The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock

Physics of the Earth and Planetary Interiors, 16(1978) 215—222 © Elsevier Scientific Publishing Company, Amsterdam — Printed in The Netherlands

215

THE DEVELOPMENT OF MAGNETIC SUSCEPTIBILITY ANISOTROPY THROUGH CRYSTALLOGRAPHIC PREFERRED ORIENTATION IN A CALCITE ROCK * W.H. OWENS and E.H. RUTTER Department of Geological Sciences, University of Birmingham, Birmingham (Great Britain) Department of Geology, Imperial College, London SW7 (Great Britain) (Accepted for publication December 8, 1977) Owens, W.H. and Rutter, E.H., 1978. The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock. Phys. Earth Planet. Inter., 16: 215—222.

High-field torque-meter measurements ofdiamagnetic susceptibility anisotropy of a suite of samples ofCarrara marble, axially shortened by amounts up to 50% at (1.5—3.0) 108 Pa confining pressure and at 20—500°C(mainly 400°C),have been compared with optical measurements ofpreferred crystallographic orientation. A revised value for the susceptibility anisotropy of calcite has been obtained from studies of single crystals, and it has been shown to be almost independent of the state of intracrystalline plastic strain. From the measured anisotropy of calcite, quantitative comparison of optical and magnetic fabric measurements is possible. It is found that these measurements agree and the implications of the observed progressive development of fabric intensity with strain are discussed.

1. Introduction It is well known that over a wide temperature range, calcite aggregates can be deformed experimentally by intracrystalline gliding, provided that the mean pressure is sufficiently high to suppress cataclastic (dilatant) behaviour, and that this leads to the development of a pronounced pattern of crystallographic preferred orientation (Turner and Weiss, 1963). The preferred orientation can be studied by standard optical X-ray methods. Thea large former are, however, tediousor and the latter are to extent restricted to rocks of fine grain size. The work reported here was undertaken to investigate the possibility of using measurements of magnetic susceptibility anisotropy as a rapid, complementary technique for studying the development of preferred orientation in such rocks. Magnetic susceptibility anisotropy is widely held, *

Presented at the U.K. Geophysical Assembly, Edinburgh, April 12—15, 1977.

probably as a result ofits original association with palaeomagnetic studies, to be a property associated only with ferrimagnetic materials (e.g., Bhathal, 1971). Paramagnetic and diamagnetic minerals can, however, exhibit a susceptibility anisotropy, of crystalline ongin (Lonsdale, 1938). Calcite, though only weakly magnetic, nevertheless exhibits a strong prolate diamagnetic anisotropy (Ikmax I > Ik1~~ I = I kmin I, where the k values are the principal susceptibilities). The generally accepted value 3) (in for S.I. the units, assuming a principal suscepdensitydifference of 2.7 tonnes m 10—6 (Krishnan et al., tibiity is 1.39 1933; Hellwege and Hellwege, 1967, p. 143). A calcite aggregate with a preferred orientation of c axes could therefore be expected to have a measurable resultant anisotropy (Daly, 1970). In this study susceptibility anisotropy and optical fabric have been measured on a suite of experimentally deformed samples of Carrara marble, and the possible effects of plastic defomration on the magnetic properties of single crystals of calcite have been exammed. .

216

2. Experimental 21. Magnetic measurements For magnetic measurements specimens were shaped either as cubes of about 1 cm side or as cylinders about 1 cm diameter by about 1 cm in length. Magnetic anisotropy measurements were made on a simple torque meter similar to that described by Stacey (1960), but capable of registering, through a worm gear, twist angles of 0.010. The torque curve for paramagnetic and diamagnetic minerals is of the sin 20 form, with amplitude proportional to the susceptibility difference in the plane of measurement and to the square of the applied field. From measurements made in three orthogonal planes the principal axis directions and principal susceptibility differences can be calculated (King and Rees, 1962). With the present instrument, sensitivity was limited by the background signal from the sample holder. Under routine operating conditions (2.5 g sample, 1 T field) the estimated standard error in corrected readings of ±0.02° corresponds to a susceptibility dif. ference of ±7.10—8. The instrument calibration facton can be calculated from its fibre constant and the field strength (King and Rees, 1962). Measurements on both single and polycrystals of calcite made over a range of field strengths demonstrated, both by the form and field dependence of the torque curves and the absence of any rotational hysteresis (Day et aL, 1970), that the anisotropy was not associated with any ferrimagnetic contamination. The question of possible paramagnetic contamination will be considered later.

