Diffractometer method

Still another method of determining crystal orientation involves the use of the diffractometer and a procedure radically different from that of either Laue method. With the essentially monochromatic radiation used in the diffractometer, a single crystal will produce a reflection only when its orientation is such that a certain set of reflecting planes is inclined to the incident beam at an angle 0 which satisfies the Bragg law for that set of planes and the characteristic radiation employed. But when the counter, fixed in position at the corresponding angle 20, discloses that a 

rotation of the crystal about various axes until a position is found for which reflection occurs, 

location of the pole of the reflecting plane on a stereographic projection from the known angles of rotation. 

Suppose the orientation of a cubic crystal is to be determined. For such crystals it is convenient to use the 111 planes as reflectors there are four sets of these and their reflecting power is usually high. First, the 29 value for the 111 reflection (or, if desired, the 222 reflection) is computed from the known spacing of the 111 planes and the known wavelength of the radiation used. The counter is then fixed in this 26 position. The specimen holder is now rotated about the diffractometer axis until its surface, and the rotation axis AA, is equally inclined to the incident beam and the diffracted beam, or rather, to the line from crystal to counter with which the diffracted beam, when formed, will coincide. The specimen holder is then fixed in this position, no further rotation about the diffractometer axis being required. Then, by rotation about the axis BB, one edge of the specimen or a line drawn on it is made parallel to the diffractometer axis. This is the initial position illustrated in Fig. 8-19. 

What we are trying to do, essentially, is to make N coincide with a 111 pole and so disclose the location of the latter on the projection. The search may be made by varying y continuously for fixed values of 4 or 5° apart the projection is then covered point by point along a series of radii. It is enough to examine one quadrant in this way since there will always be at least one III pole in any one quadrant. Once one pole has been located, the search for the second is aided by the knowledge that it must be 70.5° from the first. Although two (111) poles are enough to fix the orientation of the crystal, a third should be located as a check. 

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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. 

Hamlin, R. (1985). Multiwire area X-ray diffractometers. Method Enzymol. 114,416- 51. 

Kaye, B.H. Alliet, D. Switzer, L. Turbitt-Daoust, C. The effect of shape on intermethod correlation of techniques for characterizing the size distribution of a powder I. correlating the size distribution measured by sieving, image analysis, and diffractometer method. Part. Part. Syst. Charact. 1997, 14, 219-224. 

Diffractometer methods, usually automated, involve driving the detector and rotating the crystal to computed positions, scanning the Bragg reflection in steps and recording the X-ray intensity at each of these steps. 

Fig. 8-19 Crystal rotation axes for the diffractometer method of determining orientation...

The double-crystal diffractometer method is not topographic. However, Weissmann and his associates [8.30] have obtained semitopographic information by photographing the beam diffracted by crystal C for various angular positions of this crystal. 

The chief problem presented by a fiber texture is the identification of the fiber axis uvw This can be done fairly easily with a single diffraction photograph, and the procedure is described in this section. If, in addition, we wish to determine the amount of scatter in the texture, a diffractometer method is preferable (Sec. 9-9). 

There is not one, but several, diffractometer methods for measuring sheet texture. They fall into two groups, transmission and reflection, both being normally necessary for complete coverage of the pole figure. 

The standard diffractometer method is often called the two-exposure method, because two plane-spacing measurements are made, one of d dX j/ — 0 and one of [Pg.457]

Essentially, the quantity measured in the diffractometer method is A20 = (20 — 20j), the shift in diffraction-line position due to stress as the angle if/ is... 

This method of stress measurement is not often used today, because it is slower and less precise than the diffractometer method. However, the photographic method still has some advantages. The required apparatus is very simple a small back-reflection camera fixed to the head of a shockproof x-ray tube energized through a shockproof cable. This apparatus is smaller, lighter, more robust, and much cheaper than a mobile diffractometer. It is also more mobile and better suited to work in a confined space. 

Two exposures are made, with the incident beam inclined at a different angle to the specimen for each exposure [G.25, 16.3, 16.13, 6.8]. Only one side of the Debye ring on the film is measured in each exposure. This method is entirely analogous to the standard diffractometer method. 

Computerized x-ray diffractometer methods are routinely employed However if the amount of sample is limited, x-ray powder camera methods can be employed which requires a very small amount of material. 

B. H. Kaye, D. Alliet, L. Switzer, C. Turbin, The Effect of Shape on Intermethod Correlation of Techniques for Characterizing the Size Distribution of a Powder. Part 1 Correlating the Size Distribution measured by Sieving, Imt e Analysis, and Diffractometer Methods Part. Part. Syst. Charact., 14 (1997) in press. 

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