Triangular Plots Research Articles

Relative polarities of nine modified cyclodextrin commercial stationary phases in gas chromatographic capillaries

“Polarities” of commercial modified cyclodextrin (CD) gas chromatographic phases were rated at 100 °C by the averages of retention indices for eight McReynolds' probe solutes, by the sequence and proportion of three, and by values for two of them. All nine CDs studied are above the low polarity of a fully methyl polysiloxane, and below the high values of a polyethylene glycol. Values from some CDs are similar to those of polar substituted polysiloxanes. Modifications of α-CD are of lower polarity than their corresponding larger CDs. Dipentyl-(hydroxy remaining)-CDs are of lowest polarity and hydroxypropyl-dimethyl-CDs the highest. Esterified-(dipentyl)-γ-CDs fall between these groups, along with a supposedly fully methyl-β-CD. Surprisingly, the butyryl ester seems to be more polar than the shorter chain propionyl one. These features can be seen from a triangular plot of retention index fractions of the sum of three McReynolds' probes. The c ratios at higher temperatures, involving two different probe solutes, only seem comparable for different modifications of the same ring size CD.

The use of chemical element analyses in the study of biostratigraphically barren sequences: an example from the Triassic of the central North Sea (UKCS)

Abstract A detailed core sampling programme has been completed on biostratigraphically barren Triassic material from seven wells in the Central Graben of the central North Sea (UKCS). Sedimentological, petrographic and chemical element data from these Skagerrak Formation sequences are presented. The objective of the study was to examine the potential use of chemical stratigraphy in the stratigraphic correlation of sequences and the identification of differences in provenance using inductively coupled plasma-atomic emission spectrometry (ICP-AES). The cores examined were taken mainly from the upper parts of the preserved Skagerrak Formation and ranged in thickness from 21.6–130.5 m. Five major facies associations were identified: (1) meandering channels; (2) braided channels: (3) crevasse splays; (4) bioturbated/pedoturbated floodplain; and (5) desiccated playa/floodplain. Braided channel sandstones comprise c. 66% of the examined sequences. Detailed petrographic examination reveals that most of the sandstones are subfeldspathic, feldspathic or sublithic arenites with rarer quartz of lithic arenites. Detrital minerals comprise quartz, K-feldspar, plagioclase, mica, heavy minerals and rock fragments. Authigenic components include silica, feldspar, carbonates, pyrite, anatase, illite, chlorite, corrensite, kaolinite and illite-smectite. Within the total sample suite there are a significant number of clay-prone samples in which the clays are both detrital and authigenic in origin. An extensive ICP-AES analysis for 29 elements was performed on 563 samples. The results allow the clay-prone material to be distinguished from the sandstones owing to higher levels of Al 2 O 3 , MgO, K 2 O, TiO 2 and many trace elements (including Li, La and other transition metals) associated with the clays. Since samples were obtained only from cored intervals from the upper parts of the Triassic section, a complete stratigraphic subdivision and correlation for the study area was not attempted. Bivariate analyses of the ICP-AES data reveal diagnostic correlations between many of the major and trace elements. Moreover, excellent separation between samples from the different wells was seen on a triangular plot of Na 2 O, Fe 2 O 3 + MgO and K 2 O. This separation was even more clearly visible on a triangular plot of Li, Zn and Ni. This appears to be the first use of such a plot for distinguishing Triassic sanstone sequences, and it may yet prove applicable in other intervals. The chemical data also shows stratigraphic differences within some of the Triassic sequences examined. Two of the more extensively cored wells have clearly identifiable chemical signatures for the upper and lower parts of the sequences examined, which can be attributed to rapidly shifting sources and transport regimes during the deposition of these sediments. The extent of this chemical distinction is currently being investigated. Discriminant analysis of the ICP-AES data from the sand-prone samples permitted an excellent confirmation of the distinction between the chemical signatures for each of the wells studied. Discrimination between facies using data from the clay prone samples was not attempted owing to the limited availability of data. However, sand- and clay-prone facies can be broadly distinguished on the basis of their bulk chemistry.

