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Nanomechanics: Fundamentals and Application in NEMS Technology

  • Marcel Lucas
  • Tai De Li
  • Elisa Riedo
Part of the Nanostructure Science and Technology book series (NST)

Abstract

A nano-electromechanical system (NEMS) combines nanometer-sized actuators, sensors and electronic devices into a complex circuit. An intense effort has been made to develop versatile NEMS for the miniaturization of the existing devices and to design the new ones, with a wide range of applications in the field of electronics, chemistry and biology. All applications require a good understanding of the mechanical properties at the nanoscale and their influence on the other physical/chemical properties. In this chapter, the size dependence of the mechanical properties of nanostructures is discussed in detail and the influence of surface effects, defects and phase transitions is reviewed. The most commonly used techniques for studying the mechanical properties at the nanoscale are described and the potential applications of NEMS in biological/chemical sensing, data storage, telecommunications and electrical power generation are also presented.

Keywords

Atomic Force Microscopy Carbon Nanotubes Silver Nanowires Atomic Force Microscopy Cantilever Data Storage System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors acknowledge the financial support from the DoE (grant no. DE-FG02-06ER46293) and NSF (grant no. DMR-0120967 and no. DMR-0405319).

References

  1. 1.
    Kuchibhatla SVNT, Karakoti AS, Bera D, Seal S (2007) One dimensional nanostructured materials. Prog Mater Sci 52:699–913Google Scholar
  2. 2.
    Craighead HG (2000) Nanoelectromechanical systems. Science 290:1532–1535Google Scholar
  3. 3.
    Schwab KC, Roukes ML (2005) Putting mechanics into quantum mechanics. Phys Today 58:36–42Google Scholar
  4. 4.
    Tombler TW, Zhou C, Alexseyev L, Kong J, Dai H, Liu L, Jayanthi CS, Tang M, Wu S (2000) Reversible electromechanical characteristics of carbon nanotubes under local-probe manipulation. Nature 405:769–772Google Scholar
  5. 5.
    Cao J, Wang Q, Dai H (2003) Electromechanical properties of metallic, quasimetallic, and semiconducting carbon nanotubes under stretching. Phys Rev Lett 90:157601 1–4Google Scholar
  6. 6.
    Yamamoto T, Watanabe K (2006) Nonequilibrium Green’s function approach to phonon transport in defective carbon nanotubes. Phys Rev Lett 96:255503 1–4Google Scholar
  7. 7.
    Delimitis A, Komninou P, Dimitrakopulos GP, Kehagias T, Kioseoglou J, Karakostas T, Nouet G (2007) Strain distribution of thin InN epilayers grown on (0001) GaN templates by molecular beam epitaxy. Appl Phys Lett 90:061920 1–3Google Scholar
  8. 8.
    Roder C, Einfeldt S, Figge S, Paskova T, Hommel D, Paskov PP, Monemar B, Behn U, Haskell BA, Fini PT, Nakamura S (2006) Stress and wafer bending of a-plane GaN layers on r-plane sapphire substrates. J Appl Phys 100:103511 1–11Google Scholar
  9. 9.
    Seravalli L, Minelli M, Frigeri P, Franchi S, Guizzetti G, Patrini M, Ciabattoni T, Geddo M (2007) Quantum dot strain engineering of InAs/InGaAs nanostructures. J Appl Phys 101:024313 1–8Google Scholar
  10. 10.
    Lucas M, Young RJ (2004) Effect of uniaxial strain deformation upon the Raman radial breathing modes of single-wall carbon nanotubes in composites. Phys Rev B 69:085405 1–9Google Scholar
  11. 11.
    Sandler J, Shaffer MSP, Windle AH, Halsall MP, Montes-Morn MA, Cooper CA, Young RJ (2003) Variations in the Raman peak shift as a function of hydrostatic pressure for various carbon nanostructures: a simple geometric effect. Phys Rev B 67:035417 1–8Google Scholar
  12. 12.
    Bettinger HF (2005) The reactivity of defects at the sidewalls of single-walled carbon nanotubes: the Stone-Wales defect. J Phys Chem B 109:6922–6924Google Scholar
  13. 13.
