The Temperature–Dependence of the Volume Expansivity and the Thermal Expansion Tensor of Petalite Between 4.2 K and 600 K

Journal of Mineralogical and Petrological Sciences, J–STAGE Advance Publication, April 5, 2014

The temperature–dependence of the volume expansivity and the thermal expansion tensor of petalite between 4.2 K and 600 K

Kevin S. KNIGHT*,**

*ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Oxford, Didcot, Oxon. OX11 0QX, UK **Department of Earth Sciences, The Natural History Museum, Cromwell Road, London, SW7 5BD, UK

The temperature–dependence of the lattice parameters, unit cell volume and the thermal expansion tensor of petalite (LiAlSi4O10) have been determined from high resolution, time–of–flight powder neutron diffraction data collected at ninety temperatures between 4.2 K and 600 K. At low temperatures, after a short saturation interval, the unit cell volume decreases from 424.114(6) Å3 at 15 K, reaching a minimum of 423.470(6) Å3 at 219 K, before slowly increasing to 425.004(7) Å3 by 600 K. Petalite may be considered to be a further example of a low expansion material (defined as having a coefficient of linear thermal expansion of less than 2 × 10−6 K−1)in the well–studied Li2O–Al2O3–SiO2 system, however in this case, this technologically useful property is found to occur at low temperatures, in the interval 157 K to 298 K. From the temperature variation of the unit cell parameters, the eigenvalues (λii) and eigenvectors of the thermal expansion tensor have been calculated for the range 20 K to 600 K. The eigenvalue (λ22) associated with the unique monoclinic axis (b) is positive for all temperatures above saturation, ~ 50 K, and reaches a maximum value of 1.42 × 10−5 K−1 at 600 K. In the a–c plane, above the 20 K saturation temperatures, λ11 changes sign, negative to positive at 232 K, and λ33 is always found to be negative, but reducing in magnitude with increasing temperature. The orientation of λ11 is found to be approximately parallel to a, and λ33 is approximately parallel to c* at all temperatures. The 600 K thermal expansion coefficients associated with these two principal axes is of the order of four times smaller than that −6 −1 −6 −1 associated with λ22 (λ11: 3.2 × 10 K ; λ33: −3.4 × 10 K ). Between 20 K and 232 K, the thermal expansion tensor is therefore represented by a hyperboloid of two sheets, and above this temperature, the representation quadric changes to a hyperboloid of one sheet. The orientation of the principal axes in (010) is continuous through the change in the representation quadric, and only shows a small variation throughout the temperature interval 20 K to 600 K.

Keywords: Petalite, Thermal expansion, Neutron diffraction, Representation quadric

INTRODUCTION centred at a composition corresponding to β–eucryptite (LiAlSiO4; composition 1:1:2), the other, a more extend- The Li2O–Al2O3–SiO2 (LAS) system has been the subject ed compositional range β–spodumene solid solution, ex- of intensive study since the discovery by Hummel (1948) tends from silica–deficient spodumene, to silica–rich pet- of the technologically useful property of ultra–low linear alite (LiAlSi4O10; ideal composition 1:1:8). Technol- thermal expansion in β–spodumene (LiAlSi2O6; compo- ogical applications of glass–ceramics in the LAS system sition 1:1:4). Following on from this initial observation, are various, ranging from oven–to–table cookware, range the phase equilibria within the LAS system was subse- tops in kitchen stoves, telescope mirror blanks, laboratory quently investigated in great detail by Roy and co–work- bench tops to supersonic aircraft glazing (Strnad, 1986; ers (Roy and Osborne, 1949; Roy et al., 1950), and from Roy et al., 1989; Pannhorst, 1995), and commercially this ternary phase diagram, two regions of negative linear produced material can be found under the trade names thermal expansivity were identified by Smoke (1951) and Pyroceram, Cer–Vit, and Hercuvit. Hummel (1951). The first is a localized solid solution Crystallographically, both structure types identified with low, and negative thermal expansion may be con- doi:10.2465/jmps.130819Advance Publicationsidered as lithium stuffed Article derivatives of silica (Buerger, K.S. Knight, [email protected] Corresponding author 1954), with the lithium charge balancing the aluminium 2 K.S. Knight

