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The coprecipitation of strontium, magnesium, sodium, potassium and chloride ions with gypsum. An experimental study
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The coprecipitation of strontium, magnesium, sodium, potassium and chloride ions with gypsum. An experimental study JACOB KUSHNIR Geoscience
Group,
Isotope
Department,
(Received 4 Januury
Weizmann
1980; uccepted
Institute
in recised,form
of Science, Rehovot,
Israel
29 Muy 1980)
Abstract--The coprecipitation of Sr”, Mg’+, Na’, K+ and Cl- into gypsum was studied as a function of temperature, brine concentration and growth rate. The concentrations of the studied cations in the gypsum increase with growth rate (kinetic effect), with a tendency to reach a limiting value at high growth rates. The partition coefficients of Sr tend to increase with brine concentration and decrease with temperature. The partition coefficients of the other cations also decrease with temperature but depend only very slightly on brine concentration. The concentrations of coprecipitated chloride are negligibly small. The coprecipitation behavior is explained in terms of the relation between the rate of desorption of the coprecipitating ions from the surface of the growing crystal, and the rate of growth. The studied cations may substitute for Ca” in its normal lattice sites and/or reside in interstitial positions among the structural water molecules. The relative amount of foreign cations occupying interstitial positions increases with increasing growth rate. The elucidation of the behavior of coprecipitated ions in gypsum given here forms a basis for the utilization of these ions as geochemical indicators for the environment of deposition of gypsum. These indicators may help in reconstructing important parameters such as temperature, brine concentration and growth rate.
INTRODUCTION
GYPSUM is an important associated
primarily
sedimentary with
evaporite
mineral
which
deposits.
is
The
of the processes that are involved in the formation of evaporite deposits require the reconstruction of the physico-chemical conditions prevailing during deposition. The concentrations of coprecipitated ions have been utilized as indicators for the conditions of formation and evolution of some sedimentary minerals. In most studies an equilibrium approach was adopted; that is, the coexisting phases (solution and solid) were assumed to be in equilibrium with each other and a straight forward thermodynamic treatment was applied. In the case of gypsum, laboratory studies have dealt only with the coprecipitation of strontium (PURKAYASTHA and CHATTERJEE, 1966; USDOWSKI, 1973; ICHIKUNI and MUSHA. 1978; YAMAMO~Oand UNEKI, 1978). Studies on natural samples of gypsum, however, have included measurements of other ions too. (Sr: NOLL, 1934; HERRMANN, 1961; BUTLER, 1973; Na, K, Mg: DEAN and ANDERSON, 1973; Cl, Br: SABOURAUDROSSET, 1974). There are large discrepancies in the measured values of the partition coefficient of strontium between gypsum and the solution as reported by these workers. The partition coefficient at 25°C was found to be 0.30-0.41 by PURKAYASTHAand CHATTERJEE(1966), 0.414.64 by USDoWSKI (1973), 0.21 by ICHIKUSI and MUSHA (1978) and 0.214.33 by YAMAMOTO and U~VEKI (1978). BUTLER (1973) derived the partition coefficient of strontium between understanding
1471
gypsum and the solution from geochemical data and reported 0.19 at 28°C. BUTLER (1973) also reported a negative correlation between gypsum crystal size and the concentration of coprecipitated strontium. The results of these studies suggest that the coprecipitation of strontium with gypsum is influenced by the growth rate of the mineral. Since the growth of gypsum is a surface controlled reaction (LIU and NAW COLLAS, 1970), the coprecipitation of ions with gypsum is expected to be affected by the dynamic behavior of the growing crystal surface. The purpose of this study was to elucidate the behavior of coprecipitated ions with gypsum, paying attention to possible kinetic effects. The behavior of the following ions was studied: strontium, sodium, potassium, magnesium and chloride. Strontium was chosen because of its importance as a minor element in evaporitic environments and the extensive data in the literature of concentrations of Sr in gypsum that already exists. The other ions were chosen because of their abundance and well known behavior in the environments of gypsum deposition.
EXPERIMENTAL Gypsum was precipitated in the laboratory under well defined conditions. The compositions of the solution and the solid were then measured. The rate of growth was controlled by establishing a constant degree of supersaturation using a Ca-stat system which is shown in Fig. 1 and will be described in the following section. One hundred ml of sohmon were placed in a double walled reaction vessel which was kept at constant tempera-
1472
JACOB KUSHNIR
Fig, 1. The Ca-stat system, B-Buerette; Ca-Calcium trode; MV-magnetic valve; R-recorder; S-stirrer;
ture by a flow of thermostated water (within +OS”C). The solution was constantly stirred by a rotating bent glass rod. (To prevent crushing of the crystals a magnetic stirrer was not used). The stirring rate was kept constant in all runs. The crystals were kept in suspension except in a few runs where some crystals adhered to the PVC envelope of the Ca-selective electrode. A Ca-selective electrode (Radiometer type F2112Ca) coupled with a saturated calomel reference electrode (Radiometer type K401) were connected to a titrator (Radiometer type TTTl). The titrator was set to open a magnetic valve whenever the potential over the electrodes increased above a given value (i.e. whenever the activity of calcium ions in the solution dropped below a given value). A small amount of 1M CaCI, solution was added to the reaction vessel whenever the valve was opened. The amount of CaCI, solution added during the experiment was recorded. In the beginning of the experiment a certain volume (Vss) of IM CaCi2 was added to the solution to achieve supersaturation. This amount never exceeded 5 ml. After the desired supersaturation was achieved a volume (Vgr) of I M CaClz was added by the action of the titrator and then the experiment was stopped. The change in volume during the experiment was about 3”/, and the amount of gypsum precipitated in each run was essentially the same (about 0.5 g). The small unavoidable changes in the potential over the Ca-selective electrode were follqwed by a strip chart recorder that was connected to the titrator. The fluctuations in the potential were always less than +0.5 mV. Three artificial seawater brines resembling seawater that was evaporated to x 3, x 5 and x 8 its original concentration were prepared. The solutions were saturated with respect to gypsum at the appropriate temperature and filtered prior to the experiment. Analyses of these solutions are given in Table 1. The concentration of sulfate in these solutions was higher than the concentration of calcium and therefore the amount of sulfate in the solution changed by only I@-1%; during the experiment. Experiments were conducted at three different temperatures: 30,40 and 5O’C. At the end of each experiment the crystals were quickly separated from the solution by filtration, washed several times with distilled water and then with acetone and dried. The final clear solution was analysed for calcium and strontium. The dried crystals were identified as gypsum by X-ray diffraction and under the microscope. The crystals were-dissolved in distilled water and this solution was analysed for Sr, Na, K, Mg, Cl and Ca. Concentrations of the coprecipitated ions are reported as the molar ratio to cal-
selective electrode; K-calomel reference elecT-titrator; W-flow of thermostated water.
cium. All cation analyses were performed on a Perkin Elmer model 303 atomic absorption spectrometer. The standards for Sr, Na, K and Mg were matched to the samples in their calcium sulfate concentrations since CaSO, affects the measurement. Analytical uncertainties were lY:, for Sr/Ca, 24; for Na,Ca. 5”” for Mg/Ca and lOy~ for K/Ca. Chloride in the gypsum was very low. An attempt was made to analyse Cl using the Gran’s Plot method (Orion, 1977), but the concentrations were below the detection limit of this method (Cl/Ca < 10e4). Cations in the brines were analysed by atomic absorption spectrometry using standard techniques. Chloride in the brines was analysed by Mohr’s method and sulfate by gravimetry. Analytical uncertainties were 1”~”for Ca, Mg, K. and Cl; 2”; for Sr and Na; 2% for SO,.
RESULTS
Kinetics of crrstullization In view of the effects of growth rate on the coprecipitation of ions with gypsum (which will be demonstrated below) it is necessary to assess the kinetic parameters that are involved in the process of crystallization. The experiments were conducted at various constant degrees of supersaturation. The supersatuTable 1. Compositions of initial brines (moles/liter). C is the concentration factor (Cl in brine/Cl in normal seawater) Brine Ion
SW.3
s.w.5
S.W.8
Ca (30’ C) Ca (4o‘C) Ca (50 C) so, (3O’C) Sr (x 10m4) Na Mg K Cl C
0.0285 0.0260 0.0269 0.185 3.52 1.28 0.136 0.034 I .89 3.4
0.0223 0.0171 0.0204 0.210 4.96 2.27 0.242 0.05 I 2.58 4.7
0.0088 0.008 1 0.0083 0.255 3.64 4.07 0.42 I 0.088 4.61 8.4
1473
An experimental study 3,0 Precipltatlan
klnetlcs, experiment
B52
F----y?
_..’ ,___._...
.”
,,...’
1
0
I
40
I
I
PI
I
80
1
160
120
I
II
1
200
240
I
Fig. 2. An example of the precipitation kinetics. The volume of I M CaCI, added (Vgr) is plotted against time. ration S is defined in terms of the activity of the calcium ions in solution:
Where Q is the activity of Ca in the supersaturated brine and ucao is the activity of Ca at saturation. S was calculated from the difference in potential over the Ca-selective electrode before and after achieving supersaturation. The crystallization process was followed by recording the amount of 1M CaCl, added by the action of the titrator. The growth was preceded by an induction period which was shorter at higher degrees of supersaturation. The growth rate (amount of 1M CaClz added per min) was not constant, increasing during the growth process. This is attributed to increase in surface area of the growing crystals. An example of the crystallization process is shown in Fig. 2. The average growth rate (Rav) was calculated as: Rav (moleimin)
Vgr x 10e3 = ~-~~ -~~ growth duration
where
k is the growth
constant
(3) and
A the surface
area
(Lru and NANCOLLAS, 1970; SMITH and SWEETT, 1971). Assuming that the growth rate changes during the experiment only due to changes in A, we may rewrite eqn (3) as: of the crystals
Rav = k’s2
log Rav = log k’ + 2 log S
(5)
A plot of log Rav vs log S is linear with a slope 2 and an intercept log k’. Using this relation the growth constant for each brine at the three different temperatures was derived (Table 3). The growth constant increases with increasing brine concentration and with increasing temperature. These effects have been previously demonstrated (LIU and NANCOLLAS. 1970; BRANDSE etal., 1977). Coprecipitation
of My, Nu and K
The amounts of Mg, Na and K coprecipitated with gypsum are very small compared with their concentration in solution. The concentration in solution thus remains essentially constant during the growth process. At constant degree of supersaturation (constant concentration of Ca) we may define the partitition coeficient for the coprecipitation of X as:
(2)
where Vgr is the amount of 1M CaC12 added during the growth and the growth duration is the crystallization period minus the induction period. The slowest growth rates achieved were determined by the sensitivity of the Ca-stat setup. The experimental conditions and the kinetic parameters for the 37 experiments are given in Table 2. The growth of gypsum is related to the degree of supersaturation by: R = kAS2
or
(4)
where G stands for gypsum and B for brine; X represents Mg, Na or K and the ratios are in mole/mole. Table 4 summarizes the results for Mg, Na and K. The partition coefficients for each element depend on the experimental conditions. They increase with increasing growth rate (kinetic effect), they tend to be lower at higher temperatures and in more concentrated brines. The kinetic effect is clearly shown in Figs 3-5. The partition coefficients increase with increasing growth rate with a tendency to reach a limiting value at high growth rates. The kinetic effects are smaller at higher temperatures (Figs 68). The partition coefficients of Na range between 0.1 x IO- 4 and 3.1 x lo-“, those of K between 0.1 x 10e4 and 3.4 x lo-“ and of Mg between 0.1 x 10m5 and 4.3 x 10e5. (Under the range of conditions covered in these experiments).
JACORKUSHNIR
1474
Table 2. Experimental conditions and kinetic parameters. Symbols
are explained
in text
Ca in Ra\
vss
VP
Growth duration (min)
30
1.0
30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 40 40 40 50 so 50 50 50 so so 50 so so 50 50 50
I .7 2.7 4.7 0.9 1.5 2.6 3.1 0.6 0.7 1.5 1.7 0.2 0.9 1.0 1.1 0.9 1.5 1.9 2.9 0.6 0.6 1.3 1.8 1.0 2.0 2.4 3.5 0.2 0.3 1.4 1.7 3.1 0.4 0.6 1.3 3.0
2.X 2.3 3.0 3.0 2.9 3.0 3.0 3.0 4.6 3.0 3.0 3.0 3.0 3.0 3.1 3.0 5.2 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.1 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 2.9 3.0 3.0
461 166 102 59 290 148 65 42 5610 235 102 18 1765 94 41 23 2600 11s 58 30 306 103 36 30 280 200 61 IO 3350 140 58 48 16 300 153 57 IO
Temp No.
