Structure, ordering and cation interactions in Ca-free P2 1 /c clinopyroxenes

A suite of 14 synthetic Ca-free P2 ₁ /c low-clinopyroxenes of compositions across the enstatite-ferrosilite (En-Fs) join have been studied by X-ray powder diffraction and Mössbauer spectroscopy. The crystal structure of one sample with composition X _Fs=0.39 was determined by single-crystal X-ray diffraction. The powder diffraction data show that there is no significant (<0.25% at X _Fs=0.5) excess volume of mixing on the enstatite-ferrosilite join. The molar volumes are described by V=31.261(17)+1.677(23) X _Fs cm³.mol(MSiO₃)^–1. The linear behaviour of volume with composition arises from the compensating effects of non-linear changes in the unit-cell parameters with composition. Unweighted fits to the data yielded the relationships: a=9.6100(15)+0.105(2)X _Fs, b=8.8156(28)+0.218(12)X _Fs+0.0481(117)X ² _Fs , c?=5.1702(4)+0.0879(21)X _Fs–0.0214(21)X ² _Fs , β=108.345(8)+0.947(30)X _Fs–0.805(26)X ² _Fs . The strong positive deviation of β from linearity is directly correlated to the difference in site occupancies between M1 and M2 as determined by Mössbauer spectroscopy and arises directly from the expansion of M2-O1 and M2-O3 bonds upon initial substitution of Fe for Mg in enstatite. The hyperfine parameters from Mössbauer spectra are consistent with variations in the average local environment as recorded by the X-ray data. Asymmetric line broadening of the Mössbauer spectra provides evidence for next-nearest neighbour effects, and is consistent with no significant clustering of Fe or Mg within the samples.     

Spectral spreading from surface bubble motion

At low frequencies, surface bubbles contribute to acoustic backscattering in aggregate, and the motion of these bubble masses causes spectral spreading of the acoustic signals. This motion of the bubbles entrained in the surface waves is used to obtain the power spectrum of a low-frequency surface-scattered signal at a low grazing angle. A spectral distribution of the deterministic surface drift, augmented by breaking wave crests, is developed for the wave frequency components that are actively breaking. This motion is combined with the random motion in a wave cycle to predict the spectral widths of low-angle backscattered sound. To permit comparisons with measured data, convolutions of these spectra with simple square pulses of various durations are performed     

Schorlomite: a discussion of the crystal chemistry, formula, and inter-species boundaries

Examination of schorlomite from ijolite at Magnet Cove (USA) and silicocarbonatite at Afrikanda (Russia), using electron-microprobe and hydrogen analyses, X-ray diffraction and Mössbauer spectroscopy, shows the complexity of substitution mechanisms operating in Ti-rich garnets. These substitutions involve incorporation of Na in the eightfold-coordinated X site, Fe²⁺ and Mg in the octahedrally coordinated Y site, and Fe³⁺, Al and Fe²⁺ in the tetrahedrally coordinated Z site. Substitutions Ti⁴⁺Fe³⁺Fe³⁺_–1Si_–1 and Ti⁴⁺Al³⁺Fe³⁺_–1Si_–1 are of major significance to the crystal chemistry of schorlomite, whereas Fe²⁺ enters the Z site in relatively minor quantities (<3% Fe). There is no evidence (either structural or indirect, such as discrepancies between the measured and calculated Fe²⁺ contents) for the presence of ^[6]Ti³⁺ or ^[4]Ti⁴⁺ in schorlomite. The simplified general formula of schorlomite can be written as Ca₃Ti⁴⁺₂[Si_3-x(Fe³⁺,Al,Fe²⁺)_xO₁₂], keeping in mind that the notion of end-member composition is inapplicable to this mineral. In the published analyses of schorlomite with low to moderate Zr contents, x ranges from 0.6 to 1.0, i.e. Ti⁴⁺ in the Y site is <2 and accompanied by appreciable amounts of lower-charged cations (in particular, Fe³⁺, Fe²⁺ and Mg). For classification purposes, the mole percentage of schorlomite can be determined as the amount of ^[6]Ti⁴⁺, balanced by substitutions in the Z site, relative to the total occupancy in the Y site: (^[6]Ti⁴⁺–^[6]Fe²⁺–^[6]Mg²⁺– ^[8]Na⁺)/2. In addition to the predominant schorlomite component, the crystals examined in this work contain significant (>15 mol.%) proportions of andradite (Ca₃Fe³⁺₂Si₃O₁₂), morimotoite (Ca₃Fe²⁺TiSi₃O₁₂), and Ca₃MgTiSi₃O₁₂. The importance of accurate quantitative determination and assignment of Fe, Ti and other cations to the crystallographic sites for petrogenetic studies is discussed.

Nonlinear regression for dependent variables

Nonlinear regression methods can be used to fit functions for two related variables where both variables are subject to error. A computer program for nonlinear estimation described previously has been modified to fit such functions for a given set of data. A numerical example is provided for a second-degree equation in xand y.A closer fit to an observed set of data is possible if the error structure for the variables is specified.     

Converting bottom loss measured from a rough-layered sediment tothe equivalent `flat-bottom' loss

A correction factor is derived that can be applied to the measured data to convert it from rough surface loss to the equivalent loss if the interfaces had been smooth. With this correction, the data can be made to conform to the assumptions of the model, which should lead the inversion process to a better fitting set of parameters. Two examples of this application are shown in thin sediments in which the correction gave improved model/data correlations and lower squared errors. The choice of a random Gaussian characterization restricts the use of this correction to Damuth Provinces II and III, where the stochastic nature of the roughness is evident