A distribution-free alternative to least-squares regression and its application to Rb/Sr isochron calculations

A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated S_m and is given by the median of the set of n(n – 1)/2 slope estimators, which may be calculated by inserting pairs of points (X _i, Y_i)and (X _j, Y_j)into the slope formula S _i = (Y _i – Y_j)/(X _i – X_j),1 i < j n Once S _m is determined, outliers may be detected by calculating the residuals given by R_i = Y_i – S_mX_i where 1 i n, and chosing the median R_m. Outliers are defined as points for which |R_i – R_m| > k (median {|R _i – R_m|}). If no outliers are found, the Y-intercept is given by R_m. Confidence limits on R_m and S_m can be found from the sets of R_i and S_i, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques.     

Graphical estimations of magma densities and compositional expansion coefficients

Assuming that the partial molar volume of each chemical component in a magma is constant, the magma density, _m , is expressed as 1/ _m =C _i / _fi , whereC _i is the weight fraction, and _fi is the fractionation density of thei ^th component. Using this linear relationship between 1/ and weight fraction, the density change due to addition or subtraction of any component can be graphically estimated on 1/ vs oxide wt% diagrams. The compositional expansion coefficient of thei ^th component, _fi , is expressed as _i = _m / _fi –1. The compositional expansion coefficient of H₂O has a much larger absolute value than those of any other oxide or mineral components, showing that addition of a small amount of H₂O can significantly decrease magma density. These simple expressions facilitate the estimation of magma densities during fractionation.     

Compressional behaviour of CaNiSi2O6 clinopyroxene: bulk modulus systematic and cation type in clinopyroxenes

A single-crystal of composition CaNiSi₂O₆ (space group C2/c) was investigated at high pressure up to about 7.8 GPa by X-ray diffraction. The unit-cell parameters were measured at 18 different pressures. The P-V data were fitted by a third-order Birch-Murnaghan equation of state V₀=435.21(1) ų, K ₀=117.6(3) GPa and K^=6.4(1). The linear axial compressibilities _a, _b, _c and a sin are 2.14(1), 3.00(1), 2.43(1) and 1.63(1) × 10–3 GPa^–1. Comparing the compressibility data with other CaM1Si₂O₆ pyroxenes we suggest that the empirical K × V = constant relationships are followed in C2/c pyroxenes only if the same valence electron character is shared.     

Vertumnite,a new natural silicate

Summary A natural calcium aluminum silicate hydrate, vertumnite, is described as a new mineral. It has been found as transparent flattened hexagonal prisms resting on a layer of tobermorite inside a subspherical geode of a phonolite from a quarry at Campomorto, Montalto di Castro, Viterbo, Italy. Most of the crystals are biaxial negative and twinned. The single crystal measurements on an optically homogeneous and biaxial individual gave:a=0.5744 (5) nm,b=0.5766(5) nm,c=2.512(1) nm, =119.72(5)° and space groupP2₁/m orP2₁. The optical properties are:n =1.531(1),n =1.535(1),n =1.541(2) and 2V =62°. The chemical formula is: (Na_0.02K_0.02Ca_3.76Sr_0.06Ba_0.01)_tot=3.87 Al_4.36(P_0.03Si_3.38)_tot=3.41O_5.18 (OH)_24.66·3.09H₂O or schematically Ca₄Al₄Si₄O₆(OH)₂₄ ·3 H₂O. Both the powder data and chemical analysis suggest the mineral to be stronghly related to the synthetic Strätling's compound or hexagonal hydrated gehlenite although the different Si/Al ratios in two inhibit direct correlations.

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Vertumnit, ein neues natürliches Silikat

Zusammenfassung Ein natürliches, wasserhaltiges Calcium-Aluminium-Silikat, Vertumnit, wird als neues Mineral beschrieben. Es kommt in durchsichtigen, flachen, hexagonalen Prismen vor, die auf einer Tobermorit-Schicht in einer kugeligen Geode eines Phonoliths einer Grube in Campomorto, Montalto di Castro, Viterbo, Italien, gefunden wurden. Die meisten Kristalle sind zweiachsig negativ und verzwillingt. Einkristallmessungen an einem optisch homogenen und zweiachsigen Individuum ergaben:a=0,5744(5) nm,b=0,5766(5) nm,c=2.512(1) nm, =119.72(5)° mit RaumgruppeP2₁/m oderP2₁. Die optische Eigenschaften sind wie folgt:n =1,531(1),n =1,535(1),n =1,541(2), 2V =62°. Die chemische Formel ist: (Na_0.02K_0.02Ca_3.76Sr_0.06Ba_0.01)_tot=3.87Al_4.36(P_0.03Si_3.38)_tot=3.41 O_5.18(OH)_24.66·3,09 H₂O oder schematisch Ca₄Al₄Si₄O₆(OH)₂₄·3 H₂O. Sowohl die Pulverdaten als auch die chemische Analyse weisen auf eine Verwandtschaft mit der Strätling-Verbindung oder hexagonal hydrated gehlenite hin, obwohl die verschiedenen Si/Al-Verhältnisse in beiden direkte Beziehungen verhindern.

