The Role of Alloy Composition and T7 Heat Treatment in Enhancing Thermal Conductivity of Aluminum High Pressure Diecasti
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I.
INTRODUCTION
THE thermal conductivity of a material is equivalent to the quantity of heat, DQ, transmitted during time Dt through a thickness x in a direction normal to a surface of area A, per unit area of A, due to a temperature difference DT under steady state conditions and when the heat transfer is dependent only on the temperature gradient. The thermal conductivity (W/m Æ K) is reliant on the thermal diffusivity, and is related to it directly via the relationship: j ¼ aCp q
½1
where j is thermal conductivity, a is thermal diffusivity (m2/s), Cp is specific heat, (J/kg Æ K), and q is density in g/cm3. In metals, the total thermal conductivity is the sum of electronic thermal conductivity (je) and phonon (lattice) thermal conductivity (jp), meaning that[1]: j ¼ j e þ jp
½2
Resistivity in metals (i.e., the inverse of conductivity) results directly from impediments to the mobility of electrons and arises due to electron scattering. Three main scattering processes affect the electrical and thermal conductivities of metals: (1) electrons can ROGER N. LUMLEY, formerly Principal Research Scientist with the CSIRO Future Manufacturing Flagship, Private Bag 33, Clayton South MDC, VIC 3169, Australia, is now Technical Manager with AWBell Pty. Ltd., 145 Abbotts Rd., Dandenong South, VIC 3175, Australia. Contact e-mail: [email protected] NATALIA DEEVA, Research Assistant, is with the CSIRO Process Science and Engineering, Clayton, VIC 3169, Australia. ROBERT LARSEN, Researcher, is with the TPRL Inc., 3080 Kent Ave., West Lafayette, IN 47906. JOZEF GEMBAROVIC, formerly with the TPRL, Inc., is now Application Scientist with the TA Instruments Corp., 159 Lukens Drive, New Castle, DE 19720. JOE FREEMAN was formerly Researcher with the TPRL, Inc. Manuscript submitted December 13, 2011. Article published online September 27, 2012 1074—VOLUME 44A, FEBRUARY 2013
scatter on lattice defects such as solute atoms present on lattice sites; (2) electrons are deflected via lattice vibrations (phonons); and (3) electrons may interact directly with other electrons. If several distinct scattering mechanisms are present, then the overall resistivity in metals is the sum of those that would be present if each scattering mechanism was present individually, according to Mathiesson’s rule.[2] For metals and alloys, the electrical and thermal conductivity are also related through the Wiedemann– Franz law: L0 ¼ je =rT
½3
where L0 is the Lorentz number, r is the electrical conductivity, T is temperature in Kelvin, and je is the electronic thermal conductivity. For aluminum and its alloys, the Lorentz number has also been quoted as 2.1 9 108 V2/K2,[2] although in Si containing alloys, L0 is reported to increase with Si content right up to the eutectic concentration.[3] The value of L0 for Al-Si alloys is accepted as being 2.1 9 108 + 0.021 9 108 [Si]b V2/K2, where [Si]b is the wt pct Si in the alloy. For aluminum alloys, a correction to the Wiedemann– Franz law has also been suggested so that je ¼ L0 Tr þ c
½4
[4]
where c = 10
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