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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 YAMAHIRA, YOSHIKAZU 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[B4O5(OH)4]·2H2O, santite (K[B5O6(OH)4]·2H2O), KBO2·1.33H2O, KBO2·1.25H2O and sassolite (B(OH)3) were found deposited as boron minerals. Borax (Na2[B4O5(OH)4·8H2O) was found deposited in the boron-sodium ion system, and Li2B2O4·16H2O, Li2B4O7·5H2O, Li2B10O16·10H2O, LiB2O3(OH)·H2O and sassolite in the boron-lithium ion system. The boron isotopic analysis was con- 11 10 ducted for santite, K2[B4O5(OH)4]·2H2O, borax and Li2B2O4·16H2O. The separation factor, S, defined as the B/ B 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 coor-
dinated BO3 unit and four coordinated BO4 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
INTRODUCTION et al., 1993; Palmer et al., 1998; Honisch et al., 2004; Pagani et al., 2005). The usefulness of the method, how- Boron has two stable isotopes, 10B and 11B, and their ever, is still in dispute. To use the boron isotopic ratio as relative abundances are approximately 20 and 80%, re- a geochemical tracer, the knowledge on the accurate equi- spectively. The variation in the boron isotopic composi- librium constants of boron isotope exchange reactions tion of natural samples is large. As summarized by Palmer between two boron species in equilibrium is essential. and Swihart (1996), it is about 100‰ (permil) in the δ Boron atom is always bonded to oxygen atoms, in the expression defined as, trigonal form or in the tetrahedral form, except for some rare cases. The most important boron isotope exchange δ11 11 10 11 10 × B = {( B/ B)sample/( B/ B)standard – 1} 1000, (1) reaction is that between the boric acid molecule (B(OH)3) – 11 10 11 10 and the monoborate anion (B(OH)4 ): where ( B/ B)sample denotes the B-to- B boron iso- topic ratio of the sample and (11B/10B) that of a standard 10B(OH) + 11B(OH) – = 11B(OH) + 10B(OH) –. (2) standard. The standard used in most studies is NBS SRM 3 4 3 4 951 boric acid (Cantanzaro et al., 1970). The equilibrium constant (K ) of Reaction (2) is larger Due mainly to this large variation, boron isotopic com- B than unity, which means the heavier isotope is preferen- position has been applied to many areas of earth sciences tially fractionated into the trigonal boric acid and the and has provided valuable findings on fundamental proc- lighter one into the borate anion. The theoretical value esses in natural circumstances. One of the recent and im- based on the molecular vibrational analysis was first ob- portant applications is to estimate the ancient ocean pH tained to be 1.0194 at 25°C (Kakihana and Kotaka, 1977), using the boron isotopic composition of natural carbon- but there are experiments and observations that require ates (for instance, Hemming and Hanson, 1992; Spivack larger KB values (Vengosh et al., 1991; Palmer et al., 1987; Nomura et al., 1990). Other theoretical methods includ- ing those based on molecular orbital calculations (Oi, *Corresponding author (e-mail: [email protected]) 2000a; Zeebe, 2005) also suggest KB should be larger than Copyright © 2007 by The Geochemical Society of Japan. 1.0194 (Kakihana and Kotaka, 1977).
149 An application of the boron isotopic composition is The 95% confidence limit is typically about ±0.2%. Each to the elucidation of the origin and alteration of borate sample was measured at least twice and the arithmetic deposits (Peng and Palmer, 1995; Swihart et al., 1996). mean was taken as the isotopic ratio of the sample. To quantitatively discuss such problems, the knowledge on the exact degrees of boron isotope fractionations ac- RESULTS companying boron mineral formation from boron- bearing solutions is certainly required. To the best our Table 1 summarizes the initial solution conditions and knowledge, our previous paper (Oi et al., 1991) is only the final results of the solution and the solid phases, ex- one that reported laboratory experiments in which boron cept for the isotopic data. Many runs are omitted from minerals were precipitated from boric acid solutions and the table in which solution became mucilaginous without boron isotope fractionation upon precipitation was mea- producing precipitate by water evaporation, only a very sured. Unfortunately, the counterion was limited to the small volume of solution remained with a very large sodium ion. Precipitation experiments were then extended amount of precipitate, or while separating the precipitate to include the potassium and lithium ions. In this paper, from solution by filtration, new precipitate formed, and we report the results of boron isotope fractionations ac- so forth. In most cases, the solution and the solid (pre- companying boron mineral formations from aqueous so- cipitate) phases were separated by filtration as soon as lutions of boric acid containing potassium, sodium or we noticed the formation of precipitates. It was often very lithium ion as the counterion. difficult to determine accurately the ratio of the amount of boron precipitated to that in the initial solution.
EXPERIMENTAL Precipitates obtained An aqueous solution, in which boron concentration Potassium borate system The boron concentration, pH was about 0.3 M (1 M = 1 mol/dm3) to 1.0 M and that of and the mole ratio of potassium to boron of initial solu- the cation (K+, Na+ or Li+ ion) was about 0.2 M to 3.2 M, tion ranged from 0.61 to 1.0 M, 0.36 to 14.3 and 0.41 to was first prepared by dissolving boric acid and metal hy- 2.30, respectively. The time elapsed between the start of droxide or metal chloride into distilled water. The pH was the run and the start of separation of the solid and solu- adjusted with 5.0 M sodium hydroxide solution or conc. tion phases (deposition time) was from 4 hours to 34 days. hydrochloric acid. This pH adjusted solution was used as It must have depended on many factors such as the chemi- the stock solution of the initial solution of each run. A cal composition of the initial solution and the evapora- beaker containing 200 cm3 of this initial solution was tion speed of water. The major boron minerals identified placed in a water bath, the temperature of which was con- by XRD analysis were sassolite (B(OH)3; JCPDS No. 30- ± ° trolled at 25.0 0.2 C. (In some cases, the volumes of 0199), santite (K[B5O6(OH)4]·2H2O; JCPDS No. 25- 3 the initial solutions other than 200 cm were adopted.) 0624) and K2[B4O5(OH)4]·2H2O (JCPDS No. 29-0987; No stirring of the solution or shaking the beaker was no mineral name given; designated hereafter as K2B4O7). practiced while the beaker was kept placed in the water KBO2·1.333H2O (JCPDS No. 18-1039) and bath. No artificial manipulation such as adding a seed KBO2·1.25H2O (JCPDS No. 19-0980) were also identi- crystal to the solution was attempted to promote the pre- fied as minor boron minerals. Minerals without boron cipitation, either. A precipitate was formed from the so- component identified included KCl and K2CO3. Exam- lution by concentration of the solution due to water evapo- ples of XRD patterns of K2B4O7 and santite obtained ration. Upon precipitation, the solid and the solution are shown in Figs. 1(a) and (b), respectively. They are phases were separated by sucking filtration. The solution compared with the ones in the JCPDS files. Figure 2 shows phase was analyzed for its pH and concentrations of bo- the solution conditions (the mole ratio of potassium to ron and the cation. The precipitate was air-dried and the boron and pH of the final solution) under which minerals mineral phase was identified by X-ray powder diffrac- are supposed to have been formed. As is seen, the pH tion (XRD) analysis with a Rigaku RINT 2100V/P X-ray value of solution seems the most influential to determine spectrometer. The amount of boron in the precipitate was which mineral is formed, and the kind of mineral formed determined by measuring the boron content of the solu- is almost independent of the K/B mole ratio. Admittedly tion that was prepared by dissolving an aliquot of the pre- roughly, sassolite is deposited in the low pH region. Be- cipitate into a certain volume of distilled water. tween pH about 4.5 and about 9, the main borate depos- The boron isotopic ratios of solutions and minerals ited is santite. The pH region in which K2B4O7 precipi- were measured by the surface ionization method with a tates is approximately from 9 to 12. At very high pH, Varian MAT CH-5 mass spectrometer at Tokyo Institute KBO2·1.33H2O and KBO2·1.25H2O are found deposited. of Technology. The detailed mass spectrometry applied Sodium borate system Runs in this system were conducted is given elsewhere (Nomura et al., 1973; Oi et al., 1989). to examine reproducibility of boron isotopic data in the
150 M. Yamahira et al. O
2
1.25H
⋅
2
O
O O
O O O
O O
O
O
2 2
2 2
2 2
2 2 2
2
2H
2H
2H
2H 2H 2H
2H 2H
2H
2H
⋅
⋅
⋅
⋅ ⋅ ⋅
⋅ ⋅
⋅
⋅
]
] ]
] ] ]
] ]
]
]
4 4
4 4
4 4
4
4 4
4
O, KBO
Mineral
2
(OH)
(OH) (OH)
(OH) (OH)
(OH) (OH) (OH)
(OH)
(OH)
5 5
5 5 5
5 5
5
5
5
1.33H
O O O O
O O
O O
O
O
⋅
4 4
4 4
4 4 4
4 4
4
2
[B [B
[B [B [B
[B [B
[B [B
[B
2 2 2
2 2
2 2 2
2
2
K
K
sassolite
sassolite sassolite sassolite KBO
KCl KCl KCl KCl KCl K
santite, KCl
5)
1)
Mole fraction
2)
]
3
−
dm
⋅
pH B conc. M/B
esults other than the isotopic data
Solution phase Solid phase
4)
14d
94h
Time
3)
] [mol
3
Evap.
