Size-Dependent Materials Properties Toward a Universal Equation

Nanoscale Research Letters - Tập 5 - Trang 1132-1136 - 2010
G Guisbiers1
1UCL, Institute of Mechanics, Materials and Civil Engineering, Louvain-La-Neuve, Belgium

Tóm tắt

Due to the lack of experimental values concerning some material properties at the nanoscale, it is interesting to evaluate this theoretically. Through a “top–down” approach, a universal equation is developed here which is particularly helpful when experiments are difficult to lead on a specific material property. It only requires the knowledge of the surface area to volume ratio of the nanomaterial, its size as well as the statistic (Fermi–Dirac or Bose–Einstein) followed by the particles involved in the considered material property. Comparison between different existing theoretical models and the proposed equation is done.

Tài liệu tham khảo

Pitkethly MJ: Mate. Today. 2004,7(Supplement 1):20. 10.1016/S1369-7021(04)00627-3 Gleiter H: Acta Mater.. 2000, 48: 1. COI number [1:CAS:528:DC%2BD3cXmtVCltw%3D%3D] COI number [1:CAS:528:DC%2BD3cXmtVCltw%3D%3D] 10.1016/S1359-6454(99)00285-2 Lieber CM, Wang ZL: Bulletin. 2007, 32: 99. COI number [1:CAS:528:DC%2BD2sXjsVOlsrk%3D] COI number [1:CAS:528:DC%2BD2sXjsVOlsrk%3D] 10.1557/mrs2007.41 Sutter E, Sutter P: Nano Lett.. 2008, 8: 411. COI number [1:CAS:528:DC%2BD1cXltlCmtQ%3D%3D]; Bibcode number [2008NanoL...8..411S] COI number [1:CAS:528:DC%2BD1cXltlCmtQ%3D%3D]; Bibcode number [2008NanoL...8..411S] 10.1021/nl0719630 Yacaman MJ, Ascencio JA, Liu HB, Gardea-Torresdey J: J. Vac. Sci. Technol. B. 2001, 19: 1091. COI number [1:CAS:528:DC%2BD3MXlvVehur8%3D] COI number [1:CAS:528:DC%2BD3MXlvVehur8%3D] 10.1116/1.1387089 Sun CQ: Prog. Solid State Chem.. 2007, 35: 1. 10.1016/j.progsolidstchem.2006.03.001 Roduner E: Chem. Soc. Rev.. 2006, 35: 583. COI number [1:CAS:528:DC%2BD28Xmt1Gmu7Y%3D] COI number [1:CAS:528:DC%2BD28Xmt1Gmu7Y%3D] 10.1039/b502142c Richman EK, Hutchison JE: ACS Nano. 2009, 3: 2441. COI number [1:CAS:528:DC%2BD1MXhtFGlsrnK] COI number [1:CAS:528:DC%2BD1MXhtFGlsrnK] 10.1021/nn901112p Campbell TA: Nano Today. 2009, 4: 380. COI number [1:CAS:528:DC%2BC3cXltFGmsLo%3D] COI number [1:CAS:528:DC%2BC3cXltFGmsLo%3D] 10.1016/j.nantod.2009.06.012 Holyst R, Litniewski M: Phys. Rev. Lett.. 2008, 100: 055701. Bibcode number [2008PhRvL.100e5701H] Bibcode number [2008PhRvL.100e5701H] 10.1103/PhysRevLett.100.055701 Qi WH: Physica B. 2005, 368: 46. COI number [1:CAS:528:DC%2BD2MXhtFSmtr%2FM]; Bibcode number [2005PhyB..368...46Q] COI number [1:CAS:528:DC%2BD2MXhtFSmtr%2FM]; Bibcode number [2005PhyB..368...46Q] 10.1016/j.physb.2005.06.035 Halperin WP: Rev. Mod. Phy.. 1986, 58: 533. COI number [1:CAS:528:DyaL28Xltl2ktLg%3D]; Bibcode number [1986RvMP...58..533H] COI number [1:CAS:528:DyaL28Xltl2ktLg%3D]; Bibcode number [1986RvMP...58..533H] 10.1103/RevModPhys.58.533 Wautelet M, Duvivier D: Eur. J. Phys.. 2007, 28: 953. COI number [1:CAS:528:DC%2BD2sXhtFyjsLzN] COI number [1:CAS:528:DC%2BD2sXhtFyjsLzN] 10.1088/0143-0807/28/5/018 Guisbiers G, Buchaillot L: Phys. Lett. A. 2009, 374: 305. COI number [1:CAS:528:DC%2BD1MXhsVWru7fF]; Bibcode number [2009PhLA..374..305G] COI number [1:CAS:528:DC%2BD1MXhsVWru7fF]; Bibcode number [2009PhLA..374..305G] 10.1016/j.physleta.2009.10.054 Yang CC, Li S: Phys. Rev. B. 2007, 75: 165413. Bibcode number [2007PhRvB..75p5413Y] Bibcode number [2007PhRvB..75p5413Y] 10.1103/PhysRevB.75.165413 Shandiz MA: J. Phys.: Condens. Matter. 