American Mineralogist, Volume 80, pages 491-501, 1995 Influence of chemistry on the pyroelectric effect in tourmaline KATE D. HAWKINS. Centre for Microscopy and Microanalysis, University of Queensland, Brisbane, Queensland 4072, Australia; and School of Mechanical and Manufacturing Engineering, Queensland University of Technology, P.O. Box 2434, Brisbane, Queensland 4001, Australia IAN D. R. MACKINNON Centre for Microscopy and Microanalysis, Institut fUr Kristallographie University of Queensland, HELMUT SCHNEEBERGER.. und Mineralogie, Ludwig-Maximilians-Universitiit, Brisbane, Queensland 4072, Australia TheresienstraJ3e 41, Munich, Germany ABSTRACT Pyroelectric coefficients were measured from a series of natural tourmaline crystals between -170 and - 500 K to quantify the variation of the pyroelectric effect with chemical composition. The amount of Fe in tourmaline has a prominent influence on the pyroelectricity. Fe content linearly decreases the pyroelectric coefficient in the composition range between 0.01(1) and 14.6(2) wt% FeO. Thus, to a first approximation, tourmaline pyroelectric coefficients may be predicted directly from the chemical composition derived by routine electron probe microanalysis. The relationships between pyroelectricity and chemistry indicate that the pyroelectric coefficient is influenced to different extents by the occupancies of the X, Y, and Z cation sites in the tourmaline structure. The octahedral Y site occupancy strongly influences the pyroelectric coefficient due to the preference of Fe for this site. This work further suggests that the addition of Fe and Mg cations to the smaller Z octahedral site causes the pyroelectric coefficient to increase. However, because an extended suite of samples is not available in which the Z site contains ions other than AI, this proposed trend has not been experimentally determined. The chemistry of the ninefold coordinated X site and the population of this site do not influence the pyroelectric coefficients of tourmaline. INTRODUCTION Tourmalines are naturally occurring minerals with the general formula XY3Z6 (B03)3Si6018 (O,OH,F)4' where usually X = Na, Ca, or a vacancy, Y = AI, Li, Fe2+, FeH, and many other cations, and Z = AI, Mg, and FeH. It has been known for centuries (Dietrich, 1985) that tourmaline crystals are pyroelectric materials that develop an electrostatic charge when heated or cooled. Careful measurements of the combined primary and secondary pyroelectric effects in these minerals were first reported by Ackermann (1915). The results of that work showed that tourmaline exhibits pyroelectricity over a wide temperature range. Tourmaline is stable to high temperatures and may find application as an infrared detector where ferroelectric materials such as LaTi03 fail (Hamid, 1980). Importantly, Ackermann's (1915) measurements show that differently colored tourmalines exhibit different degrees of pyroelectricity. For example, black varieties are the weakest whereas rose colored tourmalines are the most * Present address: CSIRO Division of Minerals, P.O. Box 124, Port Melbourne, Victoria 3207, Australia. ** Present address: BahnhofstraJ3e lOa, 86551 Aichach, Germany. 0003-004X/95/0506-0491$02.00 strongly pyroelectric. Subsequent investigations support these observations and show that tourmaline pyroelectric coefficients (P'3)range between -1.8 and 5.4 ~C/(m2. K) at 296 K (Hayashi, 1912; Rontgen, 1914; Ackermann, 1915; Gladkii and Zheludev, 1965; Gavrilova, 1965; Fabel and Henish, 1971; Drozhdin et aI., 1975; Gavrilova et al. 1989; the present work). Related studies have shown that piezoelectricity, the inducement of an electric charge by an applied stress, is also stronger in translucent colored tourmalines than in certain opaque black varieties (Cady, 1946). None of these previous studies has addressed the variation in the pyroelectric coefficients with either the precise chemical composition or crystal chemistry of differently colored tourmalines. Tourmaline crystal chemistry is complex because the size and anion coordination of the X, Y, and Z cation sites are different. As a result many different cations can be accommodated in tour~ maline by coupled isomorphous substitution (e.g., Henry and Guidotti, 1985; Foit et aI., 1989; Burt, 1989). An indication of this complexity is given by the summary of natural and synthetic tourmaline end-members as well as by the references to their structural descriptions in Table 1. 491 -------..-....------ 492 HAWKINS TABLE 1. Tourmaline End-member end-member x ET AL.: PYROELECTRIC EFFECT IN TOURMALINE compositions y z First description Refined structure Natural end-members Buergerite Chromdravite Dravite Elbaite Feruvite Uddicoatite Povondraite* Schorl Tsilaisite" Uvite Na Na Na Na Ca Ca Na Na Na Ca Fe~+ Mg. Mg. (AI,U). Fe~+ (AI,U). F~+ F~+ (Mn,AI). Mg. AI. (Cr.AI) AI. AI. (AI,Mg). AI. F&.