Introduction

The structure–property relationship of cordierite, the magnesium iron aluminum silicate (Mg,Fe)2Al4Si5O18 in a simplified form, has received considerable attention as a mineral and ceramic component because of its exceptional physical properties, which are of great interest for various industrial applications (e.g., Camerucci et al. 2001). This includes the remarkable ability to sustain large temperature gradients and temperature changes on a short timescale and thermomechanical properties related to low thermal volume expansion (e.g., Hochella et al. 1979; Mirwald 1981; Ikawa et al. 1986; Haussühl et al. 2011). The cordierite structure is apparently stable over a broad pressure and temperature range and is known, in particular at high-temperature conditions, to substitute various trace elements and variable amounts of volatiles (e.g., Bertoldi et al. 2004 and references therein). In geoscience, cordierite is used as a geothermobarometer and for monitoring paleofluid compositions (e.g., Bhattacharya 1986; Harley et al. 2002; Bul’bak and Shvedenkov 2005). Structural changes and related polymorphism are well known on temperature variations and originate from the Al, Si-order within the aluminosilicate framework, as manifested by a symmetry change from ordered Cccm (=cordierite) to disordered P6/mcc (=indialite) space–group symmetry above the critical temperature of ~1,750 K (e.g., Putnis 1980a; Armbruster 1985a; Redfern et al. 1989; Daniels et al. 1994; Malcherek et al. 2001). Most recent experimental high-pressure studies suggest the pressure-induced overhydration of the orthorhombic structure above 4 GPa to take place without changes in the symmetry (Likhacheva et al. 2012, 2013), while above 6.9 GPa, cordierite transforms to a high-pressure polymorph of apparently triclinic symmetry (Miletich et al. 2014).

Recent investigations of the material structure at non-ambient conditions encompass experimental ion irradiation. Extensive investigations currently focused on material alterations related to ion beam exposure (Weikusat et al. 2008, 2010; Miletich et al. 2010), because of reported capability to sustain relatively high doses of irradiation and simultaneously showing only minor alterations on the structure. Irradiation experiments using relativistic heavy ions revealed the irradiation-induced dehydration of extra-framework H2O contents and the speciation change in trace oxocarbon channel constituents, i.e., the formation of molecular carbon monoxide (Weikusat et al. 2008, 2010). Together with defect-associated charge transfers related to the irradiation-induced formation of ferric iron, which is macroscopically evidenced by the typical radiocoloration (Nasdala et al. 2006), the subtle changes in the molecular species inside the channels are the only verifiable alterations. The structure apparently preserves the crystalline state and its crystallographic long-range order up to relatively high fluences without any indication for a typical irradiation-induced degradation of the long-range order as observed for many other minerals such as mica (Vetter et al. 1998), quartz (Ramos et al. 2000; Afra et al. 2013), or apatite (Miro et al. 2005). Raman investigations by line scans across the interface of irradiated and non-irradiated crystal domains provide clear evidence for strain and strain gradients due to an obvious size mismatch of crystalline domains, showing gradients scaling with the irradiation dose (Weikusat et al. 2010).

In the context of systematic investigations on the elastic behavior of cordierite material under various conditions (Miletich et al. 2014), this work presents effects of ion irradiation-induced structural alterations on elastic properties with particular focus on (1) the effect of irradiation on the unit-cell parameters; (2) the effect of crystal orientation and anisotropy with respect to the ion beam direction and the changes in individual lattice directions; and (3) irradiation effects on the isothermal compression behavior at room temperature (RT). We report in situ high-pressure measurements on single crystals in diamond anvil cells (DACs) analyzed by means of X-ray diffraction (XRD) and micro-Raman spectroscopy. All investigations were carried out on pristine untreated and artificially irradiated crystal specimens.

