Vertical stability and the Brunt-Väisäla frequency of deep natural waters by the example of Lake Baikal,Lake Tanganyika,and the World Ocean

Theoretical analysis, calculations, and comparison with the results of observations in Lake Baikal, Lake Tanganyika, and the World Ocean are performed for the vertical stability E and the Brunt-Väisäla frequency N in the form of N ² with regard to all components (at the constant temperature T and the salinity S, the common adiabatic form at T, S Const). The adiabatic stability E _ad and the Väisäla frequency N in the form of N _ad ² are always positive; at a change from the inverse to the direct temperature stratification, they have deep minimums reaching 10^?16 m^?1 and 10^?15 s^?2 and less; the minimums have the form of a special point, a reversal point of the first kind called a “cusp.” The reality of these reversal points is confirmed by the analysis of the investigation procedure, comparison with the results of previous theoretical (Sherstyankin, et al., 2007), and experimental (observations in Baikal, Shimaraev et al., 1994) works. The features of vertical profiles of E _ad , E andN _ad ² , N ², as well as the layers where the Brunt-Väisäla frequency is less than the inertial frequency, are studied. The analysis with regard to all components of the stability E _ad and the Brunt-Väisäla frequency N makes a great contribution to understanding of mixing processes in theoretical and experimental investigations; it is valid in all reservoirs of the Earth with inverse and direct temperature stratification, including Lake Baikal, Lake Tanganyika, and the World Ocean.     

Physicochemical model for the crystallization of rocks of the calc-alkaline series

The Al-rich region of the CaO-MgO-Al₂O₃-SiO₂ system was experimentally studied at pressures of 1.0–2.8 GPa and temperatures of 1300–1535°C. The slopes of the lines of the monovariant reactions An + Sp = Cpx + Cor + (Ga) and L = Cpx + Ga + Cor + Sp and the compositions of the phases involved in these reactions are determined. The results are utilized in the topological analysis of the aluminous region of the CaO-MgO-Al₂O₃-SiO₂ system. On this basis, the principal structure of the phase diagram is analyzed, and a phase diagram is constructed for the junction region of the quaternary system and the CaO-Al₂O₃-SiO₂ ternary system. A continuous series of the monovariant eutectic: L = Cpx + Opx + Fo + An, L = Cpx + Opx + An + Sp, L = Cpx + (Ga) + An + Sp, L = Cpx + Cor + (Ga) + An, L = An + Ga + Cpx + Ky and L = Ga + Cpx + Ky + Qz is examined within the pressure range from atmospheric to 3.0 GPa and higher. Analogous “telescoped” eutectic series are of fundamental character for interpreting the evolution of magmatic melts. A physicochemical model is suggested for the evolution of magmatic melts that produce rocks of the calc-alkaline series, with this model underlain by the fact that a change in the composition of magmatic melt at a pressure decrease should correspond to the minimum melting temperatures, i.e., to melts in the fundamental series of eutectic reactions. The comparison of our physicochemical model and rocks of the calc-alkaline series shows that the compositions of rocks of the calc-alkaline series are close to the compositions determined for the eutectic equilibria, and the mineralogical composition of xenoliths and megacrysts in volcanic and dike varieties of the rocks are similar to the subsolidus phases of the established fundamental eutectic system.     

Distribution of REE,LILE, and HFSE between biotite,feldspar, and the melt in the granulite facies migmatite,nimnyr block,Aldan shield

The behavior of trace elements under conditions of partial melting of granitoid rocks has been studied. The element’s partition coefficients between minerals and the melt D_i^min/melt depends, in the first place, on the composition of the primary melt. In biotite the HREE D_i are a little below 1, while those of LREE, especially D_i for Ce, are 1–3 orders of magnitude less. This leads to an efficient differentiation of REEs in anatexic melts especially when biotite is the main mineral phase of restite. On the contrary, there are feldspars, the D_i of which cannot provide such a magnitude of differentiation. Unlike garnets and pyroxenes, whose stability in restite permits enrichment of anatexic melts produced in migmatization zones with Nb, Ti, and Cr, the presence of biotite in restite causes depletion of melts with those elements as well as with Rb. Feldspars, under conditions of their fractional crystallization or during differentiation of an anatexic melt, deplete the latter with Sr, Ba, and Rb, but enrich it with Nb, Ti, Cr, Y, Zr, and V.     

