## Introduction

Amphiboles, hydrous silicates with the general formula AB2C5T8O22W21, are very important constituents of the Earth’s lithosphere, occurring in a diversity of rock types2. Being a structural bridge between pyroxenes and phyllosilicates, amphiboles are involved in a number of transformation processes at elevated temperatures and pressures during subduction. The ultimate effects of these processes include the oxidation of Fe and the release of water into the lower crust/mantle3,4. The strong structural anisotropy of the amphiboles results in heavily anisotropic elastic, thermoelastic, dielectric, and conductivity properties, which in turn contributes to the behavior of the host rock. The amphibole structure (see Fig. 1a) may accommodate a variety of chemical elements at the non-tetrahedrally coordinated crystallographic sites: M(1), M(2), and M(3) occupied by C-type cations, as well as at the M(4) site occupied by B-type cations, which strongly influences their properties and thermal stability5. A particularly important issue in the crystal chemistry of these minerals is the stability of Fe-bearing species, because their oxidation processes have a paramount importance in a wide spectrum of fields, including geology and geophysics, but also materials science and toxicology6,7. Early ex situ work8,9 have revealed that oxidation of CFe is intrinsically coupled with a loss of hydrogen from the hydroxyl group, in the presence of external oxygen (exO2), according to the reaction:

$$2{{\rm{Fe}}}^{2+}\!+{2}^{{\rm{W}}}{({\rm{OH}})}^{-}+{0.5}^{{\rm{ex}}}{{\rm{O}}}_{2}\rightarrow\,2{{\rm{Fe}}}^{3+}+{2}^{{\rm{W}}}{{\rm{O}}}^{2-}+{}^{{\rm{ex}}}{\rm{H}}_{2}{\rm{O}}$$
(1)

Further in situ studies have clarified the changes in the interatomic distances and site population associated with iron oxidation as well as the subsequent phase transformations5,10,11. Very recently, by combining diffraction and spectroscopic methods, thus probing the structure at different length and time scales, it has been shown that the above simple chemical reaction is preceded by multiple local-scale structural changes12,13,14,15. A particularly important issue, which has been achieved mainly via Raman spectroscopy, is the existence of a thermal state of reversible dynamic oxidation. This state consists of delocalization of electrons e from the octahedrally coordinated iron cations as well as of H+ from the W-type anions13. For temperatures within the range of dynamic oxidation, both e and H+ remain inside the crystal bulk but if the temperature decreases, they can be attached back to CFe3+ and WO2−, respectively, to form again CFe2+ and W(OH). Only when the thermal energy is high enough, the atomic vibrations trigger a readjustment of the TO4-ring geometry to match with smaller-size adjacent MO6 octahedra (see Fig. 1a), which in turn allows for the irreversible Fe2+→Fe3+ exchange and release of H+ cations from the amphibole structure13.

The delocalization of e and H+ and consequent hopping within the amphibole structure results in an increase in mineral conductivity14,16, a feature that may have a tremendous impact on the physics of hydrous silicates with a quasi one-dimensional structure and on potential mineral-inspired technologies6. Moreover, the possible development of transport and magnetic properties in iron-bearing amphiboles at elevated temperatures is of extreme interest in geophysics17,18,19,20, especially when modeling lithospheric conductivity16,21. For the latter, dehydrogenation of amphiboles and other representative hydrous silicates is also considered to play an important role for the high-temperature anomalies in subduction zones22 Besides, the dehydrogenation of amphiboles and related layered silicates can contribute to the water cycling at depth or, depending on the local rock assemblages, to the formation of abiotic H2 and CH423.