    Robinson JA, Snow ES, Badescu, Reinecke TL, Perkins FK (2006) Role of defects in single-walled carbon nanotube chemical sensors. Nano Lett 6:1747–1751Google Scholar
  14. 14.
    Li TD, Gao J, Szoszkiewicz R, Landman U, Riedo E (2007) Structured and viscous water in subnanometer gaps. Phys Rev B 75:115415 1–6Google Scholar
  15. 15.
    Butt HJ, Cappella B, Kappl M (2005) Force measurements with the atomic force microscope: Technique, interpretation and applications. Surf Sci Rep 59:1–152Google Scholar
  16. 16.
    Poncharal P, Wang ZL, Ugarte D, de Heer WA (1999) Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science 283:1513–1516Google Scholar
  17. 17.
    Liu KH, Wang WL, Xu Z, Liao L, Bai XD, Wang EG (2006) In situ probing mechanical properties of individual tungsten oxide nanowires directly grown on tungsten tips inside transmission electron microscope. Appl. Phys Lett 89:221908 1–3Google Scholar
  18. 18.
    Nam CY, Jaroenapibal P, Tham D, Luzzi DE, Evoy S, Fischer JE (2006) Diameter-dependent electromechanical properties of GaN nanowires. Nano Lett 6:153–158Google Scholar
  19. 19.
    Miyake K, Satomi N, Sasaki S (2006) Elastic modulus of polystyrene film from near surface to bulk measured by nanoindentation using atomic force microscopy. Appl Phys Lett 89:031925 1–3Google Scholar
  20. 20.
    Shin MK, Kim SI, Kim SJ, Kim SK, Lee H, Spinks GM (2006) Size-dependent elastic modulus of single electroactive polymer nanofibers. Appl Phys Lett 89:231929 1–3Google Scholar
  21. 21.
    Vigolo B, Poulin P, Lucas M, Launois P, Bernier P (2002) Improved structure and properties of single-wall carbon nanotube spun fibers. Appl Phys Lett 81:1210–1212Google Scholar
  22. 22.
    Wu B, Heidelberg A, Boland JJ (2005) Mechanical properties of ultrahigh-strength gold nanowires. Nat Mater 4:525–529Google Scholar
  23. 23.
    Haque MA, Saif MTA (2004) Deformation mechanisms in free-standing nanoscale thin films: a quantitative in situ transmission electron microscope study. Proc Natl Acad Sci USA 101:6335–6340Google Scholar
  24. 24.
    Villain P, Goudeau P, Renautl PO, Badawi KF (2002) Size effect on intragranular elastic constants in thin tungsten films. Appl Phys Lett 81:4365–4367Google Scholar
  25. 25.
    Palaci I, Fedrigo S, Brune H, Klinke C, Chen M, Riedo E (2005) Radial elasticity of multiwalled carbon nanotubes. Phys Rev Lett 94:175502 1–4Google Scholar
  26. 26.
    Yao N, Lordi V (1998) Young’s modulus of single-walled carbon nanotubes. J Appl Phys 84:1939–1943Google Scholar
  27. 27.
    Huang JY, Chen S, Wang ZQ, Kempa K, Wang YM, Jo SH, Chen G, Dresselhaus MS, Ren ZF (2006) Superplastic carbon nanotubes. Nature 439:281Google Scholar
  28. 28.
    Yakobson BI, Brabec CJ, Bernholc J (1996) Nanomechanics of carbon tubes: instabilities beyond linear regime. Phys Rev Lett 76:2511–2514Google Scholar
  29. 29.
    Champion Y, Langlois C, Guérin-Mailly S, Langlois P, Bonnentien JL, Hÿtch MJ (2003) Near-perfect elastoplasticity in pure nanocrystalline copper. Science 300:310–311Google Scholar
  30. 30.
    Lu L, Sui ML, Lu K (2000) Superplastic extensibility of nanocrystalline copper at room temperature. Science 287:1463–1466Google Scholar
  31. 31.
    Kulkarni AJ, Zhou M, Sarasamak K, Limpijumnong S (2006) Novel phase transformation in ZnO nanowires under tensile loading. Phys Rev Lett 97:105502 1–4Google Scholar
  32. 32.
