Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

Some exact sampling distributions for variogram estimators

For equally spaced observations from a one-dimensional, stationary, Gaussian random function, the characteristic function of the usual variogram estimator for a fixed lag k is derived. Because the characteristic function and the probability density function form a Fourier integral pair, it is possible to tabulate the sampling distribution of a function of a using either analytic or numerical methods. An example of one such tabulation is given for an underlying model that is simple transitive.     

Stochastic modeling of gold mineralization in the Champion lode system of Kolar gold fields (India)

Stochastic modeling of gold mineralization in the Champion lode of Kolar gold fields was carried out using assay data taken from developmental headings. After dividing the lode into 71 horizontal and 18 vertical strata, autoregressive (AR), moving average (MA), and autoregressive and moving average (ARMA) models were developed and applied. The model selection with the acf and pacf for the various strata showed that in most of the cases, ARMA modeling of first-order would forecast gold headings with a reasonable degree of confidence. This was substantiated by comparing the coefficients of variation. From a parsimony point of view, AR (1) model may also be considered valid. The best overall models are: ARMA (1, 1), ; AR (1), , where a_t is N (0, _a ² ), x is in logarithms of in-dwt, and t is in block units of 100 ft. The applications of these models to a specific stratum are given. These models would also be helpful to describe the characteristics of the gold mineralization process of this lode.     

Johillerit,Na(Mg,Zn)3 Cu(AsO4)3, ein neues Mineral aus Tsumeb,Namibia

Zusammenfassung Die chemische Analyse des neuen Minerals Johillerit mit der Elektronenmikrosonde ergab: Na₂O 5,4, MgO 18,3, ZnO 5,4, CuO 15,8 und As₂O₅ 55,8, Summe 100.7%. Aus diesem Ergebnis wurde die idealisierte Formel Na(Mg, Zn)₃ Cu(AsO₄)₃ abgeleitet. Johillerit ist monoklin mit der RaumgruppeC2/c. Die Gitterkonstanten sind:a=11,870 (3),b=12,755 (3),c=6,770 (2) , =113,42 (2)°,Z=4. Die stärksten Linien des Pulverdiagramms sind: 4,06 (5) (22 ), 3,50 (4) (310), 3,25 (8) (11 ), 2,75 (10) (330, 240), 2,64 (5) (311, 13 , 40 ), 1,952 (4) (13 , 35 ), 1,682 (4) (20 , 460), 1,660 (5) (40 , 71 , 550, 64 ), 1,522 (4) (442, 153, 13 ). Es bestehen enge strukturelle Beziehungen zwischen Johillerit und O'Danielit, Na(Zn, Mg)₃H₂(AsO₄)₃, sowie einigen synthetischen. Verbindungen.Johillerit ist violett durchscheinend. Die Spaltbarkeit nach {010} ist ausgezeichnet und nach {100} und {001} gut.H (Mohs)3.D=4,15 undD _X =4,21 g·cm^–3. Das Mineral ist optisch zweiachsig positiv, 2V80 (5)°. Die Werte der Lichtbrechung sindn =1,715 (4),n =1,743 (4) undn =1,783 (4). Die Auslöschung istn b und auf (010)n c16°. Johillerit ist stark pleochroitisch mit den AchsenfarbenX=violett-rot,Y = blauviolett undZ = grünblau. Das neue Mineral kommt in radialstrahligen Massen gemeinsam mit kupferhaltigem Adamin und Konichalcit in zersetzem Kupfererz von Tsumeb, Namibia, vor. Die Benennung erfolgte nach Prof. Dr.J.-E. Hiller (1911–1972).

