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Atomic structure of small Si clusters and thermodynamic properties of metals = 실리콘 집합체의 원자구조 및 금속의 열역학적 성질에 대한 연구
서명 / 저자 Atomic structure of small Si clusters and thermodynamic properties of metals = 실리콘 집합체의 원자구조 및 금속의 열역학적 성질에 대한 연구 / Ji-Wook Jeong.
발행사항 [대전 : 한국과학기술원, 1999].
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8010034

소장위치/청구기호

학술문화관(문화관)B1층 보존서고

DPH 99013

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We investigate the atomic structure of Si$_n$ (n = 9 - 14) clusters using the first-principles pseudopotential method within the local-density functional approximation (LDA). The equilibrium geometries of small clusters with n ≤ 12 are found to have a tendency to form capped prismatic structures. For n = 13, we find a surface-like metallic compact structure which is derived from a capped icosahedron and competes with a stable trigonal prism, while this structure is most stable for n = 14. These results are compatible with the observed stability of Si$_{13}$ and Si$_{14}$ against chemical reactions with simple molecules, as compared to nearby Sin clusters. The effect of electron-electron correlations on the energetics of isomers at n = 13 is examined through variational quantum Monte Carlo calculations, and the LDA energy ordering remains unchanged, consistent with previous diffusion quantum Monte Carlo calculations. We investigate the Hugoniot melting point of Al using a molecular-dynamics approach based on an embedded-atom method. We calculate the Gibbs free energies of the crystalline and liquid phases as a function of pressure and temperature using the coupling-constant integration method and obtain the melting curve up to 1.6 Mbar, in good agreement with experiments. We also examine the melting properties near zero pressure. The Hugoniot equation of states (EOS) up to 1.8 Mbar is obtained from the Rankine-Hugoniot relation and the isotherms determined for different temperatures. Comparing the melting curve with the Hugoniot EOS's for the solid and liquid phases, the Hugoniot melting is found to begin at 1.2 Mbar and to end at 1.4 Mbar, consistent with shock-wave data. We investigate the shock melting of transition metals using a molecular-dynamics approach based on an embedded-atom method. Cu, Pd, and Pt are chosen as prototypes for transition metals in face-centered cubic lattice. We calculate the Gibbs free energies of the crystalline and liquid phases as a function of pressure and temperature using the coupling-constant integration method and obtain the melting curves up to 4.0 Mbar, in good agreement with experiments. Comparing the melting curves with the calculated Hugoniot EOS's for the solid and liquid phases, we determine the melting intervals on the shock Hugoniot for Cu, Pd, and Pt, respectively. For Cu, the shock melting is found to begin at 1.9 Mbar and end at 2.25 Mbar, which is in good agreement with the previous estimation. We find that during the shock compression metal with heavier atomic mass melts at higher temperature and pressure in approximately linear relationship. We investigate the equilibrium and non-equilibrium thermodynamic properties of bcc transition metals using a molecular-dynamics approach based on an embedded-atom method (EAM) potential. Recently, new EAM potential formalism is proposed and proved to be very accurate to reproduce the zero-temperature structural properties, elastic, and phonon properties. Mo and W are chosen as prototypes for transition metals in body-centered cubic lattice. We calculate the Gibbs free energies of the crystalline and liquid phases as a function of pressure and temperature using the coupling-constant integration method and obtain the melting curves up to 1.0 Mbar, in good agreement with experiments. The calculated Hugoniot EOS's of Mo and W up to 1.0 Mbar are in good agreement with the shock-wave experiments.

