4 Discussion

Features appearing in the 10 $\mu$m band can be associated directly with changes in the Si-O bonding state and in particular with SiO_n structural units. It is partly for this reason that both laboratory investigators and astronomers have tended to concentrate on the analysis of the 10 $\mu$m band. However, as this paper compares spectral evolution with long-range structural evolution, it will prove instructive in the present instance to consider the evolution of the 20 $\mu$m band first.

4.1 Structural change and the 20 $\mu$m band

Annealing for 4 hours at 873 K produced three broad 20 $\mu$m band features which became more pronounced by 933 K, splitting into four features at 970 K with numerous minor additional fine-structure features appearing at 1000 K. At each of the lower temperatures the IR features appear to be insensitive to annealing time, with spectra showing little variation between the short and long annealing periods used in the experiment.

Originating generally in the vibrational modes associated with the inter-tetrahedral bend, changes in the morphology of this band are accepted as markers for changes occurring in the longer-range silicate network arrangement (Nuth & Hecht 1990). Although no direct correlation exists between the specific spectral components in this band and any physical parameters specifically related to the longer-range structure of silicates, such as the number of inter-linked tetrahedra etc. (McMillan 1984a, 1984b), the formation of fine structure in this band can be taken as indicating that the overall silicate structure does indeed evolve as a function of annealing temperature. With the exception of the 11.2 $\mu$m feature, the 20 $\mu$m band features appeared to form earlier than those at 10 $\mu$m and had quickly stabilised during the shorter annealing times. This behaviour mirrors that seen in the XRD data, which showed long-range crystal growth stabilising over a similar time scale and did not appear to evolve further with annealing time.

Figure 5: Normalised IR absorption spectra for 20 $\mu$m band of MgSiO3 annealed over the temperature range 873 K to 1000 K for short and long annealing times: (A) unprocessed sample, (B) 873 K for 4 hours, (C) 873 K for 24 hours, (D) 933 K for 4 hours, (E) 970 K for 4 hours, (F) 970 K for 24 hours, (G) 1000 K for 2 hours and (H) 1000 K for 20 hours.

Jäger et al. (1998) have published peak positions for several Mg-rich crystalline olivine (forsterite) and pyroxene (clino- and ortho-enstatite) minerals (taken from transmission measurements without background correction). For the three 20 $\mu$m band features seen in our 933 K spectra, where they are most developed, at 19.7, 21.5 and 23.7 $\mu$m, the Mg-rich pyroxene data of Jäger et al. lists peaks at 19.3, 21.6 and 23.2 $\mu$m while their synthetic forsterite data shows peaks at 19.5, 21.5 and 23.5 $\mu$m. Overall the three peaks in our 20 $\mu$m band data appear to be represented quite well by Jäger et al.'s Mg-rich forsterite figures. Considering now our 970 K spectra, the four features peak at 19.7, 20.9, 21.6 and 23.8 $\mu$m, compared to the Jäger et al. pyroxene values of 19.3, 20.6, 21.6 and 23.2 $\mu$m and synthetic forsterite values 19.5, 20.8, 21.5 and 23.5 $\mu$m. Again our data is best represented by forsterite. The assignment of these features to forsteritic olivine matches the identification of the crystallite by the XRD analysis. Interestingly, Jäger et al. attribute the forsterite vibrations at 19.5 $\mu$m to the symmetric inter-tetrahedral bend, the 20.8 and 21.5 $\mu$m features to SiO₄ rotation and their 23.5 $\mu$m feature to the translational vibration of a Me²⁺ metal ion. This last feature is the one that appears to differ most between their pyroxene and olivine samples. Jäger et al. note it as being stronger in olivine than pyroxene as well as located at different wavelengths for different Fe content and mineral type. In our data this feature appears to be the 20 $\mu$m band feature to develop first in both strength and narrowness. It is likely that the ionic translational freedom will be strongly influenced by its local molecular co-ordination and hence the feature will strongly reflect the surrounding crystal symmetry. The presence of this feature, in combination with the 11.2 $\mu$m feature (see below), is likely therefore to be a strong diagnostic for the presence of a forsteritic structure.

4.2 Structural change and the 10 $\mu$m band

Figure 6: Normalised IR absorption spectra for 10 $\mu$m band of MgSiO3 annealed over the temperature range 873 K to 1000 K for short and long annealing times: (A) unprocessed sample, (B) 873 K for 4 hours, (C) 873 K for 24 hours, (D) 933 K for 4 hours, (E) 970 K for 4 hours, (F) 970 K for 24 hours, (G) 1000 K for 2 hours and (H) 1000 K for 20 hours.

