theory of crm acquired by grain growth, and its implications for

Geophys. J. Int. (1996) 126,271-280

Theory of CRM acquired by grain growth, and its implications for TRM discrimination and palaeointensity determination in igneous rocks

Elizabeth McClelland Department of Earth Sciences, University ofoxford, Parks Road, Oxford, OX1 3PR, UK

Accepted 1996 March 22. Received 1996 March 14; in original form 1995 August 14

SUMMARY The behaviour of grain-growth CRM in SD grains can be predicted using Neel's (1949) theory for the acquisition of TRM. This theoretical approach suggests that the ratio of CRM to TRM will not be constant throughout the grain-size range for either magnetite or haematite. Hence the blocking-temperature spectra for CRM and TRM in an identical set of magnetic grains will be different, and grain-growth CRM can be identified by non-linear palaeointensity plots over certain temperature intervals. It is shown that on thermal demagnetization both CRM and TRM should unblock at the same temperature, Tb, but their magnitudes will be different, because the net fractional alignment for CRM is controlled by the blocking volume and the reaction temperature, while that for TRM is controlled by the final volume and the blocking temperature. CRM/TRM ratios for magnetite and haematite are calculated using the standard relaxation-time equation, and experimental values of spontaneous magnetization as a function of temperature. Calculation of CRM/TRM ratios for actual examples of spectra suggest that grain-growth CRM in both magnetite and haematite can be distinguished from TRM on the basis of a Thellier-Thellier palaeointensity experiment for data that span a temperature interval from room temperature up to at least 450 "C, or for smaller, high-temperature intervals. However, grain-growth CRM cannot be distinguished from TRM if pTRM checks fail below about 400°C, as the CRM/TRM ratio is close to 1 below this temperature. Single-domain CRM grown over laboratory time-scales should always be smaller than a laboratory TRM according to this model, while natural CRM formed over much longer times than available in the laboratory may be as much as twice as strong as TRM. Multidomain grain-growth CRM may always be larger than TRM, due to the difficulty of nucleating domain walls during low-temperature crystal growth.

Key words: grain-growth CRM; palaeointensity studies, TRM discrimination.

INTRODUCTION

Chemical remanent magnetization (CRM) is acquired when a new magnetic mineral is formed in the presence of a magnetic field at a, temperature below the critical blocking temperature of that grain. There are a number of processes by which the new mineral can form. Iron oxides can be exsolved from non- magnetic iron-rich silicates, and the magnetism will be acquired as the growing grain passes through a critical grain size (Haigh 1958); this is grain-growth CRM. A pre-existing magnetic mineral (e.g. titanomagnetite) can exsolve into lamellae of compositions closer to magnetite and ilmenite. A pre-existing magnetic mineral can transform into another magnetic mineral by a chemical reaction or phase change (e.g. maghemite

transforms to haematite at moderate temperatures). All of these types of processes occur in nature, and a significant proportion of natural remanence found in rocks is believed to be due to the secondary magnetization process of CRM, rather than a primary process, such as detrital remanent magnetization (DRM) in sedimentary rocks or thermoremanent magnetization (TRM) in igneous rocks.

The study of the ancient magnetism of rocks has been found to be a powerful tool in many branches of Earth Sciences. Many applications of palaeomagnetism require that the primary magnetization be identified, as this is usually the only component of remanence that can be precisely dated. Often remanence can be dated only relative to some subsequent geological event, and this leads to very large uncertainties in

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212 E. McClelland

age. In general, palaeomagnetists look for field tests to demonstrate that remanence pre- or post-dates folding, dyke intrusion or conglomerate formation, for example. Positive field tests only mean that remanence pre-dates a later event, not that the remanence is primary. Where several components of magnetization coexist, overlap of blocking temperatures of components may indicate partial CRM overprinting (McClelland Brown 1982), but identification of CRM from directional information for single-component remanence is impossible. A laboratory- based test that discriminates between secondary CRM and primary DRM or TRM would therefore be of great value.

This paper concentrates on the properties of grain-growth CRM. The purpose of this paper is to predict theoretically the CRM/TRM ratio throughout the blocking-temperature spectrum for an assemblage of single-domain (SD) grains that initially formed by exsolution from a non-magnetic host, or by nucleation during cementation in sedimentary diagenesis. This will be used to determine under what conditions linear relationships between NRM and laboratory TRM in standard palaeointensity experiments could arise from the NRM actually being a grain-growth CRM, and when linear relationships might truly indicate that the NRM is a TRM, which is the underlying assumption of palaeointensity methodology.

THEORY OF SINGLE-DOMAIN CRM A N D TRM ACQUISITION

The simplest type of CRM acquisition that can be considered is the nucleation and growth of independent single-domain grains in a non-magnetic matrix, at a reaction temperature T,. Haigh (1958) suggested that the acquisition of CRM by grain growth is controlled by thermally activated processes, and can be treated following Nkel’s ( 1949) approach for the acquisition of TRM. In this model, grains grow over a finite time span, and early during the growth history the grains are small and the barriers to a change in magnetization are low compared to the available thermal energy. The assemblage is then in equilibrium as the magnetization is able to change in response to any change in the applied field, i.e. the blocking temperature of the grains is less than T, and the system is superpara- magnetic. As an individual grain grows, its blocking temperature increases, and when this reaches a value equivalent to the reaction temperature T, (depending on the time-scale of the reaction), no further change in direction of magnetization is possible and the remanence is blocked. This occurs at the blocking volume, vb. In a natural system, not all grains will reach the blocking volume at the same time, and at the end of the period of grain growth a range of grain sizes, and hence a range of blocking temperatures, will be present.

