ARTICLE
Theoretical Calculation of Equilibrium Cadmium Isotope Fractionation Factors between Cadmium-bearing sulfides and aqueous solutions
2022 Volume 56 Issue 6 Pages 180-196
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2022 Volume 56 Issue 6 Pages 180-196
In this study, the equilibrium isotope fractionation factors between Cd-bearing aqueous solutions and minerals were predicted. The theoretical method used to calculate the Cd isotope fractionation factors is the first-principle quantum chemistry method (Cd: LANL2DZ, other atoms: 6-311 + G(d, P)). Reduced partition function ratios (RPFRs) of Cd-bearing minerals (Greenockite and Sphalerite) were modeled by the method of the volume variable cluster model (VVCM). The theoretical method of “water-droplet method” is used to simulate the solvation effect of different Cd-bearing aqueous solutions. The results show that, in most cases, the Cd-bearing aqueous solutions are enriched in 114Cd relative to Greenockite. The Cd isotope fractionation factors between Cd-bearing aqueous solutions and Greenockite are in the range of 0.433–0.083 (100°C). And the Cd isotope fractionations between different Cd-bearing species are believed to be widespread. Cd isotope fractionation factors between different reservoirs are of great theoretical significance to many geochemical processes such as surficial geochemical process and ore-forming process. These theoretical parameters are studied systematically and carefully in this study.
Cadmium (Cd) is a rare element, which is located in the fifth period, Group ⅡB of the periodic table of the elements. It is a kind of silver-white metal. In industry, pure Cd is either a by-product of Zinc (Zn) smelting or can be extracted from its independent mineral Greenockite (Rehkämper et al., 2012). Strohmeier was the first person who found Cd in 1817 in Germany. It is worth mentioning that Cd is an element in the same main group as Zn and Mercury (Hg). Cd is chemically like Zn that both elements showing strong preferences for the oxidation state of +2 (Cullen and Maldonado, 2013). While the chemistry of Cd in solution is more complex and varied (Martinotti et al., 1995; Ratié et al., 2021). Most Cd compounds (e.g., chloride, nitrate, sulfate, etc.) have significant ionic properties due to the high metallic of Cd. However, Cd was discovered much later than Hg and Zn for two reasons. One is Cd in the earth’s crust is much less abundant than Zn and is often present in Zn ore as a secondary mineral (Rehkämper et al., 2012). The associated relationship between Cd and Zn is very common in nature. Cd-bearing deposits such as Greenockite (CdS) and Otavite (CdCO3) are generally associated with Sphalerite (ZnS) and Smithsonite (ZnCO3) (Rehkämper et al., 2012). Another reason is Cd is more volatile than Zn (Lodders, 2003). In the process of smelting Zn at high temperatures, Cd is vaporized and lost much earlier than Zn that eluding people’s awareness. So, Cd has obvious characteristics of dispersity, moderate volatility, and heavy metal pollution (Lodders, 2003; Chakraborty et al., 2012).
Cd has eight stable isotopes, with abundances of 1.25%, 0.89%, 12.49%, 12.80%, 24.13%, 12.22%, 28.73% and 7.49% for 106Cd, 108Cd, 110Cd, 111Cd, 112Cd, 113Cd, 114Cd and 116Cd, respectively (Cullen and Maldonado, 2013; Pritzkow et al., 2007). The distribution of trace metal elements in aqueous solutions and suspended particles is the main factor affecting the geochemical behavior, migration and biological effects of these elements in natural water (Nriagu et al., 1981). Cd is ubiquitous in water (fresh water and sea water) and hydrothermal solution system, but the content is low (Ripperger and Rehkämper, 2007). In geological environment systems such as seawater or hydrothermal environment, Cd can form a variety of complexes. Inorganic ligands, eg. H2O, Cl–, OH– and HS– can interact with Cd2+ (Bazarkina et al., 2010; Das et al., 1996). Many systems in nature are important reservoirs of Cd, such as seawater, surface soils, silicate rocks, meteorites, and so on (Zhong et al., 2020). Therefore, it is of great significance to study the distribution and isotope composition of Cd in different reservoirs (Cullen and Maldonado, 2013; Shiel et al., 2012).
In the 1970s, Rosman and De Laeter conducted the first systematic study of isotope fractionation of Cd in meteorites (Rosman and De Laeter, 1976, 1978). Nowadays, with the improvement of instruments and analytical capabilities, more and more researchers are focusing their research interests on Cd isotopes and applying it to different geological systems (Imseng et al., 2019; Xie et al., 2017; Yan et al., 2021). Mass dependent isotope fractionation can be produced by chemical, biochemical or physical processes, either equilibrium isotope exchange or dynamic isotope separation. Cd is a common element in geochemical research. The isotope fractionation of Cd in astrochemical processes is quite large. For the fractionation between the melt phase and the Cd vapor, the isotope fractionation factor (110Cd/114Cd) of kinetic evaporation and equilibrium evaporation are 1.018 and 1.007 respectively (Wombacher et al., 2004). Previous studies have shown that evaporation/condensation and biological processes can lead to very large Cd isotope fractionation, which are also the main mechanisms for large Cd isotope fractionation (Rehkämper et al., 2012; Cullen and Maldonado, 2013; Cullen et al., 1999; Wombacher et al., 2004, 2008). The industrial Cd emission process, which involves evaporation and condensation, is a major factor in Cd isotope fractionation. Therefore, the study of Cd isotope fractionation in this process is very important in determining and tracing whether Cd comes from natural or anthropogenic sources. In the ocean, Cd is a kind of micronutrient (Xie et al., 2017). In the process of biological absorption and utilization, there will be a large fractionation of Cd isotope. The study of marine Cd isotope fractionation is of great significance, which can be used to study the cycle of micronutrients and its impact on marine productivity. Under this circumstance, Cd is generally considered as a co-factor of enzymes. At the same time, Cd isotope can be used to trace the polluted water and soil, and the change of Cd isotope composition can give us a deeper understanding of the cycle of Cd in the marine environment. Research results in the field of environmental engineering show that the main pollution sources of Cd come from sewage discharged by electroplating, mining, dyes, batteries and chemical industry (Shiel et al., 2010, 2012). The Cd2+ is easily transported and absorbed by plants and has an influence on the entire food chain (Hamid et al., 2019).
In recent years, many studies have investigated the change of Cd isotope composition in various terrestrial materials and environments (Bradac et al., 2010; Frederiksen et al., 2022). In general, these results show that there are obvious changes in Cd isotopic compositions in different geological environments, i.e., 114Cd/110Cd. The main mechanisms of large Cd isotope composition variations are partial evaporation and/or condensation of Cd or Cd absorbed by living organisms. In short, Cd isotopes have been widely used in astrochemistry, hydrochemistry and petrology (Ratié et al., 2021; Ripperger and Rehkämper, 2007; Imseng et al., 2019; Xie et al., 2017; Yan et al., 2021; Wombacher et al., 2004, 2008; Frederiksen et al., 2022; Guinoiseau et al., 2018; Horner et al., 2011; Hu et al., 2011; Murphy et al., 2014; Salmanzadeh et al., 2017; Wei et al., 2018; Yang et al., 2012; Zhang et al., 2021). Previous study has shown that the species of Cd2+ in aqueous solution/hydrothermal solution play a crucial role in the Cd isotope effect and the deposition of Cd-bearing sulfides (Guinoiseau et al., 2018). Few studies have focused on Cd isotope fractionation in hydrothermal system (Zhu et al., 2016). Isotope fractionation data of Cd between different phases are crucial for a better understanding of Cd in solution/hydrothermal systems, Cd-bearing sulfide deposition and the global Cd cycle. Up to now, there have been many theoretical studies on transition metals. However, the theoretical calculation of Cd isotope system of solution/hydrothermal fluid is still relatively few (Blanchard et al., 2017). Yang et al. and Zhao et al. (Yang et al., 2015; Zhao et al., 2021) carried out theoretical calculations on Cd isotope fractionation in hydrothermal systems and major organic ligands. Solvation effect must be considered when dealing with solutions through theoretical methods which is also an important constant ignored by previous studies. In this work, we will systematically study the Cd isotope enrichment mechanism in different phases by using “water droplet method” (solvation effect) and “VVCM” method (solid mineral). Several important Cd-bearing species were selected, including the Cd-bearing aqueous solutions, minerals and simple Cd compounds. The Cd isotope enrichment mechanism between these species was studied carefully. It is expected that these results can provide theoretical references for geochemical workers engaged in experiments and field work.
