Precision Determination of Lattice Constants with a Geiger-Counter X-Ray Diffractometer

It is shown that the Geiger-counter x-ray diffractometer can be used for precision determination of lattice constants. The zero point of the goniometer (determined by two methods) and the position of the diffraction lines ($2\theta$) were obtained with an accuracy of ±0.001°. The temperature was kept constant by a special unit within 0.05°C. An investigation of the systematic errors was made, which shows that the extrapolation of lattice constants vs ${cos}^2\theta$, according to Wilson's equation, is permissible and the vertical divergence error, as computed by Eastabrook, lies within our tolerances for $2\theta$ up to 165° and may be neglected. The lattice constants of Al, Ag, Ge, Si, Ca${\mathrm{F}}_2$, CsI, TlCl, and TlBr, determined by extrapolation, are in good agreement with published data. The limiting factor in the accuracy of the lattice constant determination is not in the error of the diffractometer, but in the x-ray wavelength.