+ AI. AI. (AI.Mg) (Mg,AI) AI. Mason et al. (1964) Rumantseva (1983) Tschermak (1885) Vernadsky (1913) Grice and Robinson (1989) Dunn et al. (1977) Walenta and Dunn (1979) Mathesius (1564) Schmetzer and Bank (1984) Dunn (1977) Barton (1969) Nuber and Schmetzer (1979) Buerger et al. (1962) Donnay and Barton (1972) n.d. Nuber and Schmetzer (1981) Grice et al. (1993) Fortier and Donnay (1975) Nuber and Schmetzer (1984) Schmetzer et al. (1979) Synthetic end-members Alkali-defect dravite "Sodium aluminum" tourmalinet Na Rosenberg and Foit (1979) Rosenberg and Foit (1979) Rosenberg Rosenberg et al. (1986) et al. (1986) Note: n.d. = not determined. Povondraite was initially termed "ferridravite" (Walenta and Dunn, 1979) with Y. = Mg. before the formula was altered to Y. * = Fe'+ crystal structure refinement (Grice et aI., 1993). · following ** Tsilaisite = manganoan elbaite. t Also called aluminobuergerite (Foit, 1975) and olenite (Burt, 1989). Primary pyroelectricity describes the development of an electric voltage at the poles of certain noncentrosymmetric crystals, such as tourmaline (space group R3m), as temperature is changed. A permanent electric dipole or spontaneous polarization is inherent along the (00./) axis in tourmaline. As temperature is varied, the charge distribution in the structure shifts to produce a voltage along this axis. This voltage dissipates as atmospheric molecules are adsorbed onto the surface, so the crystal soon reverts to electrical neutrality. The primary pyroelectric coefficient is a vector property, isolated when the external electric field, applied stress, and applied strain on a crystal are constant or zero (Nye, 1957). However, thermal expansion in a crystal held under such conditions establishes a strain field. Thus, a component of the measured pyroelectric coefficient is caused by the piezoelectric effect. This component, known as secondary pyroelectricity, is important for this work, as it produces between 75 and 90% of the observed pyroelectric effect in tourmaline (Zheludev, 1971; Bhalla and Cross, 1981; Lang, 1974). It is impractical to prevent thermal expansion of a crystal by mechanical clamping. Thus, pyroelectric coefficients of tourmaline are measured parallel to the (00./) directions and the d33 piezoelectric tensor from unclamped crystals at constant stress (0). The measured pyroelectric coefficient (P3) is the sum of these primary and secondary coefficients. A nonuniform strain field caused by a temperature gradient produces tertiary pyroelectricity (Nye, 1957). This effect produces erratic data. Therefore, tertiary pyroelectricity must be avoided by maintaining uniform heat distribution in the material during experimental determination of pyroelectric coefficients. For this study, relationships between pyroelectricity and the chemistry of tourmaline are investigated for selected samples from -170 to - 500 K. From these data, the effects of chemical composition on the P3 variation in tourmalines are determined. These data complement previous studies, which correlated the crystal chemistry of tourmalines with other material properties such as color and refractive indices (e.g., Rossman et aI., 1991; Deer et al., 1992) and magnetic and mechanical properties (e.g., Donnay et aI., 1967; Tsang et aI., 1971; Dobrovol'skaya and Kuz'min, 1975; Helme and King, 1978; Tatli, 1980, 1985; Tatli and Ozkan, 1987). EXPERIMENTAL METHODS Preparation of single-crystal plates Pyroelectric coefficients were obtained from singlecrystal tourmaline plates with normals parallel to the (00./) crystallographic directions. Crystals detailed in Table 2 were aligned by back-reflection Laue diffractographs. The diffractographs showed the error in alignment, f) < 0.5°. This tolerance produces a 0.004% error between the measured pyroelectric coefficient (PO and the true coefficient (P3) ofthe plate, by the following equation: P1 - P1 P1' = (l - cos f). (I) This equation is derived from Figure I, which schematically illustrates the relationship between coefficient vec300 and 900 ILm thick tors and a plate surface. Plates were sliced from the crystal and then polished with flatness and parallelism within a :t 1O-lLm tolerance (Hawkins, 1993). Translucent polished plates were examined with the petrographic microscope to select crystal volumes suitable for pyroelectric measurement. Material with cracks or color zoning was rejected. Regions with uniaxial conoscopic images were cut from these larger plates to form test plates for pyroelectric measurements, since biaxial fringes are evidence for internal strain or chemical zoning - HAWKINS TABLE2. ET AL.: PYROELECTRIC EFFECT IN TOURMALINE 493 Tourmaline mineral samples Sample Color and «00./) axis length, basal dial (em) S1b S3a S8 S19 S21 S32 S33a S35 S36 S37 S40 S41 S42 S43 S49 S50 dark green (3.5, 0.5) black (3.0, 0.9) green-blue (1.0, 0.7) black (0.5, 2.0) black (3.8, 1.4) dark green (2.5, 1.0) black (1.2, 0.9) dark blue (1.5, 0.7) pale aqua (1.5, 1.3) dark blue (1.5, 1.0) mauve (1.0, 2.5) black (1.0, 3.5) dark olive (0.5, 5.0) pale green (2.0, 0.5) black (3.0, 1 .0) black (5.1, 1.5) Provenance Maine, U.S.A. Harts Range, Australia Minas Gerais, Brazil Ratnapura, Sri Lanka Pakistan Brazil Rollstone Hill, U.S.A. Hindu Kush, Afghanistan Plumbago Mine, U.S.A. Usakos, Namibia Plumbago Mine, U.S.A. Tourmaline Queen, U.S.A. Madagascar Himalaya Mine, U.S.A. Black Jack, Australia unknown Museum catalogue no. S.K. Dobos S.K. Dobos Daddow's Rock Shop Smithsonian B14657 QGRS Harvard H#91844 Harvard (no cat. no.) AMNH 41859 AMNH 40730 AMNH 24116 AMNH 40732 AMNH 46244 Gemological Inst Gemologicallnst Australian D14988 D.J. Henry Note: tourmaline samples were loaned and donated from the following sources: S.K. Dobos, Department of Earth Sciences, University of Queensland, Brisbane, Australia; Daddow's Rock Shop, Stanley Street, Woolloongabba, Brisbane, Queensland, Australia; Quality