Introduction

Thermodynamic calculations and modelling are a powerful method to evaluate phase equilibria in Earth systems. In order to predict phase equilibria, compressibilities and thermal expansion coefficients, parameters to calculate the chemical potential of each phase involved, are required. For natural phases, thermo-elastic parameters are not always available, due to the fact that minerals are very frequently solid solutions. One approach is to derive the chemical potential using a self-consistent computation of parameters from a set of reactions experimentally obtained (Berman 1988; Gottschalk 1997; Holland and Powell 1998). Among the different approaches for fitting experimental data, the most widely used ‘internally consistent database’ by Holland and Powell (1990) and Berman (1988) reflects some differences due to the different protocols: Holland and Powell (1990) refine only values for Δ f H° (enthalpy of formation from the elements) and assume that all of the other parameters and functions are well known experimental data and thus fixed; Berman (1988) considers that parameters and functions for each phase component have experimental error and thus targets for optimization. Gottschalk (1997) refines values for Δ f H° and S° (entropy) and assumes all of the other parameters constrained. The approaches of Holland and Powell (1990) and Gottschalk (1997) therefore suffer from inaccuracies of the experimental data. Synthesis of pure end-members may be difficult or inaccessible, depending on many experimental variables. However, when synthesis is possible, the molar volume of pure end-members and chemically controlled solid solutions can be characterized at different P/T conditions by X-ray diffraction.

Zoisite, ideally Ca2Al3[(SiO4)(Si2O7)]O(OH), is the orthorhombic variety of the epidote group minerals (space group Pnma, Dollase 1968) and can be a modally important rock-forming mineral in metabasites, especially in blueschist, epidote–amphibolite, and eclogite facies (Franz and Liebscher 2004 and references therein). Zoisite is stable at high pressure and thus considered as an important carrier of H2O to depth in subduction zones (Poli and Schmidt 2004). The structure of zoisite hosts Al in two different crystallographic sites with sixfold coordination [M(1,2) and M(3) sites], Si is present in three fourfold coordinated sites [T(1), T(2), T(3)], and Ca is present in two [7+ (1,2)]-fold coordinated sites [Ca(1) and Ca(2)]. The most frequent solid solution observed in natural samples is due to the Fe3+/Al substitution in the M(3) site. An experimental study aimed to describe the effect of Fe3+/Al substitution in synthetic zoisite [X ps = 0.0–0.14, X ps defined as Fe3+/(Fe3+ + Al − 2)] by Liebscher et al. (2002) reported discontinuities in lattice parameters at ~0.05 X ps, which were ascribed to two distinct modifications, zoisite I (<0.05 X ps) and zoisite II (>0.05 X ps). These modifications were explained as a consequence of the expansion of the M(3) site due to Fe3+, leading to opposite rotations of corner sharing T(1) and T(2) tetrahedra of the Si2O7 group. Within the precision of Liebscher et al. (2002) data, neither framework reconstruction nor change in space group symmetry was detected between zoisite I and zoisite II. Therefore, these authors classified the transformations as an ‘isosymmetric displacive phase transition’ induced by solid solution. On the basis of the mutually related effects of composition, temperature and pressures (Heaney 2000), it was suggested that the zoisite I–zoisite II transition should also be observed changing T and P. However, a careful inspection of the published P–V–T data for zoisite does not show any clear discontinuity. Liebscher et al. (2002) suggested that the absence of the discontinuity might be due to the critical temperature of the transformation (T c), out of the P–T ranges previously investigated or by analytical uncertainties. Later on, Liebscher and Gottschalk (2004) conducted a temperature-dependent infrared spectroscopy study of the synthetic samples used in their previous study and reported change in peaks broadening of IR spectra using the autocorrelation analysis and interpreted this as a transition from zoisite I to zoisite II at 45°C for X ps = 0–0.035(12).

To date, all the diffraction experiments at high-T undertaken on zoisite have been performed using powder X-ray diffraction, although none of those led to a Rietveld refinement of the structure at high-T. Pawley et al. (1996), who performed dilatation studies, reported that the a-lattice parameter of zoisite remains essentially constant. Nevertheless, a subtle decrease in a is evident from their data. These authors suggested that the expansion of the Al octahedra upon heating will forces rotation of cross-linkages on the Si tetrahedral pairs, preventing the lengthening of the a-axis. They concluded that only single-crystal structure refinements would confirm this issue. Grevel et al. (2000) studied the behaviour of zoisite at high P and T and found that the thermal expansion of zoisite appeared to be significantly lower than that found by Pawley et al. (1996) at ambient pressure. Since Grevel et al. (2000) worked at P > 0.80 GPa, they concluded that additional measurements of the thermal expansion of zoisite at atmospheric pressure should be performed.

The (OH) group in zoisite has a strong hydrogen bond, as shown by a neutron diffraction study of Smith et al. (1987) at 15 K, and confirmed by IR-spectroscopy data by Liebscher and Gottschalk (2004). The hydrogen bond lies almost on the (100) plane. The strong anisotropic thermal behaviour of zoisite observed by Pawley et al. (1996) might be controlled by a change in the hydrogen bond configuration, which can be confidently studied by single-crystal neutron diffraction at high temperature. On the other hand, polyhedral expansion and rotation can be reliably described on the basis of single-crystal X-ray diffraction data.

