AECL-4582
ATOMIC ENERGY §KS& L'ENERGIE ATOMIQUEOF CANADA LIMITED \m£9 DU CANADA LIMITEE
SOLUBILITY OF NICKEL AND COBALT FERRITE
IN WATER UP TO 300°C
by
R.E. VON MASSOW, G.R. SULLIVAN and G.N. WAUGH
Whi teshe l l Nuc lea r Research Establ ishment
P inawa, Man i toba
June 1975
ATOMIC ENERGY OF CANADA LIMITED
SOLUBILITY OF NICKEL AND COSALT FERRIlf
IN WTER UP TO 3OQ°C
by
R.E. von Wassow
G.R. Sullivan*
G.N. Wauoh*
*Ci.-<>p stiidents
•Jhiteshell NucUar Research Establ
Pinawa, Manitoba ROE 1L0
June 19 75
Solub i l i té du f e r r i t e de cobalt et de nickeldans Teau jusqu'à 300°C
par
R.E. von Massow, G.R. Sullivan* et G.N. Waugh*•Etudiants en stage de co-op.
Résume
On s'est servi des données thermodynamiques dis-ponibles dans les publications pour calculer les concentra-tions d'ions métalliques dans une solution aqueuse en équi-libre avec les spinelles NiFe2Û4 et CoFe20 4 a des températuresallant jusqu'ï 300°C en fonction du pH st de l'H2 dissous.Les résultats font l'objet de commentaires en rapport avecle transport des produits de corrosion dans les centralesnucléai res.
L'Energie Atomique du Canada, LimitéeEtablissement de Recherches Nucléaires de Whiteshell
Pinawa, Manitoba, ROE 1L0Juin 1975
AECL-4582
SOLUBILITY OF NICKEL AND COBALT FERRITE IN WATER
UP TO 300°C
by
R.E. von MassowG. R. Sullivan*
G. N. Waugh*
ABSTRACT
Thermodynamic data available in the literature are useii 10
compute metal ion concentrations in aque.>us solution in equilibrium with
the spinels NiFe^O^ and CoFepO,, at temperatures up to 300°C as a function
jf pH and dissolved H?. The results are discussed in relation to the
transport of corrosion products in nuclear power plants.
*Co-op students
Chemical Technology Branch,
Atoaic Energy of Canad.i Limited
Vhlteshell Nuclear Research Establ i shiner.t
Pinawa, Manitoba ROE 1L0
197 5
CONTFNTS
P.icr
1. INTRODUCTION
2. THEORY
3. METHOD OF CALCULATION
3.1 Determination of the Stable Phase of M3.2 Other Ion Concentrations
4. INPUT DATA
5. RESULTS
6. DISCUSSION
7. APPLICATION OF TABLES
REFERENCES
TABLES
APPENDIX A
APPENDIX B
APPENDIX C
- 1 -
1. INTRODUCTION
The primary cooling water in nuclear reactors corrodes
the metals it comes in contact with and some of the corrosion products
are dispersed throughout the circuit. If deposited in-core, these
corrosion orodmts can foul fuel and decrease heat transfer. Subse-
quently, activated corrosion products can redeposit out-core
and create undesirable radiation fields. The movement of corrosion
products is thus of considerable importance to the reactor designer
and reactor operator. Movement may occur in a particuLate or a
solution state. We have calculated ;he equilibrium concentration of
ions in water in contact with some spinels and metal oxides, under
various conditions, in order to provide data to enable us to better
understand solution transport in reactors.
Dissolution of a metal oxide in water generally comprises
a number of chemical reactions resulting in the formation of various
ionic species. The hydrogen and oxygen concentration as well as pH and
temperature of the water control the equilibrium concentration of the
ions.
The solubility of a metal oxide is defined as the sum
of the equilibrium molar concentrations of the various ions. The
solubility of many metals and metal oxides in water has been calculated
by Macdonald et al . The same treatment has been largely followed
in this work and has been extended to two spinels, NiFejO^ and CoFe,(>...
Corrosion products in practical systems frequently consist of spinels
dxti(O
, where N i s a mixture of Fe, Ni, Co, etc . and M a
mixture of Fe, Cr, Al, etc .
We have limited ourselves to the treatment of stoichion**ri<
NiFe2Oi, and CoFejOi,, disregarding any non-stoichiometric spinels althouRh
they are known to exist.
- 2 -
In accordance with the phase rule, if the solution composition
in equilibrium with an oxide is set by temperature, pll, and hydrogen concen-
tration, the addition of another component adds another degree of freedom
and requires one more specification before the solution composition is
singularly defined. Thus for stoichiometric, two-metal spinels, only the
naxima and minima of the individual metal ion concentrations can be given.
Any solution which falls within these extremes and satisfies the solubility
product of the spinel is in equilibrium with it.
The solution maxima and minima have been computed for chemistry
conditions which are relevant for Canadian power reactors. They should be
helpful'7»8/ in the interpretation and prediction of activity transport.
Some uncertainties persist, as pointed out in the text. As better experi-
mental data become available5 the computation will be up-dated. However,
to our knowledge, the presented tables give the best available solubility
data.
- 3 -
2. THEORY
The highlights of Macdonald's treatment are recalled:
1. Metals and metal oxides react with water containing dissolved
hydrogen and hydrogen ions. In doing so, they form a varietv of
ions of different degrees of hydrolyzation and even of different
oxidation states. The relative concentration of each ion tvpe
depends on the pH, dissolved hydrogen concentration and
temperature of the water.
2. The equilibrium concentration of each ion may be calculated if tlio
standard free energy of the reaction leading to its formation is
known since
AG = 0 = AG - RT £a t P r o d u c t Sjo [Reactants]
3. To obtain the standard free energy of the reac-ion as a function
of temperature, the free energy, entropy and specific heat of the
products and reactants are required. For solid phases, these data
are generally available. For ionic species, some entropies have to
be estimated by empirical equation. The variation of the entropies
with temperature is predicted by the Criss and Cobble correspondence
principle w'uich says that the variation with temperature is the
saae for all ions of one type. With these aids, the standard free
energies of reaction are computed.
To simplify the calculation, the free energy of the elements is not
taken to be zero at all temperatures, as is conventional, but rather
a free energy variation is calculated based on zero free energy at
25°C and the specific heat of the element. Since the standard free
energy of reaction is the difference between the free energies of
products and reactants, the above deviation from convention cancels
out. The obtained standard free energies of reaction have the
conventional values.
- 4 -
4. From the standard free energy of reaction, the equilibrium
concentration of each ion may be calculated if the hydrogen
activity and pH of the solution are given;
M2O3 + H2 + 4H+ = 2M** + 3H2O (1)
AG = - RT £n — L \ (2)[H2][H"V
(where [ ] denotes activity; the activity of solidphases and water are assumed equal to unity)
5. The solubility is the sum of the equilibrium concentrations of
the individual ion species.
Thus Macdonald calculates the solubility of metal oxides.
However, if the oxide contains two or more metals, as is
the case with most spinels, solubility is not that easily defined. The
extra component provides an extra degree of freedom.
A spinel N M2 0i» may dissolve by the reaction:
TT TTT + 11 11
N n\2 0H + H2 + 6H = N + 2M + 4H2O
and the equilibrium concentrations are controlled by the equation:
AG = - RT Jin -^—Jl" J (3)
[H2][H+]6
This means that another variable has been introduced in the equation. At
constant hydrogen partial pressure and pH, the concentrations of N and1 1
M are not singularly defined but rather are related to each other by a
constant productK = [N + +] 1 / 3[M + +] 2 / 3
This is not the solubility product of the spinel, since both metals will
be present in solution as many other ionic species. Only after the
- 5 -
reactions of formation of all other ions have been considered can a
product be calculated which governs the balance in metal concentrations
in solution as determined by chemical analysis.
KsP -
The variation of the solubility product with temperature
and water chemistry conditions provides information about dissociation
or precipitation of the spinel.
The variability of the solution composition in equilibrium
with CoFezOi, is demonstrated in Figure 1. Shown are the partial molar
free energies of the metal ions in the reactions:
CoO + 2H+ -»• Co"*"*" + H20
Co + 2H+ •*• Co"*"*" + H2
+ 2H+ + V3H2 + '/sCo4"*" + 2/3Fe++ + V3H2O
+ 2H+ + V2H2 •+ Fe*4" + 3
+ 2H+ + l/3H2 •* Fe*4"
under the conditions of:
temperature 298 K
hydrogen content 446 pmol/kg H20
pH 10
Under these conditions, the sum of the partial molar free energies
'/sG. ++ + 2/3<L ++ is 56 kJ. Any two values of partial molar freeCo Fe
energies of Co4"*" and Fe44" which satisfy this equation fall on a straight
line through the point 56 kJ at 2/sFe mol fraction.