Gem Rough Supplies (QGRS), P.O. Box 129, Kyneton, Victoria, Australia; D.J. Henry, Department of Geology and Geophysics, Louisiana State University, Baton Rouge, Louisiana 70803-4101, U.S.A.; Harvard University Mineralogical Museum, 24 Oxford Street, Cambridge, Massachusetts 02138, U.S.A.; American Museum of Natural History (AMNH), Central Park West at Seventy-ninth Street, New York, New York 10024-5192, U.S.A.; National Museum of Natural History, Smithsonian Institution, Washington, DC 20560, U.S.A.; Gemological Institute, 1660 Stewart Street, Santa Monica, California 90404, U.S.A.; and the Australian Museum, 6-8 College Street, Sydney, New South Wales 2000, Australia. (Foord and Mills, 1978). These flaws may produce tertiary pyroelectric effects. For plates containing no volumes of uniaxial structure, volumes of low biaxial distortion were selected. Test plates were cut from the opaque schod without petrographic examination. These schod samples (S3a, S21, and S49) have highly mosaic structures, as shown by neutron-rocking curves across individual Bragg reflections (Hawkins, 1993). Surface areas of opaque and densely colored plates were measured from images captured with a Panasonic WVBL600 video-rate CCD camera fitted with a Canon 50 mm macro lens and extender tube. The captured images were analyzed with the MD30-plus Image Analysis System on an IBM-PC 386. Conversely, the S36 plate did not provide sufficient contrast for image analysis. The surface area for this plate was obtained from its density measured by heavy liquids and its thickness and mass. Pyroelectric coefficient measurement Pyroelectric coefficients were measured by an electronic circuit (Schneeberger, 1992) built after Byer and Roundy (1972). A Au film electrode was evaporated onto both faces of each plate of surface area A and then mounted on a heating element and cooled to -170 K. The temperature was increased at a constant rate (dT/dt) between ::t2 and ::t6 Klmin to 500 K and then decreased at a constant rate. The varying pyroelectric current (I) measured at 100 points during each increasing and decreasing temperature ramp was used to calculate the pyroelectric coefficient at each temperature, P'3 (T), by the following equation (Byer and Roundy, 1972): I pj (T) = A(dT/dt)' The measurements (2) were repeated for each plate with dif- ferent heating rates. At least two plates from each tourmaline specimen were measured to check for reproducibility. Electron probe microanalysis and structural formulae The tourmaline plates were coated with a 200 A C film. Chemical analyses were collected using a JEOL JXA8800L automated electron microprobe with four wavelength dispersive spectrometers. Thirteen elements were calibrated against the following primary standards: Si02, spessartine garnet; Ti02, Ti02; Al203, spessartine garnet; Cr203, chromite; FeO, hematite; MnO, spessartine garnet; NiO, synthetic Ni2SO.; ZnO, ZnS; MgO, MgO; CaO, wollastonite; Na20, albite; K20, orthoclase; F, MgF2. Secondary standards were analyzed prior to each session. Line scans were made approximately normal to each other across each plate with a 15-kV, 15-nA beam. Analyses were taken at 100 or 200 Jim intervals. These intervals are broad compared with the fine, 1-3 Jim zonation features in some tourmalines (e.g., Grice and Robinson, 1989; Cavarretta and Puxeddu, 1990; Henry and Du- Fig. I. Geometric relationship between the true (P,) and measured (PJ') pyroelectric coefficients and the surface of a crystal plate. -- HAWKINS 494 TABLE3. Sample SiO, TiO, AI,O, Cr,O, FeO MnO NiO ZnO MgO CaO Na,O K,O F -F= 0 Total Si B Na Ca K ~Xsite Ti AI Cr Fe Mn Ni Zn Mg Li* ~Ysite AI Mg Fe ~Zsite F OH Average ET AL.: PYROELECTRIC EFFECT of the pyroelectric IN TOURMALINE compositions and structural S1b S3a S8 S19 S21 S32 S33a S35 37.32(50) 0.18(5) 36.32(34) 0.01(2) 3.59(24) 0.98(8) 0.01(2) 0.04(4) 0.19(3) 2.11(3) 1.73(14) 0.02(1) 1.29(29) -0.54 83.25(70) 35.04(41) 0.63(7) 31.06(26) 0.01(2) 14.29(15) 0.59(4) 0.02(3) 0.08(5) 1.98(12) 0.46(5) 2.28(7) 0.07(1) 0.59(5) -0.25 86.86(58) 37.04(42) 0.01(2) 37.47(29) 0.01(2) 2.40(7) 1.41(5) 0.01(2) 1.88(7) 0.00(1) 0.04(2) 2.08(11) 0.01(1) 0.51(15) -0.21 82.64(65) 36.12(58) 1.18(20) 27.13(35) 0.08(4) 0.83(12) 0.01(2) 0.01(3) 0.03(4) 13.76(30) 3.94(50) 0.85(8) 0.01(1) 0.70(10) -0.29 84.34(96) 35.16(44) 0.60(13) 32.67(16) 0.01(1) 11.07(70) 0.45(3) 0.01(2) 0.41(7) 2.23(56) 0.11(2) 2.04(8) 0.04(1) 0.44(13) -0.19 85.31 (77) 37.04(55) 0.27(4) 35.74(29) 0.01(1) 5.98(13) 0.34(4) 0.01(1) 0.05(5) 1.10(6) 0.11(2) 2.58(8) 0.03(1) 1.33(24) -0.21 84.4(1.1) 35.12(47) 0.80(21 ) 32.88(60) 0.01(1) 11.41(19) 0.15(2) 0.01(2) 0.07(4) 3.30(27) 0.52(16) 1.98(12) 0.05(1) 0.46(14) -0.19 86.58(88) 37.74(84) 0.02(2) 36.61 (58) 0.01(1) 6.74(16) 0.52(4) 0.01(1) 0.09(4) 0.10(1) 0.12(2) 2.69(11) 0.03(1 ) 1.15(8) -0.48 85.3(1.3) 6.00 3.00 0.54 0.36 0.00 0.90 0.02 0.88 0.00 0.48 0.13 0.00 0.00 0.05 (1.44) 1.56 6.00 0.00 0.00 6.00 0.66 3.11 6.00 3.00 0.76 0.08 0.02 0.86 0.08 0.37 0.00 1.95 0.09 0.00 0.01 0.51 6.00 3.00 0.65 0.01 0.00 0.66 0.00 1.15 0.00 0.33 0.19 0.00 0.22 0.00 (1.11) 1.89 6.00 0.00 0.00 6.00 0.26 3.45 6.00 3.00 0.67 0.02 0.01 0.70 0.08 0.57 0.00 1.58 0.07 0.00 0.05 0.57 (0.08) 2.92 6.00 0.00 0.00 6.00 0.24 3.62 6.00 3.00 0.81 0.02 0.01 0.84 0.03 0.82 0.00 0.81 0.05 0.00 0.01 0.27 (1.01) 1.99 6.00 0.00 0.00 6.00 0.68 3.32 6.00 3.00 0.66 0.10 0.01 