Geochemical Journal, Vol. 41, pp. 149 to 163, 2007
Boron isotope fractionation accompanying formation of potassium,
sodium and lithium borates from boron-bearing solutions
MAMORU Y AMAHIRA, Y OSHIKAZU KIKAWADA* and TAKAO OI
Department of Chemistry, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8854, Japan
(Received March 18, 2006; Accepted June 22, 2006)
A series of experiments was conducted in which boron minerals were precipitated by water evaporation from solutions
containing boron and potassium, sodium or lithium at 25°C, and boron isotope fractionation accompanying such mineral
precipitation was investigated. In the boron-potassium ion system, K2[B4O 5(OH) 4]·2H 2O, santite (K[B 5O6(OH)4]·2H 2O),
KBO 2 ·1.33H 2 O, KBO 2 ·1.25H 2 O and sassolite (B(OH) 3 ) were found deposited as boron minerals. Borax
(Na 2[B 4O 5(OH) 4·8H 2O) was found deposited in the boron-sodium ion system, and Li 2B 2 O 4·16H 2 O, Li2 B4O 7 ·5H 2O,
Li2B10O16·10H2O, LiB2O 3(OH)·H2O and sassolite in the boron-lithium ion system. The boron isotopic analysis was conducted for santite, K2[B4O5(OH) 4]·2H 2O, borax and Li2B2O 4·16H2O. The separation factor, S, defined as the 11B/10B
isotopic ratio of the precipitate divided by that of the solution, ranged from 0.991 to 1.012.
Computer simulations for modeling boron mineral formations, in which polyborates were decomposed into three coordinated BO3 unit and four coordinated BO 4 unit for the purpose of calculation of their boron isotopic reduced partition
function ratios, were attempted to estimate the equilibrium constant, KB, of the boron isotope exchange between the boric
acid molecule (B(OH)3) and the monoborate anion (B(OH) 4–). As a result, the KB value of 1.015 to 1.029 was obtained.
The simulations indicated that the KB value might be dependent on the kind of boron minerals, which qualitatively agreed
with molecular orbital calculations independently carried out.
Keywords: boron isotopes, boron minerals, boron isotope fractionation, separation factor, reduced partition function ratio
et al., 1993; Palmer et al., 1998; Honisch et al., 2004;
Pagani et al., 2005). The usefulness of the method, however, is still in dispute. To use the boron isotopic ratio as
a geochemical tracer, the knowledge on the accurate equilibrium constants of boron isotope exchange reactions
between two boron species in equilibrium is essential.
Boron atom is always bonded to oxygen atoms, in the
trigonal form or in the tetrahedral form, except for some
rare cases. The most important boron isotope exchange
reaction is that between the boric acid molecule (B(OH)3)
and the monoborate anion (B(OH)4–):
INTRODUCTION
Boron has two stable isotopes, 10B and 11B, and their
relative abundances are approximately 20 and 80%, respectively. The variation in the boron isotopic composition of natural samples is large. As summarized by Palmer
and Swihart (1996), it is about 100‰ (permil) in the δ
expression defined as,
δ11B = {(11B/10B)sample/(11B/10B) standard – 1} × 1000, (1)
where (11B/10B) sample denotes the 11B-to-10B boron isotopic ratio of the sample and (11B/ 10B)standard that of a
standard. The standard used in most studies is NBS SRM
951 boric acid (Cantanzaro et al., 1970).
Due mainly to this large variation, boron isotopic composition has been applied to many areas of earth sciences
and has provided valuable findings on fundamental processes in natural circumstances. One of the recent and important applications is to estimate the ancient ocean pH
using the boron isotopic composition of natural carbonates (for instance, Hemming and Hanson, 1992; Spivack
10
B(OH)3 +
11
B(OH)4– = 11B(OH)3 + 10B(OH)4–. (2)
The equilibrium constant (KB) of Reaction (2) is larger
than unity, which means the heavier isotope is preferentially fractionated into the trigonal boric acid and the
lighter one into the borate anion. The theoretical value
based on the molecular vibrational analysis was first obtained to be 1.0194 at 25°C (Kakihana and Kotaka, 1977),
but there are experiments and observations that require
larger KB values (Vengosh et al., 1991; Palmer et al., 1987;
Nomura et al., 1990). Other theoretical methods including those based on molecular orbital calculations (Oi,
2000a; Zeebe, 2005) also suggest KB should be larger than
1.0194 (Kakihana and Kotaka, 1977).
*Corresponding author (e-mail: [email protected])
Copyright © 2007 by The Geochemical Society of Japan.
149
An application of the boron isotopic composition is
to the elucidation of the origin and alteration of borate
deposits (Peng and Palmer, 1995; Swihart et al., 1996).
To quantitatively discuss such problems, the knowledge
on the exact degrees of boron isotope fractionations accompanying boron mineral formation from boronbearing solutions is certainly required. To the best our
knowledge, our previous paper (Oi et al., 1991) is only
one that reported laboratory experiments in which boron
minerals were precipitated from boric acid solutions and
boron isotope fractionation upon precipitation was measured. Unfortunately, the counterion was limited to the
sodium ion. Precipitation experiments were then extended
to include the potassium and lithium ions. In this paper,
we report the results of boron isotope fractionations accompanying boron mineral formations from aqueous solutions of boric acid containing potassium, sodium or
lithium ion as the counterion.
EXPERIMENTAL
An aqueous solution, in which boron concentration
was about 0.3 M (1 M = 1 mol/dm 3) to 1.0 M and that of
the cation (K+, Na+ or Li+ ion) was about 0.2 M to 3.2 M,
was first prepared by dissolving boric acid and metal hydroxide or metal chloride into distilled water. The pH was
adjusted with 5.0 M sodium hydroxide solution or conc.
hydrochloric acid. This pH adjusted solution was used as
the stock solution of the initial solution of each run. A
beaker containing 200 cm3 of this initial solution was
placed in a water bath, the temperature of which was controlled at 25.0 ± 0.2°C. (In some cases, the volumes of
the initial solutions other than 200 cm3 were adopted.)
No stirring of the solution or shaking the beaker was
practiced while the beaker was kept placed in the water
bath. No artificial manipulation such as adding a seed
crystal to the solution was attempted to promote the precipitation, either. A precipitate was formed from the solution by concentration of the solution due to water evaporation. Upon precipitation, the solid and the solution
phases were separated by sucking filtration. The solution
phase was analyzed for its pH and concentrations of boron and the cation. The precipitate was air-dried and the
mineral phase was identified by X-ray powder diffraction (XRD) analysis with a Rigaku RINT 2100V/P X-ray
spectrometer. The amount of boron in the precipitate was
determined by measuring the boron content of the solution that was prepared by dissolving an aliquot of the precipitate into a certain volume of distilled water.
The boron isotopic ratios of solutions and minerals
were measured by the surface ionization method with a
Varian MAT CH-5 mass spectrometer at Tokyo Institute
of Technology. The detailed mass spectrometry applied
is given elsewhere (Nomura et al., 1973; Oi et al., 1989).
150 M. Yamahira et al.
The 95% confidence limit is typically about ±0.2%. Each
sample was measured at least twice and the arithmetic
mean was taken as the isotopic ratio of the sample.
RESULTS
Table 1 summarizes the initial solution conditions and
the final results of the solution and the solid phases, except for the isotopic data. Many runs are omitted from
the table in which solution became mucilaginous without
producing precipitate by water evaporation, only a very
small volume of solution remained with a very large
amount of precipitate, or while separating the precipitate
from solution by filtration, new precipitate formed, and
so forth. In most cases, the solution and the solid (precipitate) phases were separated by filtration as soon as
we noticed the formation of precipitates. It was often very
difficult to determine accurately the ratio of the amount
of boron precipitated to that in the initial solution.
Precipitates obtained
Potassium borate system The boron concentration, pH
and the mole ratio of potassium to boron of initial solution ranged from 0.61 to 1.0 M, 0.36 to 14.3 and 0.41 to
2.30, respectively. The time elapsed between the start of
the run and the start of separation of the solid and solution phases (deposition time) was from 4 hours to 34 days.
It must have depended on many factors such as the chemical composition of the initial solution and the evaporation speed of water. The major boron minerals identified
by XRD analysis were sassolite (B(OH)3; JCPDS No. 300199), santite (K[B 5 O 6 (OH) 4 ]·2H 2 O; JCPDS No. 250624) and K2[B4O5(OH)4]·2H2O (JCPDS No. 29-0987;
no mineral name given; designated hereafter as K2B4O7).
KBO 2 ·1.333H 2 O (JCPDS No. 18-1039) and
KBO2·1.25H2O (JCPDS No. 19-0980) were also identified as minor boron minerals. Minerals without boron
component identified included KCl and K2CO3. Examples of XRD patterns of K2B4O7 and santite obtained
are shown in Figs. 1(a) and (b), respectively. They are
compared with the ones in the JCPDS files. Figure 2 shows
the solution conditions (the mole ratio of potassium to
boron and pH of the final solution) under which minerals
are supposed to have been formed. As is seen, the pH
value of solution seems the most influential to determine
which mineral is formed, and the kind of mineral formed
is almost independent of the K/B mole ratio. Admittedly
roughly, sassolite is deposited in the low pH region. Between pH about 4.5 and about 9, the main borate deposited is santite. The pH region in which K2B4O7 precipitates is approximately from 9 to 12. At very high pH,
KBO2·1.33H2O and KBO2·1.25H2O are found deposited.
Sodium borate system Runs in this system were conducted
to examine reproducibility of boron isotopic data in the
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 151
K
System
200.0
200.0
200.0
K28
K29
K30
200.0
200.0
K26
K27
200.0
200.0
K24
K25
200.0
200.0
200.0
K21
K22
200.0
K20
K23
200.0
200.0
K18
K19
200.0
200.0
K16
K17
200.0
200.0
K14
K15
200.0
200.0
K12
K13
100.0
200.0
K10
100.0
K9
K11
200.0
200.0
K7
K8
200.0
200.0
K5
K6
200.0
200.0
K3
200.0
K2
K4
200.0
[cm ]
3
Vol.
K1
Run No.
7.94
9.35
9.09
9.99
10.98
11.71
12.92
14.21
5.39
6.14
0.98
7.14
7.91
9.26
5.45
6.49
7.85
9.02
10.07
10.97
10.31
10.18
11.91
10.82
10.00
8.99
8.00
6.91
6.22
6.92
pH
0.871
0.902
0.817
0.815
0.844
0.872
0.885
1.001
0.913
0.920
0.931
0.940
0.942
0.957
0.971
0.971
0.971
0.971
0.971
0.971
0.800
0.800
0.800
0.800
0.800
0.800
0.800
0.800
0.800
0.800
[mol⋅dm ]
−3
B conc.
Initial solution
0.426
0.406
1.851
1.890
1.844
1.818
1.829
1.738
0.431
0.431
0.430
0.426
0.432
0.416
0.802
0.802
0.802
0.802
0.802
0.802
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
M/B2)
10d
158.6
64h
2d
94h