- 6 -
no1
^100
9 0
8 0
7 0
6 0
5 0
4 0
30
CoO • 2H • id*
Co + 2H* - Co* * •
\ . uMax C o "
\ \
\ \
\ \
: \
X \
\ \
~ - • • - . . ,
= ^ - — -
— • — — —
SH1n C(f+
-
l i
• H
H2
\
\
• — ~ - .
|
?°C
X
\
-.—
^—
i
\
N\
\\: \<^\
^ ^
• i
+
+0,Urn
+
o
t
+
+
\l/3
C
oFe,
|
\
\
\
\\NV\Slin F^+
1 1
Fe
1/2
1/3
+ ZH* - fi*'
Fez03 • 2H+ +
Fe304 + ZH* *
Co O.I 02 Q3 Q4 Q5 0.6 0.7 0.8 0.9 Fe
FIGURE 1: REACTION FREE ENERGIES AT 298K, W8 pROL H 2/KG ^ 0 AND PHIOVERSUS IRON METAL ATOP! FRACTION
- 7 -
However, the maximum G ++ is given by the reaction
Co + 2H+ = Co4"* + H2
since under these conditions, cobalt metal is the stable cobalt phase.
The maximum G ++ is given by the reaction
VaFesO., + 2H+ + V3H2 = Fe++ + "/sHjO
Thus the variability of the solution composition of CoFe201< is limited by
the stability of the separate metal phases.
If the partial molar free energy for the spinel reaction falls
above the line connecting the two separate stable phases, the spinel is
unstable and will not form. This occurs with NiFe2Oi4 at 298 K and
446 umol Ih/kg H2O. Iu this case, there are no minimum partial molar free
energies, as indicated in Table 7, where minimum concentrations are not
given when NiFejOi, is unstable.
- 8 -
3. METHOD OF CALCULATION
The object of this computation is to establish the solution
composition limits of NiFe2Oi» and CoFeaOt, for a wide range of water
chemistry conditions which are of interest in reactor technology.
Variables
TEMPERATURE
Temperature is varied from 25 to 300°C with smaller Intervals
between 200 and 300°C.
pB
The pH at 25°C is varied from pH 9 to 12 in intervals of 0.2
from 9.4 to 10.6. The variation of pH with temperature was calculated
on the basis of constant L10H content. The method of calculating the pH
was taken from Wright et al .
The partial pressure of hydrogen as a function of temperature
was calculated on the basis of constant hydrogen content for use in out-
core conditionsi and on the basis of constant oxygen content for in-core(12)
use
The concentrations used were:
Hydrogen 0.446 mmol/kg (10 cm3/kg) Tables 6,8,14,16 andleft side of 7,9,15 and 17
0.0446 mmol/kg (1 cm3/kg) (
and 0.00446 mmol/kg (0.1 cm3/kg) [Tables 1 0 " 1 3
OxTfien °'125 Wmol/kg right side of Tables 7,9,15,17.
- 9 -
Since all equations used were written on the basis of hydrogen, the oxygen
content was converted to hydrogen partial pressure assuming equilibrium^L K
The resulting hydrogen partial pressure fits the equation:
log P u (Pa) = -92.86 + 0.2545T + 0.19A27xl0~3T2
112
The computational process which leads to the solution composition
of maximum M and minimum N in equilibrium with a spinel NMjOi, is described
below.
3.1 DETERMINATION OF THE STABLE PHASE OF M METAL
Since the solution composition extremes are determined by the
free energy of the most stable separate metal phases (Figure 1) for each
of the two component metals, the stable phase under a particular set of
conditions has to be determined. This is done by calculating the equilibrium
ion concentration of just one ion; we chose M"*"*" for all possible phases. The
one with the lowest equilibrium M*"4" concentration is the stable phase.
For instance, for the reaction
M30,, + Stf1" + H2 -> 3M4"4" + 4H2O
the standard free energy of reaction is calculated and the M** concentration
determined using
AG = 0 = AG - RT HnfH+J6 x
where [H**] and [H?] have been set above.
- 10 -
I I
The equilibrium M concentration of the stable M phase becomes the
base for the calculation of the solution composition with M at maximum
and N at minimum concentration.
3.2 OTHER ION CONCENTRATIONS
To obtain the total metal concentration in solution,
the concentration of all other ions is required. There may be:1
cations of higher oxidation state M
oxy-anions M02~, M(0H)3~etc.
acid-oxyanions
hydrolyzed cations M(0H)+, M(0H)"H"
and others, depending on the metal.
Here they were all considered to be formed by reaction with
the M ion. The reactions considered for iron and nickel are listed in
Table 1.
As an example, the concentration of Fe(OH) icn may be
calculated from the standard free energy of reaction and the Fe and H
ion concentrations by the relationship
AG - 0 - AG - RT
The concentration of N ions is related to that of M ions only with respect
to the spine] dissolution reaction
NM20i, + 6H+ + H2 - N4* + ZM*"4" + 4H2O
which gives the relation between [N ] and [H ] as
A G - 0 - A G o - RTen
The other N ion concentrations are then calculated from the [K**]
concentration and the respective standard free energy of reaction.
- 11 -
TABLE 1
IONIC REACTIONS CONSIDERED FOR NICKEL AND IRON
Ni(OH)+ + H+
HNiO2~ + 3H+
Fe(OH)"*" + H+
2H.0 - HFeO2" + 3H+
•4- I I I
2H+ - — +++
2Fe+
2Fe+
2H+
2Fe + 2H2O - 2Fe(OH)
- 12 -
4. INPUT DATA
The input data for the calculation of standard free energies
of reaction by means of the FREB computer program (Appendix B) are
listed in Table 2 and Table 3. In general, they were taken from
Macdonald^2 '3>l4'. Exceptions are the standard free energy of Fe(OH)+
where the value of the Bureau of Standards^16) was chosen, and HFe(>2~,
where a value of -411.6 kJ was chosen, since these agree best with the
few experimental observations of magnetite solubility^22*23'.
The Criss and Cobble Constants^9' have originally been
determined only up to 150°C, 100°C for acid oxy-anions. In this report
we expressed these constants as a linear function of temperature and used
the resulting expressions, listed in table 3, to extrapolate to 300°C.
Ine standard free energy of reaction, which is part of the
output of FREB and is the input to the solubility program SO.F4 (Appendix A).
is expressed as a function of temperature as
AG = A + BTlogT + CT
The reactions and the input data A, B, and C are listed in Table 4.
- 13 -
TABLE 2
THERMODYNAMiC OATA FOR THE Ni-Fe-H 0 AND Co-Fe-H ,0 SYSTEMS
Species
H+ ;H2B 2 0
S i
a l t . *NiO :Si(OH)
s i - ;Si(OH)
1 H KiOT; SiFe26.,
i1
Co•It .*
CoO1 Co,0^
Co(OH);' alt.*
Co**CoOH*HCO05Co*JCoFe^O,,
alt.*
Fe1 FeO
•It.*
alt.*Fe z O 3
* " «•re{«rHFeOj
FeO 2 ~
t e fOfl)Fe(O»)?+reOh - -
StandardFree Energyof Formation
OcJ nol"1)
00
- 237.3
00
- 211.85- 4i7.57
- 45.64- 227.76- 349.45- 973.85
0
- 214.36- 774.56- 454.69- 462.64- 54.53- 235.72- 82.97- 13*.0-1033.1
0245.3
-1016.14
- 7*2.74- 78.92- 273.82- 411.56- 295.59- 4.61- 224.58- 438.36- 467.58
o
lef.
141414
16
1616
1616
416
16
16161619
1633
1416
1616
16
16
161616
2161616
2
Standard Entropy
(U*1 nol"1)
-20.9341.307
69.96
29.89
Ref.
