准晶体及其性能研究进展
|
摘要
基于准晶体材料目前的研究现状,简要介绍了根据结构对称性的准晶体分类,讨论了周期模型的构建方法以及准晶体与其近似相的关系,总结了块体单准晶的制备工艺,塑性变形过程中缺陷演化,表面结构、表面性能以及其他物理性能的实验研究现状,分析讨论了采用连续介质力学方法、分子动力学模拟方法、Monte Carlo法以及有限元方法研究准晶体的途径和结果.针对准晶通常呈现的低表面能、低摩擦因数、耐磨损、优异的弥散强化特性、高硬度、高弹性模量、高温塑性、高热阻、抗氧化、高电阻和耐腐蚀等特点,展望其作为复合材料增强相、隔热涂层、耐磨减磨涂层材料等的应用前景.指出准晶体目前研究中所存在的高脆性、成品体积小和计算精度低等难题,提出了其工程应用需要进一步研究的问题.
Based on present research status of quasicrystal, the classification with structural symmetry, the construction of quasi-periodic model and the correlation between quasicrystal and its approximants were introduced briefly. The preparation technology of bulk single grian quasicrystal,defect evolution during plastic deformation,surface structure,surface property and other physical properties were summarized. Theoretical research such as continuum mechanics, atomistic simulation, Monte Carlo simulation and Finite Element Method were also discussed. The application of quasicrystal was prospected according to its physical properties including low surface energy,low friction coefficient and wear rate,excellent dispersion strengthening,high hardness and Young 's Modulus,plasticity at high temperature,high thermal resistance and corrosion resistance,etc. Current limitations such as brittleness and bulk volume were pointed out,and issues which remain to be solved for further engineering applications were listed.
Based on present research status of quasicrystal, the classification with structural symmetry, the construction of quasi-periodic model and the correlation between quasicrystal and its approximants were introduced briefly. The preparation technology of bulk single grian quasicrystal,defect evolution during plastic deformation,surface structure,surface property and other physical properties were summarized. Theoretical research such as continuum mechanics, atomistic simulation, Monte Carlo simulation and Finite Element Method were also discussed. The application of quasicrystal was prospected according to its physical properties including low surface energy,low friction coefficient and wear rate,excellent dispersion strengthening,high hardness and Young 's Modulus,plasticity at high temperature,high thermal resistance and corrosion resistance,etc. Current limitations such as brittleness and bulk volume were pointed out,and issues which remain to be solved for further engineering applications were listed.
引文
[1]SHECHTMAN D,BLECH I,GRATIAS D,et al.Metallic phase with long-range orientational order and no translational symmetry[J].Physical Review Letters,1984,53(20):1951-1953.DOI:10.1103/PhysRev Lett.53.1951.
[2]ZHANG Z,YE H Q,KUO K H.A new icosahedral phase with m35symmetry[J].Philosophical Magazine A,1985,52(6):L49-L52.DOI:10.1080/01418618508242135.
[3]DUBOIS J M.New prospects from potential applications of quasicrystalline materials[J].Materials Science and Engineering:A,2000,294:4-9.DOI:10.1016/S0921-5093(00)01305-8.
[4]RABSON D A.Toward theories of friction and adhesion on quasicrystals[J].Progress in Surface Science,2012,87(9):253-271.DOI:10.1016/j.progsurf.2012.10.001.
[5]OLSSON S,BROITMAN E,GARBRECHT M,et al.Mechanical and tribological properties of Al Cu Fe quasicrystal and Al(Si)Cu Fe approximant thin films[J].Journal of Materials Research,2016,31(2):232-240.DOI:10.1557/jmr.2015.384.
[6]BRUNET P,ZHANG L M,SORDELET D J,et al.Comparative study of microstructural and tribological properties of sintered,bulk icosahedral samples[J].Materials Science and Engineering:A,2000,294:74-78.DOI:10.1016/S0921-5093(00)01202-8.
[7]INOUE A,ZHANG Tao,CHEN Minwei,et al.Mechanical properties of bulk amorphous Zr-Al-Cu-Ni-Ag alloys containing nanoscale quasicrystalline particles[J].Materials Transactions,1999,40(12):1382-1389.DOI:10.2320/matertrans1989.40.1382.
[8]WITTMANN R,URBAN K,SCHANDL M,et al.Mecanical properties of single quasicrystalline Al Cu Co Si[J].Journal of Materials Research,1991,6(6):1165-1168.DOI:10.1557/JMR.1991.1165.
[9]YOKOYAMA Y,INOUE A,MASUMOTO T.Mechanical-properties,fracture mode and deformation-behavior of Al70Pd20Mn10 single quasicrystal[J].Materials Transactions Jim,1993,34(2):135-145.DOI:10.2320/matertrans1989.34.135.
[10]BLAS F J G,ALGABA J M,ALVAREZ J,et al.Application of quasicrystalline materials as thermal barriers in aeronautics and future perspectives of use for these materials[C]//MRS 1998 Fall Meeting.[S.l.]:Cambridge Univ Press,1998:447.DOI:10.1557/PROC-553-447.
[11]DUBOIS J M,KANG S S,MASSIANI Y.Application of quasicrystalline alloys to surface coating of soft metals[J].Journal of Non-Crystalline Solids,1993,153:443-445.DOI:10.1016/0022-3093(93)90392-B.
[12]MIGLIERINI M,NASU S.Magnetic,electronic and structure-properties of icosahedral quasicrystals[J].Materials Transactions Jim,1993,34(2):178-187.DOI:10.2320/matertrans1989.34.178.
[13]STROUD R M,VIANO A M,GIBBONS P C,et al.Stable Ti based quasicrystal offers prospect for improved hydrogen storage[J].Applied physics letters,1996,69(20):2998-3000.DOI:10.1063/1.117756.
[14]LUBENSKY T C,RAMASWAMY S,TONER J.Dislocation motion in quasicrystals and implications for macroscopic properties[J].Physical Review B,1986,33(11):7715-7719.DOI:10.1103/PhysRev B.33.7715.
[15]LIU P,STIGENBERG A H,NILSSON J O.Quasicrystalline and crystalline precipitation during isothermal tempering in a12Cr9Ni4Mo maraging stainless steel[J].Acta Metallurgica Et Materialia,1995,43(7):2881-2890.DOI:10.1016/0956-7151(94)00461-P.
[16]LEE K,HSU J L,NAUGLE D,et al.Multi-phase quasicrystalline alloys for superior wear resistance[J].Materials&Design,2016,108:440-447.DOI:10.1016/j.matdes.2016.06.113.
[17]ENGEL M,DAMASCENO P F,PHILLIPS C L,et al.Computational self-assembly of a one-component icosahedral quasicrystal[J].Nature Materials,2015,14(1):109-116.DOI:10.1038/nmat4152.
[18]FENG Y C,LU G,WITHERS R L.An incommensurate structure with cubic point group symmetry in rapidly solidified V-Ni-Si alloy[J].Journal of Physics Condensed Matter,1989,1(23):3695-3700.
[19]BENDERSKY L.Quasicrystal with one-dimensional translational symmetry and a tenfold rotation axis[J].Physical Review Letters,1985,55(14):1461-1463.DOI:10.1103/PhysRev Lett.55.1461.
[20]WU J S,KUO K H.Decagonal quasicrystal and related crystalline phases in Mn-Ga alloys with 52 to 63 a/o Ga[J].Metallurgical and Materials Transactions A,1997,28(13):729-742.DOI:10.1007/s11661-997-1000-y.
[21]SCHAEFER R J,BENDERSKY L.Replacement of icosahedral Al Mn by decagonal phase[J].Scripta Metallurgica,1986,20(5):745-750.DOI:10.1016/0036-9748(86)90504-1.
