c ###################################################################### c # c # SILVER PROPERTIES PACKAGE c # ------------------------- c # c # Contains functions for the calculation of the thermo-physical c # properties of pure Silver (Ag). c # c ###################################################################### c ###################################################################### real function dAg(T) c ###################################################################### c # c # Density of Silver c # c # Range: 0 <= T <= inf K c # c # References c # ---------- c # http://en.wikipedia.org/wiki/Silver c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # dAg 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 * dAg = 10490.0 c * return end c ###################################################################### real function cAg(T) c ###################################################################### c # c # Specific heat of Silver c # c # Range: 1 <= T <= 300 K c # c # References c # ---------- c # CryoComp version 3.0 c # D.R.Smith, F.R.Fickett, J. Res. NIST, 100, 119-171, (1995) c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # cAg x specific heat J/Kg K 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 c * fit variables real T0,T1 real Tmin,Tmax real a1,a2,a3 real b0,b1,b2,b3,b4 real AA,CC,a,c,na,nc data T0 / 9.785133189 / , T1 / 34.5580572 / data a1 /6.14e-03/, a2 /-9.09e-04/, a3 /1.79e-03/ data b0 /-3.515882063/, b1 /0.768177822/, & b2 /-0.072031/, b3 /5.59e-03/, & b4 /-7.55e-05/ data AA /-14331.2453/ , CC /1415.969135/ data a /217.2435636/ , c /23.862111/ data na /1.475372864/ , nc /3.091515729/ data Tmin / 1.0/, Tmax / 300.0/ save c * local variables real TT c * TT=T TT=max(TT,Tmin) TT=min(TT,Tmax) if (TT.le.T0) then cag = a1*TT + a2*TT**2 + a3*TT**3 elseif (TT.gt.T0 .and. TT.le.T1) then cag = b0 + b1*TT+ b2*TT**2 + b3*TT**3 + b4*TT**4 elseif(TT.gt.T1) then cag = AA*TT /(a+TT)**na + CC*TT**3/(c+TT)**nc endif c * return end c ###################################################################### real function kAg(T,B,RRR) c ###################################################################### c # c # Thermal conductivity of Silver c # c # Range: 0.1 <= T <= 1000 K, 0 <= B <= 100 T, 1.5 <= RRR <= 10000 c # c # References c # ---------- c # CryoComp version 3.0 c # D.R.Smith, F.R.Fickett, J. Res. NIST, 100, 119-171, (1995) 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 # kAg x thermal conductivity W/m K 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 = 1000.0) real Bmin,Bmax parameter(Bmin = 0.0, Bmax = 100.0) real RRRmin,RRRmax parameter(RRRmin = 1.5, RRRmax = 10000.0) real rho273 parameter(rho273=1.48e-8) real L0 parameter(L0=2.443e-8) real alpha2,m,n,l parameter(alpha2=7.87561879e-8, m=2.75, n=2.3, l=-2.5) real T0,k0 parameter(T0=35.0, k0=408.59712205) real cond c * local variables real TT,BB,R real rhozero,alpha,beta,wi0,wi,w0,wt,magr real magrAg 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 alpha = alpha2 * (beta/n/alpha2)**((m-n)*(m+l)) c * thermal resistivity at the temperature T and zero field B w0 = beta/TT wi = alpha*TT**n wi0 = wi+w0 if(TT.le.T0) then wt = wi0 else wt = wi0 /(1.0 + wi0 * k0*(1.0-exp(-(TT-T0)/T0))) endif c * transverse magneto-resistance factor magr = magrAg(TT,BB,R) c ---------------------------------------------------------------------- c write(6,*) TT,BB,R,rhozero,beta,alpha,w0,wi,wi0,1/wt,magr c ---------------------------------------------------------------------- c * thermal conductivity kAg = 1.0/(wt*magr) c * return end c ###################################################################### real function rAg(T,B,RRR) c ###################################################################### c # c # Electrical resistivity of Silver c # c # Range: 0.1 <= T <= 1000 K, 0 <= B <= 100 T, 1.5 <= RRR <= 10000 c # c # References c # ---------- c # CryoComp version 3.0 c # D.R.Smith, F.R.Fickett, J. Res. NIST, 100, 119-171, (1995) 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 # rAg x resistivity Ohm m 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 = 1000.0) real Bmin,Bmax parameter(Bmin = 0.0, Bmax = 100.0) real RRRmin,RRRmax parameter(RRRmin = 1.5, RRRmax = 10000.0) real rho273 parameter(rho273=1.48e-8) real p1,p2,p3,p4,p5,p6,p7 parameter(p1=1.474e-17, p2=4.82, p3=1.16e11, & p4=-1.33, p5=10.0, p6=1, p7=0.333) c * local variables real TT,BB,R,rhozero,arg,rhoi,rhoi0,rho0,magr real magrAg 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 and zero field 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 = magrAg(TT,BB,R) c * resistivity rAg = magr * rho0 c * return end c ###################################################################### c # c # Auxiliary functions and calculations c # c ###################################################################### c ###################################################################### real function magrAg(T,B,RRR) c ###################################################################### c # c # Magneto-resistivity factor of Silver, given as the ratio between c # resistivity in transverse magnetic field b to resistivity at zero c # field c # c # Range: 0.1 <= T <= 1000 K, 0 <= B <= 100 T, 1.5 <= RRR <= 10000 c # c # References c # ---------- c # CryoComp version 3.0 c # D.R.Smith, F.R.Fickett, J. Res. NIST, 100, 119-171, (1995) 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 # magrAg 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 = 1000.0) real Bmin,Bmax parameter(Bmin = 0.0, Bmax = 30.0) real RRRmin,RRRmax parameter(RRRmin = 1.5, RRRmax = 10000.0) real brrmin,brrmax parameter(brrmin = 0.0, brrmax = 10.0e3) real rho273 parameter(rho273=1.48e-8) real p1,p2,p3,p4,p5,p6,p7 parameter(p1=1.474e-17, p2=4.82, p3=1.16e11, & p4=-1.33, p5=10.0, p6=1, p7=0.333) real a1,a2,a3,a4 parameter(a1=6.5e-05, a2=1.8, a3=3.0e-3, a4=1.1) c * local variables real TT,BB,R,rhozero,arg,rhoi,rhoi0,rho0,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 * 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 * product of field and residual resistivity ratio brr = BB*rho273/rho0 brr = max(brr,brrmin) brr = min(brr,brrmax) c * fit for the transverse magneto-resistance increase if(brr .gt. 1.) then magr = a1*brr**a2/(1.0+a3*brr**a4) else magr = 0.0 endif c ---------------------------------------------------------------------- c write(6,*) TT,BB,R,rho0,brr,magr c ---------------------------------------------------------------------- c * transverse magneto-resistance factor magrAg = magr+1.0 c * return end