IntroductionWhen dealing with hard condensed matter, phase transitions and reactions generally involve high temperatures. Unfortunately, even with specialist probes, MAS is currently only possible up to about 700oC and only at spinning speeds that would not be sufficient to deal with the line widths of many quadrupolar nuclei because there are no container materials whose mechanical strength is sufficient at high temperatures to allow fast spinning. As a consequence, NMR studies of glasses and refractories are generally limited to ex-situ measurements of samples subjected to thermal treatment which are subsequently quenched. This limits the time resolution and introduces some degree of uncertainty as to whether any phases detected are genuine reaction products or merely quenching artifacts, e.g. due to recrystallization. In-situ NMR experiments at high temperature avoid these problems, but at the price of lower spectral resolution in any given time slice. This is not a problem if sharp phase transitions with a very distinct change in line shape are observed. In this paper, we show that it is not necessarily a problem either when dealing with gradual spectral changes induced by chemical reactions as long as the individual phases are characterized independently. While previous high-temperature NMR experiments were focused on recrystallization from the melt, speciation equilibria in the melt, chemical reaction in the melt phase, or structural pre-melting effects of stoichiometric crystals, we report here for the first time an application of the technique to solid-state diffusion-driven reaction kinetics.
In this study, we are dealing with the reactions between grains of quartz and sodium carbonate. The system is used as a physical model for batches typical of those used in the glass-making industry. It is important to know to what extent batch reactions are controlled by kinetics and thermodynamics, respectively, as this allows to optimize the heat profile of a float line and reduce both energy consumption and emissions. Where, as in this case, ionic diffusion in the solid state plays an important role, the grain size and the structural detail of grain interfaces are factors that can tip the balance in favor of one particular mechanism or other. This, again, is technologically relevant, and the reduction in grain size of raw material and a careful balancing of particle sizes of the various raw materials may be both ecologically beneficial and economically viable.
The two main samples studied in this investigation were batches (powder mixtures) of quartz and
sodium carbonate with a molar ratio of 1:1 ("metasilicate batch", Na2O·SiO2)
and 2:1 ("disilicate batch", Na2O·2SiO2). In addition, the raw material, sodium
carbonate (Na2CO3), and completely reacted, recrystallized metasilicate
(Na2SiO3) and disilicate
(Na2Si2O5) were also used for reference. In this paper, the sum
formulas are only used to refer to the fully reacted products, not the batches.
Fig.1: Spectrum of liquid Na2CO3. The top trace is a tenfold magnification of the baseline, showing the 23Na background signal from the probe. This is taken into account when modeling the batch spectra.
Results: Reference measurements
|Fig.2: Reference spectra of (a) the raw material Na2CO3 at
bottom) 740oC, 830oC, and 880>oC; and (b) the homogeneous products (top to
bottom) metasilicate at 840oC and 1090oC, and disilicate at 760oC. The
peak positions of the lines of the liquids are 0.8ppm, 12ppm, and 6ppm, respectively. All spectra are
scaled to have the same amplitude, hence the different signal-to-noise ratio.
The spectrum of pure Na2CO3 at 740°C shows a
broad static solid-state line shape. With increasing temperature, the line narrows
progressively due to motional averaging. The line shape at 880°C corresponds to liquid
Na2CO3. The position of the pure liquid sodium carbonate line is 0.8ppm.|
The narrow lines of metasilicate at 1090°C and disilicate at 760°C prove that these products are entirely molten. The peak positions are 12ppm for metasilicate and 6ppm for disilicate. Due to the narrower lines, peak positions can be extracted with higher accuracy from the spectra of the liquids. The solid-state metasilicate spectrum (at 840°C) indicates that the peak positions observed with the liquids apply equally to the high-temperature solids.
Results: Metasilicate batches
|Fig.3: Evolution of metasilicate batch spectra at 855oC with time (evolving
from bottom to top). Each horizontal slice is averaged over a 1min period. Amplitudes are color-coded.
The two spectra shown in the foreground are the slices taken after 3min and after 80min, corresponding to
the bottom and top slices in the two-dimensional plot in the background.