141414
1629.81 i 1538.02 1687.92 ! 16
i-170.82- 92.11
44
62.8 13131.9 ! 16
i
30.06
53.0102.5879.5562.06
-151.91-136.91- 83.3ft-Ufi.44
16
16161620
163
1 314
134.81 16
27.357.5'J58.82
146.54151.5687.46
-179.61- 50.24
62.80- 56.45-378.91-191.76- 46.05
52.67
161615161516
161613
13
1616
713
Heat Capacity ConstantsC =
PA + BT +
(J sol"1 K"1)A
_
27.330.02
17.032.66
-20.8993.37
145.7169.6167.5
19.8521.3948.32
129.12"33.37
152.94131.5
12.7317.548.891.6
98.35
B
_
3.2710.72
29.48- 1.97147.34
1
1
,6.75U.32S.54
71.51
141.5
31.724.88.37
201.8
77.87
CT ;'
C
-
0 .50.33
0- 5.59
16.29 ;
- O.BB1.67
-23.95
2.51
- 2.81
-14.86
i
Ref.
41515
1
1 7 «
151716
9Q
9161519
1 7 i15 11 5 j1 5 '•
18 i
1« i9 ;9 i9
16 ,19
i
i1715 116 ,
1 16 i1 i! 16
9
9
9
9999
• alt.Means data froe» other sources, which have not heen used.
- 14 -
The temperature dependence of the dissociation constant
of water was taken from Fisher et al^21' and expressed as:
pKW = 50.253 - O.274T + 7.662xHr'*T2 - I.OUXIO-'T1* + 5.
for 298<T<573
The dissociation constant of LiOH was taken from Wright et al
and expressed as:
\iOll " 7.137 - 0.05T + O.996xlO"'fTz + 0.106xlO"6T3 - 0.185x10"*^ + n.l21xlO~12T
for 298<T<573.
TABLE J
CRISS ANO COBBLE*9) CONSTANTS ANO THEIR EXTRAPOLATION
Constants In S»a+bS0
ton Type
Simple cation
Simple anionand OH"
Oxy-anlons
Ac id-Oxy-.intons
J/nol K
a
b
a
b
a
b
a
b
Temperature In Degrees Celsius
25
0
1.000
0
1.000
0
1.000
0
1.000
60
16.3
0.955
-21.4
0.969
-58.6
1.217
-56.5
1.380
100
43.1
0.876
-54.5
1.000
-129.8
1.476
-126.9
1.894
150
67.8
0.792
-89.2
0.989
-194.3
1.687
(209)
(2.381)
200
(97.6)
(0.711)
(-126.4)
(0.981)
(-280.5)
(2.020)
(293)
(2.960)
250
[126J
[.6241
[-162.5]
[0.9711
1-3561
12.3]
I-377J
[3.52]
300
[1521
I.540J
[-185J
[0.961]
[-440]
[2.641
[-4611
(4.071
ExtrapolationFormula
a—169+0. 561T
b-1.5-.OO169T
a-21fl.9-0.729T
b-1.03B8-O.OO013T
a-467.7-l.5BT
b—O.6828+. OO57T
O-5O1-1.68T
b=-2. 32+0.01H7T
( ) - values extrapolated by Criss and Cobble
[ ] - values extrapolated by authors
- 16 -
TABLE 4
STANDARD FREE ENERGY OF REACTION
(J) = A + BTlogT + CT (298 <T <573)
Reaction
F6304 + 6H+ + H2 = 3¥e** + 4H2O
Fe2O3 + 4H+ + H2 = 2Fe
4+ + 3H2O
Fe44" + H2O = Fe(OH)+ + H +
Fe44" + 2H2O = HFeO2 + 3H
Fe44" + 2H2O = FeO" + 4H+
2Fe"H" + 2H+ = 2Fe'K+ + H2
2Fe++ + 4H2O = 2Fe(OH)| + H2 + 2H+
2Fe++ + 2H2O = Fe2(OH)f4 + H2
BFe""" + 8H2O = 2Fe3(OH)t5 + 3H2 + 2H
+
2Fe++ + 2H2O = 2Fe(OH)++ + H2
CoFe204+H2+6H+ = Co44" + 2Fe++ + 4H2O
NiFe2O4+H2+6H = Ni + 2Fe + 4H;>0
Co + 2H+ = Co""" + H2
CoO + 2H+ = Co4"4" + H2O
Co 301, + H2 + 6H+ = 3CO4"1" + 4H20
Co (OH) 2 + 2H+ = Co44" + 2H20
Co""" + H2O = Co (OH)+ + H +
Co44" + 2H2O = HCo02 + 3H+
ZCo""" + 2H+ = ZCo 4^ + H2
Si + 2H+ = Ni44" + H2
NiO + 2H+ = Ni44" + H2O
Ni(OH)2 + 2H+ » Ni44" + 2H2O
tU4"*" + H2O = Ni(OH)+ -»• H +
Ni44" + 2H2O = HN1O2 + 3H
A
-3.0079xl05
-2.2099x105
+4.5018x10"
+2.6275x105
+3.9859xlO5
+1.0426x105
-1.5376X101*
+2.0431xl05
+6.3111xlO5
+2.0408x105
-2.3454xlOb
-3.O2739xlO5
-4.6887xlO4
-1.0095xl05
-4.2691xlO6
-9.4691X101*
+9.9234x10
+2.4181xlO5
+3.1758xlO5
-4.57O7X1O1*
-9.7340x10^
-9.5716X101*
+3.1O43X1O4*
+2.8629xlO5
B
-1.1652xlO2
-1.0275xl02
-52.07123xlO:
+8.3541xlO2
+1.3118x103
+1.5505xl02
-7.2443xl02
+6.1005xl02
+2.O346xlO3
+2.3960xl02
-7.8052
-1.1640xl02
+6,9960x10
+2.2983x10
-6.8184x10
-5.7157x10
-2.3753xlO2
+5-0Sllxl02
+1.0816xl02
+4.9774x10
+3.1931
-8.0487x10
-1.3699xlO2
+8.1742xlO2
C
+7.2757xlO2
+5.6935xlO2
+I.2010xl02
-2.^716xlO3
-3.7167xlO3
-2.3463xlO2
+2.616OxlO3
-1.6394xlO3
-5.4378xlO3
-6.6244xl02
+3.75913xlO2
7.0347xl02
-1.9826xlOz
+2.2254x10
+4.6718xlO2
+2.1515xlO2
+7.7507xl02
-1.46O7xlO3
-6.8785x10
-1.2283xlO2
+8.0200x10
+2.7162xlO2
+4.1976xlO2
-2.4095xl03
- 17 -
5. RESULTS
The results of the computation are listed in Tables 6 to 17.
An overview of their presentation is given in Table 5.
Solubility products in the form (N)l' 3(M) 2^ 3, where N and M
are the sum of the ion concentrations, are presented as a function of
temperature and pH. They are thus calculated per mol of transition metal
and can be compared readily vith other solubility data. The solubility
products are presented in the even-numbered tables.
Solubility data for NiFezO). or CoFeaOi, are presented in the
odd-numbered tables which give the maximum and minimum concentration for
both constituent metals as follows:
Columns 1 and 15
Columns 2 - 7
Columns 2 - 4
Column 2
Column 3
Column 4
Columns 5 - 7
Column 5
Column 6
Column 7
Column 8
Columns 9 - 1 4
Columns 9 - 1 1
Columns 12 - 14
temperature• C
apply to the higher of two hydrogen concentrations
composition of a solution with nickel or cobalt atmaximum concentration
the nickel or cobalt phase which is stable
total maximum nickel or cobalt concentration of thestable nickel or cobalt phase (column 2)
total minimum iron concentration
composition of a solution with iron at maximumconcentration
the stable iron phase
the total minimum nickel or cobalt concentration
the total maximum iron concentration of the stableiron phase
the pHj for which the computation was made
repeat of the left hand side for the lower of thetwo hydrogen contents
composition of solution with nickel or cobalt atmaximum concentration
composition of solution with iron at maximumconcentration
- 18 -
TABLE 5
WHERE TO FIND THE RESULTS
(Table numbers are given for the function listed for thespinel at different gas contents and pH variations)
pHdependent on T
pH constant
Gas Contentin
Umol/kg H20
H2
Oz
H2
Hz
Hz
02
446
0.125
44.6
4.46
446
0.125
Solubility Product
m¥e20tt
6
6
10
10
14
14
CoFe20i»
xable
00 C
O
12
12
16
16
Solution Maxima and Minima
NiFe2O<»
Number
7 left
7 right
11 left
11 right
15 left
15 right
CoFe2Oi,
9 left
9 right
13 left
13 right
17 left
17 right
- 19 -
6. DISCUSSION
The equilibrium solution concentrations in contact with nickel
or cobalt ferrite ha\2 not been reliably measured for reactor coolant condi-
tions. The reason is that these measurements are experimentally difficult
and time consuming, because of the very low solubilities involved. However,
in reactor coolants, even small solubility variations can lead to signifi-
cant material transport due to the high flow rates involved.