[22]WASIO N A,QUARDOKUS R C,FORREST R P,et al.Self-assembly of hydrogen-bonded two-dimensional quasicrystals[J].Nature,2014,507(7490):86-89.DOI:10.1038/nature12993.
[23]WANG N,CHEN H,KUO K H.Two-dimensional quasicrystal with eightfold rotational symmetry[J].Physical Review Letters,1987,59(9):1010-1013.DOI:10.1103/PhysRev Lett.59.1010.
[24]ISHIMASA T,NISSEN H U,FUKANO Y.New ordered state between crystalline and amorphous in Ni-Cr particles[J].Physical Review Letters,1985,55(55):511-513.DOI:10.1103/PhysRevLett.55.511.
[25]ZENG Xiangbing,UNGAR G,LIU Yongsong,et al.Supramolecular dendritic liquid quasicrystals[J].Nature,2004,428(6979):157-160.DOI:10.1038/nature02368.
[26]FISCHER S,EXNER A,ZIELSKE K,et al.Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry[J].Proceedings of the National Academy of Sciences,2011,108(5):1810-1814.DOI:10.1073/pnas.1008695108.
[27]DOTERA T,OSHIRO T,ZIHERL P.Mosaic two-lengthscale quasicrystals[J].Nature,2014,506(7487):208-211.DOI:10.1038/nature12938.
[28]周公度,郭可信.晶体和准晶体的衍射[M].北京:北京大学出版社,1999:251-252.ZHOU Gongdu,GUO Kexin.Diffraction of crystal and quasicrystal[M].Beijing:Peking University Press,1999:251-252.
[29]MERLIN R,BAJEMA K,CLARKE R,et al.Quasiperiodic gaas-alas heterostructures[J].Physical Review Letters,1985,55(17):1768-1770.DOI:10.1103/PhysRev Lett.55.1768.
[30]YADAV T P,MISHRA S S,SRIVASTAVA O N.Copper nanocubes on Al 65 Cu 20 Fe 15 quasicrystalline surface[J].Journal of Alloys and Compounds,2017,712:134-138.DOI:10.1016/j.jallcom.2017.04.058.
[31]BINDI L,STEINHARDT P J,YAO Nan,et al.Natural quasicrystals[J].science,2009,324(5932):1306-1309.DOI:10.1126/science.1170827.
[32]BINDI L,YAO N,LIN C,et al.Natural quasicrystal with decagonal symmetry[J].Scientific Reports,2015(5):9111.DOI:10.1038/srep09111.
[33]HOLLISTER L S,BINDI L,YAO N,et al.Impact-induced shock and the formation of natural quasicrystals in the early solar system.[J].Nature Communications,2014(5):4040.DOI:10.1038/ncomms5040.
[34]FRANK F C T,KASPER J S.Complex alloy structures regarded as sphere packings.II.Analysis and classification of representative structures[J].Acta Crystallographica,1959,12(7):483-499.DOI:10.1107/S0365110X59001499.
[35]FRANK F C,KASPER J S.Complex alloy structures regarded as sphere packings.I.Definitions and basic principles[J].Acta Crystallographica,1958,11(3):184-190.DOI:10.1107/S0365110X58000487.
[36]LEVINE D,STEINHARDT P J.Quasicrystals:a new class of ordered structures[J].Physical Review Letters,1984,53(26):2477-2480.DOI:10.1103/PhysRev Lett.53.2477.
[37]LEVINE D,STEINHARDT P J.Quasicrystals.I.Definition and structure[J].Physical Review B,1986,34(2):596-616.DOI:10.1103/PhysRev B.34.596.
[38]SOCOLAR J E S,STEINHARDT P J.Quasicrystals.II.Unit-cell configurations[J].Physical Review B,1986,34(2):617-647.DOI:10.1103/PhysRev B.34.617.
[39]PENROSE R.Pentaplexity a class of non-periodic tilings of the plane[J].Mathematical Intelligencer,1979,2(1):32-37.DOI:10.1007/BF03024384.
[40]STEPHENS P W,GOLDMAN A I.The structure of quasicrystals[J].Scientific American,1991,150-151(3/4):44-47.DOI:10.1038/scientificamerican0491-44.
[41]WIDOM M,STRANDBURG K J,SWENDSEN R H.Quasicrystal equilibrium state[J].Physical Review Letters,1987,58(7):706-709.DOI:10.1103/PhysRev Lett.58.706.
[42]BRUIJN N G.Algebraic theory of Penrose's non-periodic tilings of the plane.II[C]//Indagationes Mathematicae(Proceedings).North-Holland:Elsevier,1981:53-66.DOI:10.1016/1385-7258(81)90017-2.
[43]SOCOLAR J E S,STEINHARDT P J,LEVINE D.Quasicrystals with arbitrary orientational symmetry[J].Physical Review B,1985,32(8):5547-5550.DOI:10.1103/PhysRev B.32.5547.
[44]ELSER V.Indexing problems in quasicrystal diffraction[J].Physical Review B,1985,32(8):4892-4898.DOI:10.1103/PhysRev B.32.4892.
[45]WANG Z M,KUO K H.The octagonal quasilattice and electron diffraction patterns of the octagonal phase[J].Acta Crystallographica Section A:Foundations of Crystallography,1988,44(6):857-863.DOI:10.1107/S0108767388004921.
[46]ISHIHARA K N,YAMAMOTO A.Penrose patterns and related structures.I.Superstructure and generalized Penrose patterns[J].Acta Crystallographica Section A:Foundations of Crystallography,1988,44(4):508-516.DOI:10.1107/S0108767388002958.
[47]YAMAMOTO A,ISHIHARA K N.Penrose patterns and related structures.II.Decagonal quasicrystals[J].Acta Crystallographica Section A:Foundations of Crystallography,1988,44(5):707-714.DOI:10.1107/S010876738800296X.
[48]YANG Q B,WEI W D.Description of the dodecagonal quasicrystal by a projection method[J].Physical Review Letters,1987,58(10):1020-1023.DOI:10.1103/PhysRev Lett.58.1020.
[49]MIKULLA R,ROTH J,TREBIN H R.Simulation of shear-stress in2-dimensional decagonal quasicrystals[J].Philosophical Magazine B-Physics of Condensed Matter Statistical Mechanics Electronic Optical and Magnetic Properties,1995,71(5):981-989.DOI:10.1080/01418639508243601.
[50]MIKULLA R,GUMBSCH P,TREBIN H R.Dislocations in quasicrystals and their interaction with cluster-like obstacles[J].Philosophical Magazine Letters,1998,78(5):369-376.DOI:10.1080/095008398177760.
[51]MIKULLA R,STADLER J,KRUL F,et al.Crack propagation in quasicrystals[J].Physical Review Letters,1998,81(15):3163-3166.DOI:10.1103/PhysRev Lett.81.3163.
[52]ELSER V,HENLEY C L.Crystal and quasicrystal structures in AlMn-Si alloys[J].Physical review letters,1985,55(26):2883-2886.DOI:10.1103/PhysRev Lett.55.2883.
[53]TAKAKURA H,GMEZ C P,YAMAMOTO A,et al.Atomic structure of the binary icosahedral Yb-Cd quasicrystal[J].Nature Material,2007,6(6):58-63.DOI:10.1038/nmat1799.
[54]TSAI A P,GUO J Q,ABE E,et al.Alloys:A stable binary quasicrystal[J].Nature,2000,408(6812):537-538.DOI:10.1038/35046202.
[55]BAUER B,MEISTERERNST G,HAERTWIG J,et al.Czochralski growth and X-ray topographic characterization of decagonal Al Co Ni quasicrystals[J].Philosophical Magazine,2006,86(3/4/5):317-322.DOI:10.1080/14786430500253927.
