/
Eqlib.f
executable file
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Eqlib.f
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subroutine eqlib
c******************************************************************************
c This routine solves the equations of molecular dissociative
c equilibrium. the equations can include neutral and ionized molecules
c and atoms
c******************************************************************************
implicit real*8 (a-h,o-z)
include 'Atmos.com'
include 'Mol.com'
include 'Quants.com'
include 'Dummy.com'
real*8 xfic(30), xcorr(30), deltax(30), c(30,30), ans(30,30)
real*8 uu(2)
real*8 lth
integer ident(30,110)
c*****clear the arrays
iorder(1) = 0
neq = iorder(1)
tdel = (t(ntau)-t(1))/4.0 + 1.0
do k=1,30
iorder(k) = 0
xcorr(k) = 0.
do kk=1,110
ident(k,kk) = 0
enddo
enddo
c*****either read in the dissociation data for a molecular species
do jmol=1,nmol
if (amol(jmol) .ge. 100.) then
do k=1,110
if (datmol(1,k) .eq. amol(jmol)) go to 11
enddo
write (nf1out,1001) amol(jmol)
stop
11 do kk=1,6
const(kk,jmol) = datmol(kk+1,k)
enddo
c*****or read the ionization data for an atomic species
else
iatom1 = amol(jmol) + 0.0001
atom = iatom1
const(1,jmol) = xchi1(iatom1)
do kk=1,5
ti = t(1) + (kk-1)*tdel
it = ti
do jj=1,2
att = atom+0.1*(jj-1)
if (partflag(iatom1,jj) .gt. 0) then
uu(jj) = partnew(att,jj,it)
else
uu(jj) = ucalc(att,it)
endif
enddo
const(kk+1,jmol) = uu(2)/uu(1)
enddo
endif
enddo
if (molopt .ge. 2)
. write (nf1out,1002) (amol(i),(const(j,i),j=1,6),i=1,nmol)
c*****set up the molecular equilibrium array. each element of array
c*****'ident' contains the identifier (subscript of an element of
c*****array 'amol') of an ion or a molecule. the neutral atom is always
c*****understood, but is not explicitly contained in 'ident'.
nmax = 1
do jmol=1,nmol
atom = amol(jmol)
2 call sunder(atom,iatom1,iatom2)
do k=1,30
if (iatom1 .eq. iorder(k)) go to 4
enddo
neq = neq + 1
iorder(neq) = iatom1
ident(neq,1) = jmol
go to 6
4 do kk=1,nmax
if (ident(k,kk).eq.0 .or. ident(k,kk).eq. jmol) go to 7
enddo
nmax = nmax + 1
kk = nmax
7 ident(k,kk) = jmol
6 if (iatom2 .ne. 0) then
atom = iatom2
go to 2
endif
enddo
if (molopt .ge. 2) then
do i=1,neq
dummy1(i) = iorder(i)
enddo
write (nf1out,1003) (dummy1(i),i=1,neq),(amol(i),i=1,nmol)
endif
c*****now begin the loop that goes through all the atmosphere tau layers
do 21 kev=1,ntau
c*****calculate *xfic* and make a first guess at *xatom*
i = ntau + 1 - kev
lev = i
tk = 1.38054d-16*t(i)
do k=1,neq
korder = iorder(k)
xfic(k) = xabund(korder)*nhtot(i)
enddo
if (i .lt. ntau) then
do k=1,neq
xatom(k) = xatom(k)*nhtot(i)/nhtot(i+1)
enddo
else
do k=1,neq
xatom(k) = xfic(k)
enddo
endif
c*****compute the number of molecules:
c*****Here is some information about the equilibrium constants.
c*****The equilibrium constants, Kp, are defined as follows:
c
c
c P(A)*P(B) N(A)*N(B)
c Kp(AB) = --------- = kT--------- =
c P(AB) N(AB)
c
c 2*pi*kT 3/2 M(A)*M(B) 3/2 Q(A)*Q(B)
c = kT*(-------) * (---------) * --------- * exp(-D(AB)/kT)
c h^2 M(AB) Q(AB)
c
c
c*****MOOG uses: n(AB)/n(A)n(B) = kt/Kp
c
c Kp - dissociation constant, Q - partition functions, M - masses
c P - partial pressures, N - number densities, T - temperature,
c D - dissociation energy, h - plank constant. Remember to use
c masses in grams (1 amu = 1.660540E-24 g) and energy in ergs
c (1 eV = 1.60219E-12 ergs). Also, k = 1.38066E-16 erg/K,
c h = 6.626076E-27 erg s, and pi = 3.1415926536.
27 do jmol=1,nmol
atom = amol(jmol)
if (atom .ge. 100.) then
if (t(i) .gt. 12000.) then
xmol(jmol,i) = 1.0d-20
else
xmol(jmol,i) = 1.
count = 0.