    Zhou LG, Huang H (2004) Are surfaces elastically softer or stiffer? Appl Phys Lett 84:1940–1942Google Scholar
  33. 33.
    Liang H, Upmanyu M, Huang H (2005) Size-dependent elasticity of nanowires: nonlinear effects. Phys Rev B 71:241403(R) 1–4Google Scholar
  34. 34.
    Kong XY, Wang ZL (2003) Spontaneous polarization-induced nanohelixes, nanosprings, and nanorings of piezoelectric nanobelts. Nano Lett 3:1625–1634Google Scholar
  35. 35.
    Sun CT, Zhang H (2003) Size-dependent elastic moduli of platelike nanomaterials. J Appl Phys 93:1212–1218Google Scholar
  36. 36.
    Miller RE, Shenoy VB (2000) Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11:139–147Google Scholar
  37. 37.
    Ji C, Park HS (2006) Geometric effects on the inelastic deformation of metal nanowires. Appl Phys Lett 89:181916 1–3Google Scholar
  38. 38.
    Park HS, Gall K, Zimmerman JA (2005) Shape memory and pseudoelasticity in metal nanowires. Phys Rev Lett 95:255504 1–4Google Scholar
  39. 39.
    Renautl PO, Le Bourhis E, Villain P, Goudeau P, Badawi KF, Faurie D (2003) Measurement of the elastic constants of textured anisotropic thin films from x-ray diffraction data. Appl Phys Lett 83:473–475Google Scholar
  40. 40.
    Cuenot S, Frétigny C, Demoustier-Champagne S, Nysten B (2004) Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys Rev B 69:165410 1–5Google Scholar
  41. 41.
    Chen CQ, Shi Y, Zhang YS, Zhu J, Yan YJ (2006) Size dependence of Young’s modulus in ZnO nanowires. Phys Rev Lett 96:075505 1–4Google Scholar
  42. 42.
    Jing GY, Duan HL, Sun XM, Zhang ZS, Xu J, Li YD, Wang JX, Yu DP (2006) Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy. Phys Rev B 73:235409 1–6Google Scholar
  43. 43.
    Lu L, Shen Y, Chen X, Qian L, Lu K (2004) Ultrahigh strength and high electrical conductivity in copper. Science 304:422–426Google Scholar
  44. 44.
    Arzt E (1998) Size effects in materials due to microstructural and dimensional constraints: a comparable review. Acta Mater 46:5611–5626Google Scholar
  45. 45.
    Uchic MD, Dimiduk DM, Florando JN, Nix WD (2004) Sample dimensions influence strength and crystal plasticity. Science 305:986–989Google Scholar
  46. 46.
    Kiely JD, Hwang RQ, Houston JE (1998) Effect of surface steps on the plastic threshold in nanoindentation. Phys Rev Lett 81:4424–4427Google Scholar
  47. 47.
    Enomoto K, Kitakata S, Yasuhara T, Ohtake N, Kuzumaki T, Mitsuda Y (2006) Measurement of Young’s modulus of carbon nanotubes by nanoprobe manipulation in a transmission electron microscope. Appl Phys Lett 88:153115 1–3Google Scholar
  48. 48.
    Mukhopadhyay AK, Chaudhuri MR, Seal A, Dalui SK, Banerjee M, Phani KK (2001) Mechanical characterization of microwave sintered zinc oxide. Bull Mater Sci 24:125–128Google Scholar
  49. 49.
    Cuenot S, Demoustier-Champagne S, Nysten B (2000) Elastic modulus of polypyrrole nanotubes. Phys Rev Lett 85:1690–1693Google Scholar
  50. 50.
    Lucas M, Mai W, Yang R, Wang ZL, Riedo E (2007) Aspect ratio dependence of the elastic properties of ZnO nanobelts. Nano Lett 7:1314–1317Google Scholar
  51. 51.
    Kucheyev, Bradby JE, Williams JS, Jagadish C, Swain MV (2001) Mechanical deformation of single-crystal ZnO. Appl Phys Lett 80:956–958Google Scholar
  52. 52.
    Bradby JE, Kucheyev SO, Williams JS, Jagadish C, Swain MV, Munroe P, Phillips MR (2002) Contact-induced defect propagation in ZnO. Appl Phys Lett 80:4537–4539Google Scholar
  53. 53.