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With 3 Figures     

Tungsten-bearing baotite from Pierrefitte,Pyrenees, France

Summary Baotite occurs in the Garaoulére orebody, at Pierreftte, France, as an accessory mineral, included in alstonite and celsian, and associated with sphalerite, galena, pyrite, siderite and calcite in hydrothermal veins crosscutting calcareous, rutile-bearing, siltstones. Microprobe analyses revealed high W0₃ concentrations (up to 6 wt.%) in baotite. The empirical formula of W-rich baotite is Ba_3.959Ti₄(Ti_3.169W_0.393Fe_0.116Al_0.073 Cr_0.048Nb_0.024)_3.823 Si_4.05O₂₈Cl_1.166. The excess of charges due to the presence of W⁶⁺ and Nb⁵⁺ is compensated by the introduction of M³⁺ (Fe, Al, Cr) into Ti-octahedra, by the appearance of Al in Si-tetrahedra (for W-poor baotite) and by the appearance of vacancies in Ti-octahedra (3Ti⁴ -> 2W⁶⁺ + and in Ba-sites (Ti⁴⁺ Ba²⁺ W⁶⁺, ). The unit-cell parameters of W-rich baotite are: a = 19.92(2), c = 5.930(8) Å. Niobium-rich baotites (Baiyun-Obo,Semenov et al., 1961; Karlstein,Nmec, 1987) are characterized by substitutions: Ti⁴⁺(VI), Si⁴⁺(IV)Nb⁵⁺(VI), Al³⁺(IV) and 2Ti⁴⁺, Ba²⁺ 2Nb⁵⁺, .

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Wolfram führender Baotit von Pierrefitte, Pyrenäen, Frankreich

Zusammenfassung Baotit kommt in dem Garaoulére Erzkórper in Pierrefitte, Frankreich als ein akzessorisches Mineral in Einschlÿussen in Alstonit und Celsian vor. Er ist mit Zinkblende, Bleiglanz, Pyrit, Siderit und Calcit assoziiert. Diese Paragenese ist an hydrothermale Gänge gebunden, die kalkige rutil-führende Siltsteine durchsetzen. Mikrosondenanalysen zeigen hohe W0₃ Gehalte (bis zu 6 Gew.%) in Baotit. Die empirische Formel von wolfram-reichem Baotit ist: Ba_3.959Ti₄(Ti_3.169W_0.393Fe_0.116Al_0.073Cr_0.048Nb_0.024)_3.823 Si_4.05O₂₈Cl_1.66. Der durch die Anwesenheit von W⁶⁺ und Nb⁵⁺ erforderliche Ladungsausgleich ergibt sich durch das Eintreten von M³⁺ (Fe, Al; Cr) in Ti-Oktaeder, und von Al in Si-Tetraeder (für W-armen Baotit) und schließlich durch das Erscheinen von Leerstellen in Ti-Oktaedern (3Ti⁴⁺ 2W6+ + und in Ba-Stellen (Ti⁴⁺, Ba` W⁶⁺, Die Zellparameter von ldW-reichem Baotit sind: a = 19.92(2), c = 5.930(8) Å. Niob-reiche Baotite (Baiyun-Obo, Semenov et al., 1961; Karlstein, Nmec, 1987) sind durch Substitutionen charakterisiert: Ti⁴⁺(VI), Si⁴⁺(IV)Nb⁵⁺(VI), Al³⁺(IV) und 2Ti⁴⁺, Ba²⁺ 2Nb⁵⁺, .

