Geochemical Journal, Vol. 34, pp. 455 to 473, 2000
Theoretical study of tetrad effects observed in REE distribution
coefficients between marine Fe-Mn deposit and deep seawater,
and in REE(III)-carbonate complexation constants
ATSUYUKI O HTA * and I WAO KAWABE
Department of Earth and Planetary Sciences, Graduate School of Science, Nagoya University,
Chikusa-ku, Nagoya 464-8602, Japan
(Received November 12, 1999; Accepted October 4, 2000)
The series variations of logarithms of apparent distribution coefficients for rare earth elements (REE),
log Kd(REE), between Fe-Mn deposit and deep water have been examined theoretically based on the experimental log Kd(REE) between Fe oxyhydroxide precipitate and NaCl solution doped with NaHCO3
(Ohta and Kawabe, 2000). The experimental log Kd(REE) values are strongly affected by REE(III)-carbonate complexation. Those experimental ones in the system with the carbonate ion concentration similar
to seawater reproduce the characteristics of log Kd(REE) evaluated from field data except for large positive Ce anomaly. REE speciation calculation in seawater by using our REE(III)-carbonate complexation
constants indicates that the main REE species is REECO 3+ (aq) rather than REE(CO 3)2–(aq), except for heavy
REE. This is different from the result based on previous literature data for REE(III)-carbonate complexation
constants. Series variations of log {m(REE(OH) 3·nH2O)/[REE(CO3) 2–, aq]} and log {m(REE(OH)3·nH2O)/
[REECO 3+, aq]} evaluated from field data have been compared with those from our experimental data. We
have confirmed that our data of carbonate complexation constants are better to explain experimental and
natural systems simultaneously than the previous literature data. The refined spin-pairing energy theory
(RSPET) can explain the tetrad effects observed in experimental log K d(REE) and REE(III)-carbonate
complexation constants: Racah (E1 and E3) parameters decrease in the order that
REE3+(aq,octahydrate) > REECO 3+(aq) > REE(CO3) 2–(aq) ≥ REE(OH)3·nH 2O (ss).
This relationship is also compatible with field data. The tetrad effects observed in log Kd(REE) between
marine Fe-Mn deposit and seawater and in REE(III)-carbonate complexation constants can be explained
by the systematic differences in Racah parameters among the REE(III) species.
for REE incorporated into Fe-Mn deposits and
REE(III)-carbonate complexation in seawater.
Kawabe et al. (1999a, b) reported experimental
REE distribution coefficients between Fe-Mn
oxyhydroxide precipitates and aqueous NaCl solutions with and without REE(III)-carbonate
complexation.
Kawabe et al. (1999b) have also made a comparison of REE analyses for marine Fe-Mn deposits and seawater with their experimental data
I NTRODUCTION
The distribution coefficients of rare earth elements (REE) between Fe-Mn deposit and seawater
are strongly affected by REE(III)-carbonate
complexation, because the dominant seawater
REE species are REECO3+ (aq) and REE(CO3 )2–(aq)
(Byrne and Sholkovitz, 1996). Bau et al. (1996)
discussed REE analyses of marine ferromanganese
crust in terms of the surface complexing model
*Present address: Geochemistry Department, Geological Survey of Japan, 1-1-3 Higashi, Tsukuba, Ibaraki 305-8567, Japan
455
456
A. Ohta and I. Kawabe
by using REE(III)-carbonate complexation constants of Lee and Byrne (1992, 1993). Their comparison suggests that REE(III)-carbonate
complexation constants of Lee and Byrne (1992,
1993) can not satisfactorily explain both the experimental and field data for the REE distribution
coefficients.
Kawabe (1999a) pointed out that REE(III)-carbonate complexation constants show lanthanide
the tetrad effects. They can be interpreted by refined spin-pairing energy theory, RSPET
(Jørgensen, 1979; Kawabe, 1992). The polarities
and magnitudes of tetrad effects in REE(III)-carbonate complexation constants are determined by
relative differences in Racah parameters (E1 and
E3) for 4f electron repulsion of REE3+ ion among
REE 3+ (aq) , REECO 3 + (aq) and REE(CO 3 ) 2 – (aq) .
Kawabe et al. (1999a, b) also reported that logarithmic distribution coefficients of REE between
Fe-Mn oxyhydroxide precipitates and NaCl solutions show tetrad effects.
Liu and Byrne (1998) reported new experimental data of REE(III)-carbonate complexation constants by solvent extraction and ICP mass
spectrometry. Ohta and Kawabe (2000) have also
presented more detailed experimental data of REE
partitioning coefficients between Fe oxyhydroxide
precipitates and solutions with and without
NaHCO 3 , in which REE(III)-carbonate
complexation constants for all REEs except for
β ScCO + have been determined. Based on the data
3
from Ohta and Kawabe (2000), we will discuss
the following points in this paper;
(1) comparison of apparent REE distribution
coefficients between Fe-Mn deposits and deep
waters with the experimental data,
(2) examination of whether or not REE(III)carbonate complexation constants by Liu and
Byrne (1998) and by us are able to explain REE
distribution coefficients of experimental data and
field ones simultaneously, and
(3) RSPET analyses of REE distribution coefficients of the experimental data and field ones
and of REE(III)-carbonate complexation constants.
DISCUSSIONS
Kd(REE) for marine Fe-Mn deposit/deep seawater
pairs and laboratory experimental analogues
Ohta and Kawabe (2000) have recently reported the experimental REE distribution coefficients, Kd (REE), between Fe(III) oxyhydroxide
precipitates and aqueous NaCl (0.5 M) solutions
doped with NaHCO3 of 0.0~12.0 mM. The laboratory experimental results are compared with
empirical Kd(REE) values evaluated from the pairs
of marine Fe-Mn deposits and deep seawater (Fig.
1). The variation pattern of experimental log
Kd (REE) across the REE series systematically
changes with increasing NaHCO3 concentration.
When the NaHCO3 concentration in experimental solution is 1.3~1.5 mM, the variation pattern
of log Kd (REE) across the series becomes the best
duplicate of those patterns for marine Fe-Mn deposit/deep seawater pairs. However, when the
NaHCO3 concentration of either more than 5 mM
or less than 0.8 mM, the variation pattern of log
Kd (REE) across the series becomes quite dissimilar to those evaluated form the field data (Fig. 1).
The systematic variation of experimental log
Kd(REE) across the series is controlled by the
REE(III)-carbonate complexation in the NaCl solution as discussed in detail by Ohta and Kawabe
(2000). The experimental results can reproduce the
characteristic series variation of log Kd(REE) values from the pairs of marine Fe-Mn deposit and
deep seawater, except for the large Ce anomaly.
According to Ohta and Kawabe (2000), when
NaHCO3 concentration in 0.5 M NaCl solutions
is 1.3~1.5 mM, the concentration of carbonate ion
in experimental solutions is that log [CO3 2–, aq] =
–4.83~–4.58. The seawater concentration of carbonate ion, on the other hand, can be calculated
as log [CO32–, aq] = –4.67~–4.30, where we assumed for seawater that ∑CO2 = 2.35 × 10–3 M,
pH = 7.8~8.2 and salinity of 35‰. A reasonable
agreement in the series variation of log Kd(REE)
between the laboratory and field data is based on
the comparable effects of REE(III)-carbonate
complexation upon log Kd(REE) given by approxi-
Theoretical study of tetrad effects
Fig. 1. The apparent distribution coefficients of REEs
between marine Fe-Mn deposit and seawater (filled
symbols). The experimental distribution coefficients,
log K d (REE), for the systems doped with different
amounts of NaHCO3 (Ohta and Kawabe, 2000) are also
plotted for comparison. REE data for Pacific deep-sea
nodule (nd) were quoted from Ohta et al. (1999). The
average REE analyses for Northern and Southern Central Pacific crust (NCP and SCP, respectively) were
calculated from Bau et al. (1996). REE data of Pacific
deep water were quoted from Piepgras and Jacobsen
(1992) and Kawabe et al. (1998), and Y value was calculated as Y/Ho molar ratio ≈100. log Kd(REE) values
are conveniently multiplied by respective factors in
order to avoid overlapping log Kd(REE) each other.
mately the same CO3 2– concentrations between the
two systems.
