The soft-sphere model is convenient and accurate for predicting fluid phase thermodynamics. The validity of the model for describing the equation-of-state derivatives, Grueneisen's gamma and sound velocity, is shown. 7 refs., 2 figs

Shaner, J.W.

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A major purpose ot the I ecmwcal Information Center is to providethe broadest dissemination possi-ble of information contained inDOE’s Research and DevelopmentReports to business, industry, theacademic community, and federal,state and local governments.Although a small portion of this~ report is not reproducible, it isbeing made available to expeditethe availability of information on theresearch discussed herein.LA-uR--89-2485DE!89 015298-. ,.LOS Ahrnos Nmom Labo~mfY IS owrsloO by Iho Unwomiy d Calbfm Ior NW UfIM Slams tip-r-l ol Efww uneor conlmcl W.7405-ENG-WTITLE: THE SOFT-SPHERE t42DEL FOR METALS NEAR THE CRITICAL POINTAUTHOR(S): J. W. SHANERSUBMITTEO TO: MRAPT AND EHPRCPRRSSURE SCIENCEINTERNATIONAL CONFERENCEON HIGH% BMD TECHNOLOGY,JULY 1989, HIGH W’F *$*PRESSURELABORATORY, UNIVERSITYPADERBORN,FEDERAL REPUBLIC OF-GERMANYDISCLAIMERTM ropwl wu pmmrd u m icuunl of wwk S- by anqwy d lhaUnllal !WaOowrnnww Nohhcr Iha Urdkd SISIU Oowrnrmnl nor MY a~ncy Ibmof, nuc tny of Ihdr●*, maka ●ny wafran[y, SR- or ImplM, w ●um9 nny I@ Ntbility W ~.bllhy for IIM ercurncy, ctrmpletr~, w umfu%u of ●ny Intorm-kn, rnpparalus, prducl, or- dbciod, or represcnis Ihmt III um would na Infrlw privmcly ownd rl~hm Rdor.●a harein 10 ●ny qNclik cmmmcrcisl prcduct, promM, or tomb by V* nama, Irsdommk,mwwklumr, w Mharwi= dms M MUMSrlly comstitutc or imply ih ●timrmnl, rwxwmnwndmlm, w favwhi~ hy he (Inkd !$Iawo (k.wernmm ur ●y •~rrcy Ihsrwf, TIM VIOWSd opinions M ●uthors enpwd herein do not nacmmrily Mat. or rafk Ihm of the[ Jnild Slala (tirnnranl r.w●ny ~Sarcy hard.-mJIX8TRIWTION (1} “11+1SLXJCUMENT Is uNLIMI 1El)AIlaA o mm Los Alamos National LaboratoryLos Alamos,New Mexico 87545,.,, %, “,~,,,THE SOFT-SPHERE MODEL FOR METALS NEAR THE CRITICAL POINT*J. W. ShanerLoe AlamoeNational LaboratoryLoe Alarnoa, New Mexico 87545 USAABSTRACTThe eoft-ephere model ia convenient and accurate for predicting fluid phww therrno-dynarnice. The validity of the model for dtswibing the equation-of-date derivative,Griinehwn’s gamma and eound velocity, ie shown.KEY WORDSHigh preeeure fluids, liquid metals, mft-ephere modelThe soft-aphem model for fluidn wae develoPin order to model the deneeliquid thernmclynunica better than it is d-ib by the van dor Waaln’ equation.In the van der WAe’7uation the exclud~ volume ia treated crudely, eo althouqhthis equation works wel for Icnvdensity duds, there ia an unphysical singularity mthe uation of etate for denaiti- approaching the normal liquid. In order to betterT hd-i e the denm fluid an analytic fitto onte Carlo mmulationa of puticlee(interacting with ● C(U r)m repulsion hae been ●ugmented with a phenomenologicalterm accounting for t e ●ttractive tail in mal potential (Hoover et al., 1976 andShaner, 1988).The form of the equation of state for thie model isNkTf=~{ ()i+ ~~c.p”ia& + ;n(n+ 4)g7”/9(*)’’a-m’m(*)}and (1){E=NkT ~()+ cnpn~a cE+ ;(n + 4)#@9G)’’a-’m(a} -k theee equations, n ie the exponent of the repulsive part of the potential, c- isthe fcc static lattice Madelung energy, ~ = rwa/@, ●nd m in a phenomenologicdparameter which deecrib~ the ●ttractwert of the interaction. For m = 1 werecover the