Effects of Ltot-conservation and quantization of vibrational energy in statistical simulations of the reaction Cs∗ (72P12,) + H2 → CsH + H

Abstract The crossed beam experiments of L' Hermite et al.(1990–1991) on the reaction Cs ∗ (72P 1 2 , 3 2 ) + H2 → CsH + H are simulated using the statistical algorithm RRKM-SA. Good agreement between the experimental and calculated rotational quantum number distributions as well as the fractional values of total energy in different degrees of freedom, are obtained. Quantization of vibrational energy is included in the otherwise classical calculations and is shown to be important. The reaction is found to be statistical but with a very strong dependence on the conservation of total angular momentum. In a so-called triangular plot it can be seen that it is the low total available energy that makes the angular momentum restrictions so important. This constraint also means that a considerable portion of the translational energy at the exit centrifugal barrier is instead found in molecular and complex rotational energy. Branching ratios are calculated for the reaction involving both Cs(72P 1 2 ) and Cs(72P 3 2 ) and good agreement with the approximate experimental values are obtained.

A note on the use of statistics in reporting detrital clastic compositions

Error polygons and error bars are commonly used graphical methods for showing the precision associated with means on triangular diagrams and orthogonal plots, respectively. If the error or precision associated with a mean, based either upon counts of individual components or upon count ratios, is to be defined using basic statistics, the confidence interval method should be used. Standard deviation alone, which has been frequently in the literature, is not an appropriate statistic to use for this purpose. The graphical use of confidence intervals permits a rapid visualization of statistically significant differences between means, and thus more quantitative description of detrital clastic composition. Previous investigators using the standard deviation method have underestimated the precision of their data when sample sizes are large, and overestimated precision with small samples.

Automated XY plots from Microsoft Excel

We present a macro program which greatly simplifies the process of making X–Y (scatter) and triangular plots using the spreadsheet program Microsoft Excel ®. The program draws on user-defined “type-plots” to establish plot format, allowing a great amount of flexibility in style and presentation. Predefined templates can be used to define fields or lines for specific purposes and these can be retained easily from plot to plot facilitating rapid comparison of different data sets. The program requires only the addition of some simple control characters to be able to draw data from existing spreadsheets with little or no reformatting.

Radioisotope-Excitation XRF Determination of Trace Elements in Marble

The energy-dispersive x-ray fluorescence technique was employed to determine quantitatively the concentrations of trace elements in 22 pieces of thick marble of various sizes from Portugal and Thailand, with the use of the radioactive sources Fe-55, Cd-109, and Am-241 in order to cover a wide range of elements. The reliability of the concentration determination was confirmed by employing two different methods which gave the same quantitative values of iron within experimental errors. The following trace elements were found to be present in varying concentrations: manganese (0–244 ppm), iron (110–4104 ppm), copper (14–64 ppm), zinc (0–665 ppm), arsenic (0–27 ppm), strontium (100–335 ppm), and yttrium (0–12 ppm). It was found that, besides iron, which is responsible for the staining or coloring of marbles, manganese can cause dark streaks and colored patches and has values as high as 244 ppm. With the use of iron, yttrium, and strontium in a triangular plot, the pieces from Portugal and Thailand, respectively, divided into two well-defined groups which are well separated from each other, showing that it is possible to identify the origin of the marble pieces.

Graphical analysis of rare gas mixing systematics in geothermal systems.

The utility of helium and neon isotopes as tracers of mixing in geothermal systems may be enhanced by employing an appropriate method of graphical analysis. On linear 3He/4He-20Ne/4He diagrams mixing is revealed by straight lines. This is contrary to the current procedure of plotting 3He/4He against 4He/20Ne, where mixing lines are curved. Construction of triangular mixing plots with such data allows an immediate quantitative assessment of the extent to which the measured isotopic ratios reflect those of different endmembers (e.g. atmospheric, radiogenic and magmatic) and allows one to use these plots to compare the sources of rare gases in geothermal systems from different parts of the globe.