2.3. Starting material All single crystal samples were cut from a purchased batch of clear calcite rhombs, each of about 25 cm3 in volume, and stated to be of hydrothermal origin (Mexico). Planar growth bands and inclusions of presently unknown nature could be seen inside many of the crystals using a low-power stereomicroscope, but optical spectroscopy of a batch of about twelve of the crystals revealed that all impurity elements, except Mg, lay below 20 wt. ppm and Mg was always below 65 ppm. All of the samples for deformation experiments were cored within about 10°of the c crystallographic direction. No attempt was made precisely to orient each individual core. The polycrystalline calcite samples were cored in a single direction from a block of white Carrara marble. The rock has a uniform grain size of about 200 /.tm and a polygonal texture. Most grains are free from twinning and optically visible strain featunes. The total porosity is less than 1%. Occasional quartz grains are seen in thin section and are the principal contaminant (about 1% by volume). Optical spectroscopy revealed Si0 2 (2%), MgO (0.5%) and Fe203 and A12O3 at about 1000 ppm. With the exceptionof quartz, the phases that these elements represent were of too low a concentration to be detectable by X-ray diffraction analysis, even after retnoving most of the calcite with dilute acid.

3. Results 3.1. Calcite single crystals

2.2. Deformation experiments Cylindrical specimens, 2 cm long by 1 cm diameter, were shortened axially by various amounts up to 50% at confining pressures ranging between 1.5 aPd 3.0. 108 Pa at temperatures ranging between 20 and 500°Cand at strain 1,using rates ranging mostly heated between an externally tni0~apparatus and l0~which s— has been described previously axial (Rutter, 1972). Most of the experiments were carried out at 400°C.For reasons which will be made apparent, some of the experiments on single crystals were carried out on cores cut to a shorter initial length.

Table I summarises the experiments carried out on single crystals of calcite, and the susceptibility differences are plotted against strain in Fig. 1. The susceptibiity differences are defined as: (kmax kmin) ~‘~Lin=Fig. (kmax Thus =the separation of theseand quantities 1 giveskint) an indication of observed departure from a perfectly prolate susceptibility ellipsoid. Where repeat measurements are given, these refer to variations in the measuring technique (most frequently to variations in the specimen orientation specification) and were carried out to check for consistency. —

—

217 TABLE I Magnetic anisotropy measurements on calcite single crystals Specimen No.

Natural strain

Weight (g)

~kH (10~S.I.)

~kL (10~S.!.)

SCC1 SCC1 SCC1 SCC2 Xt3 Xt9 Xtllb Xtllb Xt13 Xt9

0 0 0 0 0 0 0 0 0 0.028

0.94 0.94 0.94 0.99 2.14 1.43 3.53 3.53 3.26 2.42

1.22 1.20 1.20 1.19 1.19 1.20 1.20 1.18 1.16 1.18

1.14 1.13 1.16 1.16 1.15 1.18 1.17 1.15 1.12 1.17

Xtl Xtl3b Xt5 Xt6 Xt6

0.072 0.105 0.106 0.125 0.125

2.66 2.46 1.87 2.87 2.76

1.20 1.18 1.23 1.21 1.20

1.19 1.16 1.18 1.17 1.19

1.97 1.48 2.34 1.97 1.97

Xtl3a

0.124

2.42

1.15

1.12

1.43

Xtlla Xt4 Xtllb Xtllb Xt2 Xt12 Xt3

0.184 0.220 0.246 0.246 0.280 0.375 0.574

2.66 3.21 2.54 2.32 3.42 2.60 2.42

1.16 1.18 1.00 1.06 1.13 1.14 1.02

1.13 1.16 0.93 0.98 1.12 1.11 0.92

1.54 2.32 1.50 1.50 2.52 1.55

1.2

1 A Ij~’

*

6

~

,.,t ~ .8

— — — — — — — — —

2.10

1.71

The values for undeformed specimens agree with. . m expenmental error, and for individual samples the

Calcite single crystals

difference between ~.kL= is(1.172 always within this limit. The mean~kH valueand is ~.k ±0.028).