A single-crystal X-ray and neutron diffraction study of zoisite requires a suitable size of the crystal, which has not been achieved by synthesis. The choice of a natural crystal fits this pre-requisite as far as zoisite with <0.05 X ps can be found. Gem-quality crystals from Tanzania match this requisite, as they have excellent crystalline properties, very low iron content and large size. In this light, the aim of this study is: (1) to better constrain the thermal expansion of zoisite, (2) to check for the presence of the zoisite I–zoisite II displacive phase transition while increasing T, and (3) to describe any potential change of the hydrogen bond configuration at high temperature. A comparative thermo-elastic analysis between zoisite and epidote [ideal formula Ca2Al2Fe[(SiO4)(Si2O7)]O(OH)] will be carried out. The behaviour of epidote at high temperature was recently investigated by Gatta et al. (2010, 2011) by in situ single-crystal neutron diffraction and synchrotron powder diffraction.

Experimental methods

For this study, a natural, yellow, transparent, gem-quality large single-crystal of zoisite from Merelani Hills, Arusha Region (Tanzania) was selected. Sample was kindly provided by A. Zanetti and was cut into few smaller pieces that were then used for the different diffraction techniques. Zoisite from Merelani Hills occurs in hydrothermally formed calc-silicate rocks, associated with graphitic gneiss with kyanite/sillimanite-quartz-anorthite, which were intruded by Pan-African granite pegmatites and quartz veins at ca. 600 Ma. Conditions of metamorphism were: ca. 650°C and 0.8 GPa (upper amphibolites facies). The gneisses are rich in graphite and the trace elements V, U, Mo and W (Malisa 1987; Zancanella et al. 2000; Olivier 2006).

Chemical composition

Chemical analysis was performed on the fragment used for X-ray diffraction after the experiment was finished. We used a CAMECA SX-100 microprobe at the CNR-IGG of Padova. Working conditions in wavelength-dispersive mode were an accelerating voltage of 20 kV, a beam current of 20 nA for Al, Si, K, Ca and Fe and 20 kV and 40 nA for Na, Mg, Ti, V, Mn, Sr, La and Ce. Fluorine was absent. Beam diameter was 10 μm. The following standards were used (spectral line, analysing crystal): Amelia albite (NaKα, TAP), wollastonite (CaKα, PET), diopside (SiKα, TAP), MgO (MgKα, TAP), orthoclase (KKα, PET) MnTiO3 (MnKα and TiKα, PET), vanadinite (VKα, LIF), Fe2O3 (FeKα, LiF), corundum (AlKα, TAP), celestine (SrLα, PET), and REE glass 3 (LaLα and CeLα, LIF). Data were corrected using the PAP method of Pouchou and Pichoir (1984). The empirical formula of our zoisite is (Ca1.99Sr0.01)(Al2.99V0.01) [Si2O7][SiO4]O(OH) with the OH content being assumed by stoichiometry as the crystal is F-free (Table 1).

Table 1 Average of 10 microprobe point analyses. Normalized on the basis of 13 anions
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Single-crystal X-ray diffraction

The experiment was done on a fragment (0.48 × 0.40 × 0.36 mm) of the selected grain of zoisite showing sharp optical extinction with crossed polarized light under the microscope. Due to its gem-quality, the crystal was ground using sand paper and air compressed blown in a closed cylindrical recipient, in order to reduce the secondary extinction effect, observed in some test crystals. Crystal was mounted inside a 0.5 mm inner diameter quartz vial 26 mm long, closed at the top by using oxy-methane flame. The zoisite crystal was held inside with quartz wool. The vial was mounted into a metal goniometer head on a Philips PW1100 diffractometer working with MoKα radiation at 30 mA/55 kV and using a 0.5-mm collimator and operated with FEBO software (a local developed control software). On top was placed a microfurnace consisting of a H-shaped Pt–Rh resistance and a Pt:Pt–Rh thermocouple inside a steel cylindrical cage 1 inch wide closed with a Kapton film. The device allows the collection of diffraction data up to θ max = 29° (with MoKα).

Calibration of the furnace

The furnace is controlled by a Eurotherm unit. Due to the low thermal conductivity of quartz and the distance between the thermocouple tip and the actual position of the crystal inside the quartz vial (ca. 1.5 mm), the reading of the controller is not the actual temperature of the crystal. To overcome this problem, a temperature calibration was undertaken by: (1) observing the melting of selected pure salts (see Table 2); (2) measuring the thermal expansion of quartz across the α–β phase transition. A spherical crystal of quartz was mounted on a quartz vial (see above for the mounting procedure). Lattice parameters were collected at high temperature every 25 K. Linear fitting performed on the observed melting points and on the observed transition temperature for the α–β quartz phase transition with the recorded temperature at the controller display yielded the following equation:

$$ T = 2.1265\left( {6.64} \right) + 1.0491\left( {133} \right) \times T_{\text{display}} $$

with ±1 K on the reading of the thermocouple, Gaussian error propagation yielded a 6.75 K 1σ error at room-T and 7.04 K at 973 K. Stability of temperature of the furnace while changing goniometer position was within a few K.

