由高度非對稱組成的嵌段共聚物(bcp)形成的球形微胞藉由粒子間排斥力自組裝成晶格排列。微胞堆積成緊密堆積球(CPS)相包含面心立方(FCC)和六方密積(HCP)的現象在bcp系統中極為少見。在膠體粒子系統中，高度精準的模擬研究確認了FCC比HCP晶格為更穩定的緊密堆積晶格，然而近期的研究指出了在bcp系統中，HCP反而比FCC更穩定。除了常見的FCC與HCP晶格以外，CPS相中各式各樣的多型體在無機化合物原子形成的結晶中被觀測到，其中包含4H或由六方密積層(HCPLs)照著ABAC重複序列排列堆疊成的double HCP(DHCP)相。在我們的認知中，這些多型體在bcp系統中還未被發現。

在本論文中，我們利用由聚乙二醇和聚丁二烯組成的對稱嵌段共聚物poly(ethylene oxide)-block-poly(1,4-butadiene) (PEO-b-PB)混合分子量為300克/莫耳的聚丁二烯poly(1,2-butadiene) (h-PB)來探討CPS和Frank-Kasper(FK)相的形成。我們發現了在PEO體積分率為0.173的組成中,一旦從無序排列微胞(DM)相降溫會傾向於形成DHCP相。由於DHCP相在稀土金屬中被認為是由壓力誘導的結構，這個在bcp中不常見的CPS相的形成原因被歸為由於高溫下均聚物PB的揮發造成在填滿以及完全密封的樣品槽中內部壓力的增加。增加組成非對稱性至PEO體積分率0.146誘發了在菱形晶格單元中為三方晶體空間群R3 ̅m的變形FCC相形成。這個變形FCC相也被認為是壓力誘發的穩定結構，而不是在HCP轉變成FCC過程中產生的中間結構。

此混參系統在接近六角堆積圓柱的組成邊界形成FK 相。這個晶格的四方晶胞長寬比(c/a)被發現隨著降溫明顯的下降，這個現象在過去並未被發現。最後，混參樣品的初始結構對於隨後形成之緊密堆積晶格的選擇有所影響。在去除溶劑履歷期間產生的PEO層板結晶，熔化後還未回到平衡狀的球狀微胞形態而造成了r-HCP相的形成，且這個r-HCP升溫後會逐漸轉變成FCC相。從DM相浸泡在液態氮中來驟冷微胞造成結晶侷限在PEO相區，且這些微胞排無規則排列 (LLP)，此LLP相在隨後升溫超過晶體熔點後傾向於轉化成HCP相。我們的研究結果闡釋了產生史無前例的球相的可行性、揭露了FK σ相的特殊相行為以及熱處理條件對於共聚物與均聚物的混參樣品產生之CPS相的動力學途徑影響，這些研究在軟物質冶金學領域有所貢獻。

Block copolymer (bcp) with large compositional asymmetry form spherical micelles that self-organize into long-range ordered lattices driven by the repulsive interparticle interaction. Close-packed sphere (CPS) phase with the micelles packed in face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice is highly unusual among bcp systems. In hard colloidal crystals, highly accurate simulation studies have identified FCC as a more stable close-packed lattice than HCP, while recent works suggested that HCP is favored over FCC for the close packing of bcp micelles. In addition to the ordinary FCC and HCP lattice, a variety of polytypes of CPS phase have been observed in the atomic crystallization of inorganic compounds, including the 4H or double HCP (DHCP) phase constructed by the ABAC repeating sequence for the close stacking of the hexagonal close-packed layers (HCPLs). To our knowledge, these polytypes have not been found in bcp systems.
The present study investigates the CPS and FK phase formed in the blends of a compositionally symmetric poly(ethylene oxide)-block-poly(1,4-butadiene) (PEO-b-PB) and a poly(1,2-butadiene) homopolymer (h-PB) with the molecular weight of 300 g/mol. It was found that the blend with the overall PEO volume fraction fPEO = 0.173 tended to form DHCP phase upon cooling from the disordered micelle (DM) phase. As DHCP phase has been considered as a pressure-induced structure of rare-earth metal, the stability of this unusual CPS phase in bcp was attributed to the increase of internal pressure within the well-filled and firmly sealed sample cell due to the suppression of the evaporation of h-PB at high temperature. Increasing compositional asymmetry to fPEO = 0.147 induced the formation of a distorted FCC phase with trigonal space group R3 ̅m in rhombohedral unit cell. This distorted FCC phase was also considered as a pressure-induced stable structure rather than an intermediate structure associated with HCP-FCC transition.