Assessment of the polarity of three liquid crystals used as gas chromatographic stationary phases

Attempts to evaluate the polarity of three liquid crystals used in packed gas chromatographic columns suggest that more than one method is required at different temperatures. At 120°C a triangular proportional plot of retention indices using three McReynolds' solute probes indicate azoxydiphenetole (ADP) and bis(methoxy-benzylidineanilchloroaniline) [(MBCA) 2] are reasonably strong in polarity. Bis(methoxybenzylidineanilbitoluidine) [(MBT) 2] is moderately polar, compared to normal-phase columns. At 160°C, however, using the sum of retention indices of three C 10 volatile oil constituents, ADP and (MBCA) 2 rate as only moderately polar, with (MBT) 2 now exhibiting low polarity. The polarity sequence of the three liquid crystals (unmelted, melted and supercooled) is confirmed by the second method. Their polarity rating is method-sensitive, although they change in polarity more than normal chromatographic phases with temperature alterations. The selection of a liquid crystal for particular separations is discussed.

Assessment of methane ignition potential by frictional processes from Australian coal mine rocks

A method for categorising the potential of different rocks to ignite methane gas in mine atmospheres has been developed for a suite of sedimentary and igneous samples from Australian coal mine areas, based on rock-on-rock friction behaviour in a rotating-wheel test rig. The five-point ignition potential categorization (IGCAT value) is derived from the occurrence of ignitions or non-ignitions in a gas chamber with a 7% methane atmosphere when a sample of the rock is pressed with a constant load against a rotating wheel of the same material at contact speeds of 2.2, 3.7 and 5.1 m/s. Statistical assessment of the relationship between the IGCAT values and other properties of the rocks concerned has shown that a high frictional ignition category is associated with an abundance of quartz, lithic fragments and, to a lesser extent, feldspar grains in the rocks tested, but that incendivity is reduced by the presence of carbonates, mica and clay minerals. Evaluation of incendivity based only on the percentage of quartz was found to give relatively poor correlations, irrespective of the method used to determine the quartz content. More effective predictors of ignition category include assessments using the inverse relationship between the IGCAT value and loss-on-ignition percentage, determined by heating the rock to 1050{degree}C, or by equations derived from multiple regression analyses that link percentages of key mineralogical components to the IGCAT value. A triangular diagram graphic plot has been developed to illustrate the principal relationships and provide a better framework than has been previously available for predicting rock incendivity from mineralogical characteristics. 28 refs., 12 figs., 7 tabs.

Progress in 1988–1990 with computer applications in the “hard-rock” arena: Geochemistry, mineralogy, petrology, and volcanology

This review covers rock, mineral and isotope geochemistry, mineralogy, igneous and metamorphic petrology, and volcanology. Crystallography, exploration geochemistry, and mineral exploration are excluded. Fairly extended comments on software availability, and on computerization of the publication process and of specimen collection indexes, may interest a wider audience. A proliferation of both published and commercial software in the past 3 years indicates increasing interest in what traditionally has been a rather reluctant sphere of geoscience computer activity. However, much of this software duplicates the same old functions (Harker and triangular plots, mineral recalculations, etc.). It usually is more efficient nowadays to use someone else's program, or to employ the command language in one of many general-purpose spreadsheet or statistical packages available, than to program a specialist operation from scratch in, say, FORTRAN. Greatest activity has been in mineralogy, where several journals specifically encourage publication of computer-related activities, and IMA and MSA Working Groups on microcomputers have been convened. In petrology and geochemistry, large national databases of rock and mineral analyses continue to multiply, whereas the international database IGBA grows slowly; some form of integration is necessary to make these disparate systems of lasting value to the global “hard-rock” community. Total merging or separate addressing via an intelligent “front-end” are both possibilities. In volcanology, the BBC's videodisk Volcanoes and the Smithsonian Institution's Global Volcanism Project use the most up-to-date computer technology in an exciting and innovative way, to promote public education.

