Temperature gradient analyzers for compact high-resolution X-ray spectrometers

Compact high-resolution X-ray spectrometers with a one-dimensional temperature gradient at the analyzer crystal are considered. This gradient, combined with the use of a position-sensitive detector, makes it possible to relax the usual Rowland-circle condition, allowing increased space at the sample position for a given energy resolution or arm radius. Thus, for example, it is estimated that approximately meV resolution is possible with a 3 m analyzer arm and 200 mm clearance between the sample and detector. Simple analytic formulae are provided, supported by excellent agreement with ray-tracing simulations. One variation of this method also allows the detector position sensitivity to be used to determine momentum transfer, effectively improving momentum resolution without reducing (slitting down) the analyzer size. Application to medium-resolution ( approximately 10-100 meV) inelastic X-ray scattering spectrometers with large angular acceptance is discussed, where this method also allows increased space at the sample. In some cases the application of a temperature gradient can improve the energy resolution even with a single-element detector.