3 Results

3.1 X-ray diffraction

Prior to annealing, the raw unprocessed silicate was scanned at room temperature using a wide-angle scan, 5-70$^{\circ }$ $2\theta$ (Fig. 2). The background profile of this scan was used to help determine the 15-60$^{\circ }$ $2\theta$ range of the annealing scans. Once the furnace temperature had stabilised at 1000 K it was then held constant (to within $\pm$1 K) and the sample repeatedly scanned for 19.5 hours. During this time the diffraction data showed the evolution of a crystalline phase represented by the formation of small sharp Bragg reflections (Fig. 3) and by the end of this period a more developed crystalline diffraction pattern was clearly visible in the data, superposed upon an amorphous background that had changed little throughout the annealing period. The crystalline component had begun to form during the first scan period and by the end of the third had developed to its full extent with both crystalline and amorphous components changing little from then on. A note of caution is in order though regarding the interpretation of the development sequence shown in Fig. 3. In these diffraction scans, the XRD data is collected in angle dispersive mode, thus the $2\theta$ axis is also a time axis within the scan (each data point being separated by the detector integration time and the unquantified time it takes the detector arm to move to, and settle at, the next point). Casual inspection of the bottom scan in Fig. 3 might suggest that high-angle structure develops before low angle structure, however this is not necessarily the case as the time difference between low and high angles means that the annealing time of the sample has increased by the time the detector reaches the high angle end of the scan. However, examination of normalised peak to continuum ratios for selected Bragg reflections supports the observation of crystallite development reaching a maximum after about the third scan: after $\sim$5 hours, the normalised peak intensities appear constant to within the signal to noise range of the individual diffraction patterns.

Figure 2: XRD pattern for unprocessed amorphous MgSiO3.

Reference data from the International Committee for Powder Diffraction Standards (ICPDS) database allowed the crystalline phase to be identified as forsterite (Mg₂SiO₄). At this annealing temperature no Bragg reflections were unaccounted for. It is worth noting that the open olivine Mg₂SiO₄ forsterite structure would seem to be compositionally unfavourable for a sample of MgSiO₃. Although crystalline MgSiO₃ (e.g. enstatite) can be expected to yield some diffraction peaks coincident, or close to, those of forsterite, the latter accounts for all the crystalline reflections in our data. Additionally, by comparison to enstatite reference patterns, those few reflections that did occur at enstatite positions did not correspond to any of the strongest reflections expected for the enstatite structure, strongly supporting the forsterite identification.