Unprocessed, our sample showed a shoulder at $\sim$11.2 $\mu$m which formed a feature after 4 hours annealing at 873 K. At this temperature the overall 10 $\mu$m band morphology had changed little with respect to the unprocessed sample. At 933 K further features and shoulders formed, continuing to grow at 970 K and 1000 K. Overall this band appeared more sensitive to annealing than the 20 $\mu$m band. It has long been known that spectral components within this band can be identified which correlate directly with tetrahedral species with differing numbers of NBO atoms (Nuth & Hecht 1990) and can in principle be used to determine the relative proportions of network, sheet, chain, dimer and independent tetrahedral units present in the silicate (Thompson 1996). Features within the 10 $\mu$m band originate in the Si-O fundamental stretch mode which is strongly influenced by whether the oxygen is a bridging or non-bridging atom. Lack of variation of the 10 $\mu$m band peak intensity and shape relative to the 20 $\mu$m band in amorphous systems, has previously been taken as evidence that the features within the 10 $\mu$m band are insensitive to the longer-range structure of the silicate (McMillan 1984a, 1984b). The fact that our data shows band features that vary with both time and temperature suggests that during annealing the short-range local tetrahedral environment evolves without necessarily impinging on the longer-range inter-tetrahedral network structure. At present we are unable to comment on whether the changes in the 10 $\mu$m band are precursors to eventual change in the 20 $\mu$m band or whether the 10 $\mu$m band evolution represents the short-range environment adapting to the imposition of long-range structure.

Figure 7: Normalised IR absorption spectra for 15 $\mu$m region of MgSiO3 annealed over the temperature range 873 K to 1000 K for short and long annealing times: (A) unprocessed sample, (B) 873 K for 4 hours, (C) 873 K for 24 hours, (D) 933 K for 4 hours, (E) 970 K for 4 hours, (F) 970 K for 24 hours, (G) 1000 K for 2 hours and (H) 1000 K for 20 hours.

The stability of both the 20 $\mu$m band features and long-range XRD data suggests that any physical changes associated with variations observed in the 10 $\mu$m band do not impinge on the silicate network structure, although this last statement needs some qualification. From the XRD measurements we can determine two limiting lengths. The first is the smallest real-space separation we are able to resolve using X-rays. For any angle dispersive diffraction experiment performed at a given X-ray wavelength the k-space maximum is determined by the maximum scattering angle, $\theta_{\mbox{max}}$, and in turn corresponds to a minimum real-space distance below which we can not probe,

$$d_{\rm min}=\frac{\lambda}{2\sin\theta_{\rm max}}\cdot$$ (4)

For the maximum scattering angle of 30$^{\circ }$ used in this work this gives $d_{\rm min}=\lambda=1.2995$ Å. The second limiting length is the length over which the regular crystalline structural arrangements are correlated. The latter can be estimated from the full width at half maximum (FWHM) of the crystalline Bragg reflections using the well known Scherrer equation (e.g. Warren 1969),

$$D=\frac{0.94\lambda}{B(2\theta)\cos\theta}\cdot$$ (5)

This expression relates the crystallite size, D, to the FWHM of a $2\theta$ reflection ( $B(2\theta)$, in radians) at the reflection's Bragg angle, $\theta$. Although originally derived for cubic systems, the Scherrer equation is widely used for non-cubic systems and gives a good estimate value for the crystallite size if D is interpreted as the average crystal dimension in the direction perpendicular to the reflecting lattice planes. This distance therefore represents the correlation length over which the lattice separations responsible for producing the reflection are maintained. The crystallite sizes for those peaks due to layer reflections, such as the 130 peak give consistent sizes of $\sim$$0.15~\mu$m, while for 3-dimensional lattice planes we find $\sim$$0.10~\mu$m. For the 130 d-space of 2.7 Å, this suggests that ordering extends over $\sim$555 layers.