The basic theory used in this work is Bigeleisen-Mayer formula (also called Urey model) when calculating the reduced partition function ratio (RPFR) of different Cd-bearing species (Bigeleisen and Mayer, 1947; Urey, 1947). With this model, it is possible to relate the most basic chemical parameter (equilibrium constant, K) with isotope fractionation factor commonly used in geochemistry. That is, the isotope fractionation factors can be obtained from the molecular level through the basic theoretical simulation and calculation. Taking the isotope exchange reaction between the Cd-bearing aqueous solution ([Cd(H2O)4]2+) and the Cd-bearing mineral (Greenockite) as an example:
| (1) |
In the above formula, superscripts “114” and “110” represent the species containing 114Cd and 110Cd isotopes respectively. The equilibrium constant of different substances can be expressed in the form of reduced partition function ratio.
| (2) |
Different from the field of chemistry, geochemical workers are more concerned about isotope fractionation factor, i.e., α. There is a good mathematical relationship between equilibrium constant and isotope fractionation factor:
| (3) |
In the formula 3, “n” is the number of atoms exchanged in an isotope exchange reaction. If there has only one atom exchanged in an isotope exchange reaction, α is equal to K. In this study, by default, all isotope exchange reactions exchange only one atom.
According to Urey model, the theoretical calculation formula of RPFR is as follows:
| (4) |
In the formula 4, “s” represents the symmetry number of the research object. For most complex research systems, the symmetry number does not change before and after isotope exchange, that is, “s110” is equal to “s114”. “ui” is a function of simple harmonic vibration frequencies, and its mathematical expression is as follows:
| (5) |
In the formula 5, h, kb and T are constant terms, representing Planck constant, Boltzmann constant and Kelvin temperature respectively. Therefore, in the above equation, there is only one variable namely Nu(ν). By this theory, the equilibrium isotope fractionation factors of a substance at any temperature can be obtained as long as the simple harmonic vibration frequencies are obtained accurately (Bigeleisen and Mayer, 1947; Urey, 1947; Urey and Greiff, 1935; Liu et al., 2010). When pressure and anharmonic effect are not considered, the equilibrium isotope fractionation factors are only a function of temperature, and it decreases with increasing temperature (Cao and Liu, 2011; Clayton et al., 1975; Polyakov and Kharlashina, 1994).
How to accurately obtain the simple harmonic vibration frequencies of different isotopologues become very important. With the progress of science and technology, the computing power of computers has becoming more powerful. Now, the simple harmonic vibration frequencies of macromolecules, molecular clusters and even solid substances could be accurately obtained by means of theoretical calculation. However, it should be noted that the simple harmonic vibration frequencies must be used to calculate isotope fractionation factors with the Urey model, rather than the experimental fundamental frequencies (Bigeleisen and Mayer, 1947; Liu et al., 2010). Up to now, ab initio or first-principles methods to obtain isotope fractionation factors have become a very conventional technique (Black et al., 2011; Blanchard et al., 2009; Fujii et al., 2009a, 2009b, 2010; Li and Liu, 2010, 2011; Li et al., 2009; Oi, 2000; Oi and Yanase, 2001; Polyakov et al., 2007, 2019; Polyakov and Soultanov, 2011). In this study, all calculations were carried out with suing Gaussian16 program package (Frisch et al., 2016).
Solid mineral simulation—the VVCM methodIn the past decade, theoretical computational geochemistry has developed into a very important branch of earth science and produced many influential results. Different research teams have adopted different theoretical simulation methods, but the key point is still how to accurately obtain the simple harmonic vibration frequencies of matters. We used VVCM method to calculate and obtain Cd-bearing minerals. This method has been used to study many different geological systems and obtained good results (Gao et al., 2018; He and Liu, 2015; He et al., 2016; Zhang, 2021; Zhang and Liu, 2018). Nowdays, computers have the computing power to complete systems of tens, hundreds or even thousands of atoms. Previous studies showed that in addition to model solid minerals with periodic structure, molecular cluster method can also be adopted (Gibbs, 1982). The reason is that the isotope effect is a local property of minerals (Liu and Tossell, 2005). With chemical bonds increase, the external environment has less influence on the isotope effect. If there are more than 2–3 external chemical bonds, the influence of external chemical bonds on the isotope effect of the central atom (Cd) decreases rapidly (Gao et al., 2018). In this case, the outermost atoms will be further away from the center atom (Cd). Therefore, the bonds that affect the isotope effect most strongly are those closest to the central atom.
Under the treatment of this method, the way of neutralizing residual electrons of mineral fragments is changed from adding hydrogen atoms to virtual charges. In this way, a realistic mineral-chemical environment will be obtained. Moreover, the distances between the virtual charges and the outermost atoms can be adjusted freely. Thus, when obtaining the most stable structures of a mineral fragments, several times or even a dozen times of repeated calculations are needed to obtain the final structures, i.e., the most stable structures with lowest energies. According to our experience, it’s not appropriate to use a lower theoretical base level for structural pre-optimization, and then use a higher theoretical base level for structural optimization and frequencies calculation to save time. In this way, an unstable local structure will be obtained, which cannot be eliminated even by re-optimization at a higher theoretical base level. Therefore, inaccurate theoretical calculation results will be generated. In conclusion, the same theoretical basis must be used for structural optimization and frequency calculations (Li and Liu, 2010, 2011; Li et al., 2009).
When modeling, atoms of interest (Cd) are usually placed in center of the mineral fragment. When the fragment is cut, hundreds of virtual charges are added to the outermost atoms to neutralize the remaining electrons of the fragment. The purpose of this operation is to maintain the electrical neutrality of the mineral fragment and to obtain the most stable structures and accurate harmonic frequencies. For the theoretical calculation of Cd-bearing minerals, the pseudopotential basis set LANL2DZ is used for Cd atoms, and the full electronic basis set 6-311 + G(d, P) is used for S atoms, similarly hereinafter. This is because Cd atom does not have available full electronic basis set under Gaussian16 software. The 4s and 4p orbitals of the transition metal Cd are all fully filled inner orbitals. However, due to the special electron configuration of the transition metal, the energy difference between these inner orbitals and valence orbitals is not very prominent. In many cases, these orbitals also contribute to the bonding of the Cd atom. The basis set of LANL2DZ treats 4s and 4p orbitals as valence orbitals, which can significantly improve the calculation accuracy. The molecular cluster model of Cd-bearing minerals with Cd atom in the center is shown in Fig. 1. In Fig. 1, the pictures on the left and right represent Greenockite and Sphalerite, respectively.
The sketch of cluster structures of Greenockite and Sphalerite with Cd atom in the center. The coordination numbers of central Cd atom are four for these clusters.
