Interpretation of the auger electron spectra (AES) of sulfide minerals

Auger electron spectra (AES) of sulfides are interpreted using published photoelectron spectra, sulfurK _β X-ray emission spectra (XES) and Multiple ScatteringX _α calculations on metal-sulfide molecular clusters and using newly measured spectra for ZnS, Cu₂S and MoS₂. For compounds without appreciable metald-sulfur 3p interactions, only one sulfur LVV peak or a closely spaced doublet is observed. For those with substantial metald-sulfur 3p interactions additional peaks occur, with peaks at lower electron kinetic energy arising from ejection of electrons from orbitals more tightly bound than theS3p, and those with higher kinetic energy arising from electrons in less tightly bound orbitals. Thus, for many sulfide minerals, the sulfur LVV Auger Spectrum is essentially a self-convolution of the valence band density of states weighted by the amount of S3p character, and can be predicted from a knowledge of the sulfurK _β X-ray emission spectra and the X-ray photoelectron spectra.     

Structure proof and significance of stereoisomeric 28,30-bisnorhopanes in petroleum and petroleum source rocks

Two C₂₈H₄₈-pentacyclic triterpanes were isolated from Monterey shale. X-ray crystallography of a crystal containing both compounds proved their structures as 17β,18α,21α(H)-28,30-bisnorhopane and 17β,18α,21β(H)-28,30-bisnorhopane. Several differences are found between 28,30-bisnorhopanes and the regular hopanes. Unlike the regular hopane epimers, for practical purposes the three epimeric 28,30-bisnorhopanes [17α,21β(H)-, 17β,21α(H)-, and 17β,21β(H)-]cannot be distinguished by their mass spectra. Special conditions are needed to separate them by gas chromatography. The diagenetically first-formed epimer is thought to be 17α,21β(H)- because it predominates in immature shales. The order of thermodynamic stability is 17β,2lα(H) < > 17α,21β(H) > 17β,21β(H), and all three epimers are present in petroleum. 25,28,30-Trisnorhopanes can be analyzed in similar fashion and are found to have similar thermodynamic characteristics. The percent of the ring D/E cis epimer of 28,30-bisnorhopane and/or 25,28,30-trisnorhopane is a useful maturation parameter similar to the 20S/20R sterane ratio. Evidence indicates 25-demethylation of 28,30-bisnorhopane to 25,28,30-trisnorhopane during advanced stages of biodegradation. Hence, percent ring $\text{D}\text{E}$cis 25,28,30-trisnorhopane has an application to maturation assessment in heavily biodegraded oils.     

Linear free energy relationships for metal-ligand complexation: Monodentate binding to negatively-charged oxygen donor atoms

The analysis presented below suggests that the following equation models monodentate binding to negatively-charged oxygen donor atoms with no distinction between phenolic, carboxylic or inorganic hydroxide functional groups: log K_ML = α_O log K_HL + β_O; where K_ML is the metal-ligand formation constant, K_HL is the corresponding proton-ligand formation constant, and α_O and β_O are termed the Irving-Rossotti slope and intercept, respectively. Linear free energy relationships (LFERs) of this type are presented for 24 different metal ions complexing to negatively-charged oxygen donor atoms. Ligands selected for use in LFERs meet the following criteria: (i) they contain negatively-charged oxygen donor atoms (e.g., carboxylic acids and phenols), (ii) they are capable of only monodentate binding to metal ions, (iii) steric hindrances are not expected to influence the extent of metal-ligand binding, and (iv) the negatively-charged oxygen donor atom is the only functional group that imparts charge. The intercept of all LFERs was nearly zero for all metal ions investigated (β_O ≈ 0). The magnitude of α_O indicates the relative preference of metal binding to negatively-charged oxygen donor atoms and to the proton. Values of α_O can be used in QSARs (quantitative structure activity relationships) to estimate metal-NOM (natural organic matter) binding constants employed in the Windermere Humic Aqueous Model (WHAM) version V.     