2008, 20: 325237. 10.1088/0953-8984/20/32/325237 Vanithakumari SC, Nanda KK: Phys. Lett. A. 2008, 372: 6930. COI number [1:CAS:528:DC%2BD1cXhtlGisr%2FK]; Bibcode number [2008PhLA..372.6930V] COI number [1:CAS:528:DC%2BD1cXhtlGisr%2FK]; Bibcode number [2008PhLA..372.6930V] 10.1016/j.physleta.2008.09.050 Yang CC, Jiang Q: Acta Mater.. 2005, 53: 3305. COI number [1:CAS:528:DC%2BD2MXksV2iu7k%3D] COI number [1:CAS:528:DC%2BD2MXksV2iu7k%3D] 10.1016/j.actamat.2005.03.039 Guisbiers G, Buchaillot L: Nanotechnology. 2008, 19: 435701. 10.1088/0957-4484/19/43/435701 Balluffi RW: J. Nucl. Mater.. 1978, 69: 240. Bibcode number [1978JNuM...69..240B] Bibcode number [1978JNuM...69..240B] 10.1016/0022-3115(78)90247-7 Bollmann W, Uvarov NF, Hairetdinov EF: Cryst. Res. Technol.. 1989, 24: 421. COI number [1:CAS:528:DyaL1MXltVKju7w%3D] COI number [1:CAS:528:DyaL1MXltVKju7w%3D] 10.1002/crat.2170240418 Schaefer H-E: Physica Status Solidi A. 1987, 102: 47. COI number [1:CAS:528:DyaL2sXmt1KisL4%3D]; Bibcode number [1987PSSAR.102...47S] COI number [1:CAS:528:DyaL2sXmt1KisL4%3D]; Bibcode number [1987PSSAR.102...47S] 10.1002/pssa.2211020104 Tiwari GP, Patil RV: Scripta Metallurgica. 1975, 9: 833. COI number [1:CAS:528:DyaE28XnvVSguw%3D%3D] COI number [1:CAS:528:DyaE28XnvVSguw%3D%3D] 10.1016/0036-9748(75)90564-5 Qi WH, Wang MP: J. Mater. Sci.. 2004, 39: 2529. COI number [1:CAS:528:DC%2BD2cXitFWqt7w%3D]; Bibcode number [2004JMatS..39.2529Q] COI number [1:CAS:528:DC%2BD2cXitFWqt7w%3D]; Bibcode number [2004JMatS..39.2529Q] 10.1023/B:JMSC.0000020020.60857.6a Qi WH, Wang MP, Zhou M, Hu WY: J. Phys. D Appl. Phys.. 2005, 38: 1429. COI number [1:CAS:528:DC%2BD2MXksFKntro%3D]; Bibcode number [2005JPhD...38.1429Q] COI number [1:CAS:528:DC%2BD2MXksFKntro%3D]; Bibcode number [2005JPhD...38.1429Q] 10.1088/0022-3727/38/9/016 Jiang Q, Li JC, Chi BQ: Chem. Phys. Lett.. 2002, 366: 551. COI number [1:CAS:528:DC%2BD38Xps1ahsLk%3D]; Bibcode number [2002CPL...366..551J] COI number [1:CAS:528:DC%2BD38Xps1ahsLk%3D]; Bibcode number [2002CPL...366..551J] 10.1016/S0009-2614(02)01641-X Nanda KK, Sahu SN, Behera SN: Phys. Rev. A. 2002, 66: 013208. Bibcode number [2002PhRvA..66a3208N] Bibcode number [2002PhRvA..66a3208N] 10.1103/PhysRevA.66.013208 Kim HK, Huh SH, Park JW, Jeong JW, Lee GH: Chem. Phys. Lett.. 2002, 354: 165. COI number [1:CAS:528:DC%2BD38Xhsl2jsLc%3D]; Bibcode number [2002CPL...354..165K] COI number [1:CAS:528:DC%2BD38Xhsl2jsLc%3D]; Bibcode number [2002CPL...354..165K] 10.1016/S0009-2614(02)00146-X Qi WH, Wang MP, Zhou M, Shen XQ, Zhang XF: J. Phys. Chem. Solids. 2006, 67: 851. COI number [1:CAS:528:DC%2BD28Xis1ektL8%3D]; Bibcode number [2006JPCS...67..851Q] COI number [1:CAS:528:DC%2BD28Xis1ektL8%3D]; Bibcode number [2006JPCS...67..851Q] 10.1016/j.jpcs.2005.12.003 Horváth J, Birringer R, Gleiter H: Solid State Commun.. 1987, 62: 319. Bibcode number [1987SSCom..62..319H] Bibcode number [1987SSCom..62..319H] 10.1016/0038-1098(87)90989-6 Guisbiers G, Kazan M, Van Overschelde O, Wautelet M, Pereira S: J. Phys. Chem. C. 2008, 112: 4097. COI number [1:CAS:528:DC%2BD1cXit1KjsLo%3D] COI number [1:CAS:528:DC%2BD1cXit1KjsLo%3D] 10.1021/jp077371n