The asymmetric shape of the broad feature at $\sim$ $30^{\circ}$ $2\theta$ in the raw unprocessed sample before annealing is characteristic of the presence of disordered layer-type units. If the layers were, for example, to be stacked parallel to the crystallographic 001 lattice direction, then normal crystalline reflections of the type 00l would be observed due to the regularity of stacking. However if the lateral displacements of the layers are totally irregular it is impossible to define lattice planes with more general Miller indices such as hk0 or hkl. So, apart from the 00l peaks the only other observable diffraction effects would be those originating from any 2-dimensional in-plane regularity within each separate plane. Such repeating 2-dimensional structures however would not be confined to specific Bragg angles and instead of sharp diffraction features they appear as diffuse asymmetric bands which cut off sharply on the low angle side and die away gradually on the high angle side (Whittaker 1981). These diffuse bands are characterised by two indices hk, and the low angle cut off is located close to the position that would otherwise be occupied by the hk0 reflection for the corresponding 3-dimensionally ordered structure. The powder pattern of a material comprising equally spaced parallel layers, subject to random lateral displacement, consists therefore of a single set of sharp 00l peaks and a set of broad asymmetric hk bands. The powder pattern shown in Fig. 2. recorded for our amorphous MgSiO₃ sample contains no sharp peaks at all, but the feature at $\sim$ $30^{\circ}$ is asymmetric and exhibits a sharp low angle rise with a gradual high angle decay. The 2$\theta$ rise begins at $\sim$ $27^{\circ}~2\theta$ and gives an interlayer d-space of 2.7 Å, which matches the forsterite 130 layer reflection d-spacing. The complete absence of any normal crystalline 00l-like reflections is evidence that while layer-forming forsterite components are present in our amorphous sample, initially they are not stacked parallel to each other. The feature at 60$^{\circ }$ $2\theta$ by the same argument can be associated with the forsterite 170 inter-layer stacking distance of $\sim$1.35 Å, which is half the 130 d-spacing. The morphology of the diffraction pattern for the raw sample thus shows the existence of disordered proto-forsteritic units, while the presence of the other diffraction features not associated with forsteritic layering shows the co-existence of other structural units in the pre-annealed silicate. Unfortunately, simple inspection of the diffraction pattern does not allow us to make any quantitative statement regarding the relative proportions of forsteritic and non-forsteritic structures. The appearance of the pattern itself is governed by two factors. Firstly, the exponential-like decay in intensity from low to high angle is the result of scattering interference from the internal structure of the repeating molecular units, while secondly, the broad superposed features are caused by scattering interference due to the arrangement of the repeating molecular units with respect of each other (it should also be noted that it is a well known effect in amorphous diffraction that the width and intensity of features increase and decrease, respectively, as a function of increasing angle). In silicates, the dominant contribution to the measured intensity comes from the SiO_n tetrahedra. Thus the precise form of the intra-molecular "decay'' curve will depend on the number of O atoms in the SiO_n units and will be some weighted sum of contributions from SiO, SiO₂, SiO₃ and SiO₄ as all such units may be expected to exist in the amorphous material. The inter-molecular diffraction features are determined by the radial distribution of the SiO_n and apart from the forsteritic layer features described above the origin of the other features can only be determined from detailed modelling, which must take into account the fact that the measured pattern represents an average of contributions from all SiO_n species and arrangements thereof. Initial modelling results indicate that apart from the proto-forsteritic layer features discussed above, none of the other features can be ascribed to specific arrangements of a given SiO_n, as each value of n tends to produce features located at similar positions to the ones in our data. However, a more detailed discussion of this will be addressed in a later publication.

Figure 3: XRD patterns for amorphous MgSiO3 annealed at 1000 K: bottom pattern is initial exposure, top pattern after 19.5 hours annealing, middle patterns show sample data for intermediate annealing times. Straight line sections are where the synchrotron beam was unavailable due to storage ring refills. For clarity, the data in this and subsequent figures have been offset in the y-axis direction.

Previously, Rietmeijer et al. (1986) observed annealed silicate smoke particles crystallising to forsterite and tridymite (SiO₂) rather than enstatite, which they speculatively attributed to surface energy contributions from the phases formed to the thermodynamics of crystallisation for small particles. However as already noted, the particle sizes for our sample are much larger and therefore are less likely to be susceptible to surface energy contributions. The formation of a crystalline Mg₂SiO₄ phase within a chemically well defined amorphous MgSiO₃ starting material, apparently contrary to expectations based on equilibrium thermodynamics, could also originate from the initial ordering of the pre-existing proto-forsteritic structure in the amorphous sample when it was first annealed. The non-appearance of unique reflections originating from other crystalline silicate phases, such as enstatite, has previously been attributed to the resistance to crystallisation of the other non-forsteritic amorphous structures (i.e. arrangements of SiO$_{n\neq4}$). This was suggested (Thompson & Tang 2001) as being due to the non-forsteritic amorphous arrangements being strengthened by the annealing process itself via an increase in the polymerisation of the amorphous component. One proposed mechanism by which this could occur is through annealing induced dehydrogenation of the silicate. This process could produce improvements in the amorphous silicate network connectivity and tetrahedral environment without necessarily contributing to the formation of long-range periodic (i.e. crystalline) structure. Dehydrogenation could be achieved by a recombination process such as (Shelby 1994):

$$\mbox{SiOH}+\mbox{SiH}\rightarrow \mbox{Si--O--Si}+\mbox{H}_{2}.$$ (3)

