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 θ up to 89.99°, the accuracy of a change in the lattice spacing to one part in 10⁹-10¹⁰ can be attained in proportion to tan θ. 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 10⁶. 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.