Constraints on the structure and dynamics of the β-cristobalite polymorphs of SiO2 and AlPO4 from 31P, 27Al and 29Si NMR spectroscopy to 770 K

Nuclear magnetic resonance spectroscopic data are presented for the cristobalite polymorphs of AlPO₄ and SiO₂ from RT to 770 K, through their respective α-β transitions. The nuclear magnetic resonance (NMR) data include chemical shifts for ³¹P, ²⁷Al, and ²⁹Si, ²⁷Al quadrupole coupling parameters, and ³¹P and ²⁷Al spin-lattice relaxation rates. Also presented are electron diffraction patterns of β-cristobalite AlPO₄ that show diffuse scattering similar to that reported previously for SiO₂. For the α-phases of both AlPO₄ and SiO₂, the chemical shifts decrease approximately linearly with increasing temperature from RT to T_c and discontinuously by -2 to -3 ppm from α to β. This result is consistent with a small, continuous increase in the mean T-O-T angle (〈θ〉) of the α-phases with increasing T and an increase of 〈θ〉 by about 4° across the α-β transition for both cristobalite and its AlPO₄ analogue. Based on the ²⁹Si chemical shifts, the mean Si-O-Si angle for β-cristobalite is 152.7±1° near T_c. For AlPO₄-cristobalite, the ²⁷Al nuclear quadrupole coupling constant (C_Q) decreases approximately linearly from 1.2 MHz at RT to 0.94 MHz near T_c (493±10 K). At the α-β transition the ²⁷Al C_Q approaches zero, in agreement with the cubic average structure observed by diffraction. The satellite transitions retain a small frequency distribution above the α-β transition from electric field gradients attributed to defects. The short-range cubic symmetry of the Al-site and non-linear Al-O-P angle support a dynamically disordered model of the β-cristobalite structure. Complete averaging of the ²⁷Al quadrupole coupling in the β-phase indicates that the lifetime of any short-range ordered domains must be shorter than about 1 μs.     

Angles between the rotational axis and magnetic moment in 80 pulsars from observations near 1 GHz

Data on the pulse structure and variations of the linear polarization angle at frequencies near 1 GHz have been used to estimate the angles β between the rotational axis and magnetic moment of the neutron stars assocaited with 80 pulsars. The calculations applied several methods. The minimum values of β were estimated from the observed pulse width W ₁₀ at the 10% level for the entire sample. Maximum estimates of β were obtained for six sources with small polarization position angle derivatives. Equations for the angle β were derived for various forms of the observed profile, and solutions obtained for 34 pulsars. The β values calculated using different methods are compared. For three pulsars with known interpulses, the obtained values of β demonstrate that two (PSR B1055-52 and PSR 1822-09) are aligned rotators, whereas the other (PSR B1702-19) is an orthogonal rotator. A search for interpulses and interpulse emission in PSRB1641-45, PSR1642-03, and PSR 1944+17 is necessary, and a search for an interpulse at 180° from the main pulse is required in PSR B2321-61.     

Spectroscopy and doppler mapping of the binary SS Cyg during outburst

We carried out spectroscopy of the binary SSCyg in the Hα, Hβ, and Hγ lines in its active state in August and December 2006. We have estimated the parameters of the main flow elements contributing to the spectra. Profile variations during the orbital period are analyzed, and a Doppler tomogram computed for the Hα line. We consider the evolution of the line profiles with the development of the outburst. A phenomenological model explaining the observed outburst features is suggested. In this model, the main elements of the flow determining the shape of the spectral lines are the accretion disk, a toroidal shell formed in the inner parts of the disk, an expanding spherical shell around the accreting star, a region in front of the bow shock that forms due to the orbital motion of the disk in the circumbinary envelope, and the surface of the donor star near the inner Lagrange point, L1, which is heated by radiation from the accretor.     

Test of the vibrational modelling for the λ-type transitions: Application to the α-β quartz transition

Vibrational modelling is at the present time the only known way to predict the heat capacities of the Earth's mantle minerals at high-pressure and high-temperature. To test the validity of this method for λ-type transitions, we have applied it to the α-β quartz transition (T ₀=846±1 K). Raman spectra of quartz were recorded up to 900 K. Measured frequency shifts of the α-quartz Raman modes were then used in conjunction with available high-pressure Raman data to calculate intrinsic mode anharmonicity, through the parameter a _i=(?Lnv_i/?T)_v. Vibrational modelling of the heat capacity at constant volume, Cv, and at constant pressure, Cp, including anharmonic corrections deduced from the a _i parameters, are compared to experimental data. Taking into account the soft-mode associated to the α-β quartz transition, the model reproduces the excess of Cp related to the transition. Then, this study confirms that detecting a soft-mode from vibrational data allows one to predict λ-type transitions. However, when modelling the thermodynamic properties, the contribution of a soft-mode cannot be established from spectroscopic data. Therefore, one needs first to determine this contribution in order to predict the heat capacities of Earth's mantle minerals displaying λ-type transitions. In α-quartz, this contribution has been determined as 0.007% of the total number of the optic modes in the model of the density of states.     

