固態甲烷在行星內部高壓下之熱性質

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郭靜宜(Ching-Yi Kuo) 查詢紙本館藏

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物理學系

論文名稱

固態甲烷在行星內部高壓下之熱性質
(Thermal properties of solid methane at high pressure of planetary interiors)

相關論文

★ 以第一原理計算探討應力下之複雜氧化物

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至系統瀏覽論文 (2025-12-31以後開放)

摘要(中)

一般相信，甲烷 (CH4) 是冰巨行星 (例如:天王星及海王星) 的主要成分，並在此類行星的內部結構和動力學中扮演著重要角色。若要完整瞭解冰巨行星，必須對CH4 之性質有徹底的認識，但我們卻對固態甲烷在高壓及高溫下的性質所知甚少。迄今為止，已有幾種截然不同的固態甲烷高壓結構被提出，包括 P212121、Pnma、Cmcm、P21/c、C2/c 及 R3等，且在這些結構中，每單位晶胞可有 20 至 145 個原子。而這些結構的熱力學性質，也尚未被探索。
在本論文中，我們對固態甲烷在高溫壓條件（至200 GPa, 1800 K）下之熱力學性質進行理論計算研究。我們的計算基於密度泛函理論（densify functional theory, DFT），並將上述所有結構都納入考慮。在非零溫度下的狀態方程式、密度、體積模量、熱膨脹係數、莫耳比熱、Grüneisen 參數和塊材聲速等，則以準諧近似（quasi-harmonic approximation, QHA）計算。值得注意的是，我們的計算表明：上述所有高壓結構的熱力學性質幾乎相同，儘管它們具有不同的結構特性，而其根本原因在於，這些結構的聲子譜高度相似。經由這一系列的計算結果，我們可以合理推論：原子結構對固態甲烷之熱力學性質的影響極小。因此，本研究對行星內部高溫壓下的固態甲烷之熱力學參數提供可靠的資訊。

摘要(英)

Methane (CH4) is believed to be a major constituent of ice giants (Neptune and Uranus, for example), playing a significant role in the internal structure and dynamics of this type of planet. Thorough knowledge of CH4 is thus essential to fully understand ice giants. Neverthe-less, properties of solid CH4 at high pressure (P) and temperature (T) remain largely unknown. So far, several distinct high-pressure structures for solid CH4 have been proposed, including P212121, Pnma, Cmcm, P21/c, C2/c, and R3, ranging from 20 to 145 atoms per unit cell. Ther-mal properties of these proposed structures, however, are unexplored.
In this thesis, we present our computational study for the thermal properties of solid me-thane at high P–T conditions up to 200 GPa and 1800 K. Our calculations are based on density functional theory (DFT), and all the above-mentioned proposed structures are considered. For nonzero temperature (T /= 0), the equation of state, density, bulk modulus, thermal expansivity, molar heat capacity, Grüneisen parameter, and bulk sound velocity are computed within qua-si-harmonic approximation (QHA). Remarkably, our calculations indicate that thermal proper-ties of all the proposed structures are nearly the same, despite their distinct structural properties. The underlying reason is that phonon spectra of all these structures are highly similar. Our re-sults thus suggest that effects of atomic structures on the thermal properties of solid CH4 are minimal. Therefore, our calculations provide reliable information for the thermal parameters of solid CH4 at high P–T conditions of planetary interiors.

關鍵字(中)

★ 第一原理
★ 分子晶體
★ 固態甲烷
★ 海王星
★ 天王星
★ 冰巨行星

關鍵字(英)

★ First-principles
★ molecular crystals
★ solid methane
★ Neptune
★ Uranus
★ ice giants

論文目次

中文摘要 i
Abstract ii
致謝 iii
目錄 iv
1 緒論 1
1.1 甲烷在材料科學中的角色 1
1.2 甲烷在行星科學中的角色 1
1.3 實驗上對固態甲烷的研究 3
1.4 理論計算上對固態甲烷的研究 10
2 研究內容與方法 14
2.1 密度泛函理論 15
2.1.1 Hohenberg-Kohn 定理 15
2.1.2 Kohn-Sham 理論 16
2.1.3 交換相關能近似方法 18
2.1.4 贋勢 24
2.1.5 力、應力張量及結構優化 25
2.2 聲子計算 27
2.2.1 動力學矩陣 27
2.2.2 有限位移方法 29
2.2.3 聲子 31
2.3 熱性質計算(基於聲子譜) 31
2.3.1 quasi-harmonic approximation 31
2.3.2 曲線擬合 32
2.3.3 其他物理性質 34
2.4 本文研究方法 35
3 研究結果 37
3.1 相圖 37
3.2 壓縮曲線、密度、等溫體積模數及熱膨脹係數 42
3.3 比熱 49
3.4 Grüneisen參數 50
3.5 絕熱體積模數及塊材聲速 54
3.6 Vibrational density of states 57
4 結論 58
參考文獻 59
附錄一 F(T,V)、V(P,T)及G(P,T) 62
附錄二熱力學性質數值列表 68
附錄三溫度與激發之振動頻率(標示於VDOS上) 77
附錄四二階Grüneisen參數（q） 78
附錄五固態二氧化碳之壓縮曲線（T= 300 K） 80

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指導教授

徐翰

審核日期

2022-1-25

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