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1.
The association between constant-sum variables Xi and Xj expressed as percentages can be calculated as a product-moment correlation between Xi and Xj/(100 – Xi ) and a correlation between Xj and Xi/(100 – Xj ). An asymmetric, square matrix may be formed from these coefficients, and multivariate analysis performed by two methods: singular value decomposition and canonical decomposition. Either analysis avoids problems in the interpretation of correlation coefficients determined from closed arrays, and provides information about dependencies among the variables beyond that obtained from the usual correlation coefficient between Xi and Xj.Two examples show the canonical decomposition to have the greater usefulness.  相似文献   

2.
Summary Anandite has an approximate formula of Ba(Fe3+, Fe2+)3[Si2(Fe3+, Fe2+, Si)2O10–x(OH)x] (S, Cl) (OH), withx=0–1, and belongs to the 2 O brittle mica group. It is orthorhombic; space groupPnmn;a=5.468(9) Å,b=9.489(18)Å,c=19.963(11) Å;Z=4.The structure was determined from 3dim. Weissenberg-data, starting with an approximate structure in the pseudo space groupCcmm. Least squares refinement resulted inR=0.061 for 409 photometric intensities, andR=0.131 for all 853 observedhkl-reflexions.The iron of the tetrahedral layer is concentrated in one of the two crystallographically different kinds of tetrahedra. The basal oxygen rings of the tetrahedral layer form approximate hexagons and have not the ditrigonal configuration of the common micas. This peculiarity is considered to be a consequence of the size and charge of the barium ion. The role of OH in the common micas is played partly by S2– and Cl– in anandite.
Die Kristallstruktur des 2 O Sprödglimmers Anandit
Zusammenfassung Anandit hat die ungefähre Formel Ba(Fe3+, Fe2+)3[Si2(Fe3+, Fe2+, Si)2O10–x(OH)x] (S, Cl) (OH) mitx=0–1 und gehört zur 2O Sprödglimmergruppe. Er ist rhombisch; RaumgruppePnmn; a=5,468(9) Å,b=9,489(18) Å,c=19,963(11) Å;Z=4.Die Struktur wurde aus Weissenberg-Daten bestimmt, wobei mit einer approximativen Struktur in der PseudoraumpruppeCcmm begonnen wurde. Die Verfeinerung nach der Methode der kleinsten Quadrate führte für 409 photometrierte Reflexe aufR=0,061 und für alle 853 beobachtetenhkl-Reflexe aufR=0,131.Der Eisengehalt der Tetraederschicht ist in einer der beiden kristallographisch verschiedenen Tetraederarten konzentriert. Die basalen Sauerstoffringe der Tetraederschicht bilden annäherungsweise Sechsecke und haben nicht die ditrigonale Konfiguration der gewöhnlichen Glimmer. In Anandit spielen S2– und Cl– teilweise die Rolle der Hydroxylgruppen in den gewöhnlichen Glimmern.

With 4 Figures  相似文献   

3.
Summary A number of micas of varying compositions and polytypism have been selected from the literature for multiple linear regression analysis. The c dimension in micas is found to depend on the sizes of the interlayer cation, di, and tetrahedral cation, dt, as well as on the hydroxyl content, [OH]. The regression equation obtained: cr = 5.415 + 0.071[OH] + 2.098di + 2.335dt with R2 = 90.5%, shows that the three variables affect the c-axis dimension in the order dt > di [OH]. Addition of 2- and 3-layer polytypes to the regression analysis reduces R2 to 87.2%. Application of the regression analysis to synthetic Al-rich biotites from the literature shows that the amount of [A1IVA1VI]1Y[Fe2+, MgSi]–1y in solid solution is limited and always less than [A1VIO]1z[Fe2+, MgOH]–1z (i.e. 0.35 > y z). The maximum value of the vector y in solution is slightly higher than that reported for natural Al-rich biotites.
Die Beziehung zwischen der Gitterkonstante c und den Austauschkomponenten in Glimmern
Zusammenfassung Eine Anzahl von Glimmern unterschiedlicher Zusammensetzung und Polytypie wurde aus der Literatur für eine multiple lineare Regressionsanalyse ausgewählt. Es stellte sich heraus, dass in Glimmern die Gitterkonstante c von den Grössen des Zwischenschicht-Kations di und des tetraedrischen Kations dt abhängt, ferner vorn Hydroxylgehalt, [OH]. Die erhaltene Regressionsgleichung cr = 5,415 + 0,071 [OH] + 2,098di + 2,335dt mit R2 = 90,5% zeigt, dass die drei Variablen die Grösse der c-Achse in der Reihenfolge dt > di [OH] beeinflussen. Der Einschluss von 2- und 3-Schicht Polytypen in die Regressionsanalysen verkleinert R2 auf 87,2%. Die Anwendung der Regressionsanalysen auf synthetische Al-reiche Biotite aus der Literatur zeigt, der Betrag von [A1IVA1VI]1y[Fe2+, MgSi]–1y beschränkt und immer kleiner als [A1VIO]1z[Fe2+, MgOH]–1z (mit 0,35 < y z) ist. Der Maximalwert des Vektors y in Lösung ist etwas grösser als jener, der für natürliche Al-reiche Biotite angegeben wurde.