Brine
( C)
A31 A32 A33 A34 AS1 AS2 AS3 AS4 A81 A82 AX3 A84 931 932 933 934 951 BS2 953 954 9x1 982 983 984 c31 C32 c33 c34 C51 es2 c53 c54 c5s C.81 C82 C83 C84
s.w.3 s.w.3 SW.3 s.w.3 SW.5 s.w.5 s.w.5 SW.5 S.W.8 S.W.8 SW.8 SW.8 s.w.3 SW.3 SW.3 SW.3 s.w.5 SW.5 s.w.5 s.w.5 S.W.8 S.W.8 SW.8 SW.8 SW.3 s.w.3 SW.3 s.w.3 SW.5 s.w.5 s.w.5 s.w.5 s.w.s SW.8 S.W.8 SW.8 SW.8
The concentration of Sr in solution is low (limited by the solubility of SrSO,) and the number of Sr ions coprecipitating with gypsum is comparable with the number of Sr ions in the brine. Thus the concentration of Sr in the brine changes considerably as Table 3. Growth
constants I\’ calculated eqn (4)
Temp No.
Brine
( C)
A3 AS A8 93 95 98 c3 c5 C8
SW.3 s.w.5 S.W.8 s.w.3 SW.5 S.W.8 s.w.3 SW.5 S.W.8
30 30 30 40 40 40 40 50 50
final brine
(x 10-5)
M
+ lo”,,
(x0.01)
0.61 1.4 2.9 5.1 1.0 2.0 4.6 7.1 0.082 1.3 2.9 17.0 0.17 3.2 1.6 13.0 0.2 2.6 5.2 10.0 0.98 2.9 8.3 10.0 1.1 1.5 4.9 30.0 0.09 2.1 5.2 6.2 19.0 1.0 1.9 5.3 30.0
S 0.30 0.57 0.89
3.23 4.62 6.00 7.00 3.36 4.62 5.3s 6.62 1.15 2.23 2.51 4.48 3.08 4.62 5.71 6.60 2.96 3.33 3.83 4.58 1.12 1.31 1.67 I .72 4.0X 4.42 4.64 5.48 3.25 3.40 3.75 4.00 4.48 I .06 1.13 1.31 2.13
1.59 0.30 0.61 0.96 1.21 0.17 0.68 0.89 1.21 0.18 0.78 1.21 1.58 0. I7 0.58 0.95 1.38 0.34 0.58 0.99 1.08 0.40 0.64 0.81 1.21 0.06 0.35 0.56 0.72 1.31 0.27 0.37 0.62 I .44
more gypsum crystallizes. PURKAYASTHAand CHATERJEE(1966) have shown that the distribution of Sr between solution and gypsum can be described by a Doerner-Hoskins relation (DOERNER and HOSKINS, 1925). This relation will be used here in the form:
log(l+ x$) = Wog
jl
+ ;.$j
using
k’ mol/min
(x 10-5) 2.7 5.0 5.7 5.2 6.0 8.5 11.0 12.0 14.0
mol/min
k 0.1 f 0.1 + 0.3 & 0.2 f 0.1 + 0.2 +_ 1.0 * 1.0 +_ 1.0
(7)
where N denotes total number of moles and ks, is the logarithmic partition coefficient of Sr in gypsum. The total number of moles of Ca and Sr in the brine was calculated from their concentrations in solution multiplied by (100 + Vss + Vgr) x 10 ~‘. The error introduced by the changes in volume during the growth process is less than 3”,,. The total number of moles of Sr and Ca in the gypsum were calculated as: NE = [lo0 SrEitln, - (100 + Vss + Vgr) S&r] x IO_”
(8)
An experimental study Table 4. Calculated
partition
coefficients
1475
for the coprecipitation
of Sr. Mg. Na and K with
gypsum D UA
Db
Temp No.
Brine
( C)
k
x lo-5
X 1O-4
DK x 1om4
A31 A32 A33 A34 AS1 A52 A53 A54 A81 A82 A83 A84 B31 832 B33 B34 B51 852 B53 B54 B81 B82 B83 B84 c31 c32 c33 c34 c51 C52 c53 c54 c55 C81 C82 C83 C84
SW.3 SW.3 S.W.3 S.W.3 SW.5 S.W.5 SW.5 SW.5 S.W.8 SW.8 SW.8 S.W.8 SW.3 s.w.3 s.w.3 SW.3 SW.5 s.w.5 SW.5 SW.5 SW.8 SW.8 S.W.8 SW.8 s.w.3 s.w.3 SW.3 SW.3 s.w.5 S.W.5 s.w.5 s.w.5 s.w.5 SW.8 S.W.8 SW.8 S.W.8
30 30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 40 40 40 50 50 50 50 50 50 50 50 50 50 50 50 50
0.15 0.21 0.41 0.51 0.33 0.42 0.56 0.61 0.55 0.69 0.73 0.80 0.04 0.25 0.37 0.41 0.17 0.31 0.42 0.46 0.54 0.63 0.68 0.68 0.11 0.12 0.20 0.26 0.10 0.20 0.27 0.29 0.33 0.42 0.48 0.55 0.57
1.9 2.7 3.1 4.1 1.5 2.4 3.0 3.8 1.4 1.9 2.6 4.3 0.5 1.4 2.1 2.9 0.4 1.4 3.0 4.2 0.6 1.1 2.1 2.4 0.3 0.3 1.0 2.8 0.1 0.6 1.1 1.5 2.6 0.3 0.5 1.1 2.8
0.5 0.9 1.5 2.5 0.7 1.2 2.1 3.0 0.15 0.7 1.1 3.1 0.25 1.05 1.9 2.6 0.45 1.3 1.9 2.3 0.3 0.55 0.85 0.9 0.25 0.3 0.55 0.95 0.1 0.3 0.55 0.6 0.95 0.3 0.35 0.5 0.6
0.9 1.6 2.3 2.4 0.9 1.3 1.7 2.4 0.7 0.9 1.3 3.4 0.3 1.0 1.3 1.6 0.3 0.6 1.2 1.5 0.5 0.9 1.5 1.6 0.3 0.4 0.4 0.5 0.1 0.3 0.6 0.6 0.7 0.3 0.4 0.5 0.6
and N& = (S;y!;,
(9) G
Table 4 summarizes Coorecmltotlon
the results for Sr. The partition
coefficient of Sr is much larger than that of the other ions studied. Here, too, the kinetic effect is very clear (Fig. 9). ks, tends to be higher in more concentrated brines and lower at higher temperatures (Fig. 10). The effect of the brine concentration is more apparent Coprecipitotlon
of Ma at 30°C
I
I
I
of No ot 30°C I
I
I
I
1
0
1.0 R,,(mole/mm)
(xIO-~)
Fig. 3. The partition coefficients of Mg as function of the growth rate at 30’C. (+) from brine S.W.3, ( x ) from brine S.W.5, (0) from brine S.W.8. The cross represents average errors.
I
o
3.0 t
1.0 R,, (mole/mm)
II
-I
2.0 (~10~~)
Fig, 4. The partition coefficients of Na as function of the growth rate at 30 C. (+) from brine S.W.3, ( x ) from brine S.W.5, (0) from brine S.W.8. The cross represents average errors.
1476
JACOB
than for the other ions. The partition coefficients found in these experiments range between 0.10 and 0.80 under different conditions.
KUSHNIR
Theoretical values of the partition coefficients can be calculated if the coprecipitation is assumed to follow an isomorphous substitution mechanism under equilibrium conditions. The following equation describes the partition coefficient of a divalent cation
The concentrations of Cl in gypsum were below the detection limit of the analytical method (Cl Ca < 10 ‘). The partition coefficient for Cl was thus smaller than 1 x 10Yh. Obviously no pattern could have been recorded for the behaviour of the coprecipitation of Cl with gypsum at different growth rates and temperatures.
t [1111 Copreclpltatlon I
b 3
0
7‘h
ordfv.
of’ muyt~itud~
The partition sequence
coefficients
coQi&icients
Na G
-5
c@
Q
the 0
Sr $
1.0
Fig. 7. The partition coefficients of Na as function of the growth rate in brine SW.5 at: 3O’C ( x ); 4O’C (*) and 50°C (0). The cross represents average errors.
Copreclpltotlon
I Copreclpltatatlon
I
of K at 30°C
I
I
I
I
’
’
I
I
I
I
I
loI
I]
I
I
’
’
Flp. 5. The partltlon cortlicients of K as function of the growth rate at 10 C (+) from brme S.W.3, ( x ) from brine S.W.5. 10) from hrme S.W.8. The cross represents average
0
I
I
Coprecipltation
I
I
I
I
l
I
1.0 R,,(mole/mln)
2.0
of Sr at 30°C II
I
II
l
,
0
I
X
IIIII,
‘I
(xIO-‘)
0.8
Y
0
’
Fig. 8. The partition coefficients of K as function of the growth rate in brine SW.5 at: 30°C ( x ): 40°C (*) and 5O’C (0). The cross represents average errors.
of Mg from brme S.W.5
I
’
1.0
III I
’
R,,(mole/min)
errors.
4.0 -
’
S.W.5
X
2.0
R,,(mole/min)(xIO-4)
Copreclpltatlan
’
brine
t
III
I
1.0
0
of K from
3.0
t-
tl
2.0
K > Mg > Cl
The solubilities of the respective sulfate salts (and calcium chloride) increase in the same order; i.e. the more soluble XSOs is the smaller the partition coefficient of ion X.
I
I
e
X
of the ions follow
I
I
Xi
I .o
of r/w partition
I
I
Xt
2.0
cf
DISCUSSION
I
X
3.0 t
of No from brine SW.5
I
I
I
c;i
X
X +
Cw
,I
2.0 (xIO-~)
Fig. 6. The partitton coetklents of Mg as function of the growth rate in brine SW.5 at: 30 C (x ); 4O’C (*) and 50 C’(@J_ l‘hc cross represents average errors.
Fig. 9. The partition coefficients of Sr as function of the growth rate at 30°C. (+) from brine S.W.3, ( x ) from brine S.W.5. (0) from brine S.W.8. The cross represents average errors
1477
An experimental study Copreclpltatlon
I
I
of Sr from
I
I
I
brine
I
I
S.W.5
I
1
1.
0.8 -
0.6 G=J0.4 -
Y
X
X
-x 0.2:
f
rti
1:
*
x
e
tB@
@ 3 I
0
I
I
I
I
I
I
1.0
I
II
2.0
R,,(mole/mln)
(~10~~)
Fig. 10. The partition coefficients of Sr as function of the growth rate in brme S.W.5 at: 30°C (x); 40°C (*) and 50°C (0). The cross represents average errors. X2+
into gypsum (MCINTIRE, 1963): D
=
x
~,,(CaSO,.2H20) K,(XSO, .2H20)
yx2+
G
e
Where K,, are the thermodynamic solubility products of the pure end-member minerals, y are the activity coefficients of the ions in solution and Ap is the solid solution interaction term. The activity coefficients of the ions in solution are assumed to be roughly equal. The application of this equation to the case of Sr or Mg coprecipitation with gypsum poses two problems: (a) There is no Sr mineral equivalent to gypsum (i.e. no Sr sulfate dihydrate). (b) The solid solution interaction term cannot be estimated a priori. Using the solubility product of SrSO, (2.8 x 10m7 M2) and the experimental value of the partition coefficient of Sr near equilibrium (-0.1 as Rav+ 0), the calculated solid solution interaction term is Ap 2 3.5 kcal/mol. A large solid solution interaction term implies that the isomorphous substitution causes the crystal to depart strongly from ideality. This might effect the mechanism of coprecipitation as is discussed below. The solubility product of magnesium sulfate dihydrate (Sandenite) is unknown, but the solubility products of the other magnesium sulfates (anhydrous, monohydrate and septahydrate) range between 5 and 25 M2. The calculated solid solution interaction term for Mg using DMg = 1 x 10e6 thus ranges between 0.02 and 1 kcalimol. Na and K cannot be treated by this method because of the altervalent nature of the substitution.
