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46 CHAPTER 2 Energy in the small: Integrated micro-scale energy sources Symbol t t 1/2 T v V w x Meaning Time Radionuclide half life Absolute temperature Volume Voltage Width Amplitude Distance between the neighboring atomic planes (for graphite d ¼ 0.335 nm) Particle kinetic energy transferred to lattice vibrations Energy released per atom Permittivity of vacuum, 3 0 ¼ 8.85 x 10 À14 F/cm Efficiency Period of oscillation Reduced mass Density of substance Conductivity Radionuclide mean life time Electric potential Indicates order of magnitude d D 3 e 0 h Q m r s s 4 w References [1] S. Tajima, Aluminum and manganese as anodes for dry and reserve batteries, J. Power Sources 11 (1984) 155­161. [2] Q. Li, N.J. Bjerrum, Aluminum as anode for energy storage and conversion: a review, J. Power Sources 110 (2002) 1­10. [3] W.S.D. Wilcock, P.C. Kauffman, Development of a seawater battery for deep-water applications, J. Power Sources 66 (1997) 71­75. [4] M.A. Klochko, E.J. Casey, On the possible use of titanium and its alloys and compounds as active materials in batteries: A review, J. Power Sources 2 (1977/78) 201­232 [5] S. Downey, Small Energy Sources, SRC/NSF Forum on Nano-Morphic Systems: Processes, Devices, and Architectures, Stanford University, Stanford, CA, November 8­9, 2007. [6] A. Heller, Potentially implantable miniature batteries, Anal. Bioanal. Chem. 385 (2006) 469­473. [7] W. Shin, J. Lee, Y. Kim, H. Steinfink, A. Heller, Ionic conduction in Zn 3 (PO 4 ) 2 -4H 2 O enables efficient discharge of the zinc anode in serum, J. Amer. Chem. Soc. 127 (2005) 14590. [8] W. Shin, Miniature bio-fuel cell and Zn-Ag/AgCl battery in physiological condition, SRC/NSF Forum on Nano-Morphic Systems: Processes, Devices, and Architectures, Stanford University, Stanford, CA, November 8­9, 2007. [9] N. Mano, F. Mao, W. Shin, T. Chen, A. Heller, A miniature biofuel cell operating at 0.78 V, Chem. Commun. (2003) 518­519. [10] A. Heller, Miniature biofuel cells, Phys. Chem. Chem. Phys. (2004) 209­216.