So far, studies on the stability of Fe-containing amphiboles have been mainly restricted to species from the sodium amphibole subgroup (e.g., ref. 13 and references therein), which are typical of high-pressure rocks. However, given the large compositional variety of amphiboles, it is important to study the high-temperature behavior of different amphibole subgroups, in order to understand whether the state of existing charge carriers in terms of delocalized e and H+ is a general property of all amphiboles. Hence, we have analyzed grunerite, ideally ABFe2+2CFe2+5Si8O22(OH)2, a member of the magnesium-iron-manganese amphibole subgroup24. These species are particularly common in metamorphic rocks, where they may coexist with amphiboles of the tremolite-actinolite series or with serpentine-group minerals2. Amphiboles belonging to the Mg-Fe-Mn subgroup may crystallize in orthorhombic (Pnma or Pnmn) or monoclinic (C2/m or P21/m) symmetry. The monoclinic structure is stabilized if Fe2+ dominates both as B- and as C-type cation25. In Mg-dominant amphiboles, a reversible displacive P21/m-to-C2/m phase transition may occur on heating5, with a critical temperature Tc decreasing from ~600 to ~200 K, with the increase of Fe2+ content5,26. Very recently, we have demonstrated the possibility of discriminating the crystal system of Mg-Fe-Mn and Li amphiboles by the position of a low-wavenumber Raman peak, which appears at ~75–85 cm−1 and ~60–70 cm−1 for monoclinic and orthorhombic amphiboles, respectively27. Similarly to pyroxenes28, this peak is assigned to an external TO4 mode of the silicate double chain, and mirrors the relative geometry of the silicate anion with respect to small eight‐coordinated (B-type) cations. For this reason, it is expected to be sensitive to temperature-driven phase transitions that are strongly controlled by the B-site size5.

Here, we report the results of our temperature-dependent polarized Raman spectroscopic study of grunerite heated in air or in N2 atmosphere, to follow the dynamics of multistep oxidation processes and the temperature-induced structural transformations. The most striking result is the existence of a strongly anisotropic reversible oxidation mechanism even under reducing atmosphere, which consists in direction-dependent coupled electron–phonon transition at elevated temperatures. Such temperature-induced conduction electrons associated with FeO6 octahedra, in the presence of delocalized H+, should be a universal property of all one-dimensional or two-dimensional Fe-bearing hydrous silicates. This phenomenon provides insights into the atomistic driving force for the increasing conductivity observed in subducted rocks at convergent plate margins16.

## Results

### Symmetry considerations, anomalous anisotropic Raman scattering, and selection rules

Two natural grunerite samples, designated as A85 and A8627 and with chemical formulae given in Table 1, have been studied by in situ temperature-dependent Raman spectroscopy. At each temperature parallel polarized spectra (incident-light polarization Ei parallel to the scattered-light polarization Es) were collected in backscattering geometry (the direction of propagation of the incident light, ki, is antiparallel to the direction of propagation of the scattered light, ks) from a natural crystal face in two different orientations of the crystal grain, i.e., with the crystallographic c axis parallel to Ei and the c axis perpendicular to Ei. In Porto’s notation, ki(EiEs)ks, the former geometry corresponds to $$\bar{y{\prime} }({zz})y{\prime}$$, whereas the latter to $${{\bar{y}}^{{\prime} }}(x{\prime} x{\prime} )y{\prime}$$, where z is along the c axis and x’ and y’ are two mutually perpendicular directions within the (a*,b) plane (see the sketch in Fig. 1b). In both geometries only Ag modes are observed, whose Raman polarizability tensor in 2/m point symmetry is given by29:

$$\alpha ({{\rm{A}}}_{{\rm{g}}})=\left(\begin{array}{c}{\alpha }_{xx} \cdot {\alpha }_{xz} \\ \cdot {\alpha }_{yy} \cdot \\ {\alpha }_{xz} \cdot {\alpha }_{zz}\end{array}\right)$$
(2)

Therefore, the $$\bar{y^{\prime} }({zz})y^{\prime}$$ spectra are dominated by the αzz component, whereas the $$\bar{y^{\prime} }(x^{\prime} x^{\prime} )y^{\prime}$$ spectra are determined either by both αxx and αyy components or only by αxx, depending on whether the crystal-grain face is parallel to {110} or {010} cleavage plane.

