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Chapters 1, 2, & 3: Tables of Contents, Introduction, Statement of Problem, Review of Rock Magnetic Theories
Chapter 4: Geochemistry of Iron-Titanium Oxides
Chapter 5: Sample Preparation
Chapter 6: Nonmagnetic Sample Characterization
Chapters 7 & 8: Magnetic Sample Characterization, Summary and Conclusions
Gary D. Storrick
B.S.E., The University of Pittsburgh, 1977
M.S.E.E., The University of Pittsburgh, 1981
Submitted to the Graduate Faculty of
Arts and Sciences in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
University of Pittsburgh
This study investigates the details of how Néel-type theories of multidomain TRM are violated for high quality synthetic magnetites produced by the glass-ceramic method of Worm and Markert . The glass-ceramic method provides a simple means of preparing nearly uniformly-sized, dispersed, almost chemically pure, and relatively unstressed magnetite crystals that are well-suited for this work.
Six samples were selected for detailed study. SEM observations showed well-formed magnetite crystals with diameters ranging from 0.8 to 5.8 µm, well within the multidomain range yet small enough to display pseudo-single-domain behavior. The samples were heated to slightly above the magnetite Curie temperature, then allowed to cool in an applied magnetic field. Fourteen cases per sample were run using fields ranging from 10 µT to 30 mT. The resulting TRM curves show the dependency expected at low fields, with a smooth transition towards saturation in the higher fields. Saturation was not reached, even in the 30 mT cases. The distinct thermal-activation blocking, Néel blocking, and saturation regions discussed by Schmidt [1973, 1975] are not readily apparent.
In each case, the sample was sequentially demagnetized using alternating fields ranging from 5 mT to 140 mT. The demagnetization curves for most samples show a shift in the coercivity spectrum of the grains contributing to the TRM, with an increase in the importance of the low-coercivity grains as the applied field is increased. This contradicts the behavior predicted when the Schmidt-Néel theory is applied to an assemblage of grains. The 5.8 µm sample showed anomalous behavior, which is attributed to the relatively large variation in grain size within the sample.
Theory predicts a shift in blocking temperature to lower temperatures
as the applied field is increased. This can be observed through
the field-dependence of partial TRM (PTRM), provided the high-temperature
isothermal-remanence (IRM) is taken into account as a correction.
A series of PTRM and high-temperature IRM acquisition runs demonstrated
that the predicted shifts occur, and that Thellier's Law of Additivity
of PTRMs was satisfied.
Paleomagnetism occupies a unique position among geophysical techniques due to the ability of certain rocks to preserve a record of the local Earth's magnetic field throughout geologic times. Initially even first-order interpretations of the paleomagnetic record were significant, as evidenced by the substantial support paleomagnetism provided for plate tectonic theory. More recently, paleomagnetic studies have pushed toward obtaining higher temporal and spatial resolution. The success of these efforts is critically dependent on an understanding of the remanent mechanisms operating in rocks, and in particular on the mechanism of thermoremanent magnetization (TRM), which is the principal source of remanence in igneous rocks and a likely source for the original magnetization in detrital grains in sedimentary rocks.
A rigorous theory of TRM based on first principles appears to be presently unattainable. The accepted quantum mechanical model for ferromagnetism involves a primitive cubic array of atoms with an electron spin of s= associated with each lattice site [Pathria, 1972]. Although the mathematical model [Heisenberg, 1928] is widely known, solutions have only been obtained for the Ising approximation in the one-dimensional [Ising, 1925] and the field free two-dimensional [Onsager, 1944] cases. Topological considerations [Kac and Ward, 1952] argue against obtaining three-dimensional solutions to the Ising problem by similar techniques. Considering physicists' failure to solve the Ising model despite six decades of trying, there is little reason to expect a rigorous description of TRM in real materials at any time in the immediate future.
Practical TRM theories have taken a less rigorous approach. These theories can be divided into two categories. The classical approach involves developing simple analytical models of idealized magnetic particles. Néel's two classic papers on single-domain (SD) [Néel 1949] and multidomain (MD) [Néel, 1955] magnetic grains form the starting point for most of these studies. More recent studies have invoked an intermediate "pseudo-single-domain" (PSD) grain behavior to explain the continuity of experimentally measured parameters across the predicted SD-MD boundary, but to date these efforts have been inconclusive. Some of the competing explanations for pseudo-single domain mechanisms are:
The TRM mechanism for SD grains is fairly well understood in terms of Néel's SD model, though some discrepancies remain. The agreement between experiment and the available Néel domain wall motion theories for MD grains is much less satisfactory, particularly for the small MD grains which in practice dominate the TRM of so many rocks. To date, explanations of the discrepancies have been less than satisfactory. Previous work indicates that Néel-type models of TRM are qualitatively useful but quantitatively inaccurate. This study investigates the details of how Néel-type theories of MD TRM are violated for high quality synthetic magnetites produced by the glass-ceramic method of Worm and Markert [1987b].