Separation of chemical elements in the atmospheres of CP stars under the action of light induced drift

A mechanism for the separation of chemical elements and isotopes in the atmospheres of chemically peculiar (CP) stars due to light-induced drift (LID) of ions is discussed. The efficiency of separation due to LID is proportional to the relative difference of the transport frequencies for collisions of ions of heavy elements located in the excited state (collision frequency ν _e ) and ground state (collision frequency ν _g ) with neutral buffer particles (hydrogen and helium), (ν _e ? ν _g )/ν _g . The known interaction potentials are used to numerically compute the relative difference (ν _e ^H ? ν _g ^H )/νg H for collisions between the ions Be⁺, Mg⁺, Ca⁺, Sr⁺, Cd⁺, Ba⁺, Al⁺, and C⁺ and hydrogen atoms. These computations show that, at the temperatures characteristic of the atmospheres of CP stars, T = 7000?20 000 K, values of |ν _e ^H ?ν _g ^H |/ν _g ^H ≈ 0.1?0.4 are obtained. With such relative differences in the transport collision frequencies, the LID rate of ions in the atmospheres of coolCP stars (T < 10000 K) can reach ~0.1 cm/s,which exceeds the drift rate due to light pressure by an order of magnitude. This means that, under these conditions, the separation of chemical elements under the action of LID of ions could be an order of magnitude more efficient than separation due to light pressure. Roughly the same manifestations of LID and light pressure are also expected in the atmospheres of hotter stars (20 000 > T > 10 000 K). LID of heavy ions is manifest only weakly in very hot stars (T > 20 000 K).     

Fractionation of Rare-Earth Elements in the Processes of Hydrothermal Ore Formation

The data on the distribution of elements in the Pb–Zn cross-section of the Gatsirovskaya vein (the Upper Zgid deposit, North Ossetia, Russia) have shown that the spectra of rare-earth elements (REEs) changed significantly in the ore samples during the vein formation. The sharp growth of the La_N/Yb_N, La_N/Nd_N, Gd_N/Ho_N, and Gd_N/Yb_N ratios is confined to the vein intervals, where the maximum amount of ore components is deposited. The comparison of the REE spectra of ores to the characteristics of the spectra of the rocks surrounding the vein and the host rocks suggests that the vein material deposited from the solutions in which the REE ratio changed with time. REE fractionation occurred due to the mobilization of components by hydrothermal solutions during their interaction with the Paleozoic host granites.     

Radial pulsations of helium stars and a model for BX CIR

The results of hydrodynamical calculations of radially pulsating helium stars with masses 0.5M_⊙≤M≤0.9M_⊙, bolometric luminosities 600L_⊙≤5×10³L_⊙, and effective temperatures 1.5×10⁴ K≤T_eff≤3.5×10⁴ K are presented. The pulsation instability of these stars is due to the effects of ionization of iron-group elements in layers with temperatures T～2×10⁵ K. The calculations were carried out using opacities for the relative mass abundances of hydrogen and heavy elements X=0 and Z=0.01, 0.015, and 0.02. Approximate formulas for the pulsation constant Q over the entire range of pulsation instability of the hot helium stars in terms of the mass M, radius R, effective temperature T_eff, and heavy-element abundance Z are derived. The instability of BX Cir to radial pulsations with the observed period Π=0.1066 d occurs only for a mass M≥0.55M_⊙, effective temperature T_eff≥23000 K, and heavy-element abundance Z≥0.015. The allowed mass of BX Cir is in the range 0.55M_⊙≤M≤0.8M_⊙, which corresponds to luminosities 800L_⊙≤M≤1400L_⊙ and mean radii 1.7R_⊙?R?2.1R_⊙.     