The present blend system formed Frank-Kasper phase near the boundary of the hexagonally packed cylinder phase. The aspect ratio of the tetragonal unit cell, c/a, of this quasicrystal approximant was found to decrease drastically with decreasing temperature, which has not been found in the previous studies revealing the phase of bcps. Finally, the effect of initial structure of the blend on the subsequent selection of the close-packed lattice in the blend was examined. The recovery of the spherical micelles upon the melting of the PEO crystalline lamellae formed during solvent casting led to the formation of the r-HCP phase that further transformed into FCC phase on heating. Quenching the micelles in the DM phase into liquid nitrogen led to the crystallization confined within the PEO core and the micelles packed in a liquidlike packing phase which tended to organize into HCP phase upon subsequent heating above the crystal melting point. Our results demonstrate the accessibility of the unprecedented spherical phases and reveal a special phase behavior of the Frank-Kasper σ phase and the impact of thermal processing condition on the kinetic pathway pf CPS phase formation in bcp/homopolymer blends, which shall contribute to the basic understanding of the metallurgy of soft matter.

Abstract II
摘要 IV
Table of Contents VI
Figure Contents VII
Table Contents XII
Chapter 1. General Introduction and Literature Review 1
1.1 Background of Research 1
1.2 Phase behavior of diblock copolymer 3
1.2.1 Phase behavior of neat block copolymer 3
1.2.2 Phase behavior of diblock copolymer in block copolymer/homopolymer blends 9
1.3 Close-packed sphere phase (CPS) 17
1.4 Frank-Kasper phase (F-K phase) 26
1.5 Motivation and Objective of Research 33
Chapter 2. Complex Packing Behavior of the Spherical Micelles of Block Copolymer/Homopolymer Blends 36
Introduction 36
2.2 Experiment Section 43
2.2.1 Materials and sample preparation 43
2.2.2 Small Angle X-ray Scattering (SAXS) Measurement 44
2.3.1 Emergence of quasi-HCP phase in PEO7.5k-b-PB5.5k/h-PB0.3k blends 46
2.3.2 Emergence of distorted FCC phase 54
2.3.3 Temperature-dependent lattice parameters and structural order of Frank-Kasper σ phase 62
2.3.4 Kinetic pathway of CPS phase formation 82
Chapter 3. Overall Summary 90
References 93

(1) Leibler, L. Theory of microphase separation in block copolymers. Macromolecules 1980, 13 (6), 1602-1617.
(2) Grason, G. M. The packing of soft materials: Molecular asymmetry, geometric frustration and optimal lattices in block copolymer melts. Physics reports 2006, 433 (1), 1-64.
(3) Matsen, M. W.; Bates, F. S. Unifying weak-and strong-segregation block copolymer theories. Macromolecules 1996, 29 (4), 1091-1098.
(4) Castelletto, V.; Hamley, I. W. Morphologies of block copolymer melts. Current Opinion in Solid State and Materials Science 2004, 8 (6), 426-438.
(5) Hashimoto, H.; Fujimura, M.; Hashimoto, T.; Kawai, H. Domain-boundary structure of styrene-isoprene block copolymer films cast from solutions. 7. Quantitative studies of solubilization of homopolymers in spherical domain system. Macromolecules 1981, 14 (3), 844-851.
(6) Hashimoto, T.; Fujimura, M.; Kawai, H. Domain-boundary structure of styrene-isoprene block copolymer films cast from solutions. 5. Molecular-weight dependence of spherical microdomains. Macromolecules 1980, 13 (6), 1660-1669.
(7) Matsen, M. W.; Bates, F. S. Conformationally asymmetric block copolymers. Journal of Polymer Science Part B: Polymer Physics 1997, 35 (6), 945-952.
(8) Matsen, M. W. Stabilizing new morphologies by blending homopolymer with block copolymer. Physical review letters 1995, 74 (21), 4225.