Figure 1. The crystal structure of petalite (Effenberg- er, 1980), space group P2/a, a = 11.75 Å, b = 5.14 Å, c = 7.63 Å, β = 113.0° (LiO4, plain tetrahedra; AlO4, dashed line tetrahedra; Si1O4, criss–cross tetrahedra; Si2O4 cross–dashed tetrahedra). The bond angle Si1–O1–Si1 is 180° due to the point symme- try of the anion O1. The bond angle Si2–O2–Si2 is ~ 163°. effectively substituted for silicon. The β–spodumene solid n (Tavora, 1952), is now accepted as P2/a from X–ray, solution is isostructural to keatite (Li and Peacor, 1968), and neutron single crystal diffraction data (Zemann–Hed- while the eucryptite solid solution is isomorphous with lik and Zeman, 1955; Effenberger, 1980; Tagai et al., high quartz (Winkler, 1948). The structural basis for the 1980, Tagai et al., 1982). The crystal structure of petalite low and negative thermal expansion has been studied by was determined by Zemann–Hedlik and Zeman (1955) Ostertag et al. (1968) for the β–spodumene solid solution, using two–dimensional Fourier projections, and this and by Gillery and Bush (1959), Moya et al. (1974), structure has subsequently been confirmed, and refined, Schulz (1974), and Xu et al. (1999) for the β–eucryptite by Effenberger (1980) and Tagai et al. (1980, 1982). The phase. In addition, Nara et al. (1981) have presented a neutron diffraction investigation shows no evidence for phenomenological model for the commensurate – incom- Al/Si site disorder, and the effects of trace amounts of Ga mensurate phase transition in β–eucryptite. Both crystal and Fe (Černý and London, 1983) on the crystal structure structures consist of an infinite network of corner–sharing are unknown. The crystal structure of petalite is illustrat- tetrahedra, and the thermal expansion behaviour can be ed in Figure 1 and can be seen to consist of tilted SiO4 rationalised in terms of low frequency rigid–unit modes tetrahedra in Si4O10 layers that are inter–linked by alter- that change the relative orientation of the tetrahedral nating LiO4 and AlO4 tetrahedra that share an edge (Ef- groups resulting in either 3–D, or 2–D thermal contrac- fenberger et al., 1991). The revision of the crystal struc- tion. It should be noted, however, that all the low thermal ture proposed by Liebau (1961), that retained the expansion results obtained in the LAS system have been polyhedral topology, but lowered the space group sym- derived from ceramic materials that have undergone irre- metry from P2/a to Pa to avoid an unfavourable 180° Si– versible structural phase transitions due to prior process- O–Si bond angle (see Fig. 1), was shown by Effenberger ing at high temperatures, and hence these results do not (1980) to be inconsistent with the single crystal X–ray represent the intrinsic thermal expansion behaviour of the diffraction data and physical property measurements. thermodynamically stable room temperature and pressure In the work to be reported here, we have studied the phases. The structural crystallography of petalite under temperature variation of the monoclinic unit cell of the ambient conditions has been the subject of a number of mineral phase petalite between 4.2 and 600 K. The results single crystal studies (Goßner and Mußgnug, 1930; Ta- of these measurements compliment the recent detailed vora, 1952, Zemann–Hedlik and Zeman, 1955; Liebau, and careful, experimental studies of the temperature–de- 1961; Effenberger, 1980; Tagai et al., 1980, Tagai et pendence of the elastic stiffness coefficients of petalite al., 1982), and the crystal structures of the protium (HAl made by Haussühl et al. (2012) over a similar range of Si4O10), and deuterium (DAlSi4O10) ion exchanged ana- temperature. logues have been studied by powder neutron diffraction at 5 K and 295 K (Effenberger et al., 1991). The space EXPERIMENTAL group ofAdvance petalite, initially determined as CPublication2/c (Goßner Article and Mußgnug, 1930), and subsequently revised as P21/ High resolution powder neutron diffraction data were col- Low temperature thermal expansion of petalite 3 lected using the time–of–flight diffractometer HRPD on the ISIS neutron spallation source of the Rutherford Ap- pleton Laboratory, UK. Data were collected in the time– of–flight range 50–150 ms that corresponds to a diffraction pattern with a d–spacing range of 1–3 Å in the high resolution backscattering detector bank. Approximately 4 cm3 of petalite powder were contained in a sample can of slab geometry (Knight and