Devonian volcanics in the Voronezh Crystalline Massif,East European Platform: Evolution of the melts and characteristics of crustal contamination

The rift system of the Dnieper–Donets trough (DDT) is the largest magmatic area in the East European Platform. Basalts of the Voronezh Crystalline Massif (VCM) are spatially constrained to the eastern shoulder of DDT and occur far away (at a distance of 150–200 km) from the rift axis. The rocks are hosted in the Paleoproterozoic Vorontsovskii terrane and are grouped in a few fields within an area of 200 × 100 km. Basalts at most of the fields were erupted at the boundary between mid- and late Frasnian time in the Late Devonian and can be studied exclusively in core material recovered by boreholes. Newly obtained mineralogical, geochemical, and isotopic-geochemical data show that the Devonian volcanic rocks in VCM are tholeiites (Bas) and basaltic andesites/andesites (ABas). The geological section was examined most exhaustively in the Novokhopersk area (Borehole 175). The bottom of the vertical section is made up of basaltic andesites and andesites (ABas) (thickness 34 m), which rest on an eroded surface of late Frasnian sandstones. The rocks are overlain by a thin (8 m thick) tholeiite sheet (Bas2), which gives way to ABas (13 m) upsection. The top portion of the vertical section is composed of tholeiites with petrography and geochemical evidence of crustal contamination (Bas1) (apparent thickness 5 m). Geochemical parameters of Bas (mg# 42–52 at SiO₂ 47–51 wt %) are typical of continental tholeiites. The rocks have (⁸⁷Sr/⁸⁶Sr)₀ = 0.7043–0.7048 and ε_Nd(372) = 2.1–3.5. ABas (mg# 28–31 at SiO₂ 52–60 wt %) are enriched in Y (48 ppm), and possess Nb/Nb* = 0.7–0.8 and high Zn/Cu = 1.9–2.3. The rocks have (⁸⁷Sr/⁸⁶Sr)₀ = 0.7034–0.7048 and Nd–ε_Nd(372) = 0.1. Some portions of Bas melts assimilated the upper crustal material, which was similar to Paleoproterozoic granites, and ABas are contaminated in the lower crust with derivatives of Early Cambrian alkaline mafic melts. Petrographic data and simulations of fractional crystallization show that olivine and high-Mg clinopyroxene were the first to crystallize from the melt. After this, clinopyroxene and plagioclase simultaneously crystallized at temperatures from 1070 to 1020°C in Bas and at 1040–900°C at f _O2 below QFM + 1 in ABas. The source of ABas was likely a network of hornblendite or amphibole pyroxenite veins in peridotite in the lithospheric mantle or amphibolized peridotite cumulate in an underplating zone; and Bas were derived from spinel peridotites of an asthenospheric diapir. The setting of the basalts relative to the DDT axis and the asymmetric zoning of magmatism in DDT (with kimberlites and other deep rocks constrained to the western shoulder and tholeiites occurring in the axial part of the rift and its eastern shoulder) can be explained by the model of an asymmetric rift structure with a translithospheric detachment gently dipping beneath VCM.     

Nanodiamond Formation at the Lithogenesis and Low-Stages of Regional Metamorphism

Samples of gilsonite from Adzharia, anthraxolite and graphite of coal from Taimyr, shungite from Karelia, and anthracite from Donbass are studied using Raman spectroscopy. Peaks at 1600 cm^?1, indicating the presence of nanographite, are recorded in all samples. The anthracite sample from Donbass, 1330 cm^?1, corresponds to the sp³-line of carbon hybridization conforming to a nanodiamond. It is concluded that in nature diamonds can be formed at late stages of lithogenesis (catagensis, metagenesis), and for coals, it can occur at the zeolite stage of regional metamorphism of rocks, before the green schist stage.     

The Sr,Nd, and Hf isotopic geochemistry of rocks of the gabbro–diorite–tonalite association from the Eastern Segment of the Middle Urals as an indicator of the age of the continental crust in this area

According to isotopic analysis of rocks of the Reft gabbro–diorite–tonalite complex (Middle Urals), gabbro and related diorite and dikes and vein-shaped bodies of plagiogranitoids, crosscutting gabbro, are similar to the depleted mantle substance in ε_Nd(T) = 8.6–9.7 and ε_Hf(T) = 15.9–17.9. Their model Hf ages are correlated with the time of crystallization. Here, the tonalites and quartz diorites constituting most of the Reft massif are characterized by lower values: ε_Nd(T) = 3.7–6.0, ε_Hf(T) = 11.1–12.7, and T _DM values significantly exceeding the age datings. This is evidence that Neoproterozoic crustal rocks were a source of parental magma for these rocks. The primary ⁸⁷Sr/⁸⁶Sr ratio in rocks of both groups is highly variable (0.70348–0.70495). The data obtained allow us to reach the conclusion that the Reft gabbro–diorite–tonalite complex was formed as a result of nearly synchronous processes occurring in the crust and the mantle within a limited area.     