(9) Kinning, D. J.; Thomas, E. L.; Fetters, L. J. Morphological studies of micelle formation in block copolymer/homopolymer blends. The Journal of chemical physics 1989, 90 (10), 5806-5825.
(10) Tanaka, H.; Hasegawa, H.; Hashimoto, T. Ordered structure in mixtures of a block copolymer and homopolymers. 1. Solubilization of low molecular weight homopolymers. Macromolecules 1991, 24 (1), 240-251.
(11) Hashimoto, T.; Tanaka, H.; Hasegawa, H. Ordered structure in mixtures of a block copolymer and homopolymers. 2. Effects of molecular weights of homopolymers. Macromolecules 1990, 23 (20), 4378-4386.
(12) Tanaka, H.; Hashimoto, T. Ordered structures of block polymer/homopolymer mixtures. 3. Temperature dependence. Macromolecules 1991, 24 (20), 5713-5720.
(13) Janert, P. K.; Schick, M. Phase behavior of binary homopolymer/diblock blends: Temperature and chain length dependence. Macromolecules 1998, 31 (4), 1109-1113.
(14) Hasegawa, H.; Tanaka, H.; Hashimoto, T.; Han, C. C. SANS and SAXS study of block copolymer/homopolymer mixtures. Journal of Applied Crystallography 1991, 24 (5), 672-678.
(15) Takagi, H.; Hashimoto, R.; Igarashi, N.; Kishimoto, S.; Yamamoto, K. Frank–Kasper σ phase in polybutadiene-poly (ε-caprolactone) diblock copolymer/polybutadiene blends. Journal of Physics: Condensed Matter 2017, 29 (20), 204002.
(16) Takagi, H.; Yamamoto, K. Phase boundary of Frank–Kasper σ phase in phase diagrams of binary mixtures of block copolymers and homopolymers. Macromolecules 2019, 52 (5), 2007-2014.
(17) Mueller, A. J.; Lindsay, A. P.; Jayaraman, A.; Lodge, T. P.; Mahanthappa, M. K.; Bates, F. S. Emergence of a C15 Laves phase in diblock polymer/homopolymer blends. ACS Macro Letters 2020, 9 (4), 576-582.
(18) Mahynski, N. A.; Kumar, S. K.; Panagiotopoulos, A. Z. Relative stability of the FCC and HCP polymorphs with interacting polymers. Soft Matter 2015, 11 (2), 280-289.
(19) Hsu, N.-W.; Nouri, B.; Chen, L.-T.; Chen, H.-L. Hexagonal Close-Packed Sphere Phase of Conformationally Symmetric Block Copolymer. Macromolecules 2020, 53 (21), 9665-9675.
(20) Frenkel, D.; Ladd, A. J. New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres. The Journal of chemical physics 1984, 81 (7), 3188-3193.
(21) Woodcock, L. Entropy difference between the face-centred cubic and hexagonal close-packed crystal structures. Nature 1997, 385 (6612), 141-143.
(22) Matsen, M. W. Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing. The European Physical Journal E 2009, 30 (4), 361-369.
(23) Su, R.; Neffati, D.; Zhang, Y.; Cho, J.; Li, J.; Wang, H.; Kulkarni, Y.; Zhang, X. The influence of stacking faults on mechanical behavior of advanced materials. Materials Science and Engineering: A 2021, 803, 140696.
(24) Huang, B.; Wang, X.; Wang, L.; Rong, Y. Effect of nitrogen on stacking fault formation probability and mechanical properties of twinning-induced plasticity steels. Metallurgical and Materials Transactions A 2008, 39 (4), 717-724.
(25) Lele, S. X-ray diffraction from close-packed structures with stacking faults. I. hcc crystals. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography 1974, 30 (4), 509-513.
(26) Minagawa, T. X-ray diffraction study of the structural change from 2H to 4H in CdI2 crystals. Journal of Applied Crystallography 1978, 11 (4), 243-247.
(27) Sebastian, M.; Krishna, P. X-ray diffraction effects from randomly twinned fcc crystals undergoing transformation to the hcp phase. Acta Crystallographica Section B: Structural Science 1987, 43 (5), 409-415.
(28) Sebastian, M.; Narayanan, K.; Krishna, P. X‐Ray Diffraction Effects from 2H Crystals Undergoing Transformation to the 3C Structure by the Layer Displacement Mechanism. physica status solidi (a) 1987, 102 (1), 241-249.