Selected $$\bar{y^{\prime} }({zz})y^{\prime}$$ in situ Raman spectra of near-end-member grunerite A85 in air are shown in Fig. 2a. The overall Raman scattering drastically changes above 650 K: new broad peaks appear at ~273, 470, 576, and 815 cm−1, whereas all symmetry-allowed first-order Raman peaks are suppressed, and above 750 K they cannot be resolved any longer. The only exception is the Raman-active MO6 mode that at room temperature generates a doublet ~220 cm−1. Note that in $$\bar{y{\prime} }({zz})y{\prime}$$ geometry, the polarization of the incident light Ei is parallel to the crystallographic c axis. The temperature evolution of the Raman scattering is totally different when collected with Ei c, i.e., in $$\bar{y{\prime} }(x{\prime} x{\prime} )y{\prime}$$ geometry (Fig. 2b): on heating from 295 to 850 K all Raman-active phonon modes are well preserved, gradually decreasing in wavenumber and increasing in width, as it should be expected for crystals with a positive volume thermal expansion and no phase transitions. Only at 900 K the signal-to-noise ratio degrades and the Raman scattering generated by the MO6 vibrations ~220 cm−1 is enhanced, but the overall Raman scattering characteristic of amphiboles is still retained. The $$\bar{y^{\prime} }(x^{\prime} x^{\prime} )y^{\prime}$$ spectra thus show that the amphibole structure is stable at least up to 900 K and therefore, the change in the selection rules observed in $$\bar{y^{\prime} }({zz})y^{\prime}$$ geometry at elevated temperatures cannot be related to a structural transformation. Here, we should recall that the Raman scattering of solids is a light-matter interaction process that depends not only on the equilibrium configuration of nuclei, but also on the electron density of states (DOS). In the case of non-metallic materials, if the photon energy of the excitation laser line Ephoton is smaller than the electron energy gap Eg, the selection rules are determined only by the phonon wave functions. However, when Ephoton is close to or larger than Eg, the incoming photon can excite simultaneously a phonon and an electron, and the selection rules under such resonance conditions depend on both the phonon and the electron wave functions. For insulating and semiconducting materials, the resonance Raman scattering (RRS) is achieved via the so-called Fröhlich interactions30, consisting in electrostatic interactions between electrons and longitudinal optical (LO) polar phonons. In the case of centro-symmetrical crystals as C2/m amphiboles, under non-resonance conditions (i.e., no electron transitions) the polar phonons at the Brillouin zone center are infrared-active but Raman inactive, and vice versa. Therefore, the optical phonon modes that are Raman-active under non-resonance conditions cannot participate in Fröhlich interactions because they do not carry polarity and can become forbidden under resonance conditions (i.e., when electron transitions are activated by a photon or another external stimulus)31. Moreover, the RRS owing to Fröhlich interactions is selective; a resonance enhancement is expected only for those LO polar phonons that are related to the local structural species in which the electron transition occurs and therefore can couple with the excited electron31,32,33.