Experimental

Sample material and cordierite specimen

Material used in this study was single crystals of natural, untreated hydrous low-sodium cordierite (Mg,Fe)2Al4Si5O18 samples from Mount Tsilaizina/Madagascar. The two sample specimens “Tsi1” and “CORTS” with X Fe ≈ 12 %, 0.7–0.9 wt% H2O, and <0.4 wt% CO2 are characterized by Miletich et al. (2010) and Weikusat et al. (2010). Compositions were analyzed for inhomogeneities by energy-dispersive X-ray analyses, and volatile contents were derived from relative intensities of vibrational modes in Raman spectra, following the method of Kaindl et al. (2006) and Haefeker et al. (2013). Crystal orientation (according to the crystallographic setting a ~ 17.07 Å, b ~ 9.72, and c ~ 9.35 Å) was provided by means of polarized microscopy and conventional X-ray film techniques (oscillation photographs) and through positioning according to the orientation matrices determined on a four-circle diffractometer. Double-sided polished crystal platelets with ~3 × 3 mm2 lateral dimensions were prepared from thin sections perpendicular to the oriented crystallographic axis. Sample denotations _an, _ai, _bi, _bn, _ci, and _cn correspond to the orientation (suffixes a, b, and c) and the irradiation state (n = not irradiated and i = irradiated). The thickness and orientation of the different samples together with the irradiation parameters are listed in Table 1.

Table 1 Cordierite sample crystals, their orientation, and the beam parameters for different irradiation experiments with 197Au and 209Bi ions
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Table 2 Lattice parameters a, b, and c and unit-cell volume as a function of the fluence ϕ (ions/cm2) for oriented crystal specimen irradiated along the crystallographic a-axis, b-axis, or c-axis; distortion parameter Δ = 1.094 (a − √3b) after Selkregg and Bloss (1980)
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Table 3 Lattice parameters a, b, and c and unit-cell volume V of sample Tsi1_bi (irradiated at ϕ = 1 × 1012 197Au/cm2) for different pressures; pressures are derived from unit-cell volume of quartz after Angel et al. (1997); distortion parameter Δ = 1.094 (a − √3b) after Selkregg and Bloss (1980)
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Ion irradiation experiments

Specimens of oriented crystal platelets were exposed to relativistic heavy ions (197Au, 209Bi) at the UNILAC linear accelerator and the Schwerionen Synchrotron (SIS) of the GSI Helmholtzzentrum für Schwerionenforschung (Darmstadt, Germany). At the UNILAC facility, Au ions of 1,790 and 2,187 MeV total kinetic energy (respective specific energies of 10.0 and 11.1 MeV per nucleon (MeV/u)) were used. SIS beams consisted of 3.55 GeV Au ions and 3.76 GeV Bi ions (specific energy 180 MeV/u). All irradiations were carried out under normal beam incidence with respect to the oriented crystallographic faces of the sample. Crystals of several mm in size were directly glued on Al sample holder, while small crystals (<1 mm) were packed between two 10-µm-thick Al foils. All irradiation experiments were conducted at ambient temperature, applying fluences ϕ between 1 × 1011 and 5 × 1013 ions/cm2 (Table 1). To avoid sample heating, the beam intensity was limited to about 108 ions/cm2s. Flux and fluence were controlled via a secondary electron transmission monitor (SEETRAM) calibrated with a standard Faraday cup. The range and energy loss of the ions in cordierite were calculated with the SRIM-2008 code (Ziegler et al. 1985). For samples exposed at the UNILAC, the mean energy loss of the Au ions is about 23 keV/nm varying by less than 20 % within the crystals. For all irradiations, the ion range was sufficiently large to completely penetrate through the thin platelets (~90 µm at UNILAC, ~560 µm at SIS) according to dE/dx calculated in analogy to Weikusat et al. (2010).