The lanthanide tetrad effect can be recognized
in the series variations of log Kd(REE) not only
from experimental results but also from field data
(Fig. 1). In particular, it is quite interesting that
convexity of tetrad curves for experimental log
Kd(REE) becomes less conspicuous with increasing concentration of doped NaHCO3 in the NaCl
457
solution. As REE(III)-carbonate complexation
progresses with increasing NaHCO3 concentration, the dominant REE(III) species in solution
changes from REE 3+(aq) to REECO3+ (aq) and then
to REE(CO 3 ) 2 – (aq) , as already discussed by
Kawabe et al. (1999b) and Ohta and Kawabe
(2000). This systematic change of convex tetrad
effects strongly suggests that REE 3+ (aq) ,
REECO 3 + (aq) and REE(CO 3 ) 2 – (aq) have respectively different Racah (E1 and E3 ) parameters relative to REE3+ in Fe(III) oxyhydroxide precipitates,
which is written here as REE(OH)3·nH2O(ss) . More
detailed discussion will be given in a later subsection.
The relative abundances of REECO3+ (aq) and
REE(CO 3)2– (aq) in seawater with log [CO3 2–, aq] =
–4.67~–4.30, are very important to understand the
observed convexity of tetrad effect variation of
log Kd(REE) from the marine Fe-Mn deposit-deep
seawater pairs (Fig. 1). Their relative abundances
are determined by the ratio of the stability constants for REECO3+ (aq) and REE(CO3)2– (aq), and
they are not the same across the series. In the next,
we will show our speciation calculation of
REE(III) in seawater solution by using available
stability constants for REE(III)-carbonate complexes and others.
REE speciation model in seawater
Speciation calculations of REE(III) in seawater
have been reported by many authors (e.g., Byrne
and Sholkovitz, 1996). Our concern is to know
how the relative abundances of REECO 3+(aq) and
REE(CO 3)2– (aq) vary across the lanthanide series.
In addition to the two species, we considered also
REE 3+ (aq) , REEHCO 3 2+ (aq) , REECl 2+ (aq) ,
REEOH2+(aq) and REESO4+(aq) as important REE
species in seawater. Total REE concentration
(mol/l) in seawater is written as follows;
[M]total = [M 3+ , aq ] + ∑ ∑ [MAn3 − nm , aq ]
A
n
n

= M 3+ , aq ⋅ 1 + ∑ ∑ β( A, n )⋅ A m − , aq 
A n


[
= [M
3+
, aq
]
] ⋅ (1 + θ ),
[
]
(1)
458
A. Ohta and I. Kawabe
where M3+ and A m– means each REE and anion,
respectively, β(A,n) indicates the complexation constant of M(A)n3–nm(aq) for the reaction; M3+(aq) +
nAm–(aq) = M(A)n3–nm (aq), and
[
]
[
]
θ = ∑ ∑ β( A, n ) ⋅ A m − , aq
A
n
= ∑ ∑ K( A, n ) ⋅ A m − , aq
A
n
[MA
3 − nm
, aq
n
{K
=
] / [M]
[
( A, n ) ⋅ A
m−
total
, aq
]
n
⋅ γ M 3+ ⋅ γ An m − / γ MA 3− nm
n
(1 + θ )
}.
n
n
{
}
⋅ γ M 3+ ⋅ γ An m − / γ MA 3− nm ,
n
(2 )
where K (A,n) stands for stability constant for
REE(A)n3–nm (aq) in infinite dilution and γ is the
activity coefficient for each species in seawater.
The fraction of REE3+(aq) to total REE in seawater
is given by
[M3+, aq]/[M]total = 1/(1 + θ ),
(3)
and the fraction of each REE complex to total REE
in seawater is calculated from
When we assume that total carbonate ion concentration is 2.35 × 10 –3 M in seawater with pH =
8.0 and S = 35‰, the concentrations of CO32–(aq)
and HCO3 –(aq) in seawater are 7.03 × 10–5 M and
1.54 × 10–3 M, respectively. The concentrations
of Cl–(aq) and SO42–(aq) in seawater are 0.546 M
and 0.0282 M, respectively (Chester, 1990). The
stability constants of REE(III)-complexes in infinite dilution we adopted in this study are tabulated in Table 1. The activity coefficients were
calculated according to Millero and Schreiber
(1982) and Millero (1992). The stability constants
for REECO3+(aq) and REE(CO 3)2– (aq) by Ohta and
Kawabe (2000) and by Liu and Byrne (1998) are
used in Figs. 2(a) and (b), respectively. In both
case, REECO3+ (aq) and REE(CO3 )2 –(aq) are most
dominant species among the REE complexes con-
Table 1. Infinite dilution stability constants for REE complexation constants with anions at 25°C
log K
La
Ce
Pr
Nd
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
Y
Reference
( 4)
REEOH2 +
REESO4 +
REECl2 +
REE(CO3 ) 2 –
REECO3 +
REE(CO3 ) 2 –
REECO3 +
REEHCO3 2 +
12.52
13.06
13.43
13.59
13.95
14.02
13.95
14.22
14.38
14.48
14.62
14.79
14.94
14.96
14.29
8.33
8.58
8.73
8.75
8.90
8.86
8.78
8.88
8.95
8.96
9.02
9.10
9.15
9.13
8.88
11.58
12.05
12.37
12.46
12.82
12.91
12.76
13.05
13.18
13.27
13.39
13.54
13.56
13.64
12.90
6.52
6.86
7.03
7.08
7.25
7.26
7.17
7.23
7.33
7.32
7.38
7.45
7.58
7.53
7.25
2.02
1.95
1.89
1.83
1.75
1.60
1.72
1.71
1.72
1.73
1.76
1.79
1.84
1.90
1.73
5.10
5.60
5.60
5.67
5.81
5.83
5.79
5.98
6.04
6.01
6.15
6.19
6.22
6.24
5.85*
3.21
3.29
3.27
3.26
3.28
3.37
3.25
3.20
3.15
3.16
3.15
3.07
3.06
3.01
3.08*
0.48
0.47
0.44
0.40
0.36
0.34
0.33
0.32
0.31
0.30
0.26
0.25
0.24
0.23
0.35*
(1)
(1)
(2)
(2)
(2)
(3)
(3)
(4)
(1) Ohta and Kawabe (2000); (2) Liu and Byrne (1998); (3) Millero (1992); (4) Mironov et al. (1982).
*The Y values were calculated according to Byrne and Lee (1993).
Theoretical study of tetrad effects
sidered here. The fractions of REE species except
for REE(III)-carbonate complexes decrease
roughly in the following order:
REE3+(aq) ≈ REESO 4+(aq) > REEOH2+(aq)
> REECl2+(aq) > REEHCO32+(aq). (5)
The fraction of [REEOH2+, aq] is almost constant
across the lanthanide series, but those of the other
REE species decrease with increasing of lanthanide atomic number. [REEOH2+, aq] is similar to
[REECl2+, aq] in light REE, whereas it is comparable to [REE3+, aq] and [REESO4+ , aq] in heavy
REE.
There are two essential differences between the
two speciation calculations (Figs. 2(a) and (b)).
The first is the abundance ratio of REECO3 +(aq) to
REE(CO 3 ) 2 – (aq) . Our REE(III)-carbonate
complexation constants give the result that REE
species in seawater is mainly REECO 3+(aq) except
for heavy REE (Fig. 2(a)). The relationship be-
459
tween REECO 3 + (aq) and REE(CO 3 ) 2 – (aq) abundances is reversed at around Ho, and
REE(CO 3)2– (aq) is the most dominant species only
in heavy REE. However, REE(III)-carbonate
complexation constants of Liu and Byrne (1998)
lead to the conclusion that REE(CO3 )2–(aq) is the
main species in seawater, and that REECO 3+(aq) is
dominant only in light REE (Fig. 2(b)). The second point relates to the following approximation:
[REE] total ≈ [REECO3+, aq] + [REE(CO3 )2–, aq].