With 1 Figure  相似文献   

4.
A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated Sm 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, Yi)and (X j, Yj)into the slope formula S i = (Y i – Yj)/(X i – Xj),1 i < j n Once S m is determined, outliers may be detected by calculating the residuals given by Ri = Yi – SmXi where 1 i n, and chosing the median Rm. Outliers are defined as points for which |Ri – Rm| > k (median {|R i – Rm|}). If no outliers are found, the Y-intercept is given by Rm. Confidence limits on Rm and Sm can be found from the sets of Ri and Si, 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.  相似文献   

5.
Strain analysis of the Baraitha conglomerate is attempted by direct measurements on extracted pebbles and by micrometric analysis. The overall deformation is of flattening type, with thek value lower by more than half in the matrix than in the pebbles. The viscosity contrast between pebbles and matrix (μ i/μm) is in the ratio of 2:1 and the bulk deformation appears to be strongly controlled by Ci (concentration of pebbles expressed as percentage). The total shortening (≃35%) in the Baraitha conglomerate is comparable with the shortening accomplished in the folding of the overlying Bijawar Group volcanosedimentary sequence. The bulk strain axesX t, Yt andZ t, as determined from the analysis of the deformed conglomerate, are unsymmetrically oriented with reference to folds formed by oblique flexural-slip with neitherX t norY tcoincident with the fold hinges. The lack of transection of folds by cleavage again suggests flattening deformation. The extension in theY tdirection is greater in the matrix than in the pebbles.  相似文献   

6.
The variance-based cross-variogram between two spatial processes, Z1 (·) and Z2 (·), is var (Z1 ( u ) – Z2 ( v )), expressed generally as a bivariate function of spatial locations uandv. It characterizes the cross-spatial dependence between Z1 (·) and Z2 (·) and can be used to obtain optimal multivariable predictors (cokriging). It has also been called the pseudo cross-variogram; here we compare its properties to that of the traditional (covariance-based) cross-variogram, cov (Z1 ( u ) – Z1 ( v ), Z2 ( u ) – Z2 ( v )). One concern with the variance-based cross-variogram has been that Z1 (·) and Z2 (·) might be measured in different units (apples and oranges). In this note, we show that the cokriging predictor based on variance-based cross-variograms can handle any units used for Z1 (·) and Z2 (·); recommendations are given for an appropriate choice of units. We review the differences between the variance-based cross-variogram and the covariance-based cross-variogram and conclude that the former is more appropriate for cokriging. In practice, one often assumes that variograms and cross-variograms are functions of uandv only through the difference u – v. This restricts the types of models that might be fitted to measures of cross-spatial dependence.  相似文献   