The partition coefficients of the studied cations increase with increasing growth rate. Kinetic effects like this one have been known in other systems. RIEHL er al. (1980) have developed an equation which relates the apparent partition coefficient to the degree of supersaturation, under the assumption that the growth mechanism is diffusion controlled. Their equation shows that for depletion systems (partition coeffi-
cient less than 1) the partition coefficient increases with increasing supersaturation. approaching 1 at very high degrees of supersaturation. Indeed, the partition coefficients of the cations in gypsum increase with increasing degree of supersaturation (or growth rate), with a tendency to approach a limiting value at high degrees of supersaturation. but the limiting value is less, than 1. This difference must be explained in terms of the behavior of ions at the surface of the crystal during the growth process. as the growth mechanism is surface controlled. The relationship between the partition coefficient and the average growth rate is described by the empirical equation: D = D, - (D, - Do) t? &’
(11)
where D, is the limiting value of the partition coefficient (for very large Rav). D,, is the value of the partition coefficient at Rav = 0 (i.e. at equilibrium) and (/ is a positive parameter. (A similar equation is adequatefor Sr with D replaced by /+). The values of D,. D, and y for each set of experiments at a giLen temperature and brine were calculated by an iteration program. This program determined the parameters that produced an exponential relation as in eqn (I 1I with the Il:ast RMS deviation from the experimental values. The parameters and their average errors arc summarized in table 5. The inconsistency in the partition coefficients fol strontium reported in previous studies may be explained by the differences m the methods of precipitation which probably resulted in dllferent growth rates.
An increase in temperature tends to lower the partition coefficients in this system. Let us tirst examine the erect of temperature on the equilibrium values of the partition coefficients (i.e. on D, and I;‘:,). In the case of Sr, the effect is very pronounced. For the other cations the trend is the same although the difference5 in D, at different temperatures are close to the cxperimental error. PURKAYASTHA and CHATSKJ~F (1966) reported the same temperature effect on the coprecipitation of Sr with gypsum. The following relation is known to hold for many systems (MCIWIRE. 1963): In D = ” + h T
(12)
where T is the absolute temperature and u and h arc constants. The equilibrium partition coctficients of Stin gypsum follow this relation with (I = I.6 x IO” and b = 3.9. An important phenomenon is the &cct of tempcrature on the change of partition coefficient with growth rate. AS the temperature is mcreascd. the partition coefficient changes less drastically with growth rate. In other words the curve of D (or 1\\,) 15 Kav becomes flatter and the limiting value of D at \c~I, high gt-ohth rates IID,,,) becomes smaller at higher temper-atures.
JACOBKUSHNIR
1478
Table 5. Parmaeters k’, km(for Sr), Do. D, (for Mg, Na and K) and 4 (for all ions) of eqn (I 1) as calculated by the iteration program, and the resulting RMS deviations for the partition coefficients
Sr:
Brine
Temp (‘C)
A3 A5 A8 B3 B5 88 c3 C5 C8
S.W.3 SW.3 SW.8 SW.3 SW.5 S.W.8 s.w.3 s.w.5 SW.8
30 30 30 40 40 40 50 50 50
s.w.3 SW.3 S.W.8 s.w.3 SW.5 S.W.8 SW.3 s.w.5 S.W.8
K: A3 A5 A8 B3 B5 B8 c3 C5 C8
30 30 30 40 40 40 50 50 50
Ii” 10.01
0.03 0.20 0.55 0.03 0.15 0.43 0.06 0.08 0.33
0.58 0.65 0.80 0.43 0.49 0.68 0.27 0.33 0.57
30 30 30 40 40 40 50 50 50
Dill * 0.1
0.2 0.3 0.1 0.2 0.3 0.2 0.1 0.1 0.1
10.0 8.0 3.4 3.9 2.5 I.0 1.0 1.0 0.6
30 30 30 40 40 40 50 50 50
1.5 1.0 1.3 0.2 0.3 0.3 0.1 0.1 0.1
(With the exception of Mg in brine S.W.5 at 4O’C). This effect has implications on the mechanism of coprecipitation, as is discussed below. .Eficr.s of brine concentration The concentration of the brine affects the partition coefficients of all studied cations. The effect is most apparent in the case of Sr. As the brine concentration increases the equilibrium partition coefficient of Sr (k&) increases (from 0.03 in S.W.3 to 0.55 in S.W.8 at 30°C). The increase is almost linear. Ion association of Sr” as SrSOi may be responsible for the effect of brine concentration on the partition coefficients of Sr. As the concentration of sea-water brine is increased from about x 3-x 8, the amount of unassociated strontium increases from 89-94”j0 (calculated using
rates RMS deviation for R for i,
( x 1om5i
q( x 10”) 4.06 3.42 6.0 2.6 2.74 5.42 2.32 2.9 4.9
+ 2 t & f f + k *
0.01 0.03 0.8 0.1 0.17 0.03 0.08 0.1 0.2
2.5 4.4 4.8 1.7 1.7 1.6 0.5 0.7 0.6
-
for D,
(x 10-1) 0.51 0.58 1.52 0.82 2.41 1.9 1.60 1.33 3.2
i f & + f * k i +
0.01 0.02 0.13 0.01 0.05 0.1 0.07 0.01 0.2
0.04 0.05 0.09 0.006 0.03 0.01 0.03 0.01 0.02
7.1 0.87 0.6 2.2 2.2 2.6 4.6 3.0 4.0
f 0.5 i 0.06 i 0.1 F 0.5 f 0.5 + 0.3 i_ 1.0 i 0.3 + 0.3
0.06 0.09 0.07 0.04 0.13 0.03 0.06 0.3 0.02
-
0.009 0.016 0.064 0.006 0.012 0.03 0.65 0.015 0.3
_ __-
* 0.2 5.7 4.5 4.4 3.8 7.2 4.1 3.1 3.1 3.1
0.00 1 0.006 0.2 0.07 0.65 0.1 0.84 1.4 0.6
0.001 0.002 0.015 0.004 0.01 0.004 0.015 0.007 0.002
f 0.2
0.1 0.6 0.7 0.2 0.2 0.2 0.3 0.1 0.1
(x 10-S) SW.3 SW.3 SW.8 SW.3 SW.5 S.W.8 s.w.3 s.w.5 S.W.8
growth
Do
(x 10-y
s.w.3 s.w.3 S.W.8 S.W.3 SW.5 SW.8 SW.3 s.w.5 SW.8
Mg: A3 A5 A8 B3 B5 BX c3 c5 C8
!i +0.01
(X IO_‘+)
Na: A3 A5 A8 B3 B5 B8 c3 c5 C8
and average
0.04 0.04 0.05 0.04 0.07 0.07 0.59 0.05 0.05
(x 1om3j
1.9 2.1 1.8 0.83 0.86 0.9 0.78 0.96 0.81
f f f f f f i i i
0.2 0.2 0.1 0.01 0.06 0.2 0.05 0.05 0.06
0.14 0.16 0.04 0.03 0.2 0.04 0.03 0.08 0.004
0.03 0.05 0.08 0.06 0.06 0.03 0.015 0.045 0.03
program SOLMNEQ; KHARAKA and BARNES, 1973). Thus in a more concentrated brine. relatively more strontium will be adsorbed at the surface of the growing crystal. The ion association of Sr may be responsible for an increase in the partition coefficient of about 5’:” between SW.3 and S.W.8. The actual increase of the partition coefficient is much larger. Ion association alone, therefore, cannot account for the large effect of brine concentration on the partition coefficient of Sr. The effect of brine concentration in the case of Mg, Na and K is much smaller than in the case of Sr. and the partition coefficients decrease as the brine concentration increases. This can be attributed to the effect of brine concentration on the growth rate. The growth rate for a given degree of supersaturation (or
An
0
20
4.0
6.0
8.0
experimental
10.0
Ma
2.0
4.0
6.0
Corrected
8.0
10.0
R,,(moles/m~n) (110-51
Fig. 1 I. Partition coefficients of Mg, Na and K at 30 C against the growth rate ‘corrected’ for the effect of brine concentration [eqn (14)]. (+) brine S.W.3, ( x ) brine S.W.5, (0) brine S.W.8.
Ca concentration) increases with brine concentration (Table 3). This relation is expressed as: Rav = k’(C)S’
(13)
where C is the brine concentration (the concentration of Cl relative to normal seawater). The effect of brine concentration on growth rate may be ‘corrected’ by applying the relation: Rav(C,) =
zz
Rav(C2)
(14)
2
where C, and CZ are two different brine concentrations. Plotting the partition coefficients against the ‘corrected’ values of the growth rate (Fig. 11) shows that the effect of brine concentration on the relation between the partition coefficient and growth rate may be explained by its effect on growth rate only. (Except in the case of Na in S.W.5 where the correction seems to be too large). Mechclnisn~ qf’coprecipifation The following proposed mechanism of coprecipitation is based on the effect of growth rate on the incor-
study
I419
poration of foreign cations into gypsum. In a surface controlled growth mechanism the extent to which a foreign cation will enter the crystal depends on the relative fluxes of adsorption and desorption of the coprecipitating ion to and from the growing surface. The partition coefficient will depend, in part, on the relationship between the rate of exchange of the coprecipitating ion at adsorption sites and the rate of growth. The foreign cations adsorb to, and desorb from, the surface of the growing crystal. As the flux of the major precipitating species (calcium, sulfate and water) is increased, more foreign ions are ‘trapped within the crystal structure. The partition coefficient will therefore increase with increasing growth rate. The adsorption flux of the foreign cation depends on its concentration in solution and on the available adsorption sites on the surface. As the growth rate of gypsum is increased. the flux of calcium ions to the surface increases and the number of available sites for the adsorption of the foreign cation decreases. Thus the partition coefficient approaches a limiting value at high1 growth rates due to competition with calcium ions on available adsorption sites. This suggested mechanism requires that the adsorptions desorption fluxes and the growth rate are similar in magnitude. The effect of temperature on the change of the partition coefficient with growth rate also supports this mechanism. At higher temperatures the rate of exchange of ions on adsorption sites is faster and the desorption flux of the coprecipitating ion can more easily compete with the counter flux of the major precipil.ating species. The amount of foreign ions trapped in tlhe crystal during its growth is thus smaller, and consequently the partition coefficient is less affected by the growth rate. The fact that the magnitude of the partition coefficients of Sr, Mg, Na and K follows the order of solubilities of the respective sulfates. suggests that the most probable mechanism of incorporation of these cations into gypsum is through solid solution formation. The formation of normal solid solution (where the foreign cations substitute for Ca in its normal lattice sites) requires that the foreign ion is similar in size and charge to the substituted ion. If the two endmember minerals have a similar structure. solid solution formation usually covers the full range of concentrations between the two pure end-members. This is not the case with Sr or Mg substitution for Ca in gypsum. The ionic radii of Sr” and Mg2 + are 1.13 and 0.65 8, respectively while the ionic radius of Ca’+ is 0.99 A. The radius of Mg” is about 35”,, smaller than the radius of Ca“ and extensive substitution of Mg for Ca in its normal lattice sites will cause severe increase in the free energy of the crystal (HERMANN and SUTTLE. 1961). A possible way of overcoming this is that Mg ions occupy interstitial lattice positions. The solid solution interaction term in the substitution of Sr for Ca in gypsum was shown before to be high (Ap = 3.5 kcal/mol). Such a high solid solution interaction term implies that a crystal in which Ca is par-
JACOB KUSHNIR
1480 GYPSUM, PROJECTION ON (IOO),
Fig. 12. The structure of gypsum. The asterisk indicates an interstitial position among the water molecules which may occupy a foreign ion.