2d
3d
4d
5d
10d
10d
9d
9d
10d
154.6
158.0
156.8
162.4
161.8
181.4
135.5
170.1
126.3
158.0
189.3
17d
14d

10d
12d
33d
31d
34d
5d
10d
10d
8d
9d
7d
2d
1d
4h
1.5h
Time4)
126.1
13.0
11.6
191.6
184.2
171.4
85.0
100.0
198.0
187.0
150.0
180.0
50.0
10.0
0.0
0.0
[cm ]
3
Evap.3)
8.67

9.15
11.14
12.36
13.18
13.44
14<
4.57
4.29
0.53
4.82
9.12

4.17
6.12
8.01
8.69
11.19
11.76
0.961

3.364
1.355
3.869
4.658
4.713
4.761
1.070
1.075
0.983
0.933
3.591

1.106
0.635
0.731
5.315
1.496
2.919
4.290


11.36

1.055

1.434
3.481
0.370
0.307
0.303
0.300
1.055
1.821
1.069
1.335
1.160

1.772
1.174
1.049
0.861
2.937
1.202
0.734

0.080

0.867
0.788
0.800
1.600
1.111
1.145
M/B2)
9.210
2.410
6.130
0.750
0.450
0.630
0.620
[mol⋅dm ]
−3
B conc.
14<
14<
10.50
8.78
8.16
6.77
6.89
6.90
pH
Solution phase
sassolite
santite, KCl

KCl
K 2[B 4O 5(OH) 4]⋅2H 2O


KCl
KCl


KCl
KCl


sassolite
KBO2⋅1.33H2O, KBO2⋅1.25H2O

sassolite


santite
sassolite

santite
0.720
0.736



santite
santite
K 2[B 4O 5(OH) 4]⋅2H 2O
K 2[B 4O 5(OH) 4]⋅2H 2O
K 2[B 4O 5(OH) 4]⋅2H 2O
K 2[B 4O 5(OH) 4]⋅2H 2O
K 2[B 4O 5(OH) 4]⋅2H 2O
K 2[B 4O 5(OH) 4]⋅2H 2O
K 2[B 4O 5(OH) 4]⋅2H 2O
K 2[B 4O 5(OH) 4]⋅2H 2O
K 2[B 4O 5(OH) 4]⋅2H 2O
santite
santite
santite
santite
Mineral
Solid phase
0.260
0.195
0.292
0.746
0.472
0.52


0.13
0.23
0.20
0.19
0.21
0.41
0.21
Mole fraction5)
Table 1. The initial conditions of the solution phase and the experimental results other than the isotopic data 1)
152 M. Yamahira et al.
Na
K
System
200.0
200.0
200.0
N3
N4
N5
200.0
200.0
N1
150.0
K47
N2
200.0
200.0
K45
K46
200.0
200.0
K43
K44
200.0
200.0
K41
K42
200.0
200.0
K39
K40
200.0
200.0
K37
K38
200.0
200.0
K35
K36
200.0
200.0
K33
200.0
K32
K34
200.0
[cm ]
3
Vol.
K31
Run No.
Table 1. (continued)
12.27
12.30
10.38
8.47
8.00
0.50
6.40
7.12
8.43
10.89
9.70
12.62
1.32
0.56
0.36
7.03
9.10
14.30
1.63
6.75
0.75
5.70
0.800
0.800
0.800
0.800
0.800
0.852
0.862
0.865
0.897
0.940
0.907
0.976
0.629
0.620
0.605
0.635
0.661
0.801
0.820
0.823
0.821
0.840
[mol⋅dm ]
−3
B conc.
Initial solution
pH
1.000
1.000
1.000
1.000
1.000
1.031
1.020
1.019
0.989
0.982
0.995
0.951
2.222
2.235
2.302
2.210
2.153
1.989
0.457
0.451
0.464
0.445
M/B2)
69h
200.0
150.0
64.0
98.0
163.0
48.4
113.2
103.8
8d
7d
5d
4d
3d
18h
21h
23h
49h