“Water-droplet method” was used to simulate the solvation effect of Cd-bearing aqueous solutions (Li et al., 2009; Li and Liu, 2010). A serious of Cd-bearing species exist in solutions and hydrothermal fluids were selected (Bazarkina et al., 2010; Ohtaki and Johansson, 1981; Schwartz, 2000). Species with water and hydroxyl as ligands: [Cd(H2O)4]2+, [Cd(H2O)5]2+, [Cd(H2O)6]2+, [Cd(OH)]+ and [Cd(OH)2(H2O)4]; nitrate and sulfate as ligands: [Cd(NO3)2(H2O)4] and [Cd(HS)]+; halogen atoms as ligands: [CdCl(H2O)5]+, [CdCl2(H2O)2], [CdCl2], [CdCl3(H2O)]–, [CdCl4]2–, [CdBr2(H2O)2], [CdBr2] and [CdBr4]2–.
The nearest coordination sphere around Cd should be constructed first when using the “water-droplet method” to construct the molecular cluster of aqueous solutions. In the case of [Cd(H2O)4]2+, a tetrahedral structure is formed by putting the Cd in the center and adding four water molecules around it. Then, the structure optimization and frequency calculation are carried out at the corresponding theoretical base level. After obtaining the optimized structure, six water molecules are added around it. For the sake of convenience in writing, these six water molecules are identified as the second coordination layer of Cd, forming [Cd(H2O)4]2+.(H2O)6. Using the same theoretical base level above, the structure is optimized, and the frequencies are calculated. The same method is used until the sixth layer of water is added (i.e., [Cd(H2O)4]2+.(H2O)30), and then the structure optimization and the frequencies calculation will be carried out. This structure was adopted as the final formation to simulate [Cd(H2O)4]2+ in aqueous solution. According to our experience, when water molecules are added to the sixth layer, the addition water molecules have little effect on the isotope effect of Cd-bearing aqueous solutions. That is, the influence of the outermost water environment on the isotope fractionation factors (RPFRs) of Cd can be ignored. Due to the large volume of [Cd(H2O)4]2+, little water molecules hardly well cover its surface. Consequently, in optimizations, the namely third layer of water will penetrate into the second hydration layer when they formed hydrogen bonds with the first layer of water. For other Cd-bearing aqueous species, their final aqueous structures can also be obtained with this method.
To make the results more reasonable, four parallel calculations were carried out for structural optimization and frequency calculation for aqueous species. The numerical average of the four times calculations was taken as the final calculation result. It will take a lot of time to obtain the final results of structural optimization and frequency calculation. Here, we also must consider the structure does not converge and so on. It must be emphasized that the calculations of any species must be based on the same theoretical basis. Figure 2 shows the initial coordination structures of 15 kinds of Cd-bearing aqueous solutions studied in this work. However, when the solvation effect considering, the nearest coordination spheres of Cd-bearing solutions will change greatly. As shown in Fig. 3, for [Cd(OH)]+ and [Cd(HS)]+, the second layer water molecules ((H2O)6) penetrate into the nearest coordination spheres of Cd. Taken together, the final structures of these two species are hexa-coordinate.
The first-coordination shells of different Cd-bearing coordination complexes. The circles in pale yellow, deep yellow, red, gray, green, blue and brown represent atoms of Cd, S, O, H, Cl, N and Br, respectively.
The cluster structures of [Cd(HS)]+.(H2O)30 and [Cd(OH)]+.(H2O)30. The circles in pale yellow, deep yellow, red and gray represent atoms of Cd, S, O and H, respectively.
The geometry optimization is an important step in the theoretical calculation of the harmonic vibration frequencies of substances in geochemistry. In this study, density functional theory B3LYP method with basis set LANL2DZ was used to optimize Cd compounds (halides, oxides and sulfides, etc.). The vibration frequencies were calculated at the same theoretical level. For Cd-bearing compounds, Gauss View program were used for model construction. Then, the theoretical calculations were performed using Gaussian16 program package (Frisch et al., 2016).
In this section, [Cd(H2O)4]2+, [Cd(H2O)5]2+, [Cd(H2O)6]2+, [Cd(H2O)6]2+ and [Cd(H2O)6]2+ were selected as the formations of free Cd2+ in aqueous solutions. According to our results, 103ln(RPFR)s of these Cd-bearing aqueous solutions have little difference. Our results can be compared with previous results. At 100°C, the 103ln(RPFR)s of [Cd(H2O)4]2+, [Cd(H2O)5]2+ and [Cd(H2O)6]2+, our results are 1.593, 1.497 and 1.530, and Yang et al.’s are 1.408, 1.466 and 1.489 (Yang et al., 2015). The specific 103ln(RPFR)s values are different due to different basis sets we used, but the range of these values is consistent. The isotope fractionation factor (103lnα) between [Cd(H2O)5]2+ and [Cd(H2O)6]2+ at 100°C, our calculation result is 0.33, while Yang et al.’s is 0.23. See Fig. 4A and Table 1 for the 103ln(RPFR)s of these solutions at different temperatures. As shown in Table 1, at 100°C, when the number of ligands is 6,7 and 8, the 103ln(RPFR)s are 1.530, 1.509 and 1.521. The difference between these values is very small. This shows that when the number of ligands is 7 and 8, their existence form is unstable when the solvation effect is considered.
The 103ln(RPFR)s of different Cd-bearing aqueous solutions as a function of temperature. Fig. 4(A), (B) and (C) stand for the 103ln(RPFR)s of [Cd(H2O)4]2+(aq), [Cd(H2O)5]2+(aq), [Cd(H2O)6]2+(aq), [Cd(H2O)7]2+(aq) and [Cd(H2O)8]2+(aq), [CdOH]+, [Cd(OH)2(H2O)4], [Cd(NO3)2(H2O)4] and [Cd(HS)]+, [CdCl(H2O)5]+(aq), [CdCl2](aq), [CdCl2(H2O)2](aq), [CdCl3(H2O)]–(aq), [CdCl4]2–(aq), [CdBr2(H2O)2](aq), [CdBr2](aq) and [CdBr4]2–(aq) respectively. The subscript “aq” represents aqueous solution, similarly hereinafter.