The batch spectra evolve from the Na2CO3 line shape (as this is the only sodium containing component of the batch at the beginning) toward a product spectrum. Complete reaction was observed in no case (unless the whole sample was melted). The center of gravity of the peak shifts to the left, while a distinct narrow component begins to grow at the metasilicate position after about 10min. After about 60min, the spectra cease to change noticeably with time. The asymmetry of the line and the remaining broad component indicate however that some of the raw material remains unreacted. The same general behavior is observed at all four temperatures; only the time scale and the extent to which the broad line is diminished varies.
|Fig.4: A typical metasilicate 1min in-situ spectrum. The lineshape is modeled using
four Lorentzian components for reactant, product, a quadrupolar tail component and the probe background.
The complex line shape resulting from the multi-component nature of a partially reacted batch means that it is not possible to extract quadrupolar parameters for any site from the spectrum. However, the line shape is approximated by a superposition of four Lorentzian lines. Two of these represent reactant and product (without qualification at this stage as to which particular silicate phase it may be), respectively, and one is due to the probe background discussed earlier. The fourth component is designed to make up for the quadrupolar distortion of the carbonate and silicate lines, which cannot be adequately described by symmetric Lorentzian functions. The curve fit therefore is not intended to justify directly a particular structural model on the atomic scale, but to quantify the individual components present in the batch as a function of time. When interpreting the data, it will be necessary to take account of the "quadrupolar tail" component as it contains intensity from spins located in both raw material and product. Based on the fits to individual slices and the independent probe background measurement, the positions of the four components were fixed at 0.8ppm (carbonate), 9.0ppm (silicate), -37.0ppm (quadrupolar tail component), and -22.0ppm (background). The width of the components were fixed to 12.5ppm (silicate), 50.0ppm (tail), and 23.0ppm (background). This leaves the collective fit to the entire in-situ data set with five variable parameters: the width of the reactant line and the four amplitudes.
Results: Disilicate batch
|Fig.5: Evolution of disilicate batch spectra at 880oC with time (evolving
from bottom to top). Each horizontal slice is averaged over a 1min period. Amplitudes are color-coded.
The two spectra shown in the foreground are the slices taken after 3min and after 120min, corresponding to
the bottom and top slices in the two-dimensional plot in the background.
During the first 20 minutes, the disilicate batch spectra can be modeled in exactly the same way as the metasilicate ones. After this initial period, the disilicate batch develops a much narrower component near 11ppm. The product line known from the metasilicate batches and this new one are too close to each other to be analyzed quantitatively as two separate components.
|Fig.6: Development of the intensities of the spectral components (taking into account
both amplitude and width) of metasilicate batches over time. (a) Data for the reactant (full circles),
metasilicate (open circles) and the quadrupolar tail component (crosses) from the experiment at
855o. (b) Comparison of the reactant decay at 835o C (full circles),
815o (open circles), 855o C (crosses), and 880oC (triangles).
With the reactant and product contributions separated, the kinetics of the reaction emerges. On the left, the fractions of reactant, product, and quadrupolar tail components of the metasilicate batch spectra are shown as a function of heating time at 855°C. It is worth noting that the tail component remains fairly constant over time. Therefore, the use of Lorentzian lines representing the carbonate and product components does not cause a large error in terms of the kinetics of the reaction. This observation was made at all temperatures. The decrease of the carbonate component and increase of the product component are roughly exponential. This means that the reaction is more deceleratory than any of the mechanisms suggested in the literature.
When comparing the decays of the carbonate component in each of the four in-situ metasilicate batch experiments (right), the general observation is, as may be expected, that the raw material is consumed faster as the temperature increases. However, the measurement taken at 835°C appears to be out of sequence, displaying a lower reaction rate than the one at 815°C. This is probably caused by a difference in packing density, causing different thermal conductivity across the sample and therefore a different thermal gradient. This observation makes clear that in-situ thermometry would be desirable in this kind of experiment.
|Fig.7: Ex-situ 23Na MAS NMR spectra of the batches after the end of the
in-situ experiments are shown in the top five traces; each shifted successively to the right by 25ppm for
clarity. The spectra were taken at room temperature after the in-situ experiments at
815oC, 835oC, 855oC, and 880o (front to back). The top spectrum
originates from a sample entirely melted during the in-situ experiment. The unshifted bottom trace
shows a three-site quadrupolar fit to the 815oC spectrum.