     

Silicate melts at magmatic temperatures: in-situ structure determination to 1651°C and effect of temperature and bulk composition on the mixing behavior of structural units

The abundance of coexisting structural units in K-, Na-, and Li-silicate melts and glasses from 25° to 1654°C has been determined with in-situ micro-Raman spectroscopy. From these data an equilibrium constant, K_x, for the disproportionation reaction among the structural units coexisting in the melts, Si₂O₅(2Q³)SiO₃(Q²)+SiO₂(Q⁴), was calculated (K_x is the equilibrium constant derived by using mol fractions rather than activities of the structural units). From ln K_x vs l/T relationships the enthalpy (H_x) for the disproportionation reaction is in the range of-30 to 30 kJ/mol with systematic compositional dependence. In the potassium and sodium systems, where the disproportionation reaction shifts to the right with increasing temperature, the H_x increases with silica content (M/Si decreases, M=Na, K). For melts and supercooled liquids of composition Li₂O·2SiO₂ (Li/Si=1), the H_x is indistinguishable from 0. By decreasing the Li/Si to 0.667 (composition LS3) and beyond (e.g., LS4), the disproportionation reaction shifts to the left as the temperature is increased. For a given ratio of M/Si (M=K, Na, Li), there is a positive, near linear correlation between the H_x and the Z/r² of the metal cation. The slope of the H_x vs Z/r² regression lines increases as the system becomes more silica rich (i.e., M/Si is decreased). Activity coefficients for the individual structural units, _i, were calculated from the structural data combined with liquidus phase relations. These coefficients are linear functions of their mol fraction of the form _i=a lnX _i+b, where a is between 0.6 and 0.87, and X _i is the mol fraction of the unit. The value of the intercept, b, is near 0. The relationship between activity coefficients and abundance of individual structural units is not affected by temperature or the electronic properties of the alkali metal. The activity of the structural units, however, depend on their concentration, type of metal cation, and on temperature.     

Chemistry of some Pb-(Cu,Fe)-(Sb,Bi sulfosalts from France and Portugal. Implications for the crystal chemistry of lead sulfosalts in the Cu-poor part of the Pb2S2-Cu2S-Sb2S3-Bi2-Bi2S3 system

Electron microprobe analysis of Pb-Cu(Fe)-Sb-Bi sulfosalts from Bazoges and Les Chalanches (France), and Pedra Luz (Portugal), give new data about (Bi, Sb) solid-solution and incorporation of the minor elements Cu, Fe or Ag in jaskolskiite, and in izoklakeite-giessenite and kobellite-tintinaite series. Jaskolskiite from Pedra Luz has high Sb contents (from 17.9 to 20.7 wt.%), leading to the extended general formula: Cu _x Pb_2+x (Sb_1–y Bi _y )_2–x S₅, with 0.10 x 0.22 and 0.19 y 0.41. Fe-free, Bi-rich izoklakeite from Bazoges has high Ag contents (up to 2.2 wt. %), leading to the simplified formula Cu₂Pb₂₂Ag₂(Bi, Sb)₂₂S₅₇; in Les Chalanches it contains less Ag content (1.2 wt.%), but has an excess of Cu that gives the formula: Cu_2.00 (Cu_0.49Ag_1.18)_=1.67Pb_22.70(Bi_12.63Sb_8.99)_=21.62S_57.27.In tintinaite from Pedra Luz, the variation of the Fe/Cu ratio can be explained by the substitution: Cu + (Bi, Sb) Fe + Pb; Fe-free kobellite from Les Chalanches has a Cu-excess, corresponding to the formula Cu_2.81Ag_0.54Pb_9.88(Bi_10.37Sb_5.21)_=15.38S_35.09. Eclarite from the type locality, structurally related to kobellite, shows a Cu excess too. In natural samples of the kobellite homologous series, Fe is positively correlated with Pb, and its contents never exceed that of Cu. Ag substitutes for Pb, together with (Bi, Sb). Taking into account the possibility of Cu excess, but excluding formal Cu²⁺ and Fe³⁺, general formulae can be written:     

