Mineralogy and Petrology (1993) 48:201-214

Mineralogy

Po%gy © Springer-Verlag 1993 Printed in Austria

Electrical Conductivity of Cordierite E. S c h m i d b a u e r 1 a n d P. W. M i r w a l d 2 1Institut ftir Allgemeine und Angewandte Geophysik, Universit/it Mtinchen, Federal Republic of Germany 2 Institut fiir Mineralogie und Petrographie, Universit/it Innsbruck, Austria With 8 Figures Received February 8, 1993; accepted April 9, 1993

Summary Electrical ac-conductivity parameters (real part of impedance (Z'), imaginary part of impedance ( - Z " ) and parallel capacity (Cp)) of a low iron cordierite single crystal from White Well, Australia (Mgl.91 Feo.os Mno.mA13.95 Sis.Ol (Nao.05,0.56 H20,mCO2)) (Pryce, 1973) were studied in the temperature range 200 to 820 ° C and frequency range 25 - 106 Hz with a test signal voltage of 1.0 volt. Measurements on the 4.2 x 3.4 x 4.7 mm sample were conducted in the crystallographic [001J- and [100]-directions in order to elucidate the electrical behaviour of this orthorhombic framework silicate parallel and normal to its c-parallel channel elements which host a variety of alkali and fluid components. The first heating excursion up to 900 ° C took ca. 8 hours to allow a slow degassing of the fluid components. The electrical parameters were monitored during this irreversible process. The subsequent measurement cycles did not exceed 820°C and yielded reproducible data. The data obtained in the two different crystallographic directions indicate a considerable anisotropy in electrical behaviour. While plots of the Z'- vs. - Z"-data obtained in the [001J-direction show two semicircular arcs, those in the [100J-direction display only one such arc. Each of the arcs may be related to a charge transfer process in the crystal. Estimates of the activation energies of the different inferred charge transfer processes derived from a plot of extrapolated RDc vs. 1/T are 0.75 and 0.83 eV for the [001]- and 0.85 eV for the ]-100]-direction. The occurrence of different charge transfer processes combined with large differences in the values of the Z'- and - Z"-parameters indicate a considerable anisotropic electrical behaviour of cordieritc which can clearly be related to its structural characteristics. Further work is needed to elucidate the electrical conduction mechanisms.

202

E. Schmidbauer and P. W. Mirwald

Zusammenfassung Die elektrische Leitffthigkeit des Cordierits Es wurden Wechselstromparameter (Real (Z')- und Imaginfir(Z")-Teil der Impedanz sowie Parallelkapazit~it (Cp)) an einem eisenarmen Cordierit-Einkristall ((Mgl.91 Feo.o8 Mno.ol)A13.95 Sis.ox (0.05 Na,0.56 HEO, mCO2) ) yon White Well, Australien (Pryce, 1973) in Abhfingigkeit yon Temperatur (200-800°C) in einem MeBfrequenzbereich zwischen 25 bis 106 Hz gemessen. (MeBspannung 1,0 Volt). Um das elektrische Leitf~ihigkeitsverhalten dieser Geriiststrucktur parallel und senkrecht zu ihren charakteristischen Kan/ilen zu fiberprfifen, die typischerweise Alkalien und Fluidkomponenten enthalten, wurden die Messungen in den kristallographischen Richtungen [001] und [100] einer 4.2 x 3.4 x 4.7 mm groBen Probe vorgenommen. Das erste Aufheizen der Probe bis zu 900°C erfolgte fiber ca. 8 Stunden, urn ein langsames Entgasen der Fluidkomponentenzu gew~ihrleisten. Dieser irreversible Prozef5 wurde gleichzeitig mittels Messungen der elektrischen Parameter dokumentiert. In keinem der folgenden MeBzyklen wurde 820° C fiberschritten, wobei die MeBwerte eine gute Reproduzierbarkeit aufwiesen. Die in den beiden Kristallrichtungen erhaltenen Daten weisen auf eine betr~ichtliche Anisotropie im elektrischen Verhalten des Cordierits. Bei graphischer Darstellung des Real (Z')-versus Imagin~ir (Z")-Teils der Impedanz ergeben die MeBdaten fiir die [100]Richtung zwei Halbb6gen; in der [001]-Richtung ist jedoch lediglich einer zu beobachten. Jeder der B6gen ist mit einem Vorgang eines Ladungstransportes im Kristall zu korrelieren. Die Abschfitzungen der Aktivierungsenergie der verschiedenen Ladungstransportprozesse erfolgte, indem der fiber Extrapolation gewonnene Wert ffir den Gleichstromwiderstand RDc gegen 1/T aufgetragen wurde; es ergaben sich 0.75 und 0.83 eV ffir die [001]- und 0.85 eV fiir die [100]-Richtung. Das Auftreten yon verschiedenen Ladungstransport-Prozessen in Verbindung mit grol3en Unterschieden in den Z'- und Z"-Parametern geben den Hinweis au.f.betr~ichtlich anisotrope, elektrische Eigenschaften des Cordierits. Dies steht in gutem Ubereinklang mit den Strukturmerkmalen. Weiterfiihrende Untersuchungen sind erforderlich, um den Mechanismus der elektrischen Leitffihigkeit zu erfassen.