Table 2 Melting points (and transition temperature for quartz) used for the microfurnace calibration
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The Bragg angles of selected 24 intense reflections were measured using horizontal and vertical slits. Subsequently, the Philips LAT procedure was used to obtain accurate and precise lattice constants: (1) the position of different diffraction spots having different nd-values was measured in positive and negative ω−2θ by first centring the spots using the vertical and horizontal slits then performing a selected scan in ω−2θ and calculating the observed maxima; (2) the observed nd-values were fitted producing a relative d-value and its e.s.d. The procedure was repeated for several groups of reflections (from 40 to 60, depending on the scattering power of the studied crystal), and lattice parameters were calculated by least-squares fitting of all the observed d-values.

For the zoisite crystal fragment of this X-ray diffraction study, lattice centring with 24 reflections and LAT routine on 60 groups of reflections was performed at steps of temperature of 25 K up to 1,073 K. The results are reported in Table 3 and in Fig. 1a–d.

Table 3 Lattice parameters of zoisite at different temperatures (single-crystal X-ray diffraction data)
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Fig. 1
figure 1

Evolution of lattice parameters of zoisite of this study (dots) with temperature (K). Data from Pawley et al. (1996) have been reported (open dots) for comparison

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Intensity data aimed to the structure refinements were collected at 303, 323, 423, 523, 623, 723, 823, 923, and 1,023 K. A quadrant of intensity data was collected (±h, +k, +l). Raw intensities were corrected for Lorentz and polarization effects, and a semi-empirical absorption correction based on ψ scans (North et al. 1968) was applied.

Neutron diffraction

Another fragment of the crystal (~2.7 × 3.1 × 3.2 mm) was selected for the neutron diffraction experiment. A preliminary check by polarized microscopy and single-crystal X-ray diffraction confirmed that the crystal was free of defects, twinning or zoning. The single-crystal neutron diffraction experiment was first performed at 300 K with the four-circle diffractometer HEiDi (beam line SR9) at the FRM II neutron source (Forschungsneutronenquelle Heinz Maier-Leibnitz) at Garching (München), Germany. The reactor provides a maximum undisturbed thermal neutron flux density of 8 × 1014 cm−2 s−1 at a nominal thermal power of 20 MW. The incident radiation, with a constant wavelength λ = 0.8700(2) Å, was obtained using a focusing Cu-(220) monochromator. A neutron filter (0.5 mm Er foil) was used in order to cut off the neutrons around the λ/2 area from the neutron spectrum, due to the strong λ/2 contamination caused by the hot source. The diffractometer was equipped with a ³He single counter detector [Eurisys 73NH17/5X end window counter, 50 mm entrance window, 5 bar ³He pressure and 170 mm active length for high detection probability (>90% at 0.8 Å), separation of γ radiation by pulse height discrimination]. An integrated slit system defined the cross section of the entrance window of the detector.

The unit-cell parameters were refined on the basis of selected 32 Bragg reflections at T = 300 K, giving: a = 16.190(2) Å, b = 5.546(1) Å, and c = 10.035(2) Å. Intensity data were collected with −24 ≤ h ≤ 23, −8 ≤ k ≤ 3 and 0 ≤ l ≤ 15 (2θ max = 85.66°), for a total number of 4,172 reflections. Two standard reflections were measured every 450 min throughout the experiment, and the intensity variation was within ±1σ(I). The reflection conditions confirmed the space group Pnma, as previously reported (Smith et al. 1987). Integrated intensities were then corrected for the Lorentz effect. No absorption correction was applied because of the shape and the dimensions of the sample. The discrepancy factor among the symmetry-related reflections (Laue class: mmm) was R int = 0.0222. Further details of the data collection are reported in Table 4.

Table 4 Details pertaining to the neutron data collection and refinement of zoisite at 300 and 873 K
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A further intensity data set was collected at T = 873 K, using a small water cooled mirror furnace designed at the neutron source Heinz Maier-Leibnitz (FRM II) and following the protocol used by Gatta et al. (2010). The temperature precision of this HT-device is about ±1 K. The temperature of the zoisite crystal was slowly increased (~200 K/h) from 300 to 873 K and kept at there for 3 h prior to data collection. Unit-cell parameters were first refined on the basis of the 30 Bragg reflections at 873 K, with: a = 16.177(5) Å, b = 5.605(4) Å, and c = 10.143(5) Å. Intensity data with −23 ≤ h ≤ 23, −6 ≤ k ≤ 1 and −14 ≤ l ≤ 15 were collected (2θ max = 85.07°), giving a total number of 3,740 reflections (Table 4). The lower number of reflections compared to 300 K is due to the shadowing effect of the furnace. The two standard reflections measured every 450 min throughout the experiment showed an intensity variation within ±1.5σ(I). Temperature stability over the data collection was ±5 K. The reflection conditions were consistent with the space group Pnma. After correction for Lorentz effect, the discrepancy factor among symmetry related reflections was R int = 0.0695. Further details of the data collection are reported in Table 4. After the data collection at 873 K, we realized that the crystal has turned to faint violet colour, characteristic of tanzanite, the gem variety of zoisite.