Estimation of mean trace length of discontinuities

Summary Trace lengths of discontinuities observed on finite exposures are biased due to sampling errors. These errors should be corrected in estimating mean trace length. A technique, which takes into account the sampling errors, is proposed for estimating the mean trace length on infinite, vertical sections from the observations made on finite, rectangular, vertical exposures. The method is applicable to discontinuities whose orientation is described by a probability distribution function. The method requires that the numbers of discontinuities with both ends observed, one end observed, and both ends censored be known. The lengths of observed traces and the density function of trace length are not required. The derivation assumes that midpoints of traces are uniformly distributed in the vertical plane. Also independence between trace length and orientation is assumed. Data on a Pennsylvania shale in Ohio, U. S. A., were used as an example.Notations dip direction - direction of sampling plane - acute angle between dip direction and sampling plane - dip angle - _A apparent dip angle - mean density of trace mid-points per unit area - mean trace length - D diameter of discontinuity - f (.),g (.) probability density function - h height of rectangular window - estimator of mean trace length - m sample size, number of discontinuities intersecting window - m ₀ number of discontinuities intersecting window with both ends censored - m ₂ number of discontinuities intersecting window with both ends observed - n, N expected number of discontinuities intersecting the window - n ₀,N ₀ expected number of discontinuities intersecting the window with both ends censored - n ₂,N ₂ expected number of discontinuities intersecting the window with both ends observed - Pr (.) probability - w width of rectangular window - x trace length     

The age of the sub Mid-Jurassic tropical weathering profile of andoya,northern Norway,and the implications for the late palaeozoic palaeography in the North Atlantic region

Results are given of a programme of K-Ar age determinations from an equatorial weathering profile beneath the Mid-Jurassic unconformitiy of Anøya, northern Norway. A model is presented where the original age of weathering is considered as Lower Carboniferous with partial resetting of ages during subsequent diagenesis. It is concluded that the Kaolinite of the weathering profile became a closed system of⁴⁰Ar diffusion in late Triassic times, and that a sufficient thickness of Mesozoic-Tertiary strata was never developed to occasion the resetting of the ages. The implication of the results is that a former thick cover of Upper Palaezoic age formerly existed in the region which was effectively removed by erosion in late Triassic — early Jurassic times. The results of the study are reviewed in a context of North Atlantic palaeogeographical evolution.

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Zusammenfassung Aus einem fossilen Bodenprofil unterhalb der mitteljurassischen Diskordanz in Nordnorwegen wurden K-Ar-Alter bestimmt, die auf eine Verwitterung während des Unterkarbons hinweisen. Während der folgenden Diagenese sind die Alter teilweise neu eingestellt worden. Dabei zeigt sich, daß der Kaolinite des ursprünglichen Bodenprofils erst ab Obertrias einem für Ar⁴⁰-Diffusion geschlossenen System angehört. Es folgt weiter, daß während des Mesozoikums und Tertiärs keine größere Sedimentbedeckung mehr über diesen Profilen möglich war, wohingegen eine erhebliche Mächtigkeit von jungpaläozoischen Sedimenten ehedem vorlag, die während der Obertrias abgetragen wurde. Diese Beobachtungen können mit der paläogeographischen Entwicklung des Nord-Atlantik in Zusammenhang gebracht werden.

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Résumé On a déterminé les âges K-Ar, donnés par un sol d'alteration formé pendant le Carbonifère inférieur et sous-jacent à la discordance du jurassique moyen, au nord de la Norvège. Les âges ont été en partie de nouveau déterminés, lors des diagénèses suivantes. Il en ressort que la Kaolinite du profil du sol originel n'appartient à un système fermé de diffusion Ar⁴⁰ qu'à partir du Trias supérieur. Il s'ensuit qu'un recouvrement sédimentaire épais n'a pu se déposer sur ce profil au cours du Secondaire et du Tertiaire, tandis qu'une épaisseur considérable de sédiments du Paléozoique supérieur existait, enlevès ensuite par érosion au Trias supérieur. Ces observations peuvent être mises en rapport avec le développement paléogéographique de l'Atlantique-Nord.

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An objective replacement method for censored geochemical data

Geochemical data are commonly censored, that is, concentrations for some samples are reported as less than or greater than some value. Censored data hampers statistical analysis because certain computational techniques used in statistical analysis require a complete set of uncensored data. We show that the simple substitution method for creating an uncensored dataset, e.g., replacement by3/4 times the detection limit, has serious flaws, and we present an objective method to determine the replacement value. Our basic premise is that the replacement value should equal the mean of the actual values represented by the qualified data. We adapt the maximum likelihood approach (Cohen, 1961) to estimate this mean. This method reproduces the mean and skewness as well or better than a simple substitution method using3/4 of the lower detection limit or3/4 of the upper detection limit. For a small proportion of less than substitutions, a simple-substitution replacement factor of 0.55 is preferable to3/4; for a small proportion of greater than substitutions, a simple-substitution replacement factor of 1.7 is preferable to4/3, provided the resulting replacement value does not exceed 100%. For more than 10% replacement, a mean empirical factor may be used. However, empirically determined simple-substitution replacement factors usually vary among different data sets and are less reliable with more replacements. Therefore, a maximum likelihood method is superior in general. Theoretical and empirical analyses show that true replacement factors for less thans decrease in magnitude with more replacements and larger standard deviation; those for greater thans increase in magnitude with more replacements and larger standard deviation. In contrast to any simple substitution method, the maximum likelihood method reproduces these variations. Using the maximum likelihood method for replacing less thans in our sample data set, correlation coefficients were reasonably accurately estimated in 90% of the cases for as much as 40% replacement and in 60% of the cases for 80% replacement. These results suggest that censored data can be utilized more than is commonly realized.     