[56]GILLE P,BAUER B,HAHNE M,et al.Single crystal growth of Al-based intermetallic phases being approximants to quasicrystals[J].Journal of Crystal Growth,2011,318(1):1016-1020.DOI:10.1016/j.jcrysgro.2010.10.021.
[57]CUI C,TSAI A P.Growth of large single-grain quasicrystals in the Ag-In-Yb system by Bridgman method[J].Journal of Crystal Growth,2009,312(1):131-135.DOI:10.1016/j.jcrysgro.2009.09.038.
[58]CUI C,TSAI A P.Growth of large-grain Ag-In-Yb icosahedral quasicrystals and approximant crystals[J].Journal of Alloys&Compounds,2012,536(5):91-93.DOI:10.1016/j.jallcom.2012.05.031.
[59]CUI C,TSAI A P.Synthesis of large single-grain 1/1 approximant crystals in the Ag-In-Eu system by the self-flux method[J].Philosophical Magazine,2011,91(19/20/21):2443-2449.DOI:10.1080/14786435.2010.511600.
[60]SATO T J,HIRANO T,TSAI A P.Single-crystal growth of the decagonal Al-Ni-Co quasicrystal[J].Journal of Crystal Growth,1998,191(3):545-552.DOI:10.1016/S0022-0248(98)00164-X.
[61]TSAI A P.Discovery of stable icosahedral quasicrystals:progress in understanding structure and properties[J].Chemical Society Reviews,2013,44(34):5352-5365.DOI:10.1039/C3CS35388E.
[62]SOCOLAR J E S,LUBENSKY T C,STEINHARDT P J.Phonons,phasons,and dislocations in quasicrystals[J].Physical Review B,1986,34(5):3345-3360.DOI:10.1103/PhysRev B.34.3345.
[63]WOLLGARTEN M,BEYSS M,URBAN K,et al.Direct evidence for plastic-deformation of quasicrystals by means of a dislocation mechanism[J].Physical Review Letters,1993,71(4):549-552.DOI:10.1103/PhysRev Lett.71.549.
[64]MOMPIOU F,BRESSON L,CORDIER P,et al.Dislocation climb and low-temperature plasticity of an Al-Pd-Mn quasicrystal[J].Philosophical Magazine,2003,83(27):3133-3157.DOI:10.1080/1478643031000155110.
[65]MESSERSCHMIDT U,BARTSCH M,FEUERBACHER M,et al.Friction mechanism of dislocation motion in icosahedral Al-Pd-Mn quasicrystals[J].Philosophical Magazine A,1999,79(9):2123-2135.DOI:10.1080/01418619908210412.
[66]TEXIER M,PROULT A,BONNEVILLE J,et al.Microstructure of I-Al-Pd-Mn deformed at low and intermediate temperatures[J].Materials Science and Engineering:A,2004,387:1023-1027.DOI:10.1016/j.msea.2004.01.120.
[67]ZOU Y,KUCZERA P,SOLOGUBENKO A,et al.Superior roomtemperature ductility of typically brittle quasicrystals at small sizes[J].Nature Communications,2016(7):12261.DOI:10.1038/ncomms12261.
[68]ZOU Y,KUCZERA P,STEURER W,et al.Disappearance of plastic anisotropy in decagonal quasicrystals at small scales and room temperature[J].Extreme Mechanics Letters,2016(8):229-234.DOI:10.1016/j.eml.2016.02.005.
[69]SCHALL P,FEUERBACHER M,URBAN K.Plastic deformation of decagonal Al73Ni10Co17 single quasicrystals[J].Philosophical Magazine,2004,84(7):705-718.DOI:10.1080/14786430310001624857.
[70]FEUERBACHER A,SCHALL P.Plastic behaviour of decagonal Al-Ni-Co single quasicrystals[J].Scripta Materialia,2003,49(1):25-31.DOI:10.1016/S0921-5093(00)01653-1.
[71]LAPLANCHE G,BONNEVILLE J,JOULAIN A,et al.Mechanical properties of Al-Cu-Fe quasicrystalline and crystalline phases:An analogy[J].Intermetallics,2014,50:54-58.DOI:10.1016/j.intermet.2014.02.004.
[72]PARK J Y,OGLETREE D F,SALMERON M,et al.High frictional anisotropy of periodic and aperiodic directions on a quasicrystal surface[J].Science,2005,309(5739):1354-1356.DOI:10.1126/science.1113239.
[73]FILIPPOV A E,VANOSSI A,URBAKH M.Origin of friction anisotropy on a quasicrystal surface[J].Physical review letters,2010,104(7):074302.DOI:10.1103/PhysRev Lett.104.074302.
[74]YE Z J.,MARTINI A,THIEL P,et al.Atomistic simulation of frictional anisotropy on quasicrystal approximant surfaces[J].Physical Review B,2016,91(33):4218-4229.DOI:10.1103/PhysRev B.93.235438.
[75]DUBOIS J M.Properties-and applications of quasicrystals and complex metallic alloys[J].Chemical Society Reviews,2012,41(20):6760-6777.DOI:10.1039/C2CS35110B.
[76]STEIJN R P.Friction and wear of single crystals[J].Wear,1964,7(1):48-66.DOI:10.1016/0043-1648(64)90078-X.
[77]DYER L D.Rolling friction on single crystals of copper in the plastic range[J].Acta Metallurgica,1961,9(10):928-936.DOI:10.1016/0001-6160(61)90111-0.
[78]BAILEY J M,GWATHMEY A T.Friction and surface deformation during sliding on a single crystal of copper[J].Tribology Transactions,1962,5(1):45-56.DOI:10.1080/05698196208972452.
[79]STEIJN R P.On the wear of sapphire[J].Journal of Applied Physics,1961,32(10):1951-1958.DOI:10.1063/1.1728269.
[80]BUCKLEY D H,JOHNSON R L.Friction and wear of hexagonal metals and alloys as related to crystal structure and lattice parameters in vacuum[J].Tribology Transactions,1966,9(2):121-135.DOI:10.1080/05698196608972128.
[81]BUCKLEY D H,JOHNSON R L.Influence of crystal structure on friction characteristics of rare-earth and related metals in vacuum to10-10 mm of mercury[J].Tribology Transactions,1965,8(2):123-132.DOI:10.1080/05698196508972086.
[82]UCKLEY D H.The influence of the atomic nature of crystalline materials on friction[J].Tribology Transactions,1968,11(2):89-100.DOI:10.1080/05698196808972212.
[83]GRNING O,R.WIDMER,P.RUFFIEUX,et al.Scanning tunnelling microscopy with atomic resolution on the twofold surface of the icosahedral Al Pd Mn quasicrystal[J].Philosophical Magazine,2006,86(6/7/8):773-779.DOI:10.1080/14786430500306535.
[84]SHARMA H R,FOURNE V,SHIMODA M,et al.Structure of the fivefold surface of the icosahedral Al-Cu-Fe quasicrystal:experimental evidence of bulk truncations at larger interlayer spacings[J].Physical Review Letters,2004,93(16):165502.DOI:10.1103/PhysRev Lett.93.165502.
[85]CAI T,SHI F,SHEN Z,et al.Structural aspects of the fivefold quasicrystalline Al-Cu-Fe surface from STM and dynamical LEED studies[J].Surface Science,2001,495(1/2):19-34.DOI:10.1016/S0039-6028(01)01500-X.
[86]ROUXEL D,CAI T H,JENKS C J,et al.Structural aspects of the threefold surface of icosahedral Al-Pd-Mn[J].Surface Science,2000,461(1):L521-L527.DOI:10.1016/S0039-6028(00)00513-6.