### Assignment of the observed spectral features at elevated temperatures

In our experiment, we changed the temperature, maintaining constant the excitation wavelength (λ = 514.532 nm). Actually, the temperature at which we observe drastic changes in the spectra is ~700 K, which is equivalent to ~0.06 eV, well below the photon energy of 2.4 eV corresponding to λ = 514.532 nm. Hence, the puzzling picture observed for grunerite (Fig. 2) can only be explained by temperature-activated electron transitions across Eg that interact with polar optical phonons, forming strongly anisotropic intrinsic local polarizations Ploc, i.e., mobile polarons with aligned dipole moments. These temperature-activated coupled electron–phonon excitations will change the Raman selection rules from non-resonant to resonant only when Ploc is parallel to the photon polarization Ei, to fulfill the requirement for three-particle interaction among the excited electron, the phonon, and the incoming photon. When Ploc is perpendicular to Ei, the temperature-induced polaron dipole moments do not interact with the photon polarization and hence the inelastic light scattering is realized only via photon–phonon interaction. This causes the appearance of RRS only in $$\bar{y^{\prime} }({zz})y^{\prime}$$ scattering geometry, while the $$\bar{y^{\prime} }(x^{\prime} x^{\prime} )y^{\prime}$$ spectra still correspond to non-resonant selection rules. All phonons related to the silicate anion, including the SiO4 stretching modes ~900–1100 cm−1, the SiO4-ring mode ~658 cm−1, the SiO4-chain mode ~78 cm−1, as well as the OH-stretching modes are suppressed under resonance conditions (see Fig. 2a). In contrast, phonons involving vibrations of MO6 octahedra, e.g., ~220 cm−127,34, are resonantly enhanced. Moreover, the most pronounced resonantly activated phonon mode appears ~570 cm−1, a wavenumber that is typical of Fe3+O6 stretching in CFe-bearing amphiboles27,34. Therefore, the electron transition responsible for the anisotropic RRS occurs between electron levels related to the FeO6 octahedra and has an induced dipole moment parallel to the c axis. Because of such a transition, conduction electrons form in the crystal and locally, the oxidation state of the corresponding CFen+ ions changes from divalent to trivalent. This being the case, the direction-preferred formation of conduction electrons at elevated temperatures is expected to be an intrinsic feature of all amphiboles containing octahedrally coordinated Fe, allowing for polaron mobility associated with the strips of octahedra. Note that the temperature above which we observe this phenomenon is consistent with the requirement that the threshold temperature of small polaron hopping is about half the Debye temperature of the system35,36,37.

To verify our conclusions, density-functional theory (DFT) calculations were performed on three model systems with the same structure, using that of A85, but having different occupancy at the M(1), M(2), M(3), and M(4) sites: (i) all sites occupied by Fe2+, (ii) octahedrally coordinated M(1–3) sites occupied by Fe2+, and M(4) by Mg, and (iii) octahedrally coordinated M(1–3) sites occupied by Mg, and M(4) by Fe2+. The projected electron DOS for Fe, O, Si, and Mg in different models is shown in Fig. 3. The calculated energy gap for end‐member grunerite (where M(1)M(2)M(3)M(4) = FeFeFeFe) is Eg = 0.05 eV (see Supplementary Figure 8 and Supplementary Table 5), close to the value of 0.06 eV suggested from the experiment, although one should keep in mind that in general only semi-quantitative conclusions can be gained from DFT calculations. The projected DOS for the two imaginary compounds (M(1)M(2)M(3)M(4) = FeFeFeMg and = MgMgMgFe) clearly show that Fe at M(1–3) contributes to the conduction band between ~0.001 and 0.02 eV, whereas Fe at M(4) to that ~0.6 eV ~6900 K. Therefore, we can safely state that the experimentally observed phenomena ~700 K are exclusively related to octahedrally coordinated Fe. Moreover, the orbital DOSs of Fe as well as of O atoms from the MO6-strip (see Supplementary Figures 27) suggest that the top of the valence band results from the hybridization between O 2px orbitals and Fe 3dxy orbitals, whereas the bottom of the conduction band from the hybridization between O 2px and Fe dx2–y2 orbitals. Therefore, the dipole moment related to electron transitions across Eg is along z (parallel to the crystallographic c axis), in full agreement with the conclusions derived from the experimentally observed anisotropic appearance of RRS.