7.
A new thermodynamic model for multi-component spinel solid solutions has been developed which takes into account thermodynamic consequences of cation mixing in spinel sublattices. It has been applied to the evaluation of thermodynamic functions of cation mixing and thermodynamic properties of Fe3O4–FeCr2O4 spinels using intracrystalline cation distribution in magnetite, lattice parameters and activity-composition relations of magnetite–chromite solid solutions. According to the model, cation distribution in binary spinels, (Fe1-x2+ Fex3+)[Fex2+Fe2-2y-x3+Cr2y]O4, and their thermodynamic properties depend strongly on Fe2+–Cr3+ cation mixing. Mixing of Fe2+–Fe3+ and Fe3+–Cr3+ can be accepted as ideal. If Fe2+, Fe3+ and Cr are denoted as 1, 3 and 4 respectively, the equation of cation distribution is –RT ln(x2/((1–x)(2–2y–x)))= G13* + (1–2x)W13+y(W14–W13–W34) where G13* is the difference between the Gibbs energy of inverse and normal magnetite, Wij is a Margules parameter of cation mixing and G13*, J/mol =–23,000+13.4 T, W14=36 kJ/mol, W13=W34=0. The positive nonconfigurational Gibbs energy of mixing is the main reason for changing activity–composition relations with temperature. According to the model, the solvus in Fe3O4–FeCr2O4 spinel has a critical temperature close to 500°C, which is consistent with mineralogical data.  相似文献   

8.
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  相似文献   

9.
Shear strain γ in brittle fault zones is related to final and initial grain size parameters, df and di, respectively, by an expression of the form: where μk the coefficient of kinetic friction of crushed rock and σn the normal stress across the zone at the time of faulting.Technological literature suggests that ƒ(df, di) may be given by 10 , where Wi is a material constant. The resulting relationship between shear strain and grain size seems to be compatible with existing experimental data.  相似文献   

10.
Three types of eclogite, together with a serpentinized harzburgite, coexist as blocks within granitic and pelitic gneisses along the Shaliuhe cross section, the eastern part of the North Qaidam continental-type ultrahigh-pressure (UHP) metamorphic belt, NW China. The olivine (Ol1) and orthopyroxene in the harzburgite are compositionally similar to present-day abyssal peridotites. The kyanite–eclogite is derived from a troctolitic protolith, whereas the epidote–eclogite from a gabbroic protolith, both having distinct positive Eu anomalies, low TiO2, and high Al2O3 and MgO. The kyanite–eclogite shows inherited cumulate layering. The phengite–eclogite has high TiO2, low Al2O3 and MgO with incompatible trace elements resembling enriched-type MORB. Sr–Nd isotope data indicate that the protoliths of both kyanite–eclogite and epidote–eclogite ([87Sr/86Sr]i ~ 0.703–0.704; εNd(T) ~ 5.9–8.0) are of mantle origin (e.g., ocean crust signatures). On the other hand, while the lower εNd(T) value (1.4–4.1) of phengite–eclogite is more or less consistent with an enriched MORB protolith, their high [87Sr/86Sr]i ratio (0.705–0.716) points to an additional enrichment in their history, probably in an subduction-zone environment. Field relations and geochemical analyses suggest that the serpentinized harzburgite and the three types of eclogite constitute the oceanic lithological section of an ophiolitic sequence from mantle peridotite, to cumulate, and to upper basaltic rocks. The presence of coesite pseudomorphs and quartz exsolution in omphacite plus thermobarometric calculations suggests that the eclogites have undergone ultrahigh pressure metamorphism (i.e., peak P ≥ 2.7 GPa). The harzburgite may also have experienced the same metamorphism, but the lack of garnet suggests that the pressure conditions of ≤ 3.0 GPa. Zircon U–Pb SHRIMP dating shows that the eclogites have a protolith age of 516 ± 8 Ma and a metamorphic age of 445 ± 7 Ma. These data indicate the presence of a Paleo-Qilian Ocean between Qaidam and Qilian blocks before the early Ordovician. The ophiolitic assemblage may be the relics of subducted oceanic crust prior to the subduction of continental materials during Ordovician–Silurian times and ultimate continent collision. These rocks, altogether, record a complete history of ocean crust subduction, to continental subduction, and to continental collision.  相似文献   