ckical! mean-field van der W 10’form. We have shown that molecularfluids can be deembed by Eq. (1) ●ugmented by terms in the energy equationdescribing the hILOrn~ degrees of freedom Shaner, 1988).iOne of the coneeqmncee of the eoft-op ere model ie that one of the equation-of-state aerivativee, Cruneieen’e gamma, can be expraeeed analytically ae{2 1 + l/27(n + 4)npn@(u/kT) ‘la7Cl=- 13I+2/27(n + 4)pn/9(u/k7’) lJa ‘ (2)Thio expremion ehowa that yu dependn on both density and temperature explicitly,i’ly contrast, the queaiharmonic model of the eolid pheee gives only an explicit. .. . . . . . . .. . . . .* This work ww nupporkd by tho US I;epartment of Ilncrgy,density dependence for 7@.We have mmured 70 for Ii uid lead (Hixaon ●t al., 1986a and Ron- et al.,1988a) and tantalum (Brown an 1 Shaner, 1984 and Hixson et al., 1986b) both inshock compromion md iwbaric expansion. Them data are shown along with asoft-sphere calculation for n = 8 in Fig. 1. The baaic feature of the invereion ofthe density dependence between expansion and compr~ion are clear in tbia figure.Since the temperature ia increasing with density for the shock compreAon part ofthe curve and decream‘ng with density for the isobaric expansion part of the curve thenon-monotonic density dependence of ~G is attributed to the intrineic temperaturedepe;~nt~eo~ Eq. (2).= 8 repulsive potential, which io a reaxmable ●pproximation formany liquid metals, one can show that the anund velocity around the normal liquiddensity is (Shaner, 1988)(I/aC=O.6 ~kTeM 4.14 x 10-4 )(3)where A ia Avaga&o’~ number, M ia the ●tomic weight aad Ta is the criticaltemperature. We show in Fig. 2 sound velocity data St die melting temperatureof ● number of metaln (Webber and Stephena, IfKM). One aea for group in thesame column of the periodic table the dominant M-l/s dependence, The TC1/1dependenm is alm clear u To incre= slightly for the Ii hter alkli rnetala.fThe soft+phere model has proven to be both a udu interpolative apmtion ofotate over a wide density ran e of molecular and metallic fluids and s uoeful guide!to inter reting experimental ata. Systematic adjustment of the parameter in the!3model s ould make it even more useful for dmribing sptiflc fluid tyaterns.1,0FOR FLUID METALS0,5 ~ ~’ * I b I I I I. 0.6 1,() 1,4 1,8 2,2P/P.Fig, 1, Gruneiuen gamma for liquid Pb and Ta compmed with the wft-sphere model,%!+!!.,a,Na ‘~\kK ‘\\\‘\\SOUND VELOCITIES *FOfl FLUID METALSI I I I I I20 50 100 mMFig. 2, Sound velocity of liquid metala.REFERENCESBoneq D. A.; J. M. Brown, and J. W. Shaner in Procdinge of tho 1987 APSTo ical Conference on Shock WaVa in Co~denaed Matter, Montirey, CA, NorthrHo land, Amsterdam (1!288).Brown, J, M. and J. W, Shiner in Shock Wavea in Condensed Matter-1983,E& J. Amy, R. A. Graham, and C, K, Straub, North-Holland, Amsterdam, p. 91(1984).Hixum, R. S., M. A. Winklm, and J. W, Shaner, Phyeica B w & ~, 893(1086a).Hixum R. S., M. A. Winkler, emd J. W, Shaner, High lIhmp.-High PM, u, 835( 1986bj.Hoover, W. G., G. Stell, E, Goldmark, and C. D. Degnani, J. Chem. Phy_. QQ,6435 (1975).Shaner, J. W., J, Chem, Phye. w, 1616 (1988).Webber, G.M, B, and R.W, B. Stcphene in Phyeicel Acouatiw, Ed. W. Mason,Academic Preaa, NY, V. IV13, (1968).

The soft-sphere model for metals near the critical point

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The soft-sphere model for metals near the critical point

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