Stokking & Tauxe (1990) and Pick & Tauxe (1991) have experimentally studied CRM formed during grain growth of haematite and magnetite, respectively. The results of these two studies give general support to the simple theory of grain- growth CRM, except that they obtained clear evidence that the magnetic field in which the grains grew had some control over the orientation of the easy axes of the new grains in fields between 0.001 and 7.5 mT. This reduces the intensity of CRM in magnetite below the expected values for fields greater than 1 mT. In both of these studies, the iron oxides grew freely in a solution within a stack of microfilter papers. It is not clear if the external field will have such a strong control on the crystallographic axes of iron oxides exsolved within a solid

non-magnetic matrix. A number of studies (Pucher 1969; Stokking & Tauxe 1990) have shown experimentally that the intensity of CRM acquired on grain growth to single-domain (SD) or pseudo-single-domain (PSD) sizes is significantly less than the intensity of a TRM acquired in the same material.

Various authors (Day 1977; Walton 1980 Enkin & Dunlop 1988) have suggested that Neel’s theory is unable to predict actual kinetic relationships of SD magnetite. However, experimental work by Sugiura (1980), Dunlop & Ozdemir (1993), and Smith & Verosub (1996) supports the use of NCel’s kinetic relationships between blocking temperatures over different time-scales, and Neel’s approach is followed in this paper.

Let us consider a randomly oriented assemblage of identical uniaxial grains growing in size with time. We can define a factor called the ‘net fractional alignment’ that describes the efficiency of the alignment of individual grain magnetization with the external field. If all grains had a magnetization exactly parallel to the external field then the net fractional alignment (NFA) would be 100 per cent, and if they had truly random magnetizations that cancelled out exactly then the net fractional alignment would be zero. For uniaxial anisotropy, each grain may be magnetized in only one of two anti-parallel orientations, along the easy axis. For a randomly oriented assemblage, the net fractional alignment will be much less than 100 per cent. The NFA will decrease at higher temperatures as the thermal energy increases and the activation energy required to re-orient the magnetic moment of a grain decreases. Nee1 (1949, 1955) showed that the net fractional alignment is given by the hyperbolic tangent of [vHJ, (T)] divided by thermal energy (kT). Here v is the grain volume, H is the external field, J , (T ) is the spontaneous magnetization at temperature T, and k is Boltzmann’s constant.

The magnetization of the magnetic system will be able to follow any change in the external field while all the grains are so small that the ambient temperature, T,, is greater than the blocking temperature, Tb, of the grains; the system is thus in equilibrium. The equilibrium magnetization at temperature T, is

Meq( T,) = v J,( T,) tanh [ v Hk4(T,”’]

For a randomly oriented assemblage (Stacey & Banerjee 1974) this approximates to

As the grains grow through the blocking volume, the activation energy exceeds the available thermal energy at T,, so no further change in net fractional alignment can occur. The blocked CRM remanence then grows proportionally to subsequent volume growth.

(3)

If the final grain volume is v,,, > vb, and the system cools to room temperature, To, then the final CRM will be

(4)

If this newly formed assemblage of grains then acquires a TRM, grains with volume v,,, will have blocking temperatures

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Theory of grain-growth CRM 273

greater than the reaction temperature, so &> T,. The TRM acquired by the system with grain volumes of urnax, after cooling to room temperature, will be

On thermal demagnetization, both of these remanences will unblock at the same temperature T,,, but their magnitudes will be different, since the net fractional alignment for the CRM is controlled by the blocking volume and the reaction temperature, while that for the TRM is controlled by the final volume and the blocking temperature. We would expect grain-growth CRM to be carried by a range of grain sizes between lib and urnax, with blocking temperatures between T, and Tb. From the above equations, the CRM/TRM ratio for a particular grain size (urnax) is given by

The analysis in the following sections will show that the ratio of CRM to TRM will not be constant throughout the grain- size range, and hence the blocking-temperature spectra for CRM and TRM should be different.

A theoretical comparison between CRM and TRM intensities has already been presented by Stacey & Banerjee (1974) . Following the same premises as Haigh (1958), as 1 have done here, they concluded that

(7)

and they quote a 'typical numerical value' of this ratio as 0.4. Eq. (7) simplifies to CRM/TRM =Hc(Tb)/Hc(T) using eq. (10). For magnetite, Hc(Th) is proportional to Js(Tb), so CRM/ TRM zJ,(Th)/J,(T). There is a major difference between the analysis put forward in this paper and that of Stacey & Banerjee. This earlier work simplified the relationship between CRM and TRM by assuming that the characteristic times (relaxation times, z) for CRM and TRM are comparable. The classic relaxation-time equation of Nee1 (1949),

l /z=C exp [ - ( u H c ( T ) J s V ) ) / k T I , (8) relates relaxation time, z, to activation energy, E ( T ) = (uH,(T)J,(T)), and available thermal energy (kT) . C is a frequency factor equal to about lo1' Hz. Stacey & Bannerjee's analysis therefore assumed that [u,H,(T,)J,(T,)]/kTa = [u,,,Hc( T,,)J,( &)Ilk%. In reality, grains are likely to grow considerably above their blocking volume and a spectrum of grain sizes will be created. For a particular grain size, the CRM may have blocked at a much lower temperature and smaller grain size than TRM in the same grains. Hence this simplification is not valid.