[87]SHEN Z,JENKS C J,ANDEREGG J,et al.Structure and stability of the twofold surface of icosahedral Al-Pd-Mn by low-energy electron diffraction and X-ray photoemission spectroscopy[J].Physical Review Letters,1997,78(6):1050-1053.DOI:10.1103/PhysRev Lett.78.1050.
[88]TAMURA R,YADAV T P,MCLEOD I M,et al.Scanning tunneling microscopy of a polygrain Al-Pd-Re quasicrystal:study of the relative surface stability.[J].Journal of Physics Condensed Matter,2013,25(39):395007.DOI:10.1088/0953-8984/25/39/395007.
[89]NUGENT P J,SMERDON J A,MCGRATH R,et al.Step-terrace morphology and reactivity to C60 of the five-fold icosahedral Ag-In-Yb quasicrystal[J].Philosophical Magazine,2011,91(19/20/21):2862-2869.DOI:10.1080/14786435.2010.514870.
[90]CUI C,NUGENT P J,SHIMODA M,et al.The atomic structure of the threefold surface of the icosahedral Ag-In-Yb quasicrystal[J].Journal of Physics Condensed Matter,2012,24(44):445011.DOI:10.1088/0953-8984/24/44/445011.
[91]CUI C,NUGENT P J,SHIMODA M,et al.Structure of the twofold surface of the icosahedral Ag-In-Yb quasicrystal[J].Journal of Physics:Condensed Matter,2013,26(1):015001.DOI:10.1088/0953-8984/26/1/015001.
[92]PARK J Y,OGLETREE D F,SALMERON M,et al.Atomic scale coexistence of periodic and quasiperiodic order in a 2-fold Al-NiCo decagonal quasicrystal surface[J].Physical Review B,2005,72(22):220201(1/2/3/4).DOI:10.1103/PhysRev B.72.220201.
[93]TAKAKURA H,YAMAMOTO A,TSAI A P.The structure of a decagonal Al72Ni20Co8 quasicrystal[J].Acta Crystallographica,2001,57(57):576-585.DOI:10.1107/S0108767301007942.
[94]LEDIEU J,HOEFT J T,REID D E,et al.Copper adsorption on the fivefold Al70Pd21Mn9,quasicrystal surface[J].Physical Review B,2005,72(3):035420.DOI:10.1103/PhysRev B.72.035420.
[95]LEDIEU J.Ordering of Si atoms on the fivefold Al-Pd-Mn quasicrystal surface[J].Physical Review B,2006.73(1):012204.DOI:10.1103/PhysRev B.73.012204.
[96]KRAJˇCC M,HAFNER J.Structure,stability,and electronic properties of the,i-Al Pd Mn quasicrystalline surface[J].Physical Review B,2005,71(71):054202.DOI:10.1103/PhysRev B.71.054202.
[97]LEDIEU J,LEUNG L,WEARING L H,et al.Self-assembly,structure and electronic properties of a quasiperiodic lead monolayer[J].Physical Review B,2008,77(7):439-446.DOI:10.1103/PhysRev B.77.073409.
[98]MARTIN S,HEBARD A F,KORTAN A R,et al.Transport properties of Al65Cu15Co20,and Al70Ni15Co15,decagonal quasicrystals[J].Physical Review Letters,1991,67(6):719-722.DOI:10.1103/PhysRev Lett.67.719.
[99]SMONTARA A,IVKOV J.Anisotropic magnetic,electrical,and thermal transport properties of the Y-Al-Ni-Co decagonal approximant[J].Physical Review B Condensed Matter,2008,78(10):104204.DOI:10.1103/PhysRev B.78.104204.
[100]BOBNAR M,JEGLIˇC P,KLANJEK M,et al.Intrinsic anisotropic magnetic,electrical,and thermal transport properties of d-Al-Co-Ni decagonal quasicrystals[J].Physical Review B Condensed Matter,2012,85(2):024205.DOI:10.1103/PhysRev B.85.024205.
[101]DOLINEK J.Extrinsic origin of the insulating behavior of polygrain icosahedral Al-Pd-Re quasicrystals[J].Physical Review B,2006,74(13):134201.DOI:10.1103/PhysRev B.74.134201.
[102]BOBNAR M,VRTNIK S,JAGLIˇCIˇC Z,et al.Electrical,magnetic,and thermal properties of the single-grain Ag42In42Yb16 icosahedral quasicrystal:Experiment and modeling[J].Physical Review B Condensed Matter,2011,84(13):4578-4586.DOI:10.1103/PhysRev B.84.134205.
[103]范天佑.固体与软物质准晶数学弹性与相关理论及应用[M].北京:北京理工大学出版社,2014:51-271.FAN Tianyou.Mathematical theory of elasticity and relevant topics of solid and solft-matter quasicrystals and its applications[M].Beijing:Beijing Institute of Technology Press,2014:51-271.
[104]BUNZ D,ZEGER G,ROTH J,et al.Molecular dynamic studies of atomic jumps in d-Al-Cu-Co[J].Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing,2000,294:675-679.DOI:10.1016/S0921-5093(00)01187-4.
[105]TREBIN H R,MIKULLA R,STADLER J,et al.Molecular dynamics simulations of crack propagation in quasicrystals[J].Computer Physics Communications,1999,121:536-539.DOI:10.1016/S0010-4655(99)00400-2.
[106]SCHAAF G D,ROTH J,TREBIN H R.Numerical simulation of dislocation motion in three-dimensional icosahedral quasicrystals[J].Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties,2000,80(7):1657-1668.DOI:10.1080/01418610008212142.
[107]RUDHART C,RSCH F,GHLER F,et al.Crack propagation in icosahedral model quasicrystals[J].High Performance Computing in Science&Engineering,2003:107-116.DOI:10.1007/978-3-642-55876-4_8.
[108]SCHAAF G D,ROTH J,TREBIN H R.Dislocation motion in icosahedral quasicrystals at elevated temperatures:numerical simulation[J].Philosophical Magazine,2003,83(21):2449-2465.DOI:10.1080/0141861031000113352.
[109]RUDHART C,TREBIN H R,GUMBSCH P.Crack propagation in perfectly ordered and random tiling quasicrystals[J].Journal of NonCrystalline Solids,2004,334:453-456.DOI:10.1016/j.jnoncrysol.2003.12.039.
[110]ROSCH F,RUDHART C,ROTH J,et al.Dynamic fracture of icosahedral model quasicrystals:A molecular dynamics study[J].Physical Review B,2005,72(1):014128.DOI:10.1103/PhysRev B.72.014128.
[111]SASAJIMA Y,TANAKA H,ITABA M,et al.Computer experiments of fracture of 2-dimensional henley-elser type quasi-crystals[J].Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing,1994,176(1/2):283-288.DOI:10.1016/0921-5093(94)90987-3.
[112]TREBIN H R,MIKULLA R,ROTH J.Motion of dislocations in two-dimensional decagonal quasicrystals[J].Journal of non-crystalline solids,1993,153:272-275.DOI:10.1016/0022-3093(93)90356-3.
[113]ENGEL M,UMEZAKI M,TREBIN H R,et al.Dynamics of particle flips in two-dimensional quasicrystals[J].Physical Review B Condensed Matter,2010,82(13):087201.DOI:10.1103/PhysRev B.82.134206.
[114]YANG L Z,HE F M,GAO Y.Finite element method for static problems of cubic quasicrystals[J].Acta Physica Polonica,2014,126(2):471-473.DOI:10.12693/APhys Pol A.126.471.
[115]杨连枝,何蕃民,高阳,等.二十面体Al-Pd-Mn准晶板的断裂行为研究[C]//北京力学会第20届学术年会论文集.北京:中国学术期刊电子出版社,2014:.YANG Lianzhi,HE Fanmin,GAO Yang,et al.Study of frature behavior of icosahedral Al-Pd-Mn quasicrystal slab[C]//The Proceedings of the 20th Annual Conference of Beijing Society of Theoretical and Applied Mechanics.Beijing:China Academic Journal Electronic Publishing House,2014.