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Johillerite, Na(Mg, Zn) ₃ Cu(AsO ₄ ) ₃ , a new mineral from Tsumeb, Namibia

Summary Electron microprobe analysis of the new mineral johillerite gave Na₂O 5.4, MgO 18.3, ZnO 5.4, CuO 15.8, and As₂O₅ 55.8, total 100.7%. From this result, the ideal formula is given as Na(Mg, Zn)₃ Cu(AsO₄)₃. Johillerite crystallizes monoclinic,C2/c. The unit cell dimensions are:a=11.870(3),b=12.755 (3),c=6.770 (2) , =113.42 (2)°,Z=4. The strongest lines on the X-ray powder diffraction pattern are: 4,06 (5) (22 ), 3,50 (4) (310), 3,25 (8) (11 ), 2,75 (10) (330, 240), 2,64 (5) (311, 13 , 40 ), 1,952 (4) (13 , 35 ), 1,682 (4) (20 , 460), 1,660 (5) (40 , 71 , 550, 64 ), 1,522 (4) (442, 153, 13 ). There is a close relationship between johillerite, o'danielite, Na(Zn, Mg)₃H₂(AsO₄)₃, and some synthetic compounds. Johillerite is violet in colour, transparent. Cleavage is {010} perfect, {100} and {001} good.H (Mohs)3.D=4.15 andD _X =4.21 g·cm^–3. The mineral is optically biaxial positive, 2V80 (5)°. The refractive indices are:n =1.715 (4),n =1.743 (4),n =1.783 (4). The extinction isn b and on (010)n c16°. Strongly pleochroic with axial coloursX=violet-red,Y=bluish violet andZ=greenish blue. The new mineral was found in radiated masses together with cuprian adamite and conichalcite in an oxidized copper ore from Tsumeb, Namibia. It is named in honour of Prof. Dr.J.-E. Hiller (1911–1972).

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Koritnigit,Zn[H2O|HOAsO3], ein neues Mineral aus Tsumeb,Südwestafrika

Zusammenfassung Das neue Mineral Koritnigit ist ein wasserhaltiges Zinkhydrogenarsenat der Formel Zn[H₂O|HOAsO₃]. Die chemische Analyse (Elektronenmikrosonde und T.G.A.) ergab: As₂O₅ 51,75%, ZnO 35,97% und H₂O 12,3%, Summe 100,0%. Die HOAsO₃-Ionen wurden IR-spektroskopisch nachgewiesen. Koritnigit ist löslich in kalter, verdünnter HCl und HNO₃.Die Gitterkonstanten sind:a ₀=7,948(2),b ₀=15,829(5),c ₀=6,668(2) Å, =90,86(2), =96,56(2), =90,05(2)^o,V=833,2(4)ų,V=8. Die Raumgruppe ist . Die stärksten Linien des Pulverdiagramms sind: 7,90(10) (020,100), 3,83(7) ( ), 3,16(9) ( ) 2,926(4) (150), 2,679(4) ( ), 2,461(6) ( ), 2,186(5) ( ), 1,969(4) (400), 1,649(3) (004).Koritnigit ist wasserklar bis durchscheinend weiß. Idiomorphe Kristalle sind nicht bekannt. Die Spaltbarkeit nach {010} ist ausgezeichnet und auf {010} sind Spaltspuren nach [001] und nach [100] erkennbar. Härte 2.G=3,54 g·cm^–3,D _x =3,56 g·cm^–3. Koritnigit ist optisch zweiachsig positiv, 2V70(5)^o. Die Werte der Lichtbrechung sind:n =1,632(5),n =1,652(3) undn =1,693(3).Koritnigit wurde auf der 31. Sohle der Tsumeb-Mine, Südwestafrika gefunden. Er kommt als Sekundärmineral in Paragenese mit Cu-Adamin, Stranskiit und drei weiteren, vorerst nicht identifizierten mineralen in Zersetzungshohlräumen von Tennantit vor.