Über den Hügelit

Zusammenfassung Der Hügelit, das Arsenat-Analogon zum Dumontit, gehört zu den Sekundärmineralien der Grube Michael im Weiler bei Lahr im Schwarzwald (Bundesrepublik Deutschland), wo er zusammen mit Hallimondit, Widenmannit, Mimetesit, Cerussit und Zeunerit in Drusen von hornsteinartigem Quarz auftritt. Beobachtete kristallographische Formen: {100}, {110}, {001}, {011} sowie (?) {010}.Spaltbarkeit nach {100} sehr gut, nach {110} unsicher. Bruch muschelig. Härte etwa 2 1/2; spröde.Farbe braun bis orangegelb; durchsichtig bis durchscheinend. Strich hellgelb. Keine UV-Fluoreszens. Brechungsindizes:n =1,898(5),n =1,915(5), 2V =25° (für =592 nm); sehr starke Achsenwinkeldispersion.Gitterkonstanten:a ₀=8,13,b ₀=17,27,c ₀=7,01 Å, =109°. Raumgruppe:P2₁/m oderP2₁.D _x=5,80 g·cm^–3 (mit der Formel Pb₂(UO₃)₃(AsO₄)₂(OH)₄·3H₂O undZ=2). Stärkste Linien des Pulverdiagramms: 3,73(10), 3,06(9), 3,00(7) und 2,89(7).

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On Hügelite

Summary Hügelite, the arsenate analogue of dumontite, occurs amongst the secondary minerals of the Michael Mine at Weiler near Lahr in the Black Forest (German Federal Republic), in vugs of dense quartz in association with hallimondite, widenmannite, mimetite, cerussite and zeunerite. Observed crystal forms: {100}, {110}, {001}, {011} and (?) {010}.Cleavage: {100} very good, {110} uncertain. Fracture conchoidal. Hardness about 2 1/2, brittle.Colour brown to orange yellow, transparent to translucent. Not fluorescent in ultraviolet light. Indices of refraction:n =1.898(5),n =1.915(5); 2V =25° (for =592 nm); strong dispersion of the axial angle.Unit-cell dimensions:a ₀=8.13,b ₀=17.27,c ₀=7.01 Å, =109°, space groupP2₁/m orP2₁.D _x=5.80 g·cm^–3 (with the formula Pb₂(UO₂)₃(AsO₄)₂(OH)₄·3H₂O andZ=2). Strongest lines of the powder pattern: 3.73(10); 3.06(9); 3.00(7); 2.89(7).

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Mit 2 Abbildungen

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Herrn Univ. Prof. Dr.H. Meixner zum 70. Geburtstag gewidmet.     

Rooseveltit von San Francisco de los Andes und Cerro Negro de la Aguadita,San Juan,Argentinien

Zusammenfassung Rooseveltit findet sich in der Oxidationszone der Lagerstätten San Francisco de los Andes und Cerro Negro de la Aguadita, in der Provinz San Juan, Argentinien, auf 30°22 S und 69°33 W. Er bildet sehr feinkörnige, weiß-graue, nach Bismuthinit pseudomorphe Aggregate. Die Brechungsindizes liegen zwischenn=2,10 und 2,30. Die Vickershärte beträgt 513 (4–5 der Mohs'schen Härteskala). Mittels Elektronenmikrosonde wurde folgende chemische Zusammensetzung bestimmt: As=21,5±1%, Bi=60,9±2%. Rooseveltit ist monoklin mita ₀=6,878(1)Å, b₀=7,163(1) Å, c₀=6,735(1) Å, =104° 46±1, Z=4, _calc.=6,94 g·cm^–3, RaumgruppeP 2₁/n.Rooseveltit wurde nach drei verschiedenen Methoden synthetisiert. Die Pulverdiagramme der synthetischen Produkte stimmen mit dem des Minerals überein. Die Brechungsindizes wurden mitn =2,13(2) bzw. n=2,25(2) und die Dichte mit _obs.=7,01 g·cm^–3 bestimmt. Zellparameter: a₀-6,882(1) Å, b₀=7,164(1) Å, c₀=6,734(1) Å, =104° 50,5±0,7, _calc.=6,94 g·cm^–3. Das synthetische Material schmilzt um 950°C. Selbst nach mehrstündigem Erhitzen auf 920°C läßt sich keine Veränderung im Pulverdiagramm des Minerals festellen.Es wird versucht, die natürliche Bildung des Rooseveltits zu erklären.