    Corcoran SG, Colton RJ, Lilleodden ET, Gerberich WW (1997) Anomalous plastic deformation at surfaces: nanoindentation of gold single crystals. Phys Rev B 55:16057–16060Google Scholar
  54. 54.
    Richter A, Wolf B, Nowicki M, Smith R, Usov IO, Valdez JA, Sickafus K (2006) Multi-cycling nanoindentation in MgO single crystals before and after ion irradiation. J Phys D: Appl Phys 39:3342–3349Google Scholar
  55. 55.
    Kis A, Csányi G, Salvetat JP, Lee T, Couteau E, Kulik AJ, Benoit W, Brugger J, Forr (2004) Reinforcement of single-walled carbon nanotube bundles by intertube bridging. Nat Mater 3:153–157Google Scholar
  56. 56.
    Leach AM, McDowell M, Gall K (2007) Deformation of top-down and bottom-up silver nanowires. Adv Funct Mater 17:43–53Google Scholar
  57. 57.
    Wu B, Heidelberg A, Boland JJ, Sader JE, Sun X, Li Y (2006) Microstructure-hardened silver nanowires. Nano Lett 6:468–472Google Scholar
  58. 58.
    Fleck NA, Hutchinson JW (1993) A phenomenological theory for strain gradient effects in plasticity. J Mech Phys Solids 41:1825–1857Google Scholar
  59. 59.
    Nix WD, Gao H (1998) Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids 46:411–425Google Scholar
  60. 60.
    Kiely JD, Houston JE (1998) Nanomechanical properties of Au(111), (001), and (110) surfaces. Phys Rev B 57:12588–12594Google Scholar
  61. 61.
    Kulkarni AJ, Zhou M, Ke FJ (2005) Orientation and size dependence of the elastic properties of zinc oxide nanobelts. Nanotechnology 16:2749–2756Google Scholar
  62. 62.
    Trabelsi S, Albouy PA, Rault J (2002) Stress-induced crystallization around a crack tip in natural rubber. Macromolecules 35:10054–10061Google Scholar
  63. 63.
    Diao J, Gall K, Dunn M (2003) Surface-stress-induced phase transformation in metal nanowires. Nat Mater 2:656–660Google Scholar
  64. 64.
    Zhang L, Huang H (2006) Young’s moduli of ZnO nanoplates: ab initio determinations. Appl Phys Lett 89:183111 1–3Google Scholar
  65. 65.
    Wong EW, Sheehan PE, Lieber CM (1997) Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes. Science 277:1971–1975Google Scholar
  66. 66.
    Salvetat JP, Briggs GAD, Bonard JM, Bacsa RR, Kulik AJ, Stckli T, Burnham NA, ForrÓ L (1999) Elastic and shear moduli of single-walled carbon nanotube ropes. Phys Rev Lett 82:944–947Google Scholar
  67. 67.
    Shanmugham S, Jeong J, Alkhateeb A, Aston DE (2005) Polymer nanowire elastic moduli measured with digital pulsed force mode AFM. Langmuir 21:10214–10218Google Scholar
  68. 68.
    Chen Y, Dorgan BL Jr, McIlroy DN, Aston DE (2006) On the importance of boundary conditions on nanomechanical bending behavior and elastic modulus determination of silver nanowires. J Appl Phys 100:104301 1–7Google Scholar
  69. 69.
    San Paulo A, Bokor J, Howe RT, He R, Yang P, Gao D, Carraro C, Maboudian R (2005) Mechanical elasticity of single and double clamped silicon nanobeams fabricated by the vapor-liquid-solid method. Appl Phys Lett 87:053111 1–3Google Scholar
  70. 70.
    Mai W, Wang ZL (2006) Quantifying the elastic deformation behavior of bridged nanobelts. Appl Phys Lett 89:073112 1–3Google Scholar
  71. 71.
    Lulevich V, Zink T, Chen HY, Liu FT, Liu G (2006) Cell mechanics using atomic force microscopy-based single-cell compression. Langmuir 22:8151–8155Google Scholar
  72. 72.