### Quantitative trends from heating experiments on near-end-member grunerite (A85) in air

The Raman spectra of A85 measured in air at room temperature after annealing the sample at different temperatures (Fig. 4) show an almost total recovery of the $${{\bar{y}}^{{\prime} }}({zz})y^{\prime}$$ scattering after heating up to 700 K. The non-RRS peaks, however, are gradually suppressed after heating up to 750 K and 800 K, and completely disappear after heating at 850 and 900 K. This trend can be quantified by the intensity ratio $${I}_{586}^{\rm{RRS}}/({I}_{586}^{\rm{RRS}}+{I}_{{\rm{ring}}\; {\rm{mode}}})$$, i.e., the relative intensity between the strongest RRS peak ~586 cm−1 and the strongest non-RRS peak generated by framework vibrations, namely the ring mode ~658 cm−1. Figure 4a demonstrates that the experimental data plotted versus the heating temperature follow a Boltzmann growth function with an inflection at Theatinf = 720 K. This value matches exactly the transition temperature obtained by X-ray diffraction (XRD) and X-ray absorption spectroscopy for the closely related amphibole riebeckite11,15, which further emphasizes that the irreversible RRS is related to permanent Fe oxidation. In our previous studies on riebeckite13 we showed that the MO6 mode ~146 cm−1 in $${{\bar{y}}^{{\prime} }}(x{\prime} x{\prime} )y{\prime}$$ spectra is sensitive to Fe oxidation; the fractional intensity of this mode increased in the temperature range of reversible oxidation (delocalization of e within the crystal bulk) and dropped abruptly on the verge of irreversible oxidation (ejection of e from the crystal). The same feature is observed here. In the spectra of grunerite, the corresponding MO6 mode occurs ~152 cm−1; it shows a reduction of the relative intensity in the room-temperature spectrum collected after annealing the sample at 900 K (see Fig. 4b), indicating a partial irreversible oxidation. The analysis of the temperature dependence of this mode shows a perceptible increase in the fractional intensity at 720 K and an abrupt decrease above 850 K (see Fig. 5b), marking the beginning of reversible and irreversible oxidation, respectively. These two temperatures match very well Theatinf and Theat for which room-temperature non-RRS modes completely disappears ($${I}_{586}^{\rm{RRS}}/({I}_{586}^{\rm{RRS}}+{I}_{{\rm{ring}}\; {\rm{mode}}})$$ = 1). The irreversible enhancement of the Raman scattering ~220 cm−1 relative to the signal at 180 cm−1 in the $${{\bar{y}}^{{\prime} }}(x^{\prime} x^{\prime} )y^{\prime}$$ spectrum (see Fig. 4b) should also be related to irreversible Fe oxidation, similar to the intensity ratio of the doublet ~165–175 cm−1 in the Raman spectra of riebeckite13. All this indicates strong correlation between the anisotropic RRS and the irreversible Fe2+→Fe3+ exchange, as the latter is the reason for quenched RRS at room temperature.

### In situ high-temperature experiments of near-end-member grunerite (A85) in N2

In order to determine whether the presence of exO2 is a necessary precondition for the anisotropic development of conduction (delocalized) electrons, we performed in situ Raman experiments purging the sample chamber with N2. Figure 6 shows that reversible anisotropic RRS appears also under reducing atmosphere, but at higher temperatures than in air. Therefore, the presence of exO2 favors the direction-preferred electron transition between the hybridized O 2p and Fe 3d levels, but it is not required for this process to occur. Hence, anisotropic conductivity due to mobile electrons can exist in amphiboles at elevated temperatures, independently of the external environment. Another interesting observation is that above 700 K the OH-stretching peaks can hardly be resolved in either scattering geometry, but they fully recover on cooling back to room temperature, emphasizing that the reversible delocalization of WH+ at high temperatures is also unaffected by the absence of exO2. The diffusion of these delocalized H+ cations through the crystal bulk should also contribute to the overall electrical conductivity of amphiboles. The room-temperature $${{\bar{y}}^{{\prime} }}(x^{\prime} x^{\prime} )y^{\prime}$$ spectra before and after heating in N2 are identical, whereas there are weak extra peaks ~583 and 464 cm−1 in the $${{\bar{y}}^{{\prime} }}({zz})y^{\prime}$$ spectrum measured at room temperature after heating in N2 up to 800 K. The same is observed in the $${{\bar{y}}^{{\prime} }}({zz})y^{\prime}$$ spectrum measured at room temperature after heating up to 700 K in air (see Fig. 4a). Note that in both cases the ratio between the total integrated intensity generated by OH-stretching vibrations and by the framework vibrations (below 1200 cm−1) remains unchanged within uncertainties, confirming negligible loss of H+ upon heating to 800 K in N2 or 700 K in air. Therefore, for charge-balance reasons, there should be no ejection of electrons from the crystal bulk. On the other hand, the extra peaks are indicative of presence of CFe3+27,34. This suggests that on cooling a small amount of temperature-activated conduction electrons have been trapped in deep defect levels and hence, some octahedrally coordinated iron ions could not recover their initial divalent oxidation state.