0.77 0.10 0.62 0.00 1.63 0.02 0.00 0.01 0.84 6.00 3.00 0.83 0.02 0.01 0.85 0.00 0.86 0.00 0.90 0.07 0.00 0.01 0.02 (1.14) 1.86 6.00 0.00 0.00 6.00 0.58 3.50 3.01 5.90 0.00 0.10 6.00 0.32 3.48 formulae -- Ions per formula unit 6.00 3.00 0.27 0.70 0.00 0.97 0.15 0.00 0.01 0.12 0.00 0.00 0.00 2.72 3.00 5.31 0.69 0.00 6.00 0.37 3.38 test plates 3.22 6.00 0.00 0.00 6.00 0.25 3.50 Note: n.a. = not analyzed. Values in parentheses are 1 esd of the microprobe traverse analyses. * Li ions pfu are the difference from full Y site occupancy. trow, 1992). The intervals used in this work allowed each plate to be investigated within the constraints of instrument time, yet gave sufficient data to obtain an average composition with estimated standard deviations (esd) representative of chemical variation across the plates. Structural formulae were normalized to six Si atoms per formula unit. The assumptions for cation site assignments are similar to those summarized by Rosenberg and Foit (1979). B is assumed to be present in stoichiometric amounts. Na, Ca, and K are assigned to the [91X site. Multivalent cations are assumed to be in the oxidation states Fe2+, Mn2+, and Ti4+. Al is assigned to the [6JY smaller [6JZsite and excess Al is assigned to the larger site. All remaining cations are assigned to the Y site. If there is a deficiency of Al, the smaller cations such as Mg and excess Fe2+ (in lieu of FeH) are assigned to the Z site, using crystal ion radii (Shannon, 1976) as a guide. No attempt is made to partition the same ion between both octahedral sites. An exception is the S3a schod in which Fe is partitioned between the Y and Z sites, using the ratio derived from M6ssbauer studies and refined during single-crystal X-ray structure determination (Hawkins, 1993). Some Y site vacancies are present when these criteria are followed. However, structural refinement has shown that Y site vacancies are unlikely in tourmaline (Donnay and Barton, 1972; Foit and Rosenberg, 1971; Rosenberg and Foit, 1979; Hawkins, 1993). Therefore, Y site vacancies are filled by Li ifthe mineral has a lithia-rich provenance, i.e., if it contains elbaite or liddicoatite components. The number of H ions is estimated from bond valence sums (Brese and O'Keeffe, 1991). RESULTS Test plate quality Chemical variation within the tourmaline test plates may affect their suitability for electrical measurements. Thus, two statistical tests were applied to the sets of traverse analyses to assess (1) whether there is chemical zonation within the plates and (2) whether two or more plates from the same crystal have the same average chemistry. First, the variation in concentrations along a traverse was compared with the counting statistics for each element. For this study, microprobe traverses do not show zoning at a 95% confidence level if the relative variation HAWKINS ET AL.: PYROELECTRIC EFFECT 495 IN TOURMALINE TABLE 3.-Continued 8ample 8i02 Ti02 AI203 Cr203 FeO MnO NiO ZnO MgO CaO Na20 K20 F -F=O Total 8i B Na Ca K 2: X site Ti AI Cr Fe Mn Ni Zn Mg U* 1: Y site AI Mg Fe 2: Z site F OH 836 837 840 841 842 843 849 850 38.83(26) 0.01(1) 38.32(23) 0.01(1) 2.13(21) 0.57(5) 0.01(1) 0.13(3) 0.02(1) 0.52(8) 2.18(5) 0.02(1) 0.92(6) -0.39 83.29(47) 37.68(33) 0.01(2) 36.98(38) 0.01(2) 4.84(22) 0.80(5) 0.01(2) 0.27(10) 0.03(2) 0.32(3) 2.59(7) 0.02(1) 1.13(7) -0.47 84.21(60) 39.45(76) 0.01(1) 40.39(26) 0.01(2) 0.01(1) 0.18(4) 0.01(2) 0.02(4) 0.00(1) 0.49(5) 1.65(11) 0.01(1) n.a. 34.7(1.0) 0.03(4) 35.77(25) 0.01(2) 8.84(18) 1.72(8) 0.01(3) 0.89(15) 0.05(2) 0.03(2) 1.93(9) 0.03(2) 0.49(16) -0.21 84.3(1.0) 37.87(61) 0.07(4) 38.36(63) 0.01(2) 2.29(14) 0.34(6) 0.01(3) 0.06(7) 0.03(2) 0.44(13) 2.13(10) 0.02(2) 0.87(24) -0.37 82.1(1.0) 38.18(15) 0.03(2) 38.61(24) 0.01(1) 0.79(6) 0.77(4) 0.01(2) 0.05(4) 0.01(1) 1.48(8) 1.69(4) 0.01(1) 1.10(6) -0.46 82.27(32) 35.39(80) 0.41 (23) 33.2(1.0) 0.01(2) 14.04(94) 0.16(5) 0.01(2) 0.07(8) 0.63(11 ) 0.10(6) 1.77(20) 0.04(2) 0.46(20) -0.43 86.1(1.4) 36.91(48) 0.02(2) 35.49(56) 0.01(3) 8.32(22) 0.31(4) 0.01(2) 0.20(6) 0.11(2) 0.06(2) 2.66(9) 0.03(1) 1.60(28) -0.67 85.05(73) 6.00 3.00 0.65 0.09 0.00 0.74 0.00 0.98 0.00 0.28 0.07 0.00 0.01 0.00 (1.66) 1.34 6.00 0.00 0.00 6.00 0.45 3.40 6.00 3.00 0.80 0.05 0.00 0.85 0.00 0.94 0.00 0.64 0.11 0.00 0.03 0.01 (1.28) 1.72 6.00 0.00 0.00 6.00 0.57 3.53 6.00 3.00 0.51 0.25 0.00 0.76 0.00 1.15 0.00 0.10 0.10 0.00 0.01 0.00 (1.64) 1.36 6.00 0.00 0.00 6.00 0.55 3.31 6.00 3.00 0.58 0.02 0.01 0.61 0.05 0.64 0.00 1.99 0.02 0.00 0.01 0.16 (0.13) 2.87 6.00 0.00 0.00 6.00 0.25 3.62 6.00 3.00 0.84 0.01 0.01 0.86 0.00 0.80 0.00 1.13 0.04 0.00 0.02 0.03 (0.98) 2.02 6.00 0.00 0.00 6.00 0.82 3.22 82.2(1.2) 6.00 3.00 0.49 0.08 0.00 0.57 0.00 1.24 0.00 0.00 0.02 0.00 0.00 0.00 (1.74) 1.26 6.00 0.00 0.00 6.00 n.a. 3.88-F Ions per formula unit 6.00 6.00 3.00 3.00 0.65 0.65 0.01 0.07 0.01 0.00 0.67 0.72 0.00 0.01 1.28 1.16 0.00 0.00 1.28 0.30 0.25 0.05 0.00 0.00 0.11 0.01 0.01 0.01 (0.08) (1.46) 2.92 1.54 6.00 6.00 0.00 0.00 0.00 0.00 6.00 6.00 0.27 0.44 3.62 3.38 in concentration for each element does not exceed twice the relative variation in counting statistics. By this criterion, all plates except S40 and S43 showed zoning in some elements. , Second, differences between the average chemical compositions of plates cut from the same tourmaline specimen were determined for each element within a 95% confidence interval