2)
] [cm
3
−
dm
⋅
][mol
3
Vol. pH B conc. M/B
[cm
K2 200.0 6.22 0.800 1.000 0.0 4h 6.89 0.630 1.111 0.41 santite K3 200.0 6.91 0.800 1.000 10.0 1d 6.77 0.450 1.600 0.21 santite K4 200.0 8.00 0.800 1.000 50.0 2d 8.16 0.750 0.800 0.19 santite K5 200.0 8.99 0.800 1.000 180.0 7d 8.78 6.130 0.788 0.20 K
K6 200.0 10.00 0.800 1.000 150.0 9d 10.50 2.410 0.867 0.23 K
K7 200.0 10.82 0.800 1.000 187.0 8d 14< 9.210 0.080 0.13 K K8 200.0 11.91 0.800 1.000 198.0 10d 14<
K9 100.0 10.18 0.800 1.000 100.0 10d K10 100.0 10.31 0.800 1.000 85.0 5d 11.36 4.290 0.734 0.52 K K11 200.0 10.97 0.971 0.802 171.4 34d 11.76 2.919 1.202 0.472 K
K12 200.0 10.07 0.971 0.802 184.2 31d 11.19 1.496 2.937 0.746 K K13 200.0 9.02 0.971 0.802 191.6 33d 8.69 5.315 0.861 0.292 K
K14 200.0 7.85 0.971 0.802 11.6 12d 8.01 0.731 1.049 0.195 santite K15 200.0 6.49 0.971 0.802 13.0 10d 6.12 0.635 1.174 0.260 santite K16 200.0 5.45 0.971 0.802 126.1 17d 4.17 1.106 1.772 K17 200.0 9.26 0.957 0.416 K18 200.0 7.91 0.942 0.432 189.3 10d 9.12 3.591 1.160 0.736 santite K19 200.0 7.14 0.940 0.426 158.0 10d 4.82 0.933 1.335 0.720 santite K20 200.0 0.98 0.931 0.430 126.3 9d 0.53 0.983 1.069 K21 200.0 6.14 0.920 0.431 170.1 9d 4.29 1.075 1.821 K22 200.0 5.39 0.913 0.431 135.5 10d 4.57 1.070 1.055 K23 200.0 14.21 1.001 1.738 181.4 10d 14< 4.761 0.300
K24 200.0 12.92 0.885 1.829 161.8 5d 13.44 4.713 0.303 K25 200.0 11.71 0.872 1.818 162.4 4d 13.18 4.658 0.307 K26 200.0 10.98 0.844 1.844 156.8 3d 12.36 3.869 0.370 K27 200.0 9.99 0.815 1.890 158.0 2d 11.14 1.355 3.481 K28 200.0 9.09 0.817 1.851 154.6 2d 9.15 3.364 1.434 K29 200.0 9.35 0.902 0.406
K30 200.0 7.94 0.871 0.426 158.6 64h 8.67 0.961 1.055
System Run No. Initial solution
K K1 200.0 6.92 0.800 1.000 0.0 1.5h 6.90 0.620 1.145 0.21 santite
Table 1. The initial conditions of the solution phase and the experimental r Table
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 151 O
2
1.25H
⋅
2
O
2
2H
⋅
]
4
O, KBO
O
Mineral
2
2
(OH)
5
1.5H
⋅
1.33H
3
O
⋅
4
2
[B
CO
2
2
sassolite, KCl sassolite, santite sassolite, KCl KBO
sassolite, KCl
KCl santite, KCl sassolite, KCl sassolite, KCl sassolite, KCl K
santite, sassolite, KCl KCl
borax borax borax borax borax
5)
Mole fraction
2)
]
3
−
dm
⋅
pH B conc. M/B
Solution phase Solid phase
4)
69h
Time
3)
] [mol
3
Evap.
2)
] [cm
3
−
dm
⋅
][mol
3
Vol. pH B conc. M/B
[cm
K32 200.0 0.75 0.821 0.464 84.0 47h 0.62 0.878 0.752 K33 200.0 6.75 0.823 0.451 132.2 45h 5.09 0.877 0.960 K34 200.0 1.63 0.820 0.457 106.0 41h 1.42 0.924 0.757 K35 200.0 14.30 0.801 1.989 178.2 65h 14< 3.788 0.377
K36 200.0 9.10 0.661 2.153 143.2 39h 9.20 2.316 2.034 K37 200.0 7.03 0.635 2.210 132.8 24h 5.01 0.666 5.494 K38 200.0 0.36 0.605 2.302 94.2 25h 0.02 0.937 2.766 K39 200.0 0.56 0.620 2.235 83.0 16h 0.29 0.928 2.570 K40 200.0 1.32 0.629 2.222 90.0 19h 0.98 0.985 2.590 K41 200.0 12.62 0.976 0.951 192.4 78h 14< 10.537 0.136
K42K43 200.0 200.0 9.70 10.89 0.907 0.940 0.995 0.982 181.2 43h 10.76 1.368 3.494 0.884 K K44 200.0 8.43 0.897 0.989 170.2 49h 9.02 3.146 1.532 0.428 santite, KCl K45 200.0 7.12 0.865 1.019 103.8 23h 6.85 0.438 3.206 0.699 santite, KCl K46 200.0 6.40 0.862 1.020 113.2 21h 4.72 0.879 1.999 K47 150.0 0.50 0.852 1.031 48.4 18h 0.24 0.876 1.426
N2 200.0 8.47 0.800 1.000 98.0 4d 7.43 0.84 1.440 0.41 N3 200.0 10.38 0.800 1.000 64.0 5d 10.78 0.66 1.485 0.45 N4 200.0 12.30 0.800 1.000 150.0 7d 11.84 2.69 1.052 0.046 N5 200.0 12.27 0.800 1.000 200.0 8d
System Run No. Initial solution
K K31 200.0 5.70 0.840 0.445 123.8 49h 4.81 0.981 0.868
Na N1 200.0 8.00 0.800 1.000 163.0 3d 6.19 3.61 1.205 0.18
Table 1. (continued) Table
152 M. Yamahira et al. O
2
5H
⋅
7
O
4
3
B
O O O
O
2 2
2 2
2
CO
2
5H 5H
5H 5H
⋅ ⋅
⋅ ⋅
7
7
7 7
O, Li
O
O
O
O, halite O,
2
O O O
O
2
2
2
2
4
4 4 4
O
O O O
O
O O
O
O
O, Li
2 2 2
2
2 2
2 2
2
2
Mineral
B B B
B
2 2 2
2
10H
10H
10H
10H
⋅
⋅
⋅
⋅
16H
16H
16H 16H
16H
16H 16H
16H
16H
16H
16
16 16
16
⋅
⋅
⋅ ⋅
⋅
⋅ ⋅
⋅
⋅
⋅
(OH) H
4
4 4
4
4 4 4
4
4
4
3
3
O
O O
O
O O
O
O
O O
O O
O
O
10
10 10
O
10
2 2
2 2
2
2 2
2
2
2
2
B
B B
B
B
B B B
B
B B B
B
B
CO
2
2 2
2
2 2 2
2
2 2
2 2
2
2
2
Li
LiB
Li
Li
Li Li
amorphous sassolite amorphous Li
Li
sassolite sassolite sassolite sassolite Li Li
5)
Mole fraction
2)
]
3
−
dm
⋅
on contents in the solid phase and in the initial solution.
