Rowland circles

X-rays are collected and analy2ed in ema in one of two ways. In wds, x-rays are dispersed by Bragg diffraction at a crystal and refocused onto a detector sitting on a Rowland circle. This arrangement is similar to the production of monochromati2ed x-rays for xps described above. In the other approach, edx, x-rays are all collected at the same time in a detector whose output scales with the energy of the x-ray (and hence, Z of the material which produces the x-ray.) Detectors used for ema today are almost exclusively Li-drifted Si soHd-state detectors. 

The spectrometer is necessarily quite large, and a complicated mechanism has to be precision engineered in order to enable 0 to be altered while keeping both the crystal and the detector on the Rowland circle. In order to cover the whole X-ray spectrum a range of crystals with different lattice spacings is required, which may be interchanged automatically. 

A typical instrument is equipped with four computer controlled crystal spectrometers, as well as an EDS system for preliminary qualitative analysis. A light microscope is provided for examining the specimen and also for ensuring that the specimen height is adjusted until it is on the Rowland circle. The drawing of... 

For an EDS system the beam may be scanned over, say, 100 x 100 pm, and the analysis is then an average of the area of the image on the screen. For a WDS system such scanning would excite part of the specimen surface not lying on the Rowland circle (Figure 5.5), so if an analysis of an area greater than about 5x5 pm is required by WDS, then the specimen must be scanned, and not the beam. 

Rowland circle spect A circle drawn tangent to the face of a concave diffraction grating at its midpoint, having a diameter equal to the radius of curvature of a grating surface the slit and camera for the grating should lie on this circle. ro.lsnd, s3r-k3l ... 

Rowland mounting spect A mounting for a concave grating spectrograph in which camera and grating are connected by a bar forming a diameter of the Rowland circle, and the two run on perpendicular tracks with the slit placed at their junction. ro,l3nd, maunt-ir ... 

Figure 15.5—Optical schematics of a polychromator with long focal distance and a concave grating. Reflecting mirrors can be used when lines are too close to one another. Sometimes, several polychromators are combined. To the right, principle of the Rowland circle.

Spherical aberration at the detector slit is minimized by further grinding the cry stal surface to fit the radius of the Rowland circle. With the resultant... 

We locate the EBIT source and calibration source inside the Rowland circle by design. Bragg diffraction angles of calibration lines are in the range 29-45° while the helium-like resonances are observed around 39°. The plane of crystal dispersion is parallel to the electron beam axis. The crystal acts as a polarizer at Bragg angles near 45° and radiation polarised perpendicular to the electron beam axis is the dominant diffracted component. 

Fig. 1. Spectrometer configuration at NIST EBIT note that the EBIT source is located well inside the Rowland circle. The spectrometer is in the perpendicular orientation where the axis of the spectrometer is perpendicular to the long axis of the EBIT source. The detector arm moves vertically with changes in diffraction angle.

Estimates of shifts of spectra in curved crystal geometries are often calculated for an ideal detector located on the Rowland circle. However, the detection surface is usually fiat and therefore cannot lie on the Rowland circle. Detectors located on a fixed length detector arm will additionally travel off the Rowland circle as the Bragg angle is scanned unless the crystal curvature is simultaneously scanned (which raises problems of stress hysteresis). Conventional shifts calculated for detection on the Rowland circle do not agree with shifts at a flat extended detector and this systematic error can be 100-200 ppm for any Johann curved crystal spectrometer. We have incorporated fiat surface detectors located off the Rowland circle into the general theory [18,17]. 

We have done explicit analysis to determine the error associated with the omission of the systematic shift caused by flat detector shape and location off the Rowland circle. This omission revealed a poor determination of the dispersion function and consequent errors of 100 ppm. Including this effect has allowed reduction of the dispersion function uncertainty to 20 ppm through the careful determination of systematic uncertainties. 

FIGURE 63 Schematic of a HERFD crystal array spectrometer, in this case using six spherically bent Ge(620) crystals to collect the Fe Kf region with approximately 1.0 eV resolution. The inset (left) shows the Rowland circles for each analyzer crystal (Heijboer et al., 2004). Reprinted with permission from (Heijboer et al., 2004). Copyright 2004 American Chemical Society. 

As WDS analysis is sequential, it is practical to use several spectrometers of this type around the electron column but, for obvious reasons of available space (the diameter of the Rowland circle is approximately 30 cm), we are limited to 2 spectrometers mounted obliquely or 5 vertical spectrometers. The second configuration is generally chosen since it can be used to conduct simultaneous analysis of S elements on the same point. 

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