Modern Research and Computational Science-科學研究和計算科學

1. Modern Research and Computational Science 科學研究和計算科學 Guang-Yu Guo ( 郭光宇 ) Graduate Institute of Applied Physics National Chengchi University, Taipei, Taiwan (Science Talk < 理院論壇 >, College of Science, National Chengchi University, Nov. 2, 2009) ( 國立政治大學應用物理研究所 )

3. I. Roles of computational science in modern research 1. Computer program discovers laws of physics [Science 324 (April 3, 2003) 81] 科學研究的重要目的是尋找錯綜複雜的自然和社會現象背後的運動規律 .

10. 計算科學與尖端材料研發及設計 由於高速電腦，先進數值算法和量子理論，材料科學己邁入一個全新的時代。第一原理量子力學計算可以補充，有時甚至取 代，傳統的嘗試錯誤實驗法。利用第一原理計算，科學家可以引導尖端材料的研發，可以理解材料是怎樣形成的，外界條件會產生怎樣的影響以及可以如何改造材料使其具有更佳的性能。目前，量子理論計算已成為世界上科學家探討材料新穎性質及研發和設計新功能材料不可缺少的工具。 從遠古的銅器時代到今日的半導體資訊時代，人類文明一向是以新材料來命名並透過掌握和操控新材料而進步。 材料的發展推動了經濟、社會和科學的進步，進而改變了人們日常生活的方式。 3. Ab initio calculations in materials research

11. 第一原理理論計算 發明密度泛函理論 , W. Kohn 獲 1998 年諾貝爾獎 [first principles (ab initio calculations]

12. [PRL 68 (1992) 1355] Si (111) surface reconstruction 第一原理理論計算 确定矽 (111) 表面重構后原子結構

13. For example, the structure of Au 20 - determined jointly by photoelectron spectroscopy and ab initio calculations [Science 299, 864 (2003) 1355] 量子理論計算對研究奈米材料新奇特性尤其重要。例如，量子理論計算在確定奈米材料的原子結構上扮演不可或缺的角色。

14. [predicted and subsequently synthesized by Berkeley groups in the mid-90’s] zigzag (10,0) nanotube chiral (7,3) nanotube armchair (5,5) nanotube (Iijima, 1991) 碳奈米管 Here is an example how ab initio calculations lead to a discovery that solves a long standing (60 yrs old) problem in solid state physics. [Rubio et al., PRB 1994; Chopra, et al., Science, 1994] 硼化氮 (BN) 奈米管

15. 磁鐵的用途由其矯頑力决定 , 而矯頑力來自由相對論造成的磁晶異向能 Hard disk (~100GB) Flopy disk (~1.4MB) Storage capacity vs time 相對論量子力學計算能恊助尋找具高磁晶異向能材料 .

16. Large SOC effect magnetism in 4d and 5d TM atomic chains. 3d TM linear atomic chains [Tung, Guo, PRB76(2007)094413] [Tung, Guo, PRB (submitted 2009)] 過度金属奈米線之磁晶異向能

17. Magneto-crystalline anisotropy energy in bulk metals [Guo, et al., Physica B 172 (1991) 61] [Kittel] L1 0 ordered Fe(Co)Pt alloys FePt has the largest MAE among TM alloys and is the hottest alloy. The limit based on FePt is ~1 Tbit/in 2 with perpendicular recording .

18. 1. The classic charge ordering problem is that of magnetite (1941). (1) What is magnetite? Inverted spinel structure above T V 1/3: tetrahedral (A-site) ) Fe 3+ 2/3: octahedral (B-site) Fe 3+ , Fe 2+ Ferrimagnetic A-site , B-site , T C ~ 860K M-I (Verwey) transition, T V = 122 K Fe(A) 3+ Fe(B) 3+ Fe(B) 2+ O 2- The oldest magnet known to mankind. (1913) Fe 3 O 4 magic stones (2500 yrs) II. Discovery of mechanism of Verwey transition in magneite

19. (2). Verwey charge ordering model for Verwey transition (1941): A mixed-valence compound: Fe A 3+ [Fe 2+ Fe 3+ ] B O 4 2- ; The M-I transition is due to a charge ordering of the Fe 2+ and Fe 3+ states on the B sublattice, resulting in an orthorhombic structure. Therefore, this is the oldest and classic charge ordering problem. [PRB 47 (1993) 5564] However, simple Verwey model was later disproved [Walz, JPCM 2002] and nature and mechanism of Verwey transition remains unresolved despite intensive investigations over the past 60 years.