(6)
This approximation is valid, when the carbonate
stability constants by Ohta and Kawabe (2000) are
adopted. However, if the stability constants by Liu
and Byrne (1998) are adopted, the additional species of [REE 3+, aq] and [REESO4 +, aq ] are important in light REE, because they comprise about
30% of [REE]total. Hence Eq. (6) need to be modified into the form;
Fig. 2. The calculated concentration ratios of REE 3+ (aq), REECO 3+ (aq) , REE(CO 3) 2 –(aq) , REEHCO 3 2+(aq) ,
REECl2+ (aq), REEOH 2+(aq) and REESO 4+ (aq) to the total dissolved REE in seawater. Two sets of results by using
REE(III)-carbonate complexation constants of Ohta and Kawabe (2000) and of Liu and Byrne (1998) are shown.
460
A. Ohta and I. Kawabe
[REE]total ≈ [REECO3+, aq] + [REE(CO3)2– , aq]
(7)
+ [REE 3+, aq] + [REESO4 +, aq].
The differences in the speciation calculations of
Figs. 2(a) and (b) originate from the different
REE(III)-carbonate complexation constants between Ohta and Kawabe (2000) and Liu and Byrne
(1998). Our log K REECO 3+ (log K 1 ) and log
K
(log K 2) by Fe(III) coprecipitation
method are about 1.0~1.5 larger than those reported by Liu and Byrne (1998) using solvent extraction method. Our log(K2 /K1 ) values are lower
than those of the latter by about 0.5 on the average. The abundance ratio of REECO 3 + (aq) to
REE(CO3 )2 –(aq) is determined by each values of
log(K2/K1 ).
The activity of M(OH)3·nH2 O(ss) is expressed in
terms of the mole fraction of M(OH)3 ·nH2O (ss) in
the marine Fe-Mn deposit and the activity coefficient;
aREE( OH )
3 ⋅ nH 2 O
= λ REE( OH )
= λ REE( OH )
(
3 ⋅ nH 2 O
⋅ X M ( OH )
)
3 ⋅ nH 2 O
⋅ m M(OH)3 ⋅ nH 2 O ⋅ fM ( OH )
3 ⋅ nH 2 O
3 ⋅ nH 2 O
(10)
REE ( CO 3 ) 2
−
REE partitioning reactions between Fe-Mn deposit
and deep seawater
We consider REE partitioning reactions between Fe-Mn deposit and REE(CO 3 ) 2 – (aq) in
seawater. We will write REE(III) incorporated in
marine Fe-Mn deposit like deep-sea nodules and
crusts as REE(OH)3·nH2 O(ss) in the same way as
for REE(III) incorporated with Fe(III)
oxyhydroxide precipitates in our laboratory experiments (Kawabe et al., 1999a, b; Ohta and
Kawabe, 2000). REE partitioning reactions are
written in the form,
M(OH)3·nH2 O(ss) + 2CO3 2–(aq) + 3H+(aq)
= M(CO3 )2–(aq) + (3 + n)H2 O(l).
(8)
The thermodynamic expression of the equilibrium
constant for Eq. (8), RT ln K = –∆G 0r, leads to the
following equation,


2.303RT log aM ( OH ) ⋅nH 2 O / a
− 
M ( CO 3 ) 2 
3

{
2
3
3+ n
⋅ aCO
2 − ⋅ a + / aH O
2
H
{ (
3
)
}
(
= ∆G 0f M(CO 3 )2 , aq − ∆G 0f M(OH)3 ⋅ nH 2 O
−
+(3 + n)∆G 0f (H 2 O, 1 )
(
)
(
)
−2 ∆G 0f CO 32 − , aq − 3∆G 0f H + , aq .
where X M ( OH ) 3 ⋅nH 2 O denotes the mole fraction of
M(OH)3·nH 2O(ss) in the deposit, and fM ( OH ) 3 ⋅nH 2 O
stands for the factor which converts the REE concentration in the marine Fe-Mn deposit of
m(M(OH)3·nH 2O) in mol/kg to the mole fraction
of X M ( OH ) 3 ⋅nH 2 O . The distinction between REE
concentration values in (mol/kg) and (mol/liter)
is insignificant in seawater, the activity of
M(CO3)2–(aq) is approximately expressed by;
a
M ( CO 3 ) 2
−
=γ
M ( CO 3 ) 2
−
[
]
⋅ M(CO 3 )2 , aq .
−
(11)
From Eqs. (10) and (11), Eq. (9) is re-written in
the following form;
{
(
)
[
2.303RT log m M(OH)3 ⋅ nH 2 O / M(CO 3 )2 , aq
(
)
(
−
= ∆G 0f M(CO 3 )2 , aq − ∆G 0f M(OH)3 ⋅ nH 2 O
−
)
]}


γ
−
M ( CO 3 ) 2


+2.303RT log 
.
 λ REE( OH ) 3 ⋅nH 2 O ⋅ fM ( OH ) 3 ⋅nH 2 O 


12
( )
(
)
When we are interested only in the series variation of log{m(M(OH)3 ·nH2O)/[M(CO 3)2 –, aq]},
the three terms given by ∆G 0 f (H 2 O, 1 ),
∆G 0 f (CO 3 2– , aq ) and ∆G 0 f (H + , aq ) are constant
across the series variation. The values of
)}
( 9)
f
γ
− , λ
REE ( OH ) 3 ⋅ nH 2 O and M ( OH ) 3 ⋅ nH 2 O are not
M ( CO 3 ) 2
strictly constant across the series, but they may
,
Theoretical study of tetrad effects
461
be approximately constant. Equation (12) is written in the simple form,
Mn deposit and seawater is given by using Eqs.
(13) and (14) as follows:
2.303RT log{m(M(OH)3·nH2O)/[M(CO 3)2–, aq]}
= ∆G 0f(M(CO3 )2 –, aq) – ∆G0 f(M(OH)3·nH2O)
+ const.
(13)
log Kd(M) ≡ log{m(M(OH) 3·nH2 O)/[M]total}
= log{m(M(OH) 3·nH2 O)/[M(CO3)2 –, aq]}
– log( φ + 1)
≈ {∆G0f (M(CO3)2– , aq) – ∆G0f (M(OH)3·nH2 O)}
(17)
/(2.303RT) – log( φ + 1) + const.
The series variation of {∆G 0 f (M(CO 3 ) 2 – , aq) –
∆G 0 f (M(OH) 3 ·nH 2 O)} corresponds to that of
2.303RT log{m(M(OH)3·nH2O)/[M(CO 3)2–, aq]}.
When the REE(III)-carbonate complexation
constants by Liu and Byrne (1998) are accepted,
[M]total is the sum of the concentrations of the four
species as in Eq. (7),
[M]total = [MCO3+, aq] + [M(CO3)2– , aq]
+ [M3+, aq] + [MSO 4+, aq]
= ( φ + 1)·[M(CO3)2 –, aq],
(14)
and
{β ⋅ [CO , ] + 1 + β
φ=
1
2−
3 aq
[
MSO +4
[
⋅ SO 24 − , aq
]
 β ⋅ CO 2 − , 2 
3 aq 
 2
]}
3
)
(15)
where we adopted the assumption that
γ
γ
− ≈ γ
MCO 3+ ≈ MSO +4 from Millero (1992).
M ( CO 3 ) 2
+
When only REECO 3 (aq) and REE(CO3)2 –(aq) are
important as suggested by the carbonate
complexation constants of Ohta and Kawabe
(2000), Eq. (15) becomes the simple form,
( [
φ = β1 / β 2 ⋅
CO 32 − , aq
= ( K1 / K2 ) / aCO 2 − .
3
log Kd(M)( φ) = log Kd(M) + log( φ + 1)
≈ {∆G0f(M(CO3)2–, aq) – ∆G0f(M(OH)3·nH2O)}
/(2.303RT) + const.,
(18)
where the subscript “(φ )” means that log Kd(REE)
is corrected for log( φ + 1).