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Koritnigite, Zn[H₂O|HOAsO₃], a new mineral from Tsumeb, South West Africa

Summary The new mineral koritnigite is a hydrated zinc hydrogen arsenate with the formula Zn[H₂O|HOAsO₃]. Chemical analysis (electron microprobe and t.g.a.) gave: As₂O₅ 51.75%, ZnO 35.97%, and H₂O 12.3%, total 100.0%. The HOAsO₃ ions were determined by IR spectroscopy. Koritnigite is soluble in cold diluted HCl and HNO₃. The unit cell dimensions are:a ₀=7.948(2),b ₀=15.829(5),c ₀=6.668(2)Å, =90.86(2), =96.56(2), =90.05(2)^o,V=833.2(4) ų,Z=8. The space group is . The strongest lines of the powder pattern are: 7.90(10) (020, 100), 3.83(7) ( ), 3.16(9) ( ), 2.926(4) (150), 2.679(4) ( ), 2.461(6) ( ), 2.186(5) ( ), 1.969(4)(400), 1.649(3) (004).

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

Colquiriit,ein neues Fluoridmineral aus der Zinnlagerstätte von Colquiri in Bolivien

Zusammenfassung Colquiriit tritt in Vergesellschaftung mit Ralstonit, Gearksutit, Zinkblende, Madocit und Pyrit im Bereich der Zinnlagerstätte von Colquiri in Bolivien auf. Das als selten zu betrachtende Mineral bildet maximal cm-große xenomorphe durchscheinende bis durch-sichtige Körner von weißlicher Farbe. Es zeigt keine Spaltbarkeit. Härte ca. 4; Dichte (gem.) 2,94, (ber.) 2,95 g/cm³;n 1,385±0.002,n 1,388±0,002, einachsig oder schwach zweiachsig, negativ. Colquiriit kristallisiert trigonal, Raumgruppe oderP31c,a ₀ 5,02,c ₀ 9,67 Å,Z=2. Stärkste Linien des Pulverdiagramms: 3,98(7) ; 3,23(10) ; 2,22(9) ; 1,736(8) . Eine chemische Analyse ergab: Li 3,1, Na 0,34, Mg 0,55, Ca 22,8, Al 13,4, F 58,0, Gewichtsverlust (105 °C) 0,5, Summe 98,69%, woraus sich die idealisierte Formel LiCaAlF₆ ableiten läßt. Beim Erhitzen wird das Gitter zwischen 800 und 900°C zerstört.

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Colquiriite, a new fluoride mineral from the Colquiri tin deposit in Bolivia

Summary Colquiriite occurs at the Colquiri tin deposit in Bolivia and is associated with ralstonite, gearksutite, sphalerite, madocite and pyrite. The mineral, which probably is a rare species, forms anhedral translucent to transparent white grains reaching up to 1 cm in size. No cleavage; hardness about 4; density (meas.) 2.94, density (calc.) 2.95 g/cm³;n 1.385±0.002,n 1.388±0.002, uniaxial or weakly biaxial, negative. Colquiriite is trigonal,a ₀ 5.02,c ₀ 9.67 Å, space group orP31c,Z=2. The strongest lines of the powder pattern are: 3.98(7) ; 3.23(10) ; 2.22(9) ; 1.736(8) . The chemical analysis gave: Li 3.1, Na 0.34, Mg 0.55, Ca 22.8, Al 13.4, F 58.0, weight loss (105 °C) 0.5, sum 98.69%, leading to the idealized formula LiCaAlF₆. Heating experiments show that the lattice breaks down between 800 and 900 °C. The new mineral and its name have been approved by the I.M.A. Commission on New Minerals and Mineral Names.

     

The pleochroism of a gem-quality enstatite in the region of the OH stretching frequency,with a stereochemical interpretation

Summary The pleochroic behaviour of a gem-quality enstatite from Tanzania was investigated in the region =2500 to 4000 cm^–1. Two sharp absorption bands at =3410 cm^–1 and =3510 cm^–1 are interpreted to be caused by OH stretching vibrations. As their absorption coefficients are considerably larger parallel to [001] (=direction of the silicate chains) than perpendicular to this direction, the OH dipoles have to be oriented approximately parallel to [001]. On this basis, a stereochemical interpretation of the incorporation of the OH groups into the structure is given.

