Fig. 2.17. The grain size dependence of the intensity of weak-field (0.1 mT) TRM in magnetite. After Dunlop and Argyle (1997).

metastable SD grains depends on the probability that no domain walls will have nucleated and therefore becomes a fraction of the SD remanence. For a given grain size some of the grains will have no domain walls and others will have differing numbers of walls with an average value of vi for that grain size. The TRM for any given grain size will therefore be a combination of the TRM of the metastable SD grains (no domain walls) and the multidomain TRM from the remaining grains. Fuller (1984) suggests the following relationship

For large values of w this gives the MD value and for w = 0 the SD value. The appropriate grain size relationship of w for the TRM after weak-field cooling is not known for magnetite or titanomagnetite but w ~ (r"'2 -1) will be a rough approximation, where r is the ratio of the grain size to the critical SD grain size. As shown by Fuller (1984) the TRM given by (2.3.25) predicts the fall in TRM in the PSD range shown by the experimental data of Fig. 2.17.

It is worth noting that (2.3.24) and (2.3.10) enable the Koenigsberger ratio Qt of (2.1.5) to be calculated for MD grains of magnetite, since Qn for the NRM is frequently quoted in paleomagnetic studies. After allowing for the effect of the internal demagnetizing field, Dunlop and Özdemir (1997) calculate Qt = 0.6 that is close to the experimental value for MD magnetite. For SD grains of magnetite the TRM is very much higher by at least an order of magnitude (Fig. 2.17), so that for these grains usually Qt > 10. Most rocks used for paleomagnetism have Qa > 1 so that pure multidomain TRM typically makes little contribution to the total TRM.

When carrying out laboratory tests relating to TRM in rocks, the very act of reheating the rock sample can cause chemical changes that can make the test ineffective. The acquisition of TRM involves the thermal activation of grains so that the energy barriers preventing the resetting of the magnetization in grains can be overcome. Anhysteretic remanent magnetization (ARM) is often used as an analog of TRM for laboratory testing. ARM is that remanence acquired when a sample is subjected to a decreasing alternating magnetic field in the presence of a small steady magnetic field (see Table 1.2). The alternating field must initially be of sufficient strength to be able to saturate the magnetic grains in the sample. The alternating magnetic field then becomes the low-temperature analog of thermal activation. Weak-field ARM and TRM exhibit similar alternating field demagnetization characteristics so heating of the sample can be avoided (see §3.5.3).

2.3.6 Crystallization (or Chemical) Remanent Magnetization (CRM)

CRM results from the formation of a magnetic mineral at low temperatures (below the Curie point) in the presence of an applied field. This may take the form of single-phase (or grain-growth) CRM by nucleation and growth through the critical blocking diameter dB (or corresponding volume vB) as defined in §2.3.4. Alternatively, it may take the form of two-phase (or parent-daughter) CRM through the alteration of an existing magnetic phase. CRM is often referred to as chemical remanent magnetization but this is not always strictly correct. For example, the transformation of maghemite (yFe203) to hematite (aFe203) is one from the spinel to the rhombohedral structure that occurs with no chemical change, only a restacking of the lattice.

Unfortunately, it is not always easy to recognize CRM because its unblocking temperatures and coercivities overlap those of TRM (§2.3.5) and DRM (§2.3.7). Here, three major aspects of CRM that are significant in continental studies will be considered: CRM acquisition through single-phase or grain-growth at constant temperature, CRM as it applies to redbeds, and CRM caused by the alteration of carbonates. The problem of CRM acquired through the alteration of titanomagnetites in oceanic basalts will be considered in the discussion of oceanic paleomagnetism in chapter 5.

Single-Phase or Grain-Growth CRM

Suppose a small grain is superparamagnetic at room temperature and therefore has no remanence since the thermal fluctuations are too great and the grain is magnetically unstable (§2.3.4). When such a grain nucleates and grows in a weak magnetic field, it may grow to a sufficient size to pass through the critical blocking volume vB, when the relaxation time of the grain increases very rapidly. The equilibrium magnetization then becomes "frozen in" and, as the grain grows further, subsequent changes in the field direction have no effect on the direction of magnetization. The process is analogous to the acquisition of TRM.