Determination of unit-cell parameters at ambient and high-pressure conditions

Unit-cell constants of single crystals for both ambient and high-pressure samples were measured with a Stoe AED2 or Huber 5042 four-circle diffractometer using non-monochromatized Mo radiation from a sealed-tube source. The angles of diffracted Bragg peaks were recorded using diffractometer setting as reported by Hejny et al. (2012) and by employing fitting procedures as implemented in the SINGLE software (Angel and Finger 2011). Symmetry-constrained vector-least-square refinements were carried out to obtain precise lattice parameters. The high-pressure measurements were taken in the range between 10−4 and 6.62 GPa at room temperature on sample Tsi1_bi (irradiated at ϕ = 1 × 1012 197 Au/cm2). The results of static compression were determined from two experimental loadings (run A and run B, respectively) carried out with an ETH-type (Miletich et al. 1999, 2000) DAC (~0.1-ct type Ia standard anvils; 0.6 mm culet face diameter; anvils mounted on 4-mm-thick polycrystalline Be backing plates). Both loadings were carried out using stainless steel gaskets (material type 1.4310), preindented from initial 250 µm to a starting thickness of 140 ± 5 (run A) and 105 ± 5 µm (run B). Sample crystals (size 180 × 75 × 75 µm3 in run A, 100 × 75 × 40 µm3 in run B) were loaded together with an equally sized quartz standard crystal in y-cut orientation into gasket boreholes (~250 µm in diameter) using liquefied argon as hydrostatically acting pressure medium. Pressures were adjusted by means of laser-induced fluorescence following the ruby scale (Mao et al. 1986), and precise pressure values were derived from the V/V 0 ratio of the unit-cell volumes of quartz (Angel et al. 1997). Data collection of run A yielded 7 data points and was terminated due to bridging of the 75-µm crystal specimen between the two diamond anvils at a pressure of ~5 GPa. To avoid this problem, the sample for run B was thus thinned down to ~40 µm before loading. The second run provided additional 8 data points up to ~7 GPa. The isothermal bulk moduli and individual axial compressibility coefficients (K and β −1, respectively) and its pressure derivative (∂K/∂P and ∂(β −1)/∂P, respectively), based on a third-order Birch–Murnaghan equation-of-state parameters, were obtained by fits using EosFit software (Angel 2000).

High-pressure Raman spectroscopy

In situ high-pressure Raman spectra were recorded from in total four oriented crystal samples (non-irradiated and irradiated (Tsi1_bi, Tsi1_ci, 11.1 MeV/u Au ions, 1 × 1012 ions/cm2)) cut perpendicular to the b-axis and c-axis. High-pressure sample loadings were performed with the same DAC type as described above using low-fluorescence anvils and Be backing plates with ~12° optical ports giving access into the pressure chamber. Sample crystals (bn: 130 × 100 × 55, bi: 160 × 100 × 65, cn: 140 × 110 × 70, ci: 100 × 80 × 70, all measures in µm) were loaded into boreholes (260–270 µm diameter, 135–140 µm thickness) of preindented steel gaskets. Pairs of samples of the same orientation were loaded together with small ruby spheres (Chervin et al. 2002) in one borehole using cryogenically liquefied argon. Luminescence spectra of ruby were used for pressure calibration, and considering uncertainties in the determination of line shifts, the values for derived pressures are within ±0.05 GPa. In addition to reference spectra at 1 bar outside the DAC, a series of high-pressure spectra was recorded at P = 0.32, 1.06, 2.53, 3.12, 4.41, 5.36, and 5.76 GPa (samples cn and ci) and at P = 1.69, 3.18, 4.32, 5.16, and 5.90 GPa (samples bn and bi). All spectra were measured in 180° backscattering geometry on a Jobin–Yvon HR800 confocal spectrometer equipped with an OLYMPUS BXFM-ILHS optical microscope with the instrumental setting and calibration described by Weikusat et al. (2010), i.e., a grating with 1800 grooves per mm, a notch holographic filter, and a Peltier-cooled charge-coupled device (CCD) detector (1,024 × 256 pixels, 26 µm in size). The spectra were excited using the 632.817 nm line of a He–Ne laser operated at 20 mW. A 50× long working distance objective (numerical aperture 0.70, free working distance ~10 mm) was used for laser beam focusing, allowing a lateral resolution of ~2 µm and a spectral resolution of 0.8 cm−1. All spectra were recorded with accumulation times of 1 s for the Rayleigh and neon lamp lines, 3 s for the ruby R lines, and 180 s per interval for the cordierite Raman spectra. The wave number accuracy was better than 0.5 cm−1, and the spectral resolution was determined at ~2 cm−1. Fitting was done assuming Voigt band shapes using a freeware version of FITYK (fityk.nieto.pl). Resulting band positions at different pressures are listed in Tables 4 and 5.