Estimation of source parameters and attenuation using digital waveforms of Al-Ays 2009 earthquake,Saudi Arabia

On 19 May 2009, an earthquake sequence of M _w?=?4.8 occurred at 25.20°N 37.76°E about 60 km onshore of the Red Sea coastline, Saudi Arabia. In the present study, the digital waveform data from the largest four events were used to estimate the source parameters and attenuation characteristics along the source-to-station path in the Arabian Shield. A grid search technique, combined with an assumption of circular source model, was applied to find the best-fit spectral amplitude over the space parameters: long period spectral level (Ω ₀), corner frequency (f ₀) and asymptotic high-frequency fall-off (γ). Consequently, the spectral parameters were used to estimate source parameters: seismic moment, fault radius (assumed circular rupture model) and stress drop. Seismic moments are founded to be within the range of 2.34E+14 to 2.83E+16 Nm and their corresponding moment magnitudes range from 3.5 to 4.8; the fault radius ranges from 369 to 1,498 m, and stress drops are observed in the range of 8.7 to 32.0 b. The spectral slopes beyond the corner frequency displayed ω ^?2.4 to ω ^?2.6 behaviours in contrast with Brune's source model of ω ^?2. This finding requires more detailed investigations on large data sets to distinguish the behaviour mechanism of the spectral slopes at high frequencies. By taking the ratio between observed and calculated spectra, the attenuation curves for P and S waves were derived along the source-to-station paths. The preliminarily results exhibited high quality factors of Q _α?=?3,883 and Q _β?=?3,530 for P and S waves, respectively. To this end, the ratio Q _β/Q _α is founded to be slightly less than unity indicating that the body waves from source-to-station paths crossed a crustal volume that is partially saturated with fluids causing lower attenuation effect on P waves than on S waves in the Arabian Shield.     

Pyrite,marcasite, and arsenopyrite type minerals: Crystal chemical and structural principles

Quantitative molecular orbital (MO) calculations and qualitative perturbational MO arguments are used to interpret the spectra and structure of transition metal dichalcogenides and related compounds. Competition between pyrite (FeS₂), marcasite (FeS₂) and loellingite (FeAs₂) structure types is explained in terms of the number of electrons occupying a set of MO's obtained from the mixing of dianion (A ₂) orbitals and metal (M) dσ orbitals. Direct metal-metal d orbital interaction is argued to be small. Attention is focused upon the M - A - M angles which differ substantially among the three structure types as a consequence of varying numbers of electrons in orbitals which closely resemble the pπ* orbitals of the dianions. Variations in M - A and A - A distances can also be understood in terms of the occupations of this set of MO's. Disulfide valence region photo-emission spectra are interpreted in terms of calculations on MS₆ and S₆ molecular clusters. M3d orbitals are found to progressively approach the S3p orbitals with increasing atomic number of M from Fe to Ni. For CuS₂ comparison of calculation and experiment supports an approximate electron configuration of Cu⁺¹ S ₂ ^?1 .     

Fatty acid geochemistry of a 200 m sediment core from Lake Biwa,Japan. Early diagenesis and paleoenvironmental information

Fatty acids (FAs), β- and ω-hydroxy acids, α,ω-dicarboxylic acids and n-alkanes were studied in a 200 m sediment core taken from Lake Biwa, Japan. FAs showed bimodal distribution with peaks at C₁₆ and C₂₂-C₂₈. Their distribution patterns clearly changed with depth from lower molecular weight (C₁₂-C₁₉) predominance to higher molecular weight (C₂₀-C₃₂) predominance in the upper 20 m interval. Analyses of related compounds (β- and ω-hydroxy acids and α, ω-dicarboxylic acids) suggest that β- and ω-oxidative degradation of C₁₂-C₁₉ FAs has occurred in the sediments.The ratio of bound C₁₂-C₁₉ to unbound FAs increases with depth in the upper 0–1 m sediments, suggesting that unbound FAs are more labile. However, the ratio varies significantly in deeper sections and may be associated with water temperature.In the sediments deeper than 20 m in depth, C₁₂-C₁₉ FAs gradually decrease. On the other hand, higher molecular weight FAs (HFAs: C₂₀-C₃₂), which were probably derived from terrestrial plants, increase in concentration from 20 m to 100 m, suddenly decrease at 100 m and show progressively lower concentration in deeper sediments. These fluctuations are interpreted in relation to paleolimnological changes of the lake and the drainage basin. ω-Hydroxy C₂₀-C₃₀ acids and C₂₀-C₃₀α, ω-dicarboxylic acids show a distribution pattern similar to HFAs. Branched chain FAs, ω-hydroxy acids and C₉-C₁₉α,ω-dicarboxylic acids show a major peak around 3–15 m in depth. This peak is probably caused by increased bacterial activity in the water column and surface sediments in the past, which may be associated with an increase in primary production of the lake.     