I. Introduction Cordierite is a framework silicate of the bulk composition (Mg, Fe, Mn)2 A14 Si5018" [a Na, K(?), b H20, c Co2, d noblegases, e CH-components-i a < 0.3, 0 < b < 0.9, 0 < c < 0.5; d, e: varying small amounts). The structure is characterized by (AlzSi406) ring elements stacked along the c-direction to form channels. Interconnection by MeO 6 octahedrons and A104/SiO4-tetrahedrons produces the framework structure (Fig. 1). The channels formed by the ring elements may host a variety of components as indicated in the chemical formula above. A hightemperature modification ("high-cordierite') has hexagonal symmetry due to statistical A1/Si distribution, and the low temperature polymorph ("low cordierite") is ordered and has orthorhombic symmetry (space group Cccm) (cf. Cohen et al., 1977). This polymorph is the petrologically relevant phase. Because Mg-Fe-cordierite is an important mineral phase of high grade metapelites, its stability relations have been studied intensively in the past years, e.g. Schreyer and Yoder (1964), Hensen and Green (1971), Currie (1971), Newton (1972), Holdaway and Lee (1977), Aranovich and Podlesskii (1983), Schreyer (1985). The

Electrical Conductivity of Cordierite

203

(2

Fig. 1. Crystal structure of cordierite; view down the c-axis. Open circles = oxygen; M = octahedral sites (Fe, Mg); small full circles = tetrahedral site T1 and T2 (Al-rich); T3, T4, T5 = tetrahedral sites (T3: Al-rich, T4 and T5: Si-rich); ruled areas = cross sections of the c-parallel channels containing various alkali and fluid components [after Stout (1975)]

composition of the channel filling is particularly relevant to petrogenetic problems. This applies with respect to the a m o u n t and ratio of the major fluid components H 2 0 and CO2 [Johannes and Schreyer (1981), Mirwald (1982, 1984), Jochum et al. (1983)] as well as to the sodium content where an inverse correlation with temperature may serve as a geothermometer (Mirwald, 1986). Concerning its crystal physical and chemical aspects, eordierite turns out to be a system of very complex behaviour [Langer and Sehreyer (1969), Hochella et al. (1979), Mirwald (1981), Putnis and Bish (1983) and Poon et al. (1990)]. Particularly, the behaviour and properties of the channel filling system are very interesting [Lepezin and Melenesky (1977), Goldman et al. (1977), Medenbach et al. (1980), Armbruster and Bloss (1982), Mirwald (1983), Boberski et al. (1983), Aines and Rossman (1984), Armbruster (1985a, b), Mirwald et al. (1986), Jochum et al. (1987)]. The complex behaviour of the channel c o m p o n e n t s already becomes obvious in heating experiments at one atmosphere [Iiyama (1960), Giampaolo and Putnis (1989)]. While the fluid species degasses continuously at different rates at temperatures between some 200 to 1000 ° C, the charged c o m p o n e n t s N a + and possibly O H (eventually formed as a high temperature reaction product from H 2 0 ; Mirwald unpublished data) remain in the structure. This clearly indicates different bonding strengths of the various c o m p o n e n t s to the host crystal. As to the remaining channel components, they are assumed to be tied to the structure either due to substitution reaction, such as Na + + A13+ = Si 4+, or due to compensation equilibria between positively charged cations in the channels and cation vacancies in the cordierite structure. However, this is difficult to prove analytically. In this context also the role of iron as a di- or trivalent cation seems i m p o r t a n t [Gunther et al. (1984), Bo.berski and Schreyer (1990)]. Electrical methods provide an approach to elucidate the spectrum of physicalchemical properties of cordierite, in particular the role of ionic or electronic pro-

