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I read in a government website that reflecting an x-ray from a parabolic mirror followed by a reflection from a hyperbolic mirror results in focusing the x-ray, but this was for astronomical purposes. I was wondering if in x-ray diffraction this same method is employed, or what method is employed.

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I don't believe X-ray diffraction machines focus the X-rays. Generally you want to put them in along a straight line and detect them undisturbed from the sample. The straight line input beam is just a source an energy selector and a slit (unless the machines have got a lot more complex)

The Wolter mirrors used in telescopes are because you only have very few X-rays photons from a source and so you need to concentrate them on the detector. The optics aren't cheap or convenient to use!

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Technology has evolved a bit compared to what was described by Martin Beckett. Many powder diffractometers still use the setup he describes, but mirrors are becoming more and more common at laboratory powder diffractometer sources. However, these mirrors do not aim to focus the beam, they collimate the beam (try to make sure that as much as possible of the X-rays propagate along parallel lines). The reason for collimating the beam is quite simply that the primary goal of the experiment is to measure the change in angle when the X-rays interact with the sample. To measure this change in angle accurately, the direction of the incident X-ray beam must be well defined.

On a related note, some of the newer mirrors also perform energy filtering: The mirrors are multilayers, creating an "artificial crystal". Bragg reflection from this crystal then ensures that a narrow band of wavelengths are reflected.

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Not entirely correct. Divergent beam diffractometers have been around since there were x-rays. There also exist focussing mirrors to focus x-rays onto the detector in a transmission diffraction experiment. There are pros and cons to all types of instrumentation. – masher 8 hours ago

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