Structure refinements

Neutron diffraction data

The neutron diffraction data of zoisite collected at 300 and 873 K were first processed with the program E-STATISTICS, implemented in the WinGX package (Farrugia 1999). The statistics of distributions of the normalized structure factors (E’s) showed that the structure of zoisite is centrosymmetric at both temperatures (at >83% likelihood, Table 4). Similar findings were obtained by the Sheldrick’s |E 2−1| criterion (Sheldrick 2008) (Table 4). The structure refinements against F 2 were then performed in the space group Pnma using the SHELX-97 software (Sheldrick 2008), with anisotropic thermal displacement parameters and starting from the atomic coordinates of Smith et al. (1987). The neutron scattering lengths of Ca, Al, Si, O and H have been used according to Sears (1986). The secondary isotropic extinction effect was corrected according to Larson (1970), as implemented in the SHELXL-97 package (Sheldrick 2008). When convergence was achieved, all the principal mean-square atomic displacement parameters were positively defined, including the proton site. The variance–covariance matrix showed no significant correlation among the refined parameters. At the end of the last cycle of refinements, no peaks larger than −0.7/+0.6 fm/Å3 and −2.0/+2.3 were present in the final difference-Fourier map of the nuclear density at 300 and 873 K, respectively (Table 4). The final agreement indexes were: R 1 (300 K) = 0.0272 and R 1 (873 K) = 0.0707 (Table 4). Site positions are reported in Table 5a, b, displacement parameters for the data at 300 and 873 K, are available as electronic supplemental material (ESM). Relevant bond lengths and angles are listed in Table 6a, b.

Table 5 Refined fractional atomic coordinates and equivalent isotropic temperature factors (Å2), with standard deviations in parentheses, based on the neutron diffraction data collected at (a) 300 K and (b) 873 K
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Table 6 Relevant bond distances and angles based on the neutron diffraction data collected at (a) 300 K and (b) 873 K
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X-ray diffraction data

X-Ray structure refinements against F 2 were performed in the space group Pnma using SHELX-97 (Sheldrick 2008) starting from the atomic coordinates of Smith et al. (1987). Scattering factors were taken from the International Tables for X-ray Crystallography (Wilson 1995). Occupancies of neutral versus ionised scattering factors for the O and Si sites (i.e. O vs. O2− and Si vs. Si4+) were refined, whereas fully ionized scattering factors for Al3+ [in M(1,2) and M3 sites] and Ca2+ [in Ca(1) and Ca(2) sites] were used. Anisotropic displacement parameters were refined for all the atomic sites. The H site was then located from the difference-Fourier maps and added to the refinement at fixed full occupancy. Difference-Fourier maps at convergence did not show any significant residual electron density. Details of the data collection and structure refinements are reported in Table 7. Atom coordinates, equivalent isotropic displacement parameters (U eq), and anisotropic displacement parameters (U ij ) are available as electronic supplemental information. Principal root-mean-square components (R1, R2 and R3, Å) for cation and anion sites are available as ESM. Selected interatomic distances and angles are reported in Table 8. Lists of observed and calculated structure factors are available from the correspondent author.

Table 7 Details pertaining to the X-ray intensity data collection and structure refinement of zoisite at different temperatures
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Table 8 Relevant bond distances and angles based on the X-ray structure refinements at different T
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Results and discussion

Thermo-elastic behaviour

To a first approximation, the coefficient of volume thermal expansion is T-independent, and so the variation of the unit-cell volume of zoisite with T can be fitted by least-squares to the equation:

$$ V_{\text{zoi}} \left( T \right) = V^{ 0}_{{{\text{zoi}}(P_{\text{r}} ,T_{\text{r}} )}} e^{{\alpha_{\text{zoi}}^{0} (T - T_{\text{r}} )}} $$
(1)

where \( V^{ 0}_{{{\text{zoi}}\left( {P_{\text{r}} ,T_{\text{r}} } \right)}} \) is the volume of the phase at reference pressure and temperature, \( {{\upalpha}}^{ 0}_{\text{zoi}} \) is the volume thermal expansion coefficient and T r is the reference temperature. Gottschalk (2004) reported \( {{\upalpha}}^{ 0}_{\text{zoi}} \) = 37.1(3) × 10−6 K−1 using data of Pawley et al. (1996).

The derived coefficients of volume and axial thermal expansion based on single-crystal X-ray diffraction data reported in Table 3 are: \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,V(1 bar,298K) = 35.4(3) × 10−6 K−1, \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,a(1 bar,298 K) = −1.18(3) × 10−6 K−1, \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,b(1 bar,298K) = 17.31(2) × 10−6 K−1 and \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,c(1 bar,298K) = 18.95(2) × 10−6 K−1. The thermal expansion is significantly anisotropic, being positive within the plane (100) and negative along the direction [100].

