c ###################################################################### c # c # MANGANESE PROPERTIES PACKAGE c # ---------------------------- c # c # Contains functions for the calculation of the thermo-physical c # properties of pure Manganese (Mn) c # c ###################################################################### c ###################################################################### real function dMn(T) c ###################################################################### c # c # Density of Manganese c # c # Range: 0 <= T <= 1519 K c # c # References c # ---------- c # http://en.wikipedia.org/wiki/Manganese c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # dMn 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 * dMn = 7210.0 c * return end c ###################################################################### real function cMn(T) c ###################################################################### c # c # Specific heat of Manganese c # c # Range: 1 <= T <= 900 K c # c # References c # ---------- c # Malkov (1 to 20 K) c # Toloukian crv 9 (12 to 298 K) and crv 5 shifted (300 to 900 K) c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # cMn x specific heat J/Kg K 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 real T0,T1 real Tmin,Tmax real a1,a2,a3 real b0,b1,b2,b3,b4 real AA,BB,CC,a,b,c,na,nb,nc data T0 / 13.18748185 / , T1 / 43.04374877 / data a1 / 0.25008781 / , a2 / -0.00098341 / , & a3 / 0.00042307 / data b0 / -7.499914804 / , b1 / 1.923486149 / , & b2 / -0.140172906 / , b3 / 0.005277091 / , & b4 / -4.93961E-05 / data AA / 803.11507623 / , BB / -83.20337048 / , & CC / -25.47928725 / data a / 10.48518912 / , b / 3.047203090 / , & c /3124.22837016 / data na / 8.58084902 / , nb / 5.574661389 / , & nc / 5.00000000 / data Tmin / 1.0/, Tmax / 900.0/ Save c * local variables real TT c * TT=T TT=max(TT,Tmin) TT=min(TT,Tmax) if (TT.le.T0) then cMn = a1*TT + a2*TT**2 + a3*TT**3 elseif (TT.gt.T0 .and. TT.le.T1) then cMn = b0 + b1*TT+ b2*TT**2 + b3*TT**3 + b4*TT**4 elseif(TT.gt.T1) then cMn = AA*TT**na /(a+TT)**na + BB*TT**nb / (b+TT)**nb + & CC*TT**nc /(c+TT)**nc endif c * return end c ###################################################################### real function kMn(T,B,RRR) c ###################################################################### c # c # Thermal conductivity of Manganese c # c # Range: 2 <= T <= 300 K, no B dependence, no RRR dependence c # c # References c # ---------- c # C.Y. Ho, R.W. Powell, P.E.Liley, Thernal Conductivity of the c # Elements, J. Phys. Chem. Ref. Data, 1 (2), 1972 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 # kMn x thermal conductivity W/m K c # c # c # Author : L.Bottura at Cryosoft c # Version: 1.0 October 2012 c # c ###################################################################### implicit none c * external variables real T,B,RRR c * fit variables real AA,a,na real Tmin,Tmax data AA / 11.15182809 / data a / 207.1275485 / data na / 0.622090779 / data Tmin / 2.0/, Tmax / 300.0/ save c * local variables real TT c * TT=T TT=min(TT,Tmax) TT=max(TT,Tmin) kMn = AA*TT**na / (a+TT)**na c * return end c ###################################################################### real function rMn(T,B,RRR) c ###################################################################### c # c # Electrical resistivity of Manganese c # c # Range: 1 <= T <= 700 K, no B dependence, based on RRR=20.8 data c # c # References c # ---------- c # P.D. Desai, H.M. James and C.Y.Ho, Electrical Resistivity of c # Aluminum and Manganese, J. Phys. Chem. Ref. Data, 13(4), 1131-1172, c # 1984 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 # rMn x resistivity Ohm m c # c # Author : L.Bottura at CryoSoft c # Version: 1.0 October 2012 c # c ###################################################################### implicit none c * external variables real T,B,RRR c * fit variables real Tmin,Tmax parameter(Tmin = 1, Tmax = 700.0) real Bmin,Bmax parameter(Bmin = 0.0, Bmax = 0.0) real RRRmin,RRRmax parameter(RRRmin = 1.5, RRRmax = 1000.0) real rho273 parameter(rho273=143.e-8) real p1,p2,p3,p4,p5,p6,p7 parameter(p1=1.600793422E-12, p2=2.478023947, p3=1.00e8, & p4=0.200418218, p5=995, p6=-0.484412321, & p7=259.7372926) c * local variables real TT,BB,R,rhozero,arg,rhoi,rhoi0,rho0,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 * transverse magneto-resistance factor - not used (no data) magr = 1.0 c * resistivity rMn = magr * rho0 c * return end