Table 4 Fitted positions of selected Raman bands and their uncertainties (values in cm−1) obtained for non-irradiated (“n”, first line) and irradiated (“i”, second line) crystal sections//(001); the irradiation was performed at 1 × 1012 ions/cm2
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Table 5 Fitted band positions and their uncertainties (values in cm−1) obtained from spectra of non-irradiated (“n”, first line) and irradiated (“i”, second line) crystal section//(010)
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Results and discussion

Irradiation-induced unit-cell contraction

Previous experimental studies on hydrous cordierite samples irradiated by swift heavy ions give clear evidence of strain across the interface between irradiated and non-irradiated domains (Weikusat et al. 2010). The evolution of cracks and the line shifts of Raman modes according to tensile stress across the interfaces indicates the obvious size mismatch of crystalline domains. Ion beam-induced amorphization typically leads to an expansion of the unit cell (e.g., Schouwink et al. 2010) in contrast to the here observed contraction of the cordierite unit cell (Miletich et al. 2010). Despite the fact that at higher fluences, cordierite becomes amorphous, this does not lead to a volume contraction. Therefore, the governing mechanism seems to be the ion-induced loss of water leading to a unit-cell contraction instead of amorphization-caused unit-cell expansion. Also, the defects accumulation which increases linearly with fluence is irrelevant compared to the loss of water molecules due to ion irradiation. Analyzing Raman shifts, line broadening, and the distribution of the luminescence background, depth profiles revealed gradients extending across approximately 30 µm around the stopping range of the ions. The strain gradients seem to scale with the degree of the irradiation damage and thus with the energy loss of the projectiles along their trajectory. Due to the gradients within the crystals, this earlier study did not allow to deduce lattice contraction data and anisotropies of high accuracy (Miletich et al. 2010). To minimize the occurrence of gradients, we therefore focus in this work on crystals homogeneously irradiated throughout the entire sample. The analysis includes three thick cordierite specimen (sample Tsi1) completely through irradiated at the SIS (180 MeV/u) as well as thin platelets exposed at the UNILAC (11.1 MeV/u).

Given by the homogeneous exposure conditions, the determined lattice dimensions show high accuracy with uncertainties of the individual base vectors in the order of <6 × 10−5. The values for the unit-cell parameters and their precisions are comparable to values reported earlier for non-irradiated samples (e.g., Ullrich et al. 2009; Hejny et al. 2012; Miletich et al. 2014). Table 2 lists the measurements at 1 bar of samples exposed to various ion fluences. All lattice dimensions (a, b, c, V) decrease linearly as a function of the fluence (Fig. 1). Differentiating between the directions of the irradiation vector, i.e., the ion beam being parallel to the crystallographic principle axis perpendicular to the faces of the individual crystal plates, there is no detectable orientation effect observed with the degree of unit-cell contraction depending only on the fluence but not on the orientation of the sample relative to the ion beam (Fig. 2). On the other hand, the data yield a clear anisotropy observable for the degree of irradiation-induced contraction in different lattice directions, which is approximately twice as large for the a-axis and b-axis compared to that of the c-axis. While the earlier study based on only three samples (Miletich et al. 2010) assumed quasi-isotropic lattice contraction, the fluence series of this investigation clearly indicates anisotropic behavior (Fig. 2). This anisotropy is explained by the loss of H2O molecules during irradiation and hence shrinking of the channels. Linear fits to the changes in the lattice dimensions up to fluences of ϕ = 1.3 × 1012 ions/cm2 yield a compressive strain of respective ~1.4 ± 0.1 × 10−3 and ~1.5 ± 0.1 × 10−3 for the a-axis and b-axis, while it is only ~7 ± 1 × 10−4 for the c-axis. The analyses did not consider the obvious outlier for sample CORTS_ci(6e11), having 4–5 times larger uncertainties compared to the other data points. The irradiation-induced lattice contraction is apparently isotropic within the ab-plane with no significant differences between the a-axis and b-axis directions. This explains why the distortion index (Δ = 1.094 (a − √3b)) (Putnis 1980b; Selkregg and Bloss 1980) is independent of the ion fluence. This coincides with the known empirical relationship between the distortion index Δ and the H2O content (Langer and Schreyer 1976), but is different from the finding of heat-treated cordierite, where Δ was found to be higher after thermal treatments at 900 °C (Malcherek et al. 2001). Strain originating from any thermal treatment is due to thermal expansion, indeed with values of opposite sign in most cases, but displaying an analogous anisotropy with the pronounced changes to occur within the ab-plane (cf. Malcherek et al. 2001).