Indirect experimental results are available which, with some
extrapolations and some assumptions, allow the theoretical calculation of
the solubility tables as presented.
Most directly, the data had to agree with determination of the
solubility of magnetite by Sweeton and Baes 2 2 and Styrikovich et al^ 2 3 .
For this reason, the partial molar free energy for the FeOH ion was
taken from the Bureau of Standards^16- values and not chat suggested by
Macdonald*2). At high pH, the two investigators above^22»23^ do not agree
well with each other, neither do they agree with the standard free enerpv
valueOS) for the HFeO2~ ion if it is assumed that the entropv of this ion
follows the Criss and Cobble^9' correspondence principle. Rather thar discar-
ding this principle for this ion, we chose to decrease the accepted^J 6 •* partial
molar free energy for HFeO2~ D V 8X to fit the high temperature solubility data
of Styrikovich^23^. With this base on high temperature experimental evidence,
we can offer the tables of solubility data with some confidence as guidelines
to corrosion product transport problems. A computer output which lists the
concentration of each ion is available but has not been included in this
report.
If the tables are to be used as suggested in the following
pages, the following limitations should be realized:
- 20 -
1. Under the non-equilibrium conditi ns due to radiolysis in-core,
the solubility is assumed to be controlled bv the oxygen
concentration and not by the hydrogen concentration. An oxygen concen-
tration of 0.125 pm/kg water has been analyzed, but from Tables 7 and 9
this would result in stable haematite in-core. Under pressurized
conditions this has not been found. It may be safer to use
Tables 11 right and 13 right for in-core, since these depict a
hydrogen content reduction by a factor of 100. Under these
conditions, it is still magnetite which is stable in-core.
2. Equilibrium conditions are assumed.
3. Heavy water is assumed to behave similarly to light water.
4. In applying Tables 6 to 13, it is assumed that the pH variation
with temperature is based on the changing dissociation of water
with temperature and is not affected by other reactions. If
this assumption cannot be made, Tables 14 to 17 have to be used.
- 21 -
7. APPLICATION OF TABLES
The use of the tables can be demonstrated by the following
examples.
QUESTION 1:
The reactor primary water has a PH25 of 9.8 and a hydrogen content of
0.446 mmol/kg (10 cm3/kg). At 29C°C, the water is contained by carbon
steel. Which metal or metal oxide phases should exist at this point?
What is the solution composition?
SEARCH Refer to Table 7, out-core conditions. Turn to the table for
PH25 =9.8. Go down to ?c0°C. Since containment is by carbon
steel, the solution is expected to be iron-rich at this point.
ANSWER Fe3Oj, is the stable iron phase. NiFezO* is also stable - as
seen by the fact that the nickel concentration is also specified.
The iron concentration is 10~6«6S or 2.2 x 10"7.
The nickel concentration is 10~7*95 or 1.12 x 10~8.
The pH at the temperature is 6.69.
qUESTION 2:
If this solution is cooled to 25O°C in a nickel environment, can
precipitation be e: pected? If yes, which phase will precipitate?
SEARCH Since neither pHzs nor hydrogen content changed, the same
table applies, but since the container is a nickel alloy,
the solution can be expected to become nickel-rich.
ANSWER The nickel content rises to 10~7*21 or 6.17 x 10~e. The
nickel in contact with the water will be metallic - nickel
oxide is not stable. The iron content will drop to 10"'* v
or 2.18 x 10" . Some precipitation will be in thi- form of
nickel ferrite. The extra nickel in solution is supplied
by oxidation-dissolution of nickel metal.
- 22 -
QUESTION 3:
A solution at pths 10.0 in carbon steel pipe at 0.4A6 mmol/kg H2 content
(10 cmVkg) and 25O°C enters the core and is heated to 300cC. What
are the solution concentrations and what will dissolve or precipitate?
SEARCH Again in Table 7, but at PH25 of 10.0, we find the solution
concentration for out-cor3 conditions, iron-rich in the right
part of the left side table. For in-core conditions, the right-
hand side table is used. Also Table 6 for in-core conditions
gives the new equilibrium concentration product.
A-1SWER The solution concentration has to change from
Ni 10~7'71 or 1.95 x 10"8 to Max 10~6'81 or 1.55 x 10"7
Min 10~8*62 or 1.51 x 10~9
Fe 10~6*19 or 6.46 x 10~7 to Max 10"13*6 or 2.57 x lO"1"
Min 10"11**5 or 3.16 x 10"15.
Since in-core the containment is zirconium, the solution is
not necessarily iron-rich or nickel-rich. Although the former
nickel content falls between the new maximum and minimum, both
nickel and iron have to decrease, since they are above the now
lower equilibrium concentration product of nickel ferrite.
Table 6 out-core for pH25 10 and 250°C gives the equilibrium
concentration product of NiFe20i» as -6.70.
Table 6 in-core for pH2s 10 and 300°C is -11.93.
Nickel ferrite will precipitate because of the assumed higher
oxygen content in-core. The final solution will be neither
iron- nor nickel-rich. Its composition falls within the limits
given.
- 23 -
QUESTION 4:
How does the solution composition change at pH 10.2 280°C in a nickel
environment when the hydrogen content drops from 0.446 mmol/kg
(10 cm3/kg) to 44.6 nmol/kg (1 cm3/kg)?.
SEARCH Refer to Tables 7 and 11 of nickel ferrite data. Table 11
provides data at the reduced hydrogen content. 44.6 umol
H2/kg is on the left-hand side.
ANSWER At 0.446 mmol H2 (Table 7) at pH 10.2 280°C nickel-rich,
Ni = 10~6-7 or 2.0 x 10"7, Fe = HT 6* 6 9 or 2.04 xlO"7.
At 44.6 umol H2 (Table 11) at pH 10.2 280°C nickel-rich,
Ni = 10"6-61 or 2.45 x 10"7, Fe = 10"7'23 or 5.89 x lCT8.
NOTE: At 290°C, the nickel concentration is independent of hydrogen
concentration, since at this temperature the stable nickel
phase under both conditions is NiO, which dissolves without
an oxidizing reaction.
5. QUESTION
What is the cobalt concentration of a solution at 27O°C at pH 10.6 at
0.446 mmol Ho/kg in a carbon steel pipe? How does it change when the
hydrogen content drops to 4.46 umol H2/kg?
SEARCH Refer to Tables 9 and 13 (right).
ANSWER Initial Co 1O~13«32 or 4.8 x lO""11*, CoFe20,, stable
Final Co io"13-98 or 1.05 x 10"14, COF620,, stable
NOTE; The change in concentration occurs due to the dependance
of the stability of CoFez0i, and Fe^O^ on H2 content.
- 24 -
REFERENCES
(1) D.D. Macdonald, G.R. Shierman and P. Butler, The Thermodynamiasof Metal-Water Systems at Elevated Temperatures, 1. The Waterand Copper-Water Systems, Atomic Energy of Canada Limited. ReportAECL-4136 (1972).
(2) D.D. Macdonald, G.R. Shierman and P. Butler, The Thermodynamicsof Metal-Water Systems at Elevated Temperatures, 2. The Iron-Water System. Atomic Energy of Canada Limited, Report AECL-4137 (1972),
(3) D.D. Macdonald, G.R. Shiertnan and P. Butler, The Thermodynamicsof Metal-Water Systems at Elevated Temperatures, 3. The Cobalt-Water System. Atomic Energy of Canada Limited, Report AECL-4138 (1972),
(4) D.D. Macdonald, The Thermodynamias of Metal-Water Systems atElevated Temperatures, 4. The Nickel-Water System. Atomic Energyof Canada Limited,Report AECL-4139 (1972).
(5) D.D. Macdonald and P. Butler, The Thermodynamias of the Alwiinum-Water System at Elevated Temperatures. Corrosion Science.
(6) T.E. Rummery, Chemical, Radioahemiaal and Structural Propertiesof Corrosion Products in CANDU Power Reactors. In preparation.
(7) D.E. Minns, The Contribution of Metal/Metal Oxide Solubilities toCorrosion Product Transport in Water Cooled Nuclear Reactors, 1.The Iron System, It preparation.
(8) D.E. Minns, The Contribution of Metal/Metal Oxide Solubilities toCorrosion Product Transport in Water Cooled Nuclear Reactors, 2.The Nickel/'Iron System. In preparation.