Matrix corrections in trace-element analysis by X-ray fluorescence: An extension of the Compton scattering technique to long wavelengths

Mass absorption coefficients (A₂) for a series of standard rocks, have been calculated in the wavelength region 0.492–3.03 $\text{a}\text{?}$. Plots of these data against the intensity of the Compton scattered peak [(I) Compton] give an excellent correlation for the wavelengths 0.429 $\text{a}\text{?}$ to the Fe-absorption edge (1.74 $\text{a}\text{?}$); the data confirm the observations of Reynolds. Hence, routine measurement of one peak will give the mass absorption coefficient of a sample in an analytically important region (Sn/1bK_α to Ni/1bK_α). A₂ has also been directly measured on three of the samples and systematic differences between calculated and measured are attributed to the measuring technique. At wavelengths longer than the Fe-absorption edge, (up to 3.03 $\text{a}\text{?}$) A₂ can be estimated using a combination of (I) Compton and Fe/1bK_α c.p.s. This technique enables meaningful matrix corrections to be carried out on the elements Co, Mn, Cr, V, Ti, Sc (K spectra) and Ba (L spectra). Cr and Ba results are presented for some standard rocks.     

SCF-Xα-SW MO Study of Fe-O and Fe-OH chemical bonds; applications to the mössbauer spectra and magnetochemistry of hydroxyl-bearing Fe3+ oxides and silicates

Results of SCF-Xα-SW molecular orbital calculations on (FeO₄(OH)₂)^7? and (FeO₆)^9? clusters are used to investigate the differences between Fe-O and Fe-OH bonding in hydroxyl-bearing iron oxides and silicates. The Fe³⁺-OH^? bond is more ionic, and has a smaller spinpolarization, then the Fe³⁺-O^2? bond. The smaller spinpolarizability of OH^? ligands explains why superexchange interactions between hydroxo-bridged Fe³⁺ cations are much weaker than those between oxo-bridged Fe³⁺ cations. Replacement of oxygens in the Fe³⁺ coordination environment by OH^? ligands appears to promote the covalency between Fe³⁺ centers and O^2? oxygens. The increased covalency lowers the effective spin of the Fe atom. This, in turn, explains the decreased magnetic hyperfine fields at the Fe nucleus in FeOOH polymorphs relative to those found in Fe³⁺ oxides.     

The radio emission of anomalous pulsars

Previously developed methods for estimating the angle β between the spin axis of a neutron star and its magnetic moment together with observational data for anomalous X-ray pulsars (AXPs) indicate that these objects are nearly aligned rotators, and that the drift model can be applied to them. The magnetospheres of aligned rotators are appreciably more extended than in pulsars with large values of β. With such extents for the magnetosphere, the conditions for the generation of transverse waves via the cyclotron instability are satisfied. The expected spectrum of the resulting radiation is very steep (its spectral index is α > 3), consistent with the observed radio spectra of known AXPs (α > 2). A large magnetosphere also favors the appearance of appreciable pitch angles for relativistic electrons, and therefore the generation of synchrotron emission. The maximum of this emission falls in the microwave range. This mechanism provides appreciable fluxes at frequencies of tens of gigahertz and can explain the observed enhanced AXP radiation in this range.     