tially substituted by Sr departs strongly from ideality and becomes unstable. The foreign Sr’+ ion will, thus, tend to avoid normal lattice sites even during equilibrium growth and may occupy interstitial positions. The most probable interstitial lattice positions for foreign ions in gypsum are among the water molecules. The water molecules in gypsum are arranged in layers perpendicular to the b axis (ATOJI and RUNDLE, 1958). They are directed with their hydrogen atoms toward the oxygen atoms of the adjacent sulfate ions, and form hydrogen bonds with them (Fig. 12). This structure leaves large openings among the water molecules. The radius of these openings is as large as 1 A. These openings may be filled by Mg2+, Sr’+ or Naf ions (ionic radius of Na+ 0.95 A) without distortion, and K+ ions with slight distortion of the structure (ionic radius of K+ 1.33 A). A cation in this site will be stabilized by the dipole-ion interaction with water. In other words, cations in these positions are partially hydrated. IISHI (1979) has shown that the effective charge of the oxygen atoms in the water molecules in gypsum is larger than the effective charge of the oxygen in the sulfate ion. This increases even further the stabilization of cations in the interstitial sites, among the water molecules. During the growth process some of the foreign cations may be entrapped with part of their hydration sphere and these water molecules may become part of the structural water of the crystal. This sequence of events reduces the free energy requirements on the process of coprecipitation. It is most probable that whenever a normal substitution of Ca*+ in the lattice causes severe free energy increase, the foreign ions will tend to occupy interstitial positions among the structural water molecules. One implication of this mechanism
is that the relative number of foreign ions occupying interstitial sites increases with increasing growth rate. The coprecipitation of monovalent cations into gypsum by a substitution mechanism requires a means of balancing charges over the entire crystal. It is clear that in this experimental system (and in most natural systems) no trivalent co-substitution can balance the charges and that the amount of a foreign anion (chloride) coprecipitated is not sufficient for charge balance. Also, it is unlikely that the positive charge deficiency will be balanced by anion vacancies. Such a large amount of anion vacancies will drastically decrease the stability of the crystal. It is possible, however, that the monovalent cations Na’ and K’ I.e., two monosubstitute for Ca* + stoichiometricallq: valent cations substitute for one calcium ion. The structure of the crystal will not be altered by such substitution if at least one of the pair of monovalent cations will occupy an interstitial position among the water molecules. The formation of liquid inclusions in these experiments is negligible. This is evidenced by the very small concentrations of Cl in the gypsum (Cl/Ca < 10e4). If the chloride is attributed to liquid inclusions only, and the composition of possible liquid inclusions is assumed to be that of the mother brine, the amount of Mg in liquid inclusions is less than 0.3”, of the total Mg in the gypsum; Na < O.l”,,: K < 0.04”,, and Sr < 4 x 10-5”,,. (Calculated for the lowest concentrations of the studied ions). It should be noted, however. that the amount of liquid inclusions in natural gypsum crystals may be much higher (SAROURAUD-ROSSET, 1976; KCJSHSIK. manuscript in preparation) and should be accounted for when considering coprecipitation of ions with gypsum in the natural environment. Solid inclusions of foreign minerals are possible in the case of strontium since the solubility of SrS04 (celestite) is very low. X-ray powder diffractograms do not show any celestite even at the highest concentrations of Sr in gypsum. Even enrichment of possible celestite by differential dissolution of gypsum did not reveal any celestite. It was mentioned before that Sr tends to coprecipitate with and among the water molecules because of its instability in normal lattice positions of gypsum. This causes substantial kinetic effects. It is interesting to compare this with the coprccipitation of Sr into aragonite. The solid solution interaction term of Sr in aragonite is low (strontianite and aragonite have similar structures). Sr therefore occupies normal lattice sites in aragonite, and the coprecipitation of Sr into aragonite is not affected by growth rate (KINSMAY and HOLLAND. 1969). COPRECIPITATED IONS IN GYPSUM AS GEOCHEMICAL INDICATORS The elucidation of the coprecipitation behavior of Sr, Mg. Na, K and Cl into gypsum enables us to use
An experimental
ions as indicators for the conditions of precipitation, The partition coefficients of the cations Sr’+, Mg2+, Na+ and K’ depend upon three important parameters: the temperature, the brine concentration and the growth rate. These parameters may, in principle. be evaluated from the concentrations of the studied cations in gypsum. More information is gained by studying several coprecipitated ions in the same system than by considering one ion only. Various models may be constructed based on the data presented here, in which the history of the studied samples is assumed and the conditions prevailing during deposition are derived. These models must take into account, among other factors, the variability of the parameters and the existence of liquid inclusions. Such models have been successfully applied to various modern and ancient gypsum deposits (KUSHNIR, manuscript in preparation). Analyses of recent gypsum from two locations will be given here as an example. The kinetic effect in the coprecipitation of ions with gypsum is manifested in the negative correlation between crystal size and coprecipitated ion concentrations This correlation was first reported by BUTLER(1973) for Sr in gypsum samples from Abu Dhabi and other locations. I have measured the concentrations of all studied ions in recent gypsum samples from the Bardawil sabkha in Northern Sinai and found similar correlations. The negative correlation between crystal size and coprecipitated-ion concentrations is attributed here to the kinetic effect. In the samples that were measured, small crystals represent episodes of high supersaturations and growth rate: while larger crystals represent slow growth at conditions close to equilibrium. The apparent partition coefficients of the cations in the Bardawil samples were calculated from the concentrations in the gypsum and in the coexisting brine, after correcting for liquid inclusions. It was assumed that the composition of the liquid inclusions was similar to that of the brine. and that the brine composition was fairly constant during crystal growth. One sample will be shown here as an example. This gypsum formed as a these
Table 6. Apparent
partition
coefficients
1481
study
mush of clear prismatic crystals within quartz sand from concentrated seawater brine of C = 7.8 and temperature ranging between 25 and 35°C. Table 6 shows the calculated partition coefficients for each size fraction. The negative correlation between crystal size and apparent partition coefficient exists for all cations. Using eqn (11) and the parameters given in Table 5, growth rates were calculated for each size fraction (Table 6). Good agreement exists between the values calculated for each cation in the same size fraction The agreement that exists between calculated growth rates (using the concentrations of the different coprecipitated ions) and the fact that the lowest calculated growth rates are close to zero, suggest that the concentrations of coprecipitated ions indeed reflect changes in growth rate and not fluctuations in the brine composition or diagenetic processes. Concentrations of coprecipitated ions were also measured in gypsum crystals from the Dead Sea. The apparent partition coefficients (corrected for liquid inclusions) and calculated growth rates of two representative samples are given in Table 6. Sample DSGF is composed of very fine discoidal crystals (20 pm dia) dispersed in fine silt and clay sediment, cored from the bottom of the Dead Sea at 318 m water depth. Sample DSS is a crust of cemented. large ( - 2 cm) crystals that were collected on the Dead Sea shore. Except for Mg, the concentrations of coprecipitated ions in sample DSGF yield growth rates which are similar to those calculated for the Bardawil sample. The crust from the Dead Sea shore yields much higher growth rates, which are attributed to the very intensive evaporation in this region. These examples demonstrate the possibility of using the results of this experimental work to calculate growth rates of natural gypsum crystals. The coprecipitation of cations into gypsum is particularly interesting because of the kinetic effects. Kinetic effects may, indeed, be negligible in other minerals. but whenever they exist, they may be used to derive a valuable geochemical parameter-the rate of crystallization. The use of coprecipitated ions in gypsum as geo-
and calculated growth rates for recent gypsum and the Dead Sea
samples
from
Bardawtl
sabkha
Apparent partition coefficients
No.
DS.
D Mg x 1o-5
Bardawil sabkha 223 mm I2mm 0.5-I mm 0.25-0.5 mm 10.25 mm
0.50 0.54 0.56 0.59 0.71
1.3 1.4 1.6 1.8 3.9
DSGF DSS
0.15 0.68
12.0 110
Calculated growth rates (mol,/min) (X 10-4) from D Na x 1o-4
DK x 1o-4
Sr
Mg
Na
K
0. I 8 0.26 0.38 0.69 1.1
0.60 0.55 0.59 0.72 1.31
0.0 0.14 0.29 0.54 2.2
0.0 0.15 0.47 0.81 7.1
0.0 0.10 0.33 1.2 1.8
0.35 0.15 0.36 0.85 3.5
0.3
0.54 3.9
0.16 12.0
0.25 73.0
0.12 47.0
1I.0
JACOB KUSHN~R
1482
chemical indicators also requires the knowledge of the behavior of those ions after the primary deposition of gypsum. The behavior of coprecipitated ions during early diagenesis and during phase transformations (gypsum-anhydrite) is currently under study. A complete understanding of the behavior of coprecipitated ions in gypsum and anhydrite during various processes may furnish us with valuable geochemical indicators for the conditions prevailing during formation and
diagenesis
of evaporites.
Acknowledgemenfs~I wish to thank Prof. Joel R. Gat for his help and guidance, R. A. Garber and Y. Levy for valuable comments concerning the manuscript. Dead Sea gypsum was sampled by R. A. Garber.
REFERENCES ATO~~ M. and RUNDLE R. E. (1958) Neutron diffraction study of gypsum. J. Chem. Phrs. 29, 130&1311. BRANDSE W. P., VAN ROSMALEN G. H. and BROUWER G. (1977) The influence of sodium chloride on the crystallization rate of gypsum. J. Inorg. Nucl. Chem. 39, 2007-2010. BUTLER G. P. (1973) Strontium geochemistry of modern and ancient calcium sulphate minerals. In The Persian Gulf: (ed. B. H. Purser), pp. 423452. Springer. DEAN W. E. and ANDERSON R. Y. (1973) Trace and minor clement variations in the Permian Castile Formation, Delaware Basin, Texas and New Mexico, revealed by varve calibration. In 4th Symp. Salt. Huston. Texas Geol. Sot. I Y73. 275-285. DOERNER H. A. and HOSKINS W. M. (1925) Coprecipitation of radium and barium sulfates. J. Am. Chem. Sot. 47, 662-675. HERMANN J. A. and SUTTLE J. F. (1961) Precipitation and crystallization. In Treatise on Analytical Chrmisrrp. (eds I. M. Kolthoff and P. J. Elving), Part I, Vol 3. pp. 1367-1409. HFRRMANX A. G. (1961) Zur Geochemie des Strontiums in den salinaren Zechstein abbgerunngen der Stassfurt Serie des Sudharzbezirkes. Chrm. Erde 21, 137-194.
ICHIKUNI, M. and MUSHA S. (1978) Partition of strontium between gypsum and solution. Chem. Geol. 21, 359-363. IISH~ K. (1979) Phononspectroscopy and lattice dynamical calculations of anhydrite and gypsum. Phys. Chem. Mineral. 4, 341-359. KHARAKA Y. K. and BARNES I. (1973) SOLMNEQ: Solution-mineral equilibrium computations. U.S. Geol. Sure. Comput. Contrib. PB-215899. KINSMAN D. J. J. and HOLLAND H. D. (1969) The coprecipitation of cations with calcium carbonate-IV. The coprecipitation of Sr with aragonite between 16 and 96C. Geochim. Cosmochim. Acta 33, l-1 7. IXJ S. T. and NANCOLLAS G. H. (1970) The kinetics of crystal growth of calcium sulfate dihydrate. .!. Cryst. Growth 6, 281-289. MCINTIRE W. L. (1963) Trace element partition coefficients-a review of theory and applications to geology. Geochim. Cosmochim. Acta 27, 1209-1264. NOLL W. (1934) Geochemie des Strontiums; mit Bemerkungen zur Geochemie des Bariums. Chemi. Erde 8, 587-600. ORION (1977) Analytical Methods Guide. Eighth edn Orion Research Inc. PURKAYASTHA B. C. and CHAT~ERJEE A. (1966) On the study of the uptake of strontium tracer by different forms of calcium sulphate. 1. Indian Chem. Sot. 43, 687-693. RIEHL N.. SIZMANN R. and HIDALGO S. J. P. (1960) Zur Deutung der Verteilung kleinster Fremdsubstanzmengen zwishen einem wachsenden Kristall und der Losung. Z. Phys. Chrm. Neue Folge 25, 351-359. SABOURAUD-ROSSETC. (1974) Determination par activation neutronique des rapports CI/Br des inclusions fluides de divers gypses. Correlation avec les donnes de la microcryoscopie et interpretations genetiques. Sedimentology 21.415431. SABOURAUD-ROSSETC. (1976) Solid and liquid mclusions in gypsum. These d’Etat, UniuersitP Paris Sud, Centre d’Orsay (in French). SMITH B. R. and SWEE~T F. (1971) The crystallization of calcium su!fate dihydrate. J. Colloid Interfirce Sci. 37, 612-618. Uswws~l E. (1973) Das geochemische Verhalten des Strontiums bei der Genese und Diagenese von CaKarbonat und Ca-Sulfat Mineralen. Contrib. Minerul. Petrol. 38, 177-195. YAMAMOTOM. and UNEKI Y. (1978) The distribution of Sr between gypsum and aqueous solutions. Sekko To Sekkai I%, 196-200 (in Japanese).
x0 1001-I47I%~1.01)‘0
The coprecipitation of strontium, magnesium, sodium, potassium and chloride ions with gypsum. An experimental study JACOB KUSHNIR Geoscience
Group,
Isotope
Department,
(Received 4 Januury
Weizmann
1980; uccepted
Institute
in recised,form
of Science, Rehovot,
Israel
29 Muy 1980)
Abstract--The coprecipitation of Sr”, Mg’+, Na’, K+ and Cl- into gypsum was studied as a function of temperature, brine concentration and growth rate. The concentrations of the studied cations in the gypsum increase with growth rate (kinetic effect), with a tendency to reach a limiting value at high growth rates. The partition coefficients of Sr tend to increase with brine concentration and decrease with temperature. The partition coefficients of the other cations also decrease with temperature but depend only very slightly on brine concentration. The concentrations of coprecipitated chloride are negligibly small. The coprecipitation behavior is explained in terms of the relation between the rate of desorption of the coprecipitating ions from the surface of the growing crystal, and the rate of growth. The studied cations may substitute for Ca” in its normal lattice sites and/or reside in interstitial positions among the structural water molecules. The relative amount of foreign cations occupying interstitial positions increases with increasing growth rate. The elucidation of the behavior of coprecipitated ions in gypsum given here forms a basis for the utilization of these ions as geochemical indicators for the environment of deposition of gypsum. These indicators may help in reconstructing important parameters such as temperature, brine concentration and growth rate.