When we consider REE partitioning between
marine Fe-Mn deposit and REECO 3 + (aq) in
seawater,
M(OH)3·nH2O(ss) + CO 32–(aq) + 3H+(aq)
= MCO3+(aq) + (3 + n)H2O(l).
(19)


 K1 ⋅ aCO 32 − + γ M ( CO ) − / γ M 3+ + K MSO +4 ⋅ aSO 24− 
3 2

,
=
2
K2 ⋅ aCO 2 −
(
We will write the apparent log Kd(REE) corrected
by (φ + 1) as follows,
We can obtain a similar expression to Eq. (13) for
the pair of M(OH)3·nH2 O(ss) and MCO3 +(aq) as follows;
2.303RT log{m(M(OH)3·nH2O)/[MCO 3+, aq]}
= ∆G0f(MCO3+, aq) – ∆G0f (M(OH)3·nH2O) + const.
(20)
When [M] total of seawater is expressed by the sum
of the four species, it is proportional to
[MCO3 +, aq] as follows:
[M]total = ( ω + 1)·[MCO 3+, aq],
(21)
where
])
(16)
The apparent logarithmic distribution coefficient of REE, log Kd(REE), between marine Fe-
{K ⋅ a
ω=
2
2
CO 32 −
+ γ MCO + / γ M 3+ + K MSO + ⋅ aSO 2 −
(K ⋅ a )
3
1
4
4
}.
CO 32 −
(22)
462
A. Ohta and I. Kawabe
When only the terms of [MCO 3 + , aq ] and
[M(CO3 )2–, aq] are important in Eq. (21),
ω = ( K1 / K2 ) ⋅ aCO 2 − ,
3
(23)
from Eqs. (22) and (23), we will define log Kd(M)
corrected by log(ω + 1) as follows;
log Kd (M)(ω) = log Kd (M) + log(ω + 1)
≈ {∆G 0f(MCO3 +, aq) – ∆G0 f(M(OH)3·nH2O)}
/(2.303RT) + const.,
(24)
where the subscript “(ω )” means that log Kd(M)
is corrected for log(ω + 1).
Equations (20) and (24) are also applicable to
the laboratory experimental values of log Kd(REE)
by Ohta and Kawabe (2000). Hence, the series
variation of log Kd(REE)( φ) or log Kd(REE)(ω) must
be the same between the experimental and field
data, because it is the series variation in differences of ∆G0 f ’s for each pair. However, if the
REE(III)-complexation constants, in particular,
the carbonate complexation constants are incor-
rect, the series variations of log Kd(REE) (φ) or log
Kd (REE)( ω) from the laboratory experiments and
from field data will be inconsistent as suggested
in our preliminary study (Kawabe et al., 1999b).
From this point of view, the carbonate
complexation constants are examined in the next.
Series variations of log K d(REE) corrected for
REE(III)-carbonate complexation: laboratory and
field data
A set of log Kd(REE) values from laboratory
and field data is corrected to log Kd(REE) (φ) and
log K d (REE) ( ω ) by using the carbonate
complexation constants and the other complex
formation constants adopted in the speciation calculations of Figs. 2(a) and (b). The empirical estimates of log Kd(REE) from marine Fe-Mn deposit/
deep seawater pairs shown in Fig. 1 are compared
with the experimental values of log Kd(REE) in
the systems with NaCl solutions with
[NaHCO3 , aq] = 1.30 mM and 8.23 mM, which are
distinguished by the suffix of (1.30 mM) and (8.23
mM), respectively. In the NaCl solution with
[NaHCO3, aq] = 8.23 mM, REE(CO3)2–(aq) is much
Fig. 3. The series variations of log(φ + 1) and log( ω + 1) for seawater and experimental solutions, respectively.
Open symbols indicate the results by using REE(III)-carbonate complexation constants in Ohta and Kawabe
(2000) and in Eqs. (16) and (23). Filled symbols indicate the results by using the complexation constants in Liu
and Byrne (1998) and in Eqs. (15) and (22). But, the term of K MSO+ · aSO2− in Eqs. (15) and (22) is not necessary
4
4
to calculate log(φ + 1) and log(ω + 1) values for experimental solutions.
Theoretical study of tetrad effects
more dominant than the other REE species. Hence
the series variation of log Kd (REE)(8.23mM) is approximately that of {∆G 0 f (REE(CO 3 ) 2 – , aq) –
∆G0f(REE(OH) 3 ·nH2O)}/(2.303RT).
Figures 3(a) and (b) show the values of
log(φ + 1) and log( ω + 1) for seawater solution
=
with pH = 8.0, log aCO 32− = –5.44 and log aSO 2−
4
–2.61, and for the two experimental NaCl solution with [NaHCO3] = 1.30 mM and 8.23 mM,
which are labeled as (1.30 mM) and (8.23 mM),
in Eqs. (15)
respectively. The term K MSO + · aSO 2−
4
4
and (22) is not necessary for the calculation of
log(φ + 1) and log(ω + 1) values for experimental
solutions, which contained no SO 42–(aq). In Fig.
3(a), where the carbonate complexation constants
by Liu and Byrne (1998) are used, the correction
values of log( φ + 1) for seawater solution and the
NaCl solution of (1.30 mM) are lower than 0.7,
463
and those values for another NaCl solution of (8.23
mM) are nearly zero. By contrast, the carbonate
complexation constants by Ohta and Kawabe
(2000) give fairly large log(φ + 1) values for light
REE (Fig. 3(a)), because of the dominance of
REECO3+ (aq) over REE(CO 3)2– (aq) in light REE as
shown in Fig. 2(a). The relationship of log(ω + 1)
values are almost the reverse of that of log(φ + 1)
values (Fig. 3(b)). The correction values of
log(φ + 1) and log(ω + 1) based on Liu and Byrne
(1998) show irregularities at Yb unlike the cases
based on Ohta and Kawabe (2000).
Figures 4(a) and (b) show the sets of log
Kd(REE) (φ) and log Kd(REE) (ω) based on the carbonate complexation constants by Liu and Byrne
(1998). The results indicate that three sets of log
Kd(REE) (φ) and log Kd(REE)( ω) from field data are
almost in parallel with log Kd(REE) (1.30mM,ψ) and
Fig. 4. The series variations of experimental and field data of log Kd(REE) corrected by the ( φ + 1) and ( ω + 1)
values evaluated from REE(III)-carbonate complexation constants by Liu and Byrne (1998). [A]: log
Kd(REE)(8.23mM), [B]: log K d(REE)(1.30mM), [C]: apparent log K d(REE) between ferromanganese nodule and Pacific deep water, [D]: apparent log Kd(REE) between Northern Central Pacific ferromanganese crust and Pacific
deep water, [E]: apparent log Kd(REE) between Southern Central Pacific ferromanganese crust and Pacific deep
water. Plus symbols are the data with NaHCO3 = 8.23mM, but its Lu value is set to be equal to respective Lu
values of the data with NaHCO 3 = 1.30 mM and field data. log Kd(REE) values are conveniently multiplied by
respective factors in order to avoid overlapping log Kd(REE) each other.
464
A. Ohta and I. Kawabe
log K d (REE) (1.30mM, ω ) , respectively. The log
Kd (REE)( φ) and log Kd (REE)( ω) for field data and
experimental data for (1.30 mM) are roughly in
parallel with those for (8.23 mM), but the parallelism is worse in light REE relative to heavy REE.
log Kd (REE) (ω) for field and experimental data
shows particular irregularities at Yb. They are due
to the large irregularity of log(ω + 1) in Fig. 3(b).
There are no such irregularities in the original data
as shown in Fig. 1. According to the speciation
calculation based on Liu and Byrne (1998) (Fig.
2(b)), the apparent log Kd(REE) for field data (Fig.
1) except for light REE can be expressed approximately by log Kd(REE) (φ) (log{m(M(OH)3·nH2O)/
[M(CO3 )2 – , aq ]}). However, log K d(REE) ( φ) for
field data (Fig. 4(a)) have linear patterns unlike
the apparent log Kd (REE) for field data having
convex tetrad effects (Fig. 1).
