Temperature dependencies of the oxygen, carbon, magnesium, and calcium β-factors (from 0 to 1500°C with a step of 10°C) have been determined for Ca–Mg carbonates (calcite, magnesite, dolomite, aragonite) by the “frozen phonon” approach of the density functional theory within the harmonic and quasi-harmonic approximations. For calcite, considering the Ca–Mg isomorphism, the temperature dependence of oxygen and carbon β-factors of isotope fractionation is described by the following equations: 103ln β18Ocal = (11.61731 + Δa)x – (0.35444 + Δb)x2 + (0.00908 + Δc)x3, 103ln β13Ccal = (24.74146 + Δa)x – (1.08996 + Δb)x2 + (0.03178 + Δc)x3, where x = 106/T2(K–2); Δa, Δb and Δc are the shifts of the corresponding polynomial coefficients depending on the magnesium content, calculated separately for 18O/16O and 13C/12C. The effect of pressure on oxygen and carbon β-factors for carbonates is calculated. Estimates obtained within the quasi-harmonic approximation do not exceed 1‰ in pressure intervals typical to the Earth’s crust conditions.

New 18 O/ 16 O β-factors have been calibrated against temperature for titanite (considering the principal isomorphic substitutions Al + F ⇔ Ti + O, Ti + O ⇔ Al + OH, Ti + O ⇔ Fe 3+ + OH) and ilmenite (accounting for Fe ⇔ Mg substitution) for the first time using the frozen-phonon approach of the density functional theory. The equilibrium oxygen isotope fractionation factors between titanite (CaTiSiO 5 ), ilmenite (FeTiO 3 ), and rutile (TiO 2 ) are expressed as: 1000 ln α ttn–ilm = 1000 ln β ttn – 1000 ln β ilm = 1.96836 x – 0.10514 x 2 + 0.00319 x 3 , 1000 ln α ttn–rt = 1000 ln β ttn – 1000 ln β rt = 1.80155 x – 0.09262 x 2 + 0.00288 x 3 , x = 10 6 / T 2 (K –2 ). The results can be applied to geothermometry, particularly in calc–silicate and calc–alkaline rocks of magmatic, metamorphic, and metasomatic origins.

The chemical compositions of Phanerozoic basalts of all known geodynamic settings (mid-ocean ridges, oceanic plateaus, oceanic islands, island arcs, fore-arc and back-arc basins, continental rifts, large igneous provinces) are compared with Archean basalts, including basalts of greenstone belts and high-grade gneiss complexes. Linear discriminant analysis has shown that the Archean basalts differ significantly from Phanerozoic basalts in terms of the content of the least mobile major and trace elements. In this regard, the geochemical systematics of Phanerozoic basalts in most cases cannot be used to reconstruct the geodynamic settings of Archean basalts. The results obtained are illustrated by the example of the Mesoarchean basalts of the Olondo fragment of the Tokko–Khani greenstone belt.

The β-factor dependences on temperature upon 18O/16O substitution have been originally deduced in andalusite, sillimanite and kyanite accounting for pressure effect: 1000lnβand(18O/16O) = 10.66466x – 0.19330x2 + 0.00282x3 + P(0.12748x – 0.00289x2) 1000lnβsil(18O/16O) = 10.51480x – 0.17485x2 + 0.001406x3 + P(0.12124x – 0.00286x2) 1000lnβky(18O/16O) = 10.14019x – 0.07573x2 + 0.00550x3 + P(0.09907x – 0.00206x2), x = 106/T2 (K)–2, P is pressure (GPa). The relations can be used in isotope geothermometry. Pressure produces an increase of the β-factors and consequently, δ18O$$_{{{\text{A}}{{{\text{l}}}_{{\text{2}}}}{\text{Si}}{{{\text{O}}}_{{\text{5}}}}}}$$ up to ≈0.5‰ in conditions of the “cold” subduction (at extremely low dT/dP gradients).