Price, 2008) and cooled to 4.2 K in a helium cryostat. Data were collected at 4.2 K, 10 K, and in 5 K steps to 300 K for a total of 5 µAh, there- after in 10 K intervals to 600 K for 10 µAh. An equili- bration period of 5 minutes was taken for each data collection, once the set point temperature had been achieved. The sample temperature was measured using a Rh/Fe Figure 2. Le Bail fit to data collected on petalite at 4.2 K. Ob- fi sensor, and temperature variation was of the order of served data are shown as points, the full line showing the tted powder pattern profile; below the diffraction pattern is the dif- ±0.1 K throughout data collection. ference plot (observed–calculated) and the reflection markers. The raw data at each temperature were electronically The agreement factors for this fit were: Rp = 0.12, Rwp = focussed, normalised to the incident flux distribution, and 0.14, and reduced χ2 = 1.27. corrected for wavelength–dependent detector efficiency, producing a dataset in the time–of–flight range 52–140 ms suitable for analysis using the GSAS software suite. increasing temperature above ~ 120 K. For ease of cal- The 4.2 K data were fitted using the LeBail method as culation of the thermal expansion tensor and its temper- implemented within GSAS using the lattice parameters of ature dependence, both axes have been fitted to an ex- petalite from the ambient temperature structural investi- pression of the form lðT Þ¼l0 þ k1=ðexpðj1=TÞ1Þþ gation of Effenberger (1980) as initial values. Once this k2=ðexpðj2=T Þ1Þ, where k1 < 0, and k2 > 0, and each LeBail extraction had converged, the lattice parameters term ki=ðexpðji=T Þ1Þ is related to the internal energy from the 4.2 K refinement were used as initial values of an Einstein oscillator. The calculated lattice parameter for the 10 K refinement, and this method was then carried variations and axial thermal expansion coefficients are out iteratively up to the 600 K data set. At 4.2 K, the shown as the full and dashed lines respectively in Figure refined lattice parameters were determined as a = 2. For all temperatures below ~ 530 K, the modulus of 11.75347(18) Å, b = 5.12890(6) Å, c = 7.64367(9) Å, the c axis thermal expansivity exceeds the equivalent and β = 113.0107(10)°; the estimated standard deviations measure of the a axis. However, despite the similarities on the lattice parameters showed no significant variation of the temperature–dependence of the two linear thermal with temperature. The quality of fit to the data collected expansion curves, extrapolation of the magnitude of the c at 4.2 K is illustrated in Figure 2. axis using the fitting parameters suggests that it will not develop a positive linear thermal expansion coefficient RESULTS before 975 K, the temperature at which the irreversible structural transition begins (Stewart, 1963). The variation The monoclinic lattice parameters and their associated of these two axes dominates the temperature dependence axial thermal expansion coefficients in the temperature of the unit cell volumes for temperatures below 300 K. interval 4.2 K to 600 K are illustrated in Figure 3, where By contrast, the b axis (and the inter–axial angle β) it can immediately be seen that the a and c axes behave in behave in the manner expected for a simple dielectric a non–conventional manner. Both axes show a strong material, saturation at low temperature before developing non–Grüneisen–like behaviour, with little or no evidence a positive linear thermal expansion coefficient by ~ 300 for low–temperature saturation, and both axes are char- K. Both the b axis and the β angle have been fitted to a acterised by initial negative axial thermal expansion co- single term expression lðTÞ¼l0 þ k1=ðexpðj1=TÞ1Þ, efficients for temperatures above ~ 20 K. At a tempera- where k1 > 0, and are shown as the full lines on the Fig- ture of ~ 230 K, a minimum exists for the a axis, and ure; the linear thermal expansion coefficients, shown as above this temperature the lattice parameter is found to dashed lines, were calculated from the fitting parameters. steadily increase. By contrast, the c axis exhibits negative At 600 K, the linear thermal expansion coefficient of the axial thermalAdvance expansion up to the highest Publication temperature b axis (1.42 × 10−5 K−1) exceedsArticle that of the a axis (3.2 × measured, although the rate of contraction decreases with 10−6 K−1) by a factor of ~ 5, and the behaviour of this 4 K.S. Knight