Within the experimental noise inherent in the counting statistics the crystallite appears to show no systematic growth with annealing time, although the diffraction peak intensities, when corrected for synchrotron beam decay do show an initial increase with annealing time for the first few scans, which we interpret as being due to the initial formation of crystalline structure (possibly localised). The lack of subsequent growth can be interpreted in several ways, either as a stall in the physical extent of crystalline development within the sample particles (since the reflection widths show no systematic decrease with annealing time, suggesting the number of participating layers is constant), or a stall in the total number of crystallites (since the peak intensities do not increase). This latter could be due either to the number of crystallite nucleation centres being fixed during sample manufacture, with no new centres forming during annealing, or to the physical properties of the sample particles. In preparing our sample for presentation to the synchrotron beam, the particle size distribution was not tightly constrained. The sample powder was ground by hand in a pestle and mortar, which does not produce a monotonic grain size distribution (as evidenced by SEM). From our present data we are unable to address the question as to what extent the thermodynamic contribution of particle surface area affects the crystallisation process. It is also difficult to tell from either the XRD or SEM data whether the crystallite size, D, represents a whole particle size (in which case only the smallest particles would appear to have crystallised), or whether it represents either the size of crystalline "inclusions'' within otherwise amorphous particles, or a crystallite domain size within fully crystallised particles. If D does represent the whole crystalline particle size, we would have expected a systematic increase in its value with integrated annealing time as grinding of the sample produced a range of grain sizes which we would expect to have successively succumbed to crystallisation as annealing progressed. Furthermore, the overall initial change in the amorphous component of the diffraction patterns at 1000 K (e.g. narrowing of the diffuse diffraction features relative to those in the unprocessed sample) clearly indicates that structural change does occur throughout all our sample (remember X-ray diffraction represents an average snapshot of the bulk whole-sample structure). Since crystallisation only occurs in an amorphous material at the expense of its amorphousness, it is unlikely that such apparent changes would be confined to only the very smallest particles and still show up in the diffraction patterns. Additionally, Hallenbeck et al. (1998) interpreted the formation of an Si-O stretching band morphology with well defined features near 9.8 $\mu$m and 11.2 $\mu$m as a natural consequence of the thermal evolution of amorphous silicates, rather than arising from a distinct mixture of amorphous and crystalline materials.

From the foregoing arguments, it would appear that the physical changes occurring within the silicate that give rise to some of the 10 $\mu$m band fine structure do not correlate with the observed crystalline evolution as defined within the limits of the minimum X-ray resolution or the crystallite correlation length.

The feature at $\sim$11.2 $\mu$m, initially present in the unprocessed amorphous sample as a shoulder is the first feature to develop as a peak in the 10 $\mu$m region in terms of both annealing temperature and exposure time. At the lowest annealing temperature of 873 K and 4 hours exposure it appears to develop as an obvious peak while the three 20 $\mu$m features are still somewhat broad and poorly defined. Commonly attributed to the Si-O stretch for SiO₄ species, its strength appears to grow in association with the 20 $\mu$m features as both annealing time and temperature increase. As we have identified the 20 $\mu$m features with forsteritic olivine (and in particular the 23.8 $\mu$m feature) the association of the 11.2 $\mu$m feature with forsterite appears to be confirmed along with the correlation of its strength with the formation of crystalline structure.

