Universal Calibration Research Articles

Multiarm Polycarbonate Star Polymers with a Hyperbranched Polyether Core from CO2 and Common Epoxides

Multiarm star copolymers, consisting of hyperbranched poly(ethylene oxide) (hbPEO) or poly(butylene oxide) (hbPBO) polyether copolymers with glycerol branching points as a core, and linear aliphatic polycarbonate arms generated from carbon dioxide (CO2) and epoxide monomers, were synthesized via a “core-first” approach in two steps. First, hyperbranched polyether polyols were prepared by anionic copolymerization of ethylene oxide or 1,2-butylene oxide with 8–35% glycidol with molecular weights between 800 and 389,000 g·mol–1. Second, multiple arms were grown via immortal copolymerization of CO2 with propylene oxide or 1,2-butylene oxide using the polyether polyols as macroinitiators and (R,R)-(salcy)-CoCl as a catalyst in a solvent-free procedure. Molecular weights up to 812,000 g·mol–1 were obtained for the resulting multiarm polycarbonates, determined by online viscometry with universal calibration and 1H NMR. Comparing the synthesis of different multiarm star polycarbonates, a combination of a highly r...

Calibration method of rotation and displacement systematic errors for ship-borne mobile surveying systems

Rotation and displacement errors between sensors and the Inertial Navigation System have significant effects on the accuracy of measured point clouds. In ship-borne mobile surveying systems, over and underwater targets are measured by a laser scanner and multibeam echo sounder, respectively. A simple calibration method and a universal calibration field are urgently needed to address both rotation errors and displacement problems for over and underwater sensors. First, a systematic error analytic function is established through the path that the geolocation expression of measured data is derived and substituted into the expression of known calibration planes. Then, the calibration expression that can calibrate both rotation errors and displacement is derived based on the least-squares criteria using a designed calibration pool. The calibrating results showed that for both over and underwater sensors, the accuracies of rotation errors and displacement estimation are better than 0.015° and 1.2 mm, respectively. After this calibration, the geolocation accuracy of measured points is better than 5 cm within a range of 30 m. The method can effectively calibrate systematic errors and serve as guidance to address the calibration problem for mobile surveying systems.

Tetra-detector size exclusion chromatography characterization of molecular and solution properties of soluble microbial polysaccharides from an anaerobic membrane bioreactor

Characterization of the molecular properties of soluble microbial products (SMP) is critical for understanding the membrane filtration and fouling mechanisms in anaerobic and aerobic membrane bioreactors (AnMBR & MBR). In this study, the distributions of the absolute molecular weight and intrinsic viscosity of SMP polysaccharides from an AnMBR were effectively determined by a high performance size exclusion chromatography (HPSEC) that was coupled with the refractive index (RI), diode array UV (DAUV), right and low angle light scattering (LS), and viscometer (Vis) detectors. Based on the tetra-detector HPSEC determined absolute molecular weights and intrinsic viscosity, a universal calibration relationship for the SMP polysaccharides was developed and the molecular conformations, average molecular weights, and hydrodynamic sizes of the SMP polysaccharides were also explored. Two factors which can be derived from the tetra-detector HPSEC analysis were proposed for the characterization of the viscous and osmotic pressure properties of the SMP polysaccharides. In addition, it was also extrapolated how to analyze the resistance characteristics of the concentration polarization layers formed in membrane filtration based on the molecular properties determined by the tetra-detector HPSEC analysis.

Size-exclusion liquid chromatography of poly(N-vinylformamide)s in aqueous solutions

The exclusion mechanism of the separation of poly(N-vinylformamide) and its derivatives with a cysteamine terminal group in gel permeation chromatography implemented by the suppression of polyelectrolyte swelling and the electroexclusion of macromolecules was established by the transport analytical methods of molecular hydrodynamics (HPLC, velocity sedimentation, and intrinsic viscosity). Based on an analysis of the hydrodynamic characteristics and molecular weights of polymer fractions determined by velocity sedimentation, it was found that the molecular characteristics and polydispersity of the water-soluble poly(N-vinylamide) s of aliphatic carboxylic acids and their derivatives can be calculated with the use of the Benoit universal calibration dependence.