Copper Adsorption by Chernozem Soils and Parent Rocks in Southern Russia

Laboratory data in Cu²⁺ adsorption by chernozems and parent rocks in Rostov region show that adsorption isotherms can be approximated by the Langmuir equation, whose parameters (K_l and C_∞) were calculated for all of the samples. The values of C_∞ show a strong negative correlation with the values of cationexchange capacity (CEC) (r =–0.88 at Р = 0.95), and K_l is correlated with the content of physical clay (particles <0.01 mm) (r = 0.78) and with clay (particles <0.001 mm) content in ordinary chernozem and southern chernozems of various particle size distribution (r = 0.80). Even stronger correlations were detected between these parameters in southern chernozems (r = 0.89 for the physical clay (PC) and r = 0.91 for the silt). However, none of the samples displays a significant correlation of C_∞ and K_l with the contents of physical clay and silt. This led us to conclude that the composition of the samples, for example, their organic matter, can affect Cu²⁺ adsorption by the soils and parent rocks. Acidification mechanisms of the equilibrium solutions during the Cu²⁺ adsorption by soils are discussed, as also are the reasons for the absence of balance between Cu²⁺ adsorbed by soils and exchangeable cations transferred into solution. Analysis of the fine structures of the XANES and EXAFS spectra suggests that Cu²⁺ can form coordinated chelate complex compounds with humic acids (HA) of soils and can substitute Al³⁺ at octahedral sites when interacting with clay minerals in soils.     

A Refined Model for Solid Particle Rock Erosion

A procedure for the estimation of distribution parameters of a Weibull distribution model K₁ = f(K_Ic^12/4/σ_C^23/4) for solid particle erosion, as recently suggested in Rock Mech Rock Eng, doi: 10.1007/s00603-014-0658-x, 2014, is derived. The procedure is based on examinations of elastic–plastically responding rocks (rhyolite, granite) and plastically responding rocks (limestone, schist). The types of response are quantified through SEM inspections of eroded surfaces. Quantitative numbers for the distribution parameter K₁ are calculated for 30 rock materials, which cover a wide range of mechanical properties. The ranking according to the parameter K₁ is related to qualitative rock classification schemes. A modified proposal for the erosion of schist due to solid particle impingement at normal incidence is introduced.     

The Bajocian–Bathonian plant fossil from the Hojedk formation,Lenjan section,Kerman, Iran

The Jurassic successions represent a wide distribution in North of the Kerman province. These successions include Ab-Haji, Badamu, and Hojedk formations. The Hojedk Formation contains the plant fossils. The Lenjan section is one of the suitable areas for paleontological studies on the Hojedk Formation. The study section is mostly composed of green sandstone and shale with several interbedded coal veins with different thicknesses. The thickness of the Hojedk Formation is about 200 m in the Lenjan section. In this study, seven genera and 13 species of macro plant fossils were identified and described, including Nilssonia undulata, Nilssonia bozorga, Nilssonia berriesi, Nilssonia sp., Klukia cf. exilis, Klukia exilis, Cladophlebis antarctica, Coniopteris lobata, Coniopteris murrayana, Elatocladus confertus, Podozamites sp., Equisetites sp., and Coniopteris sp. The Bajocian–Bathonian can be attributed to the Lenjan section based on the recognized flora.     

Atmospheric elemental abundances for the components of the multiple system ADS 11061. 41 Draconis

We obtained speckle interferometric and spectroscopic observations of the system 41 Dra during its periastron passage in 2001. The components’ lines are resolved in the spectral interval 3700–9200 Å. The observed wavelength dependence of the brightness difference between the components is used to estimate the B-V indices separately for each of the components: B-V = 0.511 for component a and B-V = 0.502 for component b. We derived improved effective temperatures of the components from their B-V values and hydrogen-line profiles. The observations can be described with the parameters for the components T _eff ^a = 6370 K, log g^a = 4.05 and T _eff ^b = 6410 K, log g^b = 4.20. The iron, carbon, nitrogen, and oxygen abundances in the atmospheres of the components are log N(Fe)^a = 7.55, log N(Fe)^b = 7.60, log N(C)^a = 8.52, log N(C)^b = 8.58, log N(N)^a = 8.05, log N(N)^b = 7.99, log N(O)^a = 8.73, log N(O)^b = 8.76.     