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Rooseveltite from San Francisco de los Andes and Cerro Negro de la Aguadita, San Juan, Argentina

Summary Rooseveltite occurs in the weathering zone of the San Francisco de los Andes and Cerro Negro de la Aguadita mines, located in the San Juan Province, Argentina, at 30° 22S and 69° 33W. It appears in grey, finegrained aggregates pseudomorph after bismuthinite. Refraction index ranges fromn=2.10 to 2.30. The Vickers microhardness is 513 (4–5 of Mohs' scale). Chemical composition from electron micro probe measurements is As 21.5±1% and Bi 60.9±2%. Rooseveltite is monoclinic, with a₀=6.878(1) Å, b₀=7.163(1) Å, c₀=6.735(1) Å, =104° 46±1, Z=4, _calc.=6,94 g·cm^–3, space groupP 2₁/n.The synthetic compound was prepared by three different methods. The powder pattern are the same as that of the mineral. Refraction index n=2.13(2) and n=2.25(2). The measured specific gravity is _pobs.=7,01 g·cm^–3. Cell parameters: a₀=6.882(1) Å, b₀=7.164(1) Å,c ₀=6.734(1) Å, =104° 50.5±0.7, _calc.=6,94 g·cm^–3. The synthetic material melts at about 950°C. After heating to 920°C no variations were observed in the powder diagram of the mineral.It is tried to explain the formation of rooseveltite in natural environment.

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Mit 2 Abbildungen     

Crystal structure of Di50CaTs50 synthetic clinopyroxene (CaMgo0.50AlSil1.5O6). Crystal chemistry along the Di-CaTs join

Summary The crystal structure of the Di₅₀CaTs₅₀ clinopyroxene Ca(Mg_0.5Al_0.5) (Al_0,5Si_1.5)O₆, synthesized at T=1 100°C andP=14 kb, was refined in the C 2/c space group. Cell parameters are:a=9.655,b=8.771,c= 5.278 Å, =106.22°. The finalR value is: 2.1%. Comparison with the Di and CaTs structures shows that the variation of the M 2-0, M 1-0 and T-0 bond lengths is continuous and almost linear in the clinopyroxene solid solutions along the Di-CaTs join. The modifications caused in M 2 and M 1 polyhedra by shifting in tetrahedral chains along z are significant. The different values of shifts with composition account for the anomalous trend for the angle in the DiCaTs solid solution.

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La structure cristalline du clinopyroxène synthétique CaMgo_0.5AlSil_1.5O₆ (Di₅₀CaTs₅₀). La cristallochime le long du joint Di-CaTs

Résumé La structure cristalline du clinopyroxáne Ca(Mg_0.5Al_0.5)(Al_0.5Si_1.5)O₆ (Di₅₀CaTs₅₀), cristallisé á T= 1100° etP=14 kb, a été affinée dans le groupe spatial C 2/c. Les paramétres de la maille sont:a=9.655,b=8.771,c=5.278 Å, =106.22°. La valeur finale deR est 2.1%. La comparaison avec les structures de Di et de CaTs montre que le variation des longueures de liaison M 2-0, M 1-0 et T-0 est continue et presque linéaire pour les clinopyroxénes le long du joint Di-CaTs. Le déplacement des chaines tétraédriques le long de l'axe z cause de remarquables modifications dans les polyèdres M 2 et M 1. Les différentes valeurs du déplacement le long de l'axe z avec la composition expliquent la tendance anomale du paramétre de la maille le long du joint.