170.2
43h
78h
19h
16h
25h
24h
39h
65h
41h
45h
47h
49h
Time4)
181.2
192.4
90.0
83.0
94.2
132.8
143.2
178.2
106.0
132.2
84.0
123.8
[cm ]
3
Evap.3)
2.69


0.66
0.84
3.61
0.876
0.879
0.438
3.146

1.368
10.537
0.985
0.928
0.937
0.666
2.316
3.788
0.924
0.877
0.878
0.981
[mol⋅dm ]
−3
B conc.
11.84
10.78
7.43
6.19
0.24
4.72
6.85
9.02

10.76
14<
0.98
0.29
0.02
5.01
9.20
14<
1.42
5.09
0.62
4.81
pH
Solution phase

1.052
1.485
1.440
1.205
1.426
1.999
3.206
1.532

3.494
0.136
2.590
2.570
2.766
5.494
2.034
0.377
0.757
0.960
0.752
0.868
M/B2)
K 2CO3⋅1.5H2O



0.046
0.45
0.41
0.18
borax
borax
borax
borax
borax
santite, sassolite, KCl
KCl

santite, KCl
santite, KCl

0.699
0.428
K 2[B 4O 5(OH) 4]⋅2H 2O

0.884
sassolite, KCl
sassolite, KCl


santite, KCl
sassolite, KCl


KBO2⋅1.33H2O, KBO2⋅1.25H2O
KCl


sassolite, santite
sassolite, KCl

sassolite, KCl

sassolite, KCl

Mineral
Solid phase

Mole fraction5)
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 153
7.81
200.0
L22
200.0
200.0
200.0
200.0
L25
L26
L27
L28
200.0
200.0
L21
200.0
200.0
L20
L23
200.0
L19
L24
200.0
200.0
L17
L18
200.0
200.0
L15
L16
7.76
7.78
5.72
3.32
5.77
6.63
8.41
9.56
12.54
12.56
9.17
1.80
9.03
7.64
7.92


200.0
L13
L14
9.86
12.65
200.0
200.0
L11
12.81
L12
300.0
200.0
L9
L10
7.29
7.59
200.0
400.0
L7
6.51
11.55
L8
200.0
400.0
L5
10.89
9.99
9.53
3.36
0.779
0.821
0.782
0.773
0.777
0.362
0.393
0.438
0.476
0.460
0.445
0.392
0.892
0.863
0.750

0.416
0.447
0.472
0.802
0.806
0.804
0.800
0.799
0.801
0.802
0.800
0.800
[mol⋅dm ]
−3
B conc.
Initial solution
pH
L6
200.0
200.0
L3
300.0
L2
L4
200.0
[cm ]
3
Vol.
L1
Run No.
1.022
1.027
1.021
1.018
1.027
2.128
1.980
1.854
1.748
1.796
0.943
1.026
0.994
0.934
0.973

1.888
1.834
1.829
0.500
0.500
0.502
0.503
2.003
0.999
0.996
1.001
1.004
M/B2)
16d
110d
110d


16d
16d
55d
55d
84.0
44.4
90.8
140.2
172.2
55d
5d
165.0
8d

7d
104.2
5d

9d
9d
9d

3d
6d
6d
214h
187h
248h
101h
10h
172h
166h
172h
22h
Time4)
131.4
177.8
184.0
179.8

174.6
72.2
69.2
264.0
359.6
175.2
243.5
65.7
31.9
131.9
254.5
78.1
[cm ]
3
Evap.3)


5.45
3.34
5.51
5.38
6.73
8.90

10.85
7.69
1.25
7.75
4.79
4.88
10.66
8.86
12.15
12.84
6.28
5.57
6.14
6.20
12.42
11.11
9.83
8.82
3.45
pH


0.963
0.741
0.971
0.950
2.837
2.477

0.586

0.644
4.519
4.274
7.019
0.760
1.630
0.311
0.331
4.510
6.440
4.580
1.670
0.620
0.740
1.440
4.750
0.750
[mol⋅dm ]
−3
B conc.
Solution phase


1.441
1.386
1.513
2.673
1.900
1.705

2.065

1.796
1.299
1.988
0.969
0.853
2.560
1.896
1.839
0.477
0.534
0.675
0.563
2.161
0.919
0.931
0.869
1.573
M/B2)

Li2B 10O 16⋅10H 2O
Li2B 10O 16⋅10H 2O
sassolite
sassolite



sassolite
sassolite

LiB2O 3(OH) H 2O, Li2B 4O 7⋅5H2O


Li2B2O 4⋅16H2O
Li2CO3

Li2B2O4⋅16H2O, Li2CO3


sassolite
amorphous


Li2B 10O 16⋅10H 2O
amorphous


Li2B2O 4⋅16H2O
Li2B 10O 16⋅10H2O, halite

Li2B2O 4⋅16H2O
Li2B2O 4⋅16H2O
Li2B2O 4⋅16H2O
sassolite, Li2B4O7⋅5H2O
sassolite, Li2B4O7⋅5H2O
sassolite, Li2B4O7⋅5H2O
sassolite, Li2B4O7⋅5H2O
Li2B2O 4⋅16H2O
Li2B2O 4⋅16H2O
Li2B2O 4⋅16H2O
Li2B2O 4⋅16H2O
sassolite
Mineral
Solid phase