| Solutions | Temperature (°C) | |||||||
|---|---|---|---|---|---|---|---|---|
| 0 | 25 | 50 | 100 | 150 | 200 | 300 | 500 | |
| [Cd(H2O)4]2+.(H2O)6 | 2.880 | 2.440 | 2.093 | 1.587 | 1.243 | 1.000 | 0.686 | 0.380 |
| [Cd(H2O)4]2+.(H2O)12 | 2.935 | 2.486 | 2.132 | 1.617 | 1.267 | 1.019 | 0.700 | 0.387 |
| [Cd(H2O)4]2+.(H2O)18 | 2.923 | 2.475 | 2.121 | 1.608 | 1.259 | 1.013 | 0.695 | 0.385 |
| [Cd(H2O)4]2+.(H2O)24 | 2.939 | 2.488 | 2.133 | 1.617 | 1.267 | 1.019 | 0.699 | 0.387 |
| [Cd(H2O)4]2+.(H2O)30 | 2.896 | 2.452 | 2.102 | 1.593 | 1.248 | 1.003 | 0.689 | 0.381 |
| [Cd(H2O)5]2+.(H2O)6 | 2.896 | 2.451 | 2.101 | 1.591 | 1.246 | 1.001 | 0.687 | 0.380 |
| [Cd(H2O)5]2+.(H2O)12 | 2.851 | 2.412 | 2.067 | 1.566 | 1.226 | 0.985 | 0.676 | 0.374 |
| [Cd(H2O)5]2+.(H2O)18 | 2.785 | 2.356 | 2.018 | 1.528 | 1.197 | 0.962 | 0.660 | 0.365 |
| [Cd(H2O)5]2+.(H2O)27 | 2.754 | 2.330 | 1.997 | 1.512 | 1.184 | 0.952 | 0.653 | 0.361 |
| [Cd(H2O)5]2+.(H2O)30 | 2.728 | 2.308 | 1.977 | 1.497 | 1.172 | 0.942 | 0.647 | 0.358 |
| [Cd(H2O)6]2+.(H2O)6 | 2.844 | 2.405 | 2.060 | 1.559 | 1.220 | 0.980 | 0.672 | 0.371 |
| [Cd(H2O)6]2+.(H2O)12 | 2.832 | 2.395 | 2.052 | 1.553 | 1.215 | 0.977 | 0.670 | 0.370 |
| [Cd(H2O)6]2+.(H2O)18 | 2.782 | 2.353 | 2.016 | 1.526 | 1.194 | 0.960 | 0.658 | 0.364 |
| [Cd(H2O)6]2+.(H2O)24 | 2.713 | 2.295 | 1.966 | 1.488 | 1.165 | 0.936 | 0.642 | 0.355 |
| [Cd(H2O)6]2+.(H2O)30 | 2.788 | 2.359 | 2.021 | 1.530 | 1.198 | 0.963 | 0.661 | 0.366 |
| [Cd(H2O)7]2+.(H2O)6 | 2.696 | 2.279 | 1.952 | 1.476 | 1.155 | 0.928 | 0.636 | 0.351 |
| [Cd(H2O)7]2+.(H2O)12 | 2.822 | 2.387 | 2.044 | 1.547 | 1.211 | 0.973 | 0.667 | 0.369 |
| [Cd(H2O)7]2+.(H2O)18 | 2.806 | 2.373 | 2.033 | 1.539 | 1.204 | 0.968 | 0.664 | 0.367 |
| [Cd(H2O)7]2+.(H2O)24 | 2.749 | 2.325 | 1.991 | 1.508 | 1.180 | 0.948 | 0.650 | 0.360 |
| [Cd(H2O)7]2+.(H2O)30 | 2.752 | 2.327 | 1.994 | 1.509 | 1.182 | 0.950 | 0.651 | 0.360 |
| [Cd(H2O)8]2+.(H2O)6 | 2.805 | 2.372 | 2.032 | 1.538 | 1.203 | 0.967 | 0.663 | 0.366 |
| [Cd(H2O)8]2+.(H2O)12 | 2.809 | 2.376 | 2.035 | 1.541 | 1.206 | 0.969 | 0.665 | 0.367 |
| [Cd(H2O)8]2+.(H2O)18 | 2.799 | 2.368 | 2.028 | 1.535 | 1.202 | 0.966 | 0.662 | 0.366 |
| [Cd(H2O)8]2+.(H2O)24 | 2.784 | 2.355 | 2.017 | 1.527 | 1.195 | 0.961 | 0.659 | 0.364 |
| [Cd(H2O)8]2+.(H2O)30 | 2.773 | 2.346 | 2.009 | 1.521 | 1.191 | 0.957 | 0.656 | 0.363 |
In this part, the 103ln(RPFR)s of the Cd-bearing aqueous solutions with OH–, HS– and NO3– as ligands were theoretically calculated. [CdOH]+, [Cd(OH)2(H2O)4], [Cd(NO3)2(H2O)4] and [Cd(HS)]+ were selected to represent different coordination environments. The existence form of Cd2+ in aqueous solution is directly related to the chemical environment of aqueous solution, and will be affected by pH value, concentration, adsorption of particles (Zirino and Yamamoto, 1972). For these four aqueous species, our results are [CdOH]+(aq) ≈ [Cd(OH)2(H2O)4](aq) > [Cd(NO3)2(H2O)4](aq) > [Cd(HS)]+(aq) (Fig. 4B). The 103ln(RPFR)s of [CdOH]–(aq) and [Cd(OH)2(H2O)4](aq) are close enough. This also indirectly suggests that the nearest coordination sphere around Cd is not a simple structure such as [CdOH]+ and solvation effect must be considered. Taking the 103ln(RPFR)s at 100°C as an example, these two species has values 1.464 and 1.459 respectively (Table 2). At the same temperature, for all these four substances, our results were 1.464, 1.459, 1.386 and 1.331, while Yang et al. reported that the 103ln(RPFR)s of these species were 0.883, 1.558, 1.505 and 0.514, respectively (Yang et al., 2015). The 103ln(RPFR)s of [CdOH]+(aq) and [Cd(HS)]+(aq) solutions are quite different between us. According to our calculations, if only [CdOH]+ and [Cd(HS)]+ are considered without the addition of water molecules around them, our results are 0.858 and 0.507 respectively, which are in good agreement with the results of Yang et al.’s. Although it is of no practical significance to compare the specific value of RPFR between different studies, we think that some methodological problems can be found. However, when dealing with solvation effects in aqueous solutions, one need to consider the water environment around the atoms of interest. Therefore, we have reason to believe that our results are accurate and reliable. The 103ln(RPFR)s of Sulfur-bearing solutions were calculated with the same method, and the results are in good agreement with the previous results (Zhang, 2021; Eldridge et al., 2016). Similarly, there is a large deviation between our results and those of Otake et al.’s about Sulfur isotope fractionation which may be due to the different methods we use (Otake et al., 2008). Otake et al. (2008) used the implicit solvent model (IEF-PCM), while present work only considered the explicit model.