pH B conc. M/B
10.66 0.760 0.853
Solution phase Solid phase
4)
5d
7d 7.69
Time
110d 110d
3)
] [mol
3
Evap.
2)
][cm
3
−
dm
⋅
t of the run and the start of the deposition (deposition time).
][mol
on.
3
Vol. pH B conc. M/B
[cm
on in the mineral to that in the initial solution, calculated using the bor
C. °
L2 300.0 9.53 0.800 1.001 254.5 172h 8.82 4.750 0.869 0.063 Li
L3 200.0 9.99 0.802 0.996 131.9 166h 9.83 1.440 0.931 0.385 Li
L4 200.0 10.89 0.801 0.999 31.9 172h 11.11 0.740 0.919 0.174 Li L5 200.0 11.55 0.799 2.003 65.7 10h 12.42 0.620 2.161L20 200.0 0.227 12.54 Li 0.476 1.748 L6 400.0 6.51 0.800 0.503 243.5 101h 6.20 1.670 0.563 0.181 sassolite, Li
L7 200.0 7.29 0.804 0.502 175.2 248h 6.14 4.580 0.675L22 200.0 0.264 8.41 sassolite, Li 0.393 1.980 172.2 55d 6.73 2.837 1.900 L8 400.0 7.59 0.806 0.500 359.6 187h 5.57 6.440 0.534 0.119 sassolite, Li L9 300.0 7.81 0.802 0.500 264.0 214h 6.28 4.510 0.477 0.096 sassolite, Li
L10 200.0 12.81 0.472 1.829 69.2 6d 12.84 0.331 1.839 L11 200.0 12.65 0.447 1.834 72.2 6d 12.15 0.311 1.896 0.137 Li
L12 200.0 9.86 0.416 1.888 174.6 3d 8.86 1.630 2.560 0.485 Li L13
L14 200.0 7.92 0.750 0.973 179.8 9d 4.88 7.019 0.969 L15 200.0 7.64 0.863 0.934 184.0 9d 4.79 4.274 1.988
L16 200.0 9.03 0.892 0.994 177.8 9d 7.75 4.519 1.299 L17 200.0 1.80 0.392 1.026 131.4 5d 1.25 0.644 1.796 L18 200.0 9.17 0.445 0.943 L19 200.0 12.56 0.460 1.796 104.2 8d 10.85 0.586 2.065
L21 200.0 9.56 0.438 1.854 165.0 55d 8.90 2.477 1.705
L23 200.0 6.63 0.362 2.128 140.2 55d 5.38 0.950 2.673 L24 200.0 5.77 0.777 1.027 90.8 16d 5.51 0.971 1.513 L25 200.0 3.32 0.773 1.018 44.4 16d 3.34 0.741 1.386 L26 200.0 5.72 0.782 1.021 84.0 16d 5.45 0.963 1.441 L27L28 200.0 200.0 7.78 7.76 0.821 0.779 1.027 1.022
System Run No. Initial solution
Li L1 200.0 3.36 0.800 1.004 78.1 22h 3.45 0.750 1.573 0.291 sassolite
Temperature: 25.0 Temperature: Mole ratio of metal to bor Approximate volume of water evaporated. Approximate Approximate time elapsed between the star Approximate The mole ratio of bor
1) 2) 3) 4) 5)
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 153 (a) K2[B4O5(OH)4]·2H2O (K12) 6
int. 4
2 JCPDS No. 29-0987 K/B mole ratio
0 10 20 30 40 50 60 70 0 7 14 θ α 2 (CuK 1)/degrees pH Fig. 2. The K/B mole ratio-pH plot for the potassium borate santite (K[B O (OH) ]·2H O) (K14) ᭹ ᭺ (b) 5 6 4 2 system. = K2[B4O 5(OH)4]·2H2O; = santite ᮀ (K[B5O6(OH)4]·2H2O); = sassolite (B(OH)3); = other potassium borates; × = minerals other than borates. int.
6
JCPDS No. 25-0624
4 10 20 30 40 50 60 70
θ α 2 (CuK 1)/degrees 2 Na/B mole ratio
(c) Li2B2O4·16H2O (Run L11) 0 0 7 14
int. pH Fig. 3. The Na/B mole ratio-pH plot for the sodium borate ᭹ system. = borax (Na2[B4O5(OH)4]·8H2O).