The correction values of log( φ + 1) and
log( ω + 1) derived from the carbonate
complexation constants by Ohta and Kawabe
(2000) lead to different results (Figs. 5(a) and (b)).
The three sets of log K d (REE) ( φ ) and log
Kd (REE)( ω) from field data are approximately in
parallel with not only the respective log
Kd(REE)(1.30mM,ψ) and log Kd(REE)(1.30mM,ω) but
also the respective log Kd (REE)(8.23mM,ψ) and log
Kd (REE)(8.23mM, ω) . The log K d(REE) ( φ) and log
Kd (REE)( ω) values for (1.30 mM) and field data
show steeply curved variation patterns at around
La, Ce and Pr in Figs. 5(a) and (b). This indicates
the structural change in REE(CO3 )2–(aq) series, the
detail of which will be discussed later. According
to speciation calculation in Fig. 2(a), the apparent log Kd(REE) for field data (Fig. 1) except for
heavy REE can be expressed approximately by log
Kd (REE)( ω) , log{m(M(OH)3 ·nH2O)/[MCO 3+, aq ]}.
The log Kd(REE)(φ) values for field data (Fig. 5(b))
show similar patterns with convex tetrad effect to
the apparent log Kd(REE) for field data (Fig. 1).
We have reported preliminary experimental
data of Kd(REE) in the system with NaHCO3 and
compared them with the empirical Kd(REE) evaluated from marine Fe-Mn deposit/deep water pairs
Fig. 5. The series variations of experimental and field data of log Kd(REE) corrected by the (φ + 1) and ( ω + 1)
values evaluated from REE(III)-carbonate complexation constants by Ohta and Kawabe (2000). The symbols
[A]~[E] and plus symbols are the same as in Fig. 4. log Kd(REE) values are conveniently multiplied by respective
factors in order to avoid overlapping log Kd(REE) each other.
Theoretical study of tetrad effects
(Kawabe et al., 1999b), in which we suggested
that log(K1/K2) values for light REEs given by the
REE(III)-carbonate complexation constants by
solvent-extraction method are slightly smaller than
those ought to be. The detailed examination in this
work supports our previous suggestion.
In our discussion as above, we did not refer to
some difficulties involved in our comparison of
the Kd(REE) values from laboratory and field data:
First, we are not able to know precisely the concentrations of REE and carbonate ion in the
seawater in which each marine Fe-Mn deposit was
formed. We have assumed simply the REE data
for average Pacific deep water as the seawater
solution involved in the REE partitioning reactions
with the marine deposit. Second, we have applied
the values of log( φ + 1) and log(ω + 1) based on
the stability constants at 25°C and 1 bar to log
Kd(REE) from the marine Fe-Mn deposit-Pacific
deep water pairs. The actual temperature and pressure for the marine deposits and associated deep
water are about 5°C and 200~600 bar. Nevertheless, the REE(III)-carbonate complexation constants by Ohta and Kawabe (2000) can unify the
laboratory and field data of Kd(REE) more consistently than the carbonate complexation constants by Liu and Byrne (1998), as far as such
unified understanding is geochemically sound and
meaningful.
Refined spin-pairing energy theory and tetrad effects in log K d(REE), log K1 and log K2
Kawabe et al. (1999a, b) and Ohta and Kawabe
(2000) have pointed out that lanthanide tetrad effects are recognized in the series variations of log
Kd(REE), log K1 , log K2, and log(K2 /K1 ). As is
shown in Eqs. (20) and (24), the differences between the pairs of ∆G0f ’s divided by 2.303RT determine the series variation of Kd (REE) corrected
for the complexation effects. Likewise, log K1 and
log K2 are written in the same forms,
log K1 ≈ {∆G0 f(M3+, aq) – ∆G0f (MCO3+, aq)}
/(2.303RT) + const.,
(25)
and
465
log K2 ≈ {∆G0 f(M3+, aq) – ∆G0f(M(CO3 )2–, aq)}
/(2.303RT) + const.
(26)
The step-wise stability constants for
REE(CO 3)2– (aq) is also written in the same forms,
log(K2 /K1) ≈ {∆G0 f(MCO3+ , aq)
– ∆G0f (M(CO3)2– , aq)}
/(2.303RT) + const.
(27)
According to Kawabe (1999a) and Kawabe et al.
(1999a, b), the series variation of the differences
of ∆G0f for Kd(REE) and the pair of REE(III) complex series at low temperatures comprises the following components:
(i) a tetrad effect variation when Racah (E1 and
3
E ) parameters are different between the pair of
the REE(III) complex series,
(ii) irregular variations like breaks or steps due
to structural changes in one or both REE(III) complexes of the pair across the series, when one or
both REE(III) complexes are not isomorphous in
the entire REE series, and
(iii) a smooth residual variation.
If the irregular series variations due to structural changes across the REE series are removed
from the series variations of log Kd(REE) or log
K showing tetrad effects, they can be described
by an improved equation of refined-spin pairing
energy theory (RSPET) by Kawabe (1992, 1999a,
1999b):
log Kd(M)′ or log K′
= A + (a + bq)qZ* + (9/13)n(S)C1Z*+ m(L)C3 Z*,
(28)
where the prime means that log Kd(M) or log K
has already been corrected for the structural
change effects across the series. The ground-level
electronic configuration of REE3+ is [Xe](4f)q, and
q is the number of 4f election of each REE3+. The
effective nuclear charge (Z*) for 4f electrons of
REE3+ is related to the number of 4f electrons of
q, namely, Z* = q + 25. The constants coefficients
of n(S) and m(L) are given by the total spin quantum number of S and the total orbital one of L for
466
A. Ohta and I. Kawabe
the ground-level electronic configuration of
[Xe](4f)q (Kawabe, 1992). The constants of A, a,
b, C1, and C3 are determined in the least-squares
fitting. The first and second terms in Eq. (28) express a smooth variation across the REE series.
When the differences of ∆G 0 f for the pair of
REE(III) complexes are given at the normal temperature of 25°C or lower than this, the constants
of C1 and C3 are semi-quantitatively indexes of
the differences in Racah (E 1 and E3 ) parameters
for 4f electron repulsion between the pair of
REE(III) complexes;
C1 ≈ ∆E 1/(2.303RT) and C3 ≈ ∆E 3/(2.303RT).
(29)
More detailed discussion on the approximation in
Eq. (29) has been given in Kawabe (1999a, b) and
Kawabe et al. (1999a, b).
When it is assumed that (C3/C 1) = 0.21 as in
Kawabe et al. (1999a), these two terms can be
written collectively,
(9/13)n(S)C1 Z*+ m(L)C3 Z*
≈ {n(S) + (3/10)m(L)}(9/13)C1Z*.
Fig. 6. Coefficients of n(S), m(L) and n(S)+(3/10)m(L)
in the refined spin-pairing energy theory as functions
of number of 4f electrons of Ln 3+ (Kawabe, 1992;
Kawabe et al., 1999a). Octad- and tetrad-like variations are obvious in n(S) and m(L), respectively. Tetrad effect variation is approximately giving by
{n(S)+(3/10)m(L)}C1Z*, when C3/C 1 = 0.21 (Kawabe
et al., 1999a).
(30)
Figure 6 is cited from Kawabe et al. (1999a),
which illustrates the octad-like variation of n(S)
and tetrad-like one of m(L) across the REE(III)
series, together with the tetrad effect variation by
their linear combination of {n(S) + (3/10)m(L)}.
The third and forth terms of Eq. (28) can reproduce a variety of tetrad effects by different C1 and
C3 values, namely, by the differences in Racah
(E 1 and E 3 ) parameters between the pair of
REE(III) complexes. The data of log Kd (REE) or
log K corrected for structural change effects in
their series variations are fitted to Eq. (28) by a
least-squares method, and then C1 and C3 values
related to the differences in Racah (E1 and E 3)
parameters between the pair of REE(III) complexes can be evaluated. This has been called a
RSPET analysis of log K d (REE) or log K by
Kawabe (1999a, b) and Kawabe et al. (1999a, b).