Notes on Pascal's pyramid for personal computer users

A lattice of octahedra and tetrahedra (called an “oct-tet lattice”) is a useful paradigm for understanding the structure of Pascal's pyramid, the 3D analog of Pascal's triangle. Notation for levels and coordinates of elements, a standard algorithm for generating the values of various elements, and a ratio method that is not dependent on the calculation of previous levels are discussed. The figures show a bell curve in 3D, the association of elements to primes and twin primes, and the values of elements mod( x) through patterns arranged in triangular plots. It is conjectured that the largest factor of any element is less than the level index.

Pebble Shape (and Size!)

ABSTRACT The mathematical technique of R-mode factor analysis was applied to the long, intermediate and short axes of one synthetic random data set and three sets of natural pebbles to extract the three fundamental factors related to these parameters. One factor corresponds to size, which is best described by the mean of the axes. Two further factors correspond to shape: sphericity and disc-rodness. These factors are revealed whether synthetic data or natural pebble samples are analyzed. Extending the factor analysis to include shape indices revealed which indices are equivalent, which are most useful, and which should be discarded. Sphericity is best described with the Corey shape index, S/(IL), and disc-rodness is best described with the disc-rod index, (L - I)/(L - S). Accordingly, the most effective shape diagram is a triangular plot of these two shape indices; the three end-members of shape are spheres, discs and rods. Shape is best investigated using this shape diagram; a 2-D technique such as contouring point density on this diagram should be used to determine the mean and standard deviation of shape. While others ask themselves 'What is there to do?', I ask myself 'What is there that I can avoid doing?' Masanobu Fukuoka, One Straw Revolution

TEEPLOT—A microsoft quick-basic program for the analysis of clast morphology

TEEPLOT Microsoft Quick-BASIC program is an easy-to-use, menu-driven program that aids the user in the analysis of clast morphology. The program has an editor designed especially for the input of clast data and provides output of triangular plots, histograms, and data statistics.

Petrology and Provenance of the Great Valley Group. Southern Klamath Mountains and Northern Sacramento Valley: ABSTRACT

Lower Cretaceous sandstone and conglomerate of the Great Valley Group rest depositionally on the southern Klamath Mountains at the north end of the Sacramento Valley. Exposures include nonmarine, shallow marine, and deep marine sediments, which are part of the Platina Formation (petrofacies). Approximately 150 sandstone point counts (500 points per section using Gazzi-Dickinson method) and 32 conglomerate clast counts indicate a Klamath provenance of mixed magmatic-arc and recycled orogenic character. Standard triangular plots and multivariate analyses (combined with paleocurrent and paleogeographic data) suggest discrete source areas within the Klamath terrane. However, the general homogeneity of both sandstone and conglomerate petrology is consistent with all of the units being included within the Platina petrofacies.

Production of ethanol by Clostridium thermosaccharolyticum: II. A quantitative model describing product distributions

The study of the continuous culture of Clostridium thermosaccharolyticum on xylose showed multiple steady states and hysteresis. A quantitative model based on the biochemistry and physiology of xylose fermentation by C. thermosaccharolyticum was developed. The objective in developing this model was to bring together the observations both of this study and of other researchers on the fermentation of xylose. The model equations were written based on the metabolic pathway for xylose utilization by C. thermosaccharolyticum and the requirement that the carbon, ATP, and NADH within the cell be balanced. Given the specific growth rate mu and the specific xylose utilization rate q(s), a set of product distributions (ethanol, acetate, and lactate) satisfying these balances was obtained. This set was plotted on a triangular plot and named the permitted region. The product distributions within this permitted region were shown to be affected by the environmental parameters such as iron concentration and hydrogen partial pressure. The model predicted trends in product distribution which correlate with experimentally observed phenomena. The model was also used to analyze the continuous-culture data from our experimental work.