JCPDS No. 28-0557
Lithium borate system The boron concentration, pH and 10 20 30 40 50 60 70 the mole ratio of lithium to boron of the initial solutions 2θ(CuKα )/degrees 1 ranged from 0.36 to 0.89 M, 3.32 to 12.8 and 0.50 to 2.13, Fig. 1. Examples of XRD patterns of (a) K2B4O7 respectively. The deposition time was from 10 hours to 110 days. The boron minerals identified by XRD analy- (K2[B4O5(OH)4]·2H2O) (Run K12), (b) santite sis were sassolite, Li B O ·16H O (JCPDS No. 28-0577; (K[B5O 6(OH)4]·2H2O) (Run K14) and (c) L2B2O4 2 2 4 2 (Li2B2O4·16H2O) (Run L11) obtained in the present study. Each no mineral name given; designated hereafter as L2B2O4), pattern is compared with the one in the JCPDS file. 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. previous paper (Oi et al., 1991). Only borax Other minerals without boron component included halite (Na2[B4O5(OH)4]·8H2O; JCPDS No. 12-0258) was ob- and Li2CO3. Similarly to the potassium and sodium sys- tained as sodium borate in the pH range of 6 to 12 (Fig. tems, the Li/B ratio-pH plot was made and is shown in 3). In the lower pH range, sassolite was obtained like in Fig. 4. As in the case of potassium borates, the pH of the the case of the potassium system, which is not shown in solution seems the most influential in determining which Fig. 3 or in Table 1. lithium borate is deposited. Sassolite is precipitated from
154 M. Yamahira et al. 6 Table 2. Summary of boron isotopic data
System Mineral Run No. δ11B (‰) S 4 Solution Mineral K K2B4O7 K5 +0.6 –2.4 0.997 K6 –4.1 +1.6 1.006 2 K7 –5.8 +5.8 1.012
Li/B mole ratio K10 –0.4 +2.6 1.003 K11 –10.1 +0.8 1.011 K12 –11.5 –2.5 1.009 0 K13 –1.5 –3.1 0.998 0147 K42 –8.1 +2.6 1.011 pH santite K1 +1.1 –3.4 0.996 Fig. 4. The Li/B mole ratio-pH plot for the lithium borate sys- K2 +0.6 –2.6 0.997 tem. ᭝ = Li B O ·16H O; ᭹ = Li B O ·5H O; ᮀ = sassolite K3 –2.9 –2.9 1.000 2 2 4 2 2 4 7 2 K4 –1.6 +2.6 1.004 (B(OH) ); = other lithium borates; × = minerals other than 3 K14 –2.2 –0.4 1.002 borates. K15 –2.2 –5.1 0.997 K18 –7.3 –0.9 1.007 K19 +1.4 –4.6 0.994 K44 +2.8 +3.5 1.001 1.02 K45 +1.9 –5.2 0.993
Na borax N1 –2.4 –6.8 0.996 N2 +3.6 –4.1 0.992 N3 –1.9 +3.6 1.006 N4 –1.9 +9.3 1.011
S 1.00 Li L2B2O4 L2 +2.7 –6.7 0.991 L3 +1.6 –3.4 0.995 L4 –1.5 +2.4 1.004 L5 +0.1 –0.1 1.000 0.98 L11 –4.6 –3.0 1.002 0147 L12 +0.8 –6.6 0.993 pH Fig. 5. Plot of the separation factor (S) against the pH of the ᭹ solution for the potassium borate system. = where (11B/10B) and (11B/10B) are the 11B-to-10B iso- ᭺ prec sol K2[B4O5(OH)4]·2H2O; = santite (K[B5O6(OH)4]·2H2O). The topic ratio of the mineral (precipitate) and of the solu- solid lines denote approximate correlation between S and pH, tion, respectively. Using the permil expression, S is given and the vertical broken lines indicate the crossover points. as,
S = [δ11B(mineral)/1000 + 1]/[δ11B(solution)/1000 + 1]. solutions of low pH values. At around pH 5, (4) Li2B10O16·5H2O is deposited; Li2B4O7·5H2O is formed in the pH range of 5 to 7; and L2B2O4 is precipitated at By definition, S is larger than unity when the heavier iso- pH values above 8.5. tope is preferentially deposited. Considering the 95% confidence limit expected for each isotopic ratio data, the Boron isotope fractionation error on S may typically be ±0.004. Boron isotopic measurements were made on the runs Potassium borate system Isotopic measurements were where only one kind of boron mineral was precipitated made on K2B4O7 (K2[B4O5(OH)4]·2H2O) and santite and where the solution phase was relatively easy to treat. (K[B5O6(OH)4]·2H2O). The S value ranges from 0.997 to The final solution was usually nearly saturated or over- 1.012 for K2B4O7 and from 0.993 to 1.007 for santite. saturated, and was very sticky one, often not suited for Thus, both for K2B4O7 and santite, the heavier isotope various quantitative measurements. The isotopic data in was preferentially fractionated into the precipitate in some permil expression (‰) are summarized in Table 2. The cases, while the lighter isotope was in other cases. In the separation factor, S, in the table is defined as previous paper (Oi et al., 1991), we showed that, for the borax case, the S value data were best understood when 11 10 11 10 S = ( B/ B)prec/( B/ B)sol, (3) plotted against the (final) pH of the solution phase. In
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 155 1.02 1.02 S S 1.00 1.00
0.98 0.98 0147 0147 pH pH
Fig. 6. Plot of the separation factor (S) against the pH of the Fig. 7. Plot of the separation factor (S) against the pH of the ᭹ ᭝ solution for the sodium borate system. = borax solution for the lithium borate system. = Li2B2O4·16H2O. (Na2[B4O5(OH)4]·8H2O) (this work); = borax (Oi et al., The solid line denotes approximate correlation between S and ᭺ 1991); = sborgite (Na[B5O6(OH)4]·3H2O) (Oi et al., 1991). pH. The solid line denotes approximate correlation between S and pH, and the vertical broken line indicates the crossover point.
Lithium borate system Isotopic measurements were made Fig. 5, all the data on S in the potassium borate system in on the runs where only L2B2O4 (Li2B2O4·16H2O) was Table 2 are plotted against the final pH of the solution deposited. Although Li2B4O7·5H2O was also obtained in phase given in Table 1. A trend is observed that the S some runs, it was always deposited with other boron min- value increases nearly linearly with increasing pH both erals, mostly with sassolite, and so we did not attempt to for K2B4O7 and for suntite as in the case of borax in the obtain the boron isotopic data on Li2B4O7·5H2O. The S previous paper (Oi et al., 1991). The slopes of the S-pH value for L2B2O4 ranged from 0.991 to 1.004, meaning plots for the two potassium borates seem very similar to that the lighter isotope was preferentially fractionated into each other. The crossover point where S crosses unity on the precipitate in some runs, and in the other runs the going from the low pH region to the high pH region is reverse was the case. If we take errors on the S values found at about pH 9.5 and at about 7.5 for K2B4O7 and into consideration, however, it may be more appropriate for santite, respectively. In addition, the extrapolation of to state that the S value is equal to or smaller than unity, K2B4O7 data to the lower pH region and santite data to indicating the maximum value of S is unity. The boron the higher pH region in Fig. 5 suggests that K2B4O7 has isotopic data in the lithium borate system are plotted in a smaller S value than santite at a given pH. Fig. 7. As in the cases of potassium borate and sodium Sodium borate system The isotopic data are limited to borate systems, the S value for L2B2O4 is an increasing borax (Na2[B4O5(OH)4·8H2O]) as shown in Table 2. Evi- function of pH. dently, the S value data are scattered around unity. They are plotted against the pH of the solution in Fig. 6, to- Consideration on structures and boron isotopic reduced gether with the isotopic data in the previous paper (Oi et partition function ratios of borates al., 1991). As is seen, the present isotopic data on borax Since our publication (Oi et al., 1989) on the elucida- are consistent with the previous ones in the pH depend- tion of boron isotopic compositions of boron minerals ence. The S value for borax is an increasing function of based on isotopic reduced partition function ratios (rpfrs) pH; it is smaller than unity in the pH region below ca. 9, (Bigeleisen and Mayer, 1947), it has been established and larger than unity in the pH region above ca. 10 and the is now well understood that boron with trigonal coordi- crossover point is at around 9.5. This crossover point of nation (surrounded by three oxygens) has a larger rpfr borax is nearly the same as that of K2B4O7 in Fig. 5. than boron with tetrahedral coordination (surrounded by Extrapolation of the borax data to the lower pH region four oxygens) and consequently the heavier isotope of indicates that the data point of sborgite boron is fractionated into boron with trigonal coordina- (Na[B5O6(OH)4]·3H2O; JCPDS No. 12-0265), the only tion, if the two are equilibrated. If we confine our focus sodium borate other than borax observed in our study (Oi on boron minerals, this means that the boron isotopic et al., 1991), is located above the point expected for bo- composition of a mineral is heavily dependent on the ra- rax at a given pH. This relation is similar to that observed tio of the number of BO3 units (trigonal coordination) for K2B4O7 and santite found for the potassium borate and the number of BO4 units (tetrahedral coordination) system (Fig. 5). in the polyborate anion in the mineral, and that a boron
156 M. Yamahira et al. Table 3. Chemical formulae and BO3:BO4 ratios of the potassium, sodium and lithium borates studied
Cation Mineral name Abbreviation Chemical formula BO3:BO4 in the polyanion
K (no name) K2B4O7 K2[B4O5(OH)4]·2H2O2:2
santite K[B5O6(OH)4]·2H2O4:1
Na borax Na2[B4O5(OH)4]·8H2O2:2
sborgite Na[B5O6(OH)4]·3H2O4:1
Li (no name) L2B2O4 Li2B2O4·16H2O0:2
(none) sassolite B(OH)3 1:0
1.02 (a) (b) BO3:BO4 = 2:2
1.01
BO3:BO4 = 4:1
S 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. = santite; = sborgite; = K2[B4O5(OH)4]·2H2O; ᭹ ᭝ = borax (Na2[B4O5(OH)4]·8H2O); = Li2B2O4·16H2O.
