Journal of the Mineralogical Society of Korea (한국광물학회지)

The Mineralogical Society of Korea (한국광물학회)
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Core-hole Effect on Partial Electronic Density of State and O K-edge x-ray Raman Scattering Spectra of High-Pressure SiO2 Phases

전자-정공 효과(Core-Hole Effect) 적용에 따른 SiO2 고압상들의 전자구조 및 O K-edge X-선 Raman 산란 스펙트럼 계산 결과 분석

  • Khim, Hoon (School of Earth and Environmental Sciences, Seoul National University) ;
  • Yi, Yoo Soo (School of Earth and Environmental Sciences, Seoul National University) ;
  • Lee, Sung Keun (School of Earth and Environmental Sciences, Seoul National University)
  • 김훈 (서울대학교 지구환경과학부) ;
  • 이유수 (서울대학교 지구환경과학부) ;
  • 이성근 (서울대학교 지구환경과학부)
  • Received : 2017.04.25
  • Accepted : 2017.05.29
  • Published : 2017.06.30
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Abstract

$SiO_2$ is one of the most abundant constituents of the Earth's crust and mantle. Probing its electronic structures at high pressures is essential to understand their elastic and thermodynamic properties in the Earth's interior. The in situ high-pressure x-ray Raman scattering (XRS) experiment has been effective in providing detailed bonding transitions of the low-z materials under extreme compression. However, the relationship between the local atomic structures and XRS features at high pressure has not been fully established. The ab initio calculations have been used to overcome such experimental difficulties. Here we report the partial density of states (PDOS) of O atoms and the O K-edge XRS spectra of ${\alpha}-quartz$, ${\alpha}-cristobalite$, and $CaCl_2$-type $SiO_2$ phases calculated using ab initio calculations based on the full-potential linearized augmented plane wave (FP-LAPW) method. The unoccupied O PDOSs of the $CaCl_2$-type $SiO_2$ calculated with and without applying the core-hole effects present significantly distinctive features. The unoccupied O p states of the ${\alpha}-quartz$, ${\alpha}-cristobalite$ and $CaCl_2$-type $SiO_2$ calculated with considering the core-hole effect present similar features to their calculated O K-edge XRS spectra. This confirms that characteristic features in the O K-edge XRS stem from the electronic transition from 1s to unoccupied 2p states. The current results indicate that the core-hole effects should be taken in to consideration to calculate the precise O K-edge XRS features of the $SiO_2$ polymorphs at high pressure. Furthermore, we also calculated O K-edge XRS spectrum for $CaCl_2$-type $SiO_2$ at ~63 GPa. As the experimental spectra for these high pressure phases are not currently available, the current results for the $CaCl_2$-type $SiO_2$ provide useful prospect to predict in situ high-pressure XRS spectra.

$SiO_2$는 지각과 맨틀을 구성하는 풍부한 물질로 고압 상태의 $SiO_2$ 원자구조를 결정짓는 전자구조적 특성에 대한 상세한 이해는 지구 내부의 탄성과 열역학적 성질에 대한 통찰을 제공한다. $SiO_2$처럼 경원소(low-z)로 이루어진 지구 물질의 고압상 전자구조는 in situ 고압 XRS (x-ray Raman scattering) 실험을 통해 연구되어 왔다. 하지만 기존의 고압 실험 방법으로는 물질의 국소 원자구조와 XRS 스펙트럼 간 상관관계를 밝히는데 한계가 있다. 이를 극복하고 더 높은 압력에서 존재하는 $SiO_2$에 대한 XRS 정보를 얻기 위해 밀도 범함수 이론(density functional theory; DFT)에 기반을 둔 제1원리(ab initio) 계산법을 이용한 XRS 스펙트럼 계산 연구들이 진행되고 있다. 비탄성 X-선 산란에 의하여 원자핵 주변 1s 오비탈에 만들어지는 전자-정공(core-hole)은 경원소 물질의 국소 전자구조에 크게 영향을 미치기 때문에 O K-edge XRS 스펙트럼 형태를 계산할 때 중요하게 고려해야 한다. 본 연구에서는 온-퍼텐셜 선형보충파(full-potential linearized augmented plane wave; FP-LAPW) 방법론에 기반하는 WIEN2k 프로그램을 사용하여 ${\alpha}-quartz$, ${\alpha}-cristobalite$ 그리고 $CaCl_2$-구조를 갖는 $SiO_2$에 대한 O 원자 전자 오비탈의 부분 상태밀도(partial density of states; PDOS)와 O K-edge XRS 스펙트럼을 계산하였다. 또한, $CaCl_2$-구조를 갖는 $SiO_2$의 O 원자 PDOS의 전자-정공 효과의 적용 여부에 따른 차이를 비교하여, 원자핵 부근 전자구조 변화에 따른 PDOS의 피크 세기와 위치 변화가 크게 나타났다는 사실을 확인할 수 있었다. 또한 계산된 각 $SiO_2$ 구조의 O K-edge XRS 스펙트럼이 각 $SiO_2$ 구조에서 계산된 O 원자의 $p^*$ 오비탈의 PDOS 결과와 매우 유사한 형태를 갖고 있음을 확인하였다. 이는 O K-edge XRS 스펙트럼이 갖는 대부분의 특징적인 피크들이 O 원자의 점유 1s 오비탈에서 $2p^*$ 오비탈로의 전자전이에 기인하기 때문이다. 본 연구의 결과는 $SiO_2$에 대한 정확한 O K-edge XRS 스펙트럼을 계산하는데 있어 전자-정공 효과를 고려해야 한다는 사실을 보여준다. 또한, 실험적으로는 재현이 어려운 고압 환경에 존재하는 $CaCl_2$-구조를 갖는 $SiO_2$ (~63 GPa)에 대한 O K-edge XRS 스펙트럼 계산을 통해, 제1원리 계산이 고압상 물질의 물성 연구에 이용될 수 있다는 사실을 보여준다.

Keywords

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