Resolution powder diffractometers

Figure 2.14 High resolution powder diffractometer on beam line ID31 at ESRF.

Figure 2.20 Schematic of the high resolution powder diffractometer D2B (ref 7) at ILL, Grenoble.

Figure 2.21 Typical resolution function of a high resolution powder diffractometer.

In-situ neutron diffraction was used to monitor the structural evolution of the phase decomposition of MAX phases at high-temperature in real time. Diffraction patterns were collected using WOMB AX at OPAL or the Polaris at ISIS, both are high-intensity medium-resolution powder diffractometers. Samples were mounted in a high-temperature niobium furnace which was fitted with a thin tantalum foil element and tantalum and vanadium heat shields that allows it to reach 2000°C, and operates under a high dynamic, i.e., it is continuously evacuated with a vacuum of 10 - 10 torr. A precision electronic scale was used to weigh the sample before it was loaded into the furnace. 

Nanocrystalline iron-doped Ti02 samples (as-prepared S2 and annealed at 500°C S4 [7]) and undoped samples (Si and S3 [8]) were S5mthesised by a modified sol-gel method. The details of preparation were reported earlier [7, 8]. The X-ray diffiaction of the samples was carried out at room temperature using a Philips powder diffractometer (PW 1820) with monochromatized CuXa radiation. Transmission electron microscopy (TEM) and SAED investigations were carried out by using a JEOL JEM 2010 200 kV microscope, Cs=0.5 mm, point resolution 0.19 nm. 

Both collimation methods shown in Figure 2.9 are commonly used in powder diffractometers that are employed for routine powder diffraction experiments. High resolution and low-angle scattering diffractometers require better and therefore, more complex eollimation, which to some extent overlaps with the monochromatization described below, but otherwise will not be considered in this book. ... 

Overall, powder diffractometers equipped with point detectors offer the best resolution of the resulting powder diffraction data. While the instrumental resolution increases with the increasing goniometer radius, the intensity of the diffracted beam unfortunately decreases because the incident beam produced by an analytical x-ray tube is always divergent. Therefore, typical goniometer radii vary between 150 and -300 mm. 

You are using Fe Ka radiation to collect powder diffraction data employing powder diffractometer C (see problem 4). After several quick scans, you established that the receiving slit with the aperture of 0.03° results in both acceptable resolution and intensity. Bragg peaks appear to have a full width at half maximum between 0.4 and 0.5° 20. What is the largest allowable step during data collection and why ... 

O. Zaharko, V.K. Pecharsky and K.A. Gschneidner, Jr., unpublished. Neutron diffraction data were collected using the High Resolution Position Sensitive Detector Powder Diffractometer for Thermal Neutrons at the Paul Scherrer Institute, Switzerland (http //sinq.web.psi.ch/sinq/instr/hrpt.html). The same alloy was used in the two experiments (x-ray data in section 6.10, and neutron data in this section). 

Considering Eqs. 7.6 and 7.7, it is clear that each additional crystalline phase adds multiple Bragg peaks plus a new seale factor along with a set of eorresponding peak shape and structural parameters into the non-linear least squares. Even though mathematically they are easily aceounted for, the finite accuracy of measurements as well as the limited resolution of even the most advanced powder diffractometer, usually result in lowering the quality and stability of the Rietveld refinement in the case of multiple phase samples. Thus, when the precision of structural parameters is of concern, it is best to work with single-phase materials, where Eqs. 7.3 and 7.4 are applicable. On the other hand, since individual scale factors may be independently... 

As with angle-dispersive neutron diffractometers, the design of TOE powder diffractometers can be optimised for either high resolution or high intensity or some compromise of both. An understanding of the factors that affect the resolution is therefore important. The relative uncertainty in (i-spacing, hdjd, may be determined from the equation ... 

The inverse proportionality between peak width and mean size stated by the Scherrer equation places practical limits to the range of domain sizes that produce measurable effects in a powder pattern. While the lower bound [a few ( 2)nm, depending on the specific phase] is related to the approximations used, the upper bound depends on the instrumental resolution, i.e. on the width of the instrumental profile. Traditional laboratory powder diffractometers, using standard commercial optics, typically allow the detection of domain sizes up to 200 run. Above this value, domain size effects can hardly be distinguished from the instrumental broadening. This limit, however, can considerably be extended by using suitable high resolution optics, as is the case of many diffractometers in use with synchrotron radiation. In this case the practical limit can reach several micrometres. 

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