Relationship between symmetry and estimates of the volume of the unit cell in a powder diffraction pattern

The relationship between the average of the arbitrary discrepancy _n. and the volume V of the unit cell for an n-line powder diffraction pattern is studied. A value S_n is defined by the relation S_n = _nV^2/3. It is a symmetry factor mainly dependent on the reflection conditions of a unit cell. With consideration of the impact of the completeness of the reflections on a real powder diffraction pattern, which is also related to the symmetry factor, a general relation between the real powder diffraction pattern and the volume of the unit cell is established and tested with a number of high quality powder patterns selected from NIST (National Institute of Science and Technology).