204

E. Schmidbauer and P. W. Mirwald

cesses in the structure. Measurements of electrical properties of silicates are rare. The first determination of the dielectric constant of cordierite was reported by Olhoeft (1981). Recently, very detailed work on this topic was reported by Shannon et al. (1992). In this study we present data on electrical ac-conductivity of a natural cordierite crystal at elevated temperatures obtained by impedance spectroscopy. A preliminary report was given by Mirwald und Schmidbauer (1992).

2. Theoretical Background A charge transfer process in a semiconducting electronic or ionic material can frequently be modeled by a parallel circuit consisting of a pure resistor R and a pure capacitor C. The complex plane representation of the impedance Z of this circuit is given by Z = R/(1 + i~ RC)

where ~o = 21-Iv,

with v = frequency and i = ~ / - 1.

This expression may be expanded into the form of Z = R/(1 + ~oZRZC2) - i~oR2C/(1 + ~2R2C2). k

_

_

"V'_

Z'

_

J

k

¥

)

-Z"

The RC-term represents a time constant (~) which characterizes the relaxation time of a parallel circuit (Debye relaxation). An isothermal plot of the real part Z' (resistance) versus the imaginary part, - Z " (reactance) of the impedance (Z), results in a semicircle; parameter is the frequency v. The extrapolation of the circle to the low frequency branch towards the Z'-axis yields R, which represents RDc at 0 Hz. Principally, the semicircle characterizes the type of the electrical process. Different semicircles are representative of different charge transport processes, lying in different frequency windows. For the maximum of the semicircle the equation ~oRC = 1 is valid. Frequently, the semicircles exhibit a depressed shape, thus the circle center is located below the real Z'-axis. This behaviour is interpreted as being due to a distribution of relaxation times (Cole and Cole, 1941; Bauerle 1969; MacDonald 1987).

3. Sample Description The cordierite sample was a single crystal from White Well, Australia (Pryce, 1973). It was slightly blue grey to almost colorless and transparent. Microscopic inspection of the material revealed cloudy streaks and a number of flaky (mineral) inclusions. However, in a X-ray powder diffractogram no other mineral phase was detected. Inspection of the sample after some 10 high temperature cycles under the conditins of measurement showed somewhat increased cloudiness. Microprobe analysis and lattice constants of the material studied are given in Table 1. They compare well with the original data by Pryce (1973). The mineral formula calculated from our data is (Mgl.88 Feo.o9 Mno,01)A13.97 Si5,o2(0.05 Na, 0.56 H20, cCO/) The determination of 0.56 H 2 0 by Pryce (1973) seems representative and is sup-

Electrical Conductivity of Cordierite

205

Table 1. Microprobe analysts and lattice constants of the studied

sample of White Well cordierite compared with data from Pryce (1973) Microprobe analysis (Wt~o)

this study

Pryce (1973)

SiO z Al20 3 Fe20 3 VeO MgO MnO TiO 2 P20 5 CaO K20 Na20 H20+ H20CO 2

50.37 33.75 -* 1.12 12.67 0.07 <0.01 n.d. <0.01 <0.01 0.24 +** n.d. +**

50.20 33.50 0.14 0.84 12.80 0.06 <0.01 <0.01 0.23 0.14 0.26 1.69 0.12 n.d.

98.19

99.98

Sum Lattice constants

this study

Pryce (1973)

a (4) b(A) c (A) V (A 3)

17.056 (15)*** 9.728 (5) 9.354 (4) 1552.0 (18)

17.055 (5) 9.724 (1) 9.350 (1) 1550.6 (8)

e

* Fe total determined as FeO, ** documented by IRspectroscopy, *** Si--standard; numbers in brackets refer to the last digits ported by own unpublished data on White Well cordierite material. Furthermore, IR-spectra also reveal, in addition to absorption bands of different H 2 0 types (Goldmann, 1977), the presence of CO2 in the structure channels. The sample had the approximate dimensions of 4.2 x 3.4 x 4.7 ram. The crystallographic orientation of the sample was determined optically; the long dimension of the sample was parallel to the [001J-direction; the intermediate one was parallel to the [100J-direction of the structure.

