Journal of the Mineralogical Society of Korea (한국광물학회지)

The Mineralogical Society of Korea (한국광물학회)
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A Computational Mineralogy Study of the Crystal Structure and Stability of Aluminum Silicate (Al2SiO5) Minerals

알루미늄 규산염(Al2SiO5) 광물의 결정구조와 안정성에 대한 계산광물학 연구

  • Kim, Juhyeok (Department of Geology, Kangwon National University) ;
  • Son, Sangbo (Department of Geology, Kangwon National University) ;
  • Kwon, Kideok D. (Department of Geology, Kangwon National University)
  • 김주혁 (강원대학교 자연과학대학 지질학과) ;
  • 손상보 (강원대학교 자연과학대학 지질학과) ;
  • 권기덕 (강원대학교 자연과학대학 지질학과)
  • Received : 2018.03.02
  • Accepted : 2018.03.30
  • Published : 2018.03.31
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Abstract

Aluminum silicates ($Al_2SiO_5$) undergo phase transitions among kyanite, andalusite, and sillimanite depending on temperature and pressure conditions. The minerals are often used as an important indicator of the degree of metamorphism for certain metamorphic rocks. In this study, we have applied classical molecular dynamics (MD) simulations and density functional theory (DFT) to the aluminum silicates. We examined the crystal structures as a function of applied pressure and the corresponding stabilities based on calculated enthalpies at each pressure. In terms of the lattice parameters, both methods showed that the volume decreases as the pressure increases as observed in the experiment. In particular, DFT results differed from experimental results by much less than 1%. As to the relative stability, however, both methods showed different levels of accuracy. In the MD simulations, a transition pressure at which the relative stability between two minerals reverse could not be determined because the enthalpies were insensitive to the applied pressure. On the other hand, in DFT calculations, the relative stability relation among the three minerals was consistent with experiment, although the transition pressure was strongly dependent on the choice of the electronic exchange-correlation functional.

알루미늄 규산염($Al_2SiO_5$) 광물은 온도와 압력 환경에 따라 남정석, 홍주석, 규선석으로 상전이가 일어나는 동질이상(polymorph)으로 변성암의 변성정도를 유추하는 데 사용되는 중요한 광물이다. 이번 연구에서는 고전분자동력학 시뮬레이션(classical molecular dynamic simulations)과 양자역학 계산방법인 밀도범함수이론(density functional theory)을 이용하여 압력에 따른 알루미늄 규산염 광물의 결정구조와 엔탈피를 계산하고, 상대적인 안정성을 평가하였다. 격자상수 계산결과, 분자동력학과 밀도범함수이론 계산 모두 압력에 따라 부피가 줄어드는 기존의 실험결과와 동일한 경향을 보였다. 특히, 밀도범함수이론으로 얻어진 격자상수는 실험과 약 1% 이내의 오차로 매우 정확한 결과를 보였다. 그러나 엔탈피 계산 결과, 분자동력학에서는 압력에 따른 엔탈피의 변화가 거의 없어 광물 간 안정성이 역전되는 상전이 압력을 구할 수 없었다. 밀도범함수이론 계산 결과는 실험과 동일한 경향을 보여주었지만, 전자의 교환-상관 관계를 나타내는 범함수에 따라 상전이 압력이 크게 다른 결과를 보여주었다. 밀도범함수이론 계산 결과는 결정구조와 엔탈피에 대해서 모두 높은 수준의 정확도를 보여주지만, 동질이상의 상도표 작성에는 정량적으로 큰 오차를 보여주었다.

Keywords

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