---_

I

I.0

Specimen aspect ratio

106 (hr deviation), which is significantly lower than the value of 1.39. 10—6 derived from Knishnan et al. (1933). Our result follows a trend demonstrated by

j

26 girdle

Datta (1954), who repeated many of the measurements of Knishnan and his coworkers and showed

-

.7

that they are, on average, 10% too high. There

.—

~ ~

,j,

~ .5

Carrara marble

,

2O~C ~ £ 200*C ~‘

/

A

0* .3

/

.2

400°C

500°C closed symbols — magnetics •

8

open symbols

—

optics

.1

I

o~

.

2

~ Natural Strain

~

6

~

Fig. 1. Summary of results of optical and magnetic susceptibiity anisotropy studies of calcite single crystals (open cirdes) and Carrara marble (other symbols). For each specimen the maximum—minimum and maximum—intermediate susceptibility differences are plotted and linked by a vertical line; the separation between the points indicates the departure from prolate diamagnetic anisotropy. The susceptibility difference calculated for a perfect small circle girdle of C axes at 26°to the compression direction is shown for reference. Dashed lines indicate trends in the data. Point A: mean of measurements on 9 single crystals; point B: mean of measurements on 6 marble specimens.

218 remains the possibility that our results are systematically in error, but this seems unlikely because the fibre constant has been checked and the system has

bouning grains. Two of the results appear to be anomalous (Xtl lb and Xt3), both in terms of a low average ~.k and a relatively large I~kH— ~kL. The remainder

given the accepted value for the susceptibility anisotropy, of ferrous ammonium sulphate.

show only a slight downward trend from the value determined for undeformed crystals. This may arise

Measurements on deformed single crystals are also given in Table I. Measurements were made on crystals of both high and low initial aspect ratio (ratio of initial cylinder length to diameter). The former were shown to deform for the initial 20% short-

from the localised inhomogeneous bending of the crystal structure which characteristically accompanies plastic deformation. We conclude that deformation has no marked systematic effect on the susceptibility anisotropy of calcite.

ening by easy glide dominantly on a single rhombohedral slip system whereas the latter were constrained to deform from the outset on several slip systems. They are thus more likely to approach the deformation conditions of a grain in an aggregate

for which deformation is constrained by the neigh-

3.2. Carrara marble The results of magnetic and optical measurements

made on Carrara marble are summarised in Table II.

TABLE II Results of magnetic and optical studies on experimentally deformed Carrara marble Specimen No.

CM000 CM122 CM8 CM24 * CM116 * CM13 * CM138 CM17 * CM1O CM25 CM51O CM512A CM502 CM19* CM126 CM503 CM15 CM5O1 CM512 CM504 CM507 CM505 CM508 CM509 CM57 *

Natural strain

Weight (g)

Temperature

Magnetics

Optics

Number of c axes

(°C)

i~kH

~kL

s~kH

ML

0 0.115 0.120 0.133 0.140 0.140 0.146

4.00 2.61 2.71 2.82 2.47 2.63 2.87

0.17

0.12

0.13

0.09

119

20. 20. 20. 20. 20. 20.

0.31 0.34 0.34 0.39 0.37 0.36

0.30 0.26 0.33 0.33 0.34 0.30

0.53

0.64

100

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

0.288

3.05

20.