When C1 > 0 and C3 > 0, the convex tetrad effect
variation analogous to {n(S) + (3/10)m(L)} shown
in Fig. 6 is seen in log Kd (REE)′ or log K′. But a
concave tetrad effect, which is just the reverse of
{n(S) + (3/10)m(L)} shown in Fig. 6, is seen when
C1 < 0 and C3 < 0. The sign of C1 and C 3 indicates
which REE(III) complex series of the pair has systematically larger Racah parameters than the other.
In the following subsections, we will show RSPET
analyses of REE(III)-carbonate complexation constants, and then those analyses of the sets of log
Kd (REE) in the system with and without carbonate ions.
RSPET analyses of REE(III)-carbonate
complexation constants
As shown by Eqs. (25) and (26), the series
variations of log K 1 and log K 2 are given by
{∆G 0 f (REE 3+ , aq ) – ∆G 0 f (REECO 3 + , aq )} and
{∆G0 f (REE 3+ , aq) – ∆G 0 f(REE(CO 3) 2 – , aq)}, respectively. The RSPET equation of (28) describes
the tetrad effect variation between the pair of isomorphous REE species across the lanthanide se-
Theoretical study of tetrad effects
ries. We must consider the structural change effects in the REE(III)-carbonate complex series and
in aqua REE3+ ion series as well. By contrast, in
the case of the step-wise stability constant for
REE(CO 3)2– (aq) of log(K2/K1 ), the series variation
is free from the structural change effect in aqua
REE3+ ion series as indicated by Eq. (27). This
point is very important, because it greatly helps
us separate the series variations of experimental
data of log K1 and log K2 into (i) the tetrad effect
variation, (ii) structural change effects in relevant
REE(III) complexes, and (iii) a residual smooth
variation. This point was emphasized in the
RSPET analyses by Kawabe (1999a) for the
REE(III)-carbonate complex constants reported by
Lee and Byrne (1992, 1993).
Figure 7 illustrates RSPET analyses of the experimental data of log K1 , log K2 and log K2/K1
by Ohta and Kawabe (2000). Both experimental
log K1 and log K2 values (filled circles) decrease
steeply with going from middle REE to light REE,
whereas there is no such a steep decrease in
log(K2/K1) values. The steep decrease is due to
the hydration change in aqua REE3+ ion series
(Habenschuss and Spedding, 1980; Rizkalla and
Choppin, 1991 and references therein). Aqua
REE 3+ ions from La 3+ through Nd 3+ are
nonahydrates, those between Nd3+ and Tb3+ are
transitional between nona- and octahydrates, and
those from Tb 3+ to Lu3+ are octahydrates. Kawabe
(1999b) have evaluated the thermodynamic parameter (∆Gh*) for the stabilization of real light
REE 3+(aq) relative to octahydrate REE3+ (aq). By
using ∆Gh* values for light REE 3+(aq) we can remove the hydration change effect in light REE3+(aq)
series from the experimental log K1 and log K2
values. They are shown by the open circles in Fig.
7. The corrected series variations of log K1 and
log K 2 becomes much regular, in particular,
REECO 3 + (aq) appears to be fully isomorphous
across the series. However, there still remains a
small irregular variation in the three lightest Lanthanides for log K2 . This irregularity is commonly
recognized in the series variation of log(K2/K1).
The small irregularity is attributed to a structural
change of La, Ce and Pr members relative to the
467
Fig. 7. The series variations of logarithmic stability
constants for REE(III)-carbonate complexes at 25°C
and infinite dilution (Ohta and Kawabe, 2000) and their
RSPET analyses. Solid circles: the experimental data
except for Ce. The Ce values have been interpolated
by those for La and Pr. Open circles: corrected values
for hydration changes in light REE3+ (aq) according to
Kawabe (1999b), open square: corrected values for
structural changes in light REE(CO 3)2–(aq) (see text).
Multiplication symbols: the least-squares fittings of
REE(III)-carbonate complexation constants to the
RSPET equation, and plus symbols: smooth variations
separated from the respective tetrad effect variations.
others of REE(CO 3 ) 2 – (aq) series, because
REECO 3+ (aq) series corrected for the hydration
change effect in light REE3+(aq) appears to be isomorphous (Kawabe, 1999a). It is difficult to estimate the correction factors for the structural
change of light REE(CO 3)2–(aq) different from the
hydration change of light REE 3+(aq). We repeatedly fitted log K2′ and log(K2/K1)′ to RSPET equation (28) with using various correction factors for
light REE(CO 3)2–(aq). When the respective corrections of +0.33(La), +0.15(Ce), and +0.05(Pr) are
further applied to log K2 and log(K2′/K1′), the values to the improved equation of RSPET of Eq.
(28) are satisfactory. The determined C1 and C3
values for log K1′, log K2′ and log(K2 ′/K1′) values
468
A. Ohta and I. Kawabe
Table 2. Comparison of C1 and C 3 parameters determined by the least
square fitting of REE(III)-carbonate complexation constants and log
Kd(REE) – 3pH without NaHCO3 to RSPET equation
Data set
C1 /10– 3
C3 /10– 4
Source
log K1 ′(a)
log K2 ′(a)
0.94 ± 0.21
0.56 ± 0.66
Ohta and Kawabe (2000)
1.34 ± 0.18
1.45 ± 0.57
Ohta and Kawabe (2000)
log(K2 /K1 )′(a)
0.41 ± 0.08
0.90 ± 0.26
Ohta and Kawabe (2000)
log K1 ′(a)
1.07 ± 0.21
1.59 ± 0.27
1.27 ± 0.69
2.20 ± 0.86
Liu and Byrne (1998)
Liu and Byrne (1998)
0.49 ± 0.30
1.28 ± 0.22
0.81 ± 0.95
1.90 ± 0.72
Liu and Byrne (1998)
Ohta and Kawabe (2000)
1.12 ± 0.17
1.28 ± 0.56
Kawabe et al. (1999a)
log K2 ′(a)
log(K2 /K1 )′(a)
[log Kd (REE)′( χ ) – 3pH] (b )
[log Kd (REE) – 3pH]′(c)
(a)
REE(III)-carbonate complexation constants were fitted to RSPET equation after correction for hydration change of light
REE3+(aq) and structural change of light REE(CO 3)2– (aq).
(b)
log K d(REE)′ (χ ) – 3pH means the average values of log Kd (REE) – 3pH without NaHCO 3 (pH = 6.4–6.6) for log(χ + 1),
hydration change of light REE3+(aq) and structural change of heavy REE(OH)3 ·nH2O(ss) .
(c)
The data source is the means of Fe-2 series in Kawabe et al. (1999a). The data were not corrected for the correction factor of
log(χ + 1).
of Fig. 7 derived from the experimental data by
Ohta and Kawabe (2000) are listed in Table 2.
Kawabe (1999a) reported similar C1 and C 3
values in the RSPET analyses of the REE(III)-carbonate complexation constants reported by Lee
and Byrne (1992, 1993). We have also made the
RSPET analyses of the recent experimental results
by Liu and Byrne (1998) in this study. When we
empirically adopted the respective corrections of
+0.18(La), +0.15(Ce), and +0.04(Pr) for the structural change effects in log K2 and log K2/K1 , they
are satisfactorily fitted to RSPET equation of (28).
All the C1 and C 3 values for log K1′, log K2 ′ and
log(K2/K1)′ values are summarized in Table 2. The
C1 and C3 parameters for log K1′ and log K2 ′ and
log(K2/K1 )′ show good agreement in both results,
although C3 parameters for log K1 ′ and log K2′ of
Liu and Byrne (1998) are slightly larger than those
of Ohta and Kawabe (2000). The convex tetrad
effect becomes less obvious from log K2 to log K1
in Fig. 7. The RSPET analyses of REE(III)-carbonate complexation constants strongly suggest
that the Racah (E1 and E 3) parameters of the three
REE(III) species decrease in the following order:
REE3+(aq,octahydrate)
> REECO3+(aq) > REE(CO 3)2 –(aq).
