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 / 2.2 Å À1 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 / 2.2 Å À1 was required to reveal the temperature dependence of the charge density, due to the high Debye temperature of D = 1860 K of diamond. Wide 2 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 r 2 at the bondcritical point were less than 1% and 2%, respectively.

Electron density and thermal motion of diamond at elevated temperatures

“…The relatively large negative value of r 2 BCP corroborates that the C-C interaction in diamond is covalent, in line with expectations from fundamental chemistry. The value of BCP ranges from 1.61 to 1.64, which is in excellent agreement with previous studies (Svendsen et al, 2010;Bindzus et al, 2014;Deguchi & Nishibori, 2018;Svane et al, 2021).…”

“…The diamond structure has been reported to have a Debye temperature between 1800 K and 2300 K (Schoening & Vermeulen, 1969;Zhi-Jian et al, 2009) and it exhibits only a minor thermal expansion of approximately 1 pm from 0 K to 1250 K (Jacobson & Stoupin, 2019). In combination, these properties hint at a rigid structure where the ED can be reasonably assumed constant at temperatures from 0 K to 1000 K. In fact, the ED has already been reported to be nearly identical at 300 K and 800 K (Deguchi & Nishibori, 2018). Diamond therefore serves as a good candidate structure to test the convolution approximation.…”

Atomic-Scale Visualization of Ultrafast Bond Breaking in X-Ray-Excited Diamond

“…Integrated diffraction intensity for each reflection was evaluated by the profile fitting and the Rietveld refinement. By dividing the square of structure factors of diamond measured with synchrotron radiation [25] by the integrated diffraction intensity of undamaged diamond, a geometrical correction factor was determined for each reflection. Then, the integrated diffraction intensity for x-ray-excited diamond was multiplied by the correction factor and used for structure refinement.…”

“…In this model, the electron-density distribution is simply described by the following seven parameters: the scale factor s, the isotropic displacement U iso , the radial expansion and contraction parameters for the spherical (κ) and aspherical (κ 0 ) parts, the octupole (O2-), and the hexadecapoles (H0 and H4þ). Here, κ and O2-are the main components that determine valence charge density distribution in diamond [25]. Also, H4þ is constrained to H0 by H4þ ¼ ð0.74048ÞH0 due to the symmetry of diamond.…”

“…Also, H4þ is constrained to H0 by H4þ ¼ ð0.74048ÞH0 due to the symmetry of diamond. The multipole refinement was performed using s, U iso , κ, and O2-, while the other three parameters (κ 0 , H0, H4) were set to be the same as those for undamaged diamond [25]. The refinement of the modeling resulted in excellent crystal reliability factors (R factors) [R factors: 3.0% (delay time of 0.5 fs), 5.2% (5 fs), 8.9% (10 fs), 5.5% (20 fs), 3.0% (35 fs), and 3.3% (50 fs)], which are comparable to the previous charge density studies of diamond [25,[30][31][32][33][34][35][36][37].…”