0.50

0.48

—

—

—

0.076 0.188 0.288 0.055 0.057 0.133 0.162 0.184 0.190 0.310 0.413 0.414 0.540 0.568 0.680 0.685 0.140

2.50 2.72 3.09

200. 200. 200.

0.31 0.43 0.57

0.30 0.39 0.53

—

—

—

—

—

0.76

—

400.

—

—

0.36

0.72 0.26

2.31 2.61 2.76 2.74

400. 400. 400. 400.

0.31 0.47 0.38 0.56

0.25 0.35 0.35 0.52

—

—

—

—

—

—

—

—

—

—

—

400.

—

—

0.63

0.53

2.99 3.66 3.26 3.56 3.18 3.49

400. 400. 400. 400. 400. 400.

0.63 0.70 0.70 0.83 0.77 0.72

0.60 0.66 0.67 0.81 0.69 0.68

—

400.

—

2.35

500.

0.34

—

—

200 102 —

—

108

—

—

—

—

—

0.79

0.71

—

—

—

—

—

—

—

—

—

0.82

0.78

0.32

—

—

—

128

—

156 —

Detailed data on the mechanical behaviour of these specimens are given in Rutter (1974). The strain rates at which these specimens were deformed are slower than the nominal rate specified herein, which applies to all other specimens.

219 3.2.1. Optical anatvses The optical analyses show the progressive development with strain of a maximum close to or at e {1012}. This development is best ifiustrated using inverse pole figures (Fig. 2), which for axisymmetnic fabrics show the orientation of all crystallographic directions with respect to a unique axis about which the fabric is axisymmetric (in this case the specimen shortening axis). That the fabric is in fact axisymmetric in our deformed samples was established both from magnetic measurements and by plotting c axis pole figures from the optical data. The e maximum fabric is a common fabric in both naturally and experimentally deformed calcite rocks (Turner and Weiss, 1963; Wenk et al., 1973).

cm 512

C

r~ ••

~‘.

•

C

~ç

I i~’i 4~’ •

85 ~ :~—...5-4%

~•

•

‘~

Using the split cylinder technique (Raleigh, 1965), in which a polished Pt foil is inserted between two polished faces of a longitudinally cut cylindrical specimen, upon the faces of which a set of 10 .im wide marker lines had been inscribed, it was established that the grains in this rock deform fairly homogeneously with the aggregate as a whole.

cmI5

3.22. Magnetic measurements The magnetic fabric results are characterised by a maximum absolute susceptibility axis within 10°of the compression axis (this discrepancy reflects the error in mounting these small specimens, rather than the precision of the magnetic measurements)~The susceptibility anisotropy is in all cases near prolate (Ikmax I > ~ I = Ikmin f). The strength of the anisotropy varies systematically as a function of strain, rising steeply at low strain and tending to an asymptotic value at high strain. This is shown in Table II

17-0% 97pts

and 4. Discussion Fig. 1.the The separation between ~.kHand ~kLan axisymmetric measures observed fabric. degree of departure from

•

••

:••

Quantitative comparison between the optical and

a

m

m

magnetic results is possible because the magnetic anisotropy resulting from the observed distribution of c axes can readily be calculated (Owens, 1974). c

cm504 e

cm509

c

~

49~7 ~,

•

times the applied field, so the grains may be treated

•~

:~>~L~ 99pts ~~jPts

•~~‘

Magnetic interactions between grains will be equi-

:

as being magnetically the grains observed valent 1 tonormalised are given local fields T equal the weight, orderthe ofk(i.e. resultant 10~) suscep(1) tibiity, toofindependent. unit weight, isThen, givenifby:

a

Km m Fig. 2. Inverse pole figures for Carrara marble experimentally deformed at 400°C.With each figure is given the specimen number, percentage shortening and number ofgrains measured. The complete orientation of each grain is determined from c axis and twin lamellae measurements. Labelled crystallographic planes are c {oooi e {loi2 f {o221 r {ioii and m {ioio}.