11.
Zusammenfassung Künstlicher Norsethit, BaMg(CO3)2, hat die hexagonalen Gitterkonstanten:a=5,017±0,001 Å undc=16,77±0,01 Å; Z=3. Die Struktur wurde auf Grund von 30 unabhängigen Röntgenpulverreflexen bestimmt. Sie wird in der Raumgruppe R32 mit R=0,035 durch die Sauerstoffparameter (hexagonal): x=0,199; y=–0,089 und z=0,242 beschrieben. Die übrigen Atome haben analoge Lagen wie im Dolomit. Das Magnesium ist verzerrt oktaedrisch durch Sauerstoff umgeben. Das Barium ist in Form eines trapezoedrisch verzerrten ditrigonalen Prismas durch 12 Sauerstoffatome koordiniert. Die wichtigsten Abstände sind: Mg–O=2,093Å (6X); Ba–O (kurz) =2,715Å (6X) und Ba–O (lang)=3,184Å (6X).
Summary Artificial norsethite, BaMg(CO3)2 has the hexagonal lattice constants:a=5,017±0,001 Å andc=16.77±0.01 Å; Z=3. The structure was determined on the basis of 30 independent X-ray powder reflections. In the space group R32 it is described with R=0.035 by the following oxygene parameters (hex.):x=0.199;y=–0.089 andz=0.242. The other atoms occupy analogous positions as in dolomite. Magnesium has a distorted octahedral coordination by oxygene. Barium is surrounded by 12 oxygenes at the corners of a trapezohedrally distorted ditrigonal prism. Important bond lengths are Mg–O=2.093Å (6X); Ba–O (short)=2.715Å (6X) and Ba–O (long)=3.184Å (6X).

Mit 4 Textabbildungen  相似文献   

12.
Summary The crystal structure of sarcolite from Monte Somma (Vesuvius), Na(Na, K, Fe, Mg)<1 Ca6[Al4Si6O23](OH, H2O)<2 [(Si,P)O4]0.5[(CO3, Cl)]0.5, space groupI4/m witha=12,343(5)Å,c=15,463(5)Å andZ=4, has been determined from X-ray data collected on an automatic diffractometer. The 1637 independent reflections withI>2 (I) converged to a conventionalR value of 0.054 with partially anisotropic factors.The tetrahedral framework in sarcolite has a sharing coefficient of 1.85. Mean Si–O and Al–O distances are 1.616 and 1.763 Å, respectively. Isolated (Si, P)O4, CO3, OH, H2O and Cl species occupy cavities in the tetrahedral framework in a partially disordered way. The two crystallographically different Ca atoms coordinate respectively with 5 and 6 framework oxygens; further contacts occur with available anions. Ca–O distances range from 2.34 to 2.69 Å. Na atoms coordinate with 4 oxygens of the tetrahedral frame and one from the CO3 groups.A structure analysis of a sarcolite crystal baked out at 1100°C confirmed some structural details involving atoms occupying cavities in the tetrahedral framework.
Die Kristallstruktur des Sarkoliths
Zusammenfassung Die Kristallstruktur des Sarkoliths vom Monte Somma (Vesuv), Na(Na, K, Fe, Mg)<1 Ca6[Al4Si6O23](OH, H2O)<2[(Si, P)O4]0,5[(CO3, Cl)]0,5, RaumgruppeI4/m,a 0=12,343(5)Å,c 0=15,463(5)Å,Z=4, wurde aus Röntgendaten, die auf einem automatischen Diffraktometer gesammelt worden waren, bestimmt. Der konventionelleR-Wert für 1637 kristallographisch unabhängige Reflexe mitI>2 (I) konvergierte mit partiell anisotropen Temperaturfaktoren auf 0.054.Der Verknüpfungskoeffizient des Tetraedergerüstes in Sarkolith ist 1,85. Die mittleren Si–O-bzw. Al–O-Abstände sind 1,616Å und 1,763 Å. Isolierte Strukturbestandteile (Si, P)O4, CO3, OH, H2O und Cl besetzen zum Teil ungeordnet die Hohlräume des Tetraedergerüstes. Die beiden kristallographisch verschiedenen Ca-Atome werden von funf bzw. sechs Sauerstoffen des Gerüstes koordiniert, weitere Kontakte bestehen zu verfügbaren Anionen. Die Ca–O-Abstände variieren von 2,34 bis 2,69 Å. Die Na–Atome sind von vier Sauerstoffen des Tetraedergerüstes und von einem weiteren der CO3-Gruppen koordiniert. Die Strukturanalyse eines bei 1100°C getemperten Sarkolithkristalls bestätigte einige Details über die Atome, welche die Hohlräume des Tetraedergerüstes besetzen.