This reaction is known to occur in pure amorphous SiO₂ where hydroxyl and hydride species are removed by annealing at $\sim$973 K or above. In the laboratory both are found to be completely removed over a period of hours (Shelby 1994). By plotting the percentage of hydroxyl/hydride removed as a function of time, the data for each species are found to fall on the same curve, implying that the effective diffusion coefficients are the same for both species. Measurement of the gas released during heating of other similar materials (Morimoto et al. 1992) confirms H₂ to be the major component along with very small amounts of water. Below $\sim$70$\%$ removal, the percentage removal curves approximate those expected for simple diffusion but yield an effective diffusion coefficient of 1.4 $\times 10^{-7}$ cm² s^-1 which is much lower than the expected value of 6 $\times 10^{-6}$ cm² s^-1 for simple diffusion (Shelby 1977). This experimental evidence, taken in conjunction with certain deviations of the removal curves from that of simple diffusion above 70$\%$ removal implies that it is the reaction rate of (3) and not the diffusion coefficient that controls the outflow of molecular hydrogen from the silicate (Morimoto et al. 1992). This is further supported by the activation energy of the reaction which lies between 260 kJ mol^-1 (Heslin 1993) and 266 kJ mol^-1 (van der Steen 1976) and compares well with the binding energy of the SiO-H bond (264 kJ mol^-1, Shackelford & Masaryk 1976). It is thus the breaking of this bond that should control the dehydrogenation of the silicate. Both laboratory and cosmic silicates are likely to contain OH impurities (Steel & Duley 1987; Timmermann & Larson 1993), while SiH impurities are also likely to form in silicates produced in H-rich environments (Blanco et al. 1999). The investigation of the dehydrogenation mechanism as a process for polymerisation during annealing is currently the subject of ongoing experiments.

The net effect, however, of a process such as (3) in the annealed MgSiO₃ silicate would be to increase the overall polymerisation of the amorphous network by reconnecting inter-tetrahedral Si-O-Si bridging bonds and thus raise the average number of bridging oxygen atoms per tetrahedral unit (i.e. decrease the non-bridging oxygen number per tetrahedron, NBO/T). Since the amorphous silicate will initially have a distribution of NBO/T values, annealing will at first promote the ordering of NBO/T=4 species only and crystal growth stalls when the need for more NBO/T=4 units can only be met by breaking bonds for units with $NBO/T\leq 3$. Annealing induced polymerisation would have meanwhile reduced the bulk NBO/T for these species down towards that of SiO₂ (i.e. $NBO/T\rightarrow 0$). The mixed amorphous/crystalline state would thus persist until enough energy has been input to the system to allow the increased number of multiple bridging bonds to be broken, whereupon the amorphous phase breaks down and further crystal growth becomes possible.

3.2 IR spectroscopy

Initially, for parity with the XRD measurements, IR data were collected for the raw sample and an annealing temperature of 1000 K for short and long exposure times (2 and 20 hours respectively). However the results for the annealed sample showed the formation of considerable fine structure in both the 10 $\mu$m and 20 $\mu$m regions for both annealing times. The lack of temporal discrimination in spectral development at this temperature relative to the XRD data is likely due to differences in the annealing profile of the IR method, where annealing must be done off-line, compared to that of the on-line furnace used for the diffraction measurements. Thus in order to separate out the effects of the annealing time from those of the annealing temperature we performed a series of measurements at several lower temperatures leading up to 1000 K. With the exception of the 1000 K data and one intermediate temperature, data were collected for annealing times of 4 and 24 hours. The results of these measurements are shown in Fig. 4.

