= Solution
<Diffraction thermal-expansion thermometry> needs a stable monochromatic <X-ray> beam, controlled collimation, an accurately calibrated angular scale, and an X-ray-sensitive detector with enough counts to fit reproducible line centroids. Crystal monochromators or appropriate <energy> selection are relevant here; an apparatus for visible-light interference does not directly measure these <X-ray> peaks. Sample displacement and angular-zero drift should be checked with a suitable reference standard.
The first-order angular sensitivities are about $6.93\times10^{-5}$ and $1.17\times10^{-4}$ degrees per kelvin, respectively. A one-kelvin inference therefore requires comparable centroid stability, with high count statistics and control of systematic errors; a centroid can be fitted more precisely than the line width. Fractional <wavelength> drift also mimics lattice expansion, so the desired <temperature> precision constrains $\Delta\lambda/\lambda$ relative to $\alpha_L\Delta T$.
The powder must be at a known uniform <temperature> and allowed to equilibrate. Mechanical stress, clamping, composition changes, oxidation and phase changes can also shift or broaden peaks. Accurate work requires a calibrated $a(T)$, including the actual <temperature> dependence of the <thermal expansion coefficient>, rather than assuming the supplied constant describes every <temperature> exactly. Using both lines provides a consistency check on a common cubic expansion.
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