4. Experimental Methods The ac-measurements were performed with a Hewlett Packard 4284A LCR meter in the frequency range 25 H z - 1 M H z and between 200 ° and 900 ° C. A 4-terminal pair measurement m e t h o d (Hewlett Packard, 1988) was used. The measurement principle is displayed in Fig. 2. The sample was hanging freely from two Pt-wires wrapped round the sample (Fig. 3); there are two current and two potential leads. The Pt-wires were protected by ceramic tubes which were surrounded again by thin

206

E. Schmidbauer and P. W. Mirwald 1

Fig. 2. Principle of the four-terminal-pair measurement; 1 = sample, 2 = shielding and 3 = HP LRC meter

I I

1

2

t~

Fig. 3. Configuration of the sample holder; 1 = thermocouple, 2 = Pt lead wires; 3 -- alumina tubes; 4 = stainless steel shielding tubes, connected by leads; 5 = sample; 6 = contact area

walled stainless steel tubes for shielding. The steel tubes were in contact with ceramic material only in the cold parts of the sample holder, assuring good isolation. Here, shielding was provided by brass tubes; finally coaxial cables led to the input of the LCR meter. A Pd/Pt thermocouple junction was located close to the sample (,-, 1 mm distance). Also here the thermocouple ceramic freely led to the cold end of the sample holder. The whole assembly was incorporated into a gas tight alumina tube which again was accommodated in a horizontal tube furnace. A temperature controller kept the sample temperature constant to __ 1° C. The gas tight alumina tube was flushed by N 2 gas of 99.999~o purity with a flow rate of approximately 20 cm3/min throughout the experiment. The normal test signal voltage was 1.00 V; but 20 mV was also used in order to check possible voltage dependence processes. No notable difference in measured data was noticed for the ON and O F F period of the furnace. For error estimation, impedance parameters were also determined without a sample. The geometry and size of the contact faces of the sample were imitated by two Pt-plates positioned some 2 m m apart which was roughly equivalent to that encountered in the real experiment. The parallel capacity value Cp of the entire set up (contributions by sample holder, cables and LCR-meter) amounted to 0.14 pF at 25 ° C. This value varied insignificantly (range: 0.13-016 pF) with temperature and frequency. The sample crystal was prepared as follows: For fixing the Pt-leads in the studied direction [001] and [100], small cuts were made at the sample edges close to the contact faces (Fig. 3). After the contact faces were ground with fine grained emery paper, 0.1 m m Pt-wire was wrapped round the crystal. Finally, Pt-paste (Leitplatin

Electrical Conductivity of Cordierite

207

308, Demetron) was carefully coated along the sample Pt-wire regions and the adjacent contact faces. The diluting organic fluid of the paste was evaporated by heating to 70 ° C in air. Each change of the measurement direction required a careful cleaning of the Pt-paste and slight grinding of the sample surfaces, before the new contacts could be attached. 5. Measurements

Prior to heating, air and moisture were removed from the gas tight assembly tube by a N 2 gas flow over a 5-6 hours period. During the first heating excursion (measurement orientation [001]), reading of the impedance parameters already started at room temperature in order to monitor: i) the burning-in of the coated Pt-paste at elevated temperature to remove organic impurities and to produce a film of Pt-particles strongly adhering to the sample faces, and ii) the degassing of the fluid components H 2 0 and CO 2 of the sample during the first heating. To prevent or at least to minimize oxidation, this procedure was conducted under N 2 gas flow. The first heating excursion was conducted very slowly. Degassing of cordierite which is a continuous but temperature dependent process became noticeable in the electrical parameters at 250-300 ° C. The stepwise heating (ca. 50 ° per step) to a temperature maximum of 900 ° C was achieved in 5.5 hours. After some 2.5 hours of annealing at this temperature, first valid data were taken during cooling. The results obtained on cooling during the first cycle already turned out to be representative. The data of the second and following heating cycles differed only insignificantly; however, in all these cycles 830°C were never exceeded. This result clearly shows that no further irreversible processes relevant to charge transfer occurred in the cordierite sample. Comparison of the electrical conduction values between pristine and degassed sample at 200°C shows that the impedance values for the pristine cordierite are larger roughly by a factor of 5. 6. Results