[116]吴祥法,范天佑,安冬梅.用路径守恒积分计算平面准晶裂纹扩展的能量释放率[J].计算力学学报,2000,17(1):34-42.DOI:10.3969/j.issn.1007-4708.2000.01.006.WU Xiangfa,FAN Tianyou,AN Dongmei.Energy release rate of plane quasicrystals with crack determined by path-independent Eintegral[J].Chinese Journal of Computational Mechanics,2000,17(1):34-42.DOI:10.3969/j.issn.1007-4708.2000.01.006.
[117]AMADA T,TAKAKURA H,EUCHNER H,et al.Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal[J].Iucrj,2016(3):247-258.DOI:10.1107/S2052252516007041.
[118]YAMADA T,TAKAKURA H,KONG T,et al.Atomic structure of the i-R-Cd quasicrystals and consequences for magnetism[J].Physical Review B,2016,94(6):060103.DOI:10.1103/PhysRev B.94.060103.
[119]KENZARI S,BONINA D,DUBOIS J M,et al.Quasicrystal-polymer composites for selective laser sintering technology[J].Materials&Design,2012,35:691-695.DOI:10.1016/j.matdes.2011.10.032.
[2]ZHANG Z,YE H Q,KUO K H.A new icosahedral phase with m35symmetry[J].Philosophical Magazine A,1985,52(6):L49-L52.DOI:10.1080/01418618508242135.
[3]DUBOIS J M.New prospects from potential applications of quasicrystalline materials[J].Materials Science and Engineering:A,2000,294:4-9.DOI:10.1016/S0921-5093(00)01305-8.
[4]RABSON D A.Toward theories of friction and adhesion on quasicrystals[J].Progress in Surface Science,2012,87(9):253-271.DOI:10.1016/j.progsurf.2012.10.001.
[5]OLSSON S,BROITMAN E,GARBRECHT M,et al.Mechanical and tribological properties of Al Cu Fe quasicrystal and Al(Si)Cu Fe approximant thin films[J].Journal of Materials Research,2016,31(2):232-240.DOI:10.1557/jmr.2015.384.
[6]BRUNET P,ZHANG L M,SORDELET D J,et al.Comparative study of microstructural and tribological properties of sintered,bulk icosahedral samples[J].Materials Science and Engineering:A,2000,294:74-78.DOI:10.1016/S0921-5093(00)01202-8.
[7]INOUE A,ZHANG Tao,CHEN Minwei,et al.Mechanical properties of bulk amorphous Zr-Al-Cu-Ni-Ag alloys containing nanoscale quasicrystalline particles[J].Materials Transactions,1999,40(12):1382-1389.DOI:10.2320/matertrans1989.40.1382.
[8]WITTMANN R,URBAN K,SCHANDL M,et al.Mecanical properties of single quasicrystalline Al Cu Co Si[J].Journal of Materials Research,1991,6(6):1165-1168.DOI:10.1557/JMR.1991.1165.
[9]YOKOYAMA Y,INOUE A,MASUMOTO T.Mechanical-properties,fracture mode and deformation-behavior of Al70Pd20Mn10 single quasicrystal[J].Materials Transactions Jim,1993,34(2):135-145.DOI:10.2320/matertrans1989.34.135.
[10]BLAS F J G,ALGABA J M,ALVAREZ J,et al.Application of quasicrystalline materials as thermal barriers in aeronautics and future perspectives of use for these materials[C]//MRS 1998 Fall Meeting.[S.l.]:Cambridge Univ Press,1998:447.DOI:10.1557/PROC-553-447.
[11]DUBOIS J M,KANG S S,MASSIANI Y.Application of quasicrystalline alloys to surface coating of soft metals[J].Journal of Non-Crystalline Solids,1993,153:443-445.DOI:10.1016/0022-3093(93)90392-B.
[12]MIGLIERINI M,NASU S.Magnetic,electronic and structure-properties of icosahedral quasicrystals[J].Materials Transactions Jim,1993,34(2):178-187.DOI:10.2320/matertrans1989.34.178.
[13]STROUD R M,VIANO A M,GIBBONS P C,et al.Stable Ti based quasicrystal offers prospect for improved hydrogen storage[J].Applied physics letters,1996,69(20):2998-3000.DOI:10.1063/1.117756.
[14]LUBENSKY T C,RAMASWAMY S,TONER J.Dislocation motion in quasicrystals and implications for macroscopic properties[J].Physical Review B,1986,33(11):7715-7719.DOI:10.1103/PhysRev B.33.7715.
[15]LIU P,STIGENBERG A H,NILSSON J O.Quasicrystalline and crystalline precipitation during isothermal tempering in a12Cr9Ni4Mo maraging stainless steel[J].Acta Metallurgica Et Materialia,1995,43(7):2881-2890.DOI:10.1016/0956-7151(94)00461-P.
[16]LEE K,HSU J L,NAUGLE D,et al.Multi-phase quasicrystalline alloys for superior wear resistance[J].Materials&Design,2016,108:440-447.DOI:10.1016/j.matdes.2016.06.113.
[17]ENGEL M,DAMASCENO P F,PHILLIPS C L,et al.Computational self-assembly of a one-component icosahedral quasicrystal[J].Nature Materials,2015,14(1):109-116.DOI:10.1038/nmat4152.
[18]FENG Y C,LU G,WITHERS R L.An incommensurate structure with cubic point group symmetry in rapidly solidified V-Ni-Si alloy[J].Journal of Physics Condensed Matter,1989,1(23):3695-3700.
[19]BENDERSKY L.Quasicrystal with one-dimensional translational symmetry and a tenfold rotation axis[J].Physical Review Letters,1985,55(14):1461-1463.DOI:10.1103/PhysRev Lett.55.1461.
[20]WU J S,KUO K H.Decagonal quasicrystal and related crystalline phases in Mn-Ga alloys with 52 to 63 a/o Ga[J].Metallurgical and Materials Transactions A,1997,28(13):729-742.DOI:10.1007/s11661-997-1000-y.
[21]SCHAEFER R J,BENDERSKY L.Replacement of icosahedral Al Mn by decagonal phase[J].Scripta Metallurgica,1986,20(5):745-750.DOI:10.1016/0036-9748(86)90504-1.
[22]WASIO N A,QUARDOKUS R C,FORREST R P,et al.Self-assembly of hydrogen-bonded two-dimensional quasicrystals[J].Nature,2014,507(7490):86-89.DOI:10.1038/nature12993.
[23]WANG N,CHEN H,KUO K H.Two-dimensional quasicrystal with eightfold rotational symmetry[J].Physical Review Letters,1987,59(9):1010-1013.DOI:10.1103/PhysRev Lett.59.1010.
[24]ISHIMASA T,NISSEN H U,FUKANO Y.New ordered state between crystalline and amorphous in Ni-Cr particles[J].Physical Review Letters,1985,55(55):511-513.DOI:10.1103/PhysRevLett.55.511.
[25]ZENG Xiangbing,UNGAR G,LIU Yongsong,et al.Supramolecular dendritic liquid quasicrystals[J].Nature,2004,428(6979):157-160.DOI:10.1038/nature02368.
[26]FISCHER S,EXNER A,ZIELSKE K,et al.Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry[J].Proceedings of the National Academy of Sciences,2011,108(5):1810-1814.DOI:10.1073/pnas.1008695108.
[27]DOTERA T,OSHIRO T,ZIHERL P.Mosaic two-lengthscale quasicrystals[J].Nature,2014,506(7487):208-211.DOI:10.1038/nature12938.