На основе теории функционала плотности определены зависимости от температуры b-факторов фракционирования при замещениях 18 O/ 16 O в полиморфных модификациях TiO 2 : 1000lnb rt ( 18 O/ 16 O) = 6,93039 x - 0,08158 x 2 + 0,00116 x 3 + 0,08305* P , 1000lnb ant ( 18 O/ 16 O) = 7,34275 x - 0,09906 x 2 + 0,00153 x 3 + 0,08027* P , 1000lnb brk ( 18 O/ 16 O) = 7,19088 x - 0,09157 x 2 + 0,00139 x 3 + 0,07601* P , x = 10 6 / T (K) 2 , P - давление (GPa). Полученные зависимости можно применять в изотопной геотермометрии в сочетании с β-факторами сосуществующих фаз.

Temperature relations of b-factors for 18O/16O substitutions in TiO2 polymorphs have been determined using the density functional theory (DFT): 1000lnbrt(18O/16O) = 6,93039x - 0,08158x2 + 0,00116x3 + 0,08305*P, 1000lnbant(18O/16O) = 7,34275x - 0,09906x2 + 0,00153x3 + 0,08027*P, 1000lnbbrk(18O/16O) = 7,19088x - 009157x2 + 0,00139x3 + 0,07601*P, x = 106/T(K)2, P - pressure (GPa). The relations can be applied for isotope thermometry if combined with -factors of coexisting phases.

Zircon β-factors have been calibrated against temperature for isotopic substitutions of 18O/16O and 30Si/28Si. Calculations were performed using the density functional theory (DFT) with the “frozen phonon” approach. The deduced geometric parameters of the zircon unit cell, and the phonon frequencies calculated, agree well with the experimental data. The results are expressed by the cubic polynomials on x = 106/T(K)2: 1000lnβzrn(18O/16O) = 9.83055x – 0.19499x2 + 0.00388x3; 1000lnβzrn(30Si/28Si) = 7.89907x – 0.17978x2 + 0.00377x3. The expressions deduced can be utilized to construct geothermometers if combined with β-factors of coexisting phases. New calibrations of quartz-zircon are given. The new values of 1000lnβzrn and the estimated isotope fractionation factors between quartz and zircon (1000lnβqtz–1000lnβzrn) deviate considerably from previously used experimental, empirical, and semi-empirical calibration of the isotopic equilibrium.

Equilibrium oxygen isotope (O-18/O-16) fractionations (beta-factors) for corundum are predicted from first principles using the "frozen phonon" technique within the density functional theory (DFT). Calculations of the phonon frequencies and the isotopic frequency shifts were consequently performed over 1, 3, 8, and 27 wave vectors using the supercell approach, with the Gaussian-type all-electron basis sets and hybrid functional B3LYP. The presented phonon frequencies agree with experimental infra-red and Raman data. The results of beta-factor calculations are presented in terms of the logarithmic functions, 1000ln beta(crn), computed for temperatures from 0 to 2000 degrees C with a computational step of 20 degrees C and then fitted by the conventional cubic polynomial Ax + Bx(2) + Cx(3), with x = 10(6)/T(K)(2). The following expressions corrected for incomplete Brillouin-zone sampling quantify oxygen isotope fractionation of corundum. Within the harmonic approximation: 1000 ln beta(crn) = 9.2657x - 0.12110x(2) + 0.00175x(3) (0 < T degrees C < 2000).Accounting for thermal expansion (the quasi-harmonic approximation): 1000 ln beta(crn) = 9.03363x - 0.08912x(2) + 0.00036x(3) (0 < T degrees C < 1570 ) The pressure effect on corundum beta-factors is found to be negligible below ca. 25 kbar at temperatures exceeding 500 degrees C. At ultra-high pressures the correction can be made using the expression (partial derivative(1000ln beta)/partial derivative P)(T) (kbar) = 0.00967 x 10 (6)/T(K)(2).