0.485
0.137

0.096
0.119
0.264
0.181
0.227
0.174
0.385
0.063
0.291
Mole fraction5)
2)
Temperature: 25.0 °C.
Mole ratio of metal to boron.
3)
Approximate volume of water evaporated.
4)
Approximate time elapsed between the start of the run and the start of the deposition (deposition time).
5)
The mole ratio of boron in the mineral to that in the initial solution, calculated using the boron contents in the solid phase and in the initial solution.
1)
Li
System
6
K2[B4O5(OH)4]·2H2O (K12)
K/B mole ratio
int.
(a)
JCPDS No. 29-0987
10
20
30
40
2θ(CuKα1)/degrees
(b)
50
60
4
2
0
0
70
7
14
pH
Fig. 2. The K/B mole ratio-pH plot for the potassium borate
system. 䊉 = K 2 [B 4 O 5 (OH) 4 ]·2H 2 O; 䊊 = santite
(K[B 5O6(OH) 4]·2H2O); 䊐 = sassolite (B(OH) 3); 䊏 = other
potassium borates; × = minerals other than borates.
int.
santite (K[B5O6(OH)4]·2H2O) (K14)
6
10
20
30
40
2θ(CuKα1)/degrees
(c)
50
60
70
Na/B mole ratio
JCPDS No. 25-0624
4
2
Li2B2O4·16H2O (Run L11)
int.
0
0
7
14
pH
Fig. 3. The Na/B mole ratio-pH plot for the sodium borate
system. 䊉 = borax (Na2[B4O5(OH)4]·8H2O).
JCPDS No. 28-0557
10
20
30
40
2θ(CuKα1)/degrees
50
60
70
Fig. 1. Examples of XRD patterns of (a) K2B4O7
(K 2 [B 4 O 5 (OH) 4 ]·2H 2 O) (Run K12), (b) santite
(K[B 5 O 6 (OH) 4 ]·2H 2 O) (Run K14) and (c) L2B2O4
(Li 2B2O4·16H 2O) (Run L11) obtained in the present study. Each
pattern is compared with the one in the JCPDS file.
previous paper (Oi et al., 1991). Only borax
(Na 2[B 4O5(OH)4]·8H2O; JCPDS No. 12-0258) was obtained as sodium borate in the pH range of 6 to 12 (Fig.
3). In the lower pH range, sassolite was obtained like in
the case of the potassium system, which is not shown in
Fig. 3 or in Table 1.
154 M. Yamahira et al.
Lithium borate system The boron concentration, pH and
the mole ratio of lithium to boron of the initial solutions
ranged from 0.36 to 0.89 M, 3.32 to 12.8 and 0.50 to 2.13,
respectively. The deposition time was from 10 hours to
110 days. The boron minerals identified by XRD analysis were sassolite, Li2B2O4·16H2O (JCPDS No. 28-0577;
no mineral name given; designated hereafter as L2B2O4),
Li2B4O7·5H2O (JCPDS No. 01-0112), Li2B10O16·10H2O
(JCPDS No. 27-1224) and LiB2O3(OH)·H2O (JCPDS No.
43-1498). An XRD pattern of L2B2O4 obtained is given
in Fig. 1(c), together with the pattern in the JCPDS file.
Other minerals without boron component included halite
and Li2CO3. Similarly to the potassium and sodium systems, the Li/B ratio-pH plot was made and is shown in
Fig. 4. As in the case of potassium borates, the pH of the
solution seems the most influential in determining which
lithium borate is deposited. Sassolite is precipitated from
Table 2. Summary of boron isotopic data
6
Li/B mole ratio
System
Mineral
K
K2B4O7
2
7
14
pH
santite
Fig. 4. The Li/B mole ratio-pH plot for the lithium borate system. 䉭 = Li2B2O4·16H2O; 䊉 = Li2B4O7·5H 2O; 䊐 = sassolite
(B(OH) 3); 䊏= other lithium borates; × = minerals other than
borates.
1.02
0
7
14
S
Mineral
K5
K6
K7
K10
K11
K12
K13
K42
K1
K2
K3
K4
K14
K15
K18
K19
K44
K45
+0.6
–4.1
–5.8
–0.4
–10.1
–11.5
–1.5
–8.1
+1.1
+0.6
–2.9
–1.6
–2.2
–2.2
–7.3
+1.4
+2.8
+1.9
–2.4
+1.6
+5.8
+2.6
+0.8
–2.5
–3.1
+2.6
–3.4
–2.6
–2.9
+2.6
–0.4
–5.1
–0.9
–4.6
+3.5
–5.2
0.997
1.006
1.012
1.003
1.011
1.009
0.998
1.011
0.996
0.997
1.000
1.004
1.002
0.997
1.007
0.994
1.001
0.993
Na
borax
N1
N2
N3
N4
–2.4
+3.6
–1.9
–1.9
–6.8
–4.1
+3.6
+9.3
0.996
0.992
1.006
1.011
Li
L2B2O4
L2
L3
L4
L5
L11
L12
+2.7
+1.6
–1.5
+0.1
–4.6
+0.8
–6.7
–3.4
+2.4
–0.1
–3.0
–6.6
0.991
0.995
1.004
1.000
1.002
0.993
1.00
0.98
δ1 1 B (‰)
Solution
4
0
0
S
Run No.
pH
Fig. 5. Plot of the separation factor (S) against the pH of the
solution for the potassium borate system. 䊉 =
K2[B4O 5(OH) 4]·2H2O; 䊊 = santite (K[B5O6(OH) 4]·2H2O). The
solid lines denote approximate correlation between S and pH,
and the vertical broken lines indicate the crossover points.
solutions of low pH values. At around pH 5,
Li2B10O16·5H2O is deposited; Li2B4O7·5H2O is formed
in the pH range of 5 to 7; and L2B2O4 is precipitated at
pH values above 8.5.
Boron isotope fractionation
Boron isotopic measurements were made on the runs
where only one kind of boron mineral was precipitated
and where the solution phase was relatively easy to treat.
The final solution was usually nearly saturated or oversaturated, and was very sticky one, often not suited for
various quantitative measurements. The isotopic data in
permil expression (‰) are summarized in Table 2. The
separation factor, S, in the table is defined as
S = (11B/10B) prec/(11B/10B)sol,
(3)
where (11B/10B)prec and (11B/10B)sol are the 11B-to-10B isotopic ratio of the mineral (precipitate) and of the solution, respectively. Using the permil expression, S is given
as,
S = [δ11B(mineral)/1000 + 1]/[δ 11B(solution)/1000 + 1].
(4)
By definition, S is larger than unity when the heavier isotope is preferentially deposited. Considering the 95%
confidence limit expected for each isotopic ratio data, the
error on S may typically be ±0.004.
Potassium borate system Isotopic measurements were
made on K2B4O7 (K2[B 4O 5(OH) 4]·2H 2O) and santite
(K[B5O6(OH) 4]·2H2O). The S value ranges from 0.997 to
1.012 for K2B4O7 and from 0.993 to 1.007 for santite.
Thus, both for K2B4O7 and santite, the heavier isotope
was preferentially fractionated into the precipitate in some
cases, while the lighter isotope was in other cases. In the
previous paper (Oi et al., 1991), we showed that, for the
borax case, the S value data were best understood when
plotted against the (final) pH of the solution phase. In
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 155
1.02
1.00
1.00
0.98
S
S
1.02
0
7
14
pH
Fig. 6. Plot of the separation factor (S) against the pH of the
solution for the sodium borate system. 䊉 = borax
= borax (Oi et al.,
(Na 2[B4O 5(OH)4]·8H 2O) (this work);
1991); 䊊 = sborgite (Na[B5O6(OH)4]·3H2O) (Oi et al., 1991).
The solid line denotes approximate correlation between S and
pH, and the vertical broken line indicates the crossover point.
Fig. 5, all the data on S in the potassium borate system in
Table 2 are plotted against the final pH of the solution
phase given in Table 1. A trend is observed that the S
value increases nearly linearly with increasing pH both
for K2B4O7 and for suntite as in the case of borax in the
previous paper (Oi et al., 1991). The slopes of the S-pH
plots for the two potassium borates seem very similar to
each other. The crossover point where S crosses unity on
going from the low pH region to the high pH region is
found at about pH 9.5 and at about 7.5 for K2B4O7 and
for santite, respectively. In addition, the extrapolation of
K2B4O7 data to the lower pH region and santite data to
the higher pH region in Fig. 5 suggests that K2B4O7 has
a smaller S value than santite at a given pH.
Sodium borate system The isotopic data are limited to
borax (Na2[B4O5(OH) 4·8H2O]) as shown in Table 2. Evidently, the S value data are scattered around unity. They
are plotted against the pH of the solution in Fig. 6, together with the isotopic data in the previous paper (Oi et
al., 1991). As is seen, the present isotopic data on borax
are consistent with the previous ones in the pH dependence. The S value for borax is an increasing function of
pH; it is smaller than unity in the pH region below ca. 9,
larger than unity in the pH region above ca. 10 and the
crossover point is at around 9.5. This crossover point of
borax is nearly the same as that of K2B4O7 in Fig. 5.
