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Table 3 Isotopic equilibrium fractionation between molecular clusters and their corresponding aqueous solutions

From: Improved volume variable cluster model method for crystal-lattice optimization: effect on isotope fractionation factor

Cluster

Calculated bond length (Ã…)

Experimental bond length (Ã…)

1000lnβ (cluster, 298 K, ‰)

1000lnβ (aquocomplex, 298 K, ‰)

Δ cluster-aquocomplex

(298 K, ‰)

Si–Qtz

1.63, 1.62a, 1.61b

1.61c, 1.62d

73.65

71.63

2.02 (Si isotopes)

O–Qtz

1.63

1.61c

110.31

74.26

36.05 (O isotopes)

Zn–Al LDH

2.10

2.08e

4.87

3.75

1.12 (Zn isotopes)

Cd–Cal

2.28

2.30f

2.62

\(2.88^{{\text{g}}}\)

 − 0.26 (Cd isotopes)

  1. aSi–O bond length (α–quartz, Ab initio LDF theory, Purton et al. [64])
  2. bSi–O bond length (quartz, DFT calculations, He and Liu [22])
  3. cSi–O bond length (quartz, X-ray diffraction, Hazen et al. [39])
  4. dSi–O bond length (quartz, X-ray diffraction at 848 K, Kihara [48])
  5. eZn–O bond length (X-ray diffraction and EXAFS, Gou et al. [3])
  6. fCd–O bond length (EXAFS, Bailey et al. [65])
  7. gDFT calculations (He et al. [25])