제일원리 쑤도포텐셜방법와 국소 전자밀도 근사를 사용하여 실리콘 집합체의 원자구조를 연구하였다. Si$_n$ (n ≤12)에서는 삼각기둥에 원자가 덧붙여진 구조가 가장 안정하게 되는 것으로 조사되었다. Si$_13$의 경우, icosahedron 구조로부터 금속성을 강하게 가지는 구조가 새로 발견되었고, 가장 안정한 삼각기둥형태의 구조와 비슷한 안정성을 가짐을 알 수 있었다. 반면, Si$_14$의 경우, icosahedron 구조에서 유도한 구조가 가장 안정한 것으로 조사되었다. 이 결과는 이온화된 실리콘 집합체의 화학적 반응성에 대한 최근 실험에서, Si$_13$과 Si$_14$인 경우, 다른 집합체와 비교하여 화학적으로 아주 안정한 경향이 나타난 결과와 잘 일치한다. Si$_13$의 경우, 전자간의 상관효과를 정확히 조사하기 위해 양자 Monte Carlo 계산을 수행하였고, 국소 전자밀도 근사를 이용한 구조간의 안정성 연구결과 및 종전의 확산 양자 Monte Carlo 계산결과와 같은 결론을 얻었다. 알루미늄의 고온 고압하에서의 열역학적 성질을 조사하기 위해 EAM 포텐샬과 분자동력학 방법을 이용하여 용융곡선과 Hugoniot 상태방정식을 계산하였다. 분자동력학을 이용한 열역학적 적분방법을 이용하여 주어진 온도와 압력에서 고체 및 액체 상태의 Gibbs 자유에너지를 계산하여 1.6 Mbar까지의 압력범위에 대해 용융곡선을 구하였고, 계산결과는 실험과 잘 일치하였다. 또한 알루미늄의 0 기압 용융성질을 조사하여 실험과 잘 일치함을 알 수 있었다. 분자동력학을 이용하여 구한 정온곡선과 Rankine-Hugoniot 관계식을 연립하여 1.6 Mbar까지의 Hugoniot 상태방정식을 결정하였고, 충격파 실험결과와 잘 일치함을 확인하였다. 용융곡선과 고체 및 액체상태의 Hugoniot 곡선을 비교하여 충격상태 중의 용융현상을 조사하여, 1.2 Mbar와 1.4 Mbar에 걸쳐 용융이 진행됨을 예측하였다. 면심격자구조를 가지는 천이금속인 구리, 팔라듐, 그리고 백금의 고온 고압하에서의 열역학적 성질을 조사하기 위해 EAM 포텐샬과 분자동력학 방법을 이용하여 용융곡선과 Hugoniot 상태방정식을 계산하였다. 분자동력학을 이용한 열역학적 적분방법을 이용하여 주어진 온도와 압력에서 고체 및 액체 상태의 Gibbs 자유에너지를 계산하여 4.0 Mbar까지의 압력범위에 대한 용융곡선을 구하여 실험과 비교하였다. 이론적으로 계산된 융융곡선과 고체 및 액체상태의 Hugoniot 곡선을 비교하여 충격상태 중의 용융구간을 예측하였다. 구리의 경우, 1.9 Mbar와 2.25 Mbar에 걸쳐 용융이 진행되는 것으로 예측되었고, 종전의 예측 결과와 잘 일치하였다. 면심격자금속의 용융구간에 대한 연구을 고찰하여 무거운 금속일수록 좀 더 높은 온도와 압력에서 충격상태에서의 용융현상이 이론적으로 예측됨을 알 수 있었다. 체심격자금속의 평형 및 비평형 상태에서의 열역학적 성질을 조사하기 위해 EAM 포텐샬과 분자동력학 방법을 이용하여 용융곡선과 Hugoniot 상태방정식을 계산하였다. 체심격자금속에 대해서 구조적, 탄성, 포논 성질을 정확히 기술하는 EAM 포텐샬 방법이 최근에 개발됨에 따라, 이 함수를 이용하여 몰리브덴과 텅스텐의 열역학적 성질을 조사하였다. 이론적으로 구한 Hugoniot 상태방정식은 충격실험결과와 잘 일치하였다.

서지기타정보

서지기타정보
청구기호 {DPH 99013
형태사항 ix, 89 p. : 삽화 ; 26 cm
언어 영어
일반주기 저자명의 한글표기 : 정지욱
지도교수의 영문표기 : Kee-Joo Chang
지도교수의 한글표기 : 장기주
수록 잡지명 : "First-principles study of the equilibrium structures of Si$_n$ clusters". Journal of Physics : Condensed Matters. Institute of Physics Publishing, vol. 10, no. 26, pp. 5851-5860 (1998)
학위논문 학위논문(박사) - 한국과학기술원 : 물리학과,
서지주기 Reference : p. 83-89
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The average bond length ao (in a.u.), the average coordinati ber Nc, the energy gap AE (in eV) between the HOMO and LUMO sta the LDA binding energies ETDA (in eV/atom) for Sin, 9 <n< 12.

Various isomer structures of Sin clusters, 9 <n <12

The average bond length ao (in a.u.), the average coordination num- ber Nc, the energy gap AE (in eV) between the HOMO and LUMO states, and the LDA binding energies EDDA (in eV/atom) for Sin, 9 <n< 12. The VQMC binding energies of Sii3 is compared with the diffusion quantum Monte Carlo calculations of Ref. [19]. The GGA calculational results are included in the parentheses.