The study of the calibration dependences used when testing the concrete strength by nondestructive methods

The article presents the results of the investigation of universal calibration dependences used in testing of the concrete strength by shear, rebound and ultrasound test methods. Many of the instruments currently used do not provide the required measurement accuracy, especially when using universal calibration dependences. The introduction of new more sophisticated instruments for nondestructive testing of concrete strength requires an assessment of their accuracy, taking into account the composition of concrete and other parameters. The shear test method, called “direct”, does not provide the required accuracy of measurements, and the use of this method for the calibration of sclerometers and ultrasonic devices is unacceptable.

Measuring E. coli and bacteriophage DNA in cell sonicates to evaluate the CAL1 reaction as a synthetic biology standard for qPCR

We measured the impact of the presence of total Escherichia coli (E. coli) cellular material on the performance of the Linear Regression of Efficiency (LRE) method of absolute quantitative PCR (LRE qPCR), which features the putatively universal CAL1 calibration reaction, which we propose as a synthetic biology standard. We firstly used a qPCR reaction in which a sequence present in the lone genomic BirA locus is amplified. Amplification efficiency for this reaction, a key metric for many quantitative qPCR methods, was inhibited by cellular material from bioreactor cultivation to a greater extent than material from shake flask cultivation. We then compared LRE qPCR to the Standard Curve method of absolute qPCR (SC qPCR). LRE qPCR method matched the performance of the SC qPCR when used to measure 417–4.17×107 copies of the BirA target sequence present in a shake flask-derived cell sonicates sample, and for 97–9.7×105 copies in the equivalent bioreactor-derived sample. A plasmid-encoded T7 bacteriophage sequence was next used to compare the methods. In the presence of cell sonicates from samples of up to OD600=160, LRE qPCR outperformed SC qPCR in the range of 1.54×108–1.54×1010 copies of the T7 target sequence and matched SC qPCR over 1.54×104–1.54×107 copies. These data suggest the CAL1 standard, combined with the LRE qPCR method, represents an attractive choice as a synthetic biology qPCR standard that performs well even when unpurified industrial samples are used as the source of template material.

Investigation of the Matrix Effect on the Accuracy of Quantitative Analysis of Trace Metals in Liquids Using Laser-Induced Breakdown Spectroscopy with Solid Substrates.

The detection limit of trace metals in liquids has been improved greatly by laser-induced breakdown spectroscopy (LIBS) using solid substrate. A paper substrate and a metallic substrate were used as a solid substrate for the detection of trace metals in aqueous solutions and viscous liquids (lubricating oils) respectively. The matrix effect on quantitative analysis of trace metals in two types of liquids was investigated. For trace metals in aqueous solutions using paper substrate, the calibration curves established for pure solutions and mixed solutions samples presented large variation on both the slope and the intercept for the Cu, Cd, and Cr. The matrix effects among the different elements in mixed solutions were observed. However, good agreement was obtained between the measured and known values in real wastewater. For trace metals in lubricating oils, the matrix effect between the different oils is relatively small and reasonably negligible under the conditions of our experiment. A universal calibration curve can be established for trace metals in different types of oils. The two approaches are verified that it is possible to develop a feasible and sensitive method with accuracy results for rapid detection of trace metals in industrial wastewater and viscous liquids by laser-induced breakdown spectroscopy.

Calibration of the dolomite clumped isotope thermometer from 25 to 350 °C, and implications for a universal calibration for all (Ca, Mg, Fe)CO3 carbonates