Extrapolation of the borax data to the lower pH region
indicates that the data point of sborgite
(Na[B5O6(OH) 4]·3H2O; JCPDS No. 12-0265), the only
sodium borate other than borax observed in our study (Oi
et al., 1991), is located above the point expected for borax at a given pH. This relation is similar to that observed
for K2B4O7 and santite found for the potassium borate
system (Fig. 5).
156 M. Yamahira et al.
0.98
0
7
14
pH
Fig. 7. Plot of the separation factor (S) against the pH of the
solution for the lithium borate system. 䉭 = Li 2B2O4·16H2O.
The solid line denotes approximate correlation between S and
pH.
Lithium borate system Isotopic measurements were made
on the runs where only L2B2O4 (Li2B2O 4·16H2O) was
deposited. Although Li2B4O7·5H2O was also obtained in
some runs, it was always deposited with other boron minerals, mostly with sassolite, and so we did not attempt to
obtain the boron isotopic data on Li2B4O7·5H2O. The S
value for L2B2O4 ranged from 0.991 to 1.004, meaning
that the lighter isotope was preferentially fractionated into
the precipitate in some runs, and in the other runs the
reverse was the case. If we take errors on the S values
into consideration, however, it may be more appropriate
to state that the S value is equal to or smaller than unity,
indicating the maximum value of S is unity. The boron
isotopic data in the lithium borate system are plotted in
Fig. 7. As in the cases of potassium borate and sodium
borate systems, the S value for L2B2O4 is an increasing
function of pH.
Consideration on structures and boron isotopic reduced
partition function ratios of borates
Since our publication (Oi et al., 1989) on the elucidation of boron isotopic compositions of boron minerals
based on isotopic reduced partition function ratios (rpfrs)
(Bigeleisen and Mayer, 1947), it has been established and
is now well understood that boron with trigonal coordination (surrounded by three oxygens) has a larger rpfr
than boron with tetrahedral coordination (surrounded by
four oxygens) and consequently the heavier isotope of
boron is fractionated into boron with trigonal coordination, if the two are equilibrated. If we confine our focus
on boron minerals, this means that the boron isotopic
composition of a mineral is heavily dependent on the ratio of the number of BO3 units (trigonal coordination)
and the number of BO4 units (tetrahedral coordination)
in the polyborate anion in the mineral, and that a boron
Table 3. Chemical formulae and BO3:BO4 ratios of the potassium, sodium and lithium
borates studied
(a)
Cation
Mineral name
Abbreviation
Chemical formula
K
(no name)
santite
K2B4O7
K2 [B4 O5 (OH) 4 ]·2H2 O
K[B5 O6 (OH) 4 ]·2H2 O
2:2
4:1
Na
borax
sborgite
Na 2 [B4 O5 (OH) 4 ]·8H2 O
Na[B5 O6 (OH) 4 ]·3H2 O
2:2
4:1
Li
(none)
(no name)
sassolite
Li2 B2 O4 ·16H2 O
B(OH) 3
0:2
1:0
L2B2O4
BO3 :BO4 in the polyanion
1.02
(b)
BO3:BO4 = 2:2
1.01
S
BO3:BO4 = 4:1
1.00
(c)
0.99
BO3:BO4 = 0:2
(d)
0.98
0
7
14
pH
Fig. 9. Plot of the separation factor (S) against the pH of the
solution. 䊐 = santite; 䊏 = sborgite; 䊊 = K2[B4O5(OH)4]·2H2O;
䊉 = borax (Na2[B4O5(OH) 4]·8H2O); 䉭 = Li2B2O4·16H 2O.
Fig. 8. Structures of (a) B(OH) 3 (BO 3 :BO 4 = 1:0), (b)
[B5O6(OH) 4] – (BO3:BO 4 = 4:1), (c) [B4O5(OH)4] 2– (BO3:BO4
= 2:2) and (d) [B2O(OH)6] 2– (B2O42–) (BO 3:BO4 = 0:2). The
largest black spheres represent boron atoms, and the intermediate glossy and smallest gray ones oxygen and hydrogen atoms, respectively. No significance is attached to the relative
sizes of those spheres.
mineral with a larger proportion of the BO3 component is
boron isotopically heavier than a mineral with a smaller
proportion of the BO3 component, if they are deposited
from the same solution. In this consideration, the kind of
cationic component has no significance. Thus, for instance, since the polyborate anions of borax and K2B4O7
are both composed of 2BO3 + 2BO4 and that of santite is
composed of 4BO3 + 1BO4, the isotopic compositions of
borax and K2B4O7 are similar to each other whereas that
of santite is heavier than the two minerals if they are all
formed from the common solution. In the above expression, 2BO 3 + 2BO 4 , for instance, means that the
polyborate anion consists of two BO3 units and two BO4
units with some Os replaced with OHs (Kakihana et al.,
1977; Oi et al., 1989). The chemical formulae and
BO3:BO 4 ratios of the boron minerals, for which the bo-
ron isotopic ratio measurements were made in this and
the previous studies are summarized in Table 3, and the
structures of the polyborates involved in those minerals
are drawn as computer outputs in Fig. 8.
In Fig. 9, the separation factors obtained for K2B4O7,
santite, borax, sborgite and L2B2O4 are all together plotted against the pH of solution. Based on the discussion in
the previous paragraph, boron minerals with the same
BO3:BO4 ratios should show the similar pH dependence,
irrespective of the kind of counterions. In fact, borax and
K2B4O7 can be put into one group having the 2BO3 +
2BO4 structure, sborgite and santite into another group
having the 4BO3 + 1BO4 structure, and L2B2O4 constitutes the third group with the 0BO3 + 2BO4 structure, as
is indicated by the ovals in Fig. 9, although a few data
points are located outside of the ovals.
QUALITATIVE ELUCIDATION OF THE OBSERVED
BORON I SOTOPE F RACTIONATION
The boron isotope fractionation shown in Fig. 9 can
be qualitatively elucidated on the basis of the theory on
equilibrium isotope effects (Bigeleisen and Mayer, 1947).
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 157
lnS = ln(∑xi(s)fi(s)) – ln(∑xi(l)fi(l)),
1.0
(a)
B(OH)4–
B(OH)3
B4O5(OH)42–
0.5
B3O3(OH)4–
Mole fraction
The rpfr value of B(OH)3 is larger than that of B(OH)4–,
which predicts that the heavier isotope 11B tends to be
fractionated into B(OH) 3 and 10B into B(OH)4–, when the
two boron species are in equilibrium with each other. This
is why the equilibrium constant of Eq. (1) is larger than
unity. In the present experiments, the two isotopes of boron are distributed between two phases; one is the solid
phase (boron mineral) and the other the solution phase
(aqueous solution). In this case, the separation factor, S,
is given, in terms of the rpfrs, as (Kakihana and Aida,
1973)
0.0
1.0
B2O(OH)5–
(b)
BO3 unit
(5)
BO4 unit
0.5
where fi(s) and xi(s) are the rpfr and the mole fraction of
species i in the solid phase, respectively, and the fi(l) and
x i(l) are the rpfr and the mole fraction of species i in the
solution phase, respectively. By definition, ∑xi(s) = ∑xi(l)
= 1, and the symmetry numbers are omitted in the expression of the rpfrs for simplicity. There is only one boron species in the solid phase in each of the runs for which
the isotopic measurements were made. The solution phase
is a concentrated boric acid solution, in which not only
monomeric boron species, B(OH)3 and B(OH) 4–, but also
polyborate anions such as B 3O3(OH) 4– and B3O3(OH)32–
are supposed to exist (Ingri et al., 1957; Spessard, 1970;
Mesmer et al., 1972). Their concentrations depend on,
among others, the total concentration of boron and pH of
the solution.
As mentioned above, the rpfrs of monomeric boron
species were calculated based on their observed vibrational frequencies. Unfortunately, however, rpfr calculations on polyborate anions, except for those based on
molecular orbital theories (Oi, 2000b), are not reported
presumably due to lack of information on their molecular vibrational frequencies. Thus, Eq. (5) cannot be utilized in a straightforward way.