37 call sunder(atom,iatom1,iatom2)
count = count + 1.
do k=1,neq
if (iorder(k) .eq. iatom1)
. xmol(jmol,i) = xmol(jmol,i)*xatom(k)
enddo
if (iatom2 .ne. 0) then
atom = iatom2
go to 37
endif
hion = 10.0*(amol(jmol) - dint(amol(jmol)))
th = 5040./t(i)
lth = log10(th)
xmol(jmol,i) = xmol(jmol,i)*(((1.38066d-16 * t(i))**
. (count-1.0))/(10.0**(const(2,jmol)+(const(3,jmol)*
. lth)+(const(4,jmol)*(lth**2))+(const(5,jmol)*
. (lth**3))+(const(6,jmol)*(lth**4))-
. (const(1,jmol)*th))))/(ne(i)**hion)
endif
c*****compute the number of ions:
else
delt = (t(i)-t(1))/tdel
m = min0(idint(delt)+2,5)
delt = delt - idint(delt)
u1 = const(m,jmol) +
. (const(m+1,jmol)-const(m,jmol))*delt
iatom1 = atom
do k=1,neq
if (iorder(k) .eq. iatom1) xmol(jmol,i) =
. 4.825d15*u1*t(i)**1.5/ne(i)*dexp(-1.1605d4*
. const(1,jmol)/t(i))*xatom(k)
enddo
endif
enddo
c*****compute matrix *c*, which is the derivative of each equation with
c*****respect to each atom.
do k=1,neq
deltax(k) = -xfic(k) + xatom(k)
do kk=1,neq
c(k,kk) = 0.
enddo
c(k,k) = 1.
korder = iorder(k)
do kk=1,neq
kderiv = iorder(kk)
do 28 j=1,nmax
jmol = ident(k,j)
if (jmol .eq. 0) go to 28
call discov(amol(jmol),kderiv,num2)
if (num2 .eq. 0) go to 28
call discov(amol(jmol),korder,num1)
c(k,kk) = c(k,kk) + xmol(jmol,i)*num1*num2/xatom(kk)
if (k .eq. kk) deltax(k) = deltax(k) + num1*xmol(jmol,i)
28 continue
enddo
enddo
c*****calculate array 'xcorr', the change in 'xatom'. array 'xcorr' is
c*****'deltax' multiplied by the inverse of 'c'
call invert (neq,c,ans,30)
do k=1,neq
x1 = xcorr(k)
xcorr(k) = 0.
do kk=1,neq
xcorr(k) = xcorr(k) + ans(k,kk)*deltax(kk)
enddo
enddo
c*****decide if another iteration is needed
iflag = 0
do k=1,neq
c*****here oscillations are damped out
if (x1*xcorr(k) .lt. -0.5*x1**2) xcorr(k) = 0.5*xcorr(k)
x1 = xatom(k)
if (dabs(xcorr(k)/xatom(k)) .gt. 0.005) iflag = 1
xatom(k) = xatom(k) - xcorr(k)
c*****fix element number densities which are ridiculous
if (xatom(k).le.0.0 .or. xatom(k).ge.1.001*xfic(k)) then
iflag = 1
xatom(k) = 1.0d-2*dabs(xatom(k)+xcorr(k))
endif
enddo
if (iflag .ne. 0) go to 27
c*****print out atomic and molecular partial pressures. *xamol* is the
c*****number density for each neutral atom
do k=1,neq
xamol(k,i) = xatom(k)
patom(k) = dlog10(xatom(k)*tk)
enddo
do jmol=1,nmol
pmol(jmol) = dlog10(xmol(jmol,i)*tk)
enddo
if (molopt .ge. 2) then
pglog = dlog10(pgas(lev))
write (nf1out,1004) lev,int(t(lev)+0.001),pglog,
. (patom(i),i=1,neq), (pmol(i),i=1,nmol)
endif
c*****here the big loop in tau ends
21 continue
return
c*****format statements
1001 format ('I do not know this molecule: ',f10.0)
1002 format (/'INPUT EQUILIBRIUM DATA:'/1x, 'species', 2x,
. 'D0/Chi ', 3x, 'const1', 6x, 'const2', 6x,
. 'const3', 6x, 'const4', 6x, 'const5'/
. (0pf8.1, f8.3, 1p5d12.4))
1003 format (/'MOLECULAR EQUILIBRIUM SOLUTIONS: (log partial',
. ' pressures listed under names)'/
. 2x,'i',5x,'T',2x,'Pgas',8f8.1/(15x,8f8.1))
1004 format (i3,i6,f6.2,8f8.2/(15x,8f8.2))
end