Triangular Plots and Spreadsheet Software

Spreadsheet software is being widely used in geology for the storage and manipulation of data. The built-in graphics capabilities of most spreadsheet software are limited in their scientific applications. Many of these limitations can be overcome by making full use of the flexibility of the graphics options. For example, the commonly used triangular plots with labeled field boundaries can be easily produced using Lotus 1-2-3 spreadsheet software. The basic techniques can be applied to other types of graphs to further enhance the use of this type of software for dealing with geological data.

A useful triangular plot of triatomic potential energy surfaces

A triangular plot of triatomic potential energy surfaces is suggested in which the hidden coordinate - the perimeter of the molecule or the sum of squares of the three bond distances - is allowed to relax in order to give the lowest potential energy. This graphical representation preserves the full permutational symmetry of the problem. Examples are presented for the H 3 and HO 2 systems.

Triangular characterization of gas chromatographic stationary phases

Three solute probes used by McReynolds, butanol, pyridine and octyne, were selected to check retention index ( I R) values on various packed columns. Their ratios proved more consistent than their absolute values. A triangular plot of relative I R suggested three groupings of stationary phases: polar, non-polar and intermediate. Three selected polysiloxanes should suffice to represent these groups for most work.

Petroleum isotopic and biomarker composition related to source rock organic matter and depositional environment

A multivariate approach has been developed that separates oils derived from organic matter in nonmarine shales, marine shales, and marine carbonates. Some or all of the following analyses were completed on 43 oils from known source rocks: (1) C 30-sterane and monoaromatic steroid biomarker ratios, and (2) stable carbon and hydrogen isotope compositions of whole oil, saturates, and aromatics. Three-group discriminant analysis of the 28 oils whereall biomarker and isotopic data are available results in no misclassifications at a significance level of 99%. Using only carbon and hydroogen isotopic data for whole oils, saturates, and aromatics results in correct classifications of 82% for oils derived from marine shale organic matter and 100% for oils from the other two sources. Triangular plots probabilities can be used to distinguish oils derived from the three source rock organic matter end-members. Several publications describe classifications of “marine” vs “nonmarine” oils using stable carbon isotope ratios of the whole oil or the saturate and aromatic fractions. Our results confirm that these methods do not completely differentiate oils by source.

Biliary lipid secretion in health and in cholesterol gallstone disease.

The secretory compartment for biliary lecithin and cholesterol secretion probably resides in the smooth endoplasmic reticulum of the hepatocyte. The secretory compartment for bile salts lies predominantly in the enterohepatic circulation which fluxes bile salts continuously through the smooth endoplasmic reticulum compartment and extracts lipids for secretion into bile. Most of bile lecithin is newly synthesized by the liver; most of bile cholesterol is derived from extrahepatic sources. Both cholesterol and lecithin secretion are coupled to bile salt secretion and describe output curves which can be fitted by rectangular hyperbolae: since bile salt secretion is a linear function of input, the relative proportions of cholesterol to bile salts plus lecithin in bile increase at low bile salt outputs. In health, an adequate bile salt (+ lecithin) secretion coupled with normal cholesterol secretion maintains the relative composition of bile in a stable state: fasting compositions usually lie within the micellar zone or metastable supersaturated zone of a triangular coordinate-phase diagram plot. In cholesterol gallstone disease, mean bile salt (+ lecithin) secretion rates are subnormal and/or mean cholesterol secretion rates are supranormal, especially in the fasting state. If individuals are obese there is also enhanced hypersecretion of biliary cholesterol. Either or both secretory defects lead to an elevation and persistence of cholesterol supersaturation of bile. The physical state of the secreted lipids in bile is complex and fluctuant, and probably involves vesicle structures and mixed micelles at high water and cholesterol concentrations and predominantly micellar structures at low water and cholesterol concentrations. In lithogenic bile, the physical state, proportions and nucleation potential of the lipid aggregates are probably different.(ABSTRACT TRUNCATED AT 250 WORDS)