},

},

},

},

LiR,kR1

where n is the number of grains measured, k is the grain susceptibility tensor and R, is a rotation matrix specifying the orientation of the principal axes of k of the ith grain relative to the reference axes. If, as in calcite, the grain anisotropy is uniaxial, characterised by kmax along the c axis and kmin in the basal

220

plane: kmax k=I 0

0

0 =

kmin

0 0

0

kminj

(kmax + 2kmin)

{

~

1 0

0 1

0

0

r~ 0 .1

kmin)~0

+ (kmax

opment with progressive strain, closely approaching an e maximum after about 0.6 strain (equivalent to about 45% shortening). (2) This history of fabric development is extremely rapid, the magnetic fabric being about half as strong as it will ever become after only 15—20% shortening.

1.0

0

0 0

I

0) 0

_iJ

= kt+ (M/3) C (2) where k is the mean susceptibility, ~.k the principal susceptibility difference and C a matrix of numerical coefficients. Then eq. 1 can be written as:

K = 7c1 +

~ R1CR,~’

(3) 3n from which it is clear that resultant susceptibility differences are products of ~k with a geometric function. Principal axis directions are thus independent of the value adopted for ~k, and i~.Kis scaled directly by ~k. For a perfect small circle girdle ofc axes inclined at angle 0 to the compression direction, the difference between the maximum and minimum susceptibilities is readily shown to be: 20) (4) = IKmax Kmin I = ~k(l 1.5 sin Thus the expected susceptibility difference for a perfect 26°small circle girdle of c axes (equivalent to an e maximum) of calcite grains is 0.712 ~Vc. Using the E~.kvalues obtained from the measurements~on undeformed single crystals of calcite, we have calculated L~Kusing eq. 4 together with the c axis distributions of those samples which were analysed optically. The values of ~K so obtained are shown in Table II and plotted in Fig. 1 for direct comparison with the results of the magnetic anisotropy measurements on Carrara marble. Several points may now be made: (1) The optical and magnetic results are closely comparable. Both show similar rates of fabric devel—

—

shortening. (3) The e maximum (Fig. 2) is very intense. After about 40% shortening the concentration of poles to e is about X 10 uniform. (4) Both optical and magnetic studies on undeformed Carraramarble show the fabric to be essentially uniform. In this respect the rock is ideal for experimental deformation studies. (5) Though most deformation experiments were carried out at 400°C,some were performed at 20°C, 200°Cand one at 500°C(Table II and Fig. 1). It is noteworthy that over the range of temperatures used the results are, in crude terms, temperature independent. This may mean that the relative activities of the operative glide systems are large tempera. ture insensitive over this range. (6) Despite the close comparability between the optical and magnetic results, there remains a tendency for the optical ~.K values to lie above the magnetically determined curve, though the two sets of data are equivalent within the expected limits of experimental error. In the optical analyses the contribution of the volume of the twinned portion of the deformed grains (up to about 5%) to i~.Khas been neglected, whereas the magnetic measurements include this. Assuming 5% twinning by volume the optically by about determined 7% of ~.K.This ~.Kvalues would would largelyberemove reduced the discrepancy. Further, the analysis of Carrara marble by optical spectroscopy indicates the possibffity of small quantities of paramagnetic impurity phases being present. This too would tend to depress the magnetic fabric data. Only a few weight per cent of an oriented paramagnetic mineral would be able to swamp completely the magnetic properties due to calcite. The close comparability between the optical and magnetic fabric data indicates that Carrara marble ~isan essentially pure calcite rock. In order to examine the possibility of bias in the optical analyses, a thin section CM51O (strain = 0.23) was cut normal to the shortening direction whilst all the others were cut parallel to it. From Table II and

221 Fig. 1 it will be seen that ~.Kis somewhat higher than would have been expected through interpolation of the other results. Therefore some kind ofbias probably does exist in the optical analyses despite care being taken to measure all grains along arbitrarily chosen traverse lines.