Molecular orbital studies of geometries and spectra of minerals and inorganic compounds

Extended Hückel molecular orbital theory (EHT) and simple, approximate Self-Consistent-Field MO methods are employed to explain the geometries of nontransition metal bearing minerals and inorganic compounds. The spectra of such minerals and the electronic structure of transition metal oxidic minerals are explained using the Self-Consistent-Field X α MO method. EHT provides an objective algorithm for rationalizing and correlating bond length and angle data for insular and polymerized TO ₄ ^?n tetrahedral oxyanions where T=Be, B, Al, Si, P, S, Ge, As and Se. Calculated bond overlap populations n(T-O), correlate linearly with the observed T-O bond lengths with shorter bonds tending to involve larger n(T-O) values. Such calculations show that n(T-O) is strongly dependent upon the average of the three O-T-O angles associated with a common bond, larger n(T-O) values involving wider angles. Calculations of n(T-O) as a function of the T-O-T angles in T ₂O ₇ ^?n ions, indicate that the n(T-O) values for the bonds to the bridging oxygen atoms increase nonlinearly with increasing T-O-T angle whereas those the nonbridging oxygens decrease slightly as the angle widens. In agreement with the experimental data, these results predict that shorter T-O bonds should involve wider O-T-O and T-O-T angles. The SCF-X α MO cluster model is then applied to silica and FeO. The calculations yield a satisfactory interpretation of the visible, UV and X-ray emission and X-ray photoelectron spectra of these materials. Theoretical and empirical MO diagrams are constructed and the electronic structures of the materials are discussed.     

Diagnostics for accretion disks around UX Ori stars based on Balmer, Paschen, and Brackett Lines

We have modeled the H_α, H_β, and H_γ (Balmer series), P₁₄ (Paschen series), and Br_γ (Brackett series) hydrogen lines formed in the inner regions of the accretion disk around the Herbig Ae star UX Ori. Our calculations are based on spectra obtained with the Nordic Optical Telescope (NOT) and the IRTF. We computed a grid of non-LTE models for a radiating area in the accretion disk and determined the basic parameters of the lines using the method of Sobolev. Analyzing the theoretical and observed line profiles, equivalent widths, and luminosities, we have estimated the accretion rate and electron-temperature distribution in the inner parts of the accretion disk. The accretion rate of UX Ori is about $\dot M_a = (3 - 10) \times 10^{ - 9} M_ \odot /yr$ , and the temperature distribution is consistent with the power law T(r)=T(r _*)(r/r _*)^?1/n , where the electron temperature near the stellar surface T(r _*) is 15000–20000 K and the power-law index n≈2–3 is about two to three. The resulting value for $\dot M_a $ eliminates problems connected with the application of magnetospheric accretion models to Herbig Ae/Be stars. Another important conclusion is that, at the estimated accretion rate, the energy release is substantially (about two orders of magnitude) lower than the stellar luminosity. Therefore, the optical radiation of UX Ori accretion disks cannot appreciably contribute to the observed variability of these stars, which must be determined mainly by variability in the circumstellar extinction.     

Collective supernova outbursts and the growth of supershells: Observational manifestations

Numerous supernova outbursts that are correlated in time and space are the main mechanism for the formation of powerful galactic winds and supershells of ionized hydrogen. Information about the dynamics and thermal properties of the gas in shells (bubbles) can be obtained from spectral observations, including those of optical recombination lines. The emission properties of the Hα and Hβ recombination lines and the velocity dispersion of the gas in bubbles formed by numerous supernova outbursts are studied. The appearance of the intensity vs. velocity dispersion (I(H _α)_?σ) diagram depends on the supernova rate and the age of the bubble. The temperature dependence of the I(H_α)/I(H _β) line-intensity ratio (the Balmer decrement) can be used to obtain additional constraints on the evolutionary status of a collective remnant formed by numerous supernova outbursts.     