The development of a feature at $\sim$9.3 $\mu$m in the data from 970 K onwards is also interesting. Although Jäger et al. (1998) identify the presence of a feature at this position in synthetic 100% Mg forsterite (which in their data disappears with increasing Fe content), the presence of a feature at 9.3 $\mu$m is more commonly attributed to crystalline pyroxene spectra (e.g. Koike et al. 1981, 1993; Jäger et al. 1998; Brucato et al. 1999b). Observations of Comet Hale-Bopp by Wooden et al. (1999) have shown the presence of a 9.3 $\mu$m feature that increases in strength as the comet approaches perihelion. The development of this feature in the comet spectra is also accompanied by the development of three weak features at 10.5, 10.8 and 11.8 $\mu$m which are also present in our data. Grains with pyroxene compositions are implied by the PUMA-1 results (Jessberger et al. 1988; Lawler et al. 1989) for Comet Halley and differences between the 10 $\mu$m bands for various comets have previously been attributed (at least in part) to variations in the relative abundance of crystalline/amorphous olivines and amorphous pyroxenes (as well as to the Mg:Fe ratio). Amorphous pyroxene grains have been invoked to explain the short-wavelength rise of the 10 $\mu$m band as well as the 9.8 $\mu$m peak, for example in Comet Halley (e.g. Hanner et al. 1994b; Colangeli et al. 1995). Despite this, and the identification of Mg-rich pyroxenes in certain types of interplanetary dust particles (Bradley et al. 1997), the presence of crystalline pyroxene has not been inferred from the 10 $\mu$m band spectra of comets prior to Hale-Bopp (Wooden et al. 1999). At 2.8 AU Wooden et al. observed the 10 $\mu$m band of Hale-Bopp to be similar to Halley's and fitted its spectra with a three component mineral mixture: amorphous olivine with 50% Mg (relative to Fe), crystalline olivine with 90% Mg and amorphous pyroxene with 100% Mg. At 1.7 AU they report the presence of a 9.3 $\mu$m peak along with the three features at 10.5, 10.8 and 11.8 $\mu$m and suggest the evolution of such features at short heliocentric distances to be due to the addition of a fourth mineral phase, obtaining a fit at 9.3 $\mu$m using crystalline pyroxene with a Mg content $\geq90\%$. To explain the non-appearance of this extra crystalline phase at greater distances they suggest that the high Mg content of crystalline pyroxene makes its grains less optically active and therefore cooler than Mg-rich olivine grains. An alternative possibility for the 9.3 $\mu$m feature carrier could be a pure, amorphous SiO_n such as SiO₂ or Si₂O₃ which have peak absorbances near 9.2-9.3 $\mu$m. These should also be accompanied by other features such as a shoulder at $\sim$8.4 $\mu$m and a peak at 11.4 $\mu$m for Si₂O₃ and a peak at $\sim$12.5 $\mu$m for SiO₂. However inspection of our spectra does not reveal the presence of these additional features. As a note of caution however, we draw attention to the fact that the current literature relating to laboratory silicate analogues presents results obtained from samples manufactured by a variety of methods. Thus there is a large question concerning the parity between the various results, as well as how well the various samples adequately model real cosmic silicates. Samples produced as condensates of Mg and SiO vapours not only tend to lack many full SiO₄ tetrahedra, but will also contain free silica, MgO oxides and Mg metal. Such samples are therefore (in terms of silicate) highly disordered both structurally and chemically. Samples produced by laser ablation of mineral specimen will contain condensed, non-crystalline particles as well as liquid drops and solid spall from the target. Gel desiccation on the other hand tends to produce silicates that are chemically well defined with a well established, but disordered, tetrahedral environment. The samples produced by each of these techniques are in turn also dependent on the precise details governing the manufacturing processes involved. These differences of production can ultimately lead to a difference in physical behaviour. As noted previously (Thompson & Tang 2001), samples such as vapour condensed silicate may require substatially higher annealing temperatures in order to crystallise. However cometary grains are likely to have suffered post-formation processing in stellar atmospheres, the interstellar medium and pre-solar nebular prior to incorporation into comet bodies and thus may not be best modelled by samples more representative of freshly nucleated dust grains. Therefore, whilst we acknowledge the method of manufacture of our initial silicate might yield a somewhat idealised analogue to comet dust, it should be borne in mind that the validity of fitting observed spectra with laboratory data obtained from fully crystalline materials does rely explicitly on the underlying assumption that such features can be definitively attributed to crystalline grain components with certain macroscopic structures. That we have found, using two complimentary techniques, that a sample of amorphous pyroxene composition can crystallise to a forsterite structure and still display certain pyroxene-like fine-structure features does at the very least open up the possibility that certain of the features seen in the 10 $\mu$m band of objects such as comets might not correlate directly with the macroscopic crystalline grain structure. After all, the features in this region are generally accepted as being independent of the material's long-range structure. In such instances, fits to pyroxene-like features in the 10 $\mu$m band would have to be constrained by the spectral behaviour at other wavelengths before necessarily being accepted as definitive. In the case of Hale-Bopp, features seen at longer wavelengths (19.5, 23.5 and 33.5 $\mu$m) at pre-perihelion distances have already been identified with forsterite (Crovisier et al. 1997). Presumably the appearance of crystalline pyroxene grains at perihelion should also be detectable at longer wavelengths.

There are several possible plausible explanations for the presence of these "crystalline'' enstatite features in a crystalline forsterite dominated sample. Firstly, given the absence of enstatite features in the diffraction data, they could originate from micro-crystalline enstatite structures, too small to be detected using our current diffraction apparatus, or they could represent an ultra dilute phase whose presence would require much greater detector integration times to detect than those employed in our measurements. In both cases, this would imply a 10 $\mu$m spectral response for enstatite that is very strong in relation to its physical extent (and also relative to forsterite) and presumably a 20 $\mu$m response that is correspondingly weaker so as not to be visible in this band. IR spectroscopy only returns information regarding the average bond type. Thus, while there may be sufficient "enstatite'' Si-O bonds to produce features in the 10 $\mu$m band, to produce features in the 20 $\mu$m band would require these to be arranged in an enstatite lattice, which is clearly not the case. A more realistic possibility could be that these features represent an improvement in the local SiO₃ ordering arising as a result of annealing, but without the formation of regular crystallographic structure. Such changes for example could result from wide-spread, but highly localised, changes (e.g. changes in polymerisation) that do not repeat in a regular way over macroscopic lengths, or could represent changes in the inter-linked tetrahedral environment that are not reliant on any one particular macroscopic structural arrangement being adopted. As such the appearance of these pre-crystalline enstatite features in observed spectra may only signal that the silicate has been annealed, rather than actually tell us something about the macroscopic structure of the material itself. It is therefore worth stressing that this finding could potentially offer new perspectives on the reconstruction of the thermal history of comets, even if at this stage it is deserving of more detailed study.

Previously reported XRD annealing results (Thompson & Tang 2001) show the forsterite structure formed in this MgSiO₃ powder persists as the prominent crystal phase at least up to 1173 K, whether further annealing at this, or higher, temperatures would eventually produce a phase change resulting in the expected enstatite pyroxene structure is currently unknown. The formation of macroscopic crystalline pyroxene structures from amorphous grains could in fact be harder to realise than their composition alone suggests.