The uniformity of the lattice spacing of silicon crystals was evaluated by the self-referenced lattice comparator with a resolution of    $3\times 10^{\mathrm {\mathbf {-9}}}$   . Lattice strain measurements were performed for the sample 10.5 cut from  28 Si ingot (Avo28), which was used to determine the Avogadro constant. The mapping results for samples 4.R1, XINT, and 9.R1 performed in the previous works have also been re-evaluated. The 4.R1 in the seed side of the ingot and the XINT in the middle of the ingot have small distribution of lattice spacing. The standard deviations of the lattice spacing distribution for the 4.R1 and XINT were    $4.8\times 10^{\mathrm {\mathbf {-9}}}$    and    $5.5\times 10^{\mathrm {\mathbf {-9}}}$   , respectively. In contrast, the 9.R1 and the 10.5 samples cut from the tail side of the ingot have a larger distribution of lattice spacing. These lattice spacing distributions in the ingot are consistent with the impurity distribution in the ingot.
['Atsushi Waseda', 'Hiroyuki Fujimoto', 'Xiao Wei Zhang', 'Naoki Kuramoto', 'Kenichi Fujii']
Uniformity Evaluation of Lattice Spacing of 28 Si Single Crystals