CALCULATION OF CRMlTRM RATIOS

In order to calculate CRM/TRM ratios, it is necessary first to calculate blocking volumes, blocking temperatures and maxi- mum volumes reached, and to know the variation of spontaneous magnetization with temperature. Blocking temperatures and volumes are dependent on the time available for blocking to occur (Pullaiah et al. 1975; Dodson & McClelland Brown 1980), so the time-scales of grain growth and TRM acquisition also have to be taken into account.

Experimental values of J,(T) have been taken from the work of Flanders & Scheule (1964) for haematite, and the work of Ozdemir & O'Reilly (personal communication) for magnetite; the values of j , (T) (i.e. J,(T) normalized to J,(O"C)) are tabulated in Table 1.

'Fast' CRM grown at 100 "C for 1000 s

The first CRM that will be considered is one grown at 100 "C over the same time-scale (1000 s) as subsequent laboratory TRM acquisition. The blocking volume is defined as the volume at which the blocking temperature over the time-scale of crystal growth is equal to the temperature at which the crystals are growing (i.e. 100°C in this case). The blocking volume can be calculated from the standard relaxation time equation of NCel (1949) (eq. 8). Dunlop (1973) showed that, given an exposure to an external field for time t,, all relaxation times up to 1.78 t, are activated. The activation energy for reorienting the magnetization at a particular temperature is therefore dependent on the temperature and the time-scale, and is not dependent on the mineralogy. It is the grain volume

Table 1. Parameters used to calculate the ratio of CRM to TRM.

Mawmite: fast-grown CRM at I W C over Id sec 100 0.944 0.783 1.0 1.0 1.0 1.0 200 300 400 505 515 525 535 545 555

0.868 0.774 0.646 0.442 0.404 0.365 0.318 0.258 0.190

1.080 1.70 2.84 7.05 9.04 1 1.23 14.97 23.03 43.02

0.725 1.087 0.460 1.219 0.275 1.461 0.111 2.135 0,0866 2.336 0.0697 2.586 0.0523 2.968 0.0340 3.658 0.0182 4.968

1.268 1.536 1.804 2.085 2.112 2.139 2.166 2.193 2.220

Marmelite: slow-grown CRM at IOOOC over I @ yrs 250 0.868 1.30 1.0 1.087 1.402 300 0.774 1.70 0.773 1.219 1.536 400 0.646 2.84 0.462 1.461 1.804 505 0.442 7.05 0.186 2.130 2.080 515 0.404 9.04 0.145 2.336 2.112 525 0.365 11.22 0.117 2.586 2.139 535 0.318 14.96 0.088 2.968 2.166 545 0.258 23.01 0.057 3.658 2.193 555 0.190 42.96 0.0306 4.968 2.220

0.999 0.862 0.726 0.492 0.427 0.385 0.336 0.273 0.200

1.523 1.447 1.217 0.824 0.715 0.647 0.566 0.457 0.337

Mametite: CRM at 3 W C over 1 6 sec (modelling Puchers experiments) 300 0.774 1.70 350 0.712 2.23 1.0 1.044 1.087 1.134 400 0.646 2.84 0.786 1.151 1.174 1.062 450 0.565 4.24 0.526 1.317 1.261 0.873 480 0.500 5.64 0.396 1.488 1.314 0.774 530 0.341 12.93 0.172 2.182 1.403 0.526 555 0.190 42.96 0.0519 3.916 1.445 0.293 565 0.080 245.27 0.0091 9.300 1.462 0.123

Hemarire: fmt-gi loo 1.0 200 1.0 300 0.987 400 0.966 480 0.938 520 0.906 560 0.851 600 0.783 620 0.724 640 0.616 660 0.368

rown CRM at I W C ovc 3.938 1.0 4.994 0.788 6.807 0.578 9,702 0.406 14.14 0.278 20.36 0.193 34.43 0.114 50.36 0.0782 70.47 0.0558 137.50 0.0286 1103.1 0.00357

ir ~d 1 .O 1 .O 1.013 1.035 1.066 1.104 1.175 1.277 1.381 1.623 2.717

see 1 .o 1.268 1.536 1.804 2.018 2.126 2.233 2.340 2.394 2.447 2.501

1 .o 0.999 0.899 0.758 0.597 0.453 0.299 0.234 0.184 0.113 0.0242

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274 E. McCEelland

that corresponds to this activation energy that is material- dependent. These factors can be used to calculate the activation energy for a grain that blocks at 100°C for a growth time of 1000 s; this is equal to 0.980eV. The activation energy, E, is given by

E = u K , (9) where v is grain volume and K is the anisotropy constant relevant to the process that controls the barriers to change of magnetization. For uniaxial anisotropy, the coercivity, H,, is related to the relevant anisotropy constant by the relationship

K = 1/2 p, H , J,. (10) CRM/TRM ratios for magnetite and haematite will be dis- cussed in the next sections.

Magnetite

For magnetite, the potential barriers to change of magnetization arise from magnetocrystalline anisotropy in cubic crystals, but from shape anisotropy for shapes that deviate only slightly from cubic. Shape anisotropy is much stronger than magnetocrystalline anisotropy and has uniaxial symmetry, so will be considered here.