With 4 Figures  相似文献   

13.
Voluminous granitic intrusions are distributed in the West Junggar, NW China, and they can be classified as the dioritic rocks, charnockite and alkali-feldspar granite groups. The dioritic rocks (SiO2 = 50.4–63.8 wt.%) are calc-alkaline and Mg enriched (average MgO = 4.54 wt.%, Mg# = 0.39–0.64), with high Sr/Y ratios (average = 21.2), weak negative Eu (average Eu/Eu = 0.80) and pronounced negative Nb–Ta anomalies. Their Sr–Nd and zircon Hf isotopic compositions ((87Sr/86Sr)i = 0.7035–0.7042, εNd(t) = 4.5–7.9, εHf(t) = 14.1–14.5) show a depleted mantle-like signature. These features are compatible with adakites derived from partial melting of subducted oceanic crust that interacted with mantle materials. The charnockites (SiO2 = 60.0–65.3 wt.%) show transitional geochemical characteristics from calc-alkaline to alkaline, with weak negative Eu (average Eu/Eu = 0.75) but pronounced negative Nb–Ta anomalies. Sr–Nd and zircon Hf isotopic compositions ((87Sr/86Sr)i = 0.7037–0.7039, εNd(t) = 5.2–8.0, εHf(t) = 13.9–14.7) also indicate a depleted source, suggesting melts from a hot, juvenile lower crust. Alkali-feldspar granites (SiO2 = 70.0–78.4 wt.%) are alkali and Fe-enriched, and have distinct negative Eu and Nb–Ta anomalies (average Eu/Eu = 0.26), low Sr/Y ratios (average = 2.11), and depleted Sr–Nd and zircon Hf isotopic compositions ((87Sr/86Sr)i = 0.7024–0.7045, εNd(t) = 5.1–8.9, εHf(t) = 13.7–14.2). These characteristics are also comparable with those of rocks derived from juvenile lower crust. Despite of the differences in petrology, geochemistry and possibly different origins, zircon ages indicate that these three groups of rocks were coevally emplaced at ~ 305 Ma.A ridge subduction model can account for the geochemical characteristics of these granitoids and coeval mafic rocks. As the “slab window” opened, upwelling asthenosphere provided enhanced heat flux and triggered voluminous magmatisms: partial melting of the subducting slab formed the dioritic rocks; partial melting of the hot juvenile lower crust produced charnockite and alkali-feldspar granite, and partial melting in the mantle wedge generated mafic rocks in the region. These results suggest that subduction was ongoing in the Late Carboniferous and, thus support that the accretion and collision in the Central Asian Orogenic Belt took place in North Xinjiang after 305 Ma, and possibly in the Permian.  相似文献   

14.
We carried out reversed piston-cylinder experiments on the equilibrium paragonite = jadeite + kyanite + H2O at 700°C, 1.5–2.5 GPa, in the presence of H2O-NaCl fluids. Synthetic paragonite and jadeite and natural kyanite were used as starting materials. The experiments were performed on four different nominal starting compositions: X(H2O)=1.0, 0.90, 0.75 and 0.62. Reaction direction and extent were determined from the weight change in H2O in the capsule, as well as by optical and scanning electron microscopy (SEM). At X(H2O)=1.0, the equilibrium lies between 2.25 and 2.30 GPa, in good agreement with the 2.30–2.45 GPa reversal of Holland (Contrib Miner Petrol 68:293–301, 1979). Lowering X(H2O) decreases the pressure of paragonite breakdown to 2.10–2.20 GPa at X(H2O)=0.90 and 1.85–1.90 GPa at X(H2O)=0.75. The experiments at X(H2O) = 0.62 yielded the assemblage albite + corundum at 1.60 GPa, and jadeite + kyanite at 1.70 GPa. This constrains the position of the isothermal paragonite–jadeite–kyanite–albite–corundum–H2O invariant point in the system Na2O–Al2O3–SiO2–H2O to be at 1.6–1.7 GPa and X(H2O)~0.65±0.05. The data indicate that H2O activity, a(H2O), is 0.75–0.86, 0.55–0.58, and <0.42 at X(H2O)=0.90, 0.75, and 0.62, respectively. These values approach X(H2O)2, and agree well with the a(H2O) model of Aranovich and Newton (Contrib Miner Petrol 125:200–212, 1996). Our results demonstrate that the presence or absence of paragonite can be used to place limits on a(H2O) in high-pressure metamorphic environments. For example, nearly pure jadeite and kyanite from a metapelite from the Sesia Lanzo Zone formed during the Eo-Alpine metamorphic event at 1.7–2.0 GPa, 550–650°C. The absence of paragonite requires a fluid with low a(H2O) of 0.3–0.6, which could be due to the presence of saline brines.  相似文献   

