Stress measurement line position

Every effort should, of course, be made to measure line positions precisely. If one aims at a precision of 3 parts in 100,000, equivalent to +0.0001 A in the lattice parameter, then Eq. (11-1) shows that the 29 position of a line at 29 = 160° must be measured to within 0.02° and lower angle lines even more closely. It is better to determine the line profile by step-counting with a scaler than by chartrecording with a ratemeter. In parameter measurements it is usual to take the 29 value of maximum intensity as the line position strangely, curve-fitting techniques for establishing line position, which are standard in the field of stress measurement (Sec. 16-4), are practically never used. 

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... 

Line positions cannot be measured with sufficient precision on a chart recording made with a ratemeter. Instead, a scaler is used to determine the count rate at several positions on the line profile, and from these data the position of the line center is calculated. This procedure is particularly necessary when the lines are broad, as they are from hardened steel the line width at half-maximum intensity is then 5°-10° 29. If the line is 8° wide and the stress constant AT, is 86.3 ksi/ deg A20, as given above, a stress of 50 ksi will cause the line to shift by only 7 percent of its width when the specimen is turned through 45°. Measurement of such a small shift requires that the line center be accurately located at each angle ij/. 

It is truly portable. The prototype weighs only 23 lb (10 kg) and can be carried by one man, with the aid of a neck strap and two handles, and held in position for a stress measurement. As a fixed instrument, it should be useful for monitoring stress in material coming off a production line. 

If the grains are large, the diffraction line is spotty and its position not well defined. This condition is obvious with a photographic, but not with a diffractometric, technique. If this condition is suspected, a back-reflection pinhole photograph should be made before stress measurements with a diffractometer are attempted. Or the line may be recorded on a dental film placed in front of the counter slit. 

Term 1 is the total spin-line force at any spin-line position term 2 is the spin-line force at position of maximum die swell term 3 is the force due to acceleration of spin line term 4 is force due to surface tension term S is the force due to gravity and term 6 is force due to air drag. If cross-flow is present, there will be another term. This form of force balance presents a clear picture of the terms contributing to the stress at any position. For making calculations, the integration is carried out from the take-up position, where the force is measured, up to any arbitrary spin-line position. This will eliminate from the calculation the force term at the position of maximum diameter, which is not easily evaluated. 

Measurement of Residual Stress and Strain. The displacement of the 2 -value of a particular line in a diffraction pattern from its nominal, nonstressed position gives a measure of the amount of stress retained in the crystaUites during the crystallization process. Thus metals prepared in certain ways (eg, cold rolling) have stress in their polycrystalline form. Strain is a function of peak width, but the peak shape is different than that due to crystaUite size. Usually the two properties, crystaUite size and strain, are deterrnined together by a computer program. 

Deep state experiments measure carrier capture or emission rates, processes that are not sensitive to the microscopic structure (such as chemical composition, symmetry, or spin) of the defect. Therefore, the various techniques for analysis of deep states can at best only show a correlation with a particular impurity when used in conjunction with doping experiments. A definitive, unambiguous assignment is impossible without the aid of other experiments, such as high-resolution absorption or luminescence spectroscopy, or electron paramagnetic resonance (EPR). Unfortunately, these techniques are usually inapplicable to most deep levels. However, when absorption or luminescence lines are detectable and sharp, the symmetry of a defect can be deduced from Zeeman or stress experiments (see, for example, Ozeki et al. 1979b). In certain cases the energy of a transition is sensitive to the isotopic mass of an impurity, and use of isotopically enriched dopants can yield a positive chemical identification of a level. 

Figures 20A and B show the PL spectra, recorded at 290 K, at 600 nm, and as a function of pressure, for Cs9(SmW10O36) and SmWi0O36-LDH, respectively (Park et al., 2002). For the sake of comparison, the line shapes are normalized and displaced along the vertical axis. In both cases, the peak position is red-shifted by 4—5 nm when the hydrostatic pressure increases from 1 bar to 61 kbar. It was shown that the red-shift from A to A lies solely in the deformation of the samarium complexes by the uniaxial stress exerted by the host layers, whereas the shift from B to B is also influenced by the change in the cation environment. Under the same conditions, B is not at the same position for the non-intercalated (HN (n -b u t y 1) 3) 9 (SmW10O3e) and Cs9(SmWi0O36) compounds (Park et al., 2002). Thus only peak A is available to measure the unixial stress. This observation can be used to determine the uniaxial stress, when the external pressure is zero. For the SmW10O36—LDH system, the uniaxial stress varies significantly from 75 at 28 K to 140 kbar at 290 K (Park et al., 2002).

According to this equation, the thrust profile can, in principle, be measured on the upper cone or lower plate. Note that the normal stress differences are assumed to be independent of position. By plotting He0(r) against —ln r/R), a straight line is obtained from whose slope a combination of the primary ( (jxi) - CTee) and secondary (dee - normal stress differences is obtained. Though the pressure profile is difficult to measure, the primary stress difference can be readily determined from the force F exerted on the cone or plate. The value of F is given by... 

The correction is best determined on a specimen of fine powder, which is necessarily free of macrostress. The powder should have about the same composition as the material in which stress is to be measured in order that its diffraction line occur at about the same 26 position, because the correction (A20)o itself depends to some extent on 26. 

A reasonably strong high-angle diffraction line is needed for the measurement of stress. The combination of (hkl) reflecting planes and wavelength A that will produce such a line varies from one kind of material to another. These combinations and the approximate 26 position of the line are listed in Table 16-1 for various materials. 

In the PTIS spectrum of P [49], lines have also been observed at 12.630, and 12.660meV (101.87, and 102.11cm-1), with semi-experimental excited state energy values of 0.256 and 0.226 meV, respectively, which can be ascribed to 8p i and 8/i i levels [20]. The positions of the 4/o, 5po, 6po, and 6/o lines of Sb extrapolated from absorption measurements in the high-stress limit [14] are 73.40, 75.72, 77.76, and 78.40 cm-1 (9.100, 9.388, 9.641, and 9.720 meV), respectively. It is interesting to note that in this study, no value is reported at the position expected (76.75 cm-1) for 5/o. This absence is correlated with a calculated OS for that line about two orders of magnitude smaller than those for the other lines of the series (see Table 5.21). 

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