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研究生：	葉學舫 Yeh, Hsueh-Fang
論文名稱：	第一原理方法研究鐵、鈷、鎳於非均向壓力下的結構與磁相變 Structural and magnetic phase transition of Fe, Co and Ni under anisotropic compression: Ab initio study
指導教授：	鄭靜 Cheng, Ching
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2011
畢業學年度：	99
語文別：	英文
論文頁數：	38
中文關鍵詞：	非均向、壓力、加壓、鐵、鈷、鎳
外文關鍵詞：	anisotropic, pressure, compression, Fe, Co, Ni
相關次數：	點閱：54 下載：3
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透過第一原理方法計算雙軸變形(a=b≠c)之單位晶格，鐵、鈷、鎳於非均向加壓下(P_x=P_y≠P_z)的結構相變及磁相變得以被研究。研究涵蓋的晶格結構包含了面心立方堆積，體心立方堆積和六方最密堆積，各種結構均包含磁性和非磁性相的計算。經由比較兩相之間焓的差，鐵、鈷、鎳的相圖得以被決定，領導相變的主要因素也能進而被確定。對鐵，於側向加壓下(P_x=P_y≠0,P_z=0)，其鐵磁性體心立方堆積到非磁性六方最密堆積的相變壓力遠低於均向加壓下的相變壓力(由13.7 GPa降至3.1 GPa)。此外，延側向持續加壓至115 GPa，鐵被預測相變至非磁性面心立方堆積相。對鈷，由六方最密堆積至面心立方堆積和由面心立方堆積至體心四方堆積的單純結構相變各別發生在單軸加壓壓力為1.9 GPa和3.9 GPa時。對鎳，儘管實驗上從未觀察到相變，於單軸加壓壓力3.5 GPa我們預測到一單純結構相變至鐵磁體心四方相，側向加壓壓力175 GPa時則有一由鐵磁性面心立方堆積至非磁性面心立方堆積的單純磁相變發生。鈷和鎳在非均向壓力下不同的磁性行為也被深入探討。

The structural and magnetic phase transition of iron, cobalt and nickel under anisotropic　compression (Px = Py ≠ Pz) are investigated with ab initio calculations for biaxially deformed (a = b ≠ c) unit cells. The phases included in this study are face-centered cubic (fcc), body-centered cubic (bcc), hexagonal closed-packed (hcp) structures. Both ferromagnetic (FM) and non-magnetic (NM) phases are considered. By analyzing the diﬀerence in enthalpy, we
determine the phase diagram of iron, cobalt and nickel and the leading contribution of each transition. For iron, the transition pressure from FM-bcc to NM-hcp at epitaxial compression was found pronouncedly lower than hydrostatic one, i.e., 13.7 GPa compared to 3.1 GPa. A new NM-fcc phase at epitaxial compression up to 115.3 GPa was also predicted. For Co, two pure structural phase transitions from FM-hcp to FM-fcc and from FM-fcc to FM-bct was found at uniaxial pressure 1.9 GPa and 3.9 GPa respectively. For nickel, a FM-bct phase was found upon uniaxial compression at 3.5 GPa and a pure magnetic phase transition from FM-fcc to NM-fcc occurred at epitaxial pressure 175 GPa, while no phase transition had been identiﬁed experimentally at hydrostatic condition. The diﬀerent magnetic behavior under anisotropic compression for Co and Ni are also presented.

Introduction 4
Calculation method for thermodynamics 5
1 Phase transition under hydrostatic condition[12] . . . . . . . . . . . . . . . . 5
2 Phase transition under anisotropic compression Px = Py ≠ Pz[4] . . . . . . . . 6
3 The ﬂow-chart of ﬁnding the phase diagram . . . . . . . . . . . . . . . . . . . 7
Calculation method for electronic structures 9
1 Density functional theory (DFT) . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1 The Hohenberg-Kohn (HK) theorems . . . . . . . . . . . . . . . . . . 9
1.2 The self-consistent Kohn-Sham (KS) equations . . . . . . . . . . . . . 11
2 Plane-wave implementation of DFT . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 Bloch’s theorem [21] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Kohn-Sham equations in plane-wave form . . . . . . . . . . . . . . . . 13
3 Exchange-correlation approximation . . . . . . . . . . . . . . . . . . . . . . . 14
3.1 The local-density approximation (LDA) . . . . . . . . . . . . . . . . . 14
3.2 The generalized-gradient approximation (GGA) . . . . . . . . . . . . . 14
4 The ﬂow-chart of VASP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Bulk properties 16
1 Calculation details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.1 Smearing method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 k-point mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3 Energy cutoﬀ and error bar . . . . . . . . . . . . . . . . . . . . . . . . 16
2 The phases we considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 Cobalt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Magnetic moment behavior under compression 23
1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Cobalt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Phase diagrams of Fe, Co and Ni 27
1 Phase transition under hydrostatic pressure . . . . . . . . . . . . . . . . . . . 27
2 Phase transition under anisotropic pressure . . . . . . . . . . . . . . . . . . . 30
Conclusions 33
Bibliography 35
A The ∆f Wani integration along diﬀerent paths 37
                                    

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校內：2012-07-26公開
校外：2012-07-26公開

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