by a Student t-test (Walpole and Myers, 1978). In most cases, the compositions of all elements were consistent between plates. Thus, the analyses shown in Table 3 are the averages of microprobe traverses within these confidence limits for each sample. Pyroelectricity vs. temperaturecurves In this temperature range, the pyroelectric response for tourmaline is a convex curve, as illustrated in Figure 2. Curves for the repeated temperature cycles and for several plates from the same crystal were fitted with a quadratic function. The error in P'3shown in Table 4 is calculated from the spread of the data from the fitted function (Schneeberger, 1992). In most cases, plates from the same specimen gave the same curve within these error margins. Thus, the dimensional tolerances, chemical zonation, and flaws in these tourmaline plates were ac- ------ ceptable for reproducible measurement of P'3.Repeat data collected from the same crystal were added to form the quadratic functions for P'3vs. T given in Table 4. The Sib and S41 samples are exceptions to the reproducibility generally observed within samples. The two Sib samples gave consistently different intersecting curves, as shown by the equations in Table 4. An explanation for these differences is not obvious because both plates are of similar quality. Thus, SIb results are omitted from further analysis. Similarly, one S41 plate was omitted from the average curve for this sample because it produced pyro10% higher electric coefficients that were consistently than those for three other S41 plates. This difference may be attributed to inaccurate surface-area measurement of one plate. The low-temperature form of the pyroelectric response curve is shown in Figure 2. The lowest temperature obtained in this work was limited by the liquid N2 coolant, and so the polarity inversion in tourmaline P'3 at <20 K (e.g., Drozhdin et ai., 1975; Gavrilova et ai., 1989) was not detected. The high-temperature region of the curve adopts one of two forms. First, there is an upward inflection of the curve shown in Figure 2. This behavior has been noted - ~- 496 HAWKINS ET AL.: PYROELECTRIC 10 Second, a smooth decrease in the pyroelectric coefficient was observed in the schor! S33a plate above ",430 K. This behavior, which is probably caused by the onset of electrical conductivity, has not been previously reported in tourmaline. Such conductivity is different from the electric current generated in the external circuit from the pyroelectric voltage. This tourmaline is omitted from further analysis because it produced an anomalously low Pj. This problem arose from a difficulty in the accurate determination of surface area because of chipped edges. Further upper temperature limits were encountered with S21, S32, and S41 plates, as shown in Table 4. The signals from these plates contained high levels of electronic noise at higher temperatures. 8 Q' ~6 5 u 3- 4 tJ .., ~2 0 0 200 400 Temperature (K) 600 800 Fig. 2. The general form of the pyroelectric response with temperature change for tourmaline. The approximate temperature range for the present measurements is between T, and T2. A low-temperature polarity inversion is shown at <20 K (after Gavrilova et ai., 1989). for only a pale rose sample above 450 K (Ackermann, 1915; Gavrilova et aI., 1983, 1989). However, this type of behavior was observed during one experiment of the Sl b/5 plate above -420 K and for both S49 plates above 400 K. A similar inflection has been predicted for the thermal expansion vs. temperature relationship in other minerals. For example, strong anharmonic thermal vibration above 1300 K in forsterite produces an upward inflection of the calculated thermal expansion coefficient curve (Reynard et aI., 1992). Thermal expansion causes the secondary pyroelectric effect, which is a strong effect in tourmaline. Thus, this region of the curve in Figure 2 may reflect the effects of anharmonic vibration on pyroelectricity. These results indicate that the onset of pyroelectricity that is caused by anharmonic vibration of ions in the structure and high thermal expansion may occur at a lower temperature in Slb/5 and S49 than in other tourmalines. Empirical equations for the temperature Pyroelectric equations * -0.2379 4.379 + 1.732 x 10-2TX 10-2 coefficient variation with bulk chemistry Clearly, tourmaline bulk chemistry determines the pyroelectric response of this mineral. To investigate trends between the pyroelectric coefficients and chemistry, pyroelectric coefficients were calculated from equations for 14 samples in Table 4 at two temperatures. Low-temperature behavior is represented by data at 193 K. Although 500 K, some plates most samples were measured to gave erratic responses above -400 K. Therefore, higher temperatures are represented by data at 383 K, so all 14 samples could be included in the data set. The variations in tourmaline pyroelectric coefficients with bulk chemistry are shown by the graphs in Figure 3. FeO. The linear decrease in pyroelectric coefficient with increase in Fe content (as wt% FeO), shown in Figure 3a, is the most important result. The data at 193 and 383 K are strongly linear, as the linear least-squares correlation coefficient r is -0.9 in both cases. This high correlation is statistically significant, since the random probability for 14 data points with a correlation coefficient between 