The rpfr of a polyborate anion can be calculated in an
approximate way by decomposing it into the monomeric
units (Oi et al., 1991). If the polyborate of interest consists of m BO3 units and n BO4 units with some of oxygen atoms being replaced by OH groups, then we approximate the ln(rpfr) value of the polyborate by the weighted
sum of the ln(rpfr)s of the BO 3 and BO 4 units:
lnf = [m/(m + n)]lnfB3 + [n/(m + n)]lnfB4,
(6)
where f, fB3 and fB4 are the rpfrs of the polyborate, the
BO3 unit and the BO4 unit, respectively. The decomposition of the polyborate anion of the mineral in the solid
phase into the BO3 and BO4 components is rather straightforward, since the crystal structure of the mineral is usually well known. The treatment of the solution phase is
slightly complex compared to the solid phase. We first
158 M. Yamahira et al.
0.0
0
7
14
pH
Fig. 10. The distributions of (a) the boron species and (b) the
BO3 and BO4 units as functions of the solution pH. The total
boron concentration is 0.8 M and the stability constants of the
polyborates are cited from Mesmer et al. (1972).
need to calculate the distribution of boron species at the
given boron concentration and pH, and, after decomposing each polyborate into the BO3 and BO4 units, we calculate the concentrations of BO3 and BO4 units by adding up the contributions from all the polyborates as well
as from the monomers. The BO3:BO4 ratio is heavily pH
dependent. As an example, we show the distribution of
boron species as a function of pH at the total boron concentration of 0.8 M in Fig. 10(a) and the corresponding
distribution of the BO3 and BO4 units in Fig. 10(b), using
the stability constants by Mesmer et al. (1972). Under
this assumption, Eq. (5) is simplified to
lnS = ln{xB3(s)f B3(s) + [1 – x B3(s)]fB4(s)}
– ln{x B3(l)fB3(l) + [1 – x B3(l)]fB4(l)},
(7)
where f B3(s), fB4(s) and xB3(s) are the rpfr of the BO3 unit,
that of the BO4 unit and the mole fraction of the BO3 unit
in the solid phase, respectively, and fB3(l), fB4(l) and xB3(l)
are the rpfr of the BO3 unit, that of the BO4 unit and the
mole fraction of the BO3 unit in the solution phase, respectively. We further assume that the rpfr value of the
BO3 unit is unchanged when transferred between the solid
and the solution phases, and so is the rpfr value of the
BO4 unit; fB3(s) = fB3(l) and f B4(s) = fB4(l). That is, we
assume that there is no boron isotope effect upon phase
change. This assumption is actually not very bad one.
Kakihana et al. (1977) reported that no boron isotope
fractionation was observed in cation exchange chromatography of B(OH)3 within experimental errors. Urgell et
al. (1964) reported similar results in anion exchange chromatography of B(OH)4–. In our previous paper, only small
isotope fractionation was observed between sassolite and
the boron-bearing solution in which B(OH)3 was practically the only viable boron species (Oi et al., 1991). Eq.
(7) is then further simplified as,
lnS = ln{x(s)fB3 + [1 – x(s)]fB4} – ln{x(l)fB3 + [1 – x(l)]fB4},
(8)
where fB3 is the rpfr of the BO3 unit, f B4 that of the BO4
unit, x(s) the mole fraction of the BO3 unit in the solid
phase and x(l) that in the solution phase. Since the ratio
fB3/fB4 is nothing but the equilibrium constant, KB, of Eq.
(2), we finally obtain,
S – 1 ≈ lnS = [(x(s) – x(l)](KB – 1)/[x(l)(KB – 1) + 1]. (9)
Equation (9) is the basis for the quantitative understanding of the results shown in Fig. 9. First, S is independent of the kind of cation, since it does not appear in
Eq. (9). Second, Eq. (9) states that, for a given value of
x(s), S should be a monotonously decreasing function of
x(l) with the crossover point at x(s) = x(l). Since x(l) is a
monotonously decreasing function of pH, as is shown in
Fig. 10(b), S is expected to be a monotonously increasing
function of pH, which agrees with the experimental results in Fig. 9. Finally, for a given value of x(l), i.e., at a
fixed pH, S is larger for a larger x(s). Thus, the S value
for santite and sborgite with x(s) = 0.8 is larger than that
for K2B4O7 and borax with x(s) = 0.5, which should be
larger than the S value for L2B2O4 with x(s) = 0.
COMPUTER SIMULATION OF MINERAL FORMATION
PROCESSES AND ESTIMATION OF KB
Equation (9) provides a very simple way to evaluate
the KB value from experimental data for each run. In each
run, S value is experimentally obtained, x(s) is determined
if the deposited boron mineral is identified, and x(l) can
be calculated in the way described in the preceding section using the stability constants of polyborates and the
dissociation constant of boric acid in literature.
Although it is convenient to use Eq. (9) for the qualitative explanation of the experimental results, it is not
appropriate for the quantitative treatment of the results,
since the process in which the boron mineral is precipitated is not taken into consideration.
In the following, we try to model the precipitation
processes of boron minerals to estimate KB by computer
simulation, which is based on the following assumptions
(Simulation I):
1) Polyborates in the solution phase and in the solid
phase can be decomposed into the BO3 and BO4 units for
the purpose of their rpfr calculations, as before.
2) The pH of the solution is unchanged during the
whole process of the mineral deposition. The pH at which
the mineral deposition occurs is fixed at the one of the
final solution.
3) The boron isotopic equilibrium is always maintained among various boron species in the solution phase
during the whole process of the mineral deposition.
4) The mineral is gradually deposited from the solution. This implies that boron isotope exchange equilibrium is always maintained between the liquid and the solid
phases during the whole process of the mineral deposition.
5) There is no boron isotope fractionation accompanying the transfer of a polyborate anion from the solution phase to the solid phase, that is, there is no boron
isotope fractionation upon phase change.
6) No boron species change occurs from the BO3 unit
to the BO4 unit and vice versa in the solid phase.
The boron isotopic compositions are time dependent
both in the solution phase and in the solid phase; an aliquot
deposited at the early stage of the precipitation process
has a different 11B/10B isotopic ratio from that of an aliquot
deposited later. In the computer program, mineral deposition is assumed to occur in many continuous steps, in
each of which only a very small amount of boron is deposited. Repetition of deposition is continued until the
total amount of boron deposited becomes equal to the
experimental one.
The procedure of Simulation I is as follows. The total
amount of boron (mtot), the amount of deposited boron
(mprec), the volume of the solution phase (Vsol), the experimental pH of the solution, the assumed KB value and
the initial boron isotopic ratio of the solution phase ((11B/
10
B)sol) are first given as initial inputs. The boron concentration and the BO3:BO4 ratio of the solution are then
calculated by using the input data and the stability constants of polyborates and the dissociation constant of boric acid cited from Mesmer et al. (1972). Next, the boron
isotopic ratios of the BO3 and BO 4 units in the solution
phase are calculated. A small amount of boron is transferred to the solid phase with a part as BO3 unit and the
remaining part as BO4 unit with the BO3:BO4 ratio equal
