Richard J. Harrison

FORCinel: An improved algorithm for calculating first‐order reversal curve distributions using locally weighted regression smoothing

Figure 8. Smoothing effects on LOESS smoothed FORC distributions for a natural sample of pure hematite. In Figure 8a, optimum smoothing range is shown in green. Figures 8b, 8c, and 8d correspond to smoothing factors 2, 6, and 10, respectively. Undersmoothing produces a distribution that is dominated by noise (Figure 8b). Oversmoothing produces a distribution that obscures the presence of noninteracting grains along Hu = 0 (Figure 8d). Using the optimization routine described in Figure 5, the ideal FORC distribution is SF = 6.

Lamellar magnetism in the haematite–ilmenite series as an explanation for strong remanent magnetization

Magnetic anomalies associated with slowly cooled igneous and metamorphic rocks are commonly attributed to the presence of the mineral magnetite. Although the intermediate members of the ilmenite–haematite mineral series can also carry a strong ferrimagnetic remanence, it is preserved only in rapidly cooled volcanic rocks, where formation of intergrowths of weakly magnetic haematite and paramagnetic ilmenite is suppressed. But the occurrence of unusually large and stable magnetic remanence in rocks containing such intergrowths has been known for decades, and has recently been the subject of intense investigation. These unmixed oxide phases have been shown to contain pervasive exsolution lamellae with thickness from 100 µm down to about 1 nm (one unit cell). These rocks, many of which contain only a few per cent of such oxides, show natural remanent magnetizations up to 30 A m-1—too strong to be explained even by pure haematite in an unsaturated state. Here we propose a new ferrimagnetic substructure created by ferrous–ferric ‘contact layers’ that reduce charge imbalance along lamellar contacts between antiferromagnetic haematite and paramagnetic ilmenite. We estimate that such a lamellar magnetic material can have a saturation magnetization up to 55 kA m-1—22 times stronger than pure haematite—while retaining the high coercivity and thermal properties of single-domain haematite.

Thermodynamics and kinetics of cation ordering in MgAl 2 O 4 spinel up to 1600 degrees C from in situ neutron diffraction

Abstract The temperature dependence of the cation distribution in synthetic spinel (MgAl2O4) was determined using in-situ time-of-flight neutron powder diffraction. Neutron diffraction patterns of stoichiometric MgAl2O4 and slightly non-stoichiometric Mg0.99Al2O4 samples were collected under vacuum on heating from room temperature to 1600 °C, and the cation distribution was determined directly from site occupancies obtained by Rietveld refinement. The equilibrium non-convergent ordering has been analyzed using both the O’Neill-Navrotsky and Landau thermodynamic models, both of which fit the observed behavior well over the temperature range of the measurements. Fitting the data between 560 °C and 1600 °C using the O′Neill and Navrotsky (1983) thermodynamic model yields α = 32.8 ± 0.9 kJ/mol and β = 4.7 ± 2.0 kJ/mol. The fit to the Landau expression for ordering gives values of Tc = 445 ± 109 K and c′ = 1.62 ± 0.21. This confirms suggestions that the sign of the β coefficient in FeAl2O4 and MgAl2O4 is positive, and opposite to that found in other 2-3 oxide spinels. Non-equilibrium order-disorder behavior below 600 °C has been analyzed using the Ginzburg-Landau model, and successfully explains the time-temperature dependent relaxation behavior observed in the inversion parameter. Changing the stoichiometry, even by as little as 1 mol% Mg-deficiency, significantly reduces the degree of order.

Direct imaging of nanoscale magnetic interactions in minerals

The magnetic microstructure of a natural, finely exsolved intergrowth of submicron magnetite blocks in an ulvöspinel matrix is characterized by using off-axis electron holography in the transmission electron microscope. Single-domain and vortex states in individual blocks, as well as magnetostatic interaction fields between them, are imaged at a spatial resolution approaching the nanometer scale. The images reveal an extremely complicated magnetic structure dominated by the shapes of the blocks and magnetostatic interactions. Magnetic superstates, in which clusters of magnetite blocks act collectively to form vortex and multidomain states that have zero net magnetization, are observed directly.

Vortex Ferroelectric Domains

We show experimental switching data on microscale capacitors of lead–zirconate–titanate (PZT), which reveal time-resolved domain behavior during switching on a 100 ns scale. For small circular capacitors, an unswitched domain remains in the center while complete switching is observed in square capacitors. The observed effect is attributed to the formation of a vortex domain during polarization switching in small circular capacitors. This dynamical behavior is modeled using the Landau–Lifshitz–Gilbert equations and found to be in agreement with experiment. This simulation implies rotational motion of polarization in the xy plane, a Heisenberg-like result supported by the recent model of Naumov and Fu (2007 Phys. Rev. Lett. 98 077603), although not directly measurable by the present quasi-static measurements.