The total amount of sample reacted (or carbonate unreacted) is determined independently by analyzing the last slices of each in-situ experiment and by ex-situ MAS spectroscopy of the final product. In case of the data taken in situ, the actual reactant and product fractions are obtained by adding to the intensity of the corresponding fit component a fraction of the quadrupolar tail component given by the ratio of the reactant and product line intensities. This is necessary because the relative contribution of reactant to the quadrupolar tail component, which remains nearly constant over time, decreases as carbonate is consumed.
The ex-situ MAS spectra can be modeled with a three-site quadrupolar model comprising a single crystalline metasilicate site and the two sites of the sodium carbonate structure, all of which are known from literature. The MAS spectra therefore allow to identify the product phase without doubt as pure sodium metasilicate. Since a line resembling the disilicate reference does not occur, it is obvious that metasilicate is formed directly, without an intermediate disilicate phase occurring.
|Fig.8: Comparison of the initial stages (slices after 3min) of the metasilicate
batches (top traces) with pure Na2CO3 (bottom traces) under similar conditions:
(a) 790oC/815oC (Na2CO3 and batch, respectively),
(b) 835oC, (c) 880oC. All spectra are scaled to have the same amplitude, hence the
different signal-to-noise ratio.
In order to understand the mechanism of the reaction in terms of the kinetics of the granular interface, it is useful to focus on the early stages of the reaction. The first deviation from the sodium carbonate reference pattern is almost exclusively due to Na+ ions in the interface between quartz and sodium carbonate as no homogeneous product has formed at this stage. The first slices (spectra 3min into heating) of metasilicate batch and pure sodium carbonate are compared at three different temperatures.
The spectra near 800°C (left) are below the solidus of all components. Any reaction taking place has to be a solid state reaction at the grain interface. The batch spectrum is quite similar to the reference because the reaction is rather slow at this temperature.
At 815°C (centre), both the raw materials and any product would be solid if in thermodynamic equilibrium, but the eutectic on the silica-rich side of the disilicate composition would be molten in equilibrium conditions. However, there is no liquid component in the batch spectrum at 815°C. The carbonate reference line is noticeably motionally narrowed under these conditions. This does not apply to the batch spectrum although the majority of the 23Na still reside in the carbonate phase. Therefore, the broadness of the batch spectrum at 815°C is more likely to be due to a distribution of environments in the interface than due to a lack of motional narrowing.
At 855°C (right), a wide compositional range between disilicate and silica would be molten under equilibrium conditions. The sodium carbonate reference is clearly entirely liquid at this temperature, but the batch spectrum remains broad and has certainly no liquid component. Therefore, the reaction front, driven by fast Na+ diffusion in the disordered interface, is progressing sufficiently fast through the grain interface to prevent any part of the sample from reaching thermodynamic equilibrium locally. The broadness of the line reflects not only the lack of liquid phases but also the broad range of environments in the interface.
|Fig.9: Evolution of the line width of the reactant component in metasilicate batch at
The increasingly broad range of environments is underlined by the fact that the line width of the reactant component in the in-situ spectra increases with heating time. The 23Na nuclei contributing to this component are in a progressively increasing range of chemical environments.
|Fig.10: Comparison of the disilicate (top) and metasilicate (bottom) batch line shapes
after (a) 3min, (b) 20min, and (c) 80min. The batch reactions take different pathways after about 20min.
All spectra are scaled to have the same amplitude, hence the different signal-to-noise ratio.
For the first 20 minutes, the disilicate batches follow the same reaction pathway as the metasilicate ones. This indicates that the interface between quartz and sodium carbonate grains is the rate-limiting feature rather than the chemical restructuring of the quartz grain cores themselves: The additional quartz does not deplete the Na+ supply. In order to establish at what point and how the mechanism in the disilicate batch diverges from the metasilicate case, the slices after 3min, 20min, and 80min at 880°C are compared. A much narrower component begins to grow to the right of the metasilicate line. This line is attributed to liquid disilicate.
|Fig.11: Ex-situ 23Na MAS spectra of the quenched disilicate batch after a
reaction time of (a) 39min and (b) 120min.
