Transient determinations <strong>of</strong> thermal diffusivities andemissivities <strong>of</strong> metal foilsC. E. CanadaMason urid Hurtgc,r-Silas Maso~r Cr,. Inc.. pant^..^ Pla~rt. Amurillo. Texas 79/000. H. <strong>Zinke</strong><strong>Physics</strong> <strong>Department</strong>, <strong>University</strong> <strong>of</strong> <strong>Arkansas</strong>, Fayetteville, <strong>Arkansas</strong> 72701(Received 5 July 1977; accepted for publication 21 September 1977)Diffusivities and emissivities are measured through the use <strong>of</strong> the transient technique for five metals.DitTusivity values for Al, Ag, Cu, Fe, and Ni are found to be 0.89, 1.73, 1.14, 0.216, and 0.176cm2/sec, and respective emissiviiy values are found to be 0.23, 0.031, 0.038, 0.046, and 0.054. Thesediffusivitia agree well with other values in literature and differ from values previously obtained throughuse or this tccl~nique becausc <strong>of</strong> corrections for heat reflection and possibly better heat input tc~hniqu~s.PACS numbers: 72.15.Eb, 44.40.+aINTRODUCTIONassumed that temperature excursions above ambientare small enoughthat the rate <strong>of</strong> heat dissipated fromThermal diffusivities and emissivities <strong>of</strong> surfaces <strong>of</strong>the foil surface to the surroundings can be assumed tometal foils were measured using the technique introbea linear function <strong>of</strong> (T- To). The solution where theduced by Jacovelli and <strong>Zinke</strong>.' The dissipation meainjectedheat can be considered to be a line source issurements <strong>of</strong> Jacovelli and <strong>Zinke</strong> were made with am-[carslaw and Jaeger, Eq. 10.2(9)]bient atmosphere in contact with the foils and could notbe used to determine the emissivity <strong>of</strong> the foils. Here(.r- xJ2T= Q' l,zexp(-vt--)(2)the experiments were carried out in an evacuated re- 2 WDpc(n~t) 4 ~ t Igion so that the emissivity could be calculated from the wheredissipation. The technique <strong>of</strong> injecting the heat pulseinto the foil was improved, and a temperature detectorV=~HK(W+D)/KWDZ~HK/'KD,(3)with better definition was used.andExtension <strong>of</strong> the technique to measurement in evacuatedregions revealed the possibility that systematic errorsmay have occurred in the previous measurements.Careful steps have been taken here to eliminate thosesystematic errors. Criteria were developed for systematicerror analyses, and nomographs are presentedwhich simplify the determination <strong>of</strong> reading error.Measured diffusivities and emissivities are presentedfor foils <strong>of</strong> silver, aluminum, copper, iron, and nickel.lirsults seern to be in better agreement with those <strong>of</strong>previous investigators than results <strong>of</strong> Jacovelli andZ inke.THEORYThe applied theory is relatively simple and straightforwardand depends on the production in the initialinstance <strong>of</strong> an instantaneous line source <strong>of</strong> heat in ametal sample where the width <strong>of</strong> the sample is muchsmaller than the length. The diffusing heat then producesa temperature change at some distance from theinput point. The change <strong>of</strong> temperature <strong>of</strong> the metalsample is calculated through the differential equationfor one-dimensional propagation <strong>of</strong> heat in a foil withsurface conduction to the surrounding medium. Theequation is [carslaw and Jaeger, Eq. 4.2 (2)]where K is the diffusivity, v is the dissipation constant,T is the temperature excursion above the ambient temperatureTo t is the time, and x is the distance. It isH = 4eoT: + H'. (4)The heat pulse is produced at xu and detected a distance(x - x,) from the point <strong>of</strong> production in a foil having widthW, thickness D, density p, specific heat C, and thermalconductivity K. The magnitude <strong>of</strong> the injected heat pulseis Q'. The quantity H corresponds to a coefficient <strong>of</strong>heat conduction perpendicular to the foil surface. Thisquantity can be divided into a term which depends onconduction to the surrounding gas, H', and a radiationterm with e as the surface emissivity and o as theStefan-Boltzman constant. In these experiments it wasexperimentally established that H' disappeared at pressureswell over an order <strong>of</strong> magnitude greater that thehighest pressures used for the resulting data.Consequently,andValues <strong>of</strong> K and v were determined by measuring Tat x and t for two points on the temperature pr<strong>of</strong>ile.The points chosen were the maximum value <strong>of</strong> temperatureT, occurring at t,, x,, and one <strong>of</strong> the half-maximumvalues <strong>of</strong> temperature, either TI/, or T,/, dependingon whether the designation applies to the first orsecond half-maximum. Similar designations were givento x and t. The second half-maximum was usually usedbecause <strong>of</strong> the increased reading accuracy <strong>of</strong> T31z overT,/,. The maximum temperature occurs where289 J. Appl. Phys. 49(1), January 1978 002 1 -897917814931-0289$0 1.10 O 1978 American Institute <strong>of</strong> <strong>Physics</strong> 288Downloaded 12 Jun 2009 to 130.184.237.6. Redistribution subject to AIP license or copyright; see http:lljap.aip.orgljaplcopyright.jsp
-Bulletin <strong>of</strong> the American Physj cal Society, v 22, Issue 1, D 92-92. 1977JG 6 Self-Consistency Analysis <strong>of</strong> O~ticsl Data:Aldnum.' 2. SHILES, Virginia Cmmonvealth U. andArsnne Natl. Lab. and D. Y. SMI'l'K, k ~ o ~ Iintl. n e Lob. --Ihe - .- arrtical - .- .- mo~rties -.<strong>of</strong> metallic aluminum have beeninvestigated frk the infrsred to the x-ray region ueingem d e s as a check on self-consistency <strong>of</strong> the opticalconstmts. Published compilations <strong>of</strong> data for alumjn~mby Phrcnreich, et al., Saaalti and Inokuti , a d kg-,et al.. all show violations <strong>of</strong> one or more rules exceedingexperlrrcntal or cmputational error. Re-aaalysie 02 thencst reliable experiments Indicates that available opticalconstants for aldnum belov the LII,III edge are con-sistent vith the partial f sun <strong>of</strong> 3.1 - 3.2 electronspcr ato~ predicted for the three conduction electrons perat= from Pauli principle redistribution <strong>of</strong> oscillatorstrength. K~vever, the currently accepted value8 forabsorption above the edges show an unexplainedexeeea oscillator etrength <strong>of</strong> approximstely 1.5 electronsper atom. The possibility <strong>of</strong> systematic errors in experbentor oversfnplifications in currently accepted theorywill be discussed.4Work prfomd mder the auspices <strong>of</strong> the USERDA.- a , ~as .3 K and in fields as high as 130 kG. Area databeen taken on several previously unobserved orbitseluding second zone octahedron and the third zonegym.The area data has been used to parameterizePermi surface in terms <strong>of</strong> non muffin tin KKR scattphase shifts. New cyclotron effective mess data walso be presented and discussed in terms <strong>of</strong> ,electrphonon enhancement.~010 I flection Points in SeebeckPotentia
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