(9) CM. Criss and J.M. Cobble, The Thermodynamic Properties of HighTemperature Aqueous Solutions, V. The Calculation of Ionic HeatCapacities up to 200°C. Entropies and Heat Capacities above 200°C.J. Amer. Chem.Soc. 86,, 5390-93 (1964).
(10) T.E. Rummery and D.D. Macdonald, The Thermodynamics of SelectedTransition Metal Ferrites in High Temperature Aqueous Systems.Atomic Energy of Canada Limited, Report AECL-4577 (1973).
(11) J.M. Wright, W.T. Lindsay, Jr. and T.R. Druga, The Behaviour ofElectrochemical Solutions at Elevated Temperatures as Derivedfrom Conductance Measurements, Beattis Atomic Power Laboratory,WAPD-TM-204 (1961).
(12) D.D. Macdonald and T.E. Rummery, The Thermodynamias of MetalOxides in Water Cooled Nuclear Reactors, Atomic Energy of CanadaLimited, Report AECL-4140.
- 25 -
(13) R-E. Connick and R.E. Powell, The Etitropy of Aqueous Oxi/anions,J . Chem. Phys. , 21, 2206-7 (1953).
(14) D.D. Wagman, W.H. Evans, V.B. Parker, I . Ha low, S.M. Bailey andD. Schamn, national Bureau of Standards No. 270-5 (1968).
(15) 0. Kubaschewski, E.L. Evans and C.B. Alcock, MetallurgicalThermochemistry, Pergamon Press (1967).
(16) D.D. Wagman e t a l . National Bureau of Standards Wo. 270-4, (1969).
(17) K.K. Kelley, Contributions to the Data on Theoretical Metal !u.rgu,U.S. Bureau of Mines, Bulletin 584 (1960).
(18) A.G. Wikjord, p r iva te communication.
(19) M. Pourbaix, Atlas of Electrochemical Equilibria, Pergamon Press(1964).
(20) M. Karapet'yants anc M.L. Earapet 'yants , Tlwrmodynamic Constantsof Inorganic and Organic Compounds, Ann Arbor Humphrey SciencePublishers (1970).
(21) J.R. Fisher and H.L. Barnes, The Ion Product Constant of Water to350°C, J . Phys. Chem., 7£, 90-99 (1972).
(22) F.H. S wee ton and C.F. Baes, J r . , The Solubility of Hapnelite •:>, ;Hydrolysis of Ferrous Ion in Aqueous Solutions at ElevatedTemperatures, J . Chen. Thermodynamics, 2 , 479-500(1970).
(23) M.A. Styrikovich, O.I. Martynova, I .F . Robyakov, V.L. Men'shlkovaand M.I. Reznikov, Tlie Solubility of ÎJaçpietite in Water at HijhTemperature in a Reducing Medium* Teploenergetika 1972, 19(9),85-87 (Thermal Engineering 19 (9) 127-130).
- 26 -
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29
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TABLE 10
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TABLE 12 (Cont 'd)
25
TEM C S T A S L E CO
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CO T T L F £ • S T « 9 L E f E T T L CO T T U F ï • >"H
[ N - C O H E ( a . 1 2 *CO « 1 C H
CO T T t CO TTL ( E
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-9.13-8 .31-7.37-6,8«-6,87-«.SB-4 = 93-6.96-7.08-7.00
-7.ae-7 .B2-7 ,04-7,a?- 7 . i e
FE304FE504FE304FEJ04FE304FE304FE304FE304FE304FE304FE304TE304FE304FE304
-16.27-16.»S-15.29-13.56-12.37-12.18-12.aa-11.8*•11.49•H.9S-11.43-11.31-11.88- l l . l t-11 . K
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9. SB».S29, se9. se«.se«.se9.se9,se9, se9.se9. se9.se9.se9. se
CQ304C0304C03Q4CQ304C0304C0304C0304C0304C0304C03t)«C0304C0304C0304C0304C0304
-12.19-12.88-11.44
-9 .53-8.12•7,89•7.68-7.4v-7 .32-7 ,16-7.82-6.89-6 .78-6 .69- 6 .6a
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•le.6?-18.69-17.B4-14.99-13.54-13.31•13.89-12.68-12.t«-12.91-12.34-12.19-12.04-11.98-11.77
-18,52•19.62-17,88
-is,ie-13,Î9•12.77-12.48-12.21-11,97-11.?»-11.SS•11.38-11.23-11.11-11.21
ï
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(2,446 HMOl H20>C O N C E N T » * T I Û N IN L O Î ( M O L E / K 6 )
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C S U ? L E CO TTL CO T T L F£ • S T » B L E FE T T L CO TTL FE • PH « STABLE CO T T L CO TTL fl • STtBLE FE TTL CO TT L FE TE* C
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COCOCOCOCOCOCOCOcoocoocooCOGcoocoocoo
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L FE •
8,64 •
7.51 •6.77 •6.39 •6.37 •6.40 •6.43 •6.48 •6.90 •6.sa •6.5e •6.52 •6.54 •6.97 •6.60 •
FE304FE304FE304FE304FE304FE304FE304FE304FE3O4FE304FE304FE304FE304FE304FE304
-17,e3-U.69-i4.se-13.86-11.§7-11.68-11.50-11.34-11.19-11.09-10.93-10.81-10.70-10.61-10.S2
-9.09-4.06-3.39-3.02•2.98•3.00-3.02-3.06•3.39-3.14-3.19-3.25-3.J1•3.38-3.45
ie.eeie.ee18.0018.0010.0218,0018.00IB.0212.8018.0010.0810.8018.0010.0018.00
C0304C0304C0304CQ304C0304C0304CC304C0304C0304C0304C0304C03C4C0304C0304C0304
12.9512.64IB,95
9.037.827,397.18
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FE203FE203FE203FE203FE203FE2G3FE203FE203FE203FE203FE203FE203FE203FC203FC203
-19.38•18.73•16.55-14.49•13.04-12.81-12.99-12.38-12.19-12.01-11.84-11.69-11.54-11.40-11.27 -
19.2219,9117.3B14,6012.5912.2711.9611.7111.4?11.29i i .es10.8810.7318.6110. *1
25.68.
100.190.200.212.220.230.240,290.260.270.2B0<298,308,
Continued
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- 19 -
A-l
APPENDIX A
PROGRAM SO.F4
INPUT DATA DESCRIPTION
1. Header Material, 1 card, -A1Q, A4, 2A2, 2A10
a) NSYST - name of spinel, e.g. FEAL204
b) KWRITE - output code, three types:
i) Slow - detailed output of all ionic species
ii) fast - totals of metals one and two
iii) both - both of the above.
c) NM1 - nam* of aetal one (Ml) where general fore is M1(M2)2O4
d) NM2 - name of metal two <M2)
e) NM1I - name of ionic species of metal one; all other ionicconcentrations of Ml are based on this.
f) NM2I - name of ionic species of metal two, as above.
2. Do Loop Parameter Controls, 1 card, -61
a) KM1PT - total number of principal reaction of Ml . . . . max. 5
b) KM1IT - total number of ionic reaction of Ml max. 8
c) KT - total number of temperatures max. 15
d) KPH - total number of pH's at 25°C max. 10
e) KM2PT - total number of principal reactions of M2 . . . max. 5
f) KM2IT - total number of ionic reactions of M2-Mn . . . . max. 8
3. Principal Reactions of Ml, up to 5 cards, -A10, 312, 3E10.0
a) NAM1P - name of species reacting to form Ml + n
b) AM1P - stoichiometry coefficient of «2 reacting (A)
c) BM1P - stoichiometry coefficient of H+ reacting (B)
d) CM1P - stoichiometry coefficient of Ml+n formed (C)
A-2
e) GAM1P - free energy function parameter (cal) (E)
f) GBM1P - free energy function parameter (cal) (F)
g) GCM1P - free energy function parameter (cal) (G)
The general equation for the principal reaction i s :
Ml (reactant) + A'H2 + B«H+ - OMl** + H20 (A-l)
where A, B, and C are the stoichiometry coeff ic ients . If
a negative number i s input, the role of reactant product i s
reversed.
The free energy function is of the form:
A G = E + F x T x Log(T) + G x T (A-2)
where E, F, and G are the free energy function parameters.
One of the above cards are input for each principle reaction.
A. Ionic Reactions of Ml4*1, up to 8 cards, -A10, 412, 3E10.0, 110
a) NAM1I - name of ion formed, e.g. FeO2
b) AM1I - stoichiometry coefficient of reacting Ml 4 0 (A)
c) BM1I - stoichiometry coefficient of reacting H 2 (B)
d) CH1I - stoichiometry coefficient of reacting H + (C)
e) DM1I - stoichiometry coefficient of ionic product (D)
f) GAM1I - free energy parameter (E)
g) GBM1I - free energy parameter (F)
h) GCM1I - free energy parameter (G)
1) Fl - factor indicating amount of metal one in ion product.If omitted, it is assumed one.