| Species | Temperature (°C) | |||||||
|---|---|---|---|---|---|---|---|---|
| 0 | 25 | 50 | 100 | 150 | 200 | 300 | 500 | |
| [CdOH]+.(H2O)6 | 2.851 | 2.418 | 2.076 | 1.576 | 1.236 | 0.995 | 0.684 | 0.379 |
| [CdOH]+.(H2O)12 | 2.921 | 2.474 | 2.121 | 1.608 | 1.259 | 1.013 | 0.695 | 0.385 |
| [CdOH]+.(H2O)18 | 2.794 | 2.365 | 2.027 | 1.535 | 1.203 | 0.967 | 0.663 | 0.367 |
| [CdOH]+.(H2O)24 | 2.660 | 2.250 | 1.928 | 1.460 | 1.144 | 0.920 | 0.631 | 0.349 |
| [CdOH]+.(H2O)30 | 2.665 | 2.255 | 1.932 | 1.464 | 1.147 | 0.922 | 0.633 | 0.351 |
| a[CdOH]+(aq) | 1.556 | 1.331 | 1.151 | 0.883 | 0.698 | 0.564 | 0.390 | — |
| [CdOH]+ | 1.514 | 1.295 | 1.119 | 0.858 | 0.678 | 0.548 | 0.379 | 0.211 |
| [Cd(OH)2(H2O)4].(H2O)6 | 2.809 | 2.382 | 2.045 | 1.553 | 1.218 | 0.981 | 0.674 | 0.374 |
| [Cd(OH)2(H2O)4].(H2O)12 | 2.703 | 2.289 | 1.962 | 1.488 | 1.166 | 0.938 | 0.644 | 0.357 |
| [Cd(OH)2(H2O)4].(H2O)18 | 2.647 | 2.241 | 1.921 | 1.455 | 1.140 | 0.917 | 0.630 | 0.349 |
| [Cd(OH)2(H2O)4].(H2O)24 | 2.568 | 2.174 | 1.864 | 1.413 | 1.107 | 0.890 | 0.611 | 0.339 |
| [Cd(OH)2(H2O)4].(H2O)30 | 2.653 | 2.246 | 1.925 | 1.459 | 1.144 | 0.920 | 0.632 | 0.350 |
| a[Cd(OH)2(H2O)4](aq) | 2.806 | 2.382 | 2.047 | 1.558 | 1.224 | 0.986 | 0.679 | — |
| [Cd(NO3)2(H2O)4].(H2O)6 | 2.700 | 2.283 | 1.955 | 1.480 | 1.158 | 0.931 | 0.638 | 0.353 |
| [Cd(NO3)2(H2O)4].(H2O)12 | 2.622 | 2.217 | 1.899 | 1.437 | 1.125 | 0.904 | 0.620 | 0.343 |
| [Cd(NO3)2(H2O)4].(H2O)18 | 2.637 | 2.230 | 1.909 | 1.445 | 1.131 | 0.909 | 0.623 | 0.345 |
| [Cd(NO3)2(H2O)4].(H2O)24 | 2.518 | 2.128 | 1.822 | 1.379 | 1.079 | 0.867 | 0.595 | 0.329 |
| [Cd(NO3)2(H2O)4].(H2O)30 | 2.530 | 2.139 | 1.831 | 1.386 | 1.084 | 0.871 | 0.598 | 0.331 |
| a[Cd(NO3)2(H2O)4](aq) | 2.750 | 2.325 | 1.990 | 1.505 | 1.178 | 0.946 | 0.649 | — |
| [CdHS]+.(H2O)6 | 2.412 | 2.040 | 1.746 | 1.321 | 1.033 | 0.830 | 0.569 | 0.314 |
| [CdHS]+.(H2O)12 | 2.471 | 2.089 | 1.789 | 1.353 | 1.059 | 0.850 | 0.583 | 0.322 |
| [CdHS]+.(H2O)18 | 0.854 | 0.585 | 0.323 | 0.854 | 0.585 | 0.323 | 0.854 | 0.585 |
| [CdHS]+.(H2O)24 | 2.438 | 2.061 | 1.764 | 1.334 | 1.044 | 0.838 | 0.575 | 0.318 |
| [CdHS]+.(H2O)30 | 2.431 | 2.055 | 1.759 | 1.331 | 1.041 | 0.837 | 0.574 | 0.317 |
| a[CdHS]+(aq) | 0.939 | 0.794 | 0.680 | 0.514 | 0.402 | 0.323 | 0.221 | — |
| [Cd(HS)]+ | 0.926 | 0.783 | 0.671 | 0.508 | 0.397 | 0.319 | 0.219 | 0.121 |
Note: “a” stands for the results of Yang et al. (2015).
Halogen elements are widely distributed in nature and are found in many water bodies. For the complexes of Cd2+ with halogen elements as ligands, eight aqueous species ([CdCl(H2O)5]+, [CdCl2], [CdCl2(H2O)2], [CdCl3(H2O)]–, [CdCl4]2–, [CdBr2(H2O)2], [CdBr2] and [CdBr4]2–) were selected. When the ligand is Cl–, the order of 103ln(RPFR)s of these Cd-bearing aqueous species is: [CdCl(H2O)5]+(aq) > [CdCl2] ≈ [CdCl2(H2O)2](aq) > [CdCl3(H2O)]–(aq) > [CdCl4]2–(aq) (Fig. 4C). At 100°C, the 103ln(RPFR)s of these five Cd-bearing aqueous solutions are 1.362, 1.253, 1.253, 1.181 and 1.058 respectively. At the same temperature, the results of Yang et al.’s (Yang et al., 2015) showed that the 103ln(RPFR)s of [CdCl(H2O)5]+(aq), [CdCl2], [CdCl2(H2O)2](aq) and [CdCl3(H2O)]–(aq) were 1.431, 1.307, 1.373 and 1.159, respectively (Table 3). In theoretical calculation, simply comparing the absolute value of 103ln(RPFR) is of little significance. It makes more sense to compare the isotope fractionation factors. Taking the isotope fractionation factors (103lnα) of [CdCl(H2O)5]+(aq) and [CdCl3(H2O)](aq) at 100°C as an example, our result is 0.304, while that of Yang et al. is 0.272. The difference between these two data is 0.032. It is worth mentioning that any scaling factor were used to calculate 103ln(RPFR) by using simple harmonic vibration frequencies all through this research.
| Species | Temperature (°C) | |||||||
|---|---|---|---|---|---|---|---|---|
| 0 | 25 | 50 | 100 | 150 | 200 | 300 | 500 | |
| [CdCl(H2O)5]+.(H2O)6 | 2.628 | 2.222 | 1.902 | 1.438 | 1.125 | 0.904 | 0.619 | 0.342 |
| [CdCl(H2O)5]+.(H2O)12 | 2.549 | 2.155 | 1.845 | 1.395 | 1.092 | 0.877 | 0.601 | 0.332 |
| [CdCl(H2O)5]+.(H2O)18 | 2.484 | 2.099 | 1.797 | 1.359 | 1.063 | 0.854 | 0.585 | 0.324 |
| [CdCl(H2O)5]+.(H2O)24 | 2.494 | 2.108 | 1.805 | 1.365 | 1.068 | 0.858 | 0.588 | 0.325 |
| [CdCl(H2O)5]+.(H2O)30 | 2.488 | 2.103 | 1.800 | 1.362 | 1.066 | 0.856 | 0.587 | 0.325 |
| a[CdCl(H2O)5]+(aq) | 2.615 | 2.210 | 1.892 | 1.431 | 1.119 | 0.899 | 0.616 | 0.340 |
| [CdCl2(H2O)2].(H2O)6 | 2.474 | 2.090 | 1.788 | 1.351 | 1.057 | 0.848 | 0.581 | 0.321 |
| [CdCl2(H2O)2].(H2O)12 | 2.379 | 2.010 | 1.720 | 1.300 | 1.017 | 0.816 | 0.559 | 0.309 |
| [CdCl2(H2O)2].(H2O)18 | 2.336 | 1.973 | 1.688 | 1.276 | 0.997 | 0.801 | 0.549 | 0.303 |
| [CdCl2(H2O)2].(H2O)24 | 2.318 | 1.958 | 1.675 | 1.266 | 0.990 | 0.795 | 0.544 | 0.301 |
| [CdCl2(H2O)2].(H2O)30 | 2.295 | 1.938 | 1.658 | 1.253 | 0.980 | 0.787 | 0.539 | 0.298 |
| a[CdCl2(H2O)2](aq) | 2.512 | 2.123 | 1.817 | 1.373 | 1.074 | 0.862 | 0.590 | 0.326 |
| [CdCl2].(H2O)6 | 2.394 | 2.022 | 1.730 | 1.307 | 1.021 | 0.820 | 0.561 | 0.310 |
| [CdCl2].(H2O)12 | 2.298 | 1.940 | 1.660 | 1.254 | 0.980 | 0.787 | 0.539 | 0.297 |
| [CdCl2].(H2O)18 | 2.262 | 1.910 | 1.634 | 1.234 | 0.965 | 0.775 | 0.530 | 0.293 |
| [CdCl2].(H2O)24 | 2.299 | 1.942 | 1.661 | 1.255 | 0.981 | 0.788 | 0.540 | 0.298 |
| [CdCl2].(H2O)30 | 2.293 | 1.937 | 1.657 | 1.253 | 0.980 | 0.787 | 0.539 | 0.298 |
| a[CdCl2](aq) | 2.374 | 2.011 | 1.725 | 1.307 | 1.024 | 0.823 | 0.565 | 0.312 |
| [CdCl3(H2O)]–.(H2O)6 | 2.202 | 1.858 | 1.588 | 1.198 | 0.935 | 0.750 | 0.513 | 0.283 |