15.
A method for determining the reversibility of a Markov sequence   总被引：1，自引：0，他引：1  
This paper describes, given a tally matrix with strictly positive entries, a method to determine whether the associated Markov process is reversible, and (for reversible Markov processes) methods to compute the reversibility matrix from the tally matrix. If the tally matrixN is symmetric, then it is shown that the Markov process must be reversible and the reversibility matrixC equalss (R –1NR–1), whereR is the diagonal matrix whosei th diagonal entry is the sum of the entries of thei th row ofN (for everyi) ands denotes the sum of all the entries ofN. Because a symmetric tally matrix is of special importance in applications, a 2 test is proposed for determining, in the presence of experimental errors, whether such a matrix is symmetric.  相似文献   

16.
A study of the lithogeochemistry of metavolcanics in the Ben Nevis area of Ontario, Canada has shown that factor analysis methods can distinguish lithogeochemical trends related to different geological processes, most notably, the principal compositional variation related to the volcanic stratigraphy and zones of carbonate alteration associated with the presence of sulphides and gold. Auto- and cross-correlation functions have been estimated for the two-dimensional distribution of various elements in the area. These functions allow computation of spatial factors in which patterns of multivariate relationships are dependent upon the spatial auto- and cross-correlation of the components. Because of the anisotropy of primary compositions of the volcanics, some spatial factor patterns are difficult to interpret. Isotropically distributed variables such as CO 2 are delineated clearly in spatial factor maps. For anisotropically distributed variables (SiO 2 ), as the neighborhood becomes smaller, the spacial factor maps becomes better. Interpretation of spatial factors requires computation of the corresponding amplitude vectors from the eigenvalue solution. This vector reflects relative amplitudes by which the variables follow the spatial factors. Instability of some eigenvalue solutions requires that caution be used in interpreting the resulting factor patterns. A measure of the predictive power of the spatial factors can be determined from autocorrelation coefficients and squared multiple correlation coefficients that indicate which variables are significant in any given factor. The spatial factor approach utilizes spatial relationships of variables in conjunction with systematic variation of variables representing geological processes. This approach can yield potential exploration targets based on the spatial continuity of alteration haloes that reflect mineralization.List of symbols c i Scalar factor that minimizes the discrepancy between andU i - D Radius of circular neighborhood used for estimating auto- and cross-correlation coefficients - d Distance for which transition matrixU is estimated - d ij Distance between observed valuesi andj - E Expected value - E i Row vector of residuals in the standardized model - F(d ij) Quadratic function of distanced ij F(d ij)=a+bd ij+cd ij 2 - L Diagonal matrix of the eigenvalues ofU - i Eigenvalue of the matrixU;ith diagonal element ofL - N Number of observations - p Number of variables - Q Total predictive power ofU - R Correlation matrix of the variables - R 0j Variance-covariance signal matrix of the standardized variables at origin;j is the index related tod andD (e.g.,j=1 ford=500 m,D=1000 m) - R 1j Matrix of auto- and cross-correlation coefficients evaluated at a given distance within the neighborhood - R m 2 Multiple correlation coefficient squared for themth variable - S i Column vectori of the signal values - s k 2 Residual variance for variablek - T i Amplitude vector corresponding toV i;ith row ofT=V –1 - T Total variation in the system - U Nonsymmetric transition matrix formed by post-multiplyingR 01 –1 byR ij - U i Componenti of the matrixU, corresponding to theith eigenvectorV i;U i= iViTi - U* i ComponentU i multiplied byc i - U ij Sum of componentsU i+U j - V i Eigenvector of the matrixU;ith column ofV withUV=VL - w Weighting factor; equal to the ratio of two eigenvalues - X i Random variable at pointi - x i Value of random variable at pointi - y i Residual ofx i - Z i Row vectori for the standardized variables - z i Standardized value of variable  相似文献   