The general ionic reaction for metal one is of the form:
A«Ml+n + B-H2 + Off* + H20 - D«Prod+1 (A-3)
As indicated, a minus sign reverses the roles of reactant -product.
One of the above cards is input for each ionic reaction. A
maximum of ten ionic reactions is allowed.
A-3
5. Linking Reaction, 1 card, -Ain, 412, 3E10.0
a) NLNK - name of spinel
b) ALN - stoichiometry coefficient of Ml4*1 formed (I)
c) BLN - stoichiometry coefficient of M2401 formed (J)
d) CLN - stoichiometry coefficient of H+ reacting (K)
e) DLN - stoichiometry coefficient of H2 reacting (L)
f) GALNK - free energy parameter (E)
g) GBLNK - free energy parameter (F)
h) GCLNK - free energy parameter (G)
The general equation is: (A*4)
Ml(M2)204 + K«H+ + L-Ml4*1 = J-M24® + H20 (A-4)
6. Principal Reaction for Metal Two, up to 10 cards, -A10, 312, 3E10.0
a) NAM2P - name of reacting species
b) AM2P - stoichiometry coefficient of reacting F2 (A)
c) BM2P - stoichiometry coefficient of reacting H"1" (B)
d) CM2P - stoichiometry coefficient of M2 + m formed (C)
e) GAM2P - free energy parameter (E)
f) GBM2P - free energy parameter (F)
g) GCM2P - free energy parameter (G)
The general equation is of the form (A-2). A maximum of ten
principal reactions is allowed.
7. Ionic Reactions of M2, up to 8 cards, -A10, 412, 3E10.0, 110
a) NAM2I - name of Ionic product formed
b) AM2I - stoichiometry coefficient of reacting M2+"1 (A)
c) BM2I - stoichiometry coefficient of reacting H2 (B)
d) CM2I - stoichiometry coefficient of reacting H + (C)
e) DM2I - stoichiometry coefficient of ion product (D)
f) GAM2I - free energy parameter (E)
g) GBN2I - free energy parameter (F)
h) GCM2I - free energy parameter (G)
i) F2 - factor indicating amount of metal two in the ion product(mole/mole product); if omitted» it is assumed to be one.
The ionic reaction is of the form (A-3). Up to ten reactions
are permitted.
8. pH at 25°C of system, 1 card, -20 F
a) pH25 - pH at 25°C
9. Temperature of system, 2 cards, -11F/9F
a) TEMP - temperature (kelvin)
10. Graphical output, 1 card, 1212
a) KTYP - 1 indicates reduction conditions are to be plotted;KTYP - 2 indicates both reduction and oxidation are to be plotted.
b) IG - number of pH's to be plotted.
c) KPLT - array in which the reference of the order of the pH (inputin the pH25 array) is to be plotted. A maximum of 10 pH'sis allowed.
If many plots are to be made, a time switch must be on the "Job
Card" giving extra plotter time. It is of the form:
/TPL0T:n where n is plotting time.
If a blank card is inserted, no plot will be made.
OUTPUT DESCRIPTION
1. Fast - odd numbered tablesFor each input pH and temperature the value
fM2 total]2/3 is printed
2. Fast - even numbered tables
For each input pH, a table of total Ml and M2 for both Ml rich
and M2 rich system vs temperature is output. Also Included is the pH at temp-
erature. If the system is unstable, the totals of Ml and M2 are not printed
and "SPINEL UNSTABLE" is printed.
A-5
3. Slow - optional - not included in report
A table for each hydrogen pressure temperature and pH combination
is output. Included is total Ml, total K2, pH at temperature, concentration
of each ionic species, and an indication as to the stability of the system.
4. Both
Outputs both of the above.
Optional graphical output
On a single graph, a plot of concentration of Ml and M2 vs temp-
erature, under Ml rich and M2 rich systems, is made. The hydrogen pressure
and pH are held constant.
A-6
r " i l N i J N E OROC'A^ S C . f * M*V 2 7 , 1 9 7 4
LDOUBLE PRECISION \A«ll«», NAM2P. NAM11 .NAM2 J ,»<LNK , 5TH1, STM2.
l,NSvST.NMil.Ti,T2,%M2!Pr = i.AMIP(4).aniP(5),CMIP(5)>
(8).G 3 H11C 8), IlAM?PC5),8H3P(5).CH2P(5).CiM2P(5),CBM2P(5).1AM2I(g),BM?I(8).CM2I I 3).DM21(8).GAH2I(e).G8H2!(8)>
DI MEMS TON Mil(8,15,10,2.2).M21(8,15.l?-2.2).MIT CIS.10,2.2).
Ti.T?/»STABl_E '.'UNSTABLE '/
DIMENSION SKH5.13.2)DATA IOENT/'CONCE'.'NTRAT'.'ION V'.'S rgm', 'PERAT•.HjRr• 3«' VOATA LABV/'LOG (•.•MOLE/'.'KO '.3»f VOATA LASX/'TEMPE*.'RATUR','E DEC'.' C '.2«' •/
• 100? FQRMATCA10,1001 FORMATAI)1002 rofMAKAia1003 FORMTC20F)1005 F O » M A T ( A 1 0 . 4 1 3 . 3 C 1 0 . 0 . 1 1 3 )1BB« FORMAT(11F. /9F)1007 F0RMATC12I2)2004 F 0 R M A T ( ' i » 4 X , 'CONCENTRATION Or I O M C SPECIES OF ' A 1 0 , * AT ^ 4 . 0 ,
1 ' C AP4O 0 . 1 2 5 MICROMOL 02/KC H20 IN-CORC CONOIT IONS' l 4 X / U f t ( • • • ) /2 2 0 X . ' A L L CONCENTRATIONS GIVEN I N LOG<MOL£/KS H 2 0 ) ' )
r 2Z05 F O R M A T U I i . » PH AT 25 • ,F8 .2 .38X, 'CONCENTRATION I N L.OG<MOLE/KG) • )2Z!0* rtJRMATCBX, 'TEH C STABLE ' A 2 , ' TTL ' A 2 . ' TTL ' A 2 , ' • STABLE * » 2 .
/ • TTL1 'A2,' TTL 'A2.' • PH STABLE 'AJ.' TTL «A2. 1 TTL «A2,/' • STA8LE '1A2»' TTi. 'A2,' TTL 'A2,' TEM C'/BX,'••••• ••••••••• •••••• ••••••1 • ••••••••• •••••• •••••• • •• ••••••••••• • • • • « • ••••••1 • ••••••••• •••••• •••••• ••••••)
200? FOR*ATC'*'l3X.Al0,F6.2.f — - • ?»Al0.» — »,F7.2)i 200P FORHAT(7X.F6.0)2009 FORMAT(»»'13X,A10.F6.2.F7.2,'
j 2010 F0RMATC'*'65X,'»'F6.2,' ••)2011 FORMAT(U>76X.A10,F7.2.1 --- • '.A10.' — -,F7.2)2
'' 2013 FORMAT('*'127X,F5.0)| 2014 F0RMAT('it4X,'CONCENTRATION Of IONIC SPECIES Of »A10,» AT 'F4.B,
1' C AND 0.446 M*OL H2/KG H20 OUT-COfE CONDITIONS'14X/ll6(•••)/2! 20X,'ALI. CONCENTRATIONS GIVEN IN L06(M0L/KG H20)'); 2015 FORHATf 'ÎX.'PM AT 25'Fl7.2,3f21.2)! 2W21 roftffATf' PH AT T£H^*ri6.2.3r21.2)! 2022 FORMAT(• '5X,'SPECIES'eX.A2,f RICH 'AJ.' RICH'SX.A2.' RlCH 'A2,
1 RlCH'çx.A?.1 RICH 'A2,' RICH'5X,A2»' RICH 'A2,' R I C H ' )FORMATS '5X.A10.6X.9F2016 FORMATC •5X.Al0,6X.2F7.2.6X.2F7.2,yfrX.2F7.2.6X.2F7.2>
j 2017 FORMATC »5X'T0TAL • A2, SX, 2r7.2.6X^5-7 :2,6X,2F7 .2.6X.2F7.2)( 2018 FORMATC 'M'SOLIO «A2.1 PHASE'6X,A10,3A21)' 2019 FO«MAT(» '5X.A10,M3'8X,A10,3A21,//)
A-7
2023 roR«*Tf «?BX,•OuT-CORF (2.446 MHOl Hg/KC *20)'.14*,•••.•X,
, 2*26 F0BMATC21X.A2,' 0 I CM.•9X.'••.15X.A2.' P IC*'.5X,•••,gx,•••,15*,1A2,' »TCH'.3X»•••.I1X.A2.• RICH'J
, 2324 raBNITf «*)(,!PH AT T 'FJ.7.2.3F2i .2 >20252031203?