The normalization of the measured spectra was done without taking into account the actual mass of the samples examined as such a procedure would have been unreliable for two reasons: firstly, the exact determination of the mass of the sample dispersed into the KBr was rather difficult due to the limited amount of raw material available; secondly, there were certain associated difficulties in evaluating the precise effect of the substantial mass reduction that occurred during the annealing process. In order to compare the spectra in a meaningful way, we set to zero the lowest point of each absorption spectrum in the range 8-24 $\mu$m, by subtracting from each an appropriate value. We then set to 1 the highest value in the same range, by multiplying each spectrum by the appropriate scaling factor. The range 8-24 $\mu$m was selected as being the more significant for the purpose of the present paper since it is the range where silicates, in addition to their main features, also exhibit an absorption minimum. Even if normalising all the spectra to the interval 0 to 1 by this somewhat arbitary method means we can not make a quantitative comparison between the different spectral features, it does at least allow for an easy comparison to be made of the various spectral modifications induced by the annealing process.

Figure 4: Normalised IR absorption spectra for MgSiO3 annealed over the temperature range 873 K to 1000 K for short and long annealing times.

3.2.1. Evolution of 10 $\mu$m and 20 $\mu$m bands

The evolution of fine structure is clearly visible in both regions over the entire time/temperature range (see Fig. 4). The development of features in each of the bands occurs as follows (see also Figs. 5 and 6).

Unprocessed sample: the 10 $\mu$m region consists of a single broad band with a peak at 9.8 and a shoulder at $\sim$11.2, while the 20 $\mu$m region consists of a single broad band peaking at $\sim$$22.0~\mu$m.

873 K annealed for 4 hours: the 10 $\mu$m band still peaks at 9.8 $\mu$m, but the shoulder at 11.2 $\mu$m has now developed into a peak at $\sim$$11.3~\mu$m. There is an additional weak shoulder feature discernible at $\sim$11.8 $\mu$m. The 20 $\mu$m region now contains three broad features at $\sim$19.7, 21.5 and 23.7 $\mu$m.

873 K annealed for 24 hours: the 10 $\mu$m band appears similar to the previous 4 hour data set, while the definition of each of the three 20 $\mu$m band features present in the 4 hour sample has improved.

933 K annealed for 4 hours: the 9.8 $\mu$m peak appears slightly asymmetric on its low wavelength side, a new feature at $\sim$10.7 $\mu$m has appeared and the 11.2 $\mu$m feature possesses a weak shoulder at $\sim$$11.7~\mu$m. The three features in the 20 $\mu$m region appear stronger than before and the middle one at $\sim$$21.5~\mu$m has flattened and shows evidence of beginning to split into two sub-features.

970 K annealed for 4 hours: the asymmetry of the 9.8 $\mu$m peak has evolved into a shoulder at $\sim$$9.4~\mu$m, while a weak feature at $\sim$$10.4~\mu$m has appeared in addition to the other previous features at 10.7 and 11.2 $\mu$m. The shoulder feature at $\sim$$11.7~\mu$m has developed further. In the 20 $\mu$m band, four distinct features are now present at 19.7, 20.9, 21.6 and 23.8 $\mu$m. The middle two having evolved from the splitting of the flattened 21.5 $\mu$m feature seen in the previous spectrum.

970 K annealed for 24 hours: the previous shoulder at 9.4 $\mu$m is now a discernible feature, while a further very weak feature has appeared at $\sim$10.1 $\mu$m. The weak feature at 10.4 $\mu$m that first appeared in the previous data set has developed slightly while features at 10.7, 11.2 and 11.67 $\mu$m are now well established. In the 20  $\mu$m region no new features have formed, but the existing four have improved in definition.