INTRODUCTION
GYPSUM is an important associated
primarily
sedimentary with
evaporite
mineral
which
deposits.
is
The
of the processes that are involved in the formation of evaporite deposits require the reconstruction of the physico-chemical conditions prevailing during deposition. The concentrations of coprecipitated ions have been utilized as indicators for the conditions of formation and evolution of some sedimentary minerals. In most studies an equilibrium approach was adopted; that is, the coexisting phases (solution and solid) were assumed to be in equilibrium with each other and a straight forward thermodynamic treatment was applied. In the case of gypsum, laboratory studies have dealt only with the coprecipitation of strontium (PURKAYASTHA and CHATTERJEE, 1966; USDOWSKI, 1973; ICHIKUNI and MUSHA. 1978; YAMAMO~Oand UNEKI, 1978). Studies on natural samples of gypsum, however, have included measurements of other ions too. (Sr: NOLL, 1934; HERRMANN, 1961; BUTLER, 1973; Na, K, Mg: DEAN and ANDERSON, 1973; Cl, Br: SABOURAUDROSSET, 1974). There are large discrepancies in the measured values of the partition coefficient of strontium between gypsum and the solution as reported by these workers. The partition coefficient at 25°C was found to be 0.30-0.41 by PURKAYASTHAand CHATTERJEE(1966), 0.414.64 by USDoWSKI (1973), 0.21 by ICHIKUSI and MUSHA (1978) and 0.214.33 by YAMAMOTO and U~VEKI (1978). BUTLER (1973) derived the partition coefficient of strontium between understanding
1471
gypsum and the solution from geochemical data and reported 0.19 at 28°C. BUTLER (1973) also reported a negative correlation between gypsum crystal size and the concentration of coprecipitated strontium. The results of these studies suggest that the coprecipitation of strontium with gypsum is influenced by the growth rate of the mineral. Since the growth of gypsum is a surface controlled reaction (LIU and NAW COLLAS, 1970), the coprecipitation of ions with gypsum is expected to be affected by the dynamic behavior of the growing crystal surface. The purpose of this study was to elucidate the behavior of coprecipitated ions with gypsum, paying attention to possible kinetic effects. The behavior of the following ions was studied: strontium, sodium, potassium, magnesium and chloride. Strontium was chosen because of its importance as a minor element in evaporitic environments and the extensive data in the literature of concentrations of Sr in gypsum that already exists. The other ions were chosen because of their abundance and well known behavior in the environments of gypsum deposition.
EXPERIMENTAL Gypsum was precipitated in the laboratory under well defined conditions. The compositions of the solution and the solid were then measured. The rate of growth was controlled by establishing a constant degree of supersaturation using a Ca-stat system which is shown in Fig. 1 and will be described in the following section. One hundred ml of sohmon were placed in a double walled reaction vessel which was kept at constant tempera-
1472
JACOB KUSHNIR
Fig, 1. The Ca-stat system, B-Buerette; Ca-Calcium trode; MV-magnetic valve; R-recorder; S-stirrer;
ture by a flow of thermostated water (within +OS”C). The solution was constantly stirred by a rotating bent glass rod. (To prevent crushing of the crystals a magnetic stirrer was not used). The stirring rate was kept constant in all runs. The crystals were kept in suspension except in a few runs where some crystals adhered to the PVC envelope of the Ca-selective electrode. A Ca-selective electrode (Radiometer type F2112Ca) coupled with a saturated calomel reference electrode (Radiometer type K401) were connected to a titrator (Radiometer type TTTl). The titrator was set to open a magnetic valve whenever the potential over the electrodes increased above a given value (i.e. whenever the activity of calcium ions in the solution dropped below a given value). A small amount of 1M CaCI, solution was added to the reaction vessel whenever the valve was opened. The amount of CaCI, solution added during the experiment was recorded. In the beginning of the experiment a certain volume (Vss) of IM CaCi2 was added to the solution to achieve supersaturation. This amount never exceeded 5 ml. After the desired supersaturation was achieved a volume (Vgr) of I M CaClz was added by the action of the titrator and then the experiment was stopped. The change in volume during the experiment was about 3”/, and the amount of gypsum precipitated in each run was essentially the same (about 0.5 g). The small unavoidable changes in the potential over the Ca-selective electrode were follqwed by a strip chart recorder that was connected to the titrator. The fluctuations in the potential were always less than +0.5 mV. Three artificial seawater brines resembling seawater that was evaporated to x 3, x 5 and x 8 its original concentration were prepared. The solutions were saturated with respect to gypsum at the appropriate temperature and filtered prior to the experiment. Analyses of these solutions are given in Table 1. The concentration of sulfate in these solutions was higher than the concentration of calcium and therefore the amount of sulfate in the solution changed by only I@-1%; during the experiment. Experiments were conducted at three different temperatures: 30,40 and 5O’C. At the end of each experiment the crystals were quickly separated from the solution by filtration, washed several times with distilled water and then with acetone and dried. The final clear solution was analysed for calcium and strontium. The dried crystals were identified as gypsum by X-ray diffraction and under the microscope. The crystals were-dissolved in distilled water and this solution was analysed for Sr, Na, K, Mg, Cl and Ca. Concentrations of the coprecipitated ions are reported as the molar ratio to cal-
selective electrode; K-calomel reference elecT-titrator; W-flow of thermostated water.
cium. All cation analyses were performed on a Perkin Elmer model 303 atomic absorption spectrometer. The standards for Sr, Na, K and Mg were matched to the samples in their calcium sulfate concentrations since CaSO, affects the measurement. Analytical uncertainties were lY:, for Sr/Ca, 24; for Na,Ca. 5”” for Mg/Ca and lOy~ for K/Ca. Chloride in the gypsum was very low. An attempt was made to analyse Cl using the Gran’s Plot method (Orion, 1977), but the concentrations were below the detection limit of this method (Cl/Ca < 10e4). Cations in the brines were analysed by atomic absorption spectrometry using standard techniques. Chloride in the brines was analysed by Mohr’s method and sulfate by gravimetry. Analytical uncertainties were 1”~”for Ca, Mg, K. and Cl; 2”; for Sr and Na; 2% for SO,.
RESULTS
Kinetics of crrstullization In view of the effects of growth rate on the coprecipitation of ions with gypsum (which will be demonstrated below) it is necessary to assess the kinetic parameters that are involved in the process of crystallization. The experiments were conducted at various constant degrees of supersaturation. The supersatuTable 1. Compositions of initial brines (moles/liter). C is the concentration factor (Cl in brine/Cl in normal seawater) Brine Ion
SW.3
s.w.5
S.W.8
Ca (30’ C) Ca (4o‘C) Ca (50 C) so, (3O’C) Sr (x 10m4) Na Mg K Cl C
0.0285 0.0260 0.0269 0.185 3.52 1.28 0.136 0.034 I .89 3.4
0.0223 0.0171 0.0204 0.210 4.96 2.27 0.242 0.05 I 2.58 4.7
0.0088 0.008 1 0.0083 0.255 3.64 4.07 0.42 I 0.088 4.61 8.4
1473
An experimental study 3,0 Precipltatlan
klnetlcs, experiment
B52
F----y?
_..’ ,___._...
.”
,,...’
1
0
I
40
I
I
PI
I
80
1
160
120
I
II
1
200
240
I
Fig. 2. An example of the precipitation kinetics. The volume of I M CaCI, added (Vgr) is plotted against time. ration S is defined in terms of the activity of the calcium ions in solution:
Where Q is the activity of Ca in the supersaturated brine and ucao is the activity of Ca at saturation. S was calculated from the difference in potential over the Ca-selective electrode before and after achieving supersaturation. The crystallization process was followed by recording the amount of 1M CaCl, added by the action of the titrator. The growth was preceded by an induction period which was shorter at higher degrees of supersaturation. The growth rate (amount of 1M CaClz added per min) was not constant, increasing during the growth process. This is attributed to increase in surface area of the growing crystals. An example of the crystallization process is shown in Fig. 2. The average growth rate (Rav) was calculated as: Rav (moleimin)
Vgr x 10e3 = ~-~~ -~~ growth duration
where
k is the growth
constant
(3) and
A the surface
area
(Lru and NANCOLLAS, 1970; SMITH and SWEETT, 1971). Assuming that the growth rate changes during the experiment only due to changes in A, we may rewrite eqn (3) as: of the crystals
Rav = k’s2
log Rav = log k’ + 2 log S
(5)
A plot of log Rav vs log S is linear with a slope 2 and an intercept log k’. Using this relation the growth constant for each brine at the three different temperatures was derived (Table 3). The growth constant increases with increasing brine concentration and with increasing temperature. These effects have been previously demonstrated (LIU and NANCOLLAS. 1970; BRANDSE etal., 1977). Coprecipitation
of My, Nu and K
The amounts of Mg, Na and K coprecipitated with gypsum are very small compared with their concentration in solution. The concentration in solution thus remains essentially constant during the growth process. At constant degree of supersaturation (constant concentration of Ca) we may define the partitition coeficient for the coprecipitation of X as:
(2)
where Vgr is the amount of 1M CaC12 added during the growth and the growth duration is the crystallization period minus the induction period. The slowest growth rates achieved were determined by the sensitivity of the Ca-stat setup. The experimental conditions and the kinetic parameters for the 37 experiments are given in Table 2. The growth of gypsum is related to the degree of supersaturation by: R = kAS2
or
(4)
where G stands for gypsum and B for brine; X represents Mg, Na or K and the ratios are in mole/mole. Table 4 summarizes the results for Mg, Na and K. The partition coefficients for each element depend on the experimental conditions. They increase with increasing growth rate (kinetic effect), they tend to be lower at higher temperatures and in more concentrated brines. The kinetic effect is clearly shown in Figs 3-5. The partition coefficients increase with increasing growth rate with a tendency to reach a limiting value at high growth rates. The kinetic effects are smaller at higher temperatures (Figs 68). The partition coefficients of Na range between 0.1 x IO- 4 and 3.1 x lo-“, those of K between 0.1 x 10e4 and 3.4 x lo-“ and of Mg between 0.1 x 10m5 and 4.3 x 10e5. (Under the range of conditions covered in these experiments).
JACORKUSHNIR
1474
Table 2. Experimental conditions and kinetic parameters. Symbols
are explained
in text
Ca in Ra\
vss
VP
Growth duration (min)
30
1.0
30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 40 40 40 50 so 50 50 50 so so 50 so so 50 50 50
I .7 2.7 4.7 0.9 1.5 2.6 3.1 0.6 0.7 1.5 1.7 0.2 0.9 1.0 1.1 0.9 1.5 1.9 2.9 0.6 0.6 1.3 1.8 1.0 2.0 2.4 3.5 0.2 0.3 1.4 1.7 3.1 0.4 0.6 1.3 3.0
2.X 2.3 3.0 3.0 2.9 3.0 3.0 3.0 4.6 3.0 3.0 3.0 3.0 3.0 3.1 3.0 5.2 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.1 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 2.9 3.0 3.0
461 166 102 59 290 148 65 42 5610 235 102 18 1765 94 41 23 2600 11s 58 30 306 103 36 30 280 200 61 IO 3350 140 58 48 16 300 153 57 IO
Temp No.