Charge conduction along [001]-direction: Figs. 4, 5 and 6 show plots of the Z'- and - Z " - d a t a in the complex impedance plane. Two regions may be distinguished: There is a depressed semicircle, arc I, at comparatively low impedance values and high frequencies v; in addition, at decreasing v the "high frequency" part of a further arc II appears. As seen from Fig. 4 and 5, below 500°C the low frequency branch extends to a very high impedance which, unfortunately, exceeds the measurement range of our instrument (for Z' and - Z" < 108 Ohm). In evaluating the low temperature ( < 500 ° C) data, arc I has been extrapolated towards the Z'-axis on the low frequency side by mirroring the quarter of the data arc in its vertex ("mirror method"); cf. Fig. 4 and 5. This yields an approximate intercept which represents the "DC" resistance RDc of the charge transfer process related with arc I. As mentioned before, the depressed arc I may be described by the model of a distribution of relaxation times (McDonald, 1987). According to the relation o R C = 1, we calculated for arc I in Fig. 4 and 5 Cp ~ 1 pF. Such a Iow

208

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Fig. 4. Complex impedance plane plot of the data obtained in the [001]-direction revealing semicircular arcs which may each be related to a charge transport process. Arc I at 286 ° determined by two different extrapolation methods Fig. 5. Complex impedance plane plot of the data obtained in the [001J-direction revealing a semicircular arc I at 395°C as determined by two different extrapolation methods (note Z" in RF~) capacity value is expected for single crystal material whereas interfacial electrode processes as a rule have values in the order of nF or ~-,#F (MacDonald, 1987). F r o m this we conclude with respect to our experiment, that contributions by polycrystalline surfaces and contact layers have no significant influence on the data. Above 550 ° C, arc I has shifted to very high frequencies ( > 1 MHz), which means it has moved towards the origin of the complex plane. Since arc I cannot be properly resolved any more, its construction becomes increasingly uncertain. For this reason arc II was subjected to extrapolation, indicated by the scheme in Fig. 4 and 5. The high frequency branch of arc II was backward extrapolated towards the real Z'-axis, and the intercept value thus obtained was used as RDC of arc I. This evaluation procedure gives data of lower accuracy; we estimate the error as approximately 20% at high temperatures. If the RDC values of arc I, which were obtained by this method at different temperatures, are plotted logarithmically against 1/T (Arrhenius-plot), a linear relation is found (Fig. 8). F r o m the slope of this line an activation energy E A = 0.75 eV is calculated. In the low temperature range (<250 ° C) the existence of arc II in the [001Jdirection is only documented by a steep high frequency branch. No extrapolation to lower frequencies is possible. However, increasing temperature results in increasing development of arc II. Its vertex appears in the temperature range 550800 ° C exhibiting a Cp of 300 pF. Furthermore, by a tentative extrapolation of the low frequency branch to the Z'-axis, according to the above "mirror-method", a rough estimate of RDC can be obtained. Incorporation of these RDC values in the Arrhenius diagram of Fig. 8 yields an EA of 0.83 eV.

Electrical Conductivity of Cordierite

209

In principle, this arc II m a y be related to a second charge transport process in the cordierite structure or to an interracial electrode process between Pt-paste and sample, respectively. After a n u m b e r of measuring cycles in the [001]-direction which gave reproduceable data, equivalent experiments were conducted in the [100]-direction. After reassembling, the sample was heated to 830 ° C to eliminate any influences due to sample preparation. The measurements were started again on cooling. Similar to the measurements in the [001J-direction, the second and further heating cycles yielded reproduceable data. Generally, the Z'- and - Z " - r e s u l t s (Fig. 7) differed conspicuously from those along [001] (cf. Figs. 4, 5 and 6).

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210

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At comparatively low temperature, instead of the circular arc I and arc II noted before in the (001)-direction, only a high frequency branch of a single circular arc appears. In the high temperature region, however, the essential part of the arc becomes measurable (Fig. 7) which finally allows determination of the approximate position of the vertex of the circular arc. According to the above "mirror-method", a Cp-value of 1-3 pF has been determined. This, again, is of a magnitude as expected for sample charge transport processes and is in good agreement with the result obtained in the measurements in the [001]-direction. F r o m an Arrhenius plot for Roc vs. 1/T a corresponding EA of 0.85 eV has been deduced (Fig. 8).

