Molar Volume Of Silicon Research Articles

Flotation measurements to reveal the reason for the discrepancy in the molar volume of silicon

To reveal the reason for the discrepancy of relatively 3/spl middot/10/sup -6/ in the molar volume of silicon found in crystals of different origin, the densities of crystals grown under different conditions were compared using a flotation method. The method and the apparatus used at Physikalisch-Technische Bundesanstalt, Braunschweig, Germany, and the evaluation of data using Lagrange multipliers are described. The obtained results are reported and the contributions to the standard uncertainty of the silicon density /spl rho//sub si/ of about 1.0/spl middot/10/sup -7//spl rho//sub si/ are discussed.

Density measurements of silicon crystals by hydrostatic weighing [for Avogadro constant determination

Through research for a determination of the Avogadro constant by the X-ray crystal density method, a primary density standard based on silicon crystals was established at the NRLM with a relative combined standard uncertainty of 1.0/spl times/10/sup -7/. To investigate the cause of the existing discrepancy in the molar volume of silicon in single crystals, a new hydrostatic weighing system has been developed for evaluating the consistency in the absolute density values of the silicon crystals used for the determination of the Avogadro constant. This system measures the density of a solid material under study with respect to that of a primary standard with a relative combined standard uncertainty of 1.3/spl times/10/sup -7/. Some measurement results on silicon spheres fabricated from different silicon ingots are described.

The Avogadro problem: summary of tests on crystal imperfections

International measurements of the molar volume of silicon on the basis of more than 15 different crystals have confirmed the Committee on Data for Science and Technology (CO-DATA) value of the Avogadro constant published in 1986. Only one discrepancy still exists and cannot yet be completely explained. In this paper, we summarize results of tests that relate to the perfection of the crystals used. With high probability, it turns out that imperfections of the crystal material itself and not the uncertainties of the measurement procedures are responsible fur this inconsistency. At present, the lack of exact knowledge of the degree of crystallographic perfection and, in particular, of the isotopic composition, hampers the progress of the crystal route for a new definition of the kilogram.

The molar volume of silicon: discrepancies and limitations

We offer a new representation of the silicon molar volume discrepancy by attending to a previously incorrect accounting of the early work at the National Bureau of Standards (NBS). Removal of a poorly documented correction to the NBS density scale leads to a plausibly correct description of the molar volume anomaly problem. The possibility of discrepant metrology has been previously ruled out by sample exchanges. This led to several materials characterization exercises that gave important null results as briefly summarized here. We report the first non-null results and examine their correlation with those samples with discrepant molar volume values. In the end, there is a reasonably optimistic prospect that concordant and accurate density values can emerge at an interesting level of significance (less than 10/sup -7/). A brief discussion of intrinsic limitations of melt-grown crystals is included.

New methods for determining the void content of silicon single crystals

Two methods are proposed to determine upper limits to the total void volume in silicon single crystals. Both are based on the fast interstitial diffusion of metals (Cu, in particular) in Si. The first method is based on measuring the total area of the cavity walls by forming a metal monolayer on them. The second method is based on filling the cavities with silicide precipitates. These upper limits may be useful in assessing the uncertainties in the determination of the Avogadro constant from the molar volume of silicon.

Volume and density measurements for the IMGC Avogadro experiment

Volume and density measurement efforts at the IMGC made in the framework of the Avogadro constant experiment are reviewed, and a critical analysis of the problems encountered is presented. The status of efforts directed at the determination of the molar volume of silicon is examined, with emphasis on the development and application of a new, more precise silicon standard. >

Toward the Avogadro constant-preliminary results on the molar volume of silicon

The silicon molar volume has been measured through atomic weight and density measurements. Mass spectrometric determination of the isotopic composition was performed on two differently grown samples by comparison with the US National Bureau of Standards (NBS) reference material SRM 990. The density of specimens from the same crystals was obtained through direct mass and dimension measurements on one single-crystal sphere and through hydrostatic comparison for another sphere. Compatibility with previous measurements was checked through hydrostatic comparison with IMGC Zerodur density standards. The two molar volume determinations differ by 0.14 p.p.m. The preliminary value obtained is 12.058, 843+or-0.000, 029 cm/sup 3//mol at 22.5 degrees C and in vacuo.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Avogadro constant — Recent results on the molar volume of silicon

The density p of two silicon crystals has been determined by precision hydrostatic weighing, based on very accurate solid density standards (SDS's). Densities of additional crystals were gained from density differences measured by the temperature-of-floatation method. The molar mass M of the crystals was determined by comparing the isotopie abundances against the known abundances of the National Bureau of Standards (NBS) reference material SRM 990 using activation analysis and mass spectroscopy. Combining the measured values for M and p leads to M/p = (12.058 822 ± 0.000 013) cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> /mol. With the known volume of the unit cell the following value for the Avogadro constant was calculated: N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</inf> = (6.022 137 ± 0.000 007) × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">23</sup> mol <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> .