Nature and origin of lamellar magnetism in the hematite-ilmenite series

Abstract Grains consisting of finely exsolved members of the hematite-ilmenite solid-solution series, such as are present in some slowly cooled middle Proterozoic igneous and metamorphic rocks, impart unusually strong and stable remanent magnetization. TEM analysis shows multiple generations of ilmenite and hematite exsolution lamellae, with lamellar widths ranging from millimeters to nanometers. Rock-magnetic experiments suggest remanence is thermally locked to the antiferromagnetism of the hematite component of the intergrowths, yet is stronger than can be explained by canted antiferromagnetic (CAF) hematite or coexisting paramagnetic (PM) Fe-Ti-ordered (R3̅) ilmenite alone. In alternating field demagnetization to 100 mT, many samples lose little remanence, indicating that the NRM is stable over billions of years. This feature has implications for understanding magnetism of deep rocks on Earth, or on planets like Mars that no longer have a magnetic field. Atomic-scale simulations of an R3̅ ilmenite lamella in a CAF hematite host, based on empirical cation-cation and spin-spin pair interaction parameters, show that contacts of the lamella are occupied by “contact layers” with a hybrid composition of Fe ions intermediate between Fe2+-rich layers in ilmenite and Fe3+-rich layers in hematite. Structural configurations dictate that each lamella has two contact layers magnetically in phase with each other, and out of phase with the magnetic moment of an odd non-self-canceling Fe3+-rich layer in the hematite host. The two contact layers and the odd hematite layer form a magnetic substructure with opposite but unequal magnetic moments: a lamellar “ferrimagnetism” made possible by the exsolution. Because it is confined to magnetic interaction involving the moments of just three ionic layers associated with each individual exsolution lamella, lamellar magnetism is unique and quite distinct from conventional ferrimagnetism. Simulation cells indicate that the magnetic moments of contact layers are locked to the magnetic moments of adjacent AF hematite layers and are parallel to the basal plane (001). Thus, lamellar magnetism is created at the temperature of chemical exsolution, and is a chemical remanent, rather than thermal remanent, magnetization. However, in thermal demagnetization experiments, too short for lamellar resorption, demagnetization temperatures are those of the CAF hematite, considerably higher than temperatures of original lamellae formation. Internal crystal structure cannot dictate that the contact layers of different lamellae will form magnetically in phase with each other to give the highest net magnetic moment, but magnetic moments of lamellae can be made to form in phase by the external force of the magnetizing field at the time of exsolution. A thesis of this paper is that an external magnetic field can dictate the magnetic moments and hence the chemical location of ilmenite lamellae in a hematite host, and that once in place, neither the location nor the magnetic moment will be easily disturbed. In an ilmenite host, the external magnetic field cannot control the chemical location of a hematite lamella, which is dictated by the enclosing ilmenite, but once lamellae have formed, the field can dictate their magnetic moments. These moments, however, are not locked chemically to the host, resulting in lower coercivity. The effectiveness of the external force in single crystals is dictated by their orientation with respect to the magnetizing field. In grains with (001) oriented parallel to the field, it would be effective in producing in-phase magnetic moments and very strong remanence. In grains with (001) normal to the field, the field would be less effective in producing in-phase magnetic moments, hence producing weak remanence. The most intense lamellar magnetism per formula unit occurs with in-phase magnetization, high lamellar yields, and the largest number of lamellae per unit volume (i.e., smallest lamellar size). Compared to the magnetic moment per formula unit (Mpfu) and magnetic moment per unit volume (MV) of end-member magnetite (Mpfu = 4 μB, MV = 480 kA/m) and hematite (Mpfu = 0.0115 μB, MV = 2.1 kA/m), results for some atomic models reasonably tied to natural conditions are Mpfu = 0.46-1.36 μB and MV = 84-250 kA/m

The influence of transformation twins on the seismic-frequency elastic and anelastic properties of perovskite: dynamical mechanical analysis of single crystal LaAlO3

The low-frequency mechanical properties of single crystal LaAlO3 have been investigated as a function of temperature, frequency and applied force using the technique of dynamical mechanical analysis (DMA) in three-point bend geometry. LaAlO3 undergoes a cubic to rhombohedral phase transition below 550 ◦ C. The mechanical response in the low-temperature rhombohedral phase is shown to be dominated by the viscous motion of transformation twin domain walls, resulting in a factor of 10 decrease in the storage modulus relative to the high-temperature cubic phase (super-elastic softening) and a significant increase in attenuation. Super-elastic softening is observed down to 200 ◦ C, below which the mobility of the domain walls decreases markedly, causing a rapid increase in storage modulus and a pronounced peak in attenuation (domain wall freezing). The frequency dependence of the storage modulus close to the freezing temperature is accurately described by a modified Burgers model with a Gaussian distribution of activation energies with mean value 84.1(1) kJ/mol and S.D. 10.3(1) kJ/mol. This activation energy suggests that domain walls are pinned predominantly by oxygen vacancies. Detailed analysis of the dynamic force-deflection curves reveals three distinct regimes of mechanical response. In the elastic regime, the domain walls are pinned and unable to move. The elastic response is linear with a slope determined by the intrinsic stiffness of the lattice, the initial susceptibility of the pinning potential and the bending of twin walls between the pinning sites. In the super-elastic regime, the domain walls unpin and displace by an amount determined by the balance between the applied and restoring forces. The value of the apparent super-elastic modulus is shown to be independent of the spontaneous strain and hence independent of temperature. At high values of the applied force, adjacent domain walls come into contact with each other and prevent further super-elastic deformation (saturation). The strain in the saturation regime scales with the spontaneous strain and the resulting modulus is strongly temperature dependent. The possible effects of domain wall motion on the seismic properties of minerals are discussed. It is concluded that, if these results are directly transferred to mantle-forming (Mg, Fe)(Si, Al)O 3 perovskite, the strain amplitude of a typical seismic wave would be sufficient to cause super-elastic softening. However, pinning of domain walls by oxygen vacancies leads to very short relaxation times at mantle temperatures. If translated to (Mg, Fe)(Si, Al)O 3, these would be too short to amount to significant seismic attenuation. Increased pinning of ferroelastic domain walls by defects, impurities and grain boundaries