0.85 and 0.90 is <0.1% (Taylor, 1982). The higher temperature data are more strongly linear, and the slope of this line is higher than for the 193 K data. Thus, an increase in Fe content has a stronger influence on tourmaline py- of p~ p; ["C/(m2.K)] 8ample 81b/5* 81b/6* 83a 88 819 821 832 833a* 835 836 837 840 841 842 843 849 850 dependence Pyroelectric - - TABLE4. EFFECT IN TOURMALINE 9.54 x 10-oP + 1.178 x 10-2T - 8.133 x 10-oP -0.3686 + 1.112 x 10-q - 4.259 x 10-oP -0.979 + 2.194 x 10-2T-1.873 x 10-'P -0.8659 + 1.97 x 10-2T1.652 x 10-'P -2.661 + 2.849 x 10-2T - 3.170 x 10-'P -1.588 + 2.257 x 10-Q1.976 x 10-'P -0.6975 + 1.056 x 10-Q6.903 x 10-oP -1.88 + 2.308 x 10-2T - 1.976 x 10-'P -1.19 + 2.33 x 10-2T1.987 x 10-'P -1.310 + 2.024 x 10-2T1.578 x 10-'P -0.4096 + 1.816 x 10-Q1.226 x 10-'P -0.8918 + 1.950 x 10-2T1.620 x 10-'P -0.9894 + 1.979 x 10-2T1.465 x 10-'P -0.7167 + 2.246 x 10-2T - 1.883 x 10-'P -0.9472 + 1.500 x 10-2T - 9.123 x 10-oP -1.585 + 1.954 x 10-2T1.566 x 10-'P Error 0.10 0.10 0.17 0.07 0.20 0.15 0.22 0.15 0.07 0.11 0.10 0.10 0.16 0.07 0.14 0.10 0.06 from these samples are not included in the anlaysis of p; variation with chemistry. T range (K) 170-423 170-500 170-500 170-500 170-500 170-463 170-483 170-433 170-500 170-500 170-500 170-500 170-443 170-500 170-500 170-403 170-500 HAWKINS ET AL.: PYROELECTRIC roelectricity at higher temperature. This effect could be caused by an increase in electrical conduction of Fe-rich tourmaline at elevated temperatures and is consistent with the proposed onset of electrical conductivity in schor!. The pj may approach a plateau for the Fe-rich tourmalines S3a, S21, and S49, as indicated by the term 'schor!' in Figure 3a. This small invariant region is more evident at low temperature. SiOz. The pj variation with SiOz content is linear, as shown in Figure 3b. However, this variation results from the heavy element content such as Fe, since there is only minor substitution for Si in tourmaline (e.g., Walenta and Dunn, 1979; Henry and Guidotti, 1985; Gallagher, 1988). An inverse proportionality between weight percent SiOz and weight percent FeO is seen by comparison of Figure 3a and 3b. MnOz. A weak linear relationship between pj and weight percent MnOz is shown in Figure 3c. Alz03. There are two regions denoted by 1 and 2 in circles in Figure 3d. In the AI-rich region (1), pj increases with Alz03 concentration. This region is detailed in Figure 3e. A minimum pj value corresponding to the schor! samples S3a, S21, and S49 identified in the FeO relationship in Figure 3a occurs around 31-33 wt% A1Z03. The data in this minimum region fit the linear relationship shown in Figure 3e without degrading the correlation coefficient. Therefore, the data points at this minimum are included in region 1. However, r may appear artificially high because the data set is small. With further depletion of Al from tourmaline, the pyroelectric coefficient increases again (Fig. 3d, region 2). The data point shown near 27 wt% Alz03 represents the Sl9 uvite-dravite, supporting the data in Figure 3f and indicating that incorporation oflarge amounts ofMg in the tourmaline lattice increases pj. MgO. There is a discontinuity in data between 3 wt% MgO and the S 19 uvite-dravite at 14 wt% MgO in Figure 3f. At MgO concentrations below the sharp inflection around 0.10-0.50 wt% MgO, the relationship between pj and weight percent MgO is strongly linear, despite the large composition error bars (Fig. 3g). However, a paucity of suitable dravite or uvite tourmalines prevented detailed investigation of the effect of Mg incorporation on the pyroelectric coefficients. ZnO, NazO, CaO, and F. Zn, F, and the X-site cations do not significantly affect the pyroelectric coefficients. Zno content vs. pj displays a very weak inflection around 0.10.5 wt% ZnO in a trend similar to that of MgO vs. Pj. There is a weak correlation between NazO and pj, as shown in Figure 3h. - DISCUSSION Pyroelectric coefficients of Fe-containing 497 EFFECT IN TOURMALINE b) SiO, a) FeO 6.00 ~ 5.00 ~.f...+, ; i? 4.00 I ~ 3.00 1J)(f) i;P-~ h...!.. .+ M.g ".:' 2.00 [illKJ 2 4 6 8 WIll.FeO ~..~ $- _ o 10 12 14 16 33 I 5.00 ~ b + 1 ... ~ I 3.00 +t + + :f.. 37 wt% Si02 41 39 $ e .:' + +......- t [§KJ e...~ ~CD ~++ G) + e ([).:~~..E!j 2.00 35 -@- e~ -:--r' d) AI,O, c) MnO 6.00 Mi?4.00 E *-"- ~ GJ 1.00 0.00 , GJ$0..... e '. '$ + ..-~ -+-~I" ~- e e.$. e $41 41B- -e- 1.00 0.00 6.00 0.0 e) 0.5 1.0 wt%MnO ¥ 4.00 '" ME wt% A1203 f) MaO I§] t I I +....t...:-::..- 2.00 e ..~~...-$ ([) ..~...1:(ffr E! l$~ [!§ 30 32 34 36 WIll. 38 40 42 2 0 A'zDJ 6.00 g) MgO low concentration 5.00 §]-t-- br£' ill -r " 1.00 0.00 28 30 32 34 36 38 40 42 __ + . -t"~_...'+ ....+~."'+- ~3.00 §] ".:: 2.0 26 AI"O'1 high concentration I383K I 5.00 1.5 -+--+'-'1 ~ 2.00 '1" h) + -+'" +-:c 3- --+- + + ~ -$- i!... 10 12 14 Na,O +.. .....__ 4 6 8 WIll. MgD .