Figure 3. The temperature dependence of the lattice parameters of petalite between 4.2 K and 600 K. Full lines show the fitted temperature Pn dependence of the lattice parameters according to the Einstein parameterisation lðT Þ¼l0 þ ki=ðexpðji=T Þ1Þ where n = 1, for b and β, i¼1 and n = 2, for a and c. The dashed lines show the calculated linear axial thermal expansion coefficients based on the Einstein parameterisation. axis dominates the volume expansion coefficient above 300 K. The temperature variations of the unit cell volume and the calculated volume expansion coefficient are shown in Figure 4. Two parallel lines are included in this Figure which correspond to a limiting modulus of linear thermal expansivity of 2 × 10−6 K−1, which is considered by Roy et al. (1989) to be the regime of ultra–low thermal expansion. The unit cell volume exhibits a very limited region of low temperature saturation before developing negative volume expansion between ~ 20– ~220K. The volume expansivity curve, shown as a dashed line – Figure 4. The temperature dependence of the unit cell volume of in the Figure, can be seen to correspond to the ultra low petalite between 4.2 K and 600 K. The calculated volume is thermal expansion regime for the temperature interval shown by the full line based on fitting the experimentally deter- 157–298 K, and is found to be zero at a temperature of mined unit cell volume to a two–term Einstein expression. The ~ 219 K. calculated volume expansion coefficient is shown by a dashed – Fitting parameters for the 3 axes, the inter–axial an- line with the range of values corresponding to ultra low linear thermal expansion (Roy et al., 1989) shown as the region be- gle, and the unit cell volume are listed in Table 1. tween the two horizontal dot–dashed lines. The temperature–dependence of the thermal expansion tensor of petalite was calculated using a Cartesian ^ basis suitable for monoclinic crystals (e3 ¼ c^, e2 ¼ b, 1996; Knight et al., 1999; Knight and Price, 2008). The e1 ¼ a^*Advance (Schlenker et al. 1978)) and the fiPublicationtting coeffi- principal axes of the tensor Article were determined using the cients for the lattice parameters (Table 1) (Knight, method of Knight (2010), and are illustrated in Figure Low temperature thermal expansion of petalite 5