Figure 1a–d reports the lattice parameters variation with temperature obtained in this study and those of Pawley et al. (1996). Lattice variation with temperature is quite similar beyond the dispersion of data and larger errors of Pawley et al. (1996) data. The data of this study show more accurately a faint shortening of the a-lattice parameter up to ca. 700 K, and then a clear contraction (negative thermal expansion—NTE) along [100] at T > 700 K. The absence of match of data at room temperature is mainly due to the presence of Fe3+ in the sample studied by Pawley et al. (1996)—a natural zoisite from the Moine Schist, Glenurquhart, Scotland—which contained 2.3–4.3% of the ferric end-member, Ca2A12Fe3+[Si2O7][SiO4]O(OH). As a matter of fact, Pawley et al. (1996) reported a molar volume of 136.10(2) cm3  mol−1. A fitting of the Eq. 1 in the whole studied T-range yields a value of 135.57(2) cm3  mol−1 and \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,V(1 bar,298K) = 35.4(3) × 10−6 K−1, while a fitting using data at T < 700 K yields \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,V(1 bar,298K) = 32.4(4) × 10−6 K−1and 135.65(1) cm3  mol−1, in good agreement with the observed experimental value at room-T. A fitting using data at T > 700 K yields 137.44(1) cm3  mol−1 and \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,V(1 bar,700K) = 38.2(3) × 10−6 K−1. If two T ranges (i.e. below and above 700 K) are considered, the anisotropic thermal behaviour of zoisite is maintained remarkably high (i.e. α b :α c  = 0.94; T < 700 K; α b :α c  = 0.90; T > 700 K; α a  = −0.61(7) × 10−6 K−1; T < 700 K, α a  = −2.20(9) × 10−6 K−1; T > 700 K, Table 9a).

Table 9 Calculated thermal expansion coefficients for volume and individual crystallographic axis for zoisite assuming (a) no dependency of thermal expansion coefficient on temperature; (b) linear dependency of thermal expansion coefficient on temperature; and (c) allowing for saturation of thermal expansion coefficient at high temperature (see text for a discussion)
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Before the experimental results by Pawley et al. (1996), who reported a volume thermal expansion coefficient of 38.6(5) × 10−6 K−1, there were important differences in thermal expansion coefficients reported in literature: Berman (1988) used in his data set \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,V(1 bar,298K) = 34.67 × 10−6 K−1, and Holland and Powell (1990) adopted the value of 28.0 × 10−6 K−1 reported by Hemingway et al. (1982) for their database, which was also used by Gottschalk (1997). Later on, Gottschalk (2004) recommended a value of \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,V(1 bar,298K) = 37.1(3) × 10−6 K−1 (\( {{\upalpha}}^{ 0}_{\text{zoi}} \) = 0) for zoisite using experimental data from Pawley et al. (1996). A value of \( {{\upalpha}}^{ 0}_{\text{zoi}} \) ,V(1 bar,298K) = 35.4(3) × 10−6 K−1 for data from 298 to 1,023 K is obtained in this work, closer to the data used by Berman (1988).

Physical model involving the vibrational density of states (Anderson et al. 1992) or a quasi-harmonic Einstein’s model as described by Knight (1996) requires high-quality data collected well below room-T. Nevertheless, temperature-dependence of α is expected to be small above the Debye temperature (Anderson et al. 1992), and empirical fits can be used to quantify such variation. These have the advantage that they are mathematically simple as, for example, the second-order polynomial of Berman (1988):

$$ V_{\text{zoi}} \left( T \right) = V^{0}_{{{\text{zoi}}(P_{\text{r}} ,T_{\text{r}} )}} \left[ {1 + a_{0} \left( {T - T_{\text{r}} } \right) + a_{1} \left( {T - T_{\text{r}} } \right)^{2} } \right] $$
(2)

from which ∂V/∂T = \( {{\upalpha}}_{{V,T_{\text{r}} }} \) = a 0 + 2a 1(T – T 0). Applied to our data we obtain: α V,298 = a 0 = 2.9(1) × 10−5 K−1, a 1 = 8.8(1.3) × 10−9 K−2, and \( V^{ 0}_{{{\text{zoi}}\left( {1\,{\text{bar,298}}\;{\text{K}}} \right)}} \) = 135.68(2) cm3 mol−1, which implies α V,1,023 ≈ 4.18 × 10−5 K−1. Corresponding values for axial thermal expansion coefficients for this model are reported in Table 9b. This approach fits well the behaviour of the a-lattice parameter too.

The polynomial used by Berman (1988) does not allow for saturation of α at high T. This can be accounted using the approach of Holland and Powell (1998) with:

$$ V_{\text{zoi}} \left( T \right) = V^{0}_{{{\text{zoi}}(P_{r} ,T)}} \left[ {1 + a_{0} \left( {T - T_{\text{r}} } \right) + 2a_{1} \left( {\surd T - \surd T_{\text{r}} } \right)} \right] $$
(3)