[28]周公度,郭可信.晶体和准晶体的衍射[M].北京:北京大学出版社,1999:251-252.ZHOU Gongdu,GUO Kexin.Diffraction of crystal and quasicrystal[M].Beijing:Peking University Press,1999:251-252.
[29]MERLIN R,BAJEMA K,CLARKE R,et al.Quasiperiodic gaas-alas heterostructures[J].Physical Review Letters,1985,55(17):1768-1770.DOI:10.1103/PhysRev Lett.55.1768.
[30]YADAV T P,MISHRA S S,SRIVASTAVA O N.Copper nanocubes on Al 65 Cu 20 Fe 15 quasicrystalline surface[J].Journal of Alloys and Compounds,2017,712:134-138.DOI:10.1016/j.jallcom.2017.04.058.
[31]BINDI L,STEINHARDT P J,YAO Nan,et al.Natural quasicrystals[J].science,2009,324(5932):1306-1309.DOI:10.1126/science.1170827.
[32]BINDI L,YAO N,LIN C,et al.Natural quasicrystal with decagonal symmetry[J].Scientific Reports,2015(5):9111.DOI:10.1038/srep09111.
[33]HOLLISTER L S,BINDI L,YAO N,et al.Impact-induced shock and the formation of natural quasicrystals in the early solar system.[J].Nature Communications,2014(5):4040.DOI:10.1038/ncomms5040.
[34]FRANK F C T,KASPER J S.Complex alloy structures regarded as sphere packings.II.Analysis and classification of representative structures[J].Acta Crystallographica,1959,12(7):483-499.DOI:10.1107/S0365110X59001499.
[35]FRANK F C,KASPER J S.Complex alloy structures regarded as sphere packings.I.Definitions and basic principles[J].Acta Crystallographica,1958,11(3):184-190.DOI:10.1107/S0365110X58000487.
[36]LEVINE D,STEINHARDT P J.Quasicrystals:a new class of ordered structures[J].Physical Review Letters,1984,53(26):2477-2480.DOI:10.1103/PhysRev Lett.53.2477.
[37]LEVINE D,STEINHARDT P J.Quasicrystals.I.Definition and structure[J].Physical Review B,1986,34(2):596-616.DOI:10.1103/PhysRev B.34.596.
[38]SOCOLAR J E S,STEINHARDT P J.Quasicrystals.II.Unit-cell configurations[J].Physical Review B,1986,34(2):617-647.DOI:10.1103/PhysRev B.34.617.
[39]PENROSE R.Pentaplexity a class of non-periodic tilings of the plane[J].Mathematical Intelligencer,1979,2(1):32-37.DOI:10.1007/BF03024384.
[40]STEPHENS P W,GOLDMAN A I.The structure of quasicrystals[J].Scientific American,1991,150-151(3/4):44-47.DOI:10.1038/scientificamerican0491-44.
[41]WIDOM M,STRANDBURG K J,SWENDSEN R H.Quasicrystal equilibrium state[J].Physical Review Letters,1987,58(7):706-709.DOI:10.1103/PhysRev Lett.58.706.
[42]BRUIJN N G.Algebraic theory of Penrose's non-periodic tilings of the plane.II[C]//Indagationes Mathematicae(Proceedings).North-Holland:Elsevier,1981:53-66.DOI:10.1016/1385-7258(81)90017-2.
[43]SOCOLAR J E S,STEINHARDT P J,LEVINE D.Quasicrystals with arbitrary orientational symmetry[J].Physical Review B,1985,32(8):5547-5550.DOI:10.1103/PhysRev B.32.5547.
[44]ELSER V.Indexing problems in quasicrystal diffraction[J].Physical Review B,1985,32(8):4892-4898.DOI:10.1103/PhysRev B.32.4892.
[45]WANG Z M,KUO K H.The octagonal quasilattice and electron diffraction patterns of the octagonal phase[J].Acta Crystallographica Section A:Foundations of Crystallography,1988,44(6):857-863.DOI:10.1107/S0108767388004921.
[46]ISHIHARA K N,YAMAMOTO A.Penrose patterns and related structures.I.Superstructure and generalized Penrose patterns[J].Acta Crystallographica Section A:Foundations of Crystallography,1988,44(4):508-516.DOI:10.1107/S0108767388002958.
[47]YAMAMOTO A,ISHIHARA K N.Penrose patterns and related structures.II.Decagonal quasicrystals[J].Acta Crystallographica Section A:Foundations of Crystallography,1988,44(5):707-714.DOI:10.1107/S010876738800296X.
[48]YANG Q B,WEI W D.Description of the dodecagonal quasicrystal by a projection method[J].Physical Review Letters,1987,58(10):1020-1023.DOI:10.1103/PhysRev Lett.58.1020.
[49]MIKULLA R,ROTH J,TREBIN H R.Simulation of shear-stress in2-dimensional decagonal quasicrystals[J].Philosophical Magazine B-Physics of Condensed Matter Statistical Mechanics Electronic Optical and Magnetic Properties,1995,71(5):981-989.DOI:10.1080/01418639508243601.
[50]MIKULLA R,GUMBSCH P,TREBIN H R.Dislocations in quasicrystals and their interaction with cluster-like obstacles[J].Philosophical Magazine Letters,1998,78(5):369-376.DOI:10.1080/095008398177760.
[51]MIKULLA R,STADLER J,KRUL F,et al.Crack propagation in quasicrystals[J].Physical Review Letters,1998,81(15):3163-3166.DOI:10.1103/PhysRev Lett.81.3163.
[52]ELSER V,HENLEY C L.Crystal and quasicrystal structures in AlMn-Si alloys[J].Physical review letters,1985,55(26):2883-2886.DOI:10.1103/PhysRev Lett.55.2883.
[53]TAKAKURA H,GMEZ C P,YAMAMOTO A,et al.Atomic structure of the binary icosahedral Yb-Cd quasicrystal[J].Nature Material,2007,6(6):58-63.DOI:10.1038/nmat1799.
[54]TSAI A P,GUO J Q,ABE E,et al.Alloys:A stable binary quasicrystal[J].Nature,2000,408(6812):537-538.DOI:10.1038/35046202.
[55]BAUER B,MEISTERERNST G,HAERTWIG J,et al.Czochralski growth and X-ray topographic characterization of decagonal Al Co Ni quasicrystals[J].Philosophical Magazine,2006,86(3/4/5):317-322.DOI:10.1080/14786430500253927.
[56]GILLE P,BAUER B,HAHNE M,et al.Single crystal growth of Al-based intermetallic phases being approximants to quasicrystals[J].Journal of Crystal Growth,2011,318(1):1016-1020.DOI:10.1016/j.jcrysgro.2010.10.021.
[57]CUI C,TSAI A P.Growth of large single-grain quasicrystals in the Ag-In-Yb system by Bridgman method[J].Journal of Crystal Growth,2009,312(1):131-135.DOI:10.1016/j.jcrysgro.2009.09.038.
[58]CUI C,TSAI A P.Growth of large-grain Ag-In-Yb icosahedral quasicrystals and approximant crystals[J].Journal of Alloys&Compounds,2012,536(5):91-93.DOI:10.1016/j.jallcom.2012.05.031.
[59]CUI C,TSAI A P.Synthesis of large single-grain 1/1 approximant crystals in the Ag-In-Eu system by the self-flux method[J].Philosophical Magazine,2011,91(19/20/21):2443-2449.DOI:10.1080/14786435.2010.511600.
[60]SATO T J,HIRANO T,TSAI A P.Single-crystal growth of the decagonal Al-Ni-Co quasicrystal[J].Journal of Crystal Growth,1998,191(3):545-552.DOI:10.1016/S0022-0248(98)00164-X.