Fig. 8. Structures of (a) B(OH)3 (BO3:BO4 = 1:0), (b) – 2– [B5O6(OH)4] (BO3:BO4 = 4:1), (c) [B4O5(OH)4] (BO3:BO4 2– 2– = 2:2) and (d) [B2O(OH)6] (B2O4 ) (BO3:BO4 = 0:2). The ron isotopic ratio measurements were made in this and largest black spheres represent boron atoms, and the interme- the previous studies are summarized in Table 3, and the diate glossy and smallest gray ones oxygen and hydrogen at- structures of the polyborates involved in those minerals oms, respectively. No significance is attached to the relative are drawn as computer outputs in Fig. 8. sizes of those spheres. In Fig. 9, the separation factors obtained for K2B4O7, santite, borax, sborgite and L2B2O4 are all together plot- ted against the pH of solution. Based on the discussion in mineral with a larger proportion of the BO3 component is the previous paragraph, boron minerals with the same boron isotopically heavier than a mineral with a smaller BO3:BO4 ratios should show the similar pH dependence, proportion of the BO3 component, if they are deposited irrespective of the kind of counterions. In fact, borax and from the same solution. In this consideration, the kind of K2B4O7 can be put into one group having the 2BO3 + cationic component has no significance. Thus, for in- 2BO4 structure, sborgite and santite into another group stance, since the polyborate anions of borax and K2B4O7 having the 4BO3 + 1BO4 structure, and L2B2O4 consti- are both composed of 2BO3 + 2BO4 and that of santite is tutes the third group with the 0BO3 + 2BO4 structure, as composed of 4BO3 + 1BO4, the isotopic compositions of is indicated by the ovals in Fig. 9, although a few data borax and K2B4O7 are similar to each other whereas that points are located outside of the ovals. of santite is heavier than the two minerals if they are all formed from the common solution. In the above expres- QUALITATIVE ELUCIDATION OF THE OBSERVED sion, 2BO + 2BO , for instance, means that the 3 4 BORON ISOTOPE FRACTIONATION polyborate anion consists of two BO3 units and two BO4 units with some Os replaced with OHs (Kakihana et al., The boron isotope fractionation shown in Fig. 9 can 1977; Oi et al., 1989). The chemical formulae and be qualitatively elucidated on the basis of the theory on BO3:BO4 ratios of the boron minerals, for which the bo- equilibrium isotope effects (Bigeleisen and Mayer, 1947).
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 157 – The rpfr value of B(OH)3 is larger than that of B(OH)4 , 1.0 (a) – which predicts that the heavier isotope 11B tends to be B(OH)3 B(OH)4 10 – fractionated into B(OH)3 and B into B(OH)4 , when the 2– two boron species are in equilibrium with each other. This B4O5(OH)4 is why the equilibrium constant of Eq. (1) is larger than 0.5 unity. In the present experiments, the two isotopes of bo- B O (OH) – 3 3 4 – ron are distributed between two phases; one is the solid B2O(OH)5 phase (boron mineral) and the other the solution phase (aqueous solution). In this case, the separation factor, S, 0.0 is given, in terms of the rpfrs, as (Kakihana and Aida, 1.0 1973) (b) Mole fraction
BO4 unit ∑ ∑ BO3 unit lnS = ln( xi(s)fi(s)) – ln( xi(l)fi(l)), (5) 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 xi(l) are the rpfr and the mole fraction of species i in the solution phase, respectively. By definition, ∑x (s) = ∑x (l) i i 0.0 = 1, and the symmetry numbers are omitted in the ex- 0147 pression of the rpfrs for simplicity. There is only one bo- pH ron species in the solid phase in each of the runs for which Fig. 10. The distributions of (a) the boron species and (b) the the isotopic measurements were made. The solution phase BO3 and BO4 units as functions of the solution pH. The total is a concentrated boric acid solution, in which not only boron concentration is 0.8 M and the stability constants of the – monomeric boron species, B(OH)3 and B(OH)4 , but also polyborates are cited from Mesmer et al. (1972). – 2– polyborate anions such as B3O3(OH)4 and B3O3(OH)3 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 need to calculate the distribution of boron species at the the solution. given boron concentration and pH, and, after decompos- As mentioned above, the rpfrs of monomeric boron ing each polyborate into the BO3 and BO4 units, we cal- species were calculated based on their observed vibra- culate the concentrations of BO3 and BO4 units by add- tional frequencies. Unfortunately, however, rpfr calcula- ing up the contributions from all the polyborates as well tions on polyborate anions, except for those based on as from the monomers. The BO3:BO4 ratio is heavily pH molecular orbital theories (Oi, 2000b), are not reported dependent. As an example, we show the distribution of presumably due to lack of information on their molecu- boron species as a function of pH at the total boron con- lar vibrational frequencies. Thus, Eq. (5) cannot be uti- centration of 0.8 M in Fig. 10(a) and the corresponding lized in a straightforward way. distribution of the BO3 and BO4 units in Fig. 10(b), using The rpfr of a polyborate anion can be calculated in an the stability constants by Mesmer et al. (1972). Under approximate way by decomposing it into the monomeric this assumption, Eq. (5) is simplified to units (Oi et al., 1991). If the polyborate of interest con- sists of m BO3 units and n BO4 units with some of oxy- lnS = ln{xB3(s)fB3(s) + [1 – xB3(s)]fB4(s)} gen atoms being replaced by OH groups, then we approxi- – ln{xB3(l)fB3(l) + [1 – xB3(l)]fB4(l)}, (7) mate the ln(rpfr) value of the polyborate by the weighted sum of the ln(rpfr)s of the BO3 and BO4 units: where fB3(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 lnf = [m/(m + n)]lnfB3 + [n/(m + n)]lnfB4, (6) 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 where f, fB3 and fB4 are the rpfrs of the polyborate, the mole fraction of the BO3 unit in the solution phase, re- BO3 unit and the BO4 unit, respectively. The decomposi- spectively. We further assume that the rpfr value of the tion of the polyborate anion of the mineral in the solid BO3 unit is unchanged when transferred between the solid phase into the BO3 and BO4 components is rather straight- and the solution phases, and so is the rpfr value of the forward, since the crystal structure of the mineral is usu- BO4 unit; fB3(s) = fB3(l) and fB4(s) = fB4(l). That is, we ally well known. The treatment of the solution phase is assume that there is no boron isotope effect upon phase slightly complex compared to the solid phase. We first change. This assumption is actually not very bad one.