7. Discussion

Out of a number of cordierites of different Mg/Fe-composition, the White Well material was chosen because of its low iron content in order to avoid dominant influence by the Fe-component. The sample crystal was, however, not perfectly clear and showed a number of (mineral) flakes under the microscope. Major effort was put into the degassing process which was conducted very slowly and under an inert N 2 gas atmosphere up to 900 ° C. This maximum was never exceeded in the following measurements. So far, no data on the residual channel filling have been obtained, since this would have resulted in the destruction of the sample. We suppose on the basis of literature and our own unpublished data that only fractions of H20/(OH?) and CO2 were left in the cordierite channels, while the sodium content should have been little changed. Therefore, the irreversible variation in impedance parameters during the first heating excursion must have been related to changing chemistry, in particular to that in the channels. In addition, there could have been effects due to baking the Pt-paste on the contact surfaces of the sample.

Electrical Conductivity of Cordierite

211

The results obtained in the temperature cycles after the first heating excursion were fairly well reproduceable. This allows us to conclude that a constant state with respect to electrical behaviour was reached which apparently did not change over the number of experiments performed. The choice of measurement directions was dictated by the sample geometry. We were most interested in studying conduction in the [001]-direction, since the channels are aligned in that orientation within the cordierite framework structure. From the findings of two arcs in the [001]- and a single one in the [100Jdirection, and from the large differences in value of the Z'- and -Z"-parameters between both directions which are up to an order of magnitude, we deduce a pronounced anisotropy of cordierite. The different arcs are related to different charge transfer processes. However, all arcs are not semicircular in a strict sense, but are rather of depressed shape so that the circle center is located below the Z'-axis. This may be interpreted as a distribution of relaxation times (see above) inherent to the charge transport processes. The Cp-values obtained from evaluation of the arcs yielded comparable values of approximately 1 pF for the single arc in the [100]- and arc I in the [001J-direction. However, for arc II of the [001]-direction Cp is 200 pF, which is considerably larger. The activation energies derived from Arrhenius plots of RDc vs. 1/T range between 0.75 (arc I), 0.83 (arc II) and 0.85 eV (arc in [100]). The observed anisotropy in the electrical behaviour is clearly correlated with the structure of cordierite. The channels, which are parallel to the [001]-direction, exhibit two different charge transfer processes, while in the [100J-direction only a single charge transport process was found. The two arcs (I and II) in the [001Jdirection seems to correlate with the structural heterogeneity of cordierite, represented by the framework matrix and the channel elements where alkali and (probably even after temperature treatment) relics of the fluid components are hosted (cf. Fig. 1). This leads to the suggestion that arc I is connected with a charge tranport process primarily occurring in the channels. For similar silicates which contain channels, such as leucite and Na-nepheline, charge transport in the channels has been suggested (Roth and B6hm, 1986; Palmer and Salje, 1990). The structural analogy to cordierite is obvious. The experimentally determined activation energy, EA = 0.75 eV, of the conduction process is rather low for ionic conduction, i.e. there must be a favored mechanism for ion transport. On the other hand, we have not yet performed experiments to find out whether the conduction is electronic or ionic. The former could also result in an activation energy of such a magnitude. If the above hypothesis of channel conduction is correct, arc II and the single arc in the [100]-direction could be related to charge transport processes via the framework of the cordierite structure. However, neither for arc II nor for the single arc in [100]-direction can any kind of interfacial electrode process be excluded. While this hypothesis seems supported by the relatively large Cp value of approximately 200 pF derived for arc II, it fails for the single arc in the [100J-direction. A major argument against a common interracial process is that, although surface conduction may in principle be anisotropic, it is rather unlikely; therefore we are inclined to drop this mechanism from consideration. We cannot totally exclude the possibility that charge transport related to the cloudy streaks is anisotropic, since the streaks consist of agglomerated defects such

212

E. Schmidbauer and P. W. Mirwald

as dislocations etc. These agglomerates could favor ionic or electronic conduction. It appears, that, somehow, they must be related to the channel directions. In the literature we found neither support no exclusion for assumption of such an effect.

Acknowledgement We thank Dr. Olaf Medenbach (Bochum) for carrying out the optical orientation of the sample.

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Am Mineral 60:229-234 Authors' address: Dr. E. Schmidbauer, Institut fiir Angewandte Geophysik, Universit~it Mfinchen, Theresienstrasse 47, D-80333 Miinchen, Federal Republic of Germany