Persistence of Covalent Bonding in Liquid Silicon Probed by Inelastic X-Ray Scattering

Abstract

Metallic liquid silicon at 1787K is investigated using x-ray Compton scattering. An excellent agreement is found between the measurements and the corresponding Car-Parrinello molecular dynamics simulations. Our results show persistence of covalent bonding in liquid silicon and provide support for the occurrence of theoretically predicted liquid-liquid phase transition in supercooled liquid states. The population of covalent bond pairs in liquid silicon is estimated to be 17% via a maximally-localized Wannier function analysis. Compton scattering is shown to be a sensitive probe of bonding effects in the liquid state. Silicon (Si) presents a fascinating phase diagram as is the case in other systems that form tetrahedrally coordinated networks.[1] Upon melting, Si transforms into a metal accompanied by a density increase of about 10%. The resistivity of liquid Si (l-Si) at the melting temperature T m is 0.75 µΩm, which is comparable to that of simple liquid metals such as l-Al. However, the first neighbor atomic coordination number in l-Si remains 5.5∼6 [2], which is approximately half that of simple liquid metals, hinting that covalent bonds survive even in the metallic state [3]. In fact, molecular dynamics simulations of molten Si at 1800K suggest that approximately 30% of the bonds are covalent and that these covalent bonds possess a highly dynamic nature, forming and breaking up rapidly on a time scale of 20 fs [4]. It is remarkable that two completely different types of bonds−metallic and covalent− can coexist in l-Si. In fact, the coexistence of two forms of liquid in a single component substance has been predicted to undergo a phase transition as a function of temperature and / or pressure [5], and many theoretical studies support the existence of a liquidliquid phase transition (LLPT) [6][7][8]. A recent study reports that l-Si could undergo an LLPT below about 1232K and above about -12kB, separating into a highdensity metallic liquid (HDL) and a low-density semimetallic liquid (LDL) [8]. But, 1232K is far below the melting temperature of 1683K of Si, and as a result the supercooled state has remained inaccessible to current experimental techniques. Very recently, Beye et al. have performed time-resolved x-ray measurements on Si using a femtosecond pulse-laser [9] to reveal liquid polymorphs of Si which could support an LLPT, but these experimental conditions are far from being ideal [6][7][8] so that the experimental confirmation of an LLPT in Si remains an open question.A key requirement for the possibility of an LLPT obviously is that the metallic and covalent bonds coexist in l-Si. Although experimental investigations of the atomic configuration hint at the existence of covalent bonds in l-Si, surprisingly, soft x-ray [10] and magnetic susceptibility measurements [11] of electronic properties so far do not support this viewpoint in that all four valence electrons in l-Si appear to behave like free-electrons. Emissivity and thermal conductivity of l-Si also exhibit a freeelectron like temperature depen...

How to estimate isotropic distributions and mean values in crystalline solids

“…The expressions presented here would allow the average cyclotron mass over the whole Fermi surface to be approximated from a limited set of temperature-dependencies 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 1 measured with the applied magnetic field along some small number of SDs. We also note some recent experimental work on the melting of the crystalline state, and point out that the averaging process would be applicable to liquid metals [ 54,55] . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43...…”

“…(7 -9) (left) and 1-, 2-and 3-SDs (right), determined, respectively, by ϕ=15 0 and by positive zeros of P 2 (cosΘ), P 4 (cosΘ) and P 6 (cosΘ) with Θ equals, respectively: 54 Fig. 7), facilitating the inclusion of the first five harmonics in Eq.…”

Crystallography Under Extreme Conditions: State of the Art and Perspectives

“…It was proved another time that pressure has an essential role in the production and control of superconductivity (Sun et al, 2012): it is reported that in the superconducting iron chalcogenides, a second superconducting phase suddenly re-emerges at a critical temperature Tc reaching 48.0 K and above 11.5 GPa, after the Tc drops from the first maximum of 32 K at 1 GPa. Metallic liquid silicon at 1787 K was investigated using X-ray scattering (Okada et al, 2012): the results show persistence of covalent bonding in liquid silicon and provide support for the occurrence of theoretically predicted liquid-liquid phase transition in supercooled states. To finish, it can be pointed out the crystallographic structure refinement of a protein, PthXo1 (which is a transcription activator-like, TAL, effector), encoded by an important group of harmful plant pathogens (Mak et al, 2012): understanding DNA recognition by TAL effectors may facilitate rational design of DNA-binding proteins with biotechnological applications.…”

Visualizing the Mixed Bonding Properties of Liquid Boron with High-Resolution X-Ray Compton Scattering

“…In order to hold the sample without contamination, a high temperature electrostatic levitator (HTESL) was used [23]. The detail of the HTESL for SPring-8 experiments is described in [24]. A polycrystalline sample (β-B, 99.9% purity) was used to obtain a spherical averaging Compton profile.…”

“…The energy spectrum of Compton scattered X-rays was converted to the Compton profile with a momentum resolution of 0.16 a.u. The data processing to deduce the Compton profile from the raw energy spectrum consists of following steps: background subtraction, energy dependent corrections for the Compton scattering cross section, the absorption of incident and scattered x-rays in the sample, consideration of efficiency of the analyzer and the detector, and corrections for double scattering events: see [22]. Background in the measured profile is suppressed in the levitation technique used since no material is present in the immediate vicinity of the sample at the x-ray scattering center.…”