158 M. Yamahira et al. Kakihana et al. (1977) reported that no boron isotope (Simulation I): fractionation was observed in cation exchange chroma- 1) Polyborates in the solution phase and in the solid tography of B(OH)3 within experimental errors. Urgell et phase can be decomposed into the BO3 and BO4 units for al. (1964) reported similar results in anion exchange chro- the purpose of their rpfr calculations, as before. – matography of B(OH)4 . In our previous paper, only small 2) The pH of the solution is unchanged during the isotope fractionation was observed between sassolite and whole process of the mineral deposition. The pH at which the boron-bearing solution in which B(OH)3 was practi- the mineral deposition occurs is fixed at the one of the cally the only viable boron species (Oi et al., 1991). Eq. final solution. (7) is then further simplified as, 3) The boron isotopic equilibrium is always main- tained among various boron species in the solution phase lnS = ln{x(s)fB3 + [1 – x(s)]fB4} – ln{x(l)fB3 + [1 – x(l)]fB4}, during the whole process of the mineral deposition. (8) 4) The mineral is gradually deposited from the solu- tion. This implies that boron isotope exchange equilib- where fB3 is the rpfr of the BO3 unit, fB4 that of the BO4 rium is always maintained between the liquid and the solid unit, x(s) the mole fraction of the BO3 unit in the solid phases during the whole process of the mineral deposi- phase and x(l) that in the solution phase. Since the ratio tion. fB3/fB4 is nothing but the equilibrium constant, KB, of Eq. 5) There is no boron isotope fractionation accompa- (2), we finally obtain, nying the transfer of a polyborate anion from the solu- tion phase to the solid phase, that is, there is no boron ≈ S – 1 lnS = [(x(s) – x(l)](KB – 1)/[x(l)(KB – 1) + 1]. (9) isotope fractionation upon phase change. 6) No boron species change occurs from the BO3 unit Equation (9) is the basis for the quantitative under- to the BO4 unit and vice versa in the solid phase. standing of the results shown in Fig. 9. First, S is inde- The boron isotopic compositions are time dependent pendent of the kind of cation, since it does not appear in both in the solution phase and in the solid phase; an aliquot Eq. (9). Second, Eq. (9) states that, for a given value of deposited at the early stage of the precipitation process x(s), S should be a monotonously decreasing function of has a different 11B/10B isotopic ratio from that of an aliquot x(l) with the crossover point at x(s) = x(l). Since x(l) is a deposited later. In the computer program, mineral depo- monotonously decreasing function of pH, as is shown in sition is assumed to occur in many continuous steps, in Fig. 10(b), S is expected to be a monotonously increasing each of which only a very small amount of boron is de- function of pH, which agrees with the experimental re- posited. Repetition of deposition is continued until the sults in Fig. 9. Finally, for a given value of x(l), i.e., at a total amount of boron deposited becomes equal to the fixed pH, S is larger for a larger x(s). Thus, the S value experimental one. for santite and sborgite with x(s) = 0.8 is larger than that The procedure of Simulation I is as follows. The total for K2B4O7 and borax with x(s) = 0.5, which should be amount of boron (mtot), the amount of deposited boron larger than the S value for L2B2O4 with x(s) = 0. (mprec), the volume of the solution phase (Vsol), the ex- perimental pH of the solution, the assumed KB value and the initial boron isotopic ratio of the solution phase ((11B/ COMPUTER SIMULATION OF MINERAL FORMATION 10 B)sol) are first given as initial inputs. The boron con- PROCESSES AND ESTIMATION OF KB centration and the BO3:BO4 ratio of the solution are then Equation (9) provides a very simple way to evaluate calculated by using the input data and the stability con- the KB value from experimental data for each run. In each stants of polyborates and the dissociation constant of bo- run, S value is experimentally obtained, x(s) is determined ric acid cited from Mesmer et al. (1972). Next, the boron if the deposited boron mineral is identified, and x(l) can isotopic ratios of the BO3 and BO4 units in the solution be calculated in the way described in the preceding sec- phase are calculated. A small amount of boron is trans- tion using the stability constants of polyborates and the ferred to the solid phase with a part as BO3 unit and the dissociation constant of boric acid in literature. remaining part as BO4 unit with the BO3:BO4 ratio equal Although it is convenient to use Eq. (9) for the quali- to that of the mineral experimentally deposited, and the 11 10 tative explanation of the experimental results, it is not boron isotopic ratio of the solid phase (( B/ B)prec) is appropriate for the quantitative treatment of the results, calculated. After the transfer, the amount of boron in the since the process in which the boron mineral is precipi- solution phase, and consequently, the boron concentra- 11 10 tated is not taken into consideration. tion too, decrease slightly. The ( B/ B)sol value also In the following, we try to model the precipitation changes slightly. So, the BO3:BO4 ratio and the boron processes of boron minerals to estimate KB by computer isotopic ratios of the BO3 and BO4 units in the solution simulation, which is based on the following assumptions 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 Table 4. The estimated KB values the solid phase. This manipulation is continued until the System Mineral Run No. K “Better” K total amount of deposited boron becomes equal to the B B experimental one, and the separation factor is calculated Sim. I Sim. II using the final values of the isotopic ratios in the solu- tion and solid phases. This calculated separation factor K K2B4O7 K5 1.036 1.041 1.036 K6 1.041 1.059 1.041 (Scal) is compared with the experimental one (Sexp). If Scal K7 1.021 1.021 does not agree with Sexp, the whole calculation process is K10 1.012 1.019 1.019 redone with a different KB value as the new initial input, K11 1.022 1.022 K12 1.017 1.017 and this is repeated until Scal agrees with Sexp, thus deter- mining the K value for that run. When this manipulation K13 1.011 1.013 1.013 B K42 1.031 1.031 is completed, the calculated boron isotopic ratios in the ave. 1.024 1.025 liquid and solid phases agreed with the experimental ones santite K1 1.041 1.041 1.041 within ±0.001 for every run. K2 1.029 1.029 The results of Simulation I including those obtained K3 1.000 1.000 for borax using the experimental data in the previous pa- K4 1.040 1.047 1.040 K14 1.022 1.022 per (Oi et al., 1991) are summarized in Table 4. For K15 1.015 1.016 1.016 K2B4O7, the KB value ranges from 1.011 (K13) to 1.041 K18 1.013 1.015 1.015 (K6) with the average of 1.024. For suntite, it is from K19 1.017 1.017 1.000 (K3) to 1.047 (K45) with the average of 1.025. The K44 1.002 1.002 1.002 K3 data is omitted in averaging, since, when the S value K45 1.047 1.055 1.047 ave. 1.025 1.026 is unity, the KB value becomes necessarily unity in prin- ciple under the adopted assumptions. The average KB Na borax N1 1.013 1.017 1.017 value for borax is 1.028 with the range of the KB value N2 1.017 1.021 1.021 N3 1.012 1.014 1.014 being from 1.012 to 1.065. Note that the KB values esti- mated using the data in the previous paper (Oi et al., 1991) N4 1.024 1.024 B-08* 1.031 1.031 are different from the ones listed in that paper. This dis- B-09* 1.014 1.016 1.016 crepancy is mostly due to the difference in the kind of B-10* 1.065 1.079 1.065 polyborates supposed to exist in the solution phase and B-17* 1.034 1.034 their stability constant values between this and the previ- B-18* 1.023 1.023 ous studies. In the present study, the work by Mesmer et B-23* 1.035 1.048 1.035 – – B-25* 1.044 1.048 1.044 al. (1972) is adopted where B2O(OH)5 , B3O3(OH)4 and B-27* 1.023 1.023 2– B4O5(OH)4 are assumed as polyborates, while Spessard ave. 1.028 1.029 (1970) whose data were adopted in the previous paper – Li L2B2O4 L2 1.016 1.017 1.017 (Oi et al., 1991) assumed the existence of B3O3(OH)4 , B O (OH) 2–, B O (OH) 2– and B O (OH) – as viable L3 1.009 1.009 1.009 3 3 5 4 5 4 5 6 4 L4 — polyborates in aqueous solution. The latter tends in gen- L5 1.078 1.023 1.023 eral to yield a larger KB value than the former for a given L11 — run. For L2B2O4, the estimation of the KB value for L4 L12 1.009 1.010 1.010 and L11 is abandoned. The S value in those two runs is ave. 1.028 1.015 larger than unity, which in principle yields the K value B *From Oi et al. (1991). Note that the present KB values are different smaller than unity under the adopted assumptions. We from the previous ones since the used stability constant values are dif- ferent. 