{'fraction_non_alphanumeric': 0.030921820303383897, 'fraction_numerical': 0.020420070011668612, 'mean_word_length': 5.7254901960784315, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Mass Dependence of Equilibrium Oxygen Isotope Fractionation in Carbonate, Nitrate, Oxide, Perchlorate, Phosphate, Silicate, and Sulfate Minerals

Variation in both 18O/16O and 17O/16O ratios in natural materials can now be measured with unprecedented precision, with a broad range of potential geochemical applications. In this chapter, equilibrium 18O/16O and 17O/16O fractionation factors are calculated for a selection of minerals and molecules, using first-principles density functional theory models to estimate vibrational frequencies, with a particular focus on investigating the potential for detectable signatures of high-temperature equilibrium processes. Reduced partition function ratios as well as mass-fractionation exponents are tabulated versus temperature. The results are compared with previous theoretical studies, laboratory experiments, and field-based calibrations. Effects of nuclear field shift isotope fractionation and double-well potential anharmonicity on the relationship between 18O/16O and 17O/16O are also investigated. The estimated field shift effect is much smaller than mass-dependent fractionation, yielding no more than 1 per meg in measured ∆′17O at 25 oC, and correspondingly less at higher temperatures. Anharmonic vibration in a double-well potential, such as might be found in a Si–O–Si linkage in polymerized silicates, also does not seem to generate dramatic ∆′’17O signatures for plausible potential shapes, and non-Born–Oppenheimer effects on ∆′17O signatures also appear to be limited. None of the studied effects appear likely to generate the negative ∆′17O anomalies observed in polymerized silicate mineral samples from high-temperature rocks on the Earth & Moon.