For a prolate spheroid the activation energy is 1/2 [v (N,-N,)J,'(T)], where N , and Nb are demagnetizing factors along equatorial and polar axes (after Stacey & Banerjee 1974). For particle elongation of 1 : 1.5, Nb-N, = 1.95. Using these relationships and a value of 4.8 x lo5 A m-l for J , (0) and a value of j , (T) at 100°C of 0.944 (see Table I), the blocking volume is calculated to be 0.783 x pm3. For an elongate particle with a long axis of length 2a and a short axis b=2/3 a, the volume v=4/3nabz. A blocking volume of 0.783 x pm3 translates to a grain length of 0.032 pm.

In this imaginary assemblage of magnetite grains growing at 100 "C over a time-scale of 1000 s, many grains will grow to volumes considerably greater than the blocking volume. The range of grain sizes that contribute to CRM is vb < u < u,,,. The CRM at room temperature is given by eq. (4) and equals uJ,(O) x [net fractional alignment at blocking]. Grain growth beyond the blocking volume will not change the net fractional alignment (NFA), so the CRM will simply increase proportionally to v. It is worth noting that the NFA is not time- dependent. The blocking temperature of a particular volume is changed by the time-scale, not the alignment at a particular temperature. This means that the blocking volume will be different at different time-scales.

Since the time-scale of the CRM growth in this example has been chosen to be the same as that for both laboratory thermal demagnetization and laboratory acquisition of TRM, the unblocking temperature of the smallest grain size that contributes to the CRM (vb) will be the same as the acquisition temperature, i.e: 100 "C. Smaller grains will not have acquired a CRM, but will have a partial thermoremanence (pTRM) acquired on cooling from 100°C in a field. The values of various parameters (blocking temperature/acquisition temperature;j,( Ta)/js(Tb); Ub/q,,,,) used to calculate the CRM/TRM ratio, together with that ratio, are tabulated at various unblocking temperatures in Table 1. The CRM/TRM ratio decreases from 1 at 100 "C to zero at the Curie temperature. The change in CRM/TRM ratio is dominated by the effect of z)b/V,,,.

In order to calculate the blocking relationships of CRM and

TRM, a number of assumptions have to be made about the equations that control blocking, activation energy and the demagnetizing factor. All of these assumptions apply equally to both CRM and TRM, and so the ratio of CRM to TRM should not be greatly affected by changes in the chosen values of these parameters.

Haematite

For haematite, magnetocrystalline or magnetoelastic anisotropy dominates over shape anisotropy, and has uniaxial symmetry. Haematite has a coercivity that depends on magnetoelastic effects whose temperature dependence is not well known. Experimental variation of H , with temperature can be fitted by H,(T) ccJS8 ( T ) below 550°C (Dunlop 1971) but above 550°C a power law of H J T ) oc J?(T) is a better fit to the experimental data of Flanders & Scheule (1964). Using eq. (9), the activation energy for haematite can be described by E = 1/2vAJ: ( T ) below 500 "C, and E = 1/2vBJ;(T) above 550°C, where A and B are constants. It is useful to normalize by defining E, as the activation energy at 0°C and using j,(T)= J,(T)/J,(O), so E(T)=E, j;(T) below S O T , and ~ ( 7 ) = E,B/A~:( T ) above 550 "C. The activation energy must vary continuously over all temperatures, although the power law HcocJ," is discontinuous. For E to be continuous, &As9 (550 "C) = E,B/Aj: (550 "C), so B/A = j: (550 "C). Data from Flanders & Scheule (1964) is used in this paper for the variation of J , with temperature, and is given in Table 1. From these data, j , = 0.866 at 550 "C, and jS5 (550 "C) = 0.487 = B/A. These relationships have been used to calculate grain volumes at varying blocking temperatures in a similar manner to that used above for magnetite.

'Slow' CRM grown at 100 "C for 30 000 years

Magnetite

Eq. (7) can be used to calculate the activation energy, blocking volume and equivalent laboratory unblocking temperature for a time-scale of CRM growth at 100 "C of lo1' s (30 000 years). The activation energy in this situation is 1.645eV and the blocking volume is 1.314 x pm3 (equivalent to a grain length of 0.038 km). During laboratory thermal demagnetization, the smallest grain that contributes to the CRM will unblock at 235 "C. Unblocking temperatures less than this value will carry a TRM acquired on cooling from the reaction temperature. It is evident that these predictions suggest that the blocking volume is larger for slower growth. Superficially, this appears to be paradoxical, but although the slowly growing crystals attain the required blocking volume for fast growth considerably before the end of the period t,, the time-scale is long enough for a grain with the 'fast' blocking volume to remain unblocked.

Once again, the values of the relevant parameters and the calculated CRM/TRM ratio, are tabulated in Table 1. The CRM/TRM ratio decreases from 1.523 at 250°C to zero at the Curie temperature. The slowly acquired CRM is considerably enhanced compared to TRM in the low-blocking- temperature fractions; this is analogous to the enhancement of intensity observed by increasing the cooling time-scale for TRM (Dodson & McClelland Brown 1980; Halgedahl, Day & Fuller 1980 McClelland Brown 1984). Below the minimum

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unblocking temperature of the CRM (235 "C) the initial remanence is a slow-cooled TRM, and its ratio to a laboratory TRM has been determined following the calculations of Dodson & McClelland Brown (1980).