| [CdCl3(H2O)]–.(H2O)12 | 2.206 | 1.861 | 1.590 | 1.200 | 0.937 | 0.751 | 0.514 | 0.284 |
| [CdCl3(H2O)]–.(H2O)18 | 2.211 | 1.866 | 1.595 | 1.203 | 0.940 | 0.754 | 0.516 | 0.284 |
| [CdCl3(H2O)]–.(H2O)24 | 2.188 | 1.846 | 1.578 | 1.191 | 0.930 | 0.746 | 0.511 | 0.282 |
| [CdCl3(H2O)]–.(H2O)30 | 2.170 | 1.831 | 1.565 | 1.181 | 0.922 | 0.740 | 0.506 | 0.280 |
| a[CdCl3(H2O)]–(aq) | 2.128 | 1.796 | 1.536 | 1.159 | 0.906 | 0.727 | 0.497 | 0.274 |
| [CdCl4]2–.(H2O)6 | 1.951 | 1.643 | 1.402 | 1.055 | 0.823 | 0.659 | 0.450 | 0.248 |
| [CdCl4]2–.(H2O)12 | 2.014 | 1.696 | 1.448 | 1.091 | 0.850 | 0.681 | 0.466 | 0.256 |
| [CdCl4]2–.(H2O)18 | 2.049 | 1.726 | 1.474 | 1.110 | 0.866 | 0.694 | 0.474 | 0.261 |
| [CdCl4]2–.(H2O)24 | 2.003 | 1.687 | 1.441 | 1.085 | 0.846 | 0.678 | 0.463 | 0.255 |
| [CdCl4]2–.(H2O)30 | 1.952 | 1.644 | 1.404 | 1.058 | 0.825 | 0.661 | 0.452 | 0.249 |
| [CdBr2(H2O)2].(H2O)6 | 2.183 | 1.842 | 1.575 | 1.189 | 0.928 | 0.745 | 0.510 | 0.281 |
| [CdBr2(H2O)2].(H2O)12 | 2.230 | 1.883 | 1.610 | 1.216 | 0.950 | 0.762 | 0.522 | 0.288 |
| [CdBr2(H2O)2].(H2O)18 | 2.252 | 1.902 | 1.627 | 1.229 | 0.961 | 0.771 | 0.528 | 0.292 |
| [CdBr2(H2O)2].(H2O)24 | 2.254 | 1.903 | 1.628 | 1.230 | 0.961 | 0.772 | 0.529 | 0.292 |
| [CdBr2(H2O)2].(H2O)30 | 2.245 | 1.895 | 1.621 | 1.225 | 0.957 | 0.768 | 0.526 | 0.291 |
| [CdBr2].(H2O)6 | 2.219 | 1.872 | 1.600 | 1.208 | 0.943 | 0.757 | 0.518 | 0.286 |
| [CdBr2].(H2O)12 | 2.171 | 1.833 | 1.567 | 1.183 | 0.925 | 0.742 | 0.508 | 0.280 |
| [CdBr2].(H2O)18 | 2.130 | 1.799 | 1.539 | 1.162 | 0.908 | 0.729 | 0.499 | 0.276 |
| [CdBr2].(H2O)24 | 2.103 | 1.775 | 1.518 | 1.146 | 0.896 | 0.719 | 0.492 | 0.272 |
| [CdBr2].(H2O)30 | 2.155 | 1.819 | 1.556 | 1.175 | 0.918 | 0.737 | 0.505 | 0.279 |
| [CdBr4]2–.(H2O)6 | 1.635 | 1.375 | 1.172 | 0.881 | 0.686 | 0.549 | 0.374 | 0.206 |
| [CdBr4]2–.(H2O)12 | 1.709 | 1.437 | 1.226 | 0.921 | 0.717 | 0.574 | 0.392 | 0.216 |
| [CdBr4]2–.(H2O)18 | 1.729 | 1.454 | 1.240 | 0.932 | 0.726 | 0.581 | 0.397 | 0.218 |
| [CdBr4]2–.(H2O)24 | 1.731 | 1.456 | 1.241 | 0.933 | 0.727 | 0.582 | 0.397 | 0.218 |
| [CdBr4]2–.(H2O)30 | 1.718 | 1.445 | 1.232 | 0.927 | 0.722 | 0.578 | 0.395 | 0.217 |
Note: “a” stands for the results of Yang et al. (2015).
The 103ln(RPFR)s of Cd-bearing aqueous solutions with the second most abundant halogen element Br– as ligand were also calculated. Three Cd-bearing aqueous solutions ([CdBr2(H2O)2](aq), [CdBr2](aq) and [CdBr4]2–(aq)) were selected. At 100°C, the variation order of 103ln(RPFR)s is [CdBr2(H2O)2](aq) > [CdBr2](aq) > [CdBr4]2–(aq) (Fig. 4C). The specific data are 1.225, 1.175 and 0.927 respectively (Table 3). The comparison of Cd-bearing aqueous solutions with the same structure of different halogen ligands (Cl and Br), such as [CdBr2(H2O)2](aq), [CdBr2](aq) and [CdBr4]2–(aq), with [CdCl2(H2O)2](aq), [CdCl2](aq) and [CdCl4]2–(aq), it was found that the 103ln(RPFR)s changed significantly when ligands changed from Cl– to Br–. With the increase of atomic weight of halogen ligands, isotope fractionation values will decrease significantly. That is, the heavy isotope tends to be enriched in the phase with short (strong) bonds, like Cd-Cl bond.
The 103ln(RPFR)s of Cd-bearing minerals and simple Cd compoundsIn this section, Greenockite and Sphalerite were selected, and their structure optimizations and frequency calculations were also carried out. The 103ln(RPFR)s of these minerals were calculated. The initial crystal structures were obtained from crystal database (Xu and Ching, 1993; Skinner, 1961). Then, the mineral fragment model was constructed according to the requirements of VVCM method. The model construction and structure optimization methods adopted in this work are feasible and reasonable. With this method, our calculation results show that the average bond length of central four Cd-S bonds of Greenockite and Sphalerite are 2.57 and 2.53 Å. Experimental Cd-S bond length of Greenockite is 2.53 Å (Xu and Ching, 1993). The Zn-S bond length is 2.34 for pure sphalerite (Skinner, 1961).
As shown in Table 4, with the same basis set, the 103ln(RPFR)s of Sphalerite are bigger than that of Greenockite under the same temperature conditions. The 103ln(RPFR)s of Greenockite and Sphalerite at 25°C are 1.707 and 1.832 per mil, respectively. The fragment structures of Cd-bearing minerals with Cd atom in the center. The 103ln(RPFR) decrease gradually with temperature increasing (Fig. 5).
| Mineral | Temperature (°C) | |||||||
|---|---|---|---|---|---|---|---|---|
| 0 | 25 | 50 | 100 | 150 | 200 | 300 | 500 | |
| Greenockite | 2.026 | 1.707 | 1.457 | 1.097 | 0.856 | 0.686 | 0.469 | 0.258 |
| Sphalerite | 2.173 | 1.832 | 1.565 | 1.180 | 0.921 | 0.738 | 0.505 | 0.278 |
The 103ln(RPFR)s of Greenockite and Sphalerite as a function of temperature.
To test the feasibility of this calculation method, a series of simple Cd compounds (halides, oxides and sulfides, etc.) were selected to study their Cd isotope enrichment capacity. The results show that, CdCl2 has the strongest ability to enrich 114Cd. The oxidation state of Cd is +2, almost no other oxidation state exists, so the fractionation of Cd isotope is not affected by the redox process. Previous studies have shown that the electronegativity of elements has a direct effect on isotope fractionation (Méheut and Schauble, 2014). Among all these anionic elements, chlorine has the strongest electronegativity, so CdCl2 has the strongest ability to enrich 114Cd. That is, Cd-Cl bond is strong, so it enriched in 114Cd.