Pawley et al. (1996) assigned a 1 = 0, obtaining α V,298 = a 0 = 3.86(5) × 10−5 K−1. Following the same protocol, we obtain α V,298 = a 0 = 3.54(3) × 10−5 K−1 with our data. On the other hand, Pawley et al. (1996) observed that high-T data for some hydrous minerals having very different structures could be fitted reasonably well with α V,T  = a 0–a 1/√T, and proposed a further simplification a 1 = 10(2)a 0, that was used by Holland and Powell (1998) for their internally consistent thermodynamic database. Differentiation of this equation gives the coefficient of volume thermal expansion at any T value as α V,T  = a 0(1–10/√T r), i.e. α 0 V (1–10/√T r). Fitting our data with the ‘modified’ Eq. 3 (i.e. with a 1 = 10(2)a 0), we obtain: α V0 = 5.93(5) × 10−5 K−1, and \( V^{ 0}_{{{\text{zoi}}\left( {1\,{\text{bar,298}}\;{\text{K}}} \right)}} \) = 135.72(2) cm3 mol−1, which implies α V,298 ≈ 2.49 × 10−5 K−1 and α V,1,073 ≈ 4.12 × 10−5 K−1. The latter yields a calculated molar volume at 1,073 K (V 1,073) of 139.46 cm3 mol−1, which agrees very well with our experimental data to 1,073 K, i.e., \( V_{{{\text{zoi}}\left( {1\,{\text{bar,1073}}} \right)}} \) ≈ 139.45 cm3 mol−1. Corresponding values for axial thermal expansion coefficients for this model are reported in Table 9c. However, this expression does not produce a good agreement for the a-lattice, while it reproduces very well the evolution of b and c parameters with T. Much better agreement for the a-lattice is obtained if the constraint a 1 = 10a 0 is not applied, thus obtaining a 0 = −0.545(34) × 10−5 K−1, a 1 = 10.66(84) × 10−5 K−1/2 and 16.1920(3) Å for the a-lattice length.

Structure evolution

The neutron refinement at room conditions confirms the structure model previously published (e.g. Ito et al. 1954; Hanisch and Zemann 1966; Dollase 1968; Linke 1970; Gabe et al. 1973; Smith et al. 1987), with the M(1,2) and M(3) sites occupied only by Al and with only one independent proton site. X-ray data show that the low quantity of V (0.01 a.p.f.u.) derived from the electron microprobe analyses (Table 4) is difficult to be allocated but could be plausibly assigned to the M(1,2) site, as it is the one showing a slightly lower scattering than the expected one for a full Al-occupancy. This is compatible with the observations of Tsang and Ghose (1971).

The neutron structure refinement at 300 K shows that the thermal displacement ellipsoids are only slightly pronounced (Fig. 2, see ESM). The largest anisotropy is observed for the O(3), O(8), O(9) and O(10) oxygen sites, with R1/R3 ranging between 1.7 and 2.4 (where R1 and R3 represent the longest and the shortest root-mean-square components of the thermal ellipsoids, respectively). A similar finding was also reported by Smith et al. (1987). The largest U eq value is observed for the O(9) site, and this is due to the bonding environment of this oxygen, coordinated by two cations [Si(1) and Si(2), Table 6a, b]. All the other oxygen sites are shared at least by three cations, with a lower displacement parameter. The X-ray structure refinement at 300 K confirms O(9) as the anion site with the largest U eq, with the largest anisotropy observed for the O(7), O(8), O(9) and O(10) oxygen sites (see ESM).

Fig. 2
figure 2

Crystal structure of zoisite viewed down [010] based on the atomic coordinates refined in this study at 300 K (thermal ellipsoid probability factor: 80%). The O(8)↔O(8) and O(6) ↔ O(2) distances of the ‘cage’ are shown as dotted lines

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The neutron refinement at 873 K shows that the structure model of zoisite previously obtained at room conditions is maintained. A positive thermal expansion is observed along the crystallographic b- and c-axis, but a negative thermal expansion occurs along the a-axis (Tables 3, 7, 9). The tetrahedral and octahedral bond distances and angles show a slight distortion of the polyhedra at high-T, especially for bond distances corrected for ‘rigid body motions’ (Downs et al. 1992; Downs 2000) (Table 6b). Surprisingly, the inter-polyhedral deformation mechanism of the Si2O7 group in response to temperature is opposite than that observed in epidote: the bridging angle Si(2)–O(9)–Si(1) decreases monotonically from 174.87(8)° at 15 K (Smith et al. 1987) to 173.62(7)° at 300 K, and down to 171.4(5)° at 873 K (Table 6a, b), whereas in epidote, it increases from 154.59(9)° at 298 K to 157.4(5)° at 1,070 K (Gatta et al. 2010). This can be better followed by the results of the X-ray structure refinements. Figure 3a reports the variation of Si(2)–O(9)–Si(1) with temperature. In addition, while the two tetrahedra of the disilicate group regularize slightly with temperature (with a progressive reduction of the tetrahedral angle variance parameter of Robinson et al. 1971, Fig. 3b), the isolated tetrahedron shows a more significant regularization with T (Fig. 3b), which is not accompanied with a reduction of the anisotropy of the thermal displacement ellipsoids (see ESM). After correcting bond distances for ‘rigid body motions’, tetrahedra behave mostly like rigid units (Fig. 3c). The bond distances Si(1)–O(9) and Si(2)–O(9) increase significantly after correction (Table 8a).

