c ###################################################################### c # c # ALUMINUM PROPERTIES PACKAGE c # --------------------------- c # Contains functions for the calculation of the thermo-physical c # properties of pure Aluminium (Al) c # c ###################################################################### c ###################################################################### real function dAl(T) c ###################################################################### c # c # Density of Aluminium c # c # Range: 0 <= T <= inf K c # c # References c # ---------- c # http://en.wikipedia.org/wiki/Aluminium c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # dAl x density Kg/m**3 c # c # c # Author : L.Bottura at Cryosoft c # Version: 1.0 October 2012 c # c ###################################################################### implicit none c * external variables real T c * fit variables c * local variables c * dAl = 2700.0 c * return end c ###################################################################### real function cAl(T) c ###################################################################### c # c # Specific heat of Aluminium c # c # Range: 1 <= T <= 1000 K c # c # References c # ---------- c # CryoComp version 3.0 c # V.J. Johnson, Properties of Materials at Low Temperatures (Phase 1) c # Pergamon Press, 1961 c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # cAl x specific heat J/Kg K c # c # Author : L.Bottura & C. Rosso at Cryosoft c # Version: 3.5 October 2012 c # c ###################################################################### implicit none c * external variables real T c * fit variables real T0,T1 real Tmin,Tmax real a0,a1,a2,a3 real b0,b1,b2,b3,b4 real AA,BB,CC,DD,a,b,c,d,na,nb,nc,nd data T0 / 13.0300576 / , T1 / 54.4990277 / data a0 / 0.012034041 / , a1 / 0.039172353 /, & a2 / 0.002543257 / , a3 / 0.000771961 / data b0 / -4.797655015 / , b1 / 1.249154424 /, & b2 / -0.105581366 / , b3 / 0.004593931 /, & b4 / -3.65654e-05 / data AA / 9143.27476 / , BB / -417.10708 / , & CC / 400.787649 / , DD / -7722.6604 / data a / -18.6481086 / , b / -25.7545827 / , & c / -18.1481600 / , d / -5.44742024 / data na / 0.73861474 / , nb / 1.52610058 / , & nc / 2.48698565 / , nd / 3.70977399 / data Tmin / 1.0/, Tmax / 1000.0/ save c * local variables real TT c * TT=T TT=min(TT,Tmax) TT=max(TT,Tmin) if (TT.le.T0) then cAl = a0 + a1*TT + a2*TT**2 + a3*TT**3 elseif (TT.gt.T0 .and. TT.le.T1) then cAl = b0 + b1*TT + b2*TT**2 + b3*TT**3 + b4*TT**4 elseif(TT.gt.T1) then cAl = AA*TT /(a+TT)**na + BB*TT**2/(b+TT)**nb + & CC*TT**3/(c+TT)**nc + DD*TT**4/(d+TT)**nd endif c * return end c ###################################################################### real function kAl(T,B,RRR) c ###################################################################### c # c # Thermal conductivity of Aluminium c # c # Range: 0.1 <= T <= 933.45 K, 0 <= B <= 30 T, 1.5 <= RRR <= 30000 c # c # References c # ---------- c # CryoComp version 3.0 c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # B x magnetic field T c # RRR x residual resistivity ratio - c # kAl x thermal conductivity W/m K c # c # Author : L.Bottura & C. Rosso at CryoSoft c # Version: 3.5 October 2012 c # c ###################################################################### implicit none c * external variables real T,B,RRR c * fit variables real Tmin,Tmax parameter(Tmin = 0.1, Tmax = 933.45) real Bmin,Bmax parameter(Bmin = 0.0, Bmax = 30.0) real RRRmin,RRRmax parameter(RRRmin = 1.5, RRRmax = 30000.0) real rho273 parameter(rho273=2.48e-8) real L0 parameter(L0=2.443e-8) real p1,p2,p3,p4,p5,p6 parameter (p1=4.716e-8, p2=2.446, p3=623.6, & p4=-0.16 , p5=130.9, p6=2.5) c * local variables real TT,BB,R real rhozero,beta,p7,arga,argb,argd real wt,wi0,wi,w0,wc,magr real magrAl c * TT=T TT=max(TT,Tmin) TT=min(TT,Tmax) BB=B BB=max(BB,Bmin) BB=min(BB,Bmax) R =RRR R =max(R,RRRmin) R =min(R,RRRmax) c * rhozero = rho273/(R-1.) beta = rhozero/L0 p7 = 0.8168/(beta/0.0003)**0.1661 arga = min((log(TT/380.0)/0.6)**2,30.0) argb = min((log(TT/ 94.0)/0.5)**2,30.0) argd = min((p5/TT)**p6,30.0) wc = -0.0005*log(TT/330)*exp(-arga) - & 0.0013*log(TT/110)*exp(-argb) w0 = beta/TT wi = p1*TT**p2/(1.