### Comparative analysis of the temperature behavior of the two grunerite samples

The Raman scattering analysis of A86, which contains less Fe2+ than A85 (see Table 1), reveals the same temperature-induced processes as in A85. However, they occur at temperatures ~100 K higher than the corresponding temperatures for A85. Reversible anisotropic RRS takes place at 800 K in air (see Fig. 7a) and the $${{\bar{y}}^{{\prime} }}({zz})y^{\prime}$$ spectrum measured after subsequent cooling down to room temperature contains a weak Raman scattering ~587 cm−1 attributed to CFe3+O6 due to trapped electrons, resembling the spectral features observed for A85 when heating in air up to 700 K (see Fig. 2a). Also, the OH-stretching peaks in the $${{\bar{y}}^{{\prime} }}({zz})y{\prime}$$ spectrum of A86 measured in N2 disappear at 850 K (Fig.7c), similarly to the corresponding spectrum at 750 K for A85 (Fig. 6a). Following this trend, one should expect sample A86 to exhibit $${{\bar{y}}^{{\prime} }}({zz})y^{\prime}$$ RRS in N2 ~900 K, but due to instrumental limitations this temperature could not be reached in our experiment. The complete recovery of the $${{\bar{y}}^{{\prime} }}(x^{\prime} x^{\prime} )y^{\prime}$$ spectrum of A86 after heating in air up to 950 K (Fig. 7b) demonstrates that the temperature of irreversible Fe oxidation has not been reached. This further emphasizes the importance of our results for potential technological applications based on materials comprising quasi one-dimensional octahedral systems.

At last, we have considered the temperature evolution of the SiO4-ring mode ωring ~660 cm−1 as well as of the SiO4-chain mode ωchain ~78 cm−1 in the range 100–950 K (Fig. 8). Both modes appear at slightly lower wavenumbers for A85 than for A86 due to its higher CFe2+ content27. A minimum in ωring(T) marks the temperature of SiO4-ring modification to adopt the smaller Fe3+O6 volume, triggering the release of e and H+ from the crystal, that is, the irreversible CFe oxidation13. The threshold temperature of irreversible oxidation Tirr.ox is not reached for A86 in the studied T range (Fig. 8a), whereas Tirr.ox is 850 K for A85, in excellent agreement with the value derived from the temperature dependencies of $${I}_{586}^{\rm{RRS}}/({I}_{586}^{\rm{RRS}}+{I}_{{\rm{ring}}\; {\rm{mode}}})$$ and In(152) (Fig. 5). At low temperatures, ωring(T) reaches a saturation, indicating no further change within the silicate double chains; however ωchain(T) exhibits a broad minimum ~170 K (Fig. 8b), suggesting a rearrangement of the double chain with respect to the M(4) site. A minimum in the wavenumber of a low-energy phonon points to a phase transition, especially when we know that this particular phonon mode is sensitive to the symmetry of the crystal structure27. Following the concepts of hard-mode spectroscopy38, we attribute the minimum in ωchain(T) to a P21/m ↔ C2/m phase transition of mixed displacive and order/disorder character, which has been already observed for cummingtonite26. The phase transition temperature Tc depends on the total content of Fe2+ and for x = Fe/(Fe + Mg) ranging between 0 and 0.45, Tc varies between ~600 and 200 K26. A linear extrapolation to Tc(x) suggests that grunerite with x above 0.7 should not undergo a phase transition to P21/m in agreement with the data provided by infrared spectroscopy or XRD26. Our Raman data however clearly indicate a structural instability in the silicate chain, which commonly leads to a P21/mC2/m symmetry change in both amphiboles and pyroxenes39,40, suggesting that Tc(x) follows a more complex trend. The small depth in ωchain(T) around the minimum suggests only subtle structural alteration, which could explain why such a phase transition has not been reported so far for grunerite.