Carbonate clumped isotope thermometry is based on the temperature-dependent formation of 13C18O16O22− ion groups within the lattice of solid carbonate minerals. At low temperatures the bonds between rare, heavy 13C and 18O isotopes are thermodynamically favored, and thus at equilibrium they are present in higher than random abundances. Here we calibrate the use of this temperature proxy in a previously uncalibrated carbonate phase — dolomite [CaMg(CO3)2] — over a temperature range that extends to conditions typical of shallow crustal environments, by determining the Δ47 values of CO2 extracted from synthetic or natural (proto)dolomites grown at known temperatures from 25 to 350°C and analyzed in two different laboratories using different procedures for sample analysis, purification and post-measurement data treatment. We found that the Δ47-1/T2 dependence for (proto)dolomite is linear between 25 and 350°C, independent of their Mg/Ca compositions or cation order (or the laboratory in which they were analyzed), and offset from, but parallel to, the theoretical predictions of the Δ63 dependence to temperature of the abundance of the 13C18O16O2 isotopologue inside the dolomite and calcite mineral lattices as expected from ab-initio calculations (Schauble et al., 2006). This suggests that neither the equilibrium constant for 13C–18O clumping in (proto)dolomite lattice, nor the experimental fractionation associated with acid digestion to produce CO2, depend on their formation mechanism, degree of cation order and/or stoichiometry (i.e., Mg/Ca ratio) and/or δ18O and δ13C compositions (at least over the range we explored). Thus, we suggest the following single Δ47-1/T2 linear regression for describing all dolomite minerals:Δ47CDES90=0.0428(±0.0033)∗106/T2+0.1174(±0.0248)(r2=0.997),with T in kelvin and Δ47 in the Carbon Dioxide Equilibrium Scale (CDES) of Dennis et al. (2011) and referring to CO2 extracted by phosphoric acid digestion at 90°C. The listed uncertainties on slope and intercept are 95% confidence intervals. The temperature sensitivity (slope) of this relation is lower than those based on low temperature acid digestion of carbonates, but comparable to most of those based on high temperature acid digestion (with however significantly better constraints on the slope and intercept values, notably due to the large range in temperature investigated here and the large number of Δ47 measurements performed, n=67). We also use this dataset to empirically determine that the acid fractionation factor associated with phosphoric acid digestion of dolomite at 90°C (Δ*dolomite90) is about +0.176‰. This is comparable to the Δ*calcite90 experimentally obtained for calcite (Guo et al., 2009), suggesting that the acid fractionation Δ* for acid digestion of dolomite and calcite are the same within error of measurement, with apparently no influence of the cation identity. This hypothesis is also supported by the fact that our dolomite calibration data are indistinguishable from published calibration data for calcite, aragonite and siderite generated in similar analytical conditions (i.e., carbonate digested at T⩾70°C and directly referenced into CDES), demonstrating excellent consistency among the four (Ca, Mg, Fe)CO3 mineral phases analyzed in seven different laboratories (this represents a total of 103 mean Δ47 values resulting from more than 331 Δ47 measurements). These data are used to calculate a robust composite Δ47-T universal relation for those carbonate minerals of geological interest, for temperatures between −1 and 300°C (that is statistically indistinguishable from the one described by dolomite only):Δ47CDES90=0.0422(±0.0019)∗106/T2+0.1262(±0.0207)(r2=0.985)Thus, in order to standardize the temperature estimates out of different laboratories running high temperature digestion of (Ca, Mg, Fe)CO3 carbonate minerals, we recommend the use of this single Δ47-T calibration to convert Δ47CDES data into accurate and precise temperature estimates. More widely, this study extends the use of the Δ47 thermometry to studies of diagenesis and low-grade metamorphism of carbonates with unprecedented precision on temperature estimates based on Δ47 measurements — environments where many other thermometers are generally empirical or semi-quantitative.

Calibration of dolomite clumped isotope thermometry

Use of the clumped isotope thermometer to decipher environments of dolomite formation has been inhibited by a lack of empirical data from dolomites formed at known temperatures. Calibrations for aragonite, calcite, siderite, and apatite indicate that a universal Δ47 – temperature relationship may exist across all carbonate-bearing mineral phases. However, theoretical modeling and proposed acid fractionation differences have suggested that dolomites may have different Δ47 values relative to calcites precipitated at the same temperature. To resolve this question, we analyzed five synthetic and four natural dolomites formed at known temperatures. These included synthetic dolomites grown in Mg-Ca-Cl solutions at temperatures of 200–250°C, and natural samples constrained by fluid inclusion analyses (~70°C), climate (~28 and ~27°C), and deep ocean borehole temperature (~21°C). When using calcite Δ47 acid fractionation values, these data result in a calibration line that is statistically indistinguishable from other clumped isotope calibrations. At least with current precision, we find no evidence for a consistent dolomite Δ47 offset. These results further support a universal calibration for carbonate clumped isotope thermometry and enable new investigations into conditions of dolomite formation.

