23Na,29Si, 13C MAS NMR investigation of glass-forming reactions between Na2CO3 and SiO2

AR Jones, R Winter, GN Greaves, IH Smith J Phys Chem B 109 (2005) 23154
Abstract. The glass forming reactions between sodium carbonate (Na2CO3) and silica (SiO2) have been investigated by 23Na, 29Si, and 13C magic-angle spinning (MAS) NMR spectroscopy. The multi-nuclear MAS NMR approach identifies and quantifies reaction products and intermediates, both glassy and crystalline. A series of powdered batches of initial composition Na2CO3·xSiO2 (x = 1,2) corresponding to a sodium metasilicate (Na2SiO3) and sodium disilicate (Na2Si2O5