Fig. 3
figure 3

Variation with temperature of a the bridging angle Si(2)–O(9)–Si(1) (°); b the tetrahedral angle variance (Robinson et al. 1971); the mean bond lengths for T sites corrected for rigid body motions; d the octahedral angle variance (OAV; Robinson et al. 1971) for the two octahedra; e individual M(3)–O distances [error bar for O(1) and O(2) are much smaller than the symbol size]; f Ca(2)–O(10) distance

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Another interesting issue of high-T behaviour of zoisite is the different response of the two octahedra. While M(1,2) remains essentially rigid within the T-range investigated (SRB corrected mean bond lengths and OAV are essentially unchanged; Table 8a), the M(3) octahedron shows an increasing deformation with T (Table 8b; Fig. 3d). This deformation reflects the flattening of the M(3) octahedron along [100] by reduction of M(3)–O(4) and M(3)–O(8) lengths, coupled with an increase of the M(1,2)–O(1) distance (Fig. 3e). The latter is almost parallel to the (100) plane and thus allows the expansion of the structure along b and c, while the flattening of the M(3) octahedron can explain the NTE observed for a. Interestingly, while the anisotropy of the thermal displacement ellipsoid of the M(3) site increases monotonically with T, the anisotropy of the thermal displacement ellipsoid of the M(1,2) site shows a discontinuity at T ~ 600 K (see ESM). While it is difficult to discern any disordering of the <0.01 a.p.f.u. of V between the M(1,2) and M(3) sites, it is a fact that Fe3+ orders in M(3) in iron-bearing zoisites (see Franz and Liebscher 2004 and references therein). Liebscher et al. (2002) showed that the increase of Fe3+ is coupled with an opening of the O(7)–O(9)–O(8) angle and a tightening of the Si(1)–O(9)–Si(2) angle; this is also observed in this study at high-T (Table 8b). Liebscher et al. (2002) observed also that the O(1)–O(1) distance decreases whereas the O(4)–O(8) of the M(3) octahedron increases significantly with increasing the Fe-content, but the opposite is observed in a Fe-free zoisite increasing T, as we find that O(4)–O(8) decreases from ~3.60 to ~3.55 Å, and O(1)–O(1) increases from ~2.76 to ~2.85 Å within the T-range investigated.

An open question concerns any potential relationship between the change in colour experienced by the zoisite crystal used for our high-T neutron diffraction experiment and the change in anisotropy of the thermal motion at the M(1,2) site and distortion of the M(3) polyhedron with T. Olivier (2006) based on UV/visible/NIR spectra collected from oriented samples reported that both V3+ and Ti3+ are present in the structure of blue and golden zoisite from Merelani hills and discarded the V3+ → V4+ charge transfer proposed by Zancanella et al. (2000) as responsible for the blue colour of tanzanite variety. Ti3+ has one valence electron that can be excited into a higher energy state by visible light and thus leading to different absorption frequencies in the visible spectrum (Rossman 1988). The presence of Ti3+ in zoisite was justified by the high reducing environment (graphite-rich gneisses and H2S fluid inclusion in zoisite, Olivier 2006). Olivier (2006) observed a reduction in intensity of a band at 450 nm in spectrum with E//γ (responsible for the red/yellow/green colour observed in this direction) with heating (starting at 633 K), that he ascribed to the oxidation of Ti3+ to Ti4+ and suggested the following charge transfer reaction: V4+ + 1/2 (Ti3+ + Fe2+) → V3+ + 1/2 (Ti4+ + Fe3+). After heating, the spectra with E//α and E//γ were equivalent, resulting in dichroic behaviour. Ti, V and Fe share, along with Al, the octahedral sites. We cannot exclude, therefore, that the changes observed in the geometrical configuration of the polyhedra (i.e. octahedral flattening) and in the thermal regime of the octahedral sites someway reflect the charge transfer reaction suggested by Olivier (2006).

Hydrogen bonding

In zoisite, one hydrogen bond, with O(4) as acceptor, occurs, with O(10)–H(1) ~ 0.992 Å (corrected for ‘riding motion’, Busing and Levy 1964), H(1)···O(4) ~ 1.791 Å, O(10)···O(4) ~ 2.766 Å and O(10)–H(1)···O(4) ~ 175.6° (Fig. 4; Table 6a). O(10)–H(1)···O(4) bond is also consistent with the only measured pleochroic scheme for the single O–H stretching absorption band observed in IR-spectra for zoisite, in which maximum absorption occurs parallel to [001] (Hanisch and Zemann 1966; Linke 1970). The almost linear hydrogen bond found in zoisite in this study agrees with the experimental finding of the previous low-T neutron diffraction study of Smith et al. (1987).

Fig. 4
figure 4

Configuration of the hydrogen bond in zoisite at 300 K (left side) and 873 K (right side), respectively. Thermal ellipsoid probability factor: 50%

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Liebscher et al. (2002) reported evidence of possible hydrogen bonds with O(2) as acceptor, on the basis of IR-spectroscopy studies, with a complex bifurcated configuration. The configuration of a hypothetical hydrogen bond with O(2) as acceptor is realistic, but appears to be energetically not favourable, as the angle O(10)–H(1)···O(2) is only ~102°, with O(10)···O(2) ~ 2.953 Å. Other potential H-bonds were suggested with O(3) or O(5) as acceptors. However, such bonds appear to be not realistic, as O(10)···O(3) ~ 4.121 Å with O(10)–H(1)···O(3) ~ 132°, and O(10)···O(5) ~ 3.829 Å with O(10)–H(1)···O(5) ~ 121°, based on our room-T neutron diffraction experiment.