$.h..d - *"- $-~ -<17--6)- -6)- '€r 1.00 0.00 0.00 0.05 wIll.MgD 0.10 0.15 0.5 1.0 1.5 2.0 wIll.N'zD 2.5 3.0 Fig. 3. Relationships between P'3 and the bulk chemistry of tourmaline. Error bars are :t 1 esd for chemical composition (Table 3) and P'3 (Table 4). Equations have the form p, = A + Bx, where x is the weight percent oxide; and r is the correlation coefficient of the linear least-squares fit of the line to the data. (a) FeO 193 K: A = 2.59, B = -0.08, r = -0.86; 383 K: A = 4.79, B = -0.10, r = -0.90. (b) SiOz 193 K: A = -4.51, B = 0.18, r = 0.61; 383 K: A = -5.91, B = 0.27, r = 0.73. (c) MnO 193 K: A = 1.99, B = 0.25, r = 0.27; 383 K: A = 4.02, B = 0.28, r = 0.24. (d) Alz03. (e) Alz03 193 K: A = - 2.99, B = 0.14, r = 0.83; 383 K: A = -2.94, B = 0.20, r = 0.90. (f) MgO. (g) MgO 193 K: A = 2.65, B = -9.14, r = -0.88; 383 K: A = 4.81, B = -9.92, r = -0.86. (h) NazO 193 K: A = 2.94, B = -0.39, r = -0.44; 383 K: A = 4.84, B = -0.31, r = -0.28. tourmalines These data form a basis for the prediction of tourmaline pyroelectric coefficients directly from electron microprobe FeO analyses. All tourmaline compositions studied conform to the linear relationship between weight percent FeO and pj shown in Figure 3a. Fe-rich tourmalines are often shown in this study to be black or darkly colored. Thus, this relationship supports the general observation (e.g., Dietrich, 1985) that black tourmalines exhibit weaker pyroelectric behavior than pale colored tourmalines. However, the S19 uvite-dravite is Fe-poor and has a cor- ------.- 498 HAWKINS TABLE5. ET AL.: PYROELECTRIC EFFECT IN TOURMALINE Predicted pyroelectric coefficients PO [ILC/(m2.K)] and errors for selected tourmaline end-member compositions p~ at p~ 193 K at 193 K (Fig. 4) (Eq. 3) Endmember Tourmaline (FeO = 0%) Schorl (FeO = 20.46%) Uvite Elbaite Aluminobuergerite 2.59(0.50) 1.02(0.56) p~ at 296 K (Eq.4) p~ at 383 K (Eq.5) 3.95(0.51 ) 2.03(0.57) 4.79(0.52) 2.68(0.58) 6.00 5.00 Q '"'5 4.00 ., ~3.00 I:> Fe-free tourmalines 2.45 3.08 5.75 elbaile Na(All.SLi1.5)AI6 uvite CaMg3(AlsMg) o 519 "2.00 o aluminobuergerite NaAl3 Al6 1.00 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 AI ions per formula unit respondingly high P'3 value, despite the dark brown or black color. Therefore, these results confirm that color, which has been used previously to characterize tourmalines, is not as reliable as chemistry for the prediction of the pyroelectric coefficients. Predictive equations between the P'3 and FeO content at three temperatures were devised by simple regression analysis, with weight percent oxide as the independent variable and P'3 as the dependent variable. These equations include the following: at 193 K pj = 2.594 - O.077(wt% FeO) ILC/(m2. K) at 296 K pj = 3.949 - 0.094(wt% FeO) 1LC/(m2.K) at 383 K pj (3) (4) = 4.791 - 0.103(wt% FeO) ILC/(m2. K). (5) Pyroelectric coefficients and errors calculated at 193, 296, and 383 K for an ideal schod end-member containing 20.46% FeO (Dietrich, 1985) and a tourmaline with FeO = 0% are listed in Table 5. Pyroelectric coefficients predicted for tourmalines at 296 K are in good agreement with values for similar samples reported at ambient temperature. For example the P'3 value of 2.03(57) ILC/(m2. K) at 296 K for the schod agrees extremely well with the value of 2.2 1LC/(m2.K) for a black tourmaline (Gladkii and Zheludev, 1965). This black tourmaline is probably close to a schod in composition. Further, the P'3 of 4.4 ILC/(m2. K) at ambient temperature reported for pink tourmalines (Hayashi, 1912; Ackermann, 1915) is within the error of the value 3.95(51) 1LC/(m2'K) at 296 K predicted for Fe-free tourmaline. Pink tourmaline is usually an elbaite with minor Mn substitution. The errors in P'3predicted from Equations 3-5 are calculated as a 90% confidence interval based on a Student t-test (Walpole and Myers, 1978). These intervals are large percentage errors in P'3. Such errors may be reduced only by increasing the number of samples in the data set. However, it is very difficult to obtain tourmaline crystals of the quality required for this measurement technique. For Fig. 4. The number ys. p, at 193 K. of AI ions per tourmaline formula unit example, the 14 samples used in this analysis represent only 27% of the tourmaline crystals collected for this work (Hawkins, 1993). It is surprising that the correlation between weight percent FeO and P'3 is so high, despite the assumption that Fe is divalent for all tourmaline and that the effects of Fe partitioning between the Y and Z sites have not been taken into account. The strong effect of FeO concentration may obscure the effects of other ions on P'3. Thus, an investigation of the complex crystal chemical substitutions in tourmaline is used to show the dependence of the pyroelectric response on such ions. Cation substitution effects on the pyroelectric coefficient Y site. The relationship between the number of Al ions per formula unit (pfu) andp'3 is shown in Figure 4. Above 6.5 Al ions in region 1, P'3 increases with Fe removal by the schod-elbaite substitution on the Y crystallographic site: 2Fe~+ Li~ + AR+. This substitution corresponds "" to the dependence of P'3 on weight percent FeO. Therefore, the schod-elbaite substitution is probably the dominant mechanism for Fe removal to produce high P'3coefficients in AI-rich tourmalines. In these tourmalines, Z is usually fully occupied by AI. A similar linear increase in P'3 with increased Mn suggests that Fe is also removed by the Y site cation substitution: Fe?+ Mn~+. However, this cation exchange is "" not important for all tourmaline compositions studied, since the amount ofMn incorporated by this substitution is small, <2 wt% MnO. Further, the relationship is weak, as the linear-fit correlation coefficients for data at 193 and 383 K are -0.25, as shown in Figure 3c. At high Mg Mg~+ substitutions deplete Fe concentrations the Fe?