COMPARISON O F THEORY WITH EXPERIMENTAL OBSERVATIONS

Experimental comparison of unblocking-temperature spectra of CRM and TRM was carried out by Pucher (1969) for magnetite grown by the hydrothermal high-pressure method. Pure magnetite grains between 0.2 pm and 3 pm were produced by holding a starting mixture of haematite and iron in a gold capsule at 2000 bars at 300°C for 24 hr. The material was then dried in a vacuum at 50°C for at least 12 hr. Runs were repeated with different external magnetic field strengths (0.03, 0.7 and 7 mT). The resulting CRMs were then measured, with the sample still inside the gold capsule to ensure that the crystals did not move. Stepwise thermal demagnetization of the CRM was then followed by acquisition of a full TRM in the same strength field as that used to induce the CRM. Finally, this TRM was thermally demagnetized and the demagnetization curves of CRM and TRM were compared. Stabilities of CRM and TRM to thermal demagnetization were found to be identical for fields of 0.7 and 7 mT. For weak-field (0.03 mT) CRM and TRM, CRM was found initially to demagnetize faster than TRM. Values for CRM and TRM at thermal demagnetization steps were taken from Fig. 5 of Pucher (1969) for comparison with the theoretical predictions of this paper.

In Pucher's experiments, a laboratory CRM was grown in a field of 0.03 mT at 300 "C for lo5 s. The activation energy is now calculated to be 3.20eV, the blocking volume to be 2.232 x lo-* pm3 and the laboratory unblocking temperature of the CRM blocking volume is 350°C. The values of CRM/TRM ratios are tabulated in Table 2, together with the amounts of TRM unblocked in different temperature intervals taken from Fig. 5 of Pucher. A CRM unblocking curve can be predicted from the theory using the TRM unblocking data, and this predicted curve is compared with the actual curve in Fig. l(a). The real and predicted CRM data are normalized at 300 "C, as this is the formation temperature, and all remanence below this should be TRM. The relative shapes of the real and predicted curves fit very well, given the rather poor quality of the initial measurements in Pucher (1969). The only problem point is the initial CRM data point, which is some 33 per cent greater than predicted at room temperature. This enhanced low-blocking-temperature fraction may be due to a viscous remanence (VRM) acquired during the drying process that took place at 50°C for at least a further 12 hr, or there may

Table 2. Prediction of CRM intensities from the experimental data of Pucher (1969) . Temperature Normalised interval TRM CRWRM Predicted Actual CRM

TRM (TI-TZ) ratio (Tl-TZ) cumulative (OC) CRM

20 1 .o 0.010 1.134 0.683 0.166 100 0.990 0.012 1.134 0.672 200 0.978 0.062 1.134 0.658 0.126 300 0.916 0.169 1.110 0.588 0.107 400 0.747 0.103 0.960 0.400 0.063 450 0.644 0.094 0.825 0.301 480 0.550 0.155 0.650 0.223 0.043 530 0.395 0.206 0.410 0.122 0.028 555 0.189 0.181 0.210 0.038 565 0.008 0.008 0.060 O.Oo0 0.001

be some effect of annealing of soft components during the initial thermal demagnetization.

However, the theory of grain-growth CRM presented in this paper is unable to predict the significant enhancement of TRM relative to CRM of 6 : l observed by Pucher. The absolute values of CRM predicted in Table2 accumulate to a total CRM intensity of about 70 per cent of the total TRM value (Fig. lb). There are a number of problems with Pucher's experiments that mean that the results probably cannot be used to test the theory set out in this paper. First, no tests for thermal stability of the material were carried out in Pucher's study. It is therefore possible that either initial defects in the crystals were annealed out during production of the TRM, hence the TRM state was not equivalent to the CRM state, or significant alteration of grain size took place during the initial thermal demagnetization of the CRM and the subsequent demagnetization of TRM. Second, Pucher's magnetite grains were not dispersed in any non-magnetic matrix, and the closely packed grains must have interacted magnetically. Third, the observed grain-size range of 0.2-3 pm lies in the pseudo-single- domain, not the SD, range, so a considerable number of Pucher's magnetite grains may contain domain walls. The theory is not valid for grains that contain one or more domains, and so the agreement between the shape of the predicted CRM unblocking-temperature spectrum and the actual spectrum may therefore be fortuitous.

Stokking & Tauxe (1990) synthesized haematite in various applied magnetic fields and demonstrated that CRM intensity was linearly related to applied field intensity up to 7.5 mT (the strongest field available). They carried out a simplified stepwise palaeointensity experiment by demagnetizing the initial CRM to 150°C and then inducing a pTRM by heating to 150°C in a field perpendicular to the CRM direction. The demagnetization and remagnetization were repeated, incrementally increasing the temperature by 50 "C at each step. On heating, the material was prone to alteration by aggregation of smaller grains into large, composite grains. Stokking & Tauxe assumed that they could detect alteration of the haematite by departure from a linear relationship between the CRM demagnetized and the pTRM added. They found a reasonably consistent ratio of CRM to TRM of 0.15, varying from 0.02-0.25, when they only used data from temperature intervals that gave a linear relationship between CRM removed and pTRM gained. Their paper shows data from only one sample with linearity up to 500 "C and I use their data to compare the actual spectra with the unblocking-temperature spectra predicted by the development of Nkel's theory. Actual experimental values of CRM removed and TRM added are tabulated in Table 3, together with the predicted TRM values. Again the grain- growth CRM theory does not predict CRM:TRM ratios of 1 : 6.6, as the differences between CRM and TRM intensity are expected to occur in high-blocking-temperature intervals only. When the predicted intensity of TRM is normalized to the actual TRM value by dividing by the CRM/TRM ratio of 0.02 found for this sample by Stokking & Tauxe, the predicted and the experimental slope of the CRM/TRM plot are the same up to about 400°C (Fig. 2). Note that forcing the initial CRM/TRM ratio to 0.02 does not force the slopes to match, so this is a fair test of the abilities of the theory presented here to predict relative intensities in different blocking-temperature intervals. Above 400 "C significant curvature is predicted but not observed, although only two data points fall in this interval.