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Der Pleochroismus eines Enstatits von Edelsteinqualität im Gebiet der OH-Streckfrequenz und seine kristallchemische Interpretation

Zusammenfassung Das pleochroitische Verhalten eines Enstatits von Edelsteinqualität aus Tansania wurde im Bereich =2500 bis 4000 cm^–1 untersucht. Von zwei scharfen Banden bei =3410 cm^–1 und 3510 cm^–1 wird angenommen, daß sie durch OH-Streckschwingungen herrühren. Da ihre Absorptionskoeffizienten parallel zu [001] (=Richtung der Silikatketten) beträchtlich größer sind als senkrecht dazu, müssen die OH-Dipole ungefähr parallel zu [001] liegen. Auf dieser Basis wird der Einbau der OH-Gruppen in die Struktur diskutiert.

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With 3 Figures     

Topological properties of random crack networks

The junctions of cracks in mudcrack, patterned ground, and columnar joint patterns can be categorized into Y, T,and Xtypes. The mean number of sides, ,to the polygonal areas in such nets is = 2(2J_T + 3J_Y + 4J_X)/(J_T + J_Y + 2J_X)where J_T, J_Y,and J_X are the proportions of T, Y,and Xjunctions, respectively.     

Systematic study of liquidas phase relations in olivine melilitite +H2O +CO2 at high pressures and petrogenesis of an olivine melilitite magma

Near-liquidus phase relationships of a spinel lherzolite-bearing olivine melilitite from Tasmania were investigated over a P, T range with varying , , and . At 30 kb under MH-buffered conditions, systematic changes of liquidus phases occur with increasing ( = CO₂/CO₂ +H₂O+olivine melilitite). Olivine is the liquidus phase in the presence of H₂O alone and is joined by clinopyroxene at low . Increasing eliminates olivine and clinopyroxene becomes the only liquidus phase. Further addition of CO₂ brings garnet+orthopyroxene onto the liquidus together with clinopyroxene, which disappears with even higher CO₂. The same systematic changes appear to hold at higher and lower pressures also, only that the phase boundaries are shifted to different . The field with olivine- +clinopyroxene becomes stable to higher with lower pressure and approaches most closely the field with garnet+orthopyroxene+clinopyroxene at about 27 kb, 1160 °C, 0.08 and 0.2 (i.e., 6–7% CO₂+ 7–8% H₂O). Olivine does not coexist with garnet+orthopyroxene+clinopyroxene under these MH-buffered conditions. Lower oxygen fugacities do not increase the stability of olivine to higher and do not change the phase relationships and liquidus temperatures drastically. Thus, it is inferred that olivine melilitite 2927 originates as a 5% melt (inferred from K_{2 O} and P₂O₅ content) from a pyrolite source at about 27kb, 1160 dg with about 6–7% CO₂ and 7–8% H₂O dissolved in the melt. The highly undersaturated character of the melt and the inability to find olivine together with garnet and orthopyroxene on the liquidus (in spite of the close approach of the respective liquidus fields) can be explained by reaction relationships of olivine and clinopyroxene with orthopyroxene, garnet and melt in the presence of CO₂.     

