Section 5.2.1.3. Errors of the Bragg angle

The error in the Bragg angle, , will ordinarily consist of both random and systematic components. The random components (as the name implies) have an expected value zero, but the systematic errors will affect all measurements consistently to a greater or lesser extent. The systematic errors may be, and usually are, functions of θ and/or λ. Such errors would ordinarily reveal themselves in checks of internal consistency: the values of the apparent lattice parameter, plotted as a function of θ, would show a systematic drift, not a random scatter. The success or otherwise of attempts to eliminate or account for them would be subject to statistical tests (Section 5.2.9 and Chapter 8.5 ). There is an exception to the `ordinarily'; if the variation of with θ happens to be of the form , where K does not depend on θ either explicitly or through λ, the resultant fractional error is a constant, and would not be revealed either by systematic drift of the apparent lattice parameter with θ or by statistical tests.