Various isomer structures of Sin clusters, 13 <m<14

Calculated values for 3o (in a.u.), Nc, AE (in eV), and EiDA (in eV/atom) for Sit,9조m21.

Calculated values for ao (in a.u.), Nc, AE (in eV), and EIDA (in eV /atom) for sit,9<m<14

Electronegativities for the ground state isomers of Sit clusters, 9 <n<14.

Total energies of Sin clusters as functions of supercell volume. In (a), our total energy calculations are displayed, while the results of [23] are shown in (b). The solid triangles are for the trigonal prism structure which is identified as the ground-state isomer in our calculations, the solid circles are for the surface-like distorted icosahedron 2 and the open boxes are for the trigonal anti-p

Isothermal equations of state for Al at 300 K. Filled squares rep- resent experimental data (Ref. [41]) and the dotted and solid lines denote the EAM calculations at 0 and 300 K, respectively.

The melting properties of Al at zero pressure are compared with other EAM and generalized pseudopotential theory (GPT) calculations and experiments. Here Gm,Tm, ASm) AVm, and L denote the Gibbs free energy, melting point, entropy change, volume change, and latent heat at Tm. The volume of the solid phase is given by V..

Calculated entropies of the solid and liquid phases for Al at zero pressure. Filled squares represent experimental data (Ref. [63]).

Calculated melting curve ofAlis compared with experiments (Ref. [58]) and previous theoretical calculations (Ref. [29]). Small line segments on Clausius- the cross points represent the slopes d.mm/dTm determined from the Clapeyron equation.

The solid and liquid Hugoniots of Al are plotted together with the melting curve. The solid and dot-dashed lines represent our EAM calculations and previous theoretical results (Ref. [29]), respectively. Small linesegments on the cross points represent the slopes dPm/dTm determined from the Clausius- Clapeyron equation.

The calculated Hugoniot data for Al. Here PH, TH, PH, and Umass denote the pressure, temperature, mass density, and mass velocity after shock- wave passage. The shock velocity is given by Ushock·

The static structure factor S(q) of Cu at 1500 K is plotted together with the experimental curve. The solid lineis the calculated data and the circles represent the estimation from Ref. [74].

The zero-pressure meltingproperties ofCu,Pd, and Pt are compared with experiments. Here Gm, Tm, ASm, AVm, and L denote the Gibbs free energy, melting point, entropy change, volume change, and latent heat at Tm. The volume of the solid phase is given by Vs.

The calculated entropies of Cu, Pd, and Pt are plotted together and the with the experimental data. The solid lines are the calculated results cross points represent the experiments (Ref. [63]).

The solid and liquid Hugoniots of Cu, Pd, and Pt are plotted to- gether with the melting curve. The dashed lines are the calculated melting curves and the solid line segments on each dashed line are the solid and liquid Hugoniot curves. The triangles are the experimental melting points ofPt (Ref. [71]). Small line segments on the solid circles represent the slopes dPm dTm determined from the Claus

The calculated Hugoniot data of Cu, Pd, and Pt are plotted with the shock experiments. In graph (a), the theoretical solid and liquid Hugoniot EOS's of Cu, Pd, and Pt are presented The solid lines are from our EAM calculations and the circles are from Ref. [68], the triangles are from Ref. [66] the solid boxes are from Ref. [67], and the empty boxes are from Ref. [72]. The calculated shock-wave ve

The shock melting intervals of Al (Ref. [62]), Cu, Pd, and Pt V. the atomic mass.

The linear thermal expansion coefficients ofMo and w are plotted together with the experimental curve. The solid line is the calculated data and the circles represent the estimation from Ref. [82].

The zero-pressure melting properties of Mo and W are compared with experiments. Here Gm, Tm, ASm, AVm, and L denote the Gibbs free energy, melting point, entropy change, volume change, and latent heat at Tm. The volume of the solid phase is given by V.

The calculated entropies of Mo and w are presented with the ex- perimental data. The solid lines are the calculated results and the cross points represent the experiments (Ref. [63]).

The melting curves of Mo and W are plotted together with the experiments. (Ref. [63,83]) The solid lines are the calculated meltingcurves and on the solid the circle represents the experimental value. Small line segments circles represent the slopes dPm/dTm determined from the Clausius-Clapeyron equation.

The calculated Hugoniot data of Mo and w are plotted with the shock experiments. In graph (a), the theoretical solid and liquid Hugoniot EOS's ofMo and W are presented. The solid lines are from our EAM calculations and the circles are from Ref. [68]. The calculated shock-wave velocities vs. particle velocities of Mo and W are plotted in (b).