[61]TSAI A P.Discovery of stable icosahedral quasicrystals:progress in understanding structure and properties[J].Chemical Society Reviews,2013,44(34):5352-5365.DOI:10.1039/C3CS35388E.
[62]SOCOLAR J E S,LUBENSKY T C,STEINHARDT P J.Phonons,phasons,and dislocations in quasicrystals[J].Physical Review B,1986,34(5):3345-3360.DOI:10.1103/PhysRev B.34.3345.
[63]WOLLGARTEN M,BEYSS M,URBAN K,et al.Direct evidence for plastic-deformation of quasicrystals by means of a dislocation mechanism[J].Physical Review Letters,1993,71(4):549-552.DOI:10.1103/PhysRev Lett.71.549.
[64]MOMPIOU F,BRESSON L,CORDIER P,et al.Dislocation climb and low-temperature plasticity of an Al-Pd-Mn quasicrystal[J].Philosophical Magazine,2003,83(27):3133-3157.DOI:10.1080/1478643031000155110.
[65]MESSERSCHMIDT U,BARTSCH M,FEUERBACHER M,et al.Friction mechanism of dislocation motion in icosahedral Al-Pd-Mn quasicrystals[J].Philosophical Magazine A,1999,79(9):2123-2135.DOI:10.1080/01418619908210412.
[66]TEXIER M,PROULT A,BONNEVILLE J,et al.Microstructure of I-Al-Pd-Mn deformed at low and intermediate temperatures[J].Materials Science and Engineering:A,2004,387:1023-1027.DOI:10.1016/j.msea.2004.01.120.
[67]ZOU Y,KUCZERA P,SOLOGUBENKO A,et al.Superior roomtemperature ductility of typically brittle quasicrystals at small sizes[J].Nature Communications,2016(7):12261.DOI:10.1038/ncomms12261.
[68]ZOU Y,KUCZERA P,STEURER W,et al.Disappearance of plastic anisotropy in decagonal quasicrystals at small scales and room temperature[J].Extreme Mechanics Letters,2016(8):229-234.DOI:10.1016/j.eml.2016.02.005.
[69]SCHALL P,FEUERBACHER M,URBAN K.Plastic deformation of decagonal Al73Ni10Co17 single quasicrystals[J].Philosophical Magazine,2004,84(7):705-718.DOI:10.1080/14786430310001624857.
[70]FEUERBACHER A,SCHALL P.Plastic behaviour of decagonal Al-Ni-Co single quasicrystals[J].Scripta Materialia,2003,49(1):25-31.DOI:10.1016/S0921-5093(00)01653-1.
[71]LAPLANCHE G,BONNEVILLE J,JOULAIN A,et al.Mechanical properties of Al-Cu-Fe quasicrystalline and crystalline phases:An analogy[J].Intermetallics,2014,50:54-58.DOI:10.1016/j.intermet.2014.02.004.
[72]PARK J Y,OGLETREE D F,SALMERON M,et al.High frictional anisotropy of periodic and aperiodic directions on a quasicrystal surface[J].Science,2005,309(5739):1354-1356.DOI:10.1126/science.1113239.
[73]FILIPPOV A E,VANOSSI A,URBAKH M.Origin of friction anisotropy on a quasicrystal surface[J].Physical review letters,2010,104(7):074302.DOI:10.1103/PhysRev Lett.104.074302.
[74]YE Z J.,MARTINI A,THIEL P,et al.Atomistic simulation of frictional anisotropy on quasicrystal approximant surfaces[J].Physical Review B,2016,91(33):4218-4229.DOI:10.1103/PhysRev B.93.235438.
[75]DUBOIS J M.Properties-and applications of quasicrystals and complex metallic alloys[J].Chemical Society Reviews,2012,41(20):6760-6777.DOI:10.1039/C2CS35110B.
[76]STEIJN R P.Friction and wear of single crystals[J].Wear,1964,7(1):48-66.DOI:10.1016/0043-1648(64)90078-X.
[77]DYER L D.Rolling friction on single crystals of copper in the plastic range[J].Acta Metallurgica,1961,9(10):928-936.DOI:10.1016/0001-6160(61)90111-0.
[78]BAILEY J M,GWATHMEY A T.Friction and surface deformation during sliding on a single crystal of copper[J].Tribology Transactions,1962,5(1):45-56.DOI:10.1080/05698196208972452.
[79]STEIJN R P.On the wear of sapphire[J].Journal of Applied Physics,1961,32(10):1951-1958.DOI:10.1063/1.1728269.
[80]BUCKLEY D H,JOHNSON R L.Friction and wear of hexagonal metals and alloys as related to crystal structure and lattice parameters in vacuum[J].Tribology Transactions,1966,9(2):121-135.DOI:10.1080/05698196608972128.
[81]BUCKLEY D H,JOHNSON R L.Influence of crystal structure on friction characteristics of rare-earth and related metals in vacuum to10-10 mm of mercury[J].Tribology Transactions,1965,8(2):123-132.DOI:10.1080/05698196508972086.
[82]UCKLEY D H.The influence of the atomic nature of crystalline materials on friction[J].Tribology Transactions,1968,11(2):89-100.DOI:10.1080/05698196808972212.
[83]GRNING O,R.WIDMER,P.RUFFIEUX,et al.Scanning tunnelling microscopy with atomic resolution on the twofold surface of the icosahedral Al Pd Mn quasicrystal[J].Philosophical Magazine,2006,86(6/7/8):773-779.DOI:10.1080/14786430500306535.
[84]SHARMA H R,FOURNE V,SHIMODA M,et al.Structure of the fivefold surface of the icosahedral Al-Cu-Fe quasicrystal:experimental evidence of bulk truncations at larger interlayer spacings[J].Physical Review Letters,2004,93(16):165502.DOI:10.1103/PhysRev Lett.93.165502.
[85]CAI T,SHI F,SHEN Z,et al.Structural aspects of the fivefold quasicrystalline Al-Cu-Fe surface from STM and dynamical LEED studies[J].Surface Science,2001,495(1/2):19-34.DOI:10.1016/S0039-6028(01)01500-X.
[86]ROUXEL D,CAI T H,JENKS C J,et al.Structural aspects of the threefold surface of icosahedral Al-Pd-Mn[J].Surface Science,2000,461(1):L521-L527.DOI:10.1016/S0039-6028(00)00513-6.
[87]SHEN Z,JENKS C J,ANDEREGG J,et al.Structure and stability of the twofold surface of icosahedral Al-Pd-Mn by low-energy electron diffraction and X-ray photoemission spectroscopy[J].Physical Review Letters,1997,78(6):1050-1053.DOI:10.1103/PhysRev Lett.78.1050.
[88]TAMURA R,YADAV T P,MCLEOD I M,et al.Scanning tunneling microscopy of a polygrain Al-Pd-Re quasicrystal:study of the relative surface stability.[J].Journal of Physics Condensed Matter,2013,25(39):395007.DOI:10.1088/0953-8984/25/39/395007.
[89]NUGENT P J,SMERDON J A,MCGRATH R,et al.Step-terrace morphology and reactivity to C60 of the five-fold icosahedral Ag-In-Yb quasicrystal[J].Philosophical Magazine,2011,91(19/20/21):2862-2869.DOI:10.1080/14786435.2010.514870.
[90]CUI C,NUGENT P J,SHIMODA M,et al.The atomic structure of the threefold surface of the icosahedral Ag-In-Yb quasicrystal[J].Journal of Physics Condensed Matter,2012,24(44):445011.DOI:10.1088/0953-8984/24/44/445011.
[91]CUI C,NUGENT P J,SHIMODA M,et al.Structure of the twofold surface of the icosahedral Ag-In-Yb quasicrystal[J].Journal of Physics:Condensed Matter,2013,26(1):015001.DOI:10.1088/0953-8984/26/1/015001.