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, al- though the grand average is reasonable at 1.026. The KB value ranges from 1.002 (K44) to 1.078 (L5). If the as- phase (Vsol) on KB, taking the case of Run B-10 in which sumptions 1) to 6) above all hold, KB should converge to borax deposited as an example. The results are summa- 11 10 one value irrespective of experimental conditions. That rized in Table 5. The experimental ( B/ B)prec = 4.028 is, every run should yield the same and common KB value. gives KB = 1.065. If one consider the experimental error ± 11 10 The results of Simulation I evidently lead to another di- of 0.005 on ( B/ B)prec, KB fluctuates between 1.059 11 10 rection. In this context, we examined the effect of a small and 1.072 with a large ( B/ B)prec value yielding a small 11 10 ± change in the value of such quantities as the amount of KB value. Similarly, ( B/ B)sol = 4.072 0.003 gives 11 10 deposited boron (mprec) and the volume of the solution the KB range of 1.061 to 1.069 with a large ( B/ B)sol
160 M. Yamahira et al. Table 5. Effects of slight change in the values of input parameters on KB (Run B-10)
Variable Initial solution Final solution Final solid (prec.) SKB 11 10 − 11 10 11 10 mtot B/ B Vsol pH mtot mprec ( B/ B)sol mprec ( B/ B)prec [mol] [cm3] [mol] [mol] Default 0.166 4.051 190.6 8.75 0.087 4.072 0.079 4.028 0.989 1.065 11 10 ( B/ B)prec 4.032 0.990 1.059 4.023 0.988 1.072 11 10 ( B/ B)sol 4.075 0.988 1.069 4.070 0.990 1.061
mprec 0.089 1.061 0.069 1.070
Vsol 195.6 1.066 185.6 1.065 pH 9.25 1.388 8.25 1.038
value yielding a large KB value. Table 5 also shows that given mineral (more than 0.01) by Simulation I. The re- the increase in the amount of deposited boron (mprec) and sults are summarized in the 5th column of Table 4. In the final solution volume (Vsol), respectively, decreases general, Simulation II yields a larger KB value than Simu- and increases the KB value. It is evident from Table 5 that lation I. As a result, some data get closer to the average, the above examined quantities certainly influence KB. but some do not against our expectation. This may mean However, their effects are limited. It is impossible to ob- that the assumption upon pH made in Simulation II is not tain KB of, say, 1.026, by manipulating the values of those always adequate. The most drastic improvement of KB is quantities within reasonable ranges estimated from ex- observed for L5; the KB value changes from 1.078 to perimental errors. The last two rows of Table 5 summa- 1.023. This is the only case for which Simulation II yields rize the effect of pH at which the mineral deposits on KB. a smaller KB value than Simulation I. In L5, The pH of The ±0.5 change in pH does not correspond to experi- the final solution was 12.42, highest among the pH val- mental error in pH measuring, but models the pH change ues of the runs for which isotopic analysis was conducted. from the start of the mineral deposition to the end of a At that pH, the proportion of the BO3 unit in the solution run (the end of deposition). As can be seen, the effect of phase was extremely small, and the solid phase was com- pH is substantial. If the pH value at which the mineral posed of L2B2O4 with no BO3 unit. That is, in L5, only a deposition started is different from the final pH value, at very small amount of BO3 unit in the solution phase was which we assume the deposition occurred, the expected responsible for the deviation of S from unity, and conse- KB value may be quite different from the one estimated quently a very large KB value resulted in Simulation I. by Simulation I. This situation is largely improved by assuming that the The solution pH at which the mineral is precipitated mineral deposition started at a lower pH at which the pro- is very influential on KB. A slight change in pH some- portion of the BO3 unit is larger. times causes non-negligible change in KB value. In the In the last column of Table 2 is listed the “better” KB above simulation (Simulation I), the pH value, at which value (Simulation I or Simulation II). The term “better” the mineral was supposed to deposit, is fixed at the final simply means “closer to the average”. Comparison of the pH value in every run. In some cases, the fact may be average values of KB in this column reveals a couple of that the mineral deposition started at pH that was differ- interesting points. K2B4O7 and borax have the same ent from the final one, somewhere between the initial and BO3:BO4 ratio of 2:2. Nevertheless, the KB value is larger the final values, and finished at the final pH value. In the for borax than for K2B4O7. This is against the assump- following simulation (Simulation II), this pH change dur- tion in the preceding section that the rpfr of a polyborate ing the mineral precipitation was taken into the consid- is independent of the kind of counterion. Liu and Tossell eration. The pH value at which the mineral deposition (2005) carried out molecular orbital (MO) calculations started was set at the pH value of the initial solution, and on the boron isotopic rpfrs of hydrated boric acid and the deposition was assumed to finish at the pH of the fi- monoborate anion interacting with cations like Li+ and nal solution. During the mineral depositing, the pH change Na+ ions. They assumed such boron species as + + – was assumed to be proportional to the amount of depos- Li B(OH)3(H2O)34 and Li B(OH)4 (H2O)34 and calculated ited boron. This manipulation was applied to the runs their rpfr values at the HF/6-31G* level of theory. They – whose KB values are quite apart from the average for the 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 1.020 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,
S 1.000 the both lines seem to represent the data points of borax and K2B4O7 equally well. This indicates that it is diffi- cult 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 shal- lower than the other lines, which reflects the fact that the 0.980 KB value for L2B2O4 is evidently smaller than those of 0 0.5 1 the other minerals. It is seen in Fig. 11 that for L2B2O4, Mole fraction of BO3 unit in solution phase the line does not represent the data points very well; the least-squares line of the L2B2O4 data would become Fig. 11. Plots of S against the mole fraction of BO3 unit in the ᮀ much sharper. This discrepancy may indicate the exist- solution phase. = santite (K[B5O6(OH)4]·2H2O); = ᭺ sborgite (Na[B5O 6(OH)4]·3H2O); = K2B4O7 ence of boron isotope fractionation upon the phase change, ᭹ (K2[B4O5(OH)4]·2H2O); = borax (Na2[B4O5(OH)4]·8H2O); which is against the assumption 5) above that there is no ᭝ = L2B2O4 (Li2B2O4·16H2O). – · – · – = santite (KB = 1.025); boron isotope fractionation upon phase change. – – · – – · – – = K2B4O7 (KB = 1.026); - - - = borax (KB = 1.029); — = L2B2O4 (KB = 1.015). CONCLUSIONS To summarize, we would like to make the following statements: were both slightly influenced by the existence of cationic 1) K2[B4O 5(OH)4]·2H2O (K2B4O7), santite species, indicating that K2B4O7 might show a different (K[B5O6(OH)4]·2H2O), KBO2·1.33H2O, KBO2·1.25H2O KB value from that of borax. Unfortunately, quantitative and sassolite (B(OH)3) were precipitated as boron miner- discussion is not possible here since they did not calcu- als from boron and potassium ion-bearing solutions at + ° late the effect of the K ion on the rpfrs of these boron 25.0 C. Similarly, borax (Na2[B4O5(OH)4·8H2O) was species. Another observation is that a boron mineral with obtained from boron and sodium ion-bearing solutions, a large BO3:BO4 ratio tends to yield a large KB value; KB and Li2B2O 4·16H2O (L2B2O4), Li2B4O 7·5H2O, of santite with the BO3:BO4 ratio of 4:1 was larger than Li2B10O16·10H2O, LiB2O3(OH)·H2O and sassolite from that of K2B4O7 with the BO3:BO4 ratio of 2:2 which was boron and lithium ion-bearing solutions. larger than that of L2B2L4 with the BO3:BO4 ratio of 0:2. 