Numerous studies have examined magnetic properties of titanomagnetite particles in the SD, PSD, and small MD size range. Most of these studies were hampered by the difficulties involved in preparing uniform samples for study. Recently a glass-ceramic technique has been developed which provides well-dispersed titanomagnetite particles in a silicate matrix [Worm and Markert, 1987b]. Worm  reports he has used samples prepared in this manner to verify Néel's SD theory. This study produced samples by this glass-ceramic method, then proceeded to magnetically characterize the samples with the intent of carefully understanding the details of how the MD Néel models are violated, thus providing guidance for modifying the Néel-type MD models.
Néel-type MD theories are based on domain wall motion
only, and usually on that of only a single wall. They omit the
demonstrable influence of domain wall nucleation [Boyd et al.,
1984]. Theories incorporating domain wall nucleation have been
proposed [Moon, 1985], but currently are formulated in a micromagnetic
approach requiring extensive numerical calculation. A very simple
demonstration of the inadequacy of Néel-type theories is
that they predict that for MD particles TRM acquired in a strong
field is more stable with respect to AF demagnetization than TRM
acquired by the same sample in a weak field [Schmidt, 1976], whereas
the converse is experimentally observed in small MD particles.
This has been partially, but not fully, resolved by considering
the interaction effects between walls when more than one wall
is present [Schmidt, 1975], and by taking into account demagnetizing
field effects [Bailey and Dunlop, 1983].
There is a need for a simpler model which incorporates domain wall nucleation without requiring the extensive calculations involved in the micromagnetic approach. One immediate suggestion is incorporating a potential barrier against nucleation into a Néel-type model such as Schmidt's , while introducing assemblages of different grains that may or may not contain walls. Another approach would allow multiple interacting walls in one grain, with nucleation effects determining the number. Clearly, experimental results are needed as a guide in the construction of such models.
It is generally understood that synthetic materials can provide simpler systems for theoretical modeling than natural titanomagnetites. Natural titanomagnetites are often both nonstoichiometric and impure. Most natural titanomagnetites do not lie upon the ulvöspinel-magnetite join, but are slightly oxidized towards the ilmenite-magnetite join [Nagata, 1961]. Al3+, Mg2+, Mn2+ and other cations are known to substitute for Fe3+ or Fe2+. Although numerous authors have investigated the effects of oxidation [Readman and O'Reilly, 1970; Ozima and Sakamoto, 1971; Rahman and Parry, 1978] and cation substitution [Özdemir and O'Reilly, 1978; Richards et al., 1973], natural systems still provide too many complications for convenient theoretical treatment and too much variability for comparison of results with theory. Synthetic materials can provide samples with fewer variations in composition and grain size distribution, and hence are more amenable to theoretical treatment.
Synthetic samples have been prepared by several methods:
The study samples were produced by the glass-ceramic method. The synthesis procedure consists of melting a mixture of oxides/carbonates of Ca, K, Na, Si, Fe and Ti under a controlled reducing atmosphere, then quenching the melt to a glass. Two heat treatment steps under controlled atmosphere allow nucleation and growth of titanomagnetite crystals respectively, and are followed by a final quench.
The glass-ceramic method has several advantages. First, it is amenable to crystal growth in a controlled atmosphere, and hence stoichiometry can be controlled. The resulting titanomagnetite crystals are dispersed throughout a magnetically inert matrix, minimizing the effects of intergrain interactions. The matrix acts as a barrier to oxygen, thus protecting the titanomagnetite crystals from chemical alteration. Crystals are easily produced in the grain sizes corresponding to the SD through MD transition. The heat treatment process allows one to maintain relatively close control over the size distribution for a wide range of crystal sizes. Stresses in the resulting crystals are less than those introduced by methods involving sample grinding. These advantages are illustrated by the first published results using the glass-ceramic titanomagnetites, where SD and MD hysteresis results disagree with previous studies, yet were found to be in better agreement with theory [Worm and Markert, 1987a].
Initially I proposed working with various-sized grains of a single titanomagnetite composition. I originally planned to use a moderately high-titanium titanomagnetite (approximately Fe2.5Ti0.5O4) with a fairly low Curie temperature of ~ 200 °C, thus reducing the probability of chemical alteration during the TRM experiments. Comments received during the NSF review of the research grant proposal, conversations with Dr. Worm, and the possibility of magnetite/ulvöspinel exsolution complicating the results convinced me to work with magnetite instead.
The heating and cooling for the TRM studies was performed in the TRM furnace built and described by Clauter . Although the TRM furnace is equipped for maintaining a controlled atmosphere and this feature was used in this study, the process requires careful attention and is somewhat of a nuisance. Since I did not need to exceed the Curie temperature by much in these experiments, I could not rely on using equilibrium atmospheres to prevent sample oxidation since equilibration is unlikely to occur at such low temperatures. I tried to eliminating chemical change in the samples during the magnetic experiments by isolating the samples from the atmosphere. The method I chose was to seal the samples in evacuated quartz tubes to minimize the probability of chemical alteration and to provide self-buffering. The samples were then thermally cycled from room temperature to beyond their Curie temperature until their magnetic properties stabilized. The sample preparation furnace was used because the electronic temperature controller was easily programmed to automate the desired temperature cycling process.