Brine
( C)
A31 A32 A33 A34 AS1 AS2 AS3 AS4 A81 A82 AX3 A84 931 932 933 934 951 BS2 953 954 9x1 982 983 984 c31 C32 c33 c34 C51 es2 c53 c54 c5s C.81 C82 C83 C84
s.w.3 s.w.3 SW.3 s.w.3 SW.5 s.w.5 s.w.5 SW.5 S.W.8 S.W.8 SW.8 SW.8 s.w.3 SW.3 SW.3 SW.3 s.w.5 SW.5 s.w.5 s.w.5 S.W.8 S.W.8 SW.8 SW.8 SW.3 s.w.3 SW.3 s.w.3 SW.5 s.w.5 s.w.5 s.w.5 s.w.s SW.8 S.W.8 SW.8 SW.8
The concentration of Sr in solution is low (limited by the solubility of SrSO,) and the number of Sr ions coprecipitating with gypsum is comparable with the number of Sr ions in the brine. Thus the concentration of Sr in the brine changes considerably as Table 3. Growth
constants I\’ calculated eqn (4)
Temp No.
Brine
( C)
A3 AS A8 93 95 98 c3 c5 C8
SW.3 s.w.5 S.W.8 s.w.3 SW.5 S.W.8 s.w.3 SW.5 S.W.8
30 30 30 40 40 40 40 50 50
final brine
(x 10-5)
M
+ lo”,,
(x0.01)
0.61 1.4 2.9 5.1 1.0 2.0 4.6 7.1 0.082 1.3 2.9 17.0 0.17 3.2 1.6 13.0 0.2 2.6 5.2 10.0 0.98 2.9 8.3 10.0 1.1 1.5 4.9 30.0 0.09 2.1 5.2 6.2 19.0 1.0 1.9 5.3 30.0
S 0.30 0.57 0.89
3.23 4.62 6.00 7.00 3.36 4.62 5.3s 6.62 1.15 2.23 2.51 4.48 3.08 4.62 5.71 6.60 2.96 3.33 3.83 4.58 1.12 1.31 1.67 I .72 4.0X 4.42 4.64 5.48 3.25 3.40 3.75 4.00 4.48 I .06 1.13 1.31 2.13
1.59 0.30 0.61 0.96 1.21 0.17 0.68 0.89 1.21 0.18 0.78 1.21 1.58 0. I7 0.58 0.95 1.38 0.34 0.58 0.99 1.08 0.40 0.64 0.81 1.21 0.06 0.35 0.56 0.72 1.31 0.27 0.37 0.62 I .44
more gypsum crystallizes. PURKAYASTHAand CHATERJEE(1966) have shown that the distribution of Sr between solution and gypsum can be described by a Doerner-Hoskins relation (DOERNER and HOSKINS, 1925). This relation will be used here in the form:
log(l+ x$) = Wog
jl
+ ;.$j
using
k’ mol/min
(x 10-5) 2.7 5.0 5.7 5.2 6.0 8.5 11.0 12.0 14.0
mol/min
k 0.1 f 0.1 + 0.3 & 0.2 f 0.1 + 0.2 +_ 1.0 * 1.0 +_ 1.0
(7)
where N denotes total number of moles and ks, is the logarithmic partition coefficient of Sr in gypsum. The total number of moles of Ca and Sr in the brine was calculated from their concentrations in solution multiplied by (100 + Vss + Vgr) x 10 ~‘. The error introduced by the changes in volume during the growth process is less than 3”,,. The total number of moles of Sr and Ca in the gypsum were calculated as: NE = [lo0 SrEitln, - (100 + Vss + Vgr) S&r] x IO_”
(8)
An experimental study Table 4. Calculated
partition
coefficients
1475
for the coprecipitation
of Sr. Mg. Na and K with
gypsum D UA
Db
Temp No.
Brine
( C)
k
x lo-5
X 1O-4
DK x 1om4
A31 A32 A33 A34 AS1 A52 A53 A54 A81 A82 A83 A84 B31 832 B33 B34 B51 852 B53 B54 B81 B82 B83 B84 c31 c32 c33 c34 c51 C52 c53 c54 c55 C81 C82 C83 C84
SW.3 SW.3 S.W.3 S.W.3 SW.5 S.W.5 SW.5 SW.5 S.W.8 SW.8 SW.8 S.W.8 SW.3 s.w.3 s.w.3 SW.3 SW.5 s.w.5 SW.5 SW.5 SW.8 SW.8 S.W.8 SW.8 s.w.3 s.w.3 SW.3 SW.3 s.w.5 S.W.5 s.w.5 s.w.5 s.w.5 SW.8 S.W.8 SW.8 S.W.8
30 30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 40 40 40 50 50 50 50 50 50 50 50 50 50 50 50 50
0.15 0.21 0.41 0.51 0.33 0.42 0.56 0.61 0.55 0.69 0.73 0.80 0.04 0.25 0.37 0.41 0.17 0.31 0.42 0.46 0.54 0.63 0.68 0.68 0.11 0.12 0.20 0.26 0.10 0.20 0.27 0.29 0.33 0.42 0.48 0.55 0.57
1.9 2.7 3.1 4.1 1.5 2.4 3.0 3.8 1.4 1.9 2.6 4.3 0.5 1.4 2.1 2.9 0.4 1.4 3.0 4.2 0.6 1.1 2.1 2.4 0.3 0.3 1.0 2.8 0.1 0.6 1.1 1.5 2.6 0.3 0.5 1.1 2.8
0.5 0.9 1.5 2.5 0.7 1.2 2.1 3.0 0.15 0.7 1.1 3.1 0.25 1.05 1.9 2.6 0.45 1.3 1.9 2.3 0.3 0.55 0.85 0.9 0.25 0.3 0.55 0.95 0.1 0.3 0.55 0.6 0.95 0.3 0.35 0.5 0.6
0.9 1.6 2.3 2.4 0.9 1.3 1.7 2.4 0.7 0.9 1.3 3.4 0.3 1.0 1.3 1.6 0.3 0.6 1.2 1.5 0.5 0.9 1.5 1.6 0.3 0.4 0.4 0.5 0.1 0.3 0.6 0.6 0.7 0.3 0.4 0.5 0.6
and N& = (S;y!;,
(9) G
Table 4 summarizes Coorecmltotlon
the results for Sr. The partition
coefficient of Sr is much larger than that of the other ions studied. Here, too, the kinetic effect is very clear (Fig. 9). ks, tends to be higher in more concentrated brines and lower at higher temperatures (Fig. 10). The effect of the brine concentration is more apparent Coprecipitotlon
of Ma at 30°C
I
I
I
of No ot 30°C I
I
I
I
1
0
1.0 R,,(mole/mm)
(xIO-~)
Fig. 3. The partition coefficients of Mg as function of the growth rate at 30’C. (+) from brine S.W.3, ( x ) from brine S.W.5, (0) from brine S.W.8. The cross represents average errors.
I
o
3.0 t
1.0 R,, (mole/mm)
II
-I
2.0 (~10~~)
Fig, 4. The partition coefficients of Na as function of the growth rate at 30 C. (+) from brine S.W.3, ( x ) from brine S.W.5, (0) from brine S.W.8. The cross represents average errors.
1476
JACOB
than for the other ions. The partition coefficients found in these experiments range between 0.10 and 0.80 under different conditions.
KUSHNIR
Theoretical values of the partition coefficients can be calculated if the coprecipitation is assumed to follow an isomorphous substitution mechanism under equilibrium conditions. The following equation describes the partition coefficient of a divalent cation
The concentrations of Cl in gypsum were below the detection limit of the analytical method (Cl Ca < 10 ‘). The partition coefficient for Cl was thus smaller than 1 x 10Yh. Obviously no pattern could have been recorded for the behaviour of the coprecipitation of Cl with gypsum at different growth rates and temperatures.
t [1111 Copreclpltatlon I
b 3
0
7‘h
ordfv.
of’ muyt~itud~
The partition sequence
coefficients
coQi&icients
Na G
-5
c@
Q
the 0
Sr $
1.0
Fig. 7. The partition coefficients of Na as function of the growth rate in brine SW.5 at: 3O’C ( x ); 4O’C (*) and 50°C (0). The cross represents average errors.
Copreclpltotlon
I Copreclpltatatlon
I
of K at 30°C
I
I
I
I
’
’
I
I
I
I
I
loI
I]
I
I
’
’
Flp. 5. The partltlon cortlicients of K as function of the growth rate at 10 C (+) from brme S.W.3, ( x ) from brine S.W.5. 10) from hrme S.W.8. The cross represents average
0
I
I
Coprecipltation
I
I
I
I
l
I
1.0 R,,(mole/mln)
2.0
of Sr at 30°C II
I
II
l
,
0
I
X
IIIII,
‘I
(xIO-‘)
0.8
Y
0
’
Fig. 8. The partition coefficients of K as function of the growth rate in brine SW.5 at: 30°C ( x ): 40°C (*) and 5O’C (0). The cross represents average errors.
of Mg from brme S.W.5
I
’
1.0
III I
’
R,,(mole/min)
errors.
4.0 -
’
S.W.5
X
2.0
R,,(mole/min)(xIO-4)
Copreclpltatlan
’
brine
t
III
I
1.0
0
of K from
3.0
t-
tl
2.0
K > Mg > Cl
The solubilities of the respective sulfate salts (and calcium chloride) increase in the same order; i.e. the more soluble XSOs is the smaller the partition coefficient of ion X.
I
I
e
X
of the ions follow
I
I
Xi
I .o
of r/w partition
I
I
Xt
2.0
cf
DISCUSSION
I
X
3.0 t
of No from brine SW.5
I
I
I
c;i
X
X +
Cw
,I
2.0 (xIO-~)
Fig. 6. The partitton coetklents of Mg as function of the growth rate in brine SW.5 at: 30 C (x ); 4O’C (*) and 50 C’(@J_ l‘hc cross represents average errors.
Fig. 9. The partition coefficients of Sr as function of the growth rate at 30°C. (+) from brine S.W.3, ( x ) from brine S.W.5. (0) from brine S.W.8. The cross represents average errors
1477
An experimental study Copreclpltatlon
I
I
of Sr from
I
I
I
brine
I
I
S.W.5
I
1
1.
0.8 -
0.6 G=J0.4 -
Y
X
X
-x 0.2:
f
rti
1:
*
x
e
tB@
@ 3 I
0
I
I
I
I
I
I
1.0
I
II
2.0
R,,(mole/mln)
(~10~~)
Fig. 10. The partition coefficients of Sr as function of the growth rate in brme S.W.5 at: 30°C (x); 40°C (*) and 50°C (0). The cross represents average errors. X2+
into gypsum (MCINTIRE, 1963): D
=
x
~,,(CaSO,.2H20) K,(XSO, .2H20)
yx2+
G
e
Where K,, are the thermodynamic solubility products of the pure end-member minerals, y are the activity coefficients of the ions in solution and Ap is the solid solution interaction term. The activity coefficients of the ions in solution are assumed to be roughly equal. The application of this equation to the case of Sr or Mg coprecipitation with gypsum poses two problems: (a) There is no Sr mineral equivalent to gypsum (i.e. no Sr sulfate dihydrate). (b) The solid solution interaction term cannot be estimated a priori. Using the solubility product of SrSO, (2.8 x 10m7 M2) and the experimental value of the partition coefficient of Sr near equilibrium (-0.1 as Rav+ 0), the calculated solid solution interaction term is Ap 2 3.5 kcal/mol. A large solid solution interaction term implies that the isomorphous substitution causes the crystal to depart strongly from ideality. This might effect the mechanism of coprecipitation as is discussed below. The solubility product of magnesium sulfate dihydrate (Sandenite) is unknown, but the solubility products of the other magnesium sulfates (anhydrous, monohydrate and septahydrate) range between 5 and 25 M2. The calculated solid solution interaction term for Mg using DMg = 1 x 10e6 thus ranges between 0.02 and 1 kcalimol. Na and K cannot be treated by this method because of the altervalent nature of the substitution.
