SUMMARY Anisotropy of remanent magnetization and magnetic susceptibility are highly sensitive and important indicators of geological processes which are largely controlled by mineralogical parameters of the ferrimagnetic fraction in rocks. To provide new physical insight into the complex interaction between magnetization structure, shape, and crystallographic relations, we here analyse ‘slice-and-view’ focused-ion-beam (FIB) nano-tomography data with micromagnetic modelling and single crystal hysteresis measurements. The data sets consist of 68 magnetite inclusions in orthopyroxene (Mg60) and 234 magnetite inclusions in plagioclase (An63) were obtained on mineral separates from the Rustenburg Layered Suite of the Bushveld Intrusive Complex, South Africa. Electron backscatter diffraction was used to determine the orientation of the magnetite inclusions relative to the crystallographic directions of their silicate hosts. Hysteresis loops were calculated using the finite-element micromagnetics code MERRILL for each particle in 20 equidistributed field directions and compared with corresponding hysteresis loops measured using a vibrating sample magnetometer (VSM) on silicate mineral separates from the same samples. In plagioclase the ratio of remanent magnetization to saturation magnetization (Mrs/Ms) for both model and measurement agree within 1.0 per cent, whereas the coercivity (Hc) of the average modelled curve is 20 mT lower than the measured value of 60 mT indicating the presence of additional sources of high coercivity in the bulk sample. The VSM hysteresis measurements of the orthopyroxene were dominated by multidomain (MD) magnetite, whereas the FIB location was chosen to avoid MD particles and thus contains only particles with diameters <500 nm that are considered to be the most important carriers of palaeomagnetic remanence. To correct for this sampling bias, measured MD hysteresis loops from synthetic and natural magnetites were combined with the average hysteresis loop from the MERRILL models of the FIB region. The result shows that while the modelled small-particle fraction only explains 6 per cent of the best fit to the measured VSM hysteresis loop, it contributes 28 per cent of the remanent magnetization. The modelled direction of maximal Mrs/Ms in plagioclase is subparallel to [001]plag, whereas Hc does not show a strong orientation dependence. The easy axis of magnetic remanence is in the direction of the magnetite population normal to (150)plag and the maximum calculated susceptibility (χ*) is parallel to [010]plag. For orthopyroxene, the maximum Mrs/Ms, maximum χ* and the easy axis of remanence is strongly correlated to the elongation axes of magnetite in the [001]opx direction. The maximum Hc is oriented along [100]opx and parallel to the minimum χ*, which reflects larger vortex nucleation fields when the applied field direction approaches the short axis. The maximum Hc is therefore orthogonal to the maximum Mrs/Ms, controlled by axis-aligned metastable single-domain states at zero field. The results emphasize that the nature of anisotropy in natural magnetite does not just depend on the particle orientations, but on the presence of different stable and metastable domain states, and the mechanism of magnetic switching between them. Magnetic modelling of natural magnetic particles is therefore a vital method to extract and process anisotropic hysteresis parameters directly from the primary remanence carriers.
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Numerical ellipsometry: A method for selecting a single β-gallium oxide monoclinic crystal orientation able to determine the complete permittivity tensor
Previously, the infrared permittivity tensor of monoclinic β-Ga 2 O 3 crystals has been determined using ellipsometry reflection measurements from two differently oriented monoclinic β-Ga 2 O 3 crystals with surfaces parallel to (010) and (−201). The (010) surface places the crystallographic a-c plane in the table of the instrument. The permittivity tensor consists of four complex values, and in order to compute it, four or more combinations of measurements are required at selected table rotations and incidence angles. However, the (010) orientation also places the transverse optical (TO) modes with Au symmetry parallel to the z-axis of the instrument, and we find that these modes are not fully excited and, hence, not measurable due to underlying selection rules. This makes additional measurements on surfaces other than (010) necessary. The second orientation has been the (−201) crystal, which places the crystallographic b axis in the plane of the table to access the transverse Au phonons. In prior work, the overall tensor has been determined by combining measurements of the two crystal orientations [Schubert et al., Phys. Rev. B 93, 125209 (2016)]. The goal of the work here is to find single crystal orientations for which all TO modes can be determined from measurements. The use of a set of measurements employed for such a single crystal is inextricably linked to the choice of incidence angles and table rotations. Consequently, determining suitable angles for these is linked to the selection of a crystal orientation, which is, therefore, an integral part of the overall goal. The TO contribution to the permittivity strongly dominates at or near the TO mode wavenumber resonances and, therefore, are used in this work to identify suitable orientations for a single crystal. Any such crystal orientation will also provide measurements useful to compute permittivity across the entire measured wavenumber range. In principle, any crystal orientation that does not place the direction of any TO mode at or near the z-axis may be suitable due to the underlying physics and mathematics of the problem. We discuss which of these measurement parameters contain the most sensitivity for the (111) orientation. For accuracy, we seek the best or very good orientations. Our investigation follows a previously demonstrated approach where at a single wavelength, the full tensor of an orthorhombic absorbing crystal was obtained from a low-symmetry surface of stibnite [Schubert and Dollase, Opt. Lett. 27, 2073 (2002)]. We discuss which of these measurement parameters contain the most sensitivity for the (111) orientation. The methods presented here will also be useful for other monoclinic materials as well as other materials of different crystal structures, including orthorhombic and triclinic materials.