1000 K annealed for 2 hours: well developed features are found at 9.3, 9.8, 10.7, 11.2 and 11.7 $\mu$m along with the two very weak features at 10.1 and 10.4 $\mu$m. The 20  $\mu$m band has undergone further development and now shows weak peak features at 19.6, 20.8, 21.7, 22.7, 23.4, 23.7 and 24.5 $\mu$m, with possible weak shoulders at $\sim$24.1 and 22.0 $\mu$m.

1000 K annealed for 20 hours: the 10 $\mu$m band shows five distinct features at 9.3, 9.8, 10.73, 11.24 and 11.79 $\mu$m. The weak features at 10.1 and 10.4 $\mu$m discernible in the previous data sets being no longer visible. The five main features of the 20 $\mu$m region show evidence of further fine structure modulation, with peaks at 18.2 $\mu$m (plus a very weak feature at 18.52 $\mu$m), the feature at 19.6 $\mu$m in the previous data set now appears split into two features at 19.7 and 20.0 $\mu$m. There is a feature at 20.8 $\mu$m and a broad feature centred at $\sim$21.9 $\mu$m which shows evidence of splitting into three very weak features, as does the one centred at $\sim$23.7 $\mu$m. The feature present at 24.6 $\mu$m in the previous 2 hour spectrum is also present in this spectrum. Overall, these additional fine structure modulations are very small compared to the main features themselves.

3.2.2. Evolution of the 15 $\mu$m region

Although this paper is primarily concerned with the evolution of the 10 $\mu$m and 20 $\mu$m bands, we note that several features in the region of 15 $\mu$m also evolve as a function of annealing (Figs. 4 and 7). Comparison to the behaviour of the features at 10 $\mu$m and 20 $\mu$m suggests the 15 $\mu$m band features are related to, or follow, the 10 $\mu$m band features. Like the 10 $\mu$m band their development also appears to depend largely on annealing temperature.

Unprocessed sample: the 15 $\mu$m region comprises a single broad hump stretching between $\sim$12.2 and 17 $\mu$m, peaking at $\sim$15 $\mu$m.

873 K: an asymmetric feature has developed at $\sim$14.8 $\mu$m, along with a weak broad feature at $\sim$16.1 $\mu$m. This last feature appears slightly stronger with longer annealing time.

933 K: an additional weak feature has formed at $\sim$15.4 $\mu$m with a weak double feature at $\sim$13.7 $\mu$m also being apparent.

970 K: the $\sim$15.4 $\mu$m feature and $\sim$13.7 $\mu$m double feature strengthen slightly, but appear similar to the 933 K spectrum and do not evolve with annealing time.

1000 K: the $\sim$13.7 $\mu$m double feature has now increased in strength, as has the $\sim$15.4 $\mu$m feature. The $\sim$14.8 $\mu$m feature shows signs of fine structure, while the $\sim$16.1 $\mu$m feature appears to weaken, disappearing altogether from the 20 hour spectrum. At this temperature the remaining features appear to strengthen with annealing time.

Similar features are present in certain of the crystalline silicate spectra published by Jäger et al. (1998) for forsterite and pyroxene compositions and are most likely to be due to overtone resonances of the Si-O stretch vibrations responsible for the 10 $\mu$m band features. The $\sim$14.8 $\mu$m feature in forsterite is attributed by them to a SiO₄ symmetric stretch overtone. However this feature is also present in their pyroxene data. The $\sim$16.1 $\mu$m feature corresponds to a SiO₄ asymmetric bend and is absent from their pyroxene data. The $\sim$13.7 $\mu$m double feature could possibly correspond to the symmetric stretch overtones at 13.6 and 13.8 $\mu$m in the Jäger et al. data, albeit shifted. Again, however, this feature is also present in their pyroxene data. Finally, the $\sim$15.4 $\mu$m feature is present only in Jäger et al.'s pyroxene data, but with no assignment. Thus the features in this band do not appear to be diagnostic of crystalline type. On the other hand, these features do appear to represent a clear diagnostic of intermediate annealing and should be searched for in stellar spectra as an indicator of thermal grain processing.