28332HS<
' 2035 *"QRH*T<ili.' EO'.'ILIB«IUM CONCENTRATION PRODUCT or '.tlJi.' AS
204? PORMATdBx.'UNDER IV-CORE COND1TIOMS (?.125 MKRDMOL OS/KG H20)'J2B36 FORH*T(i2x,"UNDER OUT-CORE CONDITIONS fB.466 HfOL H2/KG H20)%)
i 2333 F0RH*T<7X.'TEMP C1 , TEMP C'>
i 2B3S roR^*T(7X.F6.0.iafia.2,rB.B)C " 1 * 2 0 4 • C . H * • 0 . H 2 = * . « i • B.Mg *H20
JC A.MR * P . H 2 *C.OM *J9.H* aE.MP WHERE BsFREE ENERGY! B T<C »EAO INPUT DATA
RE AO < 5. 1BB»« >NSYST . KWRI TE, NM1. NM2. N»*l I, N121> flE »015.18B1)KHlPT,KHlIT.KT,K^H,KM2PT.KM21T' D3 i I«1.KH1PT
1 RE*D«5tlBB2>NAHlPfI),AM1PCI),RM1P(I),C*1P<!I.1CA«1P(!).CBMlPfI).GCMlPCI)00 2 Tel.K"lIT
• ? RE*O<3.XBa5)NAMli(!),AMlI(!5.B«lI<H.Cfl!U).DvilIll >.» lGA«iI(T),GBMl!(!).GCMH(I
ReAO(5.10B5)NLNDO 3 I»l.<M2PT
OS 4 I.1.KM2IT* S"A0«5.1BB5)N»H2l(l>.A«2Hl).BH2n!),c«2!CJ.DM2itt j1GAH21(I),GBH2I(I).GCH21(I).F2 cI)
!!R0WS«KPH/4
IfC GENERATE IONIC COEFF. IF NEED BE\ 00 3« t»1.8
34 CONTINUE<C CALCULATE PKW .PH.LOGlB H.ETCI 00 33 U«1.KT
00 33 t2«l.KPH
CALL PMTCMP(TEMPni),PKH,PH25<I2>.PnTlIl,12))33 CONTINUEBECIN M»JO« LOOPS VARYING ME3S-13.TE«P-U.PM-12.M^TAL BASIS-I4
A-8
DC 11 '3*1.2
\?lI 3.FQ.l)Pie = -6.629857*0.>»*2*0.4A29608E
l-4LOG10£iai333.)
l-4LOGl?(iai330.DO 11 12=1.<PH
11.12)
BASIS14 = 1GELsGtGALNK.GBLNK.GCLNK.TErtPC U J )
35 If(I4.fQ.2)Ml»(-GtL/OE*CLN»H10*OLN«Pia-BLN»M23)/*LNIff M.rfl. 2)C0 TO 30
C SfABrw TQP MOST STABLE CPD AND MlSTHKI1,DO 6 !«1GE1*S(CAM1P<I).G9M1P(I),GCM1P(I).TEMP(I1)>M12B(-GE1/DE*AM1P(I)»P10*BM1P(1)»H10)/CM1P(I)IF(I.EO.l)Ml=Hl2
C WRlTE(6.2043>NAMiP(I),GEi,M12.TEMPUl>,PW25(I2),Pl?:C2043 roP.M*T(A15.' f*ZZ 'Ell.3.' COM 'E11.3,' AT '3tll.3)
ir(Ml2.GE.Ml)G0 TO 6
M1«M126 CONTINUE
3PI CONTINUE
ir(Ml.LT.-30.)MlB-30.C FIND Ml IONIC AND TOTAL
00 7 I»1.K«1ITI
AM=(-GF.l/DE*AMlI ( 1 )»M13*9M1! ( I >«P10»CMlI ( I ) »H1B )/DMl I ( I )Mill I . U , 1 2 , 1 3 , U)»AM
7 M1T(I1.I2,I3.I4)»M1T{U.I2,I3.I4)»P»10.»»AMM1TCII.12,13.14)»ALOG10(M1T( 11,12,13, 14))ir(I4.E!Q.2)G0 TO 13
C LINK P.EATTION CALC.IF(14.EO.l)M2»(-GEL/DE*CLN»H10*DLN»Pia-ALN»Ml3)/8LN
36 1FCT.4.F.Q.DG0 TO 31C SEARCH FOR MOST STASLE H2 AND M2
STH2(I1,I2,I3)=NAM2P(1)00 8 I-1.KM2PTGE1«G(SAM2P(I),G9M2P(I).GCM2P(1),TCMP(I1))M22«(-GE1/OC*AM2P{I)«P10*BH2P<I)»H10)/CM?P(I)i r n o 2 2IF(M22.GF..M2)G0 TO 8STM2(Ii,l2,I3)=NAM2P(l)
8 CONTINUE31 CONTINUE
l,!2,13.
A-9
C CALCULATE «2 IONICS AND
30 9 I=l.<V2ITG£ 1 s G (G AM21 (1). G9-»21 { I), CC^21 (IJ , TC-H» r 11))A*s( -Gri/aE*AM?l ( I )»M23.gM2l {I )»PiP>*C"?J f I >»HJ,2 } /0M2 I {I )
!l.!2.!3.!4)a;c.3?. >A*=32.
If(I*.rQ.1( II. 12. 13, I4)/{»L*J*BLN3IffM.ra.?)G0 ?0 «5!*»2GO TO 36
1?
.UE.»"lTf 11.12,13.HJS TAK!l.
Cc oo
E50 1'E16.2335) 13. ;JS YST, v«l.
W»]T€(6.2B37)(PH25C!21.!2*l.KPmJBITE(«,2a38)00 bt I1«1.KT
6? URITE{*,281«)T,(s<(Il.12,13).12*1.61
C00 12 J2«t.KPH
ir(i2.r,T.i)!P«2
WRITE (4.2026) NHl, VM2 . Nf 1,MR ITE (6.2986 J N«i. \*i.00 12 11*1.KT
!r(ST»l(u,l2.D.NE.T2)60 TO 14
1.1.2)14 !FUCl.NE.e)WRlUie,f28jj9)STHKli,I2,l).M1T<!i.i2.i.iJ.i2'M ! I. 12.1.
ir(STAJ(!i.t2.2).VF.T2»t;o TO 1?IC1>0wR!TCC6.?Bll)STMi(U.!2.2J,MiT(li,!2.2,iJ,STM2( U.12.2}. n2 Till.121.2.2)
17
A-10
115 I F ( KUB f TT ."IE 'oOT^1 )GO TO 44
C SLOW Pt'TPi'TDO 18 11=1.KT01 IB 13=1.2
I F ( I 3 . F Q . 1 ) W R I T E C 4 , 2 0 1 4 J N S Y S T . T E M P < I 1 )ir(i3.rOn 19 IM1=N1*4
W R I T E ( 6 . 2 3 2 2 ) N H l ,J R I T E ( 6 , 2 a i 6 ) N M U . ( ( M l P d l , 1 6 . 1 3 . 1 7 ) .DO 2 0 I s l . K H l I T
( 1 ) , l ( M 1 I ( I . 1 1 , 1 6 , 1 3 . 1 7 ) , I 7 « 1 , 2 ) . 1 6 » ' U , N 2 )( ( M 2 P ( I 1 . I 6 . 1 3 , I 7 ) . I 7 = 1 . 2 ) , I 6 » N 1 . N 2 )
• 0 2 1 U 1 . K M 2 I T2 1 W R I T t ( 6 . 2 a i 6 ) N A M 2 ! ( ! ) . ( ( M 2 I t I . l l . I 6 , l 3 . I 7 ) . I 7 « l , 2 ) . t 6 " N l . N 2 )
W K I T E ( ( S , 2 ( I ) 1 7 ) N M 1 . ( ( M l T d l . 1 6 . 1 3 , 1 7 ) . I 7 » 1 . 2 > . I 6 = N 1 . N 2 >W « I T E < i S , 2 a i 7 ) N M 2 , ( ( M 2 T ( I I , 1 6 . 1 3 . 1 7 J , 1 7 . 1 . 2 ) , I 6 = N 1 . N 2 >
19 CONTINUE18 CONTINUE44 IG=0
ir(IG.fQ.a) GO TQ 45C 44 IF<IG.rQ.a)GO TO 45C 105! CONTINUEC SEARCH TOP. MAX AND « n *N0 CALCULATE THE R»*SE
LABY<5>«' AND
00 46 I2«1.KTYPYMIN«-16.