A regional gradient in the composition of metamorphic fluids in pelitic schist,Pecos Baldy,New Mexico

Two metamorphic isograds cut across graphitic schist near Pecos Baldy, New Mexico. The southern isograd marks the first coexistence of staurolite with biotite, whereas the northern isograd marks the first coexistence of andalusite with biotite. The isograds do not record changes in temperature or pressure. Instead, they record a regional gradient in the composition of the metamorphic fluid phase. Ortega Quartzite, which contains primary hematite, lies immediately north of the graphitic schist. Mineral compositions within the schist change gradually toward the quartzite, reflecting gradients in and . The chemical potential gradients, locally as high as 72 cal/m in and 9 cal/m in , controlled the positions of the two mapped isograds. The staurolite-biotite isograd records where fell below 0.80, at near 10^–23 bars; the andalusite-biotite isograd records where fell below 0.25, at near 10^–22 bars. Dehydration and oxidation were coupled by graphite-fluid equilibrium.The chemical potential gradients apparently formed during metamorphism, as graphite in schist reacted with hematite in quartzite. Local oxidation of graphite formed CO₂ which triggered dehydration reactions along the schistquartzite contact. This process created a C-O-H fluid which infiltrated into overlying rocks. Upward infiltration, local fluid-rock equilibration and additional infiltration proceeded until the composition of the infiltrating fluid evolved to that in equilibrium with the infiltrated rock. This point occurs very close to the staurolite-biotite isograd. Pelitic rocks structurally above this isograd show no petrographic evidence of infiltration, even though calculations indicate that volumetric fluid/rock ratios may have exceeded 15 and thin, rare calc-silicate beds show extensive K-metasomatism and quartz veining.     

Bivariate normal distribution fitting on discontinuity orientation clusters

A bivariate normal density function has been used to represent discontinuity orientation cluster distributions. Goodness-of-fit tests should be performed in order to make decisions on the representation of discontinuity clusters by theoretical probability distributions. In the literature, graphical procedures are available to fit a bivariate normal distribution to discontinuity clusters. However, these procedures assume no correlation between the two orientation parameters. In this paper (a) a numerical procedure, and (b) a semigraphical procedure are given to perform a ² goodness-of-fit test for bivariate normal distributions having nonzero correlation coefficient between the two parameters. These procedures were applied to a selected discontinuity cluster. The semigraphical procedure was found to be a time-consuming process. On the other hand, rapid computation can be done with the computer program developed for the numerical method. Sensitivity of the ² test results of theIXJ grid setup was investigated. Mean orientation estimation for the cluster based on the equal area polar projection was compared with the estimation based on the moment estimate method. For the cluster analyzed, estimations of bivariate normal parameters and , based on the equal-area polar projection, and values based on the moment estimation method were found to be different up to about 6.7% of the values based on the moment estimation method.     

Machatschkiit,ein neues Arsenatmineral aus der Grube Anton im Heubachtal bei Schiltach (Schwarzwald,Bundesrepublik Deutschland)

Zusammenfassung Machatschkiit ist ein neues wasserhaltiges Calciumarsenat, das in der Grube Anton bei Schiltach im mittleren Schwarzwald (BRD) 1960 gefunden wurde. Es kommt zusammen mit Gips, Pharmakolith, Pikropharmakolith und Sainfeldit als Sekundärbildung krustenförmig auf Granit vor.Als charakteristische Form tritt das Rhomboeder auf. Keine Spaltbarkeit, Bruch muschelig, Härte 2–3,G=2,5 bis 2,6 g·cm^–3,D _x =2,50 g·cm^–3, farblos, durchsichtig bis durchscheinend. Optische Daten:n =1,585±0,002,n =1,593±0,002, einachsig oder schwach zweiachsig, negativ.Gitterkonstanten:a ₀=15,10,c ₀=22,59 Å,a ₀c ₀=11,4960,Z=12;a _rh =11,52 Å, =81°52,Z=4. Mögliche Raumgruppen:R32,R3m, . Stärkste Linien des Pulverdiagramms: 8,59 (10) (110), 5,34 (8) (210), 3,59 (8) . Eine chemische Analyse ergab nach Umrechnung folgende Zusammensetzung: CaO 29,5%, As₂O₅ 40,8%, SO₃ 0,5%, H₂O 29,2%, Summe 100,0%. Dies kommt der Formel Ca₃(AsO₄)₂ · 9 H₂O sehr nahe. In verdünnter HCl und HNO₃ ist der Machatschkiit leicht löslich.