Elemental analysis of powders with surface-assisted thin film laser-induced breakdown spectroscopy

We have developed in this work a method of elemental analysis of powdered materials with laser-induced breakdown spectroscopy (LIBS). This method requires simple sample preparation. Powders are first mixed into a 75cSt base oil to obtain a paste which is then smeared onto the polished surface of a solid state substrate, aluminum plate for instance, in the form of a uniform thin film. The prepared sample is ablated by a high energy infrared (IR at 1064nm) nanosecond laser pulse. The laser beam transmits through the coating layer of the material to be analyzed and induces a strong plasma from the substrate. The initial plasma interacts in turn with the coating layer, leading to the vaporization and excitation of the incorporated powder particles. The subsequent emission from the plasma includes emission lines of the elements contained in the powder, which is preferentially captured by a suitable detection system. The analysis of the recorded spectrum allows the concentration determination of the targeted elements in the powder. We first applied the method on a cellulose powder of 20μm typical particle size. The powder was spiked with titanium dioxide (TiO2) nanoparticles for Ti concentrations ranging from 25ppm to 5000ppm by weight. Calibration graphs were thus built to deduce figures-of-merit parameters such as the coefficient of determination (R2) and the limits of detection and quantification (LoD and LoQ). We optimized especially the choice of reference line for spectrum normalization, which resulted in better analytical performances. In the second step, two sets of powders, the aforementioned cellulose powder and an alumina powder with average particle size of ≤10μm, were spiked with TiO2 nanoparticles. We then assessed the matrix effect between these two different powders for the determination of Ti by comparing their calibration curves. Our results show universal calibration curve in Ti determination in the two tested matrices. The results are further compared to the case where the powders were prepared in pellet.

Micromachining and validation of the scanning acoustic microscope spatial resolution and sensitivity calibration block for 20-230 MHz frequency range.

Scanning acoustic microscopy (SAM) is used as a routine non-destructive test tool for different diagnostic examinations: detection of defects such as microcracks, delamination, disbonding, inclusions, subsurface features in materials such as pores and cracks. SAM can be operated in a wide frequency range from Megahertz to Gigahertz. SAM measurement spatial resolution is diffraction limited by the wavelength of the acoustic wave in particular medium and also depends on individual transducers geometry. Actual SAM spatial resolution can be determined by measuring calibrated lithographically formed microstructures in high acoustic impedance materials. Numerical acoustic signal simulation method, based on the diffraction approach, was employed for the selection of the calibration block pattern geometry and linear dimensions of the elements. Universal calibration block for SAM operating in a 20-230 MHz frequency range was micromachined in high acoustic impedance ceramic substrates. Differently spaced (from 18 to 185 µm) lines of the same width and different widths (from 17 to 113 µm) but similar spacing lines were imposed in alumina ceramics employing one step lithography process, i.e. femtosecond laser ablation. Proposed SAM calibration pattern linear dimensions were characterized employing optical and scanning electron microscopy. Finally the samples were measured with SAM employing different frequency transducers and results were compared with the numerical simulations. It was obtained that resolution of SAM operating with 230 MHz transducer is not worse than 40 µm.

Viscometric Detection in Size-Exclusion Chromatography: Principles and Select Applications

Size-exclusion chromatography (SEC) has benefitted from commercially available on-line viscometers for 30 years now. Initial (and continued) interest was mostly in applying the universal calibration concept to obtain molar mass averages and distributions of macromolecules for which no appropriate calibration standards existed, and in obtaining long-chain branching information such as branching number and frequency. During the last three decades, viscometry has shown itself to be able to do much more than this, especially (but not exclusively) when employed in multi-detector set-ups which include light scattering photometers. The purpose of this review is to demonstrate the power of viscometry detection in SEC, through applications which showcase the extreme or, simply, the unusual, oftentimes as encountered by the author. A brief review of history and theory is thus followed by examples of the role of viscometry in the SEC characterization of, among others, solutions with negative viscosity, polymers which undergo morphological transformations during growth, polysaccharides with molar mass distributions extending into the hundreds of millions of g mol−1, and spectroscopically invisible macromolecules.

