Influence of partially occupied sites on the near-edge structure in $\beta$-rhombohedral boron: An X-ray Raman scattering study

Highlights

• FEFF calculations of XRS were performed considering partially occupied sites.

• s-states are responsible for the momentum transfer evolution of XRS in $\beta$-boron.

• POSs affect transitions to unoccupied exo-icosahedron molecular orbitals in $\beta$-boron.

Abstract

A study of the near-edge structure at the $K$-edge of elemental boron in its $\beta$-rhombohedral phase is presented. Momentum-transfer dependent measurements of the B 1s core-electron excitation spectra were performed by X-ray Raman scattering (XRS) spectroscopy. Spectral features were interpreted based on calculations of the XRS spectra. A method to model a system with partially occupied sites (POS) was implemented based on FEFF simulations of XRS spectra. The inclusion of POS in the crystal structure of $\beta$-rhombohedral boron in the calculations was essential in order to achieve agreement between simulated and measured spectra. Transitions from the core-level to exo-icosahedron orbitals were found to be sensitive to the presence of partially occupied sites in $\beta$-rhombohedral boron. The origin and the momentum-transfer dependence of the spectral features are discussed. Characteristic spectral features from icosahedral units and from icosahedron clusters were identified. Activation of non-dipole transitions at high momentum transfers was detected.

Introduction

Due to its physicochemical properties, elemental boron has attracted wide interest in material research. It is lighter than aluminum, has a high melting point, low reactivity at room temperature and its stable phases are almost as hard as diamond [1], [2]. Boron-rich compounds have also attracted much attention because of their diversity of promising technological properties, as, for instance, high temperature superconductibity (MgB${}_2$ [3]), super hardness (B${}_4$C, cubic-BN and cubic-BC${}_2$N [4]), high-performance hydrogen storage (LiBH${}_4$ and NH${}_3$BH${}_3$ [5]) or high thermionic emissivity (LaB${}_6$ nanowire [6]). The elemental boron can form 16 allotropes in a solid phase, but only four of them, the $\alpha$-rhombohedral, $\beta$-rhombohedral, T-192 and $\gamma$ phases, are thermodynamically stable [7]. At ambient pressure and temperatures below the melting point, $\beta$-rhombohedral boron is the stable phase with a slight difference in total energy with respect to the $\alpha$-rhombohedral phase [7]. $\beta$-boron has a very complex structure with more than 320 atoms per hexagonal unit cell (more than 106 atoms per rhombohedral unit cell) and a large number of defects, which consist of vacancies and interstitial atoms in sites with partial occupations [8]. Several vacancy and interstitial atom configurations have similar energies and play an important role in the stability of $\beta$-rhombohedral boron [9], [10]. The partially occupied sites (POS) determine the electronic structure of boron by filling the valence band and also by producing a self-doping effect, making boron behave like a $p$-type semiconductor with a band gap of 1,6 eV [11]. Due to its complex crystalline structure, along with the large number of sites with partial occupation, calculations of electronic structure and spectroscopic properties of $\beta$-rhombohedral boron have been a challenging task [1]. The inelastic x-ray scattering (IXS) techniques are a valuable tool for the study of dynamical properties of electrons in materials [12]. The specific information obtained in a particular IXS experiment depends on the relation between the energy and the momentum transfer in the interaction process and the characteristic quantities of the electron system. Particularly, inelastic X-ray scattering by core electrons or X-ray Raman scattering (XRS) provides information about unoccupied electronic states in a similar way to X-ray absorption spectroscopy (XAS), provided that the dipole approximation is satisfied (small transferred momentum compared to the reciprocal of the atomic orbital radius). The possibility of controlling the magnitude of the momentum transfer gives the capability of investigating electronic transitions other than the dipole ones. An additional advantage of XRS at the $K$-edge of light elements over soft X-ray or UV absorption spectroscopy lies in the fact that XRS uses hard X-rays, which, due to their high penetration length, allow to obtain true bulk information and to avoid spurious signals due to eventual surface contaminants.

Although synchrotron-radiation based XRS studies have been carried out on a wide variety of boron compounds [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], on elemental boron they are very scarce [24]. First reported XRS measurements on a boron sample [25], performed using Cr $K_{\alpha }$ radiation from an X-ray tube, showed an edge-like spectrum, similar to the $K$-absorption spectrum, but no fine structure was observed because of the low resolving power of those measurements. Later XRS studies on boron samples, done at the end of the 80’s [26], [27] and in the early 90’s [28], but which still used radiation from an X-ray tube, provided some controversial results. Anomalous peaks observed in the XRS spectrum around 280 eV and 300 eV energy loss [26], [28] were related to the structure of the density of electronic states of high-energy lying unoccupied bands. On the contrary, no such structure was observed in the measurements by Manninen et al. [27], performed under similar experimental conditions concerning radiation source and resolving power. The first high-resolution, synchrotron-radiation based XRS study of the boron $K$-absorption edge [24] confirmed the absence of anomalous structures up to 300 eV energy loss. Additionally, and most importantly, this high resolution experiment succeeded in showing evidence for some near-edge structure at the boron $K$-edge, though it was measured with rather poor statistical accuracy. Furthermore, this experiment was performed only at two very close to each other scattering angles, thus corresponding to very similar magnitudes of momentum transfers. This fact avoided probing electronic transitions to final states of different symmetries and investigating their relative contributions, which could be made by varying the momentum transfer on a wide range of magnitudes, going from dipole-allowed to non-dipole transitions.

In this work, we report an experimental and theoretical study of the near-edge structure at the $K$-edge of elemental boron in its $\beta$-rhombohedral phase. Momentum-transfer resolved XRS measurements of the B $K$-edge were performed with high energy resolution and in a wide range of momentum transfers, going from dipole-allowed to non-dipole core-electron transitions. The partial occupancy of crystallographic sites of $\beta$-rhombohedral boron is considered in the calculation methodology and its effects on the near-edge structures is discussed.