Photometric elements and apsidal motion of the eclipsing binary ES Lac

We have obtained high-accuracy photoelectric measurements of ES Lac, an eclipsing binary with an elliptical orbit (B9III + B9III; P = 4.459^d, e = 0.198) in 1985–2004 at the Sternberg Astronomical Institute’s Tien Shan High-Altitude Observatory. Our detailed analysis of the 19-year uniform series of measurements has yielded the first photometric elements for this system, as well as a self-consistent set of physical and geometrical parameters for the binary. The virtually identical components (M ₁ = M ₂ = 3.0 M _⊙; R ₁ = R ₂ = 4.12 R _⊙) are appreciably separated from the main sequence, and are located on the giant branch: their age is t = (3.5 ± 0.2) × 10⁸ yrs. An analysis of our observations together with previously published times of minima has enabled a considerable refinement of the period of the apsidal motion, U = 355 ± 20 years, and a first determination of the apsidal parameter reflecting the radial density distributions for the components stars: k ₂ ^obs = 0.00213(18). This value is in a good agreement with the value expected theoretically for current evolutionary models of such stars: k ₂ ^th = 0.00257(15).     

Biogeochemical characteristics of dominant gastropod species from the stony littoral of southern Baikal

The trace element composition of dominant gastropod species from the littoral of southern Baikal was investigated. Both different mollusk species and their parts (shells and soft tissues) show specific trace element characteristics. The highest Sr and Ba contents were observed in Maackia herderiana. The highest Zn, Cu, and Cd and lowest Pb contents were detected in Megalovalvata baicalensis. Choanomphalus sp. shows high Mn and Ti and very low Sr, Cu, and Cd contents. Most of Cu, Zn, and Cd and a considerable fraction of Rb, Pb, Mo, Sc, Ce, W, Ga, Y, and Th are incorporated in the gastropod bodies. The maximum concentration of U is also characteristic of the body tissues. The foot tissues of Maackia herderiana and Megalovalvata baicalensis are depleted in the majority of elements compared with their bodies. Sr and Ba are prevalent in the mollusk shells, where high Mn contents were also detected. A close relationship was observed between the chemical compositions of the gastropods, stony substrate, and bottom water. Group concentration of trace elements is common in the species investigated. Relative to the bottom water layer, the gastropod species concentrate Ti, Mn, La, Co, Y, and V and show similarly low extraction of U, W, Mo, and Cs. Compared with the bottom sediments, the mollusks accumulate Sr. In addition, Maackia herderiana and Megalovalvata baicalensis accumulate Cd and Zn. Megalovalvata baicalensis is distinguished by the ability to concentrate Cu. The following sequence is formed by the gastropods with respect to their capacity to accumulate Cd, Zn, and Cu: Megalovalvata baicalensis > Maackia herderiana > Choanomphalus sp.     

Abundances of carbon,nitrogen, oxygen,and other elements in the atmospheres of the giants 25 Mon and HR 7389

An analysis of high-resolution CCD spectra of the giant 25 Mon, which shows signs of metallicity, and the normal giant HR 7389 is presented. The derived effective temperatures, gravitational accelerations, and microturbulence velocities are T_eff = 6700 K, log g = 3.24, and ξ _t = 3.1 km/s for 25 Mon and T_eff = 6630 K, log g = 3.71, and ξ _t = 2.6 km/s for HR 7389. The abundances (log ε) of nine elements are determined: carbon, nitrogen, oxygen, sodium, silicon, calcium, iron, nickel, and barium. The derived excess carbon abundances are 0.23 dex for 25 Mon and 0.16 dex for HR 7389. 25 Mon displays a modest (0.08 dex) oxygen excess, with the oxygen excess for HR 7389 being somewhat higher (0.15 dex). The nitrogen abundance is probably no lower than the solar value for both stars. The abundances of iron, sodium, calcium (for HR 7389), barium, and nickel exceed the solar values by 0.22–0.40 dex for both stars. The highest excess (0.62 dex) is exhibited by the calcium abundance for 25 Mon. Silicon displays a nearly solar abundance in both stars—small deficits of ?0.03 dex and ?0.07 dex for 25 Mon and HR 7389, respectively. No fundamental differences in the elemental abundances were found in the atmospheres of 25 Mon and HR 7389. Based on their T_eff and log g values, as well as theoretical calculations, A. Claret estimated the masses, radii, luminosities, and ages of 25 Mon (M/M_⊙ = 2.45, log(R/R_⊙) = 0.79, log(L/L_⊙) = 1.85, t = 5.3 × 10⁸ yr) and HR 7389 (M/M_⊙ = 2.36, log(R/R_⊙) = 0.50, log(L/L_⊙) = 1.24, t = 4.6 × 10⁸ yr), and also of the stars 20 Peg (M/M_⊙ = 2.36, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.79, t = 4.9 × 10⁸ yr) and 30 LMi (M/M_⊙ = 2.47, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.88, t = 4.8 × 10⁸ yr) studied by the author earlier.     