A Method to Create a Universal Calibration Dataset for Raman Reconstruction Based on Wiener Estimation

Raman spectroscopy has been intensively explored in biomedical applications. However, Raman data acquisition is generally slow due to inherently weak Raman signals. Narrow-band Raman measurements can compensate for the weak Raman signal by performing integration in the wavenumber dimension, in which the Raman spectrum with high spectral resolution needs to be reconstructed from the narrow-band measurements. However, this method is limited in the requirement of a calibration dataset, in which the calibration samples have to be similar to test samples in Raman features. Therefore, a new calibration dataset is often needed for every type of samples. We propose a method to create a universal calibration dataset for Raman reconstruction to overcome this limitation. In our method, the Raman spectra measured from each basic biochemical component in samples instead of from actual samples are used in the calibration dataset. In this study, the proposed method was tested on 27 liquid phantoms and 56 cell measurements. The results demonstrated the excellent performance of Raman reconstruction using the universal calibration dataset compared to that using the traditional calibration dataset and the measured Raman spectra.

Transmission and division of total optical depth method: A universal calibration method for Sun photometric measurements

AbstractSun photometric measurements, which provide accurate and timely information on atmospheric components such as aerosols, clouds, and gases are important to climate research. For regions with heavy and variable aerosol loading, the traditional Langley plot method cannot be applied for Sun photometric instrument calibration, as almost no suitable prolonged periods with stable atmosphere and low‐aerosol loading occurs. An improved calibration method, namely, the transmission and division of total optical depth method, is proposed in this study. Atmospheric total optical depth variation information obtained via other methods is transmitted, and period groups with similar atmospheric extinction effects are selected for Langley regression. This method is validated through calibration of a multifilter rotating shadowband radiometer under heavy aerosol‐loading conditions. The obtained aerosol optical depth (AOD) compares well with the interpolated AOD from a Cimel Sun‐sky radiometer.

Cyclization and dispersity of poly(alkylene isophthalate)s

ABSTRACTPoly(alkylene isophthalate)s were prepared by different methods, either in solution or in bulk. The SEC measurements were evaluated in such a way that all oligomers were included. In solution (monomer conc. 0.1–0.7 mol/L) large fractions of rings were formed and high dispersities (up to 12) were obtained, which disagree with theoretical predictions. Polycondensations in bulk did neither generate cyclics by “back‐biting” nor by end‐to‐end cyclization, when the maximum temperature was limited to 210 °C. The dispersities of these perfectly linear polyesters were again higher than the theoretical values. Regardless of the synthetic method monomeric cycles were never observed. Furthermore, SEC measurements performed in tetrahydrofuran and in chloroform and SEC measurements performed in three different institutes were compared. Finally, SEC measurements of five samples were performed with universal calibration and a correction factor of 0.71 ± 0.02 was found for normal calibration with polystyrene. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016, 54, 197–208

Size‐Exclusion Chromatography and Aggregation Studies of Acetylated Lignins in N,N‐Dimethylacetamide in the Presence of Salts

The molar masses of acetylated kraft lignin and organosolv lignin are determined using both dynamic light scattering and size‐exclusion chromatography (SEC). Preparative gel fractionation of both lignins is allowed for the further analysis of low‐polydispersity lignin fractions. Fundamental information about the aggregation behavior of different molecular weight lignins in different solvent systems is provided. Two different solvent systems are used for SEC. Universal calibration is used for analysis. Applying the Flory–Fox theory, the obtained molecular weights are allowed for determining the maximum glass transition temperature at theoretical infinite molecular weight, Tg∞, of both acetylated lignins. image

Broadening of polymer chromatographic signals: Analysis, quantification and correction through effective diffusion coefficients

Average molecular weights and polydispersity indexes are some of the most important parameters considered in the polymer characterization. Usually, gel permeation chromatography (GPC) and multi angle light scattering (MALS) are used for this determination, but GPC values are overestimated due to the dispersion introduced by the column separation. Several procedures were proposed to correct such effect usually involving more complex calibration processes.In this work, a new method of calculation has been considered including diffusion effects. An equation for the concentration profile due to diffusion effects along the GPC column was considered to be a Fickian function and polystyrene narrow standards were used to determine effective diffusion coefficients. The molecular weight distribution function of mono and poly disperse polymers was interpreted as a sum of several Fickian functions representing a sample formed by only few kind of polymer chains with specific molecular weight and diffusion coefficient.Proposed model accurately fit the concentration profile along the whole elution time range as checked by the computed standard deviation. Molecular weights obtained by this new method are similar to those obtained by MALS or traditional GPC while polydispersity index values are intermediate between those obtained by the traditional GPC combined to Universal Calibration method and the MALS method.Values for Pearson and Lin coefficients shows improvement in the correlation of polydispersity index values determined by GPC and MALS methods when diffusion coefficients and new methods are used.

