CaF2structure diagram

Displaying lattice parameters for primitive cell; note that calculated cell volumes are typically overestimated on average by 3% (+/- 6%). Note the primitive cell may appear less symmetric than the conventional cell representation (see "Structure Type" selector below the 3d structure)

CaF2chemical name

We have seen that the diffraction-limited resolution of a spectrograph is given by R = Nn = Wn / d, where N is the total number of grooves in the grating, n the order of the spectrum, W the width of the grating and d the groove spacing. Hence, to increase R we can do one of three things:

CaF2structure

In general, band gaps computed with common exchange-correlation functionals such as the LDA and GGA are severely underestimated. Typically the disagreement is reported to be ~50% in the literature. Some internal testing by the Materials Project supports these statements; typically, we find that band gaps are underestimated by ~40%. We additionally find that several known insulators are predicted to be metallic.

CaF2molar mass

Calculated powder diffraction pattern; note that peak spacings may be affected due to inaccuracies in calculated cell volume, which is typically overestimated on average by 3% (+/- 6%)

Caf2chemical formula

The calculated bulk crystalline density, typically underestimated due calculated cell volumes overestimated on average by 3% (+/- 6%)

Simply inserting an echelle in place of a standard grating in a spectrograph, however, would result in multiply overlapping orders. The free spectral range is very small at high orders, hence order sorting filters are of limited use. The solution is to use an additional dispersing element, known as a cross disperser. The cross disperser, which can be either a low dispersion grating or prism, is usually mounted after the echelle grating with its dispersion axis perpendicular to it, as shown in the left-hand panel figure 99. This means that the overlapping orders are separated in the spatial direction on the detector, as shown in the right-hand panel of figure 99. Although each order has only a very narrow wavelength range, there are so many of them, each covering slightly different wavelengths, that very wide spectral coverage is achieved. To prevent the orders overlapping in the spatial direction, only a very short slit must be used. Echelle spectrographs (or high-resolution spectrographs) can deliver resolutions in excess of R = 100,000, and are most famously employed in the detection of extrasolar planets by measuring the tiny Doppler wobble of the host stars.

The energy of decomposition of this material into the set of most stable materials at this chemical composition, in eV/atom. Stability is tested against all potential chemical combinations that result in the material's composition. For example, a Co2O3 structure would be tested for decomposition against other Co2O3 structures, against Co and O2 mixtures, and against CoO and O2 mixtures.

If high-resolution spectroscopy is required, the easiest approach is to increase n which, from the grating equation, implies the use of increased angles of incidence and diffraction. A grating optimised for high-order work is known as an echelle, which comes from the French word for stairs (which describes the blazed profile of the grating). Echelle gratings do not need particularly high ruling frequencies as they operate in high orders. Typical echelles have 20-200 lines/mm and are blazed so that the maximum grating efficiency is in the range n = 10-100.

Calculated total magnetic moment for the unit cell within the magnetic ordering provided (see below). Typically accurate to the second digit.