## Discussion

Seismic and electromagnetic anomalies in subduction zones have triggered continuously growing interest on amphiboles and layer silicates, as well as of hydrogen-bearing nominally anhydrous minerals, as responsible for the electrical conductivity of the mid-crust and subduction zones16,17,18,41,42,43,44,45,46. Metasomatic processes leading to the formation of hydrous fluids may considerably contribute to the anomalies in lithospheric conductivity22,44. However, recent studies have indicated that conductive aqueous fluids alone cannot explain the anisotropic conductivity observed in some locations16,42. Moreover, although the geophysical anomalies generally depend on both temperate and pressure as thermodynamical parameters47,48, temperature rather than pressure is the major factor influencing the electrical conductivity of rock-forming minerals16,22,46. Two main temperature-activated solid-state processes have been considered to cause the rock conductivity: (i) hopping of electrons/electron holes between ferrous and ferric iron and (ii) diffusion of H+44. The former process presumes the presence of minerals with mixed-valent Fe state, that is, with coexisting Fe2+ and Fe3+ in the nominal formula, like riebeckite or arfvedsonite, leading to polaron conductivity16,45. An additional process, postulated for Fe-free minerals, involves primarily the ionic conduction: this mechanism is characterized by high activation energy (>2 eV) and has been inferred to explain the conductivity of tremolite at very high temperatures46.

As discussed above, the essence of RRS based on Fröhlich-type interactions is the formation of polarons, i.e., coupled electrons and LO phonons, allowing for the propagation of the associated local structural distortion, that is, the MO6 shrinking in the present case. Our study directly demonstrates the existence of polarons in amphiboles at high temperature; so far this process has been only assumed to be responsible for the electrical conductivity in Fe-bearing rock-forming silicates16,45, mainly based on the observed low activation energies (<1 eV) for these compounds. The observed anisotropic RRS undoubtedly shows direction-dependent temperature activation of polarons, in full accordance with the measured anisotropic conductivity of amphiboles, being five to six times higher along the c axis than along the perpendicular direction17,18,45. Moreover, our results demonstrate that mixed-valent Fe state is not necessary for the development of polaron conductivity. In fact, high temperatures naturally lead to delocalized electrons coupled with LO phonons also in amphiboles containing (at room temperature) only divalent Fe. The structural similarity between amphiboles and layer silicates (both consisting of MO6 slabs linked to TO4 slabs) suggests that the same process may occur in both structure types. Therefore, our work allows the general conclusion that anisotropically coupled electron and phonon excitations provide a robust explanation for the anisotropic conductivity of lithospheric rocks containing hydrous Fe-bearing silicates.

Diffusion of H+ as a possible source for the rock conductivity has been always considered in terms of irreversible dehydrogenation and related to the oxygen fugacity. Our results reveal that delocalized H+, hopping between different W anions, do exist in both oxygen-containing and oxygen-poor/free surroundings, although the final expulsion of H+ from the structure, in the form of water molecules (“dehydration”, a process different from “dehydrogenation”) is only possible in the presence of external oxygen. This conclusion is quite important in petrology/geophysics, because of its key role for the better understanding of water recycling in the mantle. The Raman analysis of both sodium amphiboles13 and Mg-Fe-Mn amphiboles (this study) suggests that the formation of delocalized e promotes the delocalization of H+, but there is no evidence that the motion of polarons within the crystal bulk is coupled to H+ motion, implying that polaron migration may occur also in oxo-amphiboles. Further studies are necessary to clarify whether the H+ hopping is realized predominantly within one octahedral strip or between adjacent strips. Our very recent kinetic study of riebeckite (results not yet published) indicates that the diffusion of H+ across the amphibole crystal bulk is faster perpendicular to the c axis rather than along the c axis, suggesting H+ hopping between strips. Another point to be explored in follow-up studies is whether delocalization of H+ is hindered in OH-amphiboles having a filled A site.

