Dalton (unit)
X-ray crystal density methods

Silicon single crystals may be produced today in commercial facilities with extremely high purity and with few lattice defects. This method defined the Avogadro constant as the ratio of the molar volume, V, to the atomic volume V: N A = V m V a t o m, {\displaystyle N_{\rm {A}}={\frac {V_{\rm {m}}}{V_{\rm {atom}}}},} where V = V / n and n is the number of atoms per unit cell of volume V.

The unit cell of silicon has a cubic packing arrangement of 8 atoms, and the unit cell volume may be measured by determining a single unit cell parameter, the length a of one of the sides of the cube. The CODATA value of a for silicon is 5.431 020 511 (89) × 10 m.

In practice, measurements are carried out on a distance known as d (Si), which is the distance between the planes denoted by the Miller indices {220}, and is equal to a / √ 8.

The isotope proportional composition of the sample used must be measured and taken into account. Silicon occurs in three stable isotopes (Si, Si, Si), and the natural variation in their proportions is greater than other uncertainties in the measurements. The atomic weight A for the sample crystal can be calculated, as the standard atomic weights of the three nuclides are known with great accuracy. This, together with the measured density ρ of the sample, allows the molar volume V to be determined: V m = A r M u ρ, {\displaystyle V_{\rm {m}}={\frac {A_{\rm {r}}M_{\rm {u}}}{\rho }},} where M is the molar mass constant. The CODATA value for the molar volume of silicon is 1.205 883 199 (60) × 10 m ⋅mol, with a relative standard uncertainty of 4.9 × 10.
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