X-ray diffraction study of undercooled molten silicon

Abstract

The short-range order of molten silicon was investigated in a wide temperature range from 1893 K down to 1403 K, corresponding to an undercooling of 290 K. Energy-dispersive x-ray diffraction was used in combination with electromagnetic levitation. The structure factor and the pair correlation function were determined as a function of temperature from the experimental data. A small hump on the higher wave vector side of the first peak in the structure factor was observed at all temperatures. The position of the first peak in the pair distribution function shifted to shorter distances and its height increased gradually with decreasing temperature. No discontinuous behavior was observed in the entire temperature range investigated.

In situHigh-Energy X-Ray Diffraction Study of the Local Structure of Supercooled Liquid Si

“…For direct comparison, the results of previous x-ray measurements are reproduced in Fig. 3(b) [7][8][9]. For liquids, the first shell coordination number is poorly defined, and several methods for determining N can be found in the literature [16].…”

“…For example, x-ray measurements made using conical nozzle levitation [7,8] have provided structural information for a supercooling of 230 K below the melting point (T M 1685 K) and identified a decrease in the coordination number from 6.3 at 1767 K to about 5.6 at 1458 K. This result is consistent with the predicted decrease in coordination number obtained from simulations using the SW potential as the temperature is reduced below T M , and was argued to provide strong evidence for the existence of an underlying first-order L-L transition. However, other x-ray measurements by Kimura et al [9] employing electromagnetic levitation (EML) for a supercooling of 290 K below the melting point found an increase in the average coordination number from 5.5 at 1793 K to 6.1 at 1403 K. Recent measurements by Higuchi et al [10], using EML to a supercooling of 150 K, found no change in coordination number with temperature, but obtained a rather low value for the coordination number (N 5) relative to previous investigations. The discrepancies between these results and the fact that none of the groups found evidence of a discontinuous change in the structure, indicative of a first-order L-L transition, leaves the matter of a L-L transition in supercooled liquid silicon an open question.…”

“…The use of a gas stream for levitation, together with the decreased sample penetration, raises some concerns about the impact of surface contamination upon these results. Energy dispersive x-ray diffraction studies [9] and angular dispersive measurements at 50 keV [10] on electromagnetically levitated samples 8-10 mm in diameter have found either an increasing or a constant, but lower, coordination number with decreasing temperature, respectively. The present measurements provide a more precise determination of the structure of supercooled liquid Si because of the high-vacuum environment of ESL and the use of high- energy x rays, minimizing the impact of any surface contamination and the effects of sample absorption and multiple scattering.…”

“…For liquids, the first shell coordination number is poorly defined, and several methods for determining N can be found in the literature [16]. The method chosen in previous experiments [7][8][9][10] on liquid Si was to integrate the radial distribution function, R r , up to the first minimum after the main peak. Here, R r 4 r 2 0 1 G r =4 r 0 and 0 is the average number density.…”

Levitation methods for structural and dynamical studies of liquids at high temperatures

“…This is achieved by taking subsequently spectra at different angles and fitting them simulataneously by a reverse Monte Carlo technique. This method was applied successfully for determination of the structure factor of pure silicon on ID 09 at ESRF, using electromagnetic levitation [9]. A wide temperature range, including the undercooled regime was covered, and the nearest neighbour distance as well as the coordination number was obtained as function of temperature.…”