The structural refinement at 873 K shows that no dehydration effect occurred. A careful inspection of the difference-Fourier map of the nuclear density confirms the location of only one proton site and the configuration of the H-bonding is basically maintained with temperature (Fig. 4, Table 6b). The hydrogen bond strength changes at 873 K, with the O(10)···O(4) and H(1)···O(4) distances longer (~0.1 Å) than those at 300 K. A similar trend at high temperature was also observed in epidote (Kvick et al. 1988; Gatta et al. 2010). In response to temperature, the anisotropic displacement parameters of the proton site increase significantly, although the R1/R3 ellipticity ratios at 300 and 873 K are similar (see ESM). Magnitude and orientation of the thermal ellipsoid at 873 K correspond to simple thermal motion constrained by the O(10) and O(4) atoms, without any significant evidence of control from the O(2) atoms (Fig. 4, see ESM).

Conclusions

This is the first multi-methodological study aimed to describe the structural evolution of zoisite in response to high temperature, on the basis of in situ single-crystal X-ray and neutron diffraction data.

If we compare the thermo-elastic parameters of the unit-cell volume of zoisite obtained in this study and those of a natural epidote previously reported by Gatta et al. (2011) [i.e. Ca1.925Fe0.745Al2.265Ti0.004Si3.037O12(OH)], refined on basis of the Pawley et al. (1996) and Holland and Powell (1998) protocol, we obtain only slight, but significant, differences, being α V0 = 5.93(5) × 10−5 K−1 for zoisite and 5.1(2) × 10−5 K−1 for epidote. Apparently, if we compare the two topologies, the higher the Fe-content, the lower the expansion coefficient. However, more work on Fe-richer zoisite samples is needed to support this point.

We have not found any evidences of discontinuities in lattice parameter nor change in space group symmetry, which could be ascribed to the two distinct modifications, zoisite I (<0.05 X ps) and zoisite II (>0.05 X ps) described by Liebscher et al. (2002). Therefore, the proposed ‘isosymmetric displacive phase transition’ does not occur at T > 50°C.

The structure refinements at high temperature are the key to understand the NTE of zoisite along [100]. The inter-polyhedral tilting, around oxygen atoms which act as hinges, governs the expansion observed along [001] and the contraction along [100]. Along [010], the octahedral ribbons act as ‘pillars’ (Figs. 2, 4), and the thermal expansion is mainly controlled by the intra-polyhedral bond-lengths expansion. On the (010)-plane, the inter-polyhedral rotation (e.g. between 300 and 873 K: Si(2)–O(9)–Si(1) from 173.62(7)° to 171.4(4)°, neutron refinements; Figs. 2, 3a) gives rise to the expansion of the ‘cage’ (in which the Ca(2) atoms lie) along [001], as shown by the variation of the O(8)↔O(8) distance (from 4.981(1) to 5.055(4) Å, between 300 and 873 K, neutron refinements), and to the mutual contraction along [100], as shown by the evolution of the O(6)↔O(2) distance (from 5.531(1) to 5.506(4) Å, between 300 and 873 K, neutron refinements) and Ca(2)–O(10) bond distance (Figs. 2, 3f). The shortening of Ca(2)–O(10) occurs at T > 500 K (X-ray refinements) and might be coupled with the increase of the thermal motion of Ca(2) site.

This kind of behaviour is not observed in epidote, in which positive thermal expansion is observed along [100] (Gatta et al. 2010 and references therein). The reasons of this different behaviour might be ascribed to the different crystal-chemistry and the different symmetry of epidote. The virtually linear hydrogen bond in zoisite and the pronounced deviation from the linearity in epidote (~166.7° at room-T, Gatta et al. 2010) suggest that the presence of Fe3+ at the M(3)-site in epidote leads to a weakening of the bonds (Langer and Raith 1974; Liebscher 2004), as shown by the increase of the O(10)···O(4) and H(1)···O(4) distances (Kvick et al. 1988; Gatta et al. 2010). Accordingly, Kvick et al. (1988) and Gatta et al. (2010) suggested that the deviation of the O(10)–H(1)···O(4) angle from the linearity in epidote might be ascribable to the electrostatic repulsion from the trivalent cations at the M(3)-site and from the Ca(2)-site, as M(3)···H(1) ~2.782 and Ca(2)···H(1) ~ 3.014 Å at room-T. In zoisite, the shortest Ca···H distance is Ca(2)···H(1) = 3.258(2) Å at 300 K and Ca(2)···H(1) = 3.216(8) Å at 873 K, whereas M(3)···H(1) = 2.688(2) Å at 300 K and M(3)···H(1) = 2.712(9) Å at 873 K (neutron refinements). In addition, even the Ca(1)–O(9) interaction is significantly different between zoisite and epidote: at room-T, Ca(1)–O(9) distance is 2.906(1) in zoisite (neutron refinement) and 3.002(1) in epidote (Gatta et al. 2010). As O(9) plays an important role in the deformation of the Si(2)–O(9)–Si(1) unit, the different bonding environment of this oxygen site in zoisite and epidote should be also considered, as in epidote the Si(2)–O(9)–Si(1) angle increases with T, whereas in zoisite it decreases (Table 6a, b). On the whole, despite the close-related structure topology, the different crystal-chemistry between zoisite and epidote leads to a different thermo-elastic behaviour.