     

Transformation kinetics of polycrystalline aragonite to calcite: new experimental data,modelling, and implications

Experimental data are used to model the transformation rate of polycrystalline aragonite (grain diameter 80 m) to calcite. Optimized values for nucleation and growth rates were obtained by numerically fitting the overall transformation rates from 280° to 380°C and 0.10 MPa to an expression for a grain-boundary-nucleated and interface-controlled transformation. The nucleation rate is 4–5 orders of magnitude faster than for calcite nucleated within aragonite grains, and the growing in rate is slower below 300°C than for calcite growing in aragonite single crystals. The activation enthalpy for growth in polycrystalline aggregate is 247kJ/mol compared to 163 kJ/mol for growth in single crystals. Permanent deformation of the phases limits the elastic strain energy due to the 7% volume change and reduces the coherency of the calcite/aragonite interace. Theoretical expressions are used to extrapolate the data for nucleation and growth to other temperatures, and data from 0.10 to 400 MPa are used to evaluate the effect of pressure on the grain-boundary nucleation rate. Because of permanent deformation of the phases, the effective strain energy for nucleation is 0.55 kJ/mol, which is less than a quarter of the value for purely elastic deformation. These data are used to predict the percent transformation for various P-T-t paths; without heating during uplift partial preservation of aragonite in dry blueschist facies rocks can occur if the calcite stability field is entered at 235° C, and the kinetic data are also consistent with published P-T-t paths which include heating during uplift. The predicted percent transformation is relatively insensitive to variations in the initial grain size of the aragonite, but strongly dependent on the effective strain energy.     

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some largescale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u /U).List of Symbols a speed of sound - b total mixing layer thickness betweenU ₁ – 0.1U andU ₂ + 0.1U - f normalized third moment ofu-velocity,f u ³/(U)³ - g normalized triple product ofu ² v,g u ² v/(U)³ - h normalized triple product ofu v ², h uv' ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁=₂),M _c (U ₁–U ₂)/(a ₁+a ₂) - P static pressure - r freestream velocity ratio,rU ₂/U ₁ - Re unit Reynolds number,Re U/ - s freestream density ratio,s ₂/ ₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation ofu-velocity,u u–U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - U average of freestream velocities, ¯U (U ₁ +U ₂)/2 - U freestream velocity difference,U U ₁ –U ₂ - v instantaneous transverse velocity - v deviation ofv-velocity,v v – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y –y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U –U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla     

Single-crystal X-ray diffraction study of cation distribution in MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript>–MgFe<Subscript>2</Subscript>O<Subscript>4</Subscript> spinel solid solution

Synthesis experiments in the system MgAl₂O₄–MgFe₂O₄ [MgAl_2–xFe_xO₄ (0 x 2)] were carried out using a PbF₂ flux. The crystalline products synthesized in the compositional range of 0.6 <x 1.2 consisted of two spinel phases, whereas those synthesized in the compositional ranges of 0.0 x 0.6 and 1.2 < x 2.0 crystallized as single spinel phases. Structure refinements of the spinel single crystals, which grew in the ranges of 0.0 x 0.6 and 1.2 < x 2.0, show that the degree of randomness of cation distribution between A and B sites increases as x approaches the two-phase region. This means that the degree of the size mismatch among Mg²⁺, Fe³⁺ and Al³⁺occupying each equivalent mixing site increases as x approaches the two-phase region. Consequently, if the coexistence of two spinels observed in the intermediate compositions reveals the existence of a miscibility gap at low temperatures, this increase in the degree of the size mismatch among the three cations is suggested as a factor of energetic destabilization to form the miscibility gap.     

Seismotectonic considerations on the nature of the Turkish-African plate boudary

The nature of the assumed Turkish-African plate boundary is investigated in the light of new seismological and geologic-tectonical data which are condensed in a seismotectonic map. From the observed relationship between extensional, compressional and strikeslip deformation it is concluded that the Turkish-African convergence results in a sort of complex crustal welding within a broad and diffuse zone rather than in active consumption of African lithosphere beneath the Cypriot-Tauride arc.

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Zusammenfassung Die Natur der türkisch-afrikanischen Plattengrenze wird im Lichte neuer seismologischer und geologisch-tektonischer Daten untersucht, die in einer seismotektonischen Karte zusammengestellt sind. Die beobachteten Beziehungen zwischen Dehnungs- und Kompressionsdeformation sowie Blattverschiebung werden im Sinne einer komplexen Krustenverschweißung in einer breiten und diffusen Zone gedeutet, während aktive Subduktion afrikanischer Lithosphäre unter dem Zypern-Tauridenbogen aus den existierenden Daten nicht abgeleitet werden kann.