(29) Lele, S.; Anantharaman, T.; Johnson, C. A. X‐Ray Diffraction by Hexagonal Close‐Packed Crystals Containing Extrinsic Stacking Faults. physica status solidi (b) 1967, 20 (1), 59-68.
(30) Nikolin, B.; Babkevich, A. Y. The Monte Carlo simulation of random stacking faults in close-packed structures. Acta Crystallographica Section A: Foundations of Crystallography 1989, 45 (11), 797-801.
(31) Gevers, R. The diffraction of X-rays by close-packed crystals containing bothgrowth stacking faults' anddeformation or transformation stacking faults'. Acta Crystallographica 1954, 7 (4), 337-343.
(32) Warren, B.; Warekois, E. Stacking faults in cold worked alpha-brass. Acta metallurgica 1955, 3 (5), 473-479.
(33) Balogh, L.; Ribárik, G.; Ungár, T. Stacking faults and twin boundaries in fcc crystals determined by x-ray diffraction profile analysis. Journal of applied physics 2006, 100 (2), 023512.
(34) Martin, S.; Ullrich, C.; Šimek, D.; Martin, U.; Rafaja, D. Stacking fault model of∊-martensite and its DIFFaX implementation. Journal of Applied Crystallography 2011, 44 (4), 779-787.
(35) He, H.; Naeem, M.; Zhang, F.; Zhao, Y.; Harjo, S.; Kawasaki, T.; Wang, B.; Wu, X.; Lan, S.; Wu, Z. Stacking fault driven phase transformation in CrCoNi medium entropy alloy. Nano Letters 2021, 21 (3), 1419-1426.
(36) Sebastian, M.; Krishna, P. Single crystal diffraction studies of stacking faults in close-packed structures. Progress in crystal growth and characterization 1987, 14, 103-183.
(37) Berliner, R.; Werner, S. Effect of stacking faults on diffraction: The structure of lithium metal. Physical Review B 1986, 34 (6), 3586.
(38) Varn, D. P.; Canright, G. S.; Crutchfield, J. P. Discovering planar disorder in close-packed structures from x-ray diffraction: Beyond the fault model. Physical Review B 2002, 66 (17), 174110.
(39) Sebastian, M. Diffraction of X-rays by hexagonally close-packed crystals containing extrinsic stacking faults. Philosophical Magazine B 1988, 57 (1), 93-101.
(40) Holloway, H. Diffraction by HCP Crystals with Extrinsic Faults—The Solution by Difference Equations. physica status solidi (b) 1969, 35 (1), 507-513.
(41) Johnson, C. Diffraction by face-centered cubic crystals containing extrinsic stacking faults. Acta Crystallographica 1963, 16 (6), 490-497.
(42) Sebastian, M.; Krishna, P. An X-ray diffraction study of faulting in single crystals of cubic ZnS grown from the vapour phase. Philosophical Magazine A 1984, 49 (6), 809-821.
(43) Pusey, P.; Van Megen, W.; Bartlett, P.; Ackerson, B.; Rarity, J.; Underwood, S. Structure of crystals of hard colloidal spheres. Physical review letters 1989, 63 (25), 2753.
(44) Kegel, W. K.; Dhont, J. K. “Aging” of the structure of crystals of hard colloidal spheres. The Journal of Chemical Physics 2000, 112 (7), 3431-3436.
(45) Dolbnya, I. P.; Petukhov, A. V.; Aarts, D. G. A. L.; Vroege, G. J.; Lekkerkerker, H. N. W. Coexistence of rhcp and fcc phases in hard-sphere colloidal crystals. Europhysics Letters (EPL) 2005, 72 (6), 962-968. DOI: 10.1209/epl/i2005-10325-6.
(46) Pronk, S.; Frenkel, D. Can stacking faults in hard-sphere crystals anneal out spontaneously? The Journal of chemical physics 1999, 110 (9), 4589-4592.
(47) Zhu, J.; Li, M.; Rogers, R.; Meyer, W.; Ottewill, R.; Russel, W.; Chaikin, P. Crystallization of hard-sphere colloids in microgravity. Nature 1997, 387 (6636), 883-885.