(31)
RSPET analyses of log Kd(REE) in the system without carbonate ions
Ohta and Kawabe (2000) have determined the
experimental {log Kd(REE) – 3pH} values in the
system of Fe(III) oxyhydroxide precipitate and 0.5
M NaCl solutions without NaHCO3 at a pH range
from 5.6 to 6.6, where REE3+(aq) is far more dominant than the other REE species like REECl2+(aq)
and REEOH2+(aq). The log Kd (REE) values correspond to ∆G0f for the REE partitioning reactions:
M(OH)3·nH 2O(ss) + 3H +(aq)
= M3+(aq) + (3 + n)H2O(l).
(32)
The following equation similar to Eq. (12) can be
obtained
{(
) [
2.303RT log m M(OH)3 ⋅ nH 2 O / M 3+ , aq
(
)
(
= ∆G 0f M 3+ , aq − ∆G 0f M(OH)3 ⋅ nH 2 O
)
]}

γ M 3+

+2.303RT log 
 λ M ( OH ) 3 ⋅nH 2 O ⋅ fM ( OH ) 3 ⋅nH 2 O

(


.


(33)
)
Theoretical study of tetrad effects
469
This can be written in a further simplified form as
in the case of Eq. (13),
{(
{∆G (M
=
) [
]} + 3 log aH
3+
, aq ) − ∆G 0f (M(OH)3 ⋅ nH 2 O)}
log m M(OH)3 ⋅ nH 2 O / M 3+ , aq
0
f
(2.303RT)
+
+ const.
(34)
The term of 3 log aH + is not combined into the
constant term, because the sets of experimental
log Kd(REE) values at slightly different pH conditions (pH = 6.4 to 6.6) are considered collectively. Then we have the final expression,
log{(χ + 1)·Kd(M)} – 3pH
= {∆G 0f(M3+, aq) – ∆G0f (M(OH)3·nH2O)}
/(2.303RT) + const.,
(35)
where χ = β MCl 2+ ·[Cl– , aq ] + β MOH 2+ ·[OH –, aq].
This is a factor for correcting a small difference
between [M] total and [M 3+ , aq]. Kawabe et al.
(1999a) reported the RSPET analysis of log
Kd(REE) between Fe-Mn oxyhydroxide precipitates and NaCl solutions with pH = 5.4–6.4 at room
temperature. They pointed out that REE 3+ ions in
Tm, Yb and Lu members of REE(OH) 3·nH 2O(ss)
appear to have different coordination states than
the others. In order to fit experimental {log
Kd(REE) – 3pH} values to the RSPET equation,
the corrections for structural changes in both light
REE3+(aq) and heavy REE(OH)3·nH2O(ss) series are
necessary (Kawabe et al., 1999a).
In this study, we have made a RSPET analysis
for the averages of experimental {log Kd(REE) –
3pH} in the system with no NaHCO3 at a pH range
from 6.4 to 6.6 (n = 4) at 25°C reported by Ohta
and Kawabe (2000). We have taken the
complexation effect of log(χ + 1) into consideration and adopted the respective corrections of
–0.044(Tm), –0.131(Yb) and –0.158(Lu) for the
structural change of REE(OH) 3·nH2 O(ss). We will
write the experimental values of log{( χ +
1)·Kd(REE)} – 3pH as log Kd(REE) (χ) – 3pH, and
Fig. 8. The series variation of log K d(REE)′(χ ) – 3pH
and its RSPET analysis. Solid circles: experimental
data of log K d(REE) – 3pH in the system without
NaHCO 3 at pH = 6.4 to 6.6 by Ohta and Kawabe
(2000), open circles: log Kd(REE) – 3pH data corrected
for log( χ + 1), open triangles: log Kd(REE)( χ) – 3pH
corrected values for hydration changes in light
REE3+(aq) according to Kawabe (1999b), and structural
changes in heavy REE(OH) 3·nH 2O(ss) (see text). Multiplication symbols: the least-squares fitting of log
Kd(REE)′( χ) – 3pH to the RSPET equation. Plus symbols: smooth variation separated from the tetrad effect
variation.
the values corrected further for all the structural
change effects as log Kd(REE)′ (χ) – 3pH. The fitting result of {log Kd (REE)′ (χ) – 3pH} to Eq. (28)
is shown in Fig. 8, and the determined C1 and C3
values for the tetrad effect are listed in the lowest
row of Table 2.
It is interesting that C 1 value for {log
Kd(REE)′( χ) – 3pH} is approximately the same as
the C 1 value for log K2 ′(REE(CO 3 )2 –). The C 3
value for {log Kd(REE)′(χ) – 3pH} is only slightly
larger than the C 3 value for log K2′(REE(CO 3)2–)
in Table 2. REE(OH)3·nH2O(ss) is placed on the
last position of the decreasing sequence of Racah
(E 1 and E 3) parameters:
REE3+(aq,octahydrate) > REECO3 +(aq)
> REE(CO 3)2–(aq) ≥ REE(OH)3·nH 2O(ss), (36)
where the mark of “≥” means the relationships of
C1 and C 3 collectively. The direct comparison of
the Racah (E 1 and E 3 ) parameters between
470
A. Ohta and I. Kawabe
REE(CO 3) 2– (aq) and REE(OH)3 ·nH 2O (ss), or between REECO3 +(aq) and REE(OH)3 ·nH2 O(ss) can
be made by the RSPET analyses of log Kd(REE)(φ)
and log Kd(REE) (ω) next.
RSPET analyses of log Kd(REE) in the system with
carbonate ions
Equation (20) indicates that the series variation of log K d (REE) ( φ ) is given by
{∆G0f(REE(CO3)2–, aq) – ∆G0f(REE(OH)3·nH2O)}/
(2.303RT). It involves irregular variations due to
the structural changes in light REE(CO3)2 –(aq) and
heavy REE(OH) 3 ·nH 2 O (ss) series as discussed
above. Likewise, log Kd(REE) (ω) values given by
Eq. (24) are influenced by the structural change
in heavy REE(OH)3 ·nH2 O(ss) series, but there appears to be no such a structural change in REE+(aq).
However, when log Kd(REE) is recalculated as log
Kd(REE)( ω), the correction value of log(ω + 1) also
includes the structural change of REE(CO3)2– (aq)
in Eqs. (22) and (23). Besides the structural change
effect for heavy REE(OH)3·nH2O(ss), the structural
change effect of light REE(CO3 )2–(aq) must be removed for both calculations of log( φ + 1) and
log(ω + 1). We will write log Kd (REE)( φ) and log
Kd (REE)( ω) corrected for the structural changes in
relevant REE(III) complex series as log
Kd (REE)′ (φ) and log Kd (REE)′( ω), respectively.
The series variations of log Kd (REE)′( φ) based
on log Kd (REE) values from laboratory and field
data and the REE(III)-carbonate complexation
constants by Ohta and Kawabe (2000) are fairly
parallel with each other (Fig. 9(a)). They do not
show obvious tetrad effect variations. In contrast,
when the same original log Kd (REE) values are
converted to log Kd(REE)′(ω) , they show parallel
variation patterns having convexity commonly
(Fig. 9(b)). Table 3 summarizes C1 and C3 parameter values for log K d (REE)′ ( φ ) and log
Kd (REE)′( ω) . The C 1 values for the sets of log
Fig. 9. The series variations of log Kd(REE)′(φ ) and log K d(REE)′( ω) from experimental and field data. Primes
mean that structural change effects in REE(CO3) 2–(aq) and REE(OH) 3·nH 2O(ss) series have already been corrected.
The symbols [A]~[E] are the same as in Fig. 4. Multiplication symbols: the least-square fittings of log Kd(REE)′( φ)
and log Kd(REE)′ (ω) to the RSPET equation, and plus symbols: smooth variations separated from the respective
tetrad effect variations. log Kd(REE)′( φ) and log Kd(REE)′ (ω) are conveniently multiply by respective factors in
order to avoid overlapping log Kd(REE)′ (φ ) and log K d(REE)′(ω) each other.