The partition coefficients of the studied cations increase with increasing growth rate. Kinetic effects like this one have been known in other systems. RIEHL er al. (1980) have developed an equation which relates the apparent partition coefficient to the degree of supersaturation, under the assumption that the growth mechanism is diffusion controlled. Their equation shows that for depletion systems (partition coeffi-
cient less than 1) the partition coefficient increases with increasing supersaturation. approaching 1 at very high degrees of supersaturation. Indeed, the partition coefficients of the cations in gypsum increase with increasing degree of supersaturation (or growth rate), with a tendency to approach a limiting value at high degrees of supersaturation. but the limiting value is less, than 1. This difference must be explained in terms of the behavior of ions at the surface of the crystal during the growth process. as the growth mechanism is surface controlled. The relationship between the partition coefficient and the average growth rate is described by the empirical equation: D = D, - (D, - Do) t? &’
(11)
where D, is the limiting value of the partition coefficient (for very large Rav). D,, is the value of the partition coefficient at Rav = 0 (i.e. at equilibrium) and (/ is a positive parameter. (A similar equation is adequatefor Sr with D replaced by /+). The values of D,. D, and y for each set of experiments at a giLen temperature and brine were calculated by an iteration program. This program determined the parameters that produced an exponential relation as in eqn (I 1I with the Il:ast RMS deviation from the experimental values. The parameters and their average errors arc summarized in table 5. The inconsistency in the partition coefficients fol strontium reported in previous studies may be explained by the differences m the methods of precipitation which probably resulted in dllferent growth rates.
An increase in temperature tends to lower the partition coefficients in this system. Let us tirst examine the erect of temperature on the equilibrium values of the partition coefficients (i.e. on D, and I;‘:,). In the case of Sr, the effect is very pronounced. For the other cations the trend is the same although the difference5 in D, at different temperatures are close to the cxperimental error. PURKAYASTHA and CHATSKJ~F (1966) reported the same temperature effect on the coprecipitation of Sr with gypsum. The following relation is known to hold for many systems (MCIWIRE. 1963): In D = ” + h T
(12)
where T is the absolute temperature and u and h arc constants. The equilibrium partition coctficients of Stin gypsum follow this relation with (I = I.6 x IO” and b = 3.9. An important phenomenon is the &cct of tempcrature on the change of partition coefficient with growth rate. AS the temperature is mcreascd. the partition coefficient changes less drastically with growth rate. In other words the curve of D (or 1\\,) 15 Kav becomes flatter and the limiting value of D at \c~I, high gt-ohth rates IID,,,) becomes smaller at higher temper-atures.
JACOBKUSHNIR
1478
Table 5. Parmaeters k’, km(for Sr), Do. D, (for Mg, Na and K) and 4 (for all ions) of eqn (I 1) as calculated by the iteration program, and the resulting RMS deviations for the partition coefficients
Sr:
Brine
Temp (‘C)
A3 A5 A8 B3 B5 88 c3 C5 C8
S.W.3 SW.3 SW.8 SW.3 SW.5 S.W.8 s.w.3 s.w.5 SW.8
30 30 30 40 40 40 50 50 50
s.w.3 SW.3 S.W.8 s.w.3 SW.5 S.W.8 SW.3 s.w.5 S.W.8
K: A3 A5 A8 B3 B5 B8 c3 C5 C8
30 30 30 40 40 40 50 50 50
Ii” 10.01
0.03 0.20 0.55 0.03 0.15 0.43 0.06 0.08 0.33
0.58 0.65 0.80 0.43 0.49 0.68 0.27 0.33 0.57
30 30 30 40 40 40 50 50 50
Dill * 0.1
0.2 0.3 0.1 0.2 0.3 0.2 0.1 0.1 0.1
10.0 8.0 3.4 3.9 2.5 I.0 1.0 1.0 0.6
30 30 30 40 40 40 50 50 50
1.5 1.0 1.3 0.2 0.3 0.3 0.1 0.1 0.1
(With the exception of Mg in brine S.W.5 at 4O’C). This effect has implications on the mechanism of coprecipitation, as is discussed below. .Eficr.s of brine concentration The concentration of the brine affects the partition coefficients of all studied cations. The effect is most apparent in the case of Sr. As the brine concentration increases the equilibrium partition coefficient of Sr (k&) increases (from 0.03 in S.W.3 to 0.55 in S.W.8 at 30°C). The increase is almost linear. Ion association of Sr” as SrSOi may be responsible for the effect of brine concentration on the partition coefficients of Sr. As the concentration of sea-water brine is increased from about x 3-x 8, the amount of unassociated strontium increases from 89-94”j0 (calculated using
rates RMS deviation for R for i,
( x 1om5i
q( x 10”) 4.06 3.42 6.0 2.6 2.74 5.42 2.32 2.9 4.9
+ 2 t & f f + k *
0.01 0.03 0.8 0.1 0.17 0.03 0.08 0.1 0.2
2.5 4.4 4.8 1.7 1.7 1.6 0.5 0.7 0.6
-
for D,
(x 10-1) 0.51 0.58 1.52 0.82 2.41 1.9 1.60 1.33 3.2
i f & + f * k i +
0.01 0.02 0.13 0.01 0.05 0.1 0.07 0.01 0.2
0.04 0.05 0.09 0.006 0.03 0.01 0.03 0.01 0.02
7.1 0.87 0.6 2.2 2.2 2.6 4.6 3.0 4.0
f 0.5 i 0.06 i 0.1 F 0.5 f 0.5 + 0.3 i_ 1.0 i 0.3 + 0.3
0.06 0.09 0.07 0.04 0.13 0.03 0.06 0.3 0.02
-
0.009 0.016 0.064 0.006 0.012 0.03 0.65 0.015 0.3
_ __-
* 0.2 5.7 4.5 4.4 3.8 7.2 4.1 3.1 3.1 3.1
0.00 1 0.006 0.2 0.07 0.65 0.1 0.84 1.4 0.6
0.001 0.002 0.015 0.004 0.01 0.004 0.015 0.007 0.002
f 0.2
0.1 0.6 0.7 0.2 0.2 0.2 0.3 0.1 0.1
(x 10-S) SW.3 SW.3 SW.8 SW.3 SW.5 S.W.8 s.w.3 s.w.5 S.W.8
growth
Do
(x 10-y
s.w.3 s.w.3 S.W.8 S.W.3 SW.5 SW.8 SW.3 s.w.5 SW.8
Mg: A3 A5 A8 B3 B5 BX c3 c5 C8
!i +0.01
(X IO_‘+)
Na: A3 A5 A8 B3 B5 B8 c3 c5 C8
and average
0.04 0.04 0.05 0.04 0.07 0.07 0.59 0.05 0.05
(x 1om3j
1.9 2.1 1.8 0.83 0.86 0.9 0.78 0.96 0.81
f f f f f f i i i
0.2 0.2 0.1 0.01 0.06 0.2 0.05 0.05 0.06
0.14 0.16 0.04 0.03 0.2 0.04 0.03 0.08 0.004
0.03 0.05 0.08 0.06 0.06 0.03 0.015 0.045 0.03
program SOLMNEQ; KHARAKA and BARNES, 1973). Thus in a more concentrated brine. relatively more strontium will be adsorbed at the surface of the growing crystal. The ion association of Sr may be responsible for an increase in the partition coefficient of about 5’:” between SW.3 and S.W.8. The actual increase of the partition coefficient is much larger. Ion association alone, therefore, cannot account for the large effect of brine concentration on the partition coefficient of Sr. The effect of brine concentration in the case of Mg, Na and K is much smaller than in the case of Sr. and the partition coefficients decrease as the brine concentration increases. This can be attributed to the effect of brine concentration on the growth rate. The growth rate for a given degree of supersaturation (or
An
0
20
4.0
6.0
8.0
experimental
10.0
Ma
2.0
4.0
6.0
Corrected
8.0
10.0
R,,(moles/m~n) (110-51
Fig. 1 I. Partition coefficients of Mg, Na and K at 30 C against the growth rate ‘corrected’ for the effect of brine concentration [eqn (14)]. (+) brine S.W.3, ( x ) brine S.W.5, (0) brine S.W.8.
Ca concentration) increases with brine concentration (Table 3). This relation is expressed as: Rav = k’(C)S’
(13)
where C is the brine concentration (the concentration of Cl relative to normal seawater). The effect of brine concentration on growth rate may be ‘corrected’ by applying the relation: Rav(C,) =
zz
Rav(C2)
(14)
2
where C, and CZ are two different brine concentrations. Plotting the partition coefficients against the ‘corrected’ values of the growth rate (Fig. 11) shows that the effect of brine concentration on the relation between the partition coefficient and growth rate may be explained by its effect on growth rate only. (Except in the case of Na in S.W.5 where the correction seems to be too large). Mechclnisn~ qf’coprecipifation The following proposed mechanism of coprecipitation is based on the effect of growth rate on the incor-
study
I419
poration of foreign cations into gypsum. In a surface controlled growth mechanism the extent to which a foreign cation will enter the crystal depends on the relative fluxes of adsorption and desorption of the coprecipitating ion to and from the growing surface. The partition coefficient will depend, in part, on the relationship between the rate of exchange of the coprecipitating ion at adsorption sites and the rate of growth. The foreign cations adsorb to, and desorb from, the surface of the growing crystal. As the flux of the major precipitating species (calcium, sulfate and water) is increased, more foreign ions are ‘trapped within the crystal structure. The partition coefficient will therefore increase with increasing growth rate. The adsorption flux of the foreign cation depends on its concentration in solution and on the available adsorption sites on the surface. As the growth rate of gypsum is increased. the flux of calcium ions to the surface increases and the number of available sites for the adsorption of the foreign cation decreases. Thus the partition coefficient approaches a limiting value at high1 growth rates due to competition with calcium ions on available adsorption sites. This suggested mechanism requires that the adsorptions desorption fluxes and the growth rate are similar in magnitude. The effect of temperature on the change of the partition coefficient with growth rate also supports this mechanism. At higher temperatures the rate of exchange of ions on adsorption sites is faster and the desorption flux of the coprecipitating ion can more easily compete with the counter flux of the major precipil.ating species. The amount of foreign ions trapped in tlhe crystal during its growth is thus smaller, and consequently the partition coefficient is less affected by the growth rate. The fact that the magnitude of the partition coefficients of Sr, Mg, Na and K follows the order of solubilities of the respective sulfates. suggests that the most probable mechanism of incorporation of these cations into gypsum is through solid solution formation. The formation of normal solid solution (where the foreign cations substitute for Ca in its normal lattice sites) requires that the foreign ion is similar in size and charge to the substituted ion. If the two endmember minerals have a similar structure. solid solution formation usually covers the full range of concentrations between the two pure end-members. This is not the case with Sr or Mg substitution for Ca in gypsum. The ionic radii of Sr” and Mg2 + are 1.13 and 0.65 8, respectively while the ionic radius of Ca’+ is 0.99 A. The radius of Mg” is about 35”,, smaller than the radius of Ca“ and extensive substitution of Mg for Ca in its normal lattice sites will cause severe increase in the free energy of the crystal (HERMANN and SUTTLE. 1961). A possible way of overcoming this is that Mg ions occupy interstitial lattice positions. The solid solution interaction term in the substitution of Sr for Ca in gypsum was shown before to be high (Ap = 3.5 kcal/mol). Such a high solid solution interaction term implies that a crystal in which Ca is par-
JACOB KUSHNIR
1480 GYPSUM, PROJECTION ON (IOO),
Fig. 12. The structure of gypsum. The asterisk indicates an interstitial position among the water molecules which may occupy a foreign ion.