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Machatschkiite, a new arsenate mineral from the Anton Mine in the Heubach valley near Schiltach (Black Forest, Federal Republic of Germany)

Summary Machatschkiite is a new hydrous calcium arsenate which was found 1960 in the Anton Mine near Schiltach in the central Black Forest. It is a secondary mineral which occurs in crusts on granite in association with gypsum, pharmacolite, picropharmacolite and sainfeldite.The characteristic form is the rhombohedron . No cleavage, fracture conchoidal, hardness 2–3,G=2.5–2.6 g·cm^–3,D _x =2.50 g·cm^–3, colourless, transparent to translucent. Optical data:n =1.585±0.002,n =1.593±0.002, uniaxial or weakly biaxial, negative.Unit-cell dimensions:a ₀=15.10,c ₀=22.59 Å,a ₀c ₀=11.4960,Z=12;a _rh =11.52 Å, =81°52,Z=4. Possible space groups:R32,R3m, . Strongest lines of the powder pattern: 8.59 (10) (110), 5.34 (8) (210), 3.59 (8) . A chemical analysis gave the following composition after recalculation: CaO 29.5%, As₂O₅ 40.8%, SO₃ 0.5%, H₂O 29.2%, total 100.0%. This agrees well with the formula Ca₃(AsO₄)₂ · 9 H₂O. Machatschkiite is easily soluble in diluted HCl and HNO₃.

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Mit 3 Abbildungen     

Partition of Ni between olivine and sulfide: equilibria with sulfide-oxide liquids

The partition of Ni between olivine and monosulfide-oxide liquid has been investigated at 1300–1395° C, =10^–8-9–10^–6.8, and =10^–2.0–10^–0.9, over the composition range 20–79 mol. % NiS. The product olivine compositions varied from Fo98 to Fo59 and from 0.06 to 3.11 wt% NiO. The metal/sulfur ratio of the sulfide-oxide liquid increases with increase in , decrease in , and increase in NiS content. The Ni/Fe exchange reaction has been perfectly reversed using natural olivine and pure forsterite as starting materials. The FeO and NiO contents of olivine from runs equilibrated at the same and form isobaric distributions with NiS content, which, to a first approximation, are dependent at constant temperature and total pressure on a variable term, –0.5 log ( / ). The Ni/Fe distribution coefficient (K _D3) exhibits only a weak decrease from 35 to 29 with increase in from the IW buffer to close to the FMQ buffer. At values higher than FMQ, the sulfide-oxide liquid has the approximate composition (Ni,Fe)₃±_xS₂K _D358. The present K _D3 vs O/(S+O) data define a trend which extrapolates to K _D320 at 10 wt% oxygen in the sulfide-oxide liquid. The compositions of olivine and Ni-Cu sulfides associated with early-magmatic basic rocks and komatiites are consistent, at 1400° C, with a value of -log ( / ) of about 7.7, which is equivalent to 0.0 wt% oxygen in the hypothesized immiscible sulfide-oxide liquid. Therefore, K _D3 would not be reduced significantly from the 30 to 35 range for sulfide-oxide liquids with low oxygen contents.     

A Coupled Riverine-Marine Fractionation Model for Dissolved Rare Earths and Yttrium

Fractionation of yttrium (Y) and the rare earth elements (REEs) begins in riverine systems and continues in estuaries and the ocean. Models of yttrium and rare earth (YREE) distributions in seawater must therefore consider the fractionation of these elements in both marine and riverine systems. In this work we develop a coupled riverine/marine fractionation model for dissolved rare earths and yttrium, and apply this model to calculations of marine YREE fractionation for a simple two-box (riverine/marine) geochemical system. Shale-normalized YREE concentrations in seawater can be expressed in terms of fractionation factors ( _ij ) appropriate to riverine environments ( ) and seawater ( ):

