Crystal line width

Cleaved crystals, line widths obtained with, 115, 116... 

Garnets have played an important role in the development of highly sophisticated microwave devices since the development of yttrium—iron garnet, yttrium iron oxide [12063-56-8]. The iron is strongly constrained to be trivalent in order to maintain electrical neutraUty in the crystal, which is essential for low microwave losses. Garnets have lower values of saturation magneti2ation than spinels, but provide superior performance in microwave devices because they have a narrower resonance line width. 

Figures 6.30 and 6.31 present the same information for saturated hydrocarbons. In Figure 6.30, the saturated liquid state is on the lower part of the curve and in Figure 6.31 it is on the upper part of the curve. Below T y, the line width changes, indicating that the liquid probably does not flash below that level. Note that a line has been drawn only to show the relationship between the points a curve reflecting an actual event would be smooth. Note that a liquid has much more energy per unit of volume than a vapor, especially carbon dioxide. Note It is likely that carbon dioxide can flash explosively at a temperature below the superheat limit temperature. This may result from the fact that carbon dioxide crystallizes at ambient pressure and thus provides the required number of nucleation sites to permit explosive vaporization.

Element Analyt- ical Line Wavelength, A Crystal Slit Width, in. Path Type of Detector Detector Path Length, cm Detector Window"... 

X-Ray diffraction has an important limitation Clear diffraction peaks are only observed when the sample possesses sufficient long-range order. The advantage of this limitation is that the width (or rather the shape) of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow, see for example the (111) and (200) reflections of large palladium particles in Fig. 4.5. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The two XRD patterns of supported Pd catalysts in Fig. 4.5 show that the reflections of palladium are much broader than those of the reference. The Scherrer formula relates crystal size to line width ... 

Potzel et al. [60] used a Ga/ZnO single crystal source in combination with a single crystal absorber of natural ZnO and observed a resonance line width of 0.36 0.04 pm s for the 93.3 keV transition in Zn (at 4.2 K). This, after correction for finite absorber thickness, equals, within the limit of error, the minimum observable line width as deduced from the lifetime of 13.4 ps for the 93.3 keV state. The spectra observed by these authors are shown in Fig. 7.23. 

Crystals of (TTF)[Au(C6F5)C1] have been grown by electrocrystallization [53] however, their crystal structure has not been determined. The room temperature conductivity, as measured on compacted pellets, is quite low (10-6 S cm-1). At room temperature, the EPR line width of these salts is about 10 G. This line width decreases with temperature as a result of increased spin-lattice relaxation times and a lower electrical conductivity. 

In the paramagnetic regime, the evolution of the EPR line width and g value show the presence of two transitions, observed at 142 and 61 K in the Mo salt, and at 222 and 46 K in the W salt. Based on detailed X-ray diffraction experiments performed on the Mo salt, the high temperature transition has been attributed to a structural second-order phase transition to a triclinic unit cell with apparition of a superstructure with a modulation vector q = (0,1/2, 1/2). Because of a twinning of the crystals at this transition, it has not been possible to determine the microscopic features of the transition, which is probably associated to an ordering of the anions, which are disordered at room temperature, an original feature for such centrosymmetric anions. This superstructure remains present down to the Neel... 

In order to dissipate the recoil energy Mossbauer was the first to use atoms in solid crystal lattices as emitters and also to cool both emitter and absorber. In this way it could be shown that the 7-ray emission from radioactive cobalt metal was absorbed by metallic iron. However, it was also found that if the iron sample were in any other chemical state, the different chemical surroundings of the iron nucleus produce a sufficient effect on the nuclear energy levels for absorption no longer to occur. To enable a search for the precisely required absorption frequency, a scan based on the Doppler effect was developed. It was noted that a velocity of 102 ms-1 produced an enormous Doppler shift and using the same equation (7) it follows that a readily attainable displacement of the source at a velocity of 1 cms-1 produces a shift of 108 Hz. This shift corresponds to about 100 line-widths and provides a reasonable scan width. 

The line width of the X-ray source is on the order of 1 eV for A1 or Mg Ka sources but can be reduced to better than about 0.3 eV with the use of a monochromator. A monochromator contains a quartz crystal which is positioned at the correct Bragg angle for A1 Ka radiation. The monochromator narrows this line significantly and focuses it onto the sample. It also cuts out all unwanted X-ray satellites and background radiation. An important advantage of using a monochromator is that heat and secondary electrons generated by the X-ray source cannot reach the sample. 

The Scherrer formula relates crystal size to line width ... 

The line widths and shapes to be expected for cubic crystals containing point defects have been derived by Cohen and Reif for both first and second order quadrupole interaction 97). In particular, for point defect concentrations greater than about 0.1 (in terms of probability /, of a lattice site being occupied by a defect) distributed in a random fashion over various possible lattice sites, the second order interaction gives rise to a lopsided central component whose shape is given by (97)... 

---