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Résumé La nature de la bordure entre les plaques turque et africaine est characterisée sur la base de nouvelles données sismologiques et tectoniqeus qui sont condensées dans une carte sismotectonique. Les relations observées entre les déformations de type extensif, compressional et décrochant sont interprétées en faveur d'une soudure crustale complexe dans une zone diffuse tandis qu'un modèle de subduction active de la lithosphère africaine sous l'arc Tauro-Chypriote ne répond pas aux données existantes.

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Introduction to pareto optimal mine planning

Summary Recent advances in mathematical optimization have resulted in the development of superior techniques for solving realistic decision making problems. The technique called PARETO OPTIMAL SERIAL DYNAMIC PROGRAMMING is presented here as a tool for rational mine planning. This approach always enables the identification of a set of decision alternatives considered superior to the remaining feasible, usually numerous, decision alternatives, when a number of conflicting, noncommensurable, objectives are simultaneously optimized. It is further noted that the decision makers' truly preferred decision is always one of the members identified as the superior set.Notation [A] Number of initial decision alternatives for production stage 1 - [A ] Accumulated pareto optimal stage objective vector at stage for the remainder of the stagesN – - [A] Accumulated non-pareto optimal stage objective vector at stage for the remainder of the stagesN – - [B] Number of initial decision alternatives for production stage 2 - [C] Number of initial decision alternatives for production stageN - [COG _k,] Cutoff grade for decision,k, at production stage, - [D] Number of initial pareto solutions for production stage 1 - [D ] Decision at stage - [E] Number of initial pareto solutions for production stage 2 - [F] Number of initial pareto solutions for production stageN - [j] A random objective function - [J] Number of objective functions - [LIFE _k,] Minelife for decision,k, at production stage, - [] An arbitrary production stage - [N] Final production stage - [NPV] Expected net present value - [NPV _k,] Project net present value for decision,k, at production stage - [OPR _k,] Ore production rate for decision,k, at production stage, - [S ] State of the system in stage - [ _n] Immediate state objective vector at stage      

Numerical modeling of three-dimensional contaminant migration from dissolution of multicomponent NAPL pools in saturated porous media

A three-dimensional model for contaminant transport resulting from the dissolution of multicomponent nonaqueous phase liquid (NAPL) pools in three-dimensional saturated subsurface formations is developed. The solution is obtained numerically by a finite-difference scheme, and it is suitable for homogeneous porous media with unidirectional interstitial velocity. Each dissolved component may undergo first-order decay and may sorb under local equilibrium conditions. It is also assumed that the dissolution process is mass transfer limited. The nonaqueous phase activity coefficients of the NAPL pool components are evaluated at each time step. The model behavior is illustrated through a synthetic example with a NAPL pool consisting of a mixture of TCA (1,1,2-trichloroethane) and TCE (trichloroethylene). The numerical solution presented in this work is in good agreement with a recently developed analytical solution for the special case of a single component NAPL pool. The results indicate the importance of accounting for the necessary changes in the organic phase activity which significantly affects the equilibrium aqueous solubility.Notation C liquid phase solute concentration (solute mass/liquid volume) (M L^–3) - C _s single component aqueous saturation concentration (solubility) (M L^–3) - C ^w equilibrium aqueous solubility (M L^–3) - D molecular diffusion coefficient (L² t ^–1) - D _e effective molecular diffusion coefficient (L² t ^–1) - D _x longitudinal hydrodynamic dispersion coefficient (L² t ^–1) - D _y lateral hydrodynamic dispersion coefficient (L² t ^–1) - D _z hydrodynamic dispersion coefficient in the vertical direction (L² t ^–1) - I() integer mode arithmetic operator - k local mass transfer coefficient (Lt ^–1) - k ^* average mass transfer coefficient (Lt ^–1) - L length - l _x ,l _y pool dimensions inx andy directions (L) - ll _x ,l _y x andy Cartesian coordinates of the pool origin (L) - M number of moles remaining in a pool (moles) - M initial number of moles (moles) - n finite-difference scheme time level - R retardation factor (dimensionless) - t time (t) - U _x average interstitial velocity (Lt ^–1) - x, y, z spatial Cartesian coordinates (L) - X dimensionless mole fraction - dimensionless activity coefficient - _w viscosity of water (=0.8904 cp at 25°C) - decay coefficient (t ^–1) - ^* tortuosity ( 1) - i,j, k finite-difference scheme grid indicators - p component number indicator - P total number of components - s pure single component - o nonaqueous phase - w aqueous phase