From (2.3.16), as a superparamagnetic grain grows at temperature T, its magnetization becomes stabilized at some volume vB when v,(2-3.26)

where x = 100 s and/= 109 s"1. Hematite grains, for which K - 1.2 x 104 Jm~3, are of particular interest here. Assuming the grains are spheres, then at a temperature T = 300 K (27°C), the critical blocking diameter dB « 0.1 |im. Experimental determinations suggest a slightly different value of dB « 0.2-0.3 (im (Dunlop and Özdemir, 1997). Note that when the grains have grown from a diameter of 0.10 to 0.13 (xm, the relaxation time has already increased to 109 years! Again, this is one of the basic appeals of paleomagnetism; that original CRM by grain growth can be stable over the geological time scale.

Stacey (1963) considered the CRM acquisition of SD grains, whose anisotropies are aligned in the direction of the applied field B in which they are growing at temperature T. The magnetization is given by

In small fields (0-0.1 mT), a random assemblage of such grains produces a CRM given by

Substituting values for vB from (2.3.26) for hematite gives

This suggests that the CRM of noninteracting grains of hematite is independent of the size to which the grains have grown, providing they exceed the critical volume vB and that they remain SD.

The magnetic characteristics of CRM are similar to those of TRM. Experimental work confirms that CRM magnetization is proportional to the applied field as predicted from theory. In general, the magnitude of CRM is less than that of TRM, but this depends on several factors, as studied in detail by McClelland (1996).

CRM in Redbeds

Large black crystalline hematite grains (specularite) of detrital origin are found in both red and non-red sediments. The fine-grained hematite pigment, which gives redbeds their distinctive color, may be derived from the alteration of an existing magnetic phase in three possible ways - by the oxidation of magnetite to hematite, the inversion of maghemite to hematite, or the dehydration of goethite to hematite - according to the reactions

4Fe304 + 02 => 6aFe203 YFe203 => aFe203 2aFeOOH => aFe203 + H20

in the presence of an applied field, each of the reactions results in a two-phase or daughter-parent CRM. All the reactions are slow at room temperature, but accelerate with mild heating such as during burial in a sedimentary sequence.

In all cases the lattices of the parent and daughter phases are incompatible. Therefore, a growth CRM, controlled by the applied field, would be expected to accompany each reaction. However, the growing daughter phase may also be influenced by its magnetic parent phase due to magnetostatic or exchange coupling of varying degree. In fact most experimental studies, with minor exceptions, suggest that grain-growth CRM is indeed essentially controlled by the applied field. In the case of the goethite dehydration process, all traces of goethite would have disappeared before the resulting hematite grains have grown to the critical SD size so that all memory of any previous magnetization in the goethite is lost. With continued growth therefore, the hematite pigment derived in this way acquires a true grain-growth CRM.

From (2.3.29), it was seen that the magnetization of grain-growth CRM in hematite is independent of the size to which the grains have grown, provided it exceeds the critical size. Thus, the CRM will not necessarily be related to the amount of hematite present, even if all the grains are above the critical size. The maximum CRM for a given amount of hematite will be observed when all the grains are just above the critical size. A rock specimen typically containing 1% of hematite by volume produced by grain growth in the Earth's magnetic field (0.05 mT) should thus be capable of acquiring a maximum value Mcrm ~ 0.1 Am"1. This is commonly the upper limit of magnetizations (10"3-10"' Am"1) observed in redbeds. This is stronger than the typical detrital or post-depositional magnetization of sediments (DRM or PDRM - see §2.3.7). The problem in paleomagnetic studies of redbeds is to determine how much of the magnetization is CRM carried by the hematite pigment and to discover how long after the rock formed that the pigment developed. This is discussed further in §3.4.1.

