Ultra-high-angle double-crystal X-ray diffractometry (U-HADOX) for determining a change in the lattice spacing: theory.

Advantages of high-angle double-crystal X-ray diffractometry (HADOX) have been re-examined. It is found that, by extending the Bragg angle theta up to 89.99 degrees, the accuracy of a change in the lattice spacing to one part in 10(9)-10(10) can be attained in proportion to tan theta. In such a case, the dispersion-free condition is so serious that the spacing of the two crystals should be equal within one part in 10(6). Therefore, this method is appropriate for determining the thermal expansion coefficient in a limited temperature range. To cover a wide temperature range, the temperature of the reference crystal must be adjusted according to the temperature of the specimen crystal; the lattice spacing as a function of temperature can be determined by integrating the temperature derivative of the spacing.