The MAS spectrum taken after the in-situ experiment confirms that the disilicate batch did in fact melt partially as it contains a broad Gaussian line consistent with the statistical distribution of sites expected in a disordered structure when there is no motional narrowing present. The fraction of Na+ ions located in this melt/glass phase is 75% after 39 minutes and 94% after 120 minutes. The other, narrow, peak is due to crystalline metasilicate. No unreacted Na2CO3 is present after 39 minutes.
|Fig.12: A model of the batch reactions as derived from the in-situ NMR experiments.
The reaction progresses from left to right. The second step of the disilicate batch reaction, which
involves additional SiO2 grains which were not in contact with the carbonate grain at the outset,
follows the upper pathway at high temperature i.e. where diffusion is unrestricted) and the lower
one at lower temperature, where diffusion limits the reaction rate.
The disilicate batch reaction takes place in two steps with quite distinct time scales: In the first step, which is rather fast, nearly all the Na2CO3 is consumed to form metasilicate in a solid state reaction. The second step, in which the intermediate product reacts with the remaining quartz, seems to be inhibited. It only takes place if the the temperature is high enough for the disilicate product to be liquid. If this is the case, the formation of a liquid film at the grain interface speeds up diffusion, and the reaction is driven to completion. The fact that the formation of liquid disilicate drives the entire batch reaction can be seen from the fact that the first stage, which is identical to the reaction taking place in metasilicate batches, takes place at a higher rate than in metasilicate batches themselves. At 880°C, the metasilicate batch needs about 41 minutes to form 67% of metasilicate.
After the same time at the same temperature, the disilicate batch has already reacted all Na2CO3 and formed a substantial amount of disilicate melt. If, on the other hand, the temperature is too low for a liquid film to form, the Na+ diffusion in the solid state is too slow. As a consequence, only a distribution of sodium environments, consistent with a concentration gradient across a reaction layer at the grain interface, is observed. This means that the reaction is kinetically controlled at low temperature, with solid-state diffusion being the limiting factor. It is thermodynamically controlled at high temperature, where substantial parts of the sample are above the equilibrium liquidus.
ConclusionsIn-situ high-temperature NMR spectroscopy has been used to investigate the kinetics of the silicate batch reaction. The two main advantages of the technique over ex-situ NMR experiments is the high time resolution, which cannot be achieved by preparing separate samples quenched after different times, and the fact that quenching artifacts such as recrystallization or other phase transitions can be ruled out. The main disadvantage is the broadness of the line due to the infeasibility of MAS at sufficiently high temperatures, but this can be overcome by individual MAS experiments on final products and a few quenched samples whose results are used to constrain the fit of the static in-situ line shape.
The kinetics of the reactive melting of glass-forming silicate batches was studied using a model system with fairly narrow grain size distribution. The preferred reaction product is metasilicate. It is formed by solid-state reaction even when the temperature is well above the liquidus of much of the composition space between SiO2 and Na2O·2SiO2. This means that Na+ diffusion is fast, allowing the reaction front to proceed very rapidly. Thermodynamic equilibration is lagging behind in this process, so that the liquid equilibrium phase near the eutectic is never reached. This mechanism relies on an ample supply of Na+ ions and a large interface cross-sectional area. The grain size combination chosen --large Na2CO3 grains surrounded by small quartz grains-- favors this mechanism.
In disilicate batches, where some of the quartz cannot be in direct contact with a Na+ source for geometrical reasons, the first stage of reaction is the same as in the metasilicate batches. After about 20 minutes, the mechanism changes and a liquid film of disilicate is formed. This melt phase can wet the excess quartz grains and transform the whole sample into liquid disilicate (and subsequently into glass after quenching). It is interesting to note that this second step, where thermodynamics rather than kinetics governs the reaction, drives the entire reaction to such an extent that metasilicate is formed faster as an intermediate in disilicate batches than in metasilicate batches themselves.