17.
Crystals of hydronium jarosite were synthesized by hydrothermal treatment of Fe(III)–SO4 solutions. Single-crystal XRD refinement with R1=0.0232 for the unique observed reflections (|Fo| > 4F) and wR2=0.0451 for all data gave a=7.3559(8) Å, c=17.019(3) Å, Vo=160.11(4) cm3, and fractional positions for all atoms except the H in the H3O groups. The chemical composition of this sample is described by the formula (H3O)0.91Fe2.91(SO4)2[(OH)5.64(H2O)0.18]. The enthalpy of formation (Hof) is –3694.5 ± 4.6 kJ mol–1, calculated from acid (5.0 N HCl) solution calorimetry data for hydronium jarosite, -FeOOH, MgO, H2O, and -MgSO4. The entropy at standard temperature and pressure (So) is 438.9±0.7 J mol–1 K–1, calculated from adiabatic and semi-adiabatic calorimetry data. The heat capacity (Cp) data between 273 and 400 K were fitted to a Maier-Kelley polynomial Cp(T in K)=280.6 + 0.6149T–3199700T–2. The Gibbs free energy of formation is –3162.2 ± 4.6 kJ mol–1. Speciation and activity calculations for Fe(III)–SO4 solutions show that these new thermodynamic data reproduce the results of solubility experiments with hydronium jarosite. A spin-glass freezing transition was manifested as a broad anomaly in the Cp data, and as a broad maximum in the zero-field-cooled magnetic susceptibility data at 16.5 K. Another anomaly in Cp, below 0.7 K, has been tentatively attributed to spin cluster tunneling. A set of thermodynamic values for an ideal composition end member (H3O)Fe3(SO4)2(OH)6 was estimated: Gof= –3226.4 ± 4.6 kJ mol–1, Hof=–3770.2 ± 4.6 kJ mol–1, So=448.2 ± 0.7 J mol–1 K–1, Cp (T in K)=287.2 + 0.6281T–3286000T–2 (between 273 and 400 K).  相似文献   

18.
Optimal discrimination among several groups can be achieved by simultaneous diagonalization of pooled within-group, W, and among-group, A, sums of squares and cross-product matrices formed by utilizing axial-ratio sample statistics of quartz grains belonging to different sieve grades. This method maximizes the ratio of among-group cross products to within-group cross product quadratic forms (V'AV/V'WV)and simultaneously yields discriminant scores whose correlation coefficients are zero for group means as well as for within each group. This procedure enables a simple Euclidean distance measure for partitioning the discriminant space for assignment. Although W–1 and Amatrices are symmetric, the W–1 Amatrix needed for multigroup discrimination is asymmetric and hence the eigenstructure of W–1 Ais obtained by simultaneous diagonalization of Wand Amatrices. The first four sample statistics (mean, standard deviation, skewness, kurtosis) of normalized axial-ratios are required for discrimination, although the mean and standard deviation are the most important discriminators.  相似文献   