2) The boron isotopic analysis was carried out for This observation agrees, qualitatively at least, with our K2B4O7, santite, borax and L2B2O4. For a given min- MO calculations on the rpfrs of boric acid, monoborate eral, the separation factor, S, defined as the 11B/10B iso- and polyboric acids and polyborates (Oi, 2000a, b). The topic ratio of the mineral divided by that of the solution, calculations showed that the values of the rpfrs of BO3 was in general an increasing function of the pH of the and BO4 units both became small upon polymerization, solution. At a given pH, the S value for santite was in but the degree of decrease in rpfr is more substantial for general larger than those of K2B4O7 and borax that were the BO4 unit than for the BO3 unit. in general larger than that of L2B2O4. These results were In Fig. 11, the experimentally obtained S values are consistent with the conclusion having been drawn theo- plotted against the estimated mole fraction of the BO3 retically that the boron isotopic reduced partition func- unit in the solution phase. The lines are drawn using the tion ratio (rpfr) of three-coordinated boron (trigonal co- “better” average values of KB in Table 4. Note that the ordination) is larger than that of four-coordinated boron line for santite necessarily goes through the point (0.8, (tetrahedral coordination). 1.0). Similarly, the lines for K2B4O7 and borax pass 3) Computer simulations modeling the mineral for- through the point (0.5, 1.0) and the line for L2B2O4 the mation processes yielded the value of equilibrium con- point (0, 1.0). Thus, the crossover point at which the S stant of the boron isotope exchange reaction between boric value becomes unity is the point at which the BO3:BO4 acid and monoborate anion, KB, of 1.025 for K2B4O7, ratio in the solution phase is equal to that in the solid 1.026 for santite, 1.029 for borax and 1.015 for L2B2O4. phase. This is due to the assumption 5) above that there Minerals with a larger proportion of three-coordinated
162 M. Yamahira et al. boron in its borate structure tended to have a larger KB Oi, T. (2000a) Calculations of reduced partition function ratios value, which was consistent with the results by molecu- of monomeric and dimeric boric acids and borates by the lar orbital calculations on rpfrs of polyborates having been ab initio molecular orbital theory. J. Nucl. Sci. Technol. 37, independently conducted. 166–172. Oi, T. (2000b) Ab initio molecular orbital calculations of re- duced partition function ratios of polyboric acids and Acknowledgments—Professor Y. Fujii, Tokyo Institute of polyborate anions. Z. Naturforsch. 55a, 623–628. Technology (Titech) kindly offered the use of a Varian MAT Oi, T., Nomura, M., Musashi, M., Ossaka, T., Okamoto, M. and CH-5 mass spectrometer. We acknowledge Dr. M. Nomura, Kakihana, H. (1989) Boron isotopic compositions of some Titech, for his assistance in mass spectrometric measurements boron minerals. Geochim. Cosmochim. Acta 53, 3189–3195. of boron isotopic ratios. Oi, T., Kato, J., Ossaka, T. and Kakihana, H. (1991) Boron iso- tope fractionation accompanying boron mineral formation REFERENCES from aqueous boric acid-sodium hydroxide solutions at 25°C. Geochem. J. 25, 377–385. Bigeleisen, B. and Mayer, M. G. (1947) Calculation of equilib- Pagani, M., Lemarchand, D., Spivack, A. and Gailardet, J. rium constants for isotopic exchange reactions. J. Chem. (2005) A critical evaluation of the boron isotope-pH proxy: Phys. 15, 261–267. The accuracy of ancient ocean pH estimates. Geochim. Cantanzaro, E. S., Champoin, C. E., Garner, E. L., Maintenon, Cosmochim. Acta 69, 953–961. G., Sapenfield, K. M. and Shields, W. R. (1970) NBS Spec. Palmer, M. R. and Swihart, G. H. (1996) Boron isotope Publ. (US) No. 260-17. geochemistry: an overview. Rev. Mineral. 33, 709–744. Hemming, N. G. and Hanson, G. N. (1992) Boron isotopic com- Palmer, M. R., Spivack, A. J. and Edmond, J. M. (1987) Tem- position and concentration in modern marine carbonates. perature and pH controls over isotopic fractionation during Geochim. Cosmochim. Acta 56, 537–543. adsorption of boron on marine clay. Geochim. Cosmochim. Honisch, B., Hemming, N. G., Grottoli, A. G., Amat, A., Acta 51, 2319–2323. Hanson, G. N. and Buma, J. (2004) Assessing scleractinian Palmer, M. R., Pearson, P. N. and Cobb, S. J. (1998) Recon- coals as records for paleo-pH: Empirical calibration and vital structing past ocean pH-depth profiles. Science 282, 1468– effects. Geochim. Cosmochim. Acta 68, 3675–3685. 1471. Ingri, N., Lagerstrom, G., Fryman, M. and Sillen, L. G. (1957) Peng, Q. M. and Palmer, M. R. (1995) The palaeoproterozoic Equilibrium studies of polyanions II Polyborates in NaClO4 boron deposits in eastern Liaoning, China: a metamorphosed medium. Acta Chem. Scand. 11, 1034–1058. evaporate. Precambrian Res. 72, 185–197. Kakihana, H. and Aida, M. (1973) Distribution of isotopes be- Spessard, J. E. (1970) Investigations of borate equilibria in tween two phases. Bull. Tokyo Inst. Technol. 116, 39–52. neutral salt solutions. J. Inorg. Nucl. Chem. 32, 2607–2613. Kakihana, H. and Kotaka, M. (1977) Equilibrium constants for Spivack, A. J., You, C. F. and Smith, H. J. (1993) Foraminifera boron isotope exchange reactions. Bull. Res. Lab. Nucl. boron isotope ratios as a proxy for surface ocean pH over Reactors 2, 1–12 the past 21 Myr. Nature 363, 149–151. Kakihana, H., Kotaka, M., Satoh, S., Nomura, M. and Okamoto, Swihart, G. H., McBay, E. H., Smith, D. H. and Siefke, J. W. M. (1977) Fundamental studies on the ion-exchange sepa- (1996) A boron isotopic study of a minerarologically zoned ration of boron isotopes. Bull. Chem. Soc. Jpn. 50, 158– lacustrine borate deposit: the Kramer deposit, California, 163. U.S.A. Chem. Geol. 127, 241–250. Liu, Y. and Tossell, J. A. (2005) Ab initio molecular orbital Urgell, M. M., Iglesias, J., Casas, J., Saviron, J. M. and calculations for boron isotope fractionations on boric acids Quintanilla, M. (1964) The production of stable isotopes in and borates. Geochim. Cosmochim. Acta 69, 3995–4006. Spain. Third UN Int’l. Conf. on the Peaceful Uses of Atomic Mesmer, R. E., Baes, C. F., Jr. and Sweeton, F. H. (1972) Acid- Energy, A/CONF.28/P/491, Spain. ity measurements at elevated temperatures. VI. Boric acid Vengosh, A., Kolodny, Y., Atarinsky, A., Chivas, A. R. and equilibria. Inorg. Chem. 11, 537–543. McCullouch, M. T. (1991) Coprecipitation and isotopic Nomura, M., Okamoto, M. and Kakihana, H. (1973) Determi- fractionation of boron in modern biogenic carbonates. nation of boron isotopic ratio by the surface ionization Geochim. Cosmochim. Acta 55, 2901–2910. method. Shitsuryo Bunseki 21, 277–281 (in Japanese). Zeebe, R. E. (2005) Stable isotope fractionation between dis- Nomura, M., Fujii, Y. and Okamoto, M. (1990) The isotopic – solved B(OH)3 and B(OH)4 . Geochim. Cosmochim. Acta ratios of boron in coals. Shitsuryo Bunseki 38, 95–100 (in 69, 2753–2766. Japanese).
Boron isotope fractionation accompanying formation of borates from boron-bearing solutions 163