It is worth noting that an increase in conductivity has been observed above the temperature of dehydration of amphiboles16, i.e., after the injection of e and H+ from the crystal bulk. The irreversible formation of Fe3+ certainly changes the whole electron band structure and the energy gap slightly shrinks14. Therefore, in this case the number of thermally activated conduction electrons in total should be larger than when the Fe2+–Fe3+ exchange is dynamic (reversible), but the mechanism beyond conductivity, namely coupled electron–phonon excitations is the same.

## Conclusions

The appearance of anisotropic RRS at elevated temperatures directly evidences the formation of temperature-activated polarons involving an electron transition between hybridized O 2p and Fe 3d levels with a dipole moment along the octahedral strips in the amphibole structure. These anisotropically coupled electron and phonon excitations in hydrous Fe-bearing chain/layered silicates are the atomistic source of anisotropic lithospheric conductivity, rather than phenomena limited to solid-fluid interfaces.

The presence of mobile electronic polarons and H+ cations at temperatures above 700 K, which are typical of the lithosphere and forearc regions of slab-mantle wedge interfaces in subduction zones, indicate that both types of charge carriers can contribute to the overall lithospheric conductivity.

The occurrence of either type of charge carriers does not require the initial coexistence of ferrous and ferric iron in the mineral and does not depend on the oxygen fugacity of the system. The presence of external oxygen is however required to trigger H+ expulsion as H2O molecules, thus making the amphibole an efficient carrier of water into the crust/mantle.

## Methods

### Sample characterization

The chemical composition was analyzed by wavelength-dispersive electron–microprobe (Supplementary Note 1, Supplementary Table 1). The oxidation state of iron and the site populations were further checked by Mössbauer spectroscopy (Supplementary Note 2, Supplementary Figure 1 and Supplementary Table 2). The room-temperature structure was refined to single-crystal XRD data (Supplementary Note 3, Supplementary Table 3, Supplementary Data 1, and Supplementary Data 2). The chemical formulae were calculated using the Excel sheet developed by Locock49, taking into account the Fe2+ site population from the structure refinements and Mössbauer data. Euhedral crystal grains of size ~0.1 × 0.1 × 0.5 mm3 with the prim axis along the crystallographic [001] direction and natural crystal faces parallel to the common cleavage planes ({110} or {010}) were used in the Raman spectroscopic experiments. Pristine grains of similar size have been used for each temperature run.

### Raman spectroscopy

The Raman spectra were collected with a Horiba Jobin-Yvon T64000 triple-monochromator spectrometer equipped with an Olympus BX41 microscope and a liquid-N2-cooled charge-couple-device detector, using the 514.532-nm line of a Coherent Innova 90 C FreD Ar+ laser. The spectrometer was calibrated to the Si Raman peak at 520.5 cm−1. The spectral resolution was ~1.9 cm−1, whereas the instrumental precision in determining the peak positions was ~0.35 cm−1. Prior and after the temperature runs, spectra were also collected with the 488-nm laser line, to verify the phonon origin of the peaks observed. In situ temperature-dependent experiments in N2 atmosphere were performed by a LINKAM THMS-E600, whereas in air with a LINKAM TS1200 EV-1015. Detailed information about the temperature ramps is given in Supplementary Table 4. The as-measured spectra were baseline-corrected, temperature-reduced for the Bose-Einstein population factor, and fitted with pseudo-Voigt functions (see Supplementary Note 4).

### DFT calculations

The electron band structure and DOS were calculated using the DFT based on the generalized gradient approximation of Perdew-Burke-Ernzerhof as implemented in the Vienna Ab-initio Simulation Package50. The electron and core interactions are included using the frozen-core projector augmented wave method, with the plane-wave cutoff energy chosen as 360 eV for model structures (see also Supplementary Note 5). The lattice constants and the atom coordinates are optimized until the convergence of the force on each atom is <0.01 eV/Å. The Monkhorst-Pack scheme is used to sample the Brillouin zone. The structures are fully relaxed with a mesh of 4 × 2 × 6. The number of bands per k point was set to 10 during the electronic band structure calculations.