5. Conclusions We have demonstrated that fabric parameters estimated from magnetic susceptibility measurements on experimentally deformed calcite rocks are consistent with the results of conventional optical fabric studies. The success of this comparison raises the question of the role of magnetic anisotropy measurements in fabric analysis. In magnetic measurements a resultant property of many grains is determined. The interpretation of such a resultant in terms of preferred orientation cannot of course be unique for example, both a uniform distribution of c axes and a perfect small circle girdle of 0 = sin’(l/\/l.S)° 54.7°(see eq. 4) give ~ The magnetic measurements can, however, be interpreted in the context of the externally supplied framework of a model derived, for example, from optical measurements. Thus the attributes of magnetic anisotropy measurements would appear to be twofold. Firstly, since the measurements are rapid, a greater sampling density than that obtainable with other fabric measuring techniques is possible. Secondly, since the consequences of any particular model can be expressed quantitatively in terms of susceptibifity parameters, and because a sensitive measuring technique exists whereby these values may be tested, magnetic measurements may be useful in evaluating the predictions of theoretical studies of fabric development in calcite aggregates based, for example, on the Taylor-Bishop-Hill analysis (Lister, 1974; Rutter and Rusbridge, 1976). The results clearly demonstrate, contrary to widespread opinion (but see Daly, 1970), that magnetic anisotropy measurements can be applied to diamagnetic aggregates, and the question arises of their application to the study of naturally deformed calcite rocks. In such applications, however, it must be stressed that reliable conclusions drawn from magnetic measurements can only be made if there is both —

adequate structural control to provide an interpretive model and a clear understanding of the magnetic effects of all of the mineral phases present in the rock.

Acknowledgements The rock deformation equipment used for this work was constructed through NERC Grant No. GR 3/2048. This work forms part of a study of magnetic susceptibility anisotropy of deformed rocks financed by NERC Grant No. GR 3/2240. Alan Dean performed most of the susceptibility anisotropy measurements and Margaret Rusbridge performed several of the optical fabric analyses. Chris Spiers wrote the computer programs used to plot inverse pole figures from optical orientation data. Nick Shaw arranged for the optical spectroscopic analyses of the calcite single crystals. Rob Holloway maintained the rock deformation apparatus and helped with many of the experiments. Finally, Gordon Lister is thanked for much thought provoking discussion.

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Earth

Daly, L., 1970. Etude des propriétés magnétiques des roches métamorphiques ou simplement tectonisées. D. Sc. Thesis, University of Paris, Paris. Datta, S., 1954. Accurate determination of the magnetic anisotropy of the hydrated salts of some elements of the iron group. Indian J. Phys., 28: 239—249. Day, R., O’Reilly, W. and Banerjee, S.K., 1970. Rotational hysteresis study of oxidised basalt. J. Geophys. Res., 75: 375—386. Hellwege, K.H. and Hellwege, M., 1967. Magnetic properties, II. In: H. von Borchers, H. Hausen, K.H. Hellwege, K.

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222

affecting the magnetic anisotropy of deformed rocks. 24: 115—131. Raleigh, C.B., 1965. Glide mechanisms in experimentally deformed minerals. Science, 150: 739—741. Rutter, E.H., 1972. The influence of interstitial water on the rheological behaviour ofcalcite rocks. Tectonophysics, 14: 13—33. Rutter, E.H., 1974. The influence of temperature, strain rate and interstitial water in the experimental deformation of calcite rocks. Tectonophysics, 22: 311—334. Rutter, E.H. and Rusbridge, M., 1976. The effect of nonTectonophysics,

coaxial strain paths on crystallographic preferred orientation development in the experimental deformation of a marble. Tectonophysics, 39: 73—86. Stacey, F.D., 1960. Magnetic anisotropy of igneous rocks. J. Geophys. Res., 65: 2429—2442. Turner, F.J. and Weiss, L.E., 1963. Structuial Analysis of Metamorphic Tectonites. McGraw-Hill, New York, N.Y., 545 pp. Wenk, H.R., Venkitsubramanyan, C.S. and Baker, D.W., 1973. Preferred orientation in experimentally deformed limestone. Contrib. Mineral. Petrol., 38: 81—114.