Fig. 1
figure 1

Irradiation-induced lattice contraction as a function of the fluence ϕ of 2.2 GeV (11.1 MeV/u) Au ions between 0 and 1.3 × 1012 ions/cm2: a lattice parameter a; b lattice parameter b; c lattice parameter c; and d unit-cell volume V; orientations correspond to crystal plates //(100) (gray circles), //(010) (black squares), and //(001) (open triangles); lines correspond to weighted linear fits

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Fig. 2
figure 2

Normalized lattice parameter a (black squares), b (gray circles), and c (open triangles) as a function of the fluence ϕ between 0 and 1.3 × 1012 ions/cm2 in crystal plates of different orientations: a (100) crystal plate (=sample ai); b (010) crystal plate (=sample bi); and c (001) crystal plate (=sample ci); lines correspond to weighted linear fits

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According to the linear relationship shown in Fig. 1, the volume strain of 2.5 ± 0.1 × 10−3 at a fluence of 1 × 1012 ions/cm2 can be extrapolated to 3.4 ± 0.1 × 10−3 at a fluence of ϕ = 1 × 1013 ions/cm2, which is in fair agreement with the value ~1.9 to 2.0 × 10−3 previously reported (Miletich et al. 2010). The difference in volume strain may be related to fluence uncertainties (10–20 %) when comparing different irradiation experiments.

While the same authors report that irradiated cordierite was not amorphized up to a fluence of 1 × 1013 ions/cm2 on the same irradiation conditions with Au as ion projectiles, in the present study, the two samples exposed to the highest fluences (i.e., ϕ = 1 × 1013 and 5 × 1013 ions/cm2) appear to be amorphous as evidenced by the lack of birefringence under crossed polarizers and the absence of any Bragg peak in diffraction patterns. Irradiation-induced degradation of the long-range order has been reported by Lee et al. (1986) under electron beam exposure and for 1.5 MeV/u Xe ions above a critical amorphization fluence of 7.7 × 1013 ions/cm2 at 298 K (Wang et al. 1998). Our findings show that the long-range order of the cordierite structure is preserved up to a fluence of at least ϕ = 1.0 × 1012 ions/cm2, while irradiation damages corresponding to fluences above 1013 ions/cm2 result in apparent degradation of the crystalline state.

Raman spectra of pressurized and ion-irradiated cordierite

Raman spectra at high pressures were recorded for four different b-axis- and c-axis-oriented samples, for both orientations with each one non-irradiated and irradiated specimen (samples bn, bi, cn, and ci). Fig. 3 shows the non-polarized spectra of non-irradiated (Fig. 3a) and irradiated (Fig. 3b) cordierite sections perpendicular to the c-axis at pressures up to 5.76 GPa. Argon was chosen as pressure-transmitting medium, although behaving quasi-hydrostatically (Angel et al. 2007), because both liquid and the solid phases of Ar are Raman inactive. Although being a component known as a potential channel constituent, Ar does not penetrate the structural channels on compression at RT conditions (Miletich et al. 2014); significant substitution was reported only on hydrothermal treatment (Armbruster 1985b).