19.
The polarized single-crystal Raman spectrum of synthetic fayalite, Fe2SiO4, was recorded between 5 and 773 K in order to investigate its lattice dynamic behavior. A broad absorption envelope is observed at wavenumbers between 800 and 960 cm–1 and it contains two intense bands at 816 and 840 cm–1 at 293 K in the (cc) spectrum. The integral area of the envelope decreases upon cooling from 293 K and reaches a minimum around 55 K. It then increases again with a further decrease in temperature down to 5 K. It is proposed that the envelope in the (cc) spectra consists of seven different modes, some of which are symmetry-forbidden, that arise from combination scattering of nonsymmetric internal SiO4-stretching modes of Big symmetry (i = 1, 2, 3) and low-energy excitations. The individual modes can be observed under different polarizations and agree in number and wavenumber with those obtained by fitting the broad envelope with Lorentzians. An analysis of the Raman spectrum as a function of temperature, using the known magnetic properties of fayalite, allows the assignment of the low-energy excitations to short-range magnetic interactions. Modulation of the Fe2+(1)–Fe2+(2) exchange energy leads to phonon-magnetic excitation coupling and the main role in the Fe2+(1)–Fe2+(2) magnetic interaction occurs via superexchange through the oxygens. The magnetic excitations are not magnons in the usual sense, that is as quasiparticles having a long wavelength in an ordered system. The degree of observed broadening of the SiO4-stretching modes is consonant with a Fe2+(1)–Fe2+(2) exchange energy of 4.7 cm–1 presented by Schmidt et al. (1992). At temperatures above 300 K the line width of the mode at 840 cm–1 decreases slightly, whereas those of low energy lattice modes increase. This suggests that a decrease in mode broadening due to weakened magnetic interactions compensates any thermally related broadening. Complete Fe2+ spin disorder may not be reached until at least 530 K. Results from this study show that estimates of third-law entropies for silicates using simple crystal-chemical considerations that do not account for magnetic properties cannot give accurate values for many transition-metal-containing phases.  相似文献   

20.
Summary The crystal structure of a schröckingerite from Joachimsthal, NaCa3[UO2(CO3)3](SO4) F·10H2O, triclinic, space groupP1,a=9.634(1),b=9.635(1),c=14.391(2) Å, -91.41(1), =92.33(1), =120.26(1)°,V=1151 Å3,Z=2, has been determined by X-ray diffraction and refined toR=0.026 for 5451 reflections. The structure contains NaCa3[UO2(CO3)3] (SO4) F·6H2O layers built up from UO2(CO3) 3 4– anions, NaO3(H2O)3 octahedra, three kinds of CaO5F(H2O)2 polyhedra, Ca3F pyramids and Ca-bonded SO4 tetrahedra. These layers extend atz1/5 andz4/5 parallel to (001). They are linked parallel to c exclusively by hydrogen bonds, both directly as well as via interlayer H2O molecules. The structure shows a striking trigonal pseudosymmetry within the range 0.04<z<0.96. Atz0 these parts of the structure are dislocated relative to each other by a step of 1 Å parallel to [110]. Morphologic and optical properties of schröckingerite have been investigated in the light of the known crystal structure.
Kristallstruktur und kristallographische Eigenschaften eines Schröckingerits von Joachimsthal
Zusammenfassung Die Kristallstruktur eines Schröckingerits von Joachimsthal, NaCa3[UO2(CO3)3](SO4) F·10H2O, triklin, RaumgruppeP1,a=9,634(1),b=9,635(1),c=14,391(2) Å, =91,41(1), =92,33(1), =120,26(1)°,V=1151 Å3,Z=2, wurde mit Röntgenbeugung bestimmt und für 5451 Reflexe aufR=0.026 verfeinert. Die Kristallstruktur enthält NaCa3[UO2(CO3)3] (SO4)I·6H2O Schichten, die aus UO2(CO3) 3 4– . Anionen, NaO3(H2O)3-Oktaedern, drei Arten von CaO5F(H2O)2-Polyedern, Ca3 F-Pyramiden und an Ca gebundenen SO4-Tetraedern aufgebaut sind. Diese Schichten erstrecken sich inz1/5 undz4/5 parallel zu (001). Sie sind parallel zuc ausschließlich durch Wasserstoffbrücken verknüpft, und zwar sowohl direkt als auch indirekt durch zwischen den Schichten gelegene Wassermoleküle. Die Struktur zeigt im Bereich 0,04<z<0,96 eine ausgeprägte trigonale Pseudosymmetrie. Derartige Bereiche sind inz0 um etwa 1 Å parallel zu [110] stufenartig gegeneinander versetzt. Morphologische und optische Eigenschaften von Schröckingerit wurden im Licht der bekannten Kristallstruktur untersucht.

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