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276 E. McClelland

0 100 200 300 400 500 600

TEMPERATURE (C)

1.2

h

1.0

! 0.8

3 .- .8 3, 0.6 > 4 2 v

0.4 G v)

0.2 &

0.0

~~ ~

U INITIAL GRAIN-GROWTH CRM --)- TRM

0 L- l L

1 I I

0 100 200 300 400 500

TEMPERATURE (C)

0

Figure 1. Comparison of experimental data of Pucher (1969) on demagnetization curves of laboratory-grown CRM and TRM in the same magnetite samples, grown in 0.03 mT at 350°C, with the theoretical prediction from this paper. (a) TRM and predicted CRM values are normalized at 20°C. Pucher's measured CRM intensities are normalized to predicted the CRM value at 3OO0C, the temperature at which the initial CRM was grown. (b) All intensities are plotted at their correct values relative to the initial TRM value.

Table 3. Prediction of TRM intensities from the modified Thellier experiment of Stokking & Tauxe (1990). Temperature Actual TRM Actual CRM interval CRM C R m M predicted

(W (nAm2) (nAm2) (nAm2) (nAmz)

110 0.0 0.123 0.004 1 .o 0.0 150 0.467 0.119 0.018 0.999 0.004 200 0.575 0.101 0.006 0.999 0.022 250 1.294 0.095 0.002 0.958 0.028 300 1.438 0.093 0.007 0.899 0.030 350 1.689 0.086 -0.002 0.840 0.0378 40 2.157 0.088 0.040 0.758 0.0354 450 2.840 0.048 -0.001 0.640 0.0881 500 3.4515 0.049 0.500 0.0866

added , left (Tl-TZ) ratio (T1-T2) TRM

Progressive alteration in the material during the experiments of Stokking & Tauxe cannot be precluded, even though they found linearity in TRM/CRM plots over some temperature intervals. No pTRM checks were carried out, and there are a number of examples in the literature where linear NRM/TRM plots have been obtained, although alteration was clearly indicated by the failure of pTRM checks (e.g. Aitken et al. 1988; Tanaka & Kono 1991).

It is intriguing that the only two experimental comparisons between CRM and TRM in the literature describe TRM:CRM ratios of close to 6: 1. Stacey & Banerjee (1974) predicted TRM:CRM ratios of 2.5 : 1 from TRM/CRM =: J,( T,)/J,( Tb), and I predicted a ratio of 1.5 : 1. Using my data in Table 1 for

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-.. .

---- 0 data from Stokking and Tauxe A Dredicted TRM (normalised) - 0.12

0.04 1

0.02 1 -. *. -*. -. -.. --. --. -..

0 1 2 3 4 5

TRM added (nAm2)

Figure 2. Plot of CRM lost versus TRM gained in haematite, grown in an unknown field at 97 "C, from Stokking & Tauxe (1990), their Fig. 7(a). Predicted TRM values deviate from a straight-line relationship with CRM on this plot above 400°C (solid line). Stokking & Tauxe's linear fit to their data is shown by a dotted line. Temperatures are given beside data points.

fast-grown magnetite CRM formed at 100 "C, it is possible to obtain a mean value for J,(T,)/J,(T,) of 2.38 by simply averaging the data in the table. This assumes a blocking- temperature distribution biased towards higher temperatures, hence my numerical values are clearly very similar to those used by Stacey & Banerjee. However, it will be clear from my earlier analysis that calculating an average value is not useful, as the total ratio of TRM to CRM depends on the relative contributions from different blocking-temperature fractions. Also, my assessment of Stacey & Banerjee's work earlier in this paper has shown that they had not adequately accounted for grain growth beyond the blocking volume.

Although both published works describe TRM : CRM ratios of close to 6 : 1, the difference between predicted and actual CRM values is not so consistent. Pucher's work presents the ratio of total TRM to total CRM, which the theory in this paper predicts should be 1.43: 1 for the particular blocking- temperature spectrum. In this case the predicted value is about four times larger than the measured value. Stokking & Tauxe's data are relevant to the low-blocking-temperature range only, where CRM and TRM are predicted to be equal, so the disparity between theory and experiment here is 6.6 : 1. The relative intensities of CRM at different blocking temperature intervals in both experiments can be predicted by this development of NBel's theory, but the absolute values of CRM predicted are too large. There are three possibilities for explaining this inconsistency. The first is that there is some mysterious constant missing in the theory, and grain-growth CRM can be modelled by Neel's thermal-activation equations, and CRM is really significantly less intense than TRM by a variable factor. The second possibility is that CRM cannot be likened to TRM acquisition and the theory is fundamentally flawed. The third possibility is that the experimental data are flawed by chemical alteration of the starting material during the heating processes, and/or the non-single-domain nature of the experimental material. My instinct is that the third

possibility is the most likely and that the experimental data available to date do not provide an adequate test of the theory.