The predicted 103ln(RPFR)s of CdCl2, CdBr2, CdO, CdS and CdSe are 1.329, 1.156, 0.840, 0.569 and 0.512 at 100°C (Table 5). Due to the bond strengths between these elements and Cd decrease greatly as atomic number increasing, in the same family, the enrichment ability of 114Cd becomes weaker. Therefore, Cd isotope enrichment capacity of CdCl2 is obviously greater than that of CdBr2. In the oxygen group elements, the ability to enrich Cd isotopes is also becoming weaker in order from O to Se. This is consistent with the general law of isotope enrichment. The change orders of 103ln(RPFR)s for these species are CdCl2 > CdBr2 and CdO > CdS > CdSe (Fig. 6). Calculated vibrational frequencies and optimized bond lengths were shown in Table 6. The bond lengths of dihalide calculated by this study are closer to experimental values compared to previous theoretical research results (Hargittai, 2000; Zhao et al., 2004). Our calculation results are 2.342 Å and 2.476 Å, and the experimental results are 2.284 Å and 2.394 Å, which are better than the previous calculation results 2.374 Å and 2.518 Å for CdCl2 and CdBr2, respectively. This gives evidence for the feasibility of the research method. With this method, the vibrational frequencies of dihalide are obtained.
| Species | Temperature (°C) | |||||||
|---|---|---|---|---|---|---|---|---|
| 0 | 25 | 50 | 100 | 150 | 200 | 300 | 500 | |
| CdO | 1.480 | 1.266 | 1.094 | 0.840 | 0.664 | 0.537 | 0.371 | 0.207 |
| CdS | 1.037 | 0.877 | 0.752 | 0.569 | 0.445 | 0.358 | 0.245 | 0.135 |
| CdSe | 0.944 | 0.796 | 0.679 | 0.512 | 0.399 | 0.320 | 0.219 | 0.120 |
| CdCl2 | 2.413 | 2.044 | 1.753 | 1.329 | 1.041 | 0.837 | 0.574 | 0.318 |
| CdBr2 | 2.123 | 1.792 | 1.532 | 1.156 | 0.903 | 0.724 | 0.495 | 0.273 |
The 103ln(RPFR)s of CdCl2, CdBr2, CdO, CdS and CdSe as a function of temperature.
| Species | Parameters | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Frequencies (cm–1) | Cd-X:Bond length (Å) | |||||||||||
| A | B | C | A | B | C | |||||||
| CdCl2 | 74 | 302 | 389 | 68 | 299 | 384 | 83 | 330 | 427 | 2.342 | 2.374 | 2.284 |
| CdBr2 | 55 | 188 | 293 | 50 | 184 | 286 | 60 | 210 | 315 | 2.476 | 2.518 | 2.394 |
| CdO | 572 | 1.954 | ||||||||||
| CdS | 345 | 2.327 | ||||||||||
| CdSe | 238 | 2.438 | ||||||||||
Notes: X is the notation for the different anions, Cl, Br, O, S and Se. A, B and C stand for the data of this study, Zhao et al. (2014) and experiment (Hargittai, 2000).
The isotope exchange reaction between aqueous solution and solid minerals is of great significance for determining the Cd isotope cycle (Zhu et al., 2016). With the rapid development of mass spectrometry, more and more unconventional isotope systems have been studied to indicate various environmental and geological processes (e.g., Blanchard et al., 2009, 2012, 2017; Polyakov et al., 2007, 2019; Polyakov and Soultanov, 2011).
In most cases, Cd-bearing aqueous solutions are more enriched in 114Cd isotopes than the Cd-bearing minerals, whether the ligand is water, halogen, nitrate, or hydroxyl ions (Fig. 7A, B). In general, the Cd isotope fractionation factors between solutions and minerals are less than 1 per mil. This theoretical prediction results are also consistent with those of Yang et al.’s (Yang et al., 2015). At 100°C, the isotope fractionation factors between these Cd-bearing aqueous solutions ([Cd(H2O)6]2+.(H2O)30, [Cd(OH)2(H2O)4].(H2O)30, [Cd(NO3)2(H2O)4].(H2O)30, [Cd(HS)]+.(H2O)30, [CdCl(H2O)5]+.(H2O)30, [CdCl2(H2O)2].(H2O)30 and [CdCl3(H2O)]–.(H2O)30) and Greenockite are 0.433, 0.362, 0.288, 0.234, 0.264, 0.155 and 0.083 (Table 7). At the same temperature, the Cd isotope fractionation factors between solutions ([Cd(H2O)6]2+.(H2O)30, [Cd(OH)2(H2O)4].(H2O)30, [Cd(NO3)2(H2O)4].(H2O)30, [Cd(HS)]+.(H2O)30, [CdCl(H2O)5]+.(H2O)30 and [CdCl2(H2O)2].(H2O)30) and Sphalerite are 0.349, 0.278, 0.205, 0.150, 0.181 and 0.072 (Table 7). The isotope fractionation factors between solutions and Greenockite are lagger than that between solutions and Sphalerite. Among them, [Cd(H2O)6]2+.(H2O)30 has the strongest ability of enriching 114Cd compared with the solid minerals. Overall, aqueous solutions are enriched in 114Cd relative to the minerals.
The isotope fractionation factors (l03*ln(α)s) of different solution-mineral pairs and solution-solution pairs as a function of temperature.