Fig. 3
figure 3

High-pressure Raman spectra in the frequency range of 100 to 1,000 cm−1 of a non-irradiated crystal cn and b a crystal (ci) irradiated with 1 × 1012 ions/cm2; in all spectra, the background has been corrected, and additionally, the data were smoothed by the Savitzky–Golay method in order to reduce noise; the orientation of the a-axis and b-axis in reference to the E-vector for both samples was random, causing slightly different Raman spectra

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Within the recorded range, the Raman spectra exhibit observable characteristic modes that compare well with measured and calculated spectra reported by McMillan et al. (1984), Kolesov and Geiger (2000), Geiger and Grams (2003), Nasdala et al. (2006), Weikusat et al. (2010), Kaindl et al. (2011), Likhacheva et al. (2012), and Haefeker et al. (2012, 2013). Spectra at pressures greater than ~6.5 GPa reveal a significant quality change showing much lower signal-to-background ratios and striking broadening of peaks. These changes correlate with the high-pressure phase transition reported recently (Miletich et al. 2014) and appear for non-irradiated and irradiated cordierite at 7.2 GPa. In the case of the high-pressure loading of the crystal specimens cut perpendicular to the b-axis, Raman measurements recorded at pressures above 5 GPa reveal severe changes such as three times larger half widths and uncertainties in the band position up to ±2 cm−1. These features are attributed to strain gradients and deviatoric stress, which probably originate from the bridging of the sample crystals between the culet faces of the two diamond anvils. The quality of all recorded spectra is in general characterized by relatively high noise due to the geometrical restrictions for the optical access to the pressure chamber, as limited by the geometry of the optical port in the used Be backing plates.

Characteristic bands of significant intensities are attributed to vibrational modes following the band assignment given by Kaindl et al. (2011) reported for spectra of the Fe-free end member at 1 bar (see Tables 4, 5). Apart from these bands assigned to stretching and bending modes of the framework, all high-pressure Raman spectra show a weak band at ~3,600 cm−1 (not shown), which is ascribed to the O–H stretching mode of the molecular H2O inside the channels (Kolesov and Geiger 2000; Kolesov 2006; Weikusat et al. 2008). The spectral characteristics of the assigned modes obtained from applied peak fitting procedures reveal reasonable values for the half widths (<0.8 cm−1) and band position accuracy (0.2–1.1 cm−1) for all spectra recorded under quasi-hydrostatic conditions of the used pressure medium. Non-irradiated (bn, cn) and irradiated (bi, ci, ϕ = 1.0 × 1012 ions/cm2) samples of same orientation reveal remarkable differences in the quality of the spectra. The background of irradiated crystals is in general significantly higher due to the increased luminescence (cf. Weikusat et al. 2008, 2010). This can be ascribed to the higher concentration of point defects produced by the ion beam (Nasdala et al. 2006; Miletich et al. 2010). A significant decrease can be confirmed for the O–H stretching band, which scales with the known irradiation-induced reduction in H2O content. Compared to pristine samples, the full widths at half height of any of the observed vibrational modes of irradiated crystals show no or only a small increase.

A significant pressure dependency can be reported for the band position of individual modes showing a linear shift with increasing pressure (Fig. 4). The bands located at wave numbers >400 cm−1 reveal in general the typical pressure-induced blueshift (∂ν/∂P > 0) with positive values for ∂ν/∂P between 3.4 and 6.4 cm−1 GPa−1. The position of the bands located between 200 and 400 cm−1 appears to be independent on pressure (∂ν/∂P ≈ 0, i.e., + 0.3 for ν241, −0.2 for ν 261, −0.4 for ν 297 in cm−1 GPa−1 units), while the two low-frequency lattice modes below 200 cm−1 ∂ν/∂P show negative values (−2.8 for ν 160 and −2.1 cm−1 GPa−1 for ν 120). These observations are in good agreement with the findings reported by Likhacheva et al. (2012).