Effect of fine-scale microstructures in titanohematite on the acquisition and stability of natural remanent magnetization in granulite facies metamorphic rocks, southwest Sweden: Implications for crustal magnetism

Mid-Proterozoic granulites in SW Sweden, having opaque minerals hematiteilmenite with minor magnetite, and occurring in an area with negative aeromagnetic anomalies, have strong and stable reversed natural remanent magnetization ∼9.2 A/m, with 100% remaining after demagnetization to 100 mT. Samples were characterized by optical microscopy, electron microprobe (EMP), transmission electron microscopy (TEM), and rock-magnetic measurements. Earliest oxide equilibrium was between grains of titanohematite and ferri-ilmenite at 650°–600°C. Initial contacts were modified by many exsolution cycles. Hematite and ilmenite (Ilm) hosts and lamellae by EMP are Ilm 24–25, ILm 88–93, like titanohematite, and ilmenite above 520°C on Burtons diagram [1991]. Finer hosts and lamellae by TEM are Ilm16 ±3 and Ilm 88±4, like coexisting antiferromagnetically ordered (AF) hematite and ilmenite below 520°C on Burtons diagram. This may be the first example of analytical identification, in one sample, of former hematite, now finely exsolved, and AF hematite. TEM microstructures consist of gently curving semicoherent ilmenite lamellae within hematite, flanked by precipitate-free zones and abundant ilmenite disks down to unit cell scale (1–2 nm). Strain contrast of disks suggests full coherence with the host, and probable formation at the reaction titanohematite ---> AF hematite + ilmenite at 520°C. Magnetic properties are a consequence of chemical and magnetic evolution of hematite and ilmenite with bulk compositions ilmenite-richer than Ilm 28, that apparently exsolved without becoming magnetized, down to 520°C where hematite broke down to AF hematite plus ilmenite, producing abundant AF hematite below its Neel temperature. Intensity of magnetization is greater than possible with hematite alone, and TEM work suggests that ultrafine ilmenite disks in AF hematite are associated with a ferrimagnetic moment due to local imbalance of up and down spins at coherent interfaces.

Application of real-time, stroboscopic x-ray diffraction with dynamical mechanical analysis to characterize the motion of ferroelastic domain walls

The dynamic response of ferroelastic twins to an alternating stress has been studied in situ at high temperature using a stroboscopic x-ray diffractometer and combined dynamical mechanical analyzer (XRD-DMA). The XRD-DMA is designed to allow x-ray rocking curves to be collected while the sample is undergoing simultaneous dynamical mechanical analysis in three-point-bend geometry. The detection of diffracted x-rays is synchronized with the applied load, so that rocking curves corresponding to different parts of the dynamic load cycle can be obtained separately. The technique is applied to single-crystal LaAlO3, which undergoes a cubic to rhombohedral phase transition at 550 °C, leading to the generation of characteristic “chevron” twins. The rocking-curve topology is calculated as a function of crystal orientation for each chevron type. Systematic changes in the rocking curves during heating and cooling under dynamic load demonstrate a clear preference for chevrons containing {100}pc walls perpendicular to...

Dipolar Magnetism in Ordered and Disordered Low-Dimensional Nanoparticle Assemblies

Magnetostatic (dipolar) interactions between nanoparticles promise to open new ways to design nanocrystalline magnetic materials and devices if the collective magnetic properties can be controlled at the nanoparticle level. Magnetic dipolar interactions are sufficiently strong to sustain magnetic order at ambient temperature in assemblies of closely-spaced nanoparticles with magnetic moments of ≥ 100 μB. Here we use electron holography with sub-particle resolution to reveal the correlation between particle arrangement and magnetic order in self-assembled 1D and quasi-2D arrangements of 15 nm cobalt nanoparticles. In the initial states, we observe dipolar ferromagnetism, antiferromagnetism and local flux closure, depending on the particle arrangement. Surprisingly, after magnetic saturation, measurements and numerical simulations show that overall ferromagnetic order exists in the present nanoparticle assemblies even when their arrangement is completely disordered. Such direct quantification of the correlation between topological and magnetic order is essential for the technological exploitation of magnetic quasi-2D nanoparticle assemblies.