| Pairs | Temperature (°C) | |||||||
|---|---|---|---|---|---|---|---|---|
| 0 | 25 | 50 | 100 | 150 | 200 | 300 | 500 | |
| [Cd(H2O)6]2+.(H2O)30-Gr | 0.762 | 0.651 | 0.563 | 0.433 | 0.342 | 0.277 | 0.191 | 0.107 |
| [Cd(OH)2(H2O)4].(H2O)30-Gr | 0.626 | 0.538 | 0.468 | 0.362 | 0.287 | 0.233 | 0.162 | 0.092 |
| [Cd(NO3)2(H2O)4].(H2O)30-Gr | 0.503 | 0.431 | 0.374 | 0.288 | 0.228 | 0.185 | 0.128 | 0.072 |
| [CdHS]+.(H2O)30-Gr | 0.404 | 0.348 | 0.302 | 0.234 | 0.185 | 0.150 | 0.104 | 0.059 |
| [CdCl(H2O)5]+.(H2O)30-Gr | 0.461 | 0.395 | 0.343 | 0.265 | 0.209 | 0.170 | 0.118 | 0.066 |
| [CdCl2(H2O)2].(H2O)30-Gr | 0.268 | 0.230 | 0.201 | 0.155 | 0.123 | 0.100 | 0.07 | 0.039 |
| [CdCl3(H2O)]–.(H2O)30-Gr | 0.144 | 0.123 | 0.107 | 0.083 | 0.066 | 0.054 | 0.037 | 0.021 |
| [Cd(H2O)6]2+.(H2O)30-Sp | 0.615 | 0.526 | 0.455 | 0.349 | 0.276 | 0.224 | 0.155 | 0.087 |
| [Cd(OH)2(H2O)4].(H2O)30-Sp | 0.479 | 0.413 | 0.359 | 0.278 | 0.222 | 0.181 | 0.126 | 0.071 |
| [Cd(NO3)2(H2O)4].(H2O)30-Sp | 0.356 | 0.306 | 0.265 | 0.205 | 0.162 | 0.132 | 0.092 | 0.052 |
| [CdHS]+.(H2O)30_Sp | 0.257 | 0.222 | 0.193 | 0.150 | 0.120 | 0.098 | 0.068 | 0.038 |
| [CdCl(H2O)5]+.(H2O)30-Sp | 0.314 | 0.270 | 0.234 | 0.181 | 0.144 | 0.117 | 0.082 | 0.046 |
| [CdCl2(H2O)2].(H2O)30-Sp | 0.121 | 0.105 | 0.092 | 0.072 | 0.058 | 0.047 | 0.033 | 0.019 |
In general, the Cd isotope fractionations between aqueous solutions and Greenockite are in the range of 0.433–0.083 (100°C). Under the same condition, these factors between solutions and Sphalerite are in the range of 0.349–0.072. Zhu et al. reported that the δ114/110Cd of light sphalerite and dark sphalerite are 0.43 to 0.70 per mil (‰) and 0.06 to 0.46‰, respectively (Zhu et al., 2017). Our results can provide a theoretical basis for studying the mechanism of isotope enrichment in the mineralization process. The causes and consequences of cadmium isotope fractionation in a large hydrothermal system at the Tianbaoshan Zn–Pb–Cd deposit has been investigated by previous studies (Zhu et al., 2016). As the main host of Cd, sphalerite in their study area has δ114/110Cd ranging from 0.01 to 0.57‰. Ripperger and Rehkämper (2007) reported that Cadmium-rich intermediate water from the North Pacific has isotope composition of δ114/110Cd is about 3.2. At the temperature range 100–300°C, the Cd isotope fractionation between [Cd(H2O)6]2+.(H2O)30 and Sphalerite ranging from 0.349 to 0.155‰ by our calculations. This indicates that isotopic fractionation during the deposition/growth of sediments from seawater and ore-forming fluids is not completely affected by the equilibrium process. This conclusion is consistent with previous studies that Cd isotopic compositions in ore-forming fluids are heterogeneous and 114Cd isotope enrichment in early precipitated sphalerite (Zhu et al., 2017). Data provided in this study could be treated as isotope fractionation factors between the sedimentary phase and the ore-forming fluid when isotope exchange reaction reaches equilibrium. For the study of Zhu et al. (2016), assuming that the dominant species of ore-forming fluid is [Cd(H2O)6]2+.(H2O)30 and the isotope exchange have been reached equilibrium, the isotope composition of ore-forming fluid could be gotten by working backwards. Other isotope fractionation factors obtained by this method have similar effects. Therefore, these parameters are very important for the reconstruction of the paleo-metallogenic fluid environment.
Equilibrium Cd isotope fractionation of different solution pairsThe Cd isotope fractionation factors between the main complexes in aqueous solutions have also been systematically calculated. And isotope fractionation factors of the solution pairs of [Cd(H2O)4]2+(aq) and [Cd(H2O)6]2+(aq), [Cd(OH)]+(aq) and [Cd(HS)]+(aq), [Cd(H2O)6]2+(aq) and [Cd(NO3)2(H2O)4](aq), [CdCl(H2O)5]+(aq) and [CdCl3(H2O)]–(aq) have been given (Fig. 7C). At 100°C, the Cd fractionation factors of these four solution pairs are 0.062, 0.166, 0.144 and 0.181 respectively (Table 8). Our calculations show that Cd(H2O)4]2+(aq) is slightly enriched with 114Cd relative to [Cd(H2O)6]2+(aq). Cd(H2O)4]2+(aq) is tetradentate and has stronger Cd-O bond, so it enriched in 114Cd relative to [Cd(H2O)6]2+(aq). This is different from previous study (Zhao et al., 2021). Their results show that [Cd(H2O)6]2+(aq) is enriched in 114Cd relative to Cd(H2O)4]2+(aq). If the solvation effect is not taken into account, our results also show that [Cd(H2O)6]2+(aq) is enriched in heavy isotopes relative to [Cd(H2O)4]2+(aq).
| Pairs | Temperature (°C) | |||||||
|---|---|---|---|---|---|---|---|---|
| 0 | 25 | 50 | 100 | 150 | 200 | 300 | 500 | |
| [Cd(H2O)4]2+.(H2O)30-[Cd(H2O)6]2+.(H2O)30 | 0.107 | 0.092 | 0.080 | 0.062 | 0.049 | 0.040 | 0.027 | 0.015 |
| [Cd(OH)2(H2O)4].(H2O)30-[CdHS]+.(H2O)30 | 0.289 | 0.248 | 0.215 | 0.166 | 0.132 | 0.107 | 0.074 | 0.042 |
| [Cd(H2O)6]2+.(H2O)30-[Cd(NO3)2(H2O)4].(H2O)30 | 0.258 | 0.220 | 0.189 | 0.144 | 0.113 | 0.091 | 0.063 | 0.035 |
| [CdCl(H2O)5]+.(H2O)30-[CdCl3(H2O)]–.(H2O)30 | 0.317 | 0.272 | 0.235 | 0.181 | 0.143 | 0.116 | 0.080 | 0.045 |
When only the nearest coordination sphere around Cd2+ is considered, the 103ln(RPFR)s (25°C) of [Cd(H2O)6]2+(aq) and [Cd(H2O)4]2+(aq) are 2.175 and 2.131 respectively. That is, [Cd(H2O)6]2+(aq) is slightly enriched in 114Cd relative to [Cd(H2O)4]2+(aq). However, when we consider the solvation effect for [Cd(H2O)6]2+ and [Cd(H2O)4]2+, when the (H2O)6, (H2O)12, (H2O)18, (H2O)24 and (H2O)30 are added to the outer layer of [Cd(H2O)6]2+ and [Cd(H2O)4]2+, all the average results of four parallel calculations of (H2O)6, (H2O)12, (H2O)18, (H2O)24 and (H2O)30 show that [Cd(H2O)4]2+(aq) is enriched in 114Cd relative to [Cd(H2O)6]2+(aq). At 25°C, the 103ln(RPFR)s of these two species with 6, 12, 18, 24 and 30 water molecules in their outer layers (the average of four parallel calculations) are 2.406, 2.396, 2.353, 2.293 and 2.359, 2.441, 2.487, 2.475, 2.489 and 2.452 for [Cd(H2O)6]2+(aq) and [Cd(H2O)4]2+(aq) respectively. Therefore, we conclude that [Cd(H2O)4]2+(aq) is enriched with heavy Cd isotopes relative to [Cd(H2O)6]2+(aq) when considering solvation effects.
In this work, Cd isotope fractionation between different phases was systematically studied. The results show that Cd isotopic fractionation between different Cd-bearing species is widespread. Compared with solid mineral Cd species, Cd-bearing aqueous solutions are enriched in 114Cd. In addition, when the types of inorganic ligands changed, there are also obvious 114Cd change among these Cd-bearing solutions. [Cd(H2O)4]2+(aq) is enriched in 114Cd compared to [Cd(H2O)6]2+(aq). In nature, a series of geochemical processes can affect the composition of Cd isotope. As a moderate volatile element, we also studied a range of typical simple Cd-bearing compounds. There are also obvious Cd isotope differences between these compounds. The data obtained in this investigation can provide theoretical supports for various geochemical processes such as surficial geochemistry process, mineralization process and evaporation process. Also, it could give some useful restrictions on the Cd cycle. It is expected that these data will be helpful for the future study of Cd isotopes.
This work has been financially supported by Chinese National Science Fund Projects (Nos. 42063007 and 41663007). The authors also thank the financial support from the Science and Technology Program of Guizhou (Qian Ke He platform for talents [2017]5726–58, Qianshixinmiao[2021]23). We also appreciate the experimental convenience provided by Guizhou Normal University/State Engineering Technology Institute for Karst Desertification.