    Li X, Chen W, Zhan Q, Dai L, Sowards L, Pender M, Naik RR (2006) Direct measurements of interactions between polypeptides and carbon nanotubes. J Phys Chem B 110:12621–12625Google Scholar
  73. 73.
    Song J, Wang X, Riedo E, Wang ZL (2005) Elastic property of vertically aligned nanowires. Nano Lett 5:1954–1958Google Scholar
  74. 74.
    Lucas M, Mai WJ, Yang RS, Wang ZL, Riedo E (2007) Size dependence of the mechanical properties of ZnO nanobelts. Philos Mag 87:2135–2141Google Scholar
  75. 75.
    Yamanaka K (1996) UFM observation of lattice defects in highly oriented pyrolytic graphite. Thin Solid Films 273:116–121Google Scholar
  76. 76.
    Rabe U, Arnold W (1994) Acoustic microscopy by atomic force microscopy. Appl Phys Lett 64:1493–1495Google Scholar
  77. 77.
    Zheng Y, Geer RE, Dovidenko K, Kopycinska-Müller M, Hurley DC (2006) Quantitative nanoscale modulus measurements and elastic imaging of SnO\(_2\) nanobelts. J Appl Phys 100:124308 1–6Google Scholar
  78. 78.
    Treacy MMJ, Ebbesen TW, Gibson JM (1996) Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature 381:678–680Google Scholar
  79. 79.
    Gaillard J, Skove M, Rao AM (2005) Mechanical properties of chemical vapor deposition-grown multiwalled carbon nanotubes. Appl Phys Lett 86:233109 1–3Google Scholar
  80. 80.
    Yu MF, Lourie O, Dyer MJ, Moloni K, Kelly TF, Ruoff RS (2000) Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science 287:637–640Google Scholar
  81. 81.
    Ding W, Calabri L, Chen X, Kohlhaas KM, Ruoff RS (2006) Mechanics of crystalline boron nanowires. Comp Sci Tech 66:1112–1124Google Scholar
  82. 82.
    Ashkin A, Dziedzic JM, Bjorkholm JE, Chu S (1986) Observation of a single-beam gradient force optical trap for dielectric particles. Opt Lett 11:288–290Google Scholar
  83. 83.
    Bustamante C, Bryant Z, Smith S (2003) Ten years of tension: single-molecule DNA mechanics. Nature 421:423–427Google Scholar
  84. 84.
    Li Y, Lim HS, Ng SC, Wang ZK, Kuok MH, Vekris E, Kitaev V, Peiris FC, Ogin GA (2006) Micro-Brillouin scattering from a single isolated nanosphere. Appl Phys Lett 88:023112 1–3Google Scholar
  85. 85.
    Wu G, Datar RH, Hansen KM, Thundat T, Cote RJ, Majumdar A (2001) Bioassay of prostate-specific antigen (PSA) using microcantilevers. Nat Biotech 19:856–860Google Scholar
  86. 86.
    Li M, Tang HX, Roukes ML (2007) Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications. Nat Nanotech 2:114–120Google Scholar
  87. 87.
    Mortet V, Petersen R, Haenen K, D’Olieslaeger M (2006) Wide range pressure sensor based on a piezoelectric bimorph microcantilever. Appl Phys Lett 88:133511 1–3Google Scholar
  88. 88.
    Lang HP, Hegner M, Meyer E, Gerber C (2002) Nanomechanics from atomic resolution to molecular recognition based on atomic force microscopy technology. Nanotechnology 13:R29–R36Google Scholar
  89. 89.
    Despont M, Brugger J, Drechsler U, Dürig U, Häberle W, Lutwyche M, Rothuizen H, Stutz R, Widmer R, Rohrer H, Binnig G, Vettiger P (1999) VLSI-NEMS chip for AFM data storage. Technical Digest, 12th IEEE International Micro Electro Mechanical Systems Conference (MEMS’99), Orlando, FL, January 1999, pp. 564–569Google Scholar
  90. 90.
    Vettiger P, Despont M, Dreschler U, Durig U, Haberle W, Lutwyche MI, Rothuizen HE, Stutz R, Widmer R, Binnig GK (2000) The Millipede – More than one thousand tips for future AFM data storage. IBM J Res Dev 44:323–340Google Scholar
  91. 91.