A novel method for rapid determination of alpha-cellulose content in dissolving pulps by visible spectroscopy

A novel method has been developed for the rapid determination of the alpha-cellulose content in dissolving pulps. After alkaline treatment of the sample, the alkaline-soluble portion of the filtrate was transformed into colloids in a medium containing ethanol (80 %). The colloid solution was then measured by visible spectroscopy. The results showed a linear correlation between the root of absorbance at 500 nm and the amount of the colloid in the solution. The linear regression coefficient (R2) was 0.986 for eucalyptus pulp and 0.997 for pine pulp. A universal calibration model has been developed using the partial least square regression technique. The model is robust, and the results have good accuracy, with R2, root mean squared error cross validation, and relative prediction errors of 0.972, 0.492, and 0.51 %, respectively. The model also performed well when compared with the results from the traditional alpha-cellulose measurement method. In summary, the new method is simple, practical and suitable for use to determinate alpha-cellulose content in dissolving pulps in laboratory or industrial applications.

Thin film cryogenic thermometers defined with optical lithography for thermomagnetic measurements on films.

Resistance thermometers are common secondary thermometers in cryogenic applications. Bulk RuO2 thermometers are used in dilution refrigerators because of their low magnetoresistances in addition to their temperature sensitivity. Thermoelectric and thermomagnetic measurements require multiple thermometers to measure temperature differences. Here, we present a method to fabricate thin film RuO2 thermometers directly onto an experimental substrate. This enhances thermal contact between thermometers and films whose thermoelectric or thermomagnetic properties may be measured. Commercial thermometers have higher temperature sensitivities than the thermometers presented in this study, but commercial thermometers must be carefully heat sunk to the cryostat or sample to be useful. Thin film thermometers can be patterned with ultraviolet (UV) lithography. This allows both the size of the thermometer and its distance from the sample, when also patterned with UV lithography, to be on the order of micrometers. A universal calibration curve for these thin film thermometers has not been produced. The efficacy of these thermometers has been demonstrated through measurements of the Nernst effect in Nb. In this study, the thin film thermometers were calibrated using the cryostat thermometers.

Laboratory calibration of the calcium carbonate clumped isotope thermometer in the 25–250 °C temperature range

Many fields of Earth sciences benefit from the knowledge of mineral formation temperatures. For example, carbonates are extensively used for reconstruction of the Earth’s past climatic variations by determining ocean, lake, and soil paleotemperatures. Furthermore, diagenetic minerals and their formation or alteration temperature may provide information about the burial history of important geological units and can have practical applications, for instance, for reconstructing the geochemical and thermal histories of hydrocarbon reservoirs.Carbonate clumped isotope thermometry is a relatively new technique that can provide the formation temperature of carbonate minerals without requiring a priori knowledge of the isotopic composition of the initial solution. It is based on the temperature-dependent abundance of the rare 13C–18O bonds in carbonate minerals, specified as a Δ47 value. The clumped isotope thermometer has been calibrated experimentally from 1°C to 70°C. However, higher temperatures that are relevant to geological processes have so far not been directly calibrated in the laboratory.In order to close this calibration gap and to provide a robust basis for the application of clumped isotopes to high-temperature geological processes we precipitated CaCO3 (mainly calcite) in the laboratory between 23 and 250°C. We used two different precipitation techniques: first, minerals were precipitated from a CaCO3 supersaturated solution at atmospheric pressure (23–91°C), and, second, from a solution resulting from the mixing of CaCl2 and NaHCO3 in a pressurized reaction vessel at a pressure of up to 80bar (25–250°C).The calibration lines of both experimental approaches overlap and agree in the slopes with theoretical estimates and with other calibration experiments in which carbonates were reacted with phosphoric acid at temperatures above 70°C. Our study suggests a universal Δ47-T calibration (T in K, Δ47 in ‰):Δ47=0.98(±0.01)·(-3.407·109/T4+2.365·107/T3-2.607·103/T2-5.880/T)+0.293(±0.004)This new Δ47-T calibration (given in the absolute reference frame), that extends the experimentally calibrated temperature range for clumped isotopes to 250°C, can be applied to carbonates that grew at intermediate temperatures (20–250°C).