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- NSF-PAR ID:
- 10393126
- Date Published:
- Journal Name:
- Journal of Vacuum Science & Technology A
- Volume:
- 41
- Issue:
- 1
- ISSN:
- 0734-2101
- Page Range / eLocation ID:
- 013402
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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The anisotropic permittivity parameters of monoclinic single crystal lutetium oxyorthosilicate, Lu2SiO5 (LSO), have been determined in the terahertz spectral range. Using terahertz generalized spectroscopic ellipsometry (THz-GSE), we obtained the THz permittivities along the a, b, and c⋆ crystal directions, which correspond to the εa, εb, and εc⋆ on-diagonal tensor elements. The associated off diagonal tensor element εac⋆ was also determined experimentally, which is required to describe LSO's optical response in the monoclinic a–c crystallographic plane. From the four tensor elements obtained in the model fit, we calculate the direction of the principal dielectric axes in the a–c plane. We find good agreement when comparing THz-GSE permittivities to the static permittivity tensors from previous infrared and density functional theory studies.
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null (Ed.)Abstract We performed deformation experiments on dry natural single crystals of magnetite and ilmenite to determine the rheological behavior of these oxide minerals as a function of temperature, orientation, and oxygen fugacity. Samples were deformed at temperatures of 825–1150 $$\,^{\circ }$$ ∘ C to axial strains of up to 15–24% under approximately constant stress conditions up to 120 MPa in a dead-load-type creep rig at ambient pressure in a controlled gas atmosphere. Oxygen fugacity ranged from 10 $$^{-9.4}$$ - 9.4 to 10 $$^{-4}$$ - 4 atm. Ilmenite creep was insensitive to oxygen fugacity, while magnetite displayed a strong, non-monotonic oxygen fugacity dependence, with creep rates varying as $$f_{O_{2}}^{-0.7}$$ f O 2 - 0.7 and $$f_{O_{2}}^{0.4}$$ f O 2 0.4 at more reducing and more oxidizing conditions, respectively. Dislocation creep rates of magnetite single crystals were weakly dependent on crystallographic orientation with stress exponents that varied between 2.8 and 4.3 (mean 3.5 ± 0.4). Magnetite compressed parallel to <100>, <110>, and <111> axes exhibited apparent activation energies of 315±5, 345±30, and 290±5 kJ/mol, respectively. We estimated $${f_O}_2$$ f O 2 -independent magnetite activation energies of 715 ± 150, 725 ± 145, and 690 ± 150 kJ/mol for <100>, <110>, and <111> orientations, respectively, in the region of negative $${f_O}_2$$ f O 2 -dependence. Ilmenite single crystals were compressed parallel, normal, and inclined to the c-axis. Stress exponents of 3.4, 4.3, and 3.9 indicate dislocation creep with activation energies of 420 ± 35, 345 ± 30, and 360 ± 40 kJ/mol, respectively, for these orientations. Mechanical anisotropy in ilmenite is notably higher than in magnetite, as expected from its lower crystal symmetry. Constitutive equations were formulated for ilmenite and magnetite creep.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1116/6.0002235