Inverted high-temperature quartz

Fifty-two samples of inverted high-temperature quartz from volcanic rocks were investigated by Guinier-Jago powder diffractometry and differential scanning calorimetry (DSC). Quartz megacrysts from Clear Lake and Cinder Cone, California show a variability of ?2.5 ° K in their α-β transition temperature (T _α-β). Quartz phenocrysts and quartz from crystalline rocks give a range of 0.5 ° K in T _α-β. Neutron activation analysis of single crystals demonstrates that Al is the principal impurity (17–380 ppm). Its concentration is inversely correlated with T _α-β. A very small variation was found in the a and c lattice parameters among the specimens of volcanic quartz studied. This variation does not correlate with Al content or transition temperature. Mean values at 22 ° C (a=4.1934±0.0004 Å, c=5.4046±0.0006 Å) are similar to those of quartz grown at low temperatures. Enthalpy of the α-β transition (ΔH _α-β), obtained over 9.0 ° from DSC runs, is dependent upon sample grain size and for a crushed powder with zero hysteresis (T _α-β on heating=T _α-β on cooling) is 92.0 ±1.4 cal/mol. In contrast, a single piece of quartz requires ΔH _α-β be 107.7±1.4 cal/mol and has a T _α-β hysteresis of 1.1 ° K. Regression of published data provides equations for the variation of the molar volume (cc/mol) of quartz with v. These equations imply a ΔV _α-β of 0.205±0.031 cc/- mol. Expressions are also provided for the temperature dependence of the thermal coefficient of expansion, α, the compressibility, β, and (?/gb/?T)_p (which is identically -(?α/?P) _T ). DSC heat capacity measurements over the range 400 to 900 ° K were fitted to extended Maier-Kelley type expressions to give: $$\begin{gathered} C_P = 10.31 + 9.116 \times 10^{ - 3} T - \frac{{1.812 \times 10^5 }}{{T^2 }} \hfill \\ - {\text{5}}{\text{.630}} \times 10^{ - 2} {\text{ }}\frac{T}{{(T - 848)}} - 0.3553\frac{T}{{(T - 848)^2 }} \hfill \\ - 0.9011\frac{T}{{\left( {T - 848} \right)^3 }} \hfill \\ (400{\text{ to 842}}^ \circ {\text{K), and}} \hfill \\ C_P = - 318.8 + 0.2532T \hfill \\ {\text{ + }}\frac{{8.687 \times 10^7 }}{{T^2 }} + 0.1603\frac{T}{{\left( {T - 848} \right)^4 }} \hfill \\ \end{gathered} $$ (851 to 900 ° K), which together with the values of ΔH _α?β measured over the range 842–851° K give 7875.3 cal/mol for H₉₀₀-H₄₀₀. The behavior of α, β, and C _p as a function of T emphasizes that structural changes which occur at the α?β transition do so over a broad temperature interval.     

Partition of Elements Between Solid and Liquid Phases in Aquatic Environments

The average composition of natural waters such as rivers, lakes, ocean, and hydrothermal vents and corresponding solids in equilibrium (e.g., river-suspended particles or shale; lake sediments; oceanic pelagic clay, organisms, and manganese nodules; and the mid-ocean ridge basalts) do not change randomly. The observed positive correlation between the electron binding energy (I _z [*I _z ]) and logarithms of bulk distribution coefficient (log K _d ) for cations with charge of 1?C4, and the negative correlation between I _z [*I _z ] and log K _d for anions in various aquatic systems are consistent with the prediction from the surface complexation model. In other words, the bond strength between the adsorbed cation and the surface oxygen of hydrated metal oxides, and between the oxygen of adsorbed oxyanion and the surface metal of hydrated metal oxides control the partition of elements between solid and associated liquid in natural aquatic systems. For Mn, Co, Ce, Pb, and Tl, the oxidative uptake at the solid?Cwater interface in the ocean is an additional important process. For alkali and alkaline-earth cations with large ionic radius (such as Cs, Rb, K, and Ba), their relatively small secondary solvation energy further enhances their adsorption onto solid particles. For living and non-living organic matter, the adsorbed B-type cations form extra strong bindings with hydrophilic functional groups such as ?CSH and ?CNH₂ on organic matter surface.     

Estimation of maximum temperature of mudstone by two kinetic parameters; epimerization of sterane and hopane

A geochemical method for estimation of the maximum temperature of mudstones is proposed. The extents of epimerization of the sterane and the hopane are used. The temperature function is:

$\text{T}{}_{\mathrm{max.}}\text{(°C) =}\text{6060}\text{15.0?In(dU}\text{dU}\text{dV)}\text{?273}$

where U = ln (1 ? α/0.54), V = ln(1 ? β/0.61), α = 20S-/20S- + 20R-24-ethyl-5α(H), 14α(H), 17α(H)-cholestane(C₂₉-sterane) and β = 22S-/22S- + 22R-17α(H), 21β(H)-bishomohopane(C₃₂-hopane). The value of dU/dV can be obtained from the tangent to the evolution curve in the UversusV. This temperature function is applicable to the temperature analysis in the range of 50°C–150°C.