Fig. 4
figure 4

Shift of selected Raman bands as a function of pressure for non-irradiated samples (bn (filled circle) and cn (filled triangle)) and samples irradiated with 1 × 1012 ions/cm2 (bi (open circle) and ci (open triangle)); the accuracy of the pressure measurements is within 0.05 GPa; lines correspond to the linear fits used to determine the change in band position with pressure (∂ν/∂P)

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In the case of irradiated samples, the only differences compared to non-irradiated samples appear for the two low-frequency bands at 122 and 158 cm−1 related to translational and librational modes of larger framework units, respectively. While for the non-irradiated sample, ∂ν/∂P of these two modes is negative, it changes to slightly positive value (+0.6 cm−1 GPa−1 for ν 122 and +0.1 cm−1GPa−1 for ν 158) for the irradiated sample. As redshifts of modes in high-pressure spectra are indicative of tensile strain, the evolution of these lattice modes is probably related to the compressional anisotropy within the ab-plane. Since these modes are assigned to bending modes between tetrahedral units, this radiation-induced change might reflect the increasing diversification between the a-axis and b-axis, as exemplified by Miletich et al. (2014) showing the a-axis to stiffen up, while the b-axis undergoes elastic softening.

Comparative equation-of-state measurements

The results of high-precision XRD measurements of sample Tsi1_bi (irradiated at ϕ = 1 × 1012 Au/cm2, UNILAC irradiation) with respect to unit-cell edges and volumes on static compression are summarized in Table 3. The irradiation caused slight peak broadening but does not impact the determination of unit-cell parameters. The evolution of a, b, c, and V as a function of pressure (hydrostatic compression in argon) is shown in Fig. 5a comparing the compressibility data of non-irradiated and irradiated hydrous cordierite below the critical pressure of the orthorhombic-to-triclinic phase transition at ~7 GPa (Miletich et al. 2014). Data points measured above 7 GPa are characterized by significant changes in the XRD Bragg peak profiles, which indicate metrical changes, the existence of more than one crystal domain, and the occurrence of structural gradients across domain boundary walls. Comparing the results of equation-of-state fits of the irradiated sample to the fitted parameters of non-irradiated hydrous cordierite, the isothermal bulk moduli and its pressure derivative (based on a third-order Birch–Murnaghan equation-of-state fit) yield K 0,298 = 117.1 ± 1.1 GPa and ∂K/∂P = −0.6 ± 0.3 for compression at room temperature (T = 298 K). These values imply a higher compressibility of the irradiated sample relative to any non-irradiated one (i.e., 137.8 ± 1.5 GPa in H2O, 127.7 ± 2.3 GPa in Ar, and 131.0 ± 1.3 GPa in methanol–ethanol, cf. Miletich et al. 2014).

Fig. 5
figure 5

Compression behavior of irradiated (full symbols) and non-irradiated (open symbols) Tsi1_bi (irradiated at ϕ = 1 × 1012 197Au/cm2) cordierite samples between room pressure and 6 GPa. Lines represent the equations of state fitted to the datasets with the parameters given in Table 6; a unit-cell volume as a function of pressure, non-irradiated (open triangles) and irradiated (black squares) both compressed in argon, and non-irradiated compressed in H2O (plus signs); b normalized lattice parameters a/a 0 (black squares), b/b 0 (gray circle), and c/c 0 (open triangles) plotted versus pressure

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The degree of compression for irradiated hydrous cordierite, which is about 10–11 % higher in comparison with the hydrous cordierite samples, can be attributed to the lower amount of H2O inside the channels corresponding to the irradiation-induced dehydration (Weikusat et al. 2008, 2010; Miletich et al. 2010). Again, the result of this study provides evidence for the anomalous compressibility, as expressed by the value for ∂K/∂P being close to zero, which can be attributed to the elastic softening preceding the first-order transition at ~7 GPa. The compression data do not reveal any pressure-induced volume gain in analogy to the observed penetration of excess fluid components, as manifested by the overhydration effect reported by Likhacheva et al. (2013).