Aluminum partitioning between olivine and ultrabasic silicate liquid to 6 GPa

Trace element analyses of 1-atm and high-pressure experiments show that in komatiite and peridotite, the olivine (OL)/liquid (L) distribution coefficient for Al₂O₃ ( ) increases with pressure and temperature. Olivine in equilibrium with liquid accepts as much as 0.2 wt% Al₂O₃ in solution at 6 GPa. Convergence to equilibrium compositions at this high level is shown by cation diffusion of Al into synthetic forsterite crystals of low-Al contents in the presence of melt. Convergence to low-Al equilibrium compositions at lower P and T is shown by diffusion of Al out of synthetic forsterite with high initial Al content. Isobaric and isothermal experimental data subsets reveal that temperature and pressure variations both have real effects on . Variation in silicate melt composition has no detectable effect on within the limited range of experimentally investigated mixtures. Least-squares regression for 24 experiments, using komatiite and peridotite, performed at 1 atm to 6 GPa and 1300 to 1960°C, gives the best fit equation: Increase in with increasingly higher-pressure melting is consistent with incorporation of a spinel-like component of low molar volume into olivine, although other substitutions possibly involving more complex coupling cannot be ruled out. High P-T ultrabasic melting residues, if pristine, may be recognized by the high calculated from microprobe analyses of Al₂O₃ concentrations in residual olivines and estimated Al₂O₃ concentration in the last liquid removed. In general the low levels of Al in natural olivine from mantle xenoliths suggest that pristine residues are rarely recovered.     

The volatile component of quaternary ignimbrite magmas from the North Island,New Zealand

Ignimbrites from the central North Island consist mainly of glass or its devitrified product (70–95%); their phenocryst mineralogy is varied and includes plag., hyp., ti-mag., ilm., aug., hblende, biot., san., qtz, ol., with accessory apatite, zircon and pyrrhotite. The Fe-Mg minerals can be used to divide the ignimbrites into four groups with hyp.+aug. reflecting high quench temperatures and biot.+hblende +hyp.+aug., low quench temperatures. Oxygen fugacities lie above the QMF buffer curve and even in ignimbrites with low crystal contents the solid phases apparently buffered fO₂. Some ignimbrites contain the assemblage actinolite, gedrite, magnetite and hematite, reflecting post-eruption oxidation. The mineralogy also allows estimation of using pyrrhotite and thence , . The assemblage biotite-sanidine can be used to estimate and thence . Water fugacity is calculated in a variety of ways using both biotite and hornblende as well as the combining reaction . It is high and approaches P _total in most ignimbrites (~4kb) but is lower in unwelded pumice breccias. Comparison of temperature estimates using mineral geothermometers for the various phenocryst phases suggests that the ignimbrite magmas showed temperature differences of 60–100 °C and pressure differences of several kilobars. Individual magma chambers therefore, would have extended over several kilometres vertically. The chemical potential of water may have been constant through the magma.     

Single crystal raman studies of pyrite-type RuS2, RuSe2, OsS2, OsSe2, PtP2, and PtAs2

Single crystal Raman spectra of pyrite-type RuS₂, RuSe₂, OsS₂, OsSe₂, PtP₂, and PtAs₂ are presented and discussed with reference to the energies of the X-X stretching modes _x-x (A _g, F _g) and the X₂ librations (E, 2F_g). The main results obtained are (i) strong Raman resonance effects, (ii) different sequences for _x-x (A _g) and (E _g), i.e., R_{x_2 } $$ " align="middle" border="0"> for PtP₂ and PtAs₂ and R_{x_2 } $$ " align="middle" border="0"> for OsS₂, owing to the interplay of intraionic and interionic lattice forces, (iii) greater strengths for the intraionic P-P and As-As bonds compared to the S-S and Se-Se bonds, respectively, and (iv) a strong influe_gnce of the metal ions on the strength of the X-X bonds.This is contribution LXI of a series of papers on lattice vibration spectra     