PREDICTED CRM FROM REAL

OF TRM

The CRM/TRM ratios in Table 1 can be used to predict a CRM demagnetization curve from a known TRM demagnetization curve. The example used here is from a sample (MRA2-6) used in a palaeointensity experiment by McClelland & Briden (1996). The remanence is carried by magnetite, and MD contributions to NRM have been removed by suitable AF demagnetization, so the TRM curve is believed to be SD in nature. The CRM values are calculated from the TRM demagnetization data assuming that the CRM grew at 100°C over lo3 s and 10'' s. A standard Thellier-Thellier palaeointensity plot can be produced from this data, plotting the predicted CRM remaining at each step of a hypothetical progressive remagnetization experiment against the pTRM added. This is depicted in Fig. 3 for both the slow-grown and the fast-grown CRM.

It is evident that a straight line could be fitted to the low- temperature part of the plot for both of these growth rates, i.e. from 0 to 350 "C. This is not a feature related to the particular blocking spectrum of this sample, but is seen for all types of Tb spectra. This means that the palaeointensity technique cannot discriminate between low-temperature grain-growth CRM and TRM in the low-blocking-temperature region. This is problematic as this is generally the part of a palaeointensity experiment that is believed to give the best results, as alteration often starts at 300-400°C, and data are discarded above the temperature at which pTRM checks fail. In fact, it is only the high-temperature regions above 400 "C where TRM and CRM have significantly different intensities and CRM can be identified by curvature in NRM/TRM plots.

UNBLOCKING-TEMPERATURE SPECTRA

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278 E. McClelland

loo0 0 MAGNEmE

Cl fast-grown CRh4 A slow-grown CRM

0 200 400 600 800 1000

TRMADDED

Figure 3. Magnetite: synthetic plot of CRM remaining versus TRM added for real TRM blocking data from sample MRA2-6 of McClelland & Briden (1996) The CRM values are those predicted from the TRM data using the theory in this paper. The dashed lines indicate the portion of the data that can be fitted by a straight line. The fast-grown CRM was assumed to have been grown at 100°C over lo3 s and the slow-grown CRM was assumed to have been grown at 100 "C over about 30 000 years. Treatment temperatures are indicated by the data points.

Finally, a synthetic pTRM acquisition curve has been created for an imaginary haematite-bearing sample, and the demagnetization data for a CRM acquired over laboratory time- scales has been calculated and the resulting Thellier-Thellier plot is displayed in Fig. 4. Again, the low-temperature part of the plot is linear below 400 "C.

the optimum number of domain walls. Once a grain grows large enough, a domain wall will nucleate a t the surface. However, a t the reaction temperature, movement of this domain wall into the interior of the grain will be strongly resisted by the large energy barriers, and a metastable ' S D grain (or a grain with few domains) will result. On acquisition of a TRM, the domain walls can reorganize and renucleate at

MULTIDOMAIN A N D ALTERATION CRM

- high temperatures, and the grain will have a significantly lower remanence than for the CRM state (O'Reilly 1984). Again, a

The acquisition of grain-growth C R M once grains grow above the SD/MD threshold has not been modelled because the CRM domain state is likely to be metastable with fewer than

difference in blocking-temperature spectra would be expected between T R M and CRM, but CRM should be more intense than TRM.

0 200 400 600 800 1000

TRMADDEQ

Figure4. Haematite: synthetic plot of CRM remaining versus TRM added for imaginary TRM blocking data. The CRM values are those predicted from the TRM data using the theory in this paper. The dashed line indicates the portion of the data that can be fitted by a straight line. The CRM was assumed to have been grown at 100 "C over lo3 s. Treatment temperatures are indicated by data points.

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Theory of grain-growth C R M 219

There is some experimental evidence that this phenomenon does actually occur. McClelland & Briden (1996) have moni- tored the growth of CRM in MD grains during a progressive Thellier-Thellier experiment. Their pTRM checks showed that new MD material was formed mostly between 200 and 420 "C, although some alteration occurs throughout the experiment. Some of this new material has blocking temperatures less than its formation temperature and carries a pTRM, and some has Tb greater than formation temperature and carries a CRM. On subsequent remagnetizations between 420 and 500 "C, the total intensity at successive remagnetization steps decreases, as the new CRM is replaced by a weaker pTRM.

In reality, in igneous rocks acquisition of new magnetization by pure grain growth in the absence of pre-existing magnetic phases will be limited to the exsolution of new magnetic material from non-magnetic iron silicates. In many cases, new CRM will be created by alteration of pre-existing magnetic material (for example the oxidation exsolution of titanomagnetite into magnetite-ilmenite intergrowths). There is no satisfactory theory available for alteration CRM, and blocking- temperature relationships with respect to TRM are unknown. This should be a fruitful field for experimental work.

DISCUSSION

Data from the two experimental studies that compare grain- growth CRM produced on laboratory time-scales with laboratory TRM (Pucher 1969; Stokking & Tauxe 1990) suggest that CRM is considerably less intense than TRM in the same material. Unfortunately, Pucher's magnetite grains were PSD and magnetically interacting, and neither study contains adequate checks for alteration of the synthetic material during heating; moreover, Stokking & Tauxe show that large amounts of haematite migrate to form aggregates on heating to high temperatures in their material. This means that there are no reliable experimental data available to test the theoretical predictions made in this paper adequately. However, the relative shape of the unblocking curve of CRM is satisfactorily predicted for both experimental studies. If alteration has occurred during heating in these studies then it is interesting that this relative shape is preserved. It is fairly common for linearity of NRM/TRM plots from Thellier experiments to occur, despite the existence of progressive alteration (determined from pTRM checks); this is another manifestation of preservation of the shape of the blocking-temperature spectrum of a remanence, even though that remanence is being progressively altered.

