰁄󰁄󰁓 󰁤󰁩󰁦󰁦󰁲󰁡󰁣󰁴󰁯󰁭󰁥󰁴󰁥󰁲    Dr. Radu Nicula Physics Dept., Rostock University e-mail :     Contents 1. Overview 1.1 Introduction 1.2 Theory of X-ray Diffraction Using Area Detector 1.2.1 X-ray Powder Diffraction 1.2.2 Two Dimensional X-ray Powder Diffraction (XRD 2 ) 1.3 Geometry Conventions 1.3.1 Diffraction Cones and Conic Sections on 2D Detectors 1.3.2 Diffraction Cones and Laboratory Axes 1.3.3 Sample Orientation and Position in the Laboratory System 1.3.4 Detector Position in the Laboratory System 1.4 Diffraction Data Measured by Area Detector 2. System Configuration 2.1 X-ray Generator 2.1.1 Radiation Energy 2.1.2 X-ray Spectrum and Characteristic Lines 2.1.3 Focal Spot and Takeoff Angle 2.1.4 Focal Spot Brightness and Profile 2.1.5 Operation of the X-ray Generator 2.2 X-ray Optics 2.2.1 Monochromator 2.2.2 Pinhole Collimator 2.2.3 Sample-to-Detector Distance and Angular Resolution 2.2.4 Cross-Coupled Göbel Mirrors 2.3 Goniometer and Stages 2.4 Sample Alignment and Monitor Systems 2.5 HI-STAR Area Detector 2.6 Microdiffraction GADDS System  1. Overview   Introduction GADDS  (General Area Detector Diffraction System), introduced by Bruker AXS, Inc. (formerly Siemens AXS), is the most advanced X-ray diffraction system in the world . The core of GADDS is the high performance two-dimensional (2D) detector  – Bruker AXS HI-STAR  area detector. HI-STAR is the most sensitive area detector, a true photon counter in a large area. The speed of data collection with an area detector can be 104 times faster than with a point detector and about 10 4  times faster than with a linear position-sensitive detector. And most important, the data has large dynamic range and 2D diffraction information. Compared to one-dimensional diffraction profiles measured with a conventional diffraction system, a 2D image collected with GADDS contains far more information for various applications. By introduction of the innovative two-dimensional X-ray diffraction (XRD 2 ) theory, GADDS has opened a new dimension in X-ray powder diffraction. Phase identification  (Phase ID) can be done by integration over a selected range of two theta (2 θ ) and chi ( χ ). A direct link to the ICDD database, profile fitting with conventional peak shapes and fundamental parameters, quantification of phases, and lattice parameter indexing and refinement make powder diffraction analysis easy and fast. Due to the integration along the Debye rings, the integrated data gives better intensity and statistics for phase ID and quantitative analysis, especially for those samples with texture, large grain size, or small quantity. Texture  measurement using an area detector is extremely fast compared to the measurement using a scintillation counter or a linear position-sensitive detector (PSD). The area detector collects texture data and background values simultaneously for multiple poles and multiple directions. Due to the high measurement speed, GADDS can measure pole figures   at very fine steps, allowing detection of very sharp textures. GADDS is the best tool for quantitative texture analysis. Stress measurement using the two-dimensional area detector is based on a new 2D stress algorithm developed by Bruker AXS, which gives a direct relationship between the stress tensor and the diffraction cone distortion. Since the whole or a part of the Debye ring is used for stress calculation, GADDS can measure stress with high sensitivity, high speed, and high accuracy. It is very suitable for samples with large crystals and textures. Simultaneous measurement of stress and texture is also possible since 2D data consists of both stress and texture information. Percent crystallinity  can be measured faster and more accurate with the data analysis over the 2D frames, especially for samples with anisotropic distribution of crystalline orientation. The amorphous region can be defined externally within a user-defined region. Or the amorphous region can be defined with the crystalline region included when the crystalline region and the amorphous region overlap. GADDS can also calculate and display the Compton scattering so the Compton effect can be excluded from the amorphous result. The “rolling ball algorithm” calculates the percent crystallinity by extracting an amorphous background frame. Small angle X-ray scattering  (SAXS) data can be collected at high speed. Anisotropic features from specimens, such as polymers, fibrous materials, single crystals, and biomaterials, can be analyzed and displayed in two dimension. De-smearing correction is not necessary due to the collimated point X-ray beam. Since one exposure takes all the SAXS information, it is easy to scan over the sample to map the structure information from the small angle diffraction. Microdiffraction data is collected with speed and accuracy. X-ray diffraction from small sample amount or small sample area has always been a slow process due to limited beam intensity, difficulty in sample positioning, and slow point detectors. In the GADDS Microdiffraction system, we have solutions for all these problems. The cross-coupled Göbel Mirrors and the MonoCap TM  optics can deliver high intensity beams. The laser-video sample alignment system can align the  intended measurement spot of a sample accurately to the instrument center where the X-ray beam hits. The motorized XYZ stage can move the measurement spot to the instrument center and map many sample spots automatically. The 2D detector captures the whole or a large portion of the diffraction rings, so spotty, textured, or weak diffraction data can be integrated over the selected diffraction rings. Thin film samples with a mixture of single crystal, random polycrystalline layers and highly textured layers can be measured with all the features appearing simultaneously in diffraction frames. Stress and texture can be measured with speed or even simultaneously with the new stress and texture approach developed for XRD 2 . The texture can be displayed as a pole figure or fiber plot. The weak and spotty diffraction pattern can be compensated by integration over the 2D diffraction pattern. 1.2 Theory of X-ray Diffraction Using Area Detector 1.2.1 X-ray Powder Diffraction X-ray diffraction (XRD) is a technique used to measure the atomic arrangement of materials. When a monochromatic X-ray beam hits a sample, in addition to absorption and other phenomena, we observe X-ray scattering with the same wavelength as the incident beam, called coherent X-ray scattering. The coherent scattering of X-ray from a sample is not evenly distributed in space but is a function of the electron distribution in the sample. The atomic arrangement in materials can be ordered like a single crystal or disordered like glass or liquid. As such, the intensity and spatial distributions of the scattered X-rays form a specific diffraction pattern, which is the “fingerprint” of the sample. There are many theories and equations about the relationship between the diffraction pattern and the material structure. Bragg’s law is a simple way to describe the diffraction of X-rays by a crystal. In Figure 1-1, the incident X-rays hit the crystal planes in an angle θ , and the reflection angle is also θ . The diffraction pattern is a delta function when the Bragg condition is satisfied: λ  = 2 d sin θ   where λ        is the wavelength, d   is the distance between each adjacent crystal plane (d-spacing), and θ        is the Bragg angle at which one observes a diffraction peak. Fig. 1-1  The incident and reflected X-rays make an angle θ  hkl   symmetric to the normal of the crystal plane (hkl). The diffraction peak for the crystal plane (hkl) is then observed at the Bragg angle θ  hkl   (right). Figure 1-1 is an oversimplified model. For real materials, the diffraction patterns vary from theoretical delta functions with discrete relationships between points to continuous distributions with spherical symmetry. Figure 1-2 shows the diffraction from a single crystal specimen (left) and from a polycrystalline sample. The X-ray diffracted beams from a single crystal point to discrete directions, each corresponding to a family of diffraction planes. The diffraction pattern from a polycrystalline (powder) sample forms a series of diffraction cones if a large number of crystals oriented randomly in the space are covered by the incident X-ray beam. Each diffraction cone
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