The compressional anisotropy is in analogy to that of non-irradiated samples with the a-axis and b-axis being less compressible than the c-axis (Fig. 5b). One remarkable difference is observed for the compression within the ab-plane, which is much more isotropic for the irradiated sample than for non-irradiated cordierite. The relative small differences in the compressibilities of the a-axis and b-axis do not develop into the pronounced diversification as described by Miletich et al. (2014) on approaching the critical transition. The similar behavior in axial compressibilities is not only restricted to low pressures up to 3 GPa, such as observed for non-irradiated cordierite, but can be extended to the highest pressure points of this study. Accordingly, the distortion index Δ (Putnis 1980b; Selkregg and Bloss 1980) appears to be independent on pressure. The absolute values for Δ are in the range of values observed for non-irradiated samples (i.e., 0.246–0.269) and do not provide any significant difference for the deviation from the pseudo-hexagonal metrics of the primitive subcell. The remarkable elastic softening effects with significant negative ∂(β −1)/∂P coefficients are confirmed even to be expressed by the axial compressibilities, displaying equal ∂(β −1)/∂ P coefficients for all three main axis, but all of them marginally negative or close to zero (Table 6).

Table 6 Results of the fits for the pressure dependencies of the crystallographic axes and the unit-cell volumes to third-order Birch–Murnaghan equations of state obtained by fits using EosFit (Angel 2000) for sample Tsi1_bi (irradiated at ϕ = 1 × 1012 197Au/cm2)
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Conclusions

Applying static high-pressure methods and high-precision measurements of lattice vectors allowed us to determine volume compression and the anisotropy of the elastic properties. The bulk modulus of the investigated sample exposed to 1 × 1012 Au ions/cm2 was found to be 10–11 % smaller compared to any non-irradiated cordierite specimen. While the significantly higher compressibility is attributed to the previously reported irradiation-induced loss of extra-framework H2O, the anomalous elasticity as expressed by elastic softening appears to be related to the framework stability independent of the exposure of the ion beam. The pressure derivative of the bulk modulus ∂K/∂P, as well of the individual axial compressibility coefficients ∂(β −1)/∂P, reveals equivalent behavior indicating the instability of the structure on approaching the critical pressure P c of transformation at approximately 7 GPa. The experimental investigations by means of Raman spectroscopy and single-crystal X-ray diffraction yield evidence for a symmetry-breaking structural transition as observed in non-irradiated cordierite samples. Comparing the compression behavior between the non-irradiated and irradiated samples, the main striking feature of irradiated cordierite is the lack of the diversification between the compressibilities of the a-axis and b-axis on approaching P c. This is manifested by the distortion index Δ to be zero within the experimental uncertainties independent on the pressure variations, while it was reported earlier to increase significantly at pressures above ~4 GPa. The quasi-isotropic behavior within the ab-plane direction might also be reflected by the redshift of low-frequency modes in the high-pressure Raman spectra to turn seemingly to a blueshift for the bending modes between tetrahedral framework units. Moreover, the precise determination of lattice parameters of crystals exposed to various ion fluences confirms irradiation-induced unit-cell contractions due to the removal of H2O. The measurements revealed a volume strain of 3.4 × 10−3 up to the maximum fluence of 1.3 × 1012 ions/cm2, which corresponds to an equivalent compression of non-irradiated cordierite at only ~480 ± 10 MPa. While the irradiation-induced unit-cell contraction was found to be anisotropic (in c-axis direction only half as large as within the ab-plane), a dependency on the direction of the ion beam relative to the crystal orientation is not observed. The extent of anisotropy for the irradiation-induced contraction is opposite to the pressure-induced compressional anisotropy and is more like the anisotropy known from thermal expansion.