20. Each corner-sharing B Fe tetrahedron should contain two Fe 2+ and two Fe 3+ ions in order to minimize the electrostatic energy. (3). Anderson criterion [PR102 (1956) 1008] R.G. Melko et al. PRL 87 , 067304 S. T. Bramwell et al. Science, 294 , 1495 Ho2Ti2O7

22. (4). Other interesting properties A half-metal for spintronics? [Jeng, Guo, PRB 65 (2002) 94429]

23. 2. Discovery of a t 2g -orbital order Nature of the electronic structure in low temperature phase from LDA+U calculations) Low T monoclinic structure [Wright et al. 2001, 2002] Space group P2/c, 56 atom/cell, a=5.9444 Å , b=5.925 Å , c =16.775 Å ,  =90.2368 º . fcc lattice constant a = 8.394 Å . Fe(B1a,b) Fe(B2a,b) Fe(B3) Fe(B4)

24. LDA+U band structure of (a) cubic and (b) monoclinic phases [Jeng, Guo, Huang, PRL 93, 156403 (2004)]

25. Charge ordering Table I: Valence charge (e), spin moment (  B ), and spin-decomposed 3d charge (e) of the B Fe in monoclinic Fe 3 O 4 . Furthermore, the charge (spin) ordering can be considered as the superposition of [001] c and [00 ] c charge (spin) density wave modulations. [1] Wright et al., 2002. Expt.[1] charge LDA+U charge spin 3d  3d  Fe (B1) Fe (B2) Fe (B3) Fe (B4) 5.6 5.4 5.4 5.6 5.57 3.45 5.41 3.90 5.44 3.81 5.58 3.39 4.41 0.97 4.54 0.65 4.51 0.71 4.39 1.01

26. (b) (c) Calculated charge distribution indicating t 2g -orbital ordering on B-site sublattice. (a) Low T monoclinic structure [Wright et al. 2001, 2002] (a) (b) (c)                  Central finding (result)

27. Orbital ordering (a) Density of states projected onto the B Fe d-orbitals. The Fermi level E f is at the zero energy. (b) Schematic energy level diagram for the spin-down B Fe d-orbitals.

28. 3. Entropy change at the Verwey transition is another long standing enigma. [Shepherd et al. PRB 31 (85) 1107]  S V = Rln2 = 5.76 (J/mol-K) [R = 8.314 (J/mol-K)] (Rln2 = 0.693R)

29. (1) Completely disorder to fully order transition: a) high-T disorder phase N=2nN A B-sites (Fe B 3+ : ＋ , Fe B 2+ : － ): W = 2 N states; Thus, S hT = klnW = kln2 N = R2ln2 per mol. b) low-T long-range order phase S lT = klnW = kln1= 0. Thus,  S V = 2Rln2 = 11.52 (J/mol-K). (2) Short-range order: [similar to the residual entropy water ice and spin ice] Short-range 2(Fe 3+ )-2(Fe 2+ ) order: N-sites, N/4 disconnected tetrahedra (2 sets) W = (3/8) N/4 *6 N/4 = (3/2) N/2 S = kln(3/2) N/2 = Rln(3/2) = 0.405R per mol. (C 4 2 ) N/4 = 6 N/4 states Possibility of correct states = (6*3 4 )/(6 4 ) = 3/8 Anderson’s 2-2 charge ordering model + + + + + + － － － － － －

31. Our opinion: If you don’t see it, doesn’t mean it is not there! Using Fe K-edge absorption 4. Confirmation by resonant x-ray scattering experiments

32. [D.J. Huang, et al., Phys. Rev. Lett. 96, 096401 (2006)] Unoccupied O 2p orbital ordering pattern

33. O K-edge X-ray absorption and resonant scattering spectra from Fe 3 O 4 . [D.J. Huang, et al., Phys. Rev. Lett. 96, 096401 (2006)]

34. [Cond-mat/0605096 (2006)]

35. Fe K-edge RXRD at 50 K

36. Fe K-edge RXRD at 90 K.

37. Thank you for your attention