The crystal structure of a 2M 1 muscovite has been refined by the Rietveld method using X-ray powder-diffraction data collected in reflection and transmission geometries, and compared with the results of single-crystal structure-refinement and electron-microprobe analysis of the same material. The Rietveld refinements converged to R wp = 12.4, 8.7% (R exp = 8.1, 5.9%) and R B = 2.3, 2.5% for transmission- and reflection-geometry data, respectively; the single-crystal structure-refinement converged to an R index of 4.1% for 981 reflections measured with MoKalpha X-radiation. Cell dimensions, interatomic distances and angles, and site occupancies obtained by Rietveld refinement agree well with those from the single-crystal structure-refinement. Comparison of the experimental powder-diffraction patterns with the powder pattern calculated from the results of the single-crystal structure-refinement shows preferred-orientation effects in the experimental patterns. However, comparison of the experimental powder-diffraction patterns with the calculated patterns from the Rietveld refinement shows no sign of any residual preferred-orientation effects, indicating that the algorithm for handling preferred orientation in the Rietveld-refinement procedure is effective.