An original fragment of each sample was preserved for comparison
to determine the extent of chemical alteration during the thermal
cycling process, and the characterization process was repeated
after the magnetic experiments were completed to determine the
extent and nature of any changes. The synthesized magnetites were
characterized by x-ray diffraction, SEM, and electron microprobe.
Magnetic hysteresis properties were measured on Material Engineering's
vibrating sample magnetometer equipped with a temperature controlled
sample holder. Isothermal remanent magnetization (IRM) curves
were measured using the Paleomagnetism Laboratory's spinner magnetometer,
while TRM, partial TRM (PTRM), and additional IRM properties were
measured in the Paleomagnetism Laboratory's cryogenic magnetometer.
Two classic experiments were performed. The first was to measure TRM acquisition versus the strength of an externally applied field. The second was to measure the shift in blocking temperature versus applied field by making a series of PTRM measurements. The first reaction of the reader may well be that this appears to be a rather old-fashioned approach, and it is, at least in its initial stages. The problem with the newer theoretical models that are being used is that they have tended to a micromagnetic approach. While obviously desirable, they have the disadvantage of requiring detailed knowledge of grain size and shape. Also, at present they are not easily generalized to bulk properties, which is what one must work with in the laboratory.
The strength of the Néel models has always been their simplicity. They clearly err in the direction of being generalizations that are too broad, and the MD model in particular may be faulted as missing the mark entirely if, for instance, domain nucleation is a more important process than domain wall displacement, or if moments intrinsic to the domain structure such as wall moments are of overriding importance. What one needs are experimental results that show just which predictions of the old Néel models are correct and which are not, for the new class of glass-ceramic synthetic titanomagnetites.
In two early papers, Schmidt [1973, 1976] pointed out the critical role that the variation of blocking temperature plays in both the SD and MD Néel models. It is evident that the broad behavior demonstrated in the 1976 paper of TB(H) must in fact be operational. Only if TB(H) decreases with increasing field H can one obtain the observed and universal rule that TRM approaches IRM in all its properties as H becomes large compared to microscopic coercivity. From this, it is easy to show that the MD Néel model predicts that unblocking should take place at a lower temperature than blocking. The formal argument is summarized in Section 3.2.
Worm et al.'s  recent work shows that the synthetic glass-ceramic samples support the earlier work reported by Bolshakov and Shcherbakov , which was carried out on traditionally prepared samples, in which a partial TRM acquired in a moderate temperature range is not demagnetized in zero field until a much higher temperature. This appears to fly in the face of the TB(H) behavior just discussed, but may reflect instead complications that are not present in the basic Néel models, such as interactions between domain walls and nucleation effects.
Thus, one of the highest priorities was to repeat some of the experiments of Clauter [Clauter, 1979; Clauter and Schmidt, 1981] in which it was shown that the partial TRM spectrum did in fact shift to lower temperatures as the field H increases. Note that this is not the same experiment done by Worm et al. , which tests the relation between blocking and unblocking temperatures, but directly tests the TB(H) dependence. If Clauter's results are borne out in the synthetic samples, then there would be a basis for extending the original Néel MD model, based on the TB(H) dependence, but searching for additional terms that would reverse the blocking-unblocking relation.
First, I made measurements of TRM acquisition versus applied field. Previous workers [Dunlop, 1975; Day, 1977] have reported power-law dependencies in TRM(H) acquisition curves, while Clauter  failed to find such a dependence for carefully-sized synthetic samples. A problem in interpreting these results is that grain size and shape variation within each bulk sample tends to smear out the breaks between the three segments of the acquisition curve predicted by the Néel MD theory (low-field linear during thermal fluctuation blocking, approach to saturation in which the effect of the demagnetizing field is dominant, and finally saturation). The relatively uniform sizes and shapes of the dispersed magnetite grains produced by the glass-ceramic method yield much clearer and more reliable results, perhaps at last settling in the negative a very old question as to whether these power-law segments are in fact real.
Second, I investigated the variation of the blocking temperatures versus applied field, along the lines used by Clauter and Schmidt . This was accomplished through a series of PTRM acquisitions. Worm et al.  performed some thermal demagnetization of PTRMs as part of a viscous magnetization study, but their experiments were limited to low field strengths (0.05-0.5 mT) and included only a single PTRM temperature interval. This work included more complete PTRM study and provides valuable data on the effect of applied field on blocking and unblocking temperatures, and hence provides valuable insight on the TRM mechanism in small MD grains. To this end, the PTRM acquisition spectra were supplemented by alternating-field demagnetization curves for individual PTRMs as well as for total TRMs.
In each case past work has indicated violation of the quantitative predictions of Néel-type models; by carefully measuring these deviations I hoped to gain some insight into the mechanisms not considered in the Néel models. These are summarized in Sections 7 and 8.