C ###################################################################### C # C # TITANIUM PROPERTIES PACKAGE C # --------------------------- C # Contains functions for the calculation of the thermal and electrical C # properties of Titanium (Ti) C # C ###################################################################### c ###################################################################### real function dTi(T) c ###################################################################### c # c # Density of Titanium c # c # Range: 0 <= T <= inf K c # c # References c # ---------- c # http://en.wikipedia.org/wiki/Titanium c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # dTi 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 * dTi = 4506.0 c * return end c ###################################################################### real function cTi(T) c ###################################################################### c # c # Specific heat of Titanium c # c # Range: 1 <= T <= 300 K c # c # References c # ---------- c # CryoComp version 3.0 c # c # variable I/O meaning units c # -------------------------------------------------------------------- c # T x absolute temperature K c # cTi x specific heat J/Kg K c # c # Author : L.Bottura & C. Rosso at Cryosoft c # Version: 3.3b October 2012 c # c ###################################################################### implicit none c * external variables real T c * fit variables real T0 real AA1,BB1,CC1,DD1,a1,b1,c1,d1,na1,nb1,nc1,nd1 real AA2,BB2,CC2,DD2,a2,b2,c2,d2,na2,nb2,nc2,nd2 real Tmin,Tmax data T0 / 27.24124722 / data AA1 / 221.0632567 / , BB1 / 0.012692317 / , & CC1 / -3074.905099 / , DD1 / -0.005859014 / data a1 / 0.165330317 / , b1 / 70.13933338 / , & c1 / 0.12134103 / , d1 / 34.76887014 / data na1 / 4.177013494 / , nb1 / 3.008257379 / , & nc1 / 6.956115796 / , nd1 / 3.492776049 / data AA2 / 6.20e-07 / , BB2 / -0.295159486 / , & CC2 / -7.58e-06 / , DD2 / -5.05e-05 / data a2 / 22.10080159 / , b2 / 0.176368155 / , & c2 / 96.26393089 / , d2 / 6.199487173 / data na2 / 7.000555277 / , nb2 / 6.785978929 / , & nc2 / 4.173913655 / , nd2 / 6.964458443 / 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 cTi = AA1*(TT/(1+TT/a1))**na1 + BB1*(TT/(1+TT/b1))**nb1 + & CC1*(TT/(1+TT/c1))**nc1 + DD1*(TT/(1+TT/d1))**nd1 else cTi = AA2*(TT/(1+TT/a2))**na2 + BB2*(TT/(1+TT/b2))**nb2 + & CC2*(TT/(1+TT/c2))**nc2 + DD2*(TT/(1+TT/d2))**nd2 endif c * return end c ###################################################################### real function kTi(T,B,RRR) c ###################################################################### c # c # Thermal conductivity of Titanium c # c # Range: 1 <= T <= 300 K, no B dependence, no RRR dependence 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 # kTi x thermal conductivity W/m K c # c # Author : L.Bottura & C. Rosso at CryoSoft c # Version: 3.3a October 2012 c # c ###################################################################### implicit none c * external variables real T,B,RRR c * fit variables real AA,BB,CC,DD,a,bx,c,d,na,nb,nc,nd real Tmin,Tmax data AA / 76813749.1 / , BB / -399771.24 / , & CC / 86.5283573 / , DD / -48.398841 / data a / 46.79349727 / , bx / 17.22226266 / , & c / 4.566204438 / , d / 0.153605786 / data na / 3.77004774 / , nb / 3.84520961 / , & nc / 2.66372800 / , nd / 3.57572912 / data Tmin / 1.0/, Tmax / 300.0/ save c * local variables real TT c * TT=T TT=max(TT,Tmin) TT=min(TT,Tmax) kTi = AA*TT /(a+TT)**na + BB*TT**2/(bx+TT)**nb + & CC*TT**3/(c+TT)**nc + DD*TT**4/(d+TT)**nd c * return end c ###################################################################### real function rTi(T,B,RRR) c ###################################################################### c # c # Electrical resistivity of Titanium c # c # Range: 1 <= T <= 1100 K, no B dependence, based on RRR=15.8 data c # c # References c # ---------- c # John T. Milck, ELECTRICAL RESISTIVITY DATA AND BIBLIOGRAPHY ON c # TITANIUM AND TITANIUM ALLOYS, Air Force Materials Laboratory, c # March 1970 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 # rTi 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 = 1100.0) real Bmin,Bmax parameter(Bmin = 0.0, Bmax = 0.0) real RRRmin,RRRmax parameter(RRRmin = 1.5, RRRmax = 1000.0) real rho273 parameter(rho273=3.14e-7) real p1,p2,p3,p4,p5,p6,p7 parameter(p1=1.645e-13, p2=1.8523, p3=1.00e6, & p4=-1.101, p5=100, p6=-1.9645, p7=94.71) 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 rTi = magr * rho0 c * return end