CRM in Altered Carbonates

Extensive investigations of North American Paleozoic sedimentary rocks have established that both carbonates and redbeds were remagnetized during the Late Carboniferous. Useful reviews of this topic are given by McCabe and Elmore (1989) and Elmore and McCabe (1991). Such remagnetization is widespread on both sides of the Atlantic, not only in the Appalachians and Hercynian belts but also in stable platform areas. Particularly interesting from the paleomagnetic viewpoint is the low-temperature CRM carried by authigenic or diagenetically

Fig. 2.18. Scanning electron microscope images of small magnetite grains in thin sections of carbonates from New York State, (a) Spheroidal aggregates of mostly magnetite but with occasional bright cores (arrow) where relict pyrite is found. The interpretation is that magnetite is replacing the pyrite. (b-d) Similar spheroidal aggregates in voids or cracks. Note the octahedral crystal shape. The matrix is calcite. The scale is indicated by the bars. From Suk et al. (1990), reproduced with permission from Nature.

Fig. 2.18. Scanning electron microscope images of small magnetite grains in thin sections of carbonates from New York State, (a) Spheroidal aggregates of mostly magnetite but with occasional bright cores (arrow) where relict pyrite is found. The interpretation is that magnetite is replacing the pyrite. (b-d) Similar spheroidal aggregates in voids or cracks. Note the octahedral crystal shape. The matrix is calcite. The scale is indicated by the bars. From Suk et al. (1990), reproduced with permission from Nature.

altered magnetites in undeformed and only mildly heated platform carbonates. This is thought to have been caused by the migration of chemically active and perhaps hot fluids during plate convergence and subsequent mountain building.

Not all platform carbonates are remagnetized and the problem has been to distinguish between the remagnetized and the unremagnetized. Originally the mere presence of magnetite in a sedimentary rock was usually interpreted as evidence of detrital origin and early acquisition of the remanence. Because of the low concentration of magnetite in remagnetized carbonates (typically about 10 ppm), distinct observation and characterization of the magnetic carriers has been difficult. However, magnetic extracts from remagnetized carbonates have been studied by scanning electron microscopy and show spheroidal and botryoidal morphologies that are consistent with a diagenetic origin (Fig. 2.18). In addition, the magnetic properties of remagnetized and unremagnetized carbonates are distinctly different (Channell and McCabe, 1994). The remagnetized carbonates contain fine-grained high-coercivity SD magnetite with a high proportion of SP magnetite. Magnetite in unremagnetized carbonates appears to be concentrated in PSD grains. These differences are explained in more detail in §3.5.4.

A direct connection between CRM acquisition and alteration by fluids has also been established around mineralized veins. Several carbonate units that are hydrocarbon bearing also contain CRM carried by authigenic magnetite. It seems that the chemical conditions created by the hydrocarbons caused the precipitation of the authigenic magnetite and the acquisition of the associated CRM. This could have significance for oil exploration.

2.3.7 Detrital and Post-Depositional Remanent Magnetization

The process of alignment of magnetic particles by an applied magnetic field as they fall through water and then settle on the water sediment interface at the bottom is termed detrital (or depositional) remanent magnetization (DRM). However, DRM is not finally set in orientation until the sediment has been compacted by the weight of later deposits and the water has been excluded in the consolidation process. After deposition, wet unconsolidated sediments are often disturbed through bioturbation and slumping so that DRM should lose most of its directional coherence. Irving and Major (1964) proposed that magnetic particles would still remain free to rotate in the water-filled interstitial holes of a water saturated sediment until compaction and reduction of the water content eventually restricted their movement. This process is termed post-depositional remanent magnetization (PDRM).

Detrital Remanent Magnetization

Suppose a spherical or near-spherical grain of diameter d (volume nd 3/6) and remanence M is falling through water with viscosity r| («10"3 Pa s at room temperature) in the presence of an applied field B. There is a couple L, turning the magnetic moment of the grain toward the field direction (§2.1.1, Fig. 2.1), given by

where 9 is the angle between M and B. The motion of such grains is likely to be highly damped so that inertia can be neglected. Under these conditions the couple can be equated to the viscous drag on the rotation of the grain so that

If the angle 0 is given by 0O at time t = 0, then for small angles

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