+p1*p3*TT**(p2+p4)*exp(-argd))+wc wi0 = p7*wi*w0/(wi+w0) wt = w0+wi+wi0 magr = magrAl(TT,BB,R) c * kAl = 1.0/(wt*magr) c * return end c ###################################################################### real function rAl(T,B,RRR) c ###################################################################### c # c # Electrical resistivity of Aluminium c # c # Range: 0.1 <= T <= 933.45 K, 0 <= B <= 30 T, 1.5 <= RRR <= 30000 c # c # References c # ---------- c # CryoComp version 3.0 c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # B x magnetic field T c # RRR x residual resistivity ratio - c # rAl x resistivity Ohm m c # c # Author : L.Bottura and C. Rosso at Cryosoft c # Version: 3.5 October 2012 c # c ###################################################################### implicit none c * real t,b,rrr c * fit variables real Tmin,Tmax parameter(Tmin = 0.1, Tmax = 933.45) real Bmin,Bmax parameter(Bmin = 0.0, Bmax = 30.0) real RRRmin,RRRmax parameter(RRRmin = 1.5, RRRmax = 30000.0) real rho273 parameter(rho273=2.48e-8) real p1,p2,p3,p4,p5,p6,p7 parameter (p1=0.09052e-16, p2=4.551, p3=5.173e10, & p4=-1.26, p5=13.64, p6=1.0, p7=0.7416) c * local variables real TT,BB,R,rhozero,arg,rhoi,rhoi0,rho0,magr real magrAl c * TT=T TT=max(TT,Tmin) TT=min(TT,Tmax) BB=B BB=max(BB,Bmin) BB=min(BB,Bmax) R =RRR R =max(R,RRRmin) R =min(R,RRRmax) c * resistivity at absolute zero rhozero = rho273/(R-1.0) c * resistivity at the temperature t arg = min((p5/TT)**p6,30.0) rhoi = p1*TT**p2/(1.+p1*p3*TT**(p2+p4)*exp(-arg)) rhoi0 = p7*rhoi*rhozero/(rhoi+rhozero) rho0 = rhozero+rhoi+rhoi0 c * transverse magneto-resistance factor magr = magrAl(TT,BB,R) c * resistivity rAl = magr * rho0 c * return end c ###################################################################### c # c # Auxiliary functions and calculations c # c ###################################################################### c ###################################################################### real function magrAl(T,B,RRR) c ###################################################################### c # c # Magneto-resistivity factor of Aluminium, given as the ratio between c # resistivity in transverse magnetic field b to resistivity at zero c # field c # c # Range: 0.1 <= T <= 933.45 K, 0 <= B <= 30 T, 1.5 <= RRR <= 30000 c # c # References c # ---------- c # CryoComp version 3.0 c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # B x magnetic field T c # RRR x residual resistivity ratio - c # magrAl x magneto-resistivity factor - c # c # Author : L.Bottura and C. Rosso at Cryosoft c # Version: 1.1 October 2012 c # c ###################################################################### implicit none c * external variables real T,B,RRR c * fit variables real Tmin,Tmax parameter(Tmin = 0.1, Tmax = 933.45) real Bmin,Bmax parameter(Bmin = 0.0, Bmax = 30.0) real RRRmin,RRRmax parameter(RRRmin = 1.5, RRRmax = 30000.0) real brrmin,brrmax parameter(brrmin = 0.0, brrmax = 40.0e3) real rho273,rhorrr parameter(rho273=2.48e-8,rhorrr=4.52e-8) real p1,p2,p3,p4,p5,p6,p7 parameter (p1=0.09052e-16, p2=4.551, p3=5.173e10, & p4=-1.26, p5=13.64, p6=1.0, p7=0.7416) real g1,g2,g3,g4,g5,g6,g7 parameter (g1 = 0.116587e-04, g2 = 0.776391e-01, & g3 = 0.687100e+00, g4 = 0.536580e-05, & g5 = 0.135597e+01, g6 = 0.534860e-05, & g7 = 0.181991e+01) c * local variables real TT,BB,R,rhozero,rhoice,arg,rhoi,rhoi0,rho0,rr,brr,magr c * TT=T TT=max(TT,Tmin) TT=min(TT,Tmax) BB=B BB=max(BB,Bmin) BB=min(BB,Bmax) R =RRR R =max(R,RRRmin) R =min(R,RRRmax) c * resistivity at absolute zero rhozero = rho273/(R-1.0) c * fit for the resistivity at the ice temperature rhoice = rho273 + rhorrr/R c * resistivity at the temperature t arg = min((p5/TT)**p6,30.0) rhoi = p1*TT**p2/(1.+p1*p3*TT**(p2+p4)*exp(-arg)) rhoi0 = p7*rhoi*rhozero/(rhoi+rhozero) rho0 = rhozero+rhoi+rhoi0 c * resistivity ration at temperature t rr = rhoice/rho0 c * product of field and residual resistivity ratio brr = BB*rr brr = max(brr,brrmin) brr = min(brr,brrmax) c * fit for the transverse magneto-resistance increase if(brr .gt. 1.) then magr = g1*rr**(g2*TT**g3)*brr**g7*(1+g4*brr)/ & (TT**g5*(1+g6*brr**g7)) else magr = 0.0 endif c * transverse magneto-resistance factor magrAl = magr + 1.0 c * return end