Diffractometer

On integration of (2.20) with respect to x from 0 to t, the total scattered intensity 7(2 ) from a sample of thickness t is given by 

If the sample is sufficiently thick in comparison to x, that is, if the penetration of the beam to the other side of the sheet is negligibly small, we may let fit oo in (2.22), and the absorption factor becomes equal to 1/2/x, which is independent of the scattering angle and thus obviates the need for absorption correction. 

A similar calculation for the symmetrical transmission mode can be made as follows. In the layer of thickness dx at depth x within the sample, the volume irradiated by a beam of cross-sectional area A is equal to dx - Af cos 9. The distance of travel by the beam within the sample is equal to l + l2, where l = jc/cos 0 and l2 = (t — x)/cos 9. The intensity of scattering due to the layer dx is then 

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X-ray powder diffraction studies are perfonned both with films and with counter diffractometers. The powder photograph was developed by P Debye and P Scherrer and, independently, by A W Hull. The Debye-Scherrer camera has a cylindrical specimen surrounded by a cylindrical film. In another commonly used powder... 

Powder diffraction studies with neutrons are perfonned both at nuclear reactors and at spallation sources. In both cases a cylindrical sample is observed by multiple detectors or, in some cases, by a curved, position-sensitive detector. In a powder diffractometer at a reactor, collimators and detectors at many different 20 angles are scaimed over small angular ranges to fill in the pattern. At a spallation source, pulses of neutrons of different wavelengdis strike the sample at different times and detectors at different angles see the entire powder pattern, also at different times. These slightly displaced patterns are then time focused , either by electronic hardware or by software in the subsequent data analysis. 

Interplanar Spacings. Diffractometer alignment procedures require the use of a well-prepared polycrystalline specimen. Two standard samples found to be suitable are silicon and a-quartz (including Novaculite). The 26 values of several of the most intense reflections for these materials are listed in Table 7.6 (Tables of Interplanar Spacings d vs. Diffraction Angle 26 for Selected Targets, Picker Nuclear, White Plains, N.Y., 1966). To convert to d for Ka or to d for Ka2, multiply the tabulated d value (Table 7.6) for Ka by the factor given below ... 

Fig. 15. Size data for a metal powder obtained by A, image analysis, and B, on a diffractometer.

An x-ray area detector can be used to collect the intensities of many reflections at a time. The crystal must be oriented in many different settings with respect to the incident beam but the detector needs to be positioned at only a few positions to collect all of the data. A charge coupled device (CCD) is used as the area detector on the Siemens SMART single crystal diffractometer system. The SMART detector consists of a flat 6-cm circular phosphorescent screen that converts x-ray photons to visible light photons. The screen is coupled to a tapered fiber optics bundle which is then coupled to a one inch by one inch square CCD chip. The CCD chip has 1024 x 1024 pixels each of which stores an electrical charge proportional to the number of... 

Typically it takes two to three days to collect a complete data set using a single-reflection detector. The new SMART diffractometer with its CCD detector can collect two or three data sets pet day. 

Fig. 12. Siemens SMART Single Crystal X-ray Diffractometer System.

Step 3. The computer collects about 45 frames of data. The crystal is rotated about the vertical axis for 0.3 degree for each frame. Usually the crystal is exposed to x-rays for about 5 seconds for each frame. The computer finds the centers of many reflections (typically 25 to several hundred) and determines indices for these reflections. It then determines the unit cell parameters and the orientation of the unit cells with respect to the diffractometer. 

At this point the crystal may be removed from the diffractometer making the instmment available to analy2e another sample. 

Bragg-Brentano Powder Diffractometer. A powder diffraction experiment differs in several ways from a single-crystal diffraction experiment. The sample, instead of being a single crystal, usually consists of many small single crystals that have many different orientations. It may consist of one or more crystalline phases (components). The size of the crystaUites is usually about 1—50 p.m in diameter. The sample is usually prepared to have a fiat surface. If possible, the experimenter tries to produce a sample that has a random distribution of crystaUite orientations. 

Fig. 14. Focusing schemes in powder diffraction (a) conventional para-focusing Bragg-Brentano diffractometer (b) parallel-beam diffractometer using a...

Position Sensitive Detectors. By replacing the scintillation detector in a conventional powder diffractometer with a Position Sensitive Detector (PSD), it is possible to speed data collection. For each x-ray photon received a PSD records the angle at which it was detected. Typically, a conventional scintillation detector records x-ray photons in a range of a few hundredths of a degree at a time. A PSD can measure many degrees (in 20) of a powder pattern simultaneously. Thus, for small samples, data collection, which could require hours with a conventional detector, could take minutes or even seconds with a PSD. 

Area Detectors. A two-dimensional or area detector attached to a powder diffractometer can gready decrease data collection time. Many diffraction appHcations require so much time with a conventional detector that they are only feasible if an area detector is attached to the iastmment. The Siemens General Area Detector Diffraction System (GADDS) uses a multiwire area detector (Fig. 17). This detector measures an x- and ajy-position for each x-ray photon detected. The appHcations foUow. 

Texture Analysis with GADDS. With a conventional detector, a data collection for a pole figure analysis with a powder diffractometer with a texture attachment could take 12 h or more. With an area detector, it is possible to collect enough data for several pole figures (required for an ODF analysis) ia a few minutes. 

For x-ray investigations, the diffractometer method is generally used. The lattice constants indicate purity or composition of soHd solutions the rapid counting-tube goniometric method can be used at the manufacturing plant for quaUty control. The rotating-crystal and neutron diffraction methods are sometimes used for stmcture elucidation. 

The most common detectors in HPLC are ultraviolet, fluorescence, electrochemical detector and diffractometer. However, despite all improvements of these techniques it seems necessary to have a more selectivity and sensitivity detector for the purposes of the medical analysis. It should be therefore improvements to couple analytical techniques like infrared IR, MS, nuclear magnetic resonance (NMR), inductively coupled plasma-MS (ICP-MS) or biospecific detectors to the LC-system and many efforts have been made in this field. 

Figure 3 Bragg-Brentano dHfractometar (a) and Saemann-Bohlin diffractometer (b).

Figure 6 LEED diffractometer. The vidicon camera can be interfaced with a computer to...

Measurements of surface disorder require a high resolving power (the ability to distinguish two close-lying points in the diffraction pattern). Quantitative measurements of surface disorder are limited in the following manner, the worse the resolving power, the smaller the maximum scale of surface disorder that can be detected. For example, if the maximum resolvable distance of the diffractometer is 100 A, then a surface that has steps spaced more than 100 A apart will look perfect to the instrument. The theoretical analysis of disorder is much simpler than that for atomic positions. 

Grazing Incidence X-Ray Diffraction Grazing Incidence X-Ray Diffraction Double Crystal Diffractometer... 

Fig. 4. Schematic showing the SAXS measurement on the Siemens D5000 diffractometer. The wave-vector, k, is determined as (2-kIX) ss, where s and s are the umt veetors defining the directions of the seattered and incident radiation respectively.

Once mounted in the diffractometer, the crystal is irradiated with X rays, usually so-called Cu/Cg radiation with a wavelength of 0.154 nm. When the X rays strike the enzyme crystal, they interact with electrons in the molecule and are scattered into a diffraction pattern, which, when delected and visualized, appears as a scries of intense spots against a null background. 

X-ray crystallography, 864-865 X-ray diffractometer. 865 oXylene, ozonolysis of, 542 Xylose, configuration of, 982... 

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