Chapter 1. THEORETICAL and EXPERIMENTAL ASPECTS of ISOTOPIC FRACTIONATION

Statistico-mechanical methods require approximations and assumptions for calculations involving solids and liquids.

“As pointed out by Hulston (1978) and O'Neil (1986), the statistico-mechanical methods are -ur tt t a y i itr proximations and assumptions are required for calculations involving solids and liquids.”

Oxygen isotope fractionation between crystalline phases containing oxygen is temperature-dependent at thermodynamic equilibrium because of diminishing differences in the physico-chemical properties of the isotopes 16O, 17O and 18O with increasing temperatures.

“Oxygen isotope fractionation between crystalline phases containing oxygen (such as silicate, carbonate and oxides) is temperature-dependent at thermodynamic equilibrium”

Experimental calibrations of stable isotope fractionation factors are generally considered essential for geothermometric and geochemical applications.

“experimental calibrations of stable isotope fractionation factors are generally considered essential for geothermetric and geochemical applications (e.g., O'Neil, 1986; Clayton and Kieffer, 1991; Chacko et al ., 2001; Zeebe, 2009).”

The statistico-mechanics method is only considered strictly valid for ideal gases; further approximations and assumptions are required for calculations involving solids and liquids.

“As a result, the statistico-mechanics method is only considered strictly valid for ideal gases; further approximations and assumptions are required for calculations involving solids and liquids (Hulston, 1978; O'Neil, 1986).”

Statistico-mechanics calculations were generally considered unsuccessful for crystalline minerals.

“As a consequence, such calculations were generally considered unsuccessful to crystalline minerals (O'Neil, 1986).”

The SM calculations of stable isotope fractionation factors are not limited for solid phases as previously admonished by O'Neil (1986).

“This demonstrates that the SM calculations of stable isotope fractionation factors are not limited for solid phases as previously admonished by O'Neil (1986).”

Resting on assumptions whose validity remains to be independently demonstrated is also common to all calculations by different varieties of the statistico-mechanics method and quantum-chemistry method.

“This is also common from all calculations by different varieties of the statistico-mechanics method (Hulston, 1978; O'Neil, 1986) and quantum-chemistry method (Schauble et al ., 2006; Zeebe, 2009).”

If heavy carbonate ions move more sluggishly than light ones, then a dolomite crystal that grew at the high growth rate corresponding to times t4 and T should have lower δ18O and δ13C values than another that had grown at a lower rate.

“If heavy carbonate ions, 13 C 18 O 3 2Ϫ , move more sluggishly than light ones, 12 C 16 O 3 2Ϫ (O'Neil, 1986, p. 2), then we can expect that a dolomite crystal that grew at the high growth rate corresponding to times t 4 and T in figure 5A should have lower ␦ 18 O and ␦ 13 C values than another that had grown at a lower rate, say, that between times t 1 and t 4 .”