(48) Verhaegh, N. A.; Van Duijneveldt, J. S.; van Blaaderen, A.; Lekkerkerker, H. N. Direct observation of stacking disorder in a colloidal crystal. The Journal of chemical physics 1995, 102 (3), 1416-1421.
(49) Jensen, K.; Pennachio, D.; Recht, D.; Weitz, D.; Spaepen, F. Rapid growth of large, defect-free colloidal crystals. Soft Matter 2013, 9 (1), 320-328.
(50) Hoogenboom, J. P.; Derks, D.; Vergeer, P.; van Blaaderen, A. Stacking faults in colloidal crystals grown by sedimentation. The Journal of chemical physics 2002, 117 (24), 11320-11328.
(51) Marechal, M.; Hermes, M.; Dijkstra, M. Stacking in sediments of colloidal hard spheres. The Journal of chemical physics 2011, 135 (3), 034510.
(52) Martelozzo, V.; Schofield, A. B.; Poon, W.; Pusey, P. Structural aging of crystals of hard-sphere colloids. Physical Review E 2002, 66 (2), 021408.
(53) Mori, A.; Suzuki, Y.; Yanagiya, S.-i.; Sawada, T.; Ito, K. Shrinking stacking fault through glide of the Shockley partial dislocation in hard-sphere crystal under gravity. Molecular Physics 2007, 105 (10), 1377-1383.
(54) Chen, L.-T.; Huang, Y.-T.; Chen, C.-Y.; Chen, M.-Z.; Chen, H.-L. Thermodynamically Originated Stacking Fault in the Close-Packed Structure of Block Copolymer Micelles. Macromolecules 2021, 54 (19), 8936-8945.
(55) Lindsay, A. P.; Lewis III, R. M.; Lee, B.; Peterson, A. J.; Lodge, T. P.; Bates, F. S. A15, σ, and a quasicrystal: Access to complex particle packings via bidisperse diblock copolymer blends. ACS Macro Letters 2020, 9 (2), 197-203.
(56) Lee, S.; Bluemle, M. J.; Bates, F. S. Discovery of a Frank-Kasper σ phase in sphere-forming block copolymer melts. Science 2010, 330 (6002), 349-353.
(57) Lindsay, A. P.; Cheong, G. K.; Peterson, A. J.; Weigand, S.; Dorfman, K. D.; Lodge, T. P.; Bates, F. S. Complex Phase Behavior in Particle-Forming AB/AB′ Diblock Copolymer Blends with Variable Core Block Lengths. Macromolecules 2021, 54 (15), 7088-7101.
(58) Sluiter, M. H.; Pasturel, A.; Kawazoe, Y. Prediction of site preference and phase stability of transition metal based Frank-Kasper phases. In The Science of Complex Alloy Phases ashfield at the 134th TMS Annual Meeting. San Francisco, 2005.
(59) Li, W.; Duan, C.; Shi, A.-C. Nonclassical spherical packing phases self-assembled from AB-type block copolymers. ACS Publications: 2017.
(60) Lee, S.; Leighton, C.; Bates, F. S. Sphericity and symmetry breaking in the formation of Frank–Kasper phases from one component materials. Proceedings of the National Academy of Sciences 2014, 111 (50), 17723-17731.
(61) Schulze, M. W.; Lewis III, R. M.; Lettow, J. H.; Hickey, R. J.; Gillard, T. M.; Hillmyer, M. A.; Bates, F. S. Conformational asymmetry and quasicrystal approximants in linear diblock copolymers. Physical review letters 2017, 118 (20), 207801.
(62) Chang, A. B.; Bates, F. S. Impact of Architectural Asymmetry on Frank–Kasper Phase Formation in Block Polymer Melts. ACS nano 2020, 14 (9), 11463-11472.
(63) Matsen, M. W. Effect of architecture on the phase behavior of AB-type block copolymer melts. Macromolecules 2012, 45 (4), 2161-2165.
(64) Liu, M.; Qiang, Y.; Li, W.; Qiu, F.; Shi, A.-C. Stabilizing the Frank-Kasper phases via binary blends of AB diblock copolymers. ACS Macro Letters 2016, 5 (10), 1167-1171.
(65) Magruder, B. R.; Park, S. J.; Collanton, R. P.; Bates, F. S.; Dorfman, K. D. Laves Phase Field in a Diblock Copolymer Alloy. Macromolecules 2022, 55 (7), 2991-2998.