Discriminant analysis was performed for representative sets of igneous rocks with adakitic geochemical signatures (granitoids of Archean tonalite–trondhjemite–granodiorite suites, island-arc adakites, and adakites and adakitic granitoids of collisional to postcollisional geodynamic settings). It was shown that the granitoids of Archean tonalite–trondhjemite–granodiorite suites are significantly different from islandarc adakites, as well as from collisional to postcollisional adakites and adakitic granitoids. The following discriminant function was proposed for the geodynamic classification of island arc and collisional-postcollisional adakites and adakitic granitoids on the basis of chemical composition: DF3 =–1.69324TiO2–0.25537Al2O3–0.21269FeO* + 0.06076MgO–0.09796CaO + 0.47377Na2O + 0.29270K2O + 3.57821P2O5 + 0.00431Rb + 0.00036Sr + 0.03119Y + 0.00006Zr + 0.01088Nb–0.00048Ba + 0.01366La + 0.0004Ce + 0.02319Nd–0.18584Sm + 1.29135Eu–0.62229Gd + 0.3819Dy + 2.06583Er–2.62769Yb + 1.6464.

The isotope fractionation β-factors have been determined for hydroxyapatite, fluorapatite, and carbon–apatite upon 18 O/ 16 O, 13 C/ 12 C, and 44 Ca/ 40 Ca substitutions depending on the temperature. Calculations were performed based on density functional theory (DFT). The results are expressed in terms of cubic polynomials against x = 10 6 / T (K) 2 and can be utilized as geothermometers if combined with β-factors of the coexisting phases. The new values of β-factors completely supersede the conventional semi-empirical (estimated by the method of increments) calibrations of isotopic equilibria involving apatite.

The β-factors of corundum were estimated on the basis of DFT calculations of vibrational frequency changes due to 16O–18O isotope substitution in a harmonic approximation using an all-electron Gaussian-type basis set and the B3LYP hybrid functional (the CRYSTAL program). Calculations were performed accounting for eight phonon wave vectors within the first Brillouin zone. The results are approximated by the relation 1000ln β crn = 9.19874x–0.12326x 2 + 0.00213x 3 (x = 106/T(K)2, 400 < T(K) < 1300), which can be used in isotope geochemical studies in combination with the known temperature effects on the β-factors of other phases.

Based on the density functional theory (DFT), frequency shifts of garnet end-members upon isotope substitutions ( 18 O/ 16 O, as well as “non-traditional” stable isotopes) were calculated. According to the calculations, the temperature dependencies of fractionation factors (β-factors) suggested for garnets: 1000lnβ prp = 9.68511 x –0.19204 x 2 + 0.00567 x 3 ; 1000lnβ grs = 9.14697 x –0.15682 x 2 + 0.00412 x 3 ; 1000lnβ adr = 8.72470 x –0.15092 x 2 + 0.00402 x 3 ; 1000lnβ uvr = 8.71526 x –0.14749 x 2 + 0.00385 x 3 ; 1000lnβ sps = 9.33600 x –0.17598 x 2 + 0.00499 x 3 ; 1000lnβ alm = 9.45295 x –0.18465 x 2 + 0.00539 x 3 , x = 10 6 / T (K) 2 . The values obtained combined with with the known values of β-factors may be applied in geothermometry of garnet-bearing rocks.

The Thala Hills area occupies a key position in Gondwanaland reconstructions near the India-Sri Lanka-Antarctica junction. We present U-Pb zircon isotopic age determinations from SHRIMP II obtained on four granite gneiss samples. Three high-temperature tectonomagmatic episodes may be distinguished in the study area at c. 980-970, c. 780-720 and c. 545530 Ma. The c. 980-970 Ma event corresponds to the Rayner Structural Episode that affected East Antarctica, including the Sor Rondane Mountains to the west and Kemp Land to the east. The c. 780-720 Ma episode included two events at approximately 780 Ma (high-grade anatexis) and 720 Ma (syntectonic granitoid emplacement), and was roughly coeval with tectonomagmatic events in Dronning Maud Land of East Antarctica, as well as in other Gondwanaland regions, such as Madagascar, Sri Lanka and eastern Africa. The c. 780-720 Ma episode may be correlated with the East African Orogeny. These correlations argue for a similar geological evolution and conjugate position for Dronning Maud Land and Enderby Land despite a postulated Cambrian Lutzow-Holm Bay suture separating them. The Cambrian (c. 545-530 Ma) episode was manifested by high-grade anatexis that confirms previously identified late Neoproterozoic-Cambrian tectonothermal activities in the study area.

Trace element compositions of zircons and whole-rock chemical compositions obtained by previous studies.