+ "" then increases, as shown from the structure. The P'3value in Figure 3f. Around the minimum inflection of the weight percent AI203 vs. P'3 relationship in Figure 4, Fe removal frorr the Y site and substitutions for Al on the Z site occur HAWKINS ET AL.: PYROELECTRIC The effect of Al content on pj is probably a result of the substitution of AI for Y and Z site cations, particularly Fe. However, there may be properties of AI, Fe, and other ions that affect polarity in the structure and pyroelectric behavior. Z and X sites. The regions in Figure 4 that are low and intermediate in Al content, shown as region 2, indicate that a further set of cation substitutions may affect the pj values in these tourmalines. A line cannot be drawn from these data because there are insufficient data points. Thus, the data from samples S19, S3a, and S21 (labeled) are discussed individually. The low Al content of these tourmalines suggests that there are other cations on the Z site. For example, the S 19 uvite-dravite structural formula (given in Table 3) is depleted in AI. Thus, 0.69 Mg ions and 5.31 Al ions are incorporated in the Z site by the uvite substitution Nait + AH+-= Ca~++ Mgi+.Powder electron-spin resonance data collected at 130 K 499 EFFECT IN TOURMALINE uvite CaMg3(AlsMg) 1.00 0.0 0.5 1.0 1.5 2.0 2.5 Mg ions per fonnula unit 3.0 Fig. 5. The number of Mg ions per tourmaline YS.p, at 193 K. 3.5 4.0 formula unit ~ (Hawkins, 1993) indicate that there is also minor Fe3+ on the Z site of S19. In addition, the S3a schorl has been shown by M6ssbauer studies and population parameter refinement during least-squares structure analysis (Hawkins, 1993) to contain 0.10 Fe ions per six Z sites. This analysis suggests that a 13% substitution of Mg for Al and a 1.7% substitution of Fe for Al on the Z site in the S 19 uvite-dravite and S3a schorl, respectively, may strongly increase the pyroelectric coefficient. Other ions, for example Mn (Johnston and Duncan, 1975), partition to the tourmaline Z site. Thus, there are many possible Z site substitutions for Al that may affect Pj. Pyroelectric coefficients for Fe-free tourmaline There are several Fe-free end-members shown in Table 1. Pyroelectric coefficients of the elbaite [XY3Z6 = Na(AII.5Lil.5)AI6)' uvite [CaMg3(AI5Mg»), and aluminobuergerite (NaAI3AI6) end-members are shown by extrapolation in Figures 4 and 5. There are sufficient data for the schorl-elbaite substitution series in Figure 4 to extrapolate a value of pj for elbaite, which is included in the summary of pj values in Table 5. Similarly, the pj for uvite is extrapolated in region 2 of Figure 5, although there are fewer data points than in region 1. It may be difficult to obtain samples in this composition range with further work because there is a miscibility gap reported in the AI-Mg (elbaite-dravite) phase field for natural tourmalines (e.g., Donnay and Barton, 1972; Taylor and Slack, 1984; Henry and Guidotti, 1985; Cavarretta and Puxeddu, 1990; Kassoli-Foumaraki, 1990). The prediction of aluminobuergerite pyroelectric behavior from Figure 4 is justified only if the same linear trend continues from the schorl-elbaite region to higher AI compositions. It may be difficult to explore this relationship further using the present pyroelectric apparatus because large crystals are required. Aluminobuergerite is a synthetic end-member (Foit, 1975) produced when AI content on the Y site is increased by the liddicoatite, aluminobuergerite, and olenite substitutions (Henry and Guidotti, 1985; Burt, 1989). Only crystals < 1 mm in size ---...-- are produced by hydrothermal synthesis (e.g., Taylor and Terrell, 1967; Foit, 1975; Vorbach, 1989). ACKNOWLEDGMENTS This study could not have been completed without many beautiful tourmaline specimens that were made available by colleagues and friends. Steve Dobos and Darrell Henry kindly donated tourmalines from their own mineral collections. The curators of the Harvard University Mineralogical Museum, American Museum of Natural History, National Museum of Natural History (Smithsonian Institution), the Gemological Institute, and the Australian Museum kindly loaned crystals of line quality for this work. We (KD.H. and H.S.) thank L. Bohaty of the LudwigMaximilians-Universitiit (now at Universitat KOln, Germany), and S. Haussiihl ofUniversitiit KOln for many helpful discussions. Thanks to H. Schmid, Universite de Geneve, Switzerland, for helpful discussions that alerted us (KD.H.) to potential problems with biaxial crystals for pyroelectric measurement. The Australian Institute for Nuclear Science and Engineering (AINSE) supported KD.H. by means of a postgraduate studentship. REFERENCES CITED Ackermann, W. (1915) Beobachtungen iiber Pyroelektrizitiit in ihrer Abhangigkeit von der Temperatur. Annalen der Physik, 46, 197-220. Barton, R., Jr. (1969) Relinement of the crystal structure of buergerite and the absolute orientation of tourmalines. Acta Crystallographica, B25, 1524-1533. Bhalla, A.S., and Cross, L.E. (1981) Primary and secondary pyroelectricity in proper and improper ferroelectrics. Ferroelectrics, 38, 935-938. Brese, N.E., and O'Keeffe, M. (1991) Bond-valence parameters for solids. Acta Crystallographica, B4 7, 192-197. Buerger, M.J., Burnham, C.W., and Peacor, D.R. (1962) Assessment of the several structures proposed for tourmaline. 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