to that of the mineral experimentally deposited, and the
boron isotopic ratio of the solid phase ((11B/10B)prec) is
calculated. After the transfer, the amount of boron in the
solution phase, and consequently, the boron concentration too, decrease slightly. The ( 11B/ 10B) sol value also
changes slightly. So, the BO3:BO4 ratio and the boron
isotopic ratios of the BO3 and BO 4 units in the solution
phase are recalculated while keeping the pH unchanged.
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 159
The same small amount of boron is again transferred to
the solid phase. This manipulation is continued until the
total amount of deposited boron becomes equal to the
experimental one, and the separation factor is calculated
using the final values of the isotopic ratios in the solution and solid phases. This calculated separation factor
(Scal) is compared with the experimental one (Sexp). If Scal
does not agree with Sexp, the whole calculation process is
redone with a different KB value as the new initial input,
and this is repeated until Scal agrees with Sexp, thus determining the KB value for that run. When this manipulation
is completed, the calculated boron isotopic ratios in the
liquid and solid phases agreed with the experimental ones
within ±0.001 for every run.
The results of Simulation I including those obtained
for borax using the experimental data in the previous paper (Oi et al., 1991) are summarized in Table 4. For
K2B4O7, the KB value ranges from 1.011 (K13) to 1.041
(K6) with the average of 1.024. For suntite, it is from
1.000 (K3) to 1.047 (K45) with the average of 1.025. The
K3 data is omitted in averaging, since, when the S value
is unity, the KB value becomes necessarily unity in principle under the adopted assumptions. The average K B
value for borax is 1.028 with the range of the KB value
being from 1.012 to 1.065. Note that the KB values estimated using the data in the previous paper (Oi et al., 1991)
are different from the ones listed in that paper. This discrepancy is mostly due to the difference in the kind of
polyborates supposed to exist in the solution phase and
their stability constant values between this and the previous studies. In the present study, the work by Mesmer et
al. (1972) is adopted where B2O(OH)5–, B3O3(OH)4– and
B4O5(OH)42– are assumed as polyborates, while Spessard
(1970) whose data were adopted in the previous paper
(Oi et al., 1991) assumed the existence of B3O3(OH)4–,
B 3O 3 (OH)5 2–, B 4O 5(OH) 42– and B 5O 6(OH)4 – as viable
polyborates in aqueous solution. The latter tends in general to yield a larger KB value than the former for a given
run. For L2B2O4, the estimation of the KB value for L4
and L11 is abandoned. The S value in those two runs is
larger than unity, which in principle yields the KB value
smaller than unity under the adopted assumptions. We
judge such data are totally inadequate. The average KB
value of four data for L2B2O4 thus becomes 1.028.
As a whole, the degree of data scattering is large, although the grand average is reasonable at 1.026. The KB
value ranges from 1.002 (K44) to 1.078 (L5). If the assumptions 1) to 6) above all hold, KB should converge to
one value irrespective of experimental conditions. That
is, every run should yield the same and common KB value.
The results of Simulation I evidently lead to another direction. In this context, we examined the effect of a small
change in the value of such quantities as the amount of
deposited boron (mprec) and the volume of the solution
160 M. Yamahira et al.
Table 4. The estimated KB values
System
K
Mineral
K2B4O7
santite
Na
Li
borax
L2B2O4
Run No.
KB
“Better” KB
Sim. I
Sim. II
K5
K6
K7
K10
K11
K12
K13
K42
ave.
K1
K2
K3
K4
K14
K15
K18
K19
K44
K45
ave.
1.036
1.041
1.021
1.012
1.022
1.017
1.011
1.031
1.024
1.041
1.029
1.000
1.040
1.022
1.015
1.013
1.017
1.002
1.047
1.025
1.041
1.059
N1
N2
N3
N4
B-08*
B-09*
B-10*
B-17*
B-18*
B-23*
B-25*
B-27*
ave.
1.013
1.017
1.012
1.024
1.031
1.014
1.065
1.034
1.023
1.035
1.044
1.023
1.028
1.017
1.021
1.014
L2
L3
L4
L5
L11
L12
ave.
1.016
1.009
—
1.078
—
1.009
1.028
1.017
1.009
1.017
1.009
1.023
1.023
1.010
1.010
1.015
1.019
1.013
1.041
1.047
1.016
1.015
1.002
1.055
1.016
1.079
1.048
1.048
1.036
1.041
1.021
1.019
1.022
1.017
1.013
1.031
1.025
1.041
1.029
1.000
1.040
1.022
1.016
1.015
1.017
1.002
1.047
1.026
1.017
1.021
1.014
1.024
1.031
1.016
1.065
1.034
1.023
1.035
1.044
1.023
1.029
*From Oi et al. (1991). Note that the present KB values are different
from the previous ones since the used stability constant values are different.
phase (Vsol) on KB, taking the case of Run B-10 in which
borax deposited as an example. The results are summarized in Table 5. The experimental (11B/10B) prec = 4.028
gives KB = 1.065. If one consider the experimental error
of ±0.005 on ( 11B/10B)prec, KB fluctuates between 1.059
and 1.072 with a large (11B/10B)prec value yielding a small
KB value. Similarly, (11B/10B) sol = 4.072 ± 0.003 gives
the KB range of 1.061 to 1.069 with a large (11B/10B)sol
Table 5. Effects of slight change in the values of input parameters on KB (Run B-10)
Variable
Initial solution
mtot
[mol]
Default
(11B/10B)prec
0.166
Final solution
Vsol
[cm 3]
pH
mtot−mprec
[mol]
(11B/10B)sol
m prec
[mol]
(11B/10B)prec
4.051
190.6
8.75
0.087
4.072
0.079
4.028
4.032
4.023
(11B/10B)sol
4.075
4.070
m prec
Vsol
pH
Final solid (prec.)
B/10B
11
0.089
0.069
195.6
185.6
9.25
8.25
value yielding a large KB value. Table 5 also shows that
the increase in the amount of deposited boron (mprec) and
the final solution volume (Vsol), respectively, decreases
and increases the KB value. It is evident from Table 5 that
the above examined quantities certainly influence KB.
However, their effects are limited. It is impossible to obtain KB of, say, 1.026, by manipulating the values of those
quantities within reasonable ranges estimated from experimental errors. The last two rows of Table 5 summarize the effect of pH at which the mineral deposits on KB.
The ±0.5 change in pH does not correspond to experimental error in pH measuring, but models the pH change
from the start of the mineral deposition to the end of a
run (the end of deposition). As can be seen, the effect of
pH is substantial. If the pH value at which the mineral
deposition started is different from the final pH value, at
which we assume the deposition occurred, the expected
KB value may be quite different from the one estimated
by Simulation I.
The solution pH at which the mineral is precipitated
is very influential on KB. A slight change in pH sometimes causes non-negligible change in KB value. In the
above simulation (Simulation I), the pH value, at which
the mineral was supposed to deposit, is fixed at the final
pH value in every run. In some cases, the fact may be
that the mineral deposition started at pH that was different from the final one, somewhere between the initial and
the final values, and finished at the final pH value. In the
following simulation (Simulation II), this pH change during the mineral precipitation was taken into the consideration. The pH value at which the mineral deposition
started was set at the pH value of the initial solution, and
the deposition was assumed to finish at the pH of the final solution. During the mineral depositing, the pH change
was assumed to be proportional to the amount of deposited boron. This manipulation was applied to the runs
whose KB values are quite apart from the average for the
S
KB
0.989
0.990
0.988
0.988
0.990