Manganese olivine I: Electrical conductivity

To investigate the point defect chemistry and the kinetic properties of manganese olivine Mn₂SiO₄, electrical conductivity () of single crystals was measured along either the [100] or the [010] direction. The experiments were carried out at temperatures T=850–1200 °C and oxygen fugacities atm under both Mn oxide (MO) buffered and MnSiO₃ (MS) buffered conditions. Under the same thermodynamic conditions, charge transport along [100] is 2.5–3.0 times faster than along [010]. At high oxygen fugacities, the electrical conductivity of samples buffered against MS is 1.6 times larger than that of samples buffered against MO; while at low oxygen fugacities, the electrical conductivity is nearly identical for the two buffer cases. The dependencies of electrical conductivity on oxygen fugacity and temperature are essentially the same for conduction along the [100] and [010] directions, as well as for samples coexisting with a solid-state buffer of either MO or MS. Hence, it is proposed that the same conduction mechanisms operate for samples of either orientation in contact with either solid-state buffer.The electrical conductivity data lie on concave upward curves on a log-log plot of vs , giving rise to two regimes with different oxygen fugacity exponents. In the low- regime , the exponent, m, is 0, the MnSiO₃-activity exponent, q, is 0, and the activation energy, Q, is 45 kJ/mol. In the high regime 10^{ - 7} {\text{atm}}} \right)$$ " align="middle" border="0"> , m=1/6, q=1/4–1/3, and Q=45 and 200 kJ/mol for T<1100 °c=" and=">T>1100 °C, respectively.     

Morphologische Betrachtungen an den Heidelberger synthetischen Quarzen

Zusammenfassung Die von Dr.Baumann, Heidelberg, synthetisierten Quarze zeichnen sich nicht nur durch eine außerordentliche Klarheit, sondern auch durch eine auffallende Morphologie aus. Es werden drei grundsätzlich verschiedene Typen beschrieben. Typ I ist pseudorhombisch; eine der a-Achsen verleiht ihm stark polare Gestalt. Als größte Fläche ist das re. trig. Prisma II. St. , entwickelt. Das Trapezoeder erscheint an zwei Stellen vizinal. Typ II ist nach einer der Winkelhalbierenden der a-Achsen gestreckt. In dieser Richtung betrachtet erscheint der Kristall tetragonal, da auf diese Weise die unter rechtem Winkel stehenden Flächen , (0001), und das Quadrat begrenzen. Dies sind zugleich die größtentwickelten Flächen. Typ III ist isometrisch; sämtliche Flächen (Prismen, beide Rhomboeder sowie das Basisendflächenpaar) sind etwa gleich stark entwickelt. In Richtung auf das pos. Rhomboeder betrachtet, erweckt dieser Typ den Eindruck eines kubischen Kristalles. Hier fehlen trig. Prisma und das Trapezoeder.

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Summary Quarz crystals, grown by Dr.Baumann, Heidelberg, are remarkable not only for their extraordinary transparency but also for a conspicuous morphology. Three completely different types are described. Type I is pseudo-orthorhombic; one of the a-axes causes a strongly polar appearance. Largest face is the right trig. prism II. position . The trapezohedron appears in two positions as vicinals. Type II is alongated parallel to one of the bisectrices of the a-axes. Viewed in this direction the crystal seems to be tetragonal, as the faces , (0001), and , which are at right angles to each other, form a square; these faces are at the same time the largest ones. Typ III is isometric; all the faces (prisms, both rhombohedrons, and the pinacoid) are of approximately the same size. Viewed in the direction upon the pos. rhombohedron this type appears to be cubic. The trig. prism and the trapezohedron are here missing.

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Mit 4 Figuren und 3 Textabbildungen

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Herrn Professor Dr.F. Machatschki zum 70. Geburtstag gewidmet.