Structure factors and charge-density study of diamond at 800 K

Abstract

The structure factors of diamond were determined by synchrotron radiation X-ray powder diffraction at 800 K at sin θ/λ ≤ 2.2 Å−1 reciprocal resolution. The structure factors were estimated using six powder profiles measured on beamline BL02B2 at SPring-8 (Hyogo, Japan). A high reciprocal resolution at sin θ/λ ≤ 2.2 Å−1 was required to reveal the temperature dependence of the charge density, due to the high Debye temperature of θD = 1860 K of diamond. Wide 2θ angle data with the highest counting statistics are crucial for accurate data analysis. The periodic noise of every six-pixel step was observed in the highest counting statistics imaging plate (IP) data scanned by a BAS2500 IP scanner. It was found that the noise originated from the six-sided polygonal mirror in the scanner. The intensity fluctuation at every six-pixel step was also found in the Fourier series expansion of the powder profiles. The ratio of the maximum fluctuation was estimated as 0.4% by summing all six-pixel step data. The powder profiles were corrected by multiplying the ratios. The intensity fluctuation in the background region was reduced to less than 50% of the uncorrected data. The weak 888 Bragg reflection, with an intensity of 0.005% of that of the 111 Bragg reflection at 800 K, was readily observed in the corrected data. Finally, the structure factors determined at 800 K were successfully applied to a charge-density study by multipole modelling. The reliability factors and multipole parameters at 800 K are in agreement with those at 300 K. The differences in the charge density at the bond midpoint and ∇2ρ at the bond-critical point were less than 1% and 2%, respectively.