Helium and argon isotopes in lower crustal xenoliths from the belomorian mobile belt

The isotopic systematics of noble gases (He and Ar) were studied in Neoarchean and Paleoproterozoic lower crustal xenoliths from the Belomorian mobile belt. The xenolith suite is dominated by garnet granulites (Grt + Cpx + Pl ± Opx ± Qtz ± Kfs ± Phl ± Hbl) and two-pyroxene or garnet pyroxenites (Cpx + Pl ± Grt ± Opx ± Hbl ± Qtz). The xenoliths and the host Devonian ultramafic lamprophyres forming diatremes and explosion dikes contain fluid with similar He and Ar isotopic compositions. It was found that the fluid was trapped by the rocks and xenolith minerals approximately simultaneously with the formation of the lamprophyres. This conclusion is based on the identical K-Ar ages of the majority of xenoliths and ultramafic lamprophyres. When the xenoliths were transported toward the surface by high-temperature ultrabasic melts, the noble gases occurring in them were partly (Ar) or completely (He) lost. The melts were contaminated by meteoric waters during their emplacement in the upper crust, which resulted in that the Ar isotopic composition of lamprophyres approached the composition of atmospheric Ar. The fluid phase that was liberated during melt crystallization severely affected the xenoliths, diminishing the difference between the isotope compositions of He and Ar in the xenoliths and ultramafic lamprophyres. The He isotope composition includes an admixture of mantle ³He, which is suggested by the high measured ³He concentrations, exceeding the calculated values, and high ³He/³⁶Ar ratios in the xenoliths and their host lamprophyres. The fraction of the mantle component in the fluid trapped by the xenoliths was estimated as ～20%.     

First Data on the Age and <Emphasis Type="Italic">P</Emphasis>–<Emphasis Type="Italic">T</Emphasis> Formation Conditions of Zones of Low-Angle Dip Schistosity of the Belomorian Mobile Belt

The low-angle dip schistosity zones of the Belomorian mobile belt of northern Karelia are zones of plastic flow of thrust origin. They were formed from 1.85 to 1.90 Ga: 1879 ± 21 Ma according to ⁴⁰Ar/³⁹Ar for amphibole from amphibolites and 1857 ± 13 Ma according to the Sm–Nd isochron in amphibolites. The P–T parameters of rock metamorphism in low-angle dip schistosity zones correspond to the boundary of amphibolite and granulite facies of metamorphism: T = 640–765°C, rarely rising to 826°C; P = 8.0–11.7 kbar. The hypothesis of the two-stage Paleoproterozoic metamorphism of rocks of the Belomorian mobile belt was introduced.     

Development of a technique for IR spectroscopic determination of nitrogen content and aggregation degree in diamond crystals

A technique for IR spectroscopic determination of the total nitrogen content N _S in the form of A-and B ₁-defects is suggested. It provides for the computer processing and decomposition of IR spectra into constituent bands, calculation of the total absorption band area S _N and individual areas S _A and S _B1 and their normalization with respect to the total area of the diamond intrinsic absorption S ₀, with the normalization coefficients K _S , K _A , and K _B1 being calculated. Based on the analysis of the IR spectra of 60 octahedral diamond crystals from the Mir and Yubileinaya pipes (Sakha-Yakutiya), the empirical functions N _S = 911.85 K _S ^0.9919 ppm (R ² = 0.9859), N _A = 1185.6 K _A ^1.1511 ppm (R ² = 0.8703), and N _B1 = 911.85 K _S ^0.9919 ? 1185.6 K _A ^1.1511 ppm have been defined.