    Nam HJ, Kim YS, Lee CS, Jin WH, Jang SS, Choa IJ, Bua JU, Choi WB, Choi SW (2007) Silicon nitride cantilever array integrated with silicon heaters and piezoelectric detectors for probe-based data storage. Sens Actuators A 134:329–333Google Scholar
  92. 92.
    Turyan I, Krasovec UO, Orel B, Saraidorov T, Reisfeld R, Mandler D (2000) “Writing-reading-erasing” on tungsten oxide films using the scanning electrochemical microscope. Adv Mater 12:330–333Google Scholar
  93. 93.
    Cho Y, Fujimoto K, Hiranaga Y, Wagatsuma Y, Onoe A, Terabe K, Kitamura K (2002) Tbit/inch2 ferroelectric data storage based on scanning nonlinear dielectric microscopy. Appl Phys Lett 81:4401–4403Google Scholar
  94. 94.
    Dragoman M, Takacs A, Muller AA, Hartnagel H, Plana R, Grenier K, Dubuc D (2007) Nanoelectromechanical switches based on carbon nanotubes for microwave and millimeter waves. Appl Phys Lett 90:113102 1–3Google Scholar
  95. 95.
    Culpepper ML, DiBiasio CM, Panas RM, Magleby S, Howell LL (2006) Simulation of a carbon nanotube-based compliant parallel-guiding mechanism: A nanomechanical building block. Appl Phys Lett 89:203111 1–3Google Scholar
  96. 96.
    Suh W, Yanik MF, Solgaard O, Fan S (2003) Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs. Appl Phys Lett 82:1999–2001Google Scholar
  97. 97.
    Kim P, Lieber CM (1999) Nanotube nanotweezers. Science 286:2148–2150Google Scholar
  98. 98.
    Jager EWH, Smela E, Ingans O (2000) Microfabricating conjugated polymer actuators. Science 290:1540–1545Google Scholar
  99. 99.
    Pelah A, Seemann R, Jovin TM (2007) Reversible cell deformation by a polymeric actuator. J Am Chem Soc 129:468–469Google Scholar
  100. 100.
    Mylvaganam K, Zhang LC (2006) Deformation-promoted reactivity of single-walled carbon nanotubes. Nanotechnology 17:410–414Google Scholar
  101. 101.
    Wang B, Král P, Thanopulos I (2006) Docking of chiral molecules on twisted and helical nanotubes: nanomechanical control of catalysis. Nano Lett 6:1918–1921Google Scholar
  102. 102.
    Meyer JC, Paillet M, Roth S (2005) Single-molecule torsional pendulum. Science 309:1539–1541Google Scholar
  103. 103.
    Sasaki K, Osaki Y, Okazaki J, Hosaka H, Itao K (2005) Vibration-based automatic power-generation system. Microsyst Technol 11:965–969Google Scholar
  104. 104.
    Wang X, Song J, Liu J, Wang ZL (2007) Direct-current nanogenerator driven by ultrasonic waves. Science 316:102–105Google Scholar
  105. 105.
    Van der Heyden FHJ, Bonthuis DJ, Stein D, Meyer C, Dekker C (2007) Power generation by pressure-driven transport of ions in nanofluidic channels. Nano Lett 7:1022–1025Google Scholar
  106. 106.
    Smalley RE, Li Y, Moore VC, Price BK, Colorado R, Schmidt HK, Hauge RH, Barron AR, Tour JM (2006) Single wall carbon nanotube amplification: en route to a type-specific growth mechanism. J Am Chem Soc 128:15824–15829Google Scholar
  107. 107.
    Szoszkiewicz R, Okada T, Jones SC, Li TD, King WP, Marder SR, Riedo E (2007) High-speed, sub-15 nm feature size thermochemical nanolithography. Nano Lett 7:1064–1069Google Scholar
  108. 108.
    Pfeifer MA, Williams GJ, Vartanyants IA, Harder R, Robinson IK (2006) Three-dimensional mapping of a deformation field inside a nanocrystal. Nature 442:63–66Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Marcel Lucas
  • Tai De Li
  • Elisa Riedo
    • 1
  1. 1.School of PhysicsGeorgia Institute of TechnologyUSA

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