tially substituted by Sr departs strongly from ideality and becomes unstable. The foreign Sr’+ ion will, thus, tend to avoid normal lattice sites even during equilibrium growth and may occupy interstitial positions. The most probable interstitial lattice positions for foreign ions in gypsum are among the water molecules. The water molecules in gypsum are arranged in layers perpendicular to the b axis (ATOJI and RUNDLE, 1958). They are directed with their hydrogen atoms toward the oxygen atoms of the adjacent sulfate ions, and form hydrogen bonds with them (Fig. 12). This structure leaves large openings among the water molecules. The radius of these openings is as large as 1 A. These openings may be filled by Mg2+, Sr’+ or Naf ions (ionic radius of Na+ 0.95 A) without distortion, and K+ ions with slight distortion of the structure (ionic radius of K+ 1.33 A). A cation in this site will be stabilized by the dipole-ion interaction with water. In other words, cations in these positions are partially hydrated. IISHI (1979) has shown that the effective charge of the oxygen atoms in the water molecules in gypsum is larger than the effective charge of the oxygen in the sulfate ion. This increases even further the stabilization of cations in the interstitial sites, among the water molecules. During the growth process some of the foreign cations may be entrapped with part of their hydration sphere and these water molecules may become part of the structural water of the crystal. This sequence of events reduces the free energy requirements on the process of coprecipitation. It is most probable that whenever a normal substitution of Ca*+ in the lattice causes severe free energy increase, the foreign ions will tend to occupy interstitial positions among the structural water molecules. One implication of this mechanism
is that the relative number of foreign ions occupying interstitial sites increases with increasing growth rate. The coprecipitation of monovalent cations into gypsum by a substitution mechanism requires a means of balancing charges over the entire crystal. It is clear that in this experimental system (and in most natural systems) no trivalent co-substitution can balance the charges and that the amount of a foreign anion (chloride) coprecipitated is not sufficient for charge balance. Also, it is unlikely that the positive charge deficiency will be balanced by anion vacancies. Such a large amount of anion vacancies will drastically decrease the stability of the crystal. It is possible, however, that the monovalent cations Na’ and K’ I.e., two monosubstitute for Ca* + stoichiometricallq: valent cations substitute for one calcium ion. The structure of the crystal will not be altered by such substitution if at least one of the pair of monovalent cations will occupy an interstitial position among the water molecules. The formation of liquid inclusions in these experiments is negligible. This is evidenced by the very small concentrations of Cl in the gypsum (Cl/Ca < 10e4). If the chloride is attributed to liquid inclusions only, and the composition of possible liquid inclusions is assumed to be that of the mother brine, the amount of Mg in liquid inclusions is less than 0.3”, of the total Mg in the gypsum; Na < O.l”,,: K < 0.04”,, and Sr < 4 x 10-5”,,. (Calculated for the lowest concentrations of the studied ions). It should be noted, however. that the amount of liquid inclusions in natural gypsum crystals may be much higher (SAROURAUD-ROSSET, 1976; KCJSHSIK. manuscript in preparation) and should be accounted for when considering coprecipitation of ions with gypsum in the natural environment. Solid inclusions of foreign minerals are possible in the case of strontium since the solubility of SrS04 (celestite) is very low. X-ray powder diffractograms do not show any celestite even at the highest concentrations of Sr in gypsum. Even enrichment of possible celestite by differential dissolution of gypsum did not reveal any celestite. It was mentioned before that Sr tends to coprecipitate with and among the water molecules because of its instability in normal lattice positions of gypsum. This causes substantial kinetic effects. It is interesting to compare this with the coprccipitation of Sr into aragonite. The solid solution interaction term of Sr in aragonite is low (strontianite and aragonite have similar structures). Sr therefore occupies normal lattice sites in aragonite, and the coprecipitation of Sr into aragonite is not affected by growth rate (KINSMAY and HOLLAND. 1969). COPRECIPITATED IONS IN GYPSUM AS GEOCHEMICAL INDICATORS The elucidation of the coprecipitation behavior of Sr, Mg. Na, K and Cl into gypsum enables us to use
An experimental
ions as indicators for the conditions of precipitation, The partition coefficients of the cations Sr’+, Mg2+, Na+ and K’ depend upon three important parameters: the temperature, the brine concentration and the growth rate. These parameters may, in principle. be evaluated from the concentrations of the studied cations in gypsum. More information is gained by studying several coprecipitated ions in the same system than by considering one ion only. Various models may be constructed based on the data presented here, in which the history of the studied samples is assumed and the conditions prevailing during deposition are derived. These models must take into account, among other factors, the variability of the parameters and the existence of liquid inclusions. Such models have been successfully applied to various modern and ancient gypsum deposits (KUSHNIR, manuscript in preparation). Analyses of recent gypsum from two locations will be given here as an example. The kinetic effect in the coprecipitation of ions with gypsum is manifested in the negative correlation between crystal size and coprecipitated ion concentrations This correlation was first reported by BUTLER(1973) for Sr in gypsum samples from Abu Dhabi and other locations. I have measured the concentrations of all studied ions in recent gypsum samples from the Bardawil sabkha in Northern Sinai and found similar correlations. The negative correlation between crystal size and coprecipitated-ion concentrations is attributed here to the kinetic effect. In the samples that were measured, small crystals represent episodes of high supersaturations and growth rate: while larger crystals represent slow growth at conditions close to equilibrium. The apparent partition coefficients of the cations in the Bardawil samples were calculated from the concentrations in the gypsum and in the coexisting brine, after correcting for liquid inclusions. It was assumed that the composition of the liquid inclusions was similar to that of the brine. and that the brine composition was fairly constant during crystal growth. One sample will be shown here as an example. This gypsum formed as a these
Table 6. Apparent
partition
coefficients
1481
study
mush of clear prismatic crystals within quartz sand from concentrated seawater brine of C = 7.8 and temperature ranging between 25 and 35°C. Table 6 shows the calculated partition coefficients for each size fraction. The negative correlation between crystal size and apparent partition coefficient exists for all cations. Using eqn (11) and the parameters given in Table 5, growth rates were calculated for each size fraction (Table 6). Good agreement exists between the values calculated for each cation in the same size fraction The agreement that exists between calculated growth rates (using the concentrations of the different coprecipitated ions) and the fact that the lowest calculated growth rates are close to zero, suggest that the concentrations of coprecipitated ions indeed reflect changes in growth rate and not fluctuations in the brine composition or diagenetic processes. Concentrations of coprecipitated ions were also measured in gypsum crystals from the Dead Sea. The apparent partition coefficients (corrected for liquid inclusions) and calculated growth rates of two representative samples are given in Table 6. Sample DSGF is composed of very fine discoidal crystals (20 pm dia) dispersed in fine silt and clay sediment, cored from the bottom of the Dead Sea at 318 m water depth. Sample DSS is a crust of cemented. large ( - 2 cm) crystals that were collected on the Dead Sea shore. Except for Mg, the concentrations of coprecipitated ions in sample DSGF yield growth rates which are similar to those calculated for the Bardawil sample. The crust from the Dead Sea shore yields much higher growth rates, which are attributed to the very intensive evaporation in this region. These examples demonstrate the possibility of using the results of this experimental work to calculate growth rates of natural gypsum crystals. The coprecipitation of cations into gypsum is particularly interesting because of the kinetic effects. Kinetic effects may, indeed, be negligible in other minerals. but whenever they exist, they may be used to derive a valuable geochemical parameter-the rate of crystallization. The use of coprecipitated ions in gypsum as geo-
and calculated growth rates for recent gypsum and the Dead Sea
samples
from
Bardawtl
sabkha
Apparent partition coefficients
No.
DS.
D Mg x 1o-5
Bardawil sabkha 223 mm I2mm 0.5-I mm 0.25-0.5 mm 10.25 mm
0.50 0.54 0.56 0.59 0.71
1.3 1.4 1.6 1.8 3.9
DSGF DSS
0.15 0.68
12.0 110
Calculated growth rates (mol,/min) (X 10-4) from D Na x 1o-4
DK x 1o-4
Sr
Mg
Na
K
0. I 8 0.26 0.38 0.69 1.1
0.60 0.55 0.59 0.72 1.31
0.0 0.14 0.29 0.54 2.2
0.0 0.15 0.47 0.81 7.1
0.0 0.10 0.33 1.2 1.8
0.35 0.15 0.36 0.85 3.5
0.3
0.54 3.9
0.16 12.0
0.25 73.0
0.12 47.0
1I.0
JACOB KUSHN~R
1482
chemical indicators also requires the knowledge of the behavior of those ions after the primary deposition of gypsum. The behavior of coprecipitated ions during early diagenesis and during phase transformations (gypsum-anhydrite) is currently under study. A complete understanding of the behavior of coprecipitated ions in gypsum and anhydrite during various processes may furnish us with valuable geochemical indicators for the conditions prevailing during formation and
diagenesis
of evaporites.
Acknowledgemenfs~I wish to thank Prof. Joel R. Gat for his help and guidance, R. A. Garber and Y. Levy for valuable comments concerning the manuscript. Dead Sea gypsum was sampled by R. A. Garber.
REFERENCES ATO~~ M. and RUNDLE R. E. (1958) Neutron diffraction study of gypsum. J. Chem. Phrs. 29, 130&1311. BRANDSE W. P., VAN ROSMALEN G. H. and BROUWER G. (1977) The influence of sodium chloride on the crystallization rate of gypsum. J. Inorg. Nucl. Chem. 39, 2007-2010. BUTLER G. P. (1973) Strontium geochemistry of modern and ancient calcium sulphate minerals. In The Persian Gulf: (ed. B. H. Purser), pp. 423452. Springer. DEAN W. E. and ANDERSON R. Y. (1973) Trace and minor clement variations in the Permian Castile Formation, Delaware Basin, Texas and New Mexico, revealed by varve calibration. In 4th Symp. Salt. Huston. Texas Geol. Sot. I Y73. 275-285. DOERNER H. A. and HOSKINS W. M. (1925) Coprecipitation of radium and barium sulfates. J. Am. Chem. Sot. 47, 662-675. HERMANN J. A. and SUTTLE J. F. (1961) Precipitation and crystallization. In Treatise on Analytical Chrmisrrp. (eds I. M. Kolthoff and P. J. Elving), Part I, Vol 3. pp. 1367-1409. HFRRMANX A. G. (1961) Zur Geochemie des Strontiums in den salinaren Zechstein abbgerunngen der Stassfurt Serie des Sudharzbezirkes. Chrm. Erde 21, 137-194.
ICHIKUNI, M. and MUSHA S. (1978) Partition of strontium between gypsum and solution. Chem. Geol. 21, 359-363. IISH~ K. (1979) Phononspectroscopy and lattice dynamical calculations of anhydrite and gypsum. Phys. Chem. Mineral. 4, 341-359. KHARAKA Y. K. and BARNES I. (1973) SOLMNEQ: Solution-mineral equilibrium computations. U.S. Geol. Sure. Comput. Contrib. PB-215899. KINSMAN D. J. J. and HOLLAND H. D. (1969) The coprecipitation of cations with calcium carbonate-IV. The coprecipitation of Sr with aragonite between 16 and 96C. Geochim. Cosmochim. Acta 33, l-1 7. IXJ S. T. and NANCOLLAS G. H. (1970) The kinetics of crystal growth of calcium sulfate dihydrate. .!. Cryst. Growth 6, 281-289. MCINTIRE W. L. (1963) Trace element partition coefficients-a review of theory and applications to geology. Geochim. Cosmochim. Acta 27, 1209-1264. NOLL W. (1934) Geochemie des Strontiums; mit Bemerkungen zur Geochemie des Bariums. Chemi. Erde 8, 587-600. ORION (1977) Analytical Methods Guide. Eighth edn Orion Research Inc. PURKAYASTHA B. C. and CHAT~ERJEE A. (1966) On the study of the uptake of strontium tracer by different forms of calcium sulphate. 1. Indian Chem. Sot. 43, 687-693. RIEHL N.. SIZMANN R. and HIDALGO S. J. P. (1960) Zur Deutung der Verteilung kleinster Fremdsubstanzmengen zwishen einem wachsenden Kristall und der Losung. Z. Phys. Chrm. Neue Folge 25, 351-359. SABOURAUD-ROSSETC. (1974) Determination par activation neutronique des rapports CI/Br des inclusions fluides de divers gypses. Correlation avec les donnes de la microcryoscopie et interpretations genetiques. Sedimentology 21.415431. SABOURAUD-ROSSETC. (1976) Solid and liquid mclusions in gypsum. These d’Etat, UniuersitP Paris Sud, Centre d’Orsay (in French). SMITH B. R. and SWEE~T F. (1971) The crystallization of calcium su!fate dihydrate. J. Colloid Interfirce Sci. 37, 612-618. Uswws~l E. (1973) Das geochemische Verhalten des Strontiums bei der Genese und Diagenese von CaKarbonat und Ca-Sulfat Mineralen. Contrib. Minerul. Petrol. 38, 177-195. YAMAMOTOM. and UNEKI Y. (1978) The distribution of Sr between gypsum and aqueous solutions. Sekko To Sekkai I%, 196-200 (in Japanese).