(66) Nouri, B.; Chen, C.-Y.; Huang, Y.-S.; Mansel, B. W.; Chen, H.-L. Emergence of a Metastable Laves C14 Phase of Block Copolymer Micelle Bearing a Glassy Core. Macromolecules 2021, 54 (19), 9195-9203.
(67) Chen, L.-T.; Huang, Y.-T.; Chen, C.-Y.; Chen, M.-Z.; Chen, H.-L. Thermodynamically Originated Stacking Fault in the Close-Packed Structure of Block Copolymer Micelles. Macromolecules 2021.
(68) Auer, S.; Frenkel, D. Prediction of absolute crystal-nucleation rate in hard-sphere colloids. Nature 2001, 409 (6823), 1020-1023.
(69) Chen, L.-T.; Chen, C.-Y.; Chen, H.-L. FCC or HCP: The stable close-packed lattice of crystallographically equivalent spherical micelles in block copolymer/homopolymer blend. Polymer 2019, 169, 131-137.
(70) Nutt, S. Defects in silicon carbide whiskers. Journal of the American Ceramic Society 1984, 67 (6), 428-431.
(71) Jepps, N.; Page, T. Polytypic transformations in silicon carbide. Progress in crystal growth and characterization 1983, 7 (1-4), 259-307.
(72) Hamaya, N.; Sakamoto, Y.; Fujihisa, H.; Fujii, Y.; Takemura, K.; Kikegawa, T.; Shimomura, O. Crystal structure of the distorted FCC high-pressure phase of praseodymium. Journal of Physics: Condensed Matter 1993, 5 (31), L369.
(73) Grosshans, W.; Vohra, Y.; Holzapfel, W. Evidence for a soft phonon mode and a new structure in rare-earth metals under pressure. Physical Review Letters 1982, 49 (21), 1572.
(74) Porsch, F.; Holzapfel, W. Novel reentrant high pressure phase transtion in lanthanum. Physical review letters 1993, 70 (26), 4087.
(75) Vohra, Y.; Vijayakumar, V.; Godwal, B.; Sikka, S. Structure of the distorted fcc high-pressure phase of the trivalent rare-earth metals. Physical Review B 1984, 30 (10), 6205.
(76) Pravica, M.; Quine, Z.; Romano, E. X-ray diffraction study of elemental thulium at pressures up to 86 GPa. Physical Review B 2006, 74 (10), 104107.
(77) Pravica, M. G.; Romano, E.; Quine, Z. X-ray diffraction study of elemental erbium to 70 GPa. Physical Review B 2005, 72 (21), 214122.
(78) Porsch, F.; Holzapfel, W. Symmetry change at the fcc–distorted-fcc phase transition of lanthanides under pressure. Physical Review B 1994, 50 (22), 16212.
(79) Saxena, S.; Dubrovinsky, L.; Häggkvist, P.; Cerenius, Y.; Shen, G.; Mao, H. Synchrotron X-ray study of iron at high pressure and temperature. Science 1995, 269 (5231), 1703-1704.
(80) Saxena, S. K.; Shen, G.; Lazor, P. Experimental evidence for a new iron phase and implications for Earth's core. Science 1993, 260 (5112), 1312-1314.
(81) Rao, R.; Modak, P.; Godwal, B.; Sikka, S. Stability of the pressure-induced orthorhombic phase of iron. Physical Review B 1999, 59 (21), 13498.
(82) Nishiyama, Z. Martensitic transformation; Elsevier, 2012.
(83) Wentzcovitch, R. M.; Lam, P. K. fcc-to-hcp transformation: A first-principles investigation. Physical Review B 1991, 44 (17), 9155.
(84) Bergman, G.; Shoemaker, D. P. The determination of the crystal structure of the σ phase in the iron–chromium and iron–molybdenum systems. Acta Crystallographica 1954, 7 (12), 857-865.
(85) Berne, C.; Sluiter, M.; Kawazoe, Y.; Hansen, T.; Pasturel, A. Site occupancy in the Re-W sigma phase. Physical Review B 2001, 64 (14), 144103.
(86) van de Waal, B. W. Can the Lennard-Jones solid be expected to be fcc? Physical review letters 1991, 67 (23), 3263.