Theoretical study of tetrad effects
Kd(REE)′( φ) are very close to zero, but the C3 values for those sets of log Kd(REE)′ (φ) are positive
though their uncertainties are fairly large. The
numerical results of C1 and C3 for log Kd(REE)′( φ)
and log Kd(REE)′( ω) are well in agreement with
the differences of C1 and C 3 values between log
Kd(REE)′( χ) – 3pH and log K2′ or log K1 ′. This
strongly supports the relationship of (36).
The REE patterns in Figs. 9(a) and (b) are corresponding to those in Figs. 5(a) and (b), respectively, because the results of Figs. 9(a) and (b) are
obtained from those of Figs. 5(a) and (b) by correcting all the structural change effects of relevant
REE(III) species. All of log Kd(REE)′( φ) and log
Kd(REE)′( ω) for experimental and field data show
good parallelism in Figs. 9(a) and (b), and there
are no irregularities at light REE side (La-Pr) unlike those shown in Figs 5(a) and (b). The comparisons of Figs. 9(a) and (b) illustrate that the
lanthanide tetrad effects recognized in log
Kd(REE) (Fig. 1) can never be understood fully
by the corrections only for the carbonate
complexation in the seawater solution or experimental NaCl solutions. The additional considerations as to the structural changes in light REE3+(aq),
light REE(CO 3)2 –(aq), heavy REE(OH)3 ·nH2 O(ss)
series are absolutely necessary for our quantitative understanding of the tetrad effects by the re-
471
fined spin-pairing energy theory.
It is also important to emphasize that quantitative understanding of the tetrad effects given by
the inequality of (36), apart from the structural
change effects, is not so difficult. In the discussion on the systematic change of convex tetrad
effects of Fig. 1, we emphatically noted that convexity of tetrad curves for experimental log
Kd(REE) becomes less conspicuous with increasing concentration of doped NaHCO3 in the NaCl
solution. With increasing NaHCO3 concentration,
the dominant REE(III) species in solution changes
from REE 3+ (aq) to REECO 3 + (aq) , and then to
REE(CO3)2–(aq). Therefore the diminishing convex
tetrad effect in Fig. 1 suggests that the differences
of Racah (E 1 and E 3 ) parameters of REE 3+(aq),
REECO 3 + (aq) and REE(CO 3 ) 2 – (aq) relative to
REE(OH)3·nH2O(ss) systematically decrease in this
order. What is suggested is just the relationship
of (36). We can make this intuitive understanding
of the results of Fig. 1 immediately, only if we
accept the essence of the refined spin-pairing energy theory represented by Eqs. (28), (29) and
(30).
The conspicuous convex tetrad effect of field
data in Fig. 1 can also be interpreted by the systematically different Racah (E1 and E 3) parameters. The apparent log Kd(REE) between marine
Table 3. Comparison of C1 and C 3 parameters determined by the least squares fitting of log K d(REE)′( φ) and
log Kd(REE)′( ω) to RSPET equation(a)
Data set
By differences in Table 1(b )
log Kd (REE) (8 .2 3 mM)
log Kd (REE) (1 .3 0 mM)
log Kd (REE) between ferromanganese nodule and
Pacific deep water
log Kd (REE) between NCP(d ) and Pacific deep water
log Kd (REE) between SCP(d ) and Pacific deep water
log Kd (REE)′( φ )
log Kd (REE)′( ω)
C1 /10– 3
C3 /10– 4
C1 /10– 3
C3 /10– 4
–0.06 ± 0.28
–0.19 ± 0.22
–0.12 ± 0.32
0.02 ± –0.20(c)
0.45 ± 0.92
0.23 ± 0.69
0.35 ± 1.02
0.72 ± 0.60(c)
0.34 ± 0.30
0.22 ± 0.21
0.29 ± 0.32
0.43 ± 0.20(c)
1.34 ± 0.98
1.13 ± 0.69
1.26 ± 1.01
1.63 ± 0.60(c)
0.00 ± 0.13
–0.02 ± 0.10
0.70 ± 0.41
0.18 ± 0.31
0.41 ± 0.13
0.38 ± 0.10
1.60 ± 0.41
1.08 ± 0.31
The prime and subscripts ( φ) or (ω ) mean that log Kd(REE) have been corrected for structural change of heavy REE(OH)3·nH2O
and for log( φ + 1) or log( ω + 1), respectively. The correction values of log( φ + 1) and log(ω + 1) were calculated after the
structural change of REE(CO 3 )2–(aq) was removed. The sources of data sets are given in Fig. 1.
(b)
For estimation of the difference C 1 and C 3 values between log K d(REE) ′( χ) – 3pH, and log K 2 ′ or log K1 ′ in Table 1.
(c)
RSPET analysis was made by omitting the datum point of La.
(d)
NCP and SCP mean Northern and Southern Central Pacific ferromanganese crust, respectively.
(a)
472
A. Ohta and I. Kawabe
Fe-Mn deposit and deep seawater can be expressed
approximately by log m(REE(OH) 3 ·nH 2 O)/
[REECO3 +, aq] from speciation calculation using
our REE(III)-carbonate complexation constants
(Fig. 2(a)). Their conspicuous convex tetrad effect is due to moderate differences of Racah (E1
and E3 ) parameters between REECO 3 + (aq) and
REE(OH)3·nH2O (ss) in as (36).
(4) The log Kd(REE) – 3pH, log K1 and log K2
values reported by Ohta and Kawabe (2000) are
satisfactorily fitted to the RSPET equation after
they are corrected for hydration change effect in
light REE3+(aq), and structural change effects in
light REE(CO 3 ) 2 – (aq) , and in heavy
REE(OH)3·nH2 O(ss). We have inferred that Racah
(E1 and E3 ) parameters decrease in the following
order;
CONCLUSION
REE3+(aq,octahydrate) > REECO3+(aq)
> REE(CO3 )2 –(aq) ≥ REE(OH) 3·nH2 O(ss).
(1) The series variations of apparent REE distribution coefficients between ferromanganese
nodule and crust, and deep water can be reproduced by the REE partitioning experiments between Fe oxyhydroxide precipitates and solutions
with similar carbonate ion concentrations to
seawater, except for Ce anomalies.
(2) The speciation calculation of REE species
in seawater using our REE(III)-carbonate
complexation constants (Ohta and Kawabe, 2000)
is different from the calculation using the constants by Liu and Byrne (1998): First, our
complexation constants indicate that the dominant
species is REECO3 +(aq), except for heavy REE,
while those from Liu and Byrne (1998) show that
REE(CO 3 ) 2 – (aq) is more dominant than
REECO3 +(aq) except for light REE. Second, total
REE concentration in seawater is approximately
the sum of the concentrations of REECO3+ (aq) and
REE(CO3 )2 –(aq) in the speciation calculation using our complexation constants. But when those
by Liu and Byrne (1998) are adopted, the additional species of [REE3+, aq] and [REESO 4+ , aq]
need to be considered for light REE.
(3) We have examined which set of REE(III)carbonate complexation constants is better to explain natural and laboratory systems, ours or those
by Liu and Byrne (1998). By comparison of the
series variations of log{m(REE(OH) 3 ·nH 2 O)/
[REE(CO3)2 –, aq]} and log{m(REE(OH)3·nH2O)/
[REECO3 +, aq ]} between field and experimental
data, we have confirmed that our complexation
constants are better to explain laboratory and field
data simultaneously than those by Liu and Byrne
(1998).
This relationship is also confirmed by RSPET
analyses of log Kd(REE)′( φ) and log Kd(REE)′( ω)
from experimental and field data. The systematic
change of the convexity of tetrad curves for experimental log Kd(REE) and the conspicuous convex tetrad effect of field data in Fig. 1 also immediately suggest this relationship.
Acknowledgments—This work was supported partly
by the grants Nos. 03402018 and 06453007 from the
Ministry of Education, Science, Sports and Culture,
Japan to I.K.
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