The single-domain CRM/TRM ratio is predicted to be controlled by the difference in time-scale of acquisition of CRM and TRM, and the blocking temperature of the grains formed. Grains with low blocking temperatures can have CRM intensities considerably enhanced compared to TRM intensities of the same grains if the CRM was acquired over a much longer time-scale than the TRM. This is a highly likely scenario for natural CRM being compared to a laboratory TRM.

Grains with high blocking temperatures should have significantly reduced CRM intensities compared to TRM; in the model presented in this paper, the CRM/TRM ratio goes to zero at the Curie temperature for all time-scales. This means that for material that is dominated by high-blocking- temperature grains, the total intensity will be dominated by the contribution from those high Tb grains, which will be

much stronger for TRM than CRM. The ratio of total CRM to total TRM is therefore predicted to vary, perhaps between 2 and 0.2 for SD magnetite, depending on growth rate and T b

spectra. Multidomain CRM may be more intense than SD CRM for the same amount of magnetic material.

The underlying assumption of the palaeointensity technique is that a linear relationship between NRM demagnetized and pTRM added during a Thellier-Thellier experiment is indica- tive of the NRM being a primary cooling TRM. The theory developed in this paper suggests that grain-growth CRM will also have a linear relationship between remanence removed and pTRM added, over low temperatures up to 350°C for both magnetite- and haematite-bearing samples. Observations of linear segments on NRM/TRM plots with successful pTRM checks, which give significant discrepancies within and between sites, have caused several authors (e.g. Tanaka & Kono 1991) to debate whether such variability could be caused by CRM. It may not be possible to identify grain-growth CRM by discrepancies in intensity determined from different samples, as the slope of the linear segment will depend on the time- scale of CRM growth, not the blocking-temperature spectrum of the new CRM-carrying material. This means that the slope would be expected to be consistent between samples. A conse- quence of these theoretical predictions is that linear slopes that extend to at least 450°C (with satisfactory pTRM checks) should be obtained from at least some samples within a suite of material subjected to Thellier-Thellier palaeointensity determination to ensure that the possibility of grain-growth CRM can be adequately tested.

It could be argued that use of Neel's kinetic relationships is not valid, and that more complex equations are required. The main conclusions of this paper would not be contradicted by the use of different kinetics. As long as the CRM is thermally activated, then both CRM and TRM will follow the same relationships. It is likely that the main difference in intensity between CRM and TRM in different blocking-temperature intervals will be controlled by the difference in blocking volume at which CRM alignment is frozen in, and the final volume to which the grain grows (this controls the blocking temperature of the grain on acquisition of TRM). Whatever the kinetic relationships controlling thermal activation, the low- temperature parts of the Tb spectrum of CRM and TRM are likely to be very similar, as the blocking volume and final volume will be similar over this range.

CONCLUSIONS

Single-domain TRM is predicted to be preferentially enhanced compared to CRM in larger grains since the net fractional alignment for the CRM is controlled by the blocking volume and the reaction temperature, while that for the TRM is controlled by the final volume and the blocking temperature. The difference between CRM and TRM carried by the same magnetic grains should vary with blocking temperature. Calculation of CRM/TRM ratios for actual examples of Tb

spectra suggests that grain-growth CRM in magnetite can be distinguished from TRM on the basis of a Thellier-Thellier palaeointensity experiment only if data span a temperature interval from room temperature up to at least 450 "C, or span a smaller, high-temperature window. However, CRM cannot be distinguished from TRM if pTRM checks fail below about 400 "C. This means that all efforts should be concentrated on

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280 E. McClelland

obtaining palaeointensity data from high-temperature intervals. McClelland & Briden (1996) demonstrate that failure of pTRM checks does not necessarily indicate that alteration of high-blocking-temperature material has occurred. They suggest an extension to the usual Thellier-Thellier experimental sequence that may allow information to be extracted from high-T, fractions, despite alteration, if the alteration product has only low blocking temperatures.

Experimental data by Pucher (1969) and Stokking & Tauxe (1990) on unblocking temperatures of grain-growth CRM and TRM in the same samples has been compared to the theory. Relative differences between CRM and TRM intensities in different blocking-temperature fractions follow theoretical predictions, but the total intensity of CRM in both studies is much less than the predicted value. Unfortunately, both studies are suspect as neither used adequate tests for magnetic alteration. The theory also predicts variable ratios of total CRM to total TRM, depending upon growth rate and Tb spectra of the material, Single-domain CRM grown over laboratory time- scales should always be smaller than a laboratory TRM, while natural CRM formed over much longer times than available in the laboratory may be as much as twice as strong as TRM. It is suggested that multidomain grain-growth CRM may be significantly larger than TRM, due to the difficulty of nucleating domain walls during low-temperature crystal growth.

ACKNOWLEDGMENTS

This work was carried out while E M was in receipt of a Royal Society University Research Fellowship. This is gratefully acknowledged.

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theory of crm acquired by grain growth, and its implications for

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