Amount of substance measurement homogeneity principle: The discrepancy between XRCD and watt balance results

Amount of substance is one of the base quantities that form the International System of units. The quantity measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons and other particles. In order to count atoms with a relative uncertainty of better than 2 x 10(-8), here we formulate the amount of substance measurement homogeneity principle. A consequence of this principle is that the accuracy of a measurement of amount of substance is limited by the homogeneity of the sample. We propose a criterion of sample preparation for the accurate determination of molar mass which is to ensure complete chemical conversions, no fractionation, homogeneity at the molecular level and less contamination. Based on this philosophy, a more accurate molar mass of natural single crystal silicon was achieved. We found that there was an isotope fractionation in the preparation process of the NaOH solution method. It led to an Avogadro constant value 1.0 x 10(-6) lower. The corrected value is higher than previous data, and compatible with recent values of the Planck constant.