C Y M I N a H l T d , 1 . 1 . 1 )C VMAX«Y«INC 00 40 K»KSTP.Kf>MC 00 4a IsS.KTC 00 40 H s i . 2C IF(YMIN.GT.M1T(I,K.L.M))YHIN«M1T(I,K,L.M>C ir trHAX.LT.MlTd.KiL. f ))YMAX««1T(I,K,L.W)C IFCYMIN.6T.M2T<I,K.L.M)>YHIN3M2T<I,K,L.H>C 40 I P ( Y M A X . L T . H 2 T ( I , K , U . M ) ) V M A X « M 2 T ( I . K , L . M )
IF<YMIN.LT.-11.0>Y*IN«-H.0IF(YMIN.GT.-11.0)rMlN»-11.0IF(YMIM.EQ.-1B.0)DY«2.JJir(YHIN.EO.-ll.B)OY«l.eURITE(A,2034)
C PLOT ROUTINE00 53 Tl=3.KT
9? TC(I1-2)«TEMP(I1)-273.1500 41 Nsl.IG
A-ll
6> JPU25<L1>ir(L2.ir3.2>ENCO0Et22!.2C>33. 2 DENT ( 6 ) 1P»25 <Ll >
JsKT-200 41 i3=1.2DO 42 Ks3.KT
45 S0L(<-?)3MlT(K.Ul.LCiLL SPLOT(1,6.M.1DEMT.LASX,LA9Y.TC,SOL.10?..25..8.
00 43 «=3.<TS0Lf*<-?)='i?"r<»<.l.l.LCALL SPLOT(I.6.^.!OENT.LAax,LABYfTr.S0L.lB?..25..6.
4146«5 STOP
A-12
READ HEADINGSOUTPUT CODE ANDDC LOOP PARAMETER
READ MlREACTION CO-ORD
READ SPINELREACTION CO-ORD
- * •
READ M2
REACFiON CO-ORD
GENERATEIONIC
COEFFICIENTS
FIND pKw VS. TEMP?\
CALL PH TEMP
A-13
cDO 8 FOR EACHPRESSURE
YES NO
PRESS = 20 ,000 Pa PRESS = F(T)
i U\J o rOK u/iLH i
V TEMPERATURE Jr0DO 8 FOR EACH
PH FOR 25C H \
/ ^ C a l c . - R x T x 2 . 3 O 3 \V^and LOG ( H + ) J
YES IS
'SYSTEM M fRICH?
NO
SEARCH FORMOST STABLEMl COMPOUNDAND [M1]
I Ml = F CM2D
CALCULATE MlIONICS FROMINPUT DATA,pH PRESSURE ,H-.CALCULATE1 TOTAL
A-14
YES
M2 = F CM ID
CALCULATE M2IONICS FROMINPUT DATAAND TOTAL
NO
SET SYSTEMTO M2 RICH
I
FAST
FAST OUTPUT
NO
1SEARCH FORMOST STABLEM2 COMPOUNDAND CM2J
SLOW
BOTHDETAIL ANDFAST OUTPUT
DETAILOUTPUT
B-l
APPENDIX B
PROGRAM FREB
Location - File FREB-FA
Purpose - This is a program based on McDonald's program FER. The programcalculates the free energy of reaction of the form
aA + bB + cC "dD + eE + fF B-l
INPUT DATA
1. Headings, 1 card - (2A10, A5, 21)
EL - titleUNIT - units desired "JOULES" or "CAL" ( lef t justified)KWRITE - if "COEFF" (left jus t i f ied) then the free energies of
reaction are output in the form:
AG = A + B«T'LOG(T) + C«T B-2
KT - numbe of temperatures1C - number of Criss and Cobble parameters to be input
( i . e . 4 x KT) if 1C is zero then the Criss and Cobbleparameters are generated internally.
2. Temperature, 1 card - (301)
TT - tempereture of free energies (degrees Celsius)
B-2
3. Criss and Cobble Parameters (if necessary), 1 card - (60F)
CC - Criss and Cobble parameters of the form A^, A2 ..
BI, B2 ... BKT, Clt C2 ... CRT. DJ, D2 ... D K T
where
A = cation solubility code 11B = simple anion plus OH" solubility code 12C = oxyanion solubility code 13D = acid oxyanion solubility code 14
If energies of formation are known at the temperatures of concern,the following input is used - A10, 12, 30F
SPEC - name of speciesISC - solubility code (a zero indicates the end of data)G - energies of formation, one for each temperature.
On the last card of this series ISC is 00 and input KT O.'sas the next data will be misread.
Species of which the free energies of formation are to be calcu-lated. A10, 12, 5E
SPEC - name of speciesISC - solubility code (a zero indicates the end of data, a 10
is used for heat capacity type calculations)G - free energy of formation in calories or joules as specified
in (1) at 25°CS - entropyCP - heat capacity function as reported by Kubaschewski, the
factor of 10"3 and 10+5 have been accounted for (i.e.input number exactly as reported by Kubaschewski).
Reactions up to 30 cards (121)
ISTO - the a b c d e and f*s of equation 1-1.ICOL - the A B C D E of equation 1-1 coded as per their input
(SPEC). To end the file, input twelve zeroes (free format).
B-3
OUTPUT KWRITE = COEFF
1. Table of input values2. Table of free energy of formation vs temperature3. List of reactions4. List of free energy of reaction coefficients
KWRITE * COEFF
1. Table of input values2. Table of free energies of formation vs temperature3. List of reactions4. Table of free energies of reaction vs temperature
SUBROUTINES
1. Hilton (KT,2,Z,X)
KT - total number of input valuesZ - 50 dimensional vector containing free energy of reactionX - 30 x 2 array where
X(T,1) - T x log (T)X(T,2) - T
2. Rite (K,NAM,ISTO,JCm
K - reaction numberNAM - name of species to be printedISTO - stolchiometry of aboveJCD - code to Input the arrow and type of arrow (changed in
subroutine)
ARRAY SIZES
Variable Max.T 30Reactions 30Input Species 20Products 3Reactants 3
C-l
APPENDIX C
SUBROUTINES
1. PHTEMP (T,PKW,PJ1,PHTE)
This subroutine is located in file PHT-F4 and is called bv
uhe mainline program SQ.F4. The subroutine calls subroutine RT (XCOF,
PN1.HT). The variables are:
T - tenperature (K)
PKW - pkw of water at T
PHI - pH at 25°C
PHTE - pH at T output by PHTEMP
2. PT (XCOF,PHI,HT)
This subroutine is located in file PHT^rt and is called the sub-
routine PHTEMP described above. The variables are:
XCOF - a four word vector containing, KWT**2, KWT*, KIWSK,KBDSE*CT, KBDSF.
PHI - pH at 25°C
H.I - 0.1
The above two subroutines describe the behaviour of lion witl
temperature. If no variance of pH with temperature is desired, the file
PHK>F4 is loaded with the SO.F4 (mainline).
3. PHTEMP (A,B,C,D)
This subroutine is called by the mainline (SO.F4) and is located
in file PHK-F4. The variables are:
A = temperature (K)
B = pkw
C - pH at 25DC
D = C
C-2
/,. SPLOT (I,N,M.IDENT,LABX,LABY,X,Y,XMIN,DX,XLEN,YMIN,DY,YLEN)
1 = number of points to be plotted
N = order of polynomial fit
M = plotting symbol
IDENT = title
LABX = label of X axis
LABY = label of Y axis
X = solubility
Y = temperature
T>V = units per inch
YLEN = length of X axis
This is a systems library subroutine (described by K. Witzke)
and does not have to be loaded with the mainline program.
C-3
CC
E PHT*>D L i 1
OOUatE PRECISION«EAl.HTe.l
6100 61 U«l.«
CALU
x';OF(i},HTf«v,xi1X?nTe,l
S2«.XC0F(2J«HTRY
DO 34 I4«1.5(92
TO 85
94 *0'
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