1.065
1.059
1.072
1.069
1.061
1.061
1.070
1.066
1.065
1.388
1.038
given mineral (more than 0.01) by Simulation I. The results are summarized in the 5th column of Table 4. In
general, Simulation II yields a larger KB value than Simulation I. As a result, some data get closer to the average,
but some do not against our expectation. This may mean
that the assumption upon pH made in Simulation II is not
always adequate. The most drastic improvement of KB is
observed for L5; the KB value changes from 1.078 to
1.023. This is the only case for which Simulation II yields
a smaller KB value than Simulation I. In L5, The pH of
the final solution was 12.42, highest among the pH values of the runs for which isotopic analysis was conducted.
At that pH, the proportion of the BO3 unit in the solution
phase was extremely small, and the solid phase was composed of L2B2O4 with no BO3 unit. That is, in L5, only a
very small amount of BO3 unit in the solution phase was
responsible for the deviation of S from unity, and consequently a very large KB value resulted in Simulation I.
This situation is largely improved by assuming that the
mineral deposition started at a lower pH at which the proportion of the BO3 unit is larger.
In the last column of Table 2 is listed the “better” KB
value (Simulation I or Simulation II). The term “better”
simply means “closer to the average”. Comparison of the
average values of KB in this column reveals a couple of
interesting points. K2B4O7 and borax have the same
BO3:BO4 ratio of 2:2. Nevertheless, the KB value is larger
for borax than for K2B4O7. This is against the assumption in the preceding section that the rpfr of a polyborate
is independent of the kind of counterion. Liu and Tossell
(2005) carried out molecular orbital (MO) calculations
on the boron isotopic rpfrs of hydrated boric acid and
monoborate anion interacting with cations like Li+ and
Na + ions. They assumed such boron species as
Li+B(OH)3(H2O)34 and Li+B(OH)4–(H2O)34 and calculated
their rpfr values at the HF/6-31G* level of theory. They
reported that the rpfrs of hydrated B(OH)3 and B(OH)4–
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 161
S
1.020
1.000
0.980
0
0.5
1
Mole fraction of BO3 unit in solution phase
Fig. 11. Plots of S against the mole fraction of BO3 unit in the
solution phase. 䊐 = santite (K[B 5 O 6 (OH) 4 ]·2H 2 O); 䊏 =
sborgite (Na[B 5 O 6 (OH) 4 ]·3H 2 O); 䊊 = K2B4O7
(K 2[B 4O5(OH) 4]·2H 2O); 䊉 = borax (Na2[B4O5(OH) 4]·8H 2O);
䉭 = L2B2O4 (Li2B2O4·16H 2O). – · – · – = santite (KB = 1.025);
– – · – – · – – = K2B4O7 (K B = 1.026); - - - = borax (KB = 1.029);
— = L2B2O4 (KB = 1.015).
were both slightly influenced by the existence of cationic
species, indicating that K2B4O7 might show a different
KB value from that of borax. Unfortunately, quantitative
discussion is not possible here since they did not calculate the effect of the K+ ion on the rpfrs of these boron
species. Another observation is that a boron mineral with
a large BO3:BO4 ratio tends to yield a large KB value; KB
of santite with the BO 3:BO4 ratio of 4:1 was larger than
that of K2B4O7 with the BO3:BO4 ratio of 2:2 which was
larger than that of L2B2L4 with the BO 3:BO 4 ratio of 0:2.
This observation agrees, qualitatively at least, with our
MO calculations on the rpfrs of boric acid, monoborate
and polyboric acids and polyborates (Oi, 2000a, b). The
calculations showed that the values of the rpfrs of BO3
and BO4 units both became small upon polymerization,
but the degree of decrease in rpfr is more substantial for
the BO4 unit than for the BO3 unit.
In Fig. 11, the experimentally obtained S values are
plotted against the estimated mole fraction of the BO3
unit in the solution phase. The lines are drawn using the
“better” average values of KB in Table 4. Note that the
line for santite necessarily goes through the point (0.8,
1.0). Similarly, the lines for K2B4O7 and borax pass
through the point (0.5, 1.0) and the line for L2B2O4 the
point (0, 1.0). Thus, the crossover point at which the S
value becomes unity is the point at which the BO3:BO4
ratio in the solution phase is equal to that in the solid
phase. This is due to the assumption 5) above that there
162 M. Yamahira et al.
is no boron isotope fractionation upon phase change. The
slope of a line is determined by the value of KB with a
large KB yielding a (negatively) steep slope. The lines for
santite and for K2B4O7 are nearly parallel since their KB
values are close to each other. Although the KB value for
borax is larger than that of K2B4O7, and consequently
the line for borax is slightly steeper than that for K2B4O7,
the both lines seem to represent the data points of borax
and K2B4O7 equally well. This indicates that it is difficult to distinguish KB = 1.026 and 1.029 by the present
experimental method with a large degree of scattering of
isotopic data. The line for L2B2O4 is apparently shallower than the other lines, which reflects the fact that the
KB value for L2B2O4 is evidently smaller than those of
the other minerals. It is seen in Fig. 11 that for L2B2O4,
the line does not represent the data points very well; the
least-squares line of the L2B2O4 data would become
much sharper. This discrepancy may indicate the existence of boron isotope fractionation upon the phase change,
which is against the assumption 5) above that there is no
boron isotope fractionation upon phase change.
CONCLUSIONS
To summarize, we would like to make the following
statements:
1) K 2 [B 4 O 5 (OH) 4 ]·2H 2 O (K2B4O7), santite
(K[B5O6(OH)4]·2H2O), KBO2·1.33H 2O, KBO2·1.25H2O
and sassolite (B(OH)3) were precipitated as boron minerals from boron and potassium ion-bearing solutions at
25.0°C. Similarly, borax (Na 2 [B 4 O 5 (OH) 4 ·8H 2 O) was
obtained from boron and sodium ion-bearing solutions,
and Li 2 B 2 O 4 ·16H 2 O (L2B2O4), Li 2 B 4 O 7 ·5H 2 O,
Li2B10O16·10H2O, LiB2O3(OH)·H2O and sassolite from
boron and lithium ion-bearing solutions.
2) The boron isotopic analysis was carried out for
K2B4O7, santite, borax and L2B2O4. For a given mineral, the separation factor, S, defined as the 11B/10B isotopic ratio of the mineral divided by that of the solution,
was in general an increasing function of the pH of the
solution. At a given pH, the S value for santite was in
general larger than those of K2B4O7 and borax that were
in general larger than that of L2B2O4. These results were
consistent with the conclusion having been drawn theoretically that the boron isotopic reduced partition function ratio (rpfr) of three-coordinated boron (trigonal coordination) is larger than that of four-coordinated boron
(tetrahedral coordination).
3) Computer simulations modeling the mineral formation processes yielded the value of equilibrium constant of the boron isotope exchange reaction between boric
acid and monoborate anion, KB, of 1.025 for K2B4O7,
1.026 for santite, 1.029 for borax and 1.015 for L2B2O4.
Minerals with a larger proportion of three-coordinated
boron in its borate structure tended to have a larger KB
value, which was consistent with the results by molecular orbital calculations on rpfrs of polyborates having been
independently conducted.
Acknowledgments—Professor Y. Fujii, Tokyo Institute of
Technology (Titech) kindly offered the use of a Varian MAT
CH-5 mass spectrometer. We acknowledge Dr. M. Nomura,
Titech, for his assistance in mass spectrometric measurements
of boron isotopic ratios.
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