Diffraction thermal-expansion thermometry ($d(2\theta )/dT=-2{\alpha }_L\tan \theta$)

At fixed radiation wavelength, differentiating Bragg's law for an isotropically expanding cubic specimen gives the displayed angular sensitivity, with angles in radians. Accurate temperature inference requires a calibrated lattice-parameter versus temperature curve, stable wavelength and angular zero, and separation of thermal expansion from stress or composition shifts. Counting statistics can permit centroid precision finer than the observed diffraction-line width.