Table 1. Fitting coefﬁcients* for the temperature–dependence of the lattice parameters of petalite in the temperature range 4.2 K–600 K

P2 * lðTÞ¼l0 þ ki=ðexpðji=TÞ1Þ i¼1

Figure 5. The temperature dependence of the principal axes of the thermal expansion tensor of petalite (λ22 || b, λ11 is approximately parallel to a) and the orientation of λ11 to c. At 232 K (shown by the vertical line) the representation quadric surface changes from a hyperboloid of two sheets to a hyperboloid of one sheet.

5. Consideration of Neumann’s principle shows one prin- tion quadric is a hyperboloid of one sheet, the principal −6 −1 cipal axis lies parallel to the crystallographic b axis, and axes have the magnitudes λ11 = 1.2 × 10 K , λ22 = 1.19 −5 −1 −6 −1 this axis is designated λ22 in the Figure. The remaining ×10 K , and λ33 = −7.0 × 10 K . The orientations two orthogonal axes lie in the a – c plane and are desig- of the principal axes with respect to the crystal structure nated λ11 and λ33; the orientation angle of λ11 with respect of petalite are illustrated in Figure 6. to the c axis (+c to +a) is also shown in Figure 5. It is These results are in excellent agreement with the clear from this Figure, that for temperatures less than magnitudes and directions of the calculated principal axes ~ 232 K, λ22 > 0, and both λ11 and λ33 < 0, and hence of the thermal expansion tensor derived from the thermal the representation quadric surface is a hyperboloid of two strain data at 293 K presented by Haussühl et al. (2012). ^ sheets (Banchoff and Wermer, 1992). Above this temper- Using the alternative basis of e3 ¼ c^*, e2 ¼ b, e1 ¼ a^ to ature, both λ11 and λ22 > 0 and λ33 < 0, and hence the measure the thermal strain (Haussühl et al. 2012), the representation quadric surface changes to a hyperboloid thermal expansion tensor has components: α11 = 9.74 × −7 −1 −5 −1 −6 −1 of one sheet (Banchoff and Wermer, 1992). Figure 5 10 K , α22 = 1.169 × 10 K , α33 = −7.35 × 10 K , −7 −1 shows that this change in representation quadric is con- α13 =2.4×10 K , which on diagonalisation yields −7 −1 tinuous through 232 K and hence is not associated with principal axis magnitudes of λ11 = 0.98 × 10 K , λ22 −5 −1 −6 −1 any signiﬁcant structural change. At 300 K the principal = 1.17 × 10 K , and λ33 = −7.4 × 10 K with eigen- ^ axis with eigenvalue λ11 lies at angles of −70.35° and vectors ~ a^, b and ~ c^* respectively. 109.65° to the c axis (+c to +a), and hence, as β(300K) = 113.032°, this eigenvector lies close to parallel to the a DISCUSSION axis, whilst λ33 is approximately parallel to c*. At 100 K, when the representation quadric is a hyperboloid of two Petalite shows a complex evolution of the thermal expan- sheets, the principal axes of petalite have the magnitudes sion tensor between 4.2 K and 600 K, with the low tem- λ − −6 −1 λ −6 −1 λ – 11 = 3.4Advance × 10 K , 22 = 2.5 × 10 K Publication, and 33 = perature behaviour dominated Article by the non Grüneisen be- −1.03 × 10−5 K−1, whilst at 293 K, when the representa- haviour of the c axis, and to a lesser extent, the equivalent 6 K.S. Knight

Figure 6. The orientation of the principal axes of the thermal expansion tensor at 300 K to the crystal structure of petalite (polyhedral symbols as in Fig. 1). behaviour of the a axis. Both axes show only a limited K, i.e., above the temperatures of the minimums associ- low temperature range of lattice parameter saturation, and ated with the a– and c–axis expansivities, additional rigid hence the structural mechanism underlying the low tem- body rotations start to become signiﬁcant as the length- perature thermal expansion is probably related to the ex- ening of the Al–O, and Li–O bonds permit the two struc- citation of a set of low energy, rigid–unit lattice modes, turally independent SiO4 groups to move relative to one similar to those inferred to exist in the gillespite–struc- another in the third dimension resulting in the change in tured phase Ba0.5Sr0.5CuSi4O10 (Knight and Henderson, the representation quadric surface of the thermal expan- 2007), β–spodumene (Ostertag et al., 1968), and β–eu- sion tensor. cryptite (Xu et al., 1999). Consideration of the crystal The true structural basis for this unusual thermal ex- structure of petalite (Fig. 1 and 6) shows that rigid unit pansion will require detailed crystallographic studies, rotation of the edge–sharing LiO4 and AlO4 about the b however, if an assumption of near–rigid–unit polyhedra axis direction could occur, and if this occurred as a single were assumed, the lattice parameter data determined in unit, then this would result in reducing the lengths of the this study could provide some insight to the possible a and c axes through co–operative rotations of the corner structural mechanism if used in conjunction with analysis linked SiO4 groups. Evidence for anomalous behaviour using distance least squares. Possible low temperature ap- of the phonons at low temperatures has been discussed by plications of petalite ceramics will require the ability to Haussühl et al. (2012) in the context of the isobaric heat densify at temperatures below the irreversible phase tran- capacity, where the deviation from the expected T3–de- sition temperature. pendence was observed at temperatures as low as 3 K. The thermal expansion behaviour of petalite is therefore ACKNOWLEDGMENTS essentially two dimensional at low temperatures due to the largeAdvance saturation interval associated with Publication the b axis I am grateful to the suggestions Article of two anonymous refer- (Fig. 3). However, for temperatures greater than ~ 120 ees that have led to improvements in the manuscript and Low temperature thermal expansion of petalite 7

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Zeitschrift für Kristallographie, 126, Manuscript received August 19, 2013 46–65. Manuscript accepted February 2, 2014 Liebau, F. (1961) Untersuchungen an schichtsilikaten des formel- typsAdvance Am(Si2O5)n. III Zur kristallstruktur von petalite,Publication LiAlSi4 Manuscript handled by Kazumasa Article Sugiyama