[92]PARK J Y,OGLETREE D F,SALMERON M,et al.Atomic scale coexistence of periodic and quasiperiodic order in a 2-fold Al-NiCo decagonal quasicrystal surface[J].Physical Review B,2005,72(22):220201(1/2/3/4).DOI:10.1103/PhysRev B.72.220201.
[93]TAKAKURA H,YAMAMOTO A,TSAI A P.The structure of a decagonal Al72Ni20Co8 quasicrystal[J].Acta Crystallographica,2001,57(57):576-585.DOI:10.1107/S0108767301007942.
[94]LEDIEU J,HOEFT J T,REID D E,et al.Copper adsorption on the fivefold Al70Pd21Mn9,quasicrystal surface[J].Physical Review B,2005,72(3):035420.DOI:10.1103/PhysRev B.72.035420.
[95]LEDIEU J.Ordering of Si atoms on the fivefold Al-Pd-Mn quasicrystal surface[J].Physical Review B,2006.73(1):012204.DOI:10.1103/PhysRev B.73.012204.
[96]KRAJˇCC M,HAFNER J.Structure,stability,and electronic properties of the,i-Al Pd Mn quasicrystalline surface[J].Physical Review B,2005,71(71):054202.DOI:10.1103/PhysRev B.71.054202.
[97]LEDIEU J,LEUNG L,WEARING L H,et al.Self-assembly,structure and electronic properties of a quasiperiodic lead monolayer[J].Physical Review B,2008,77(7):439-446.DOI:10.1103/PhysRev B.77.073409.
[98]MARTIN S,HEBARD A F,KORTAN A R,et al.Transport properties of Al65Cu15Co20,and Al70Ni15Co15,decagonal quasicrystals[J].Physical Review Letters,1991,67(6):719-722.DOI:10.1103/PhysRev Lett.67.719.
[99]SMONTARA A,IVKOV J.Anisotropic magnetic,electrical,and thermal transport properties of the Y-Al-Ni-Co decagonal approximant[J].Physical Review B Condensed Matter,2008,78(10):104204.DOI:10.1103/PhysRev B.78.104204.
[100]BOBNAR M,JEGLIˇC P,KLANJEK M,et al.Intrinsic anisotropic magnetic,electrical,and thermal transport properties of d-Al-Co-Ni decagonal quasicrystals[J].Physical Review B Condensed Matter,2012,85(2):024205.DOI:10.1103/PhysRev B.85.024205.
[101]DOLINEK J.Extrinsic origin of the insulating behavior of polygrain icosahedral Al-Pd-Re quasicrystals[J].Physical Review B,2006,74(13):134201.DOI:10.1103/PhysRev B.74.134201.
[102]BOBNAR M,VRTNIK S,JAGLIˇCIˇC Z,et al.Electrical,magnetic,and thermal properties of the single-grain Ag42In42Yb16 icosahedral quasicrystal:Experiment and modeling[J].Physical Review B Condensed Matter,2011,84(13):4578-4586.DOI:10.1103/PhysRev B.84.134205.
[103]范天佑.固体与软物质准晶数学弹性与相关理论及应用[M].北京:北京理工大学出版社,2014:51-271.FAN Tianyou.Mathematical theory of elasticity and relevant topics of solid and solft-matter quasicrystals and its applications[M].Beijing:Beijing Institute of Technology Press,2014:51-271.
[104]BUNZ D,ZEGER G,ROTH J,et al.Molecular dynamic studies of atomic jumps in d-Al-Cu-Co[J].Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing,2000,294:675-679.DOI:10.1016/S0921-5093(00)01187-4.
[105]TREBIN H R,MIKULLA R,STADLER J,et al.Molecular dynamics simulations of crack propagation in quasicrystals[J].Computer Physics Communications,1999,121:536-539.DOI:10.1016/S0010-4655(99)00400-2.
[106]SCHAAF G D,ROTH J,TREBIN H R.Numerical simulation of dislocation motion in three-dimensional icosahedral quasicrystals[J].Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties,2000,80(7):1657-1668.DOI:10.1080/01418610008212142.
[107]RUDHART C,RSCH F,GHLER F,et al.Crack propagation in icosahedral model quasicrystals[J].High Performance Computing in Science&Engineering,2003:107-116.DOI:10.1007/978-3-642-55876-4_8.
[108]SCHAAF G D,ROTH J,TREBIN H R.Dislocation motion in icosahedral quasicrystals at elevated temperatures:numerical simulation[J].Philosophical Magazine,2003,83(21):2449-2465.DOI:10.1080/0141861031000113352.
[109]RUDHART C,TREBIN H R,GUMBSCH P.Crack propagation in perfectly ordered and random tiling quasicrystals[J].Journal of NonCrystalline Solids,2004,334:453-456.DOI:10.1016/j.jnoncrysol.2003.12.039.
[110]ROSCH F,RUDHART C,ROTH J,et al.Dynamic fracture of icosahedral model quasicrystals:A molecular dynamics study[J].Physical Review B,2005,72(1):014128.DOI:10.1103/PhysRev B.72.014128.
[111]SASAJIMA Y,TANAKA H,ITABA M,et al.Computer experiments of fracture of 2-dimensional henley-elser type quasi-crystals[J].Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing,1994,176(1/2):283-288.DOI:10.1016/0921-5093(94)90987-3.
[112]TREBIN H R,MIKULLA R,ROTH J.Motion of dislocations in two-dimensional decagonal quasicrystals[J].Journal of non-crystalline solids,1993,153:272-275.DOI:10.1016/0022-3093(93)90356-3.
[113]ENGEL M,UMEZAKI M,TREBIN H R,et al.Dynamics of particle flips in two-dimensional quasicrystals[J].Physical Review B Condensed Matter,2010,82(13):087201.DOI:10.1103/PhysRev B.82.134206.
[114]YANG L Z,HE F M,GAO Y.Finite element method for static problems of cubic quasicrystals[J].Acta Physica Polonica,2014,126(2):471-473.DOI:10.12693/APhys Pol A.126.471.
[115]杨连枝,何蕃民,高阳,等.二十面体Al-Pd-Mn准晶板的断裂行为研究[C]//北京力学会第20届学术年会论文集.北京:中国学术期刊电子出版社,2014:.YANG Lianzhi,HE Fanmin,GAO Yang,et al.Study of frature behavior of icosahedral Al-Pd-Mn quasicrystal slab[C]//The Proceedings of the 20th Annual Conference of Beijing Society of Theoretical and Applied Mechanics.Beijing:China Academic Journal Electronic Publishing House,2014.
[116]吴祥法,范天佑,安冬梅.用路径守恒积分计算平面准晶裂纹扩展的能量释放率[J].计算力学学报,2000,17(1):34-42.DOI:10.3969/j.issn.1007-4708.2000.01.006.WU Xiangfa,FAN Tianyou,AN Dongmei.Energy release rate of plane quasicrystals with crack determined by path-independent Eintegral[J].Chinese Journal of Computational Mechanics,2000,17(1):34-42.DOI:10.3969/j.issn.1007-4708.2000.01.006.
[117]AMADA T,TAKAKURA H,EUCHNER H,et al.Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal[J].Iucrj,2016(3):247-258.DOI:10.1107/S2052252516007041.
[118]YAMADA T,TAKAKURA H,KONG T,et al.Atomic structure of the i-R-Cd quasicrystals and consequences for magnetism[J].Physical Review B,2016,94(6):060103.DOI:10.1103/PhysRev B.94.060103.
[119]KENZARI S,BONINA D,DUBOIS J M,et al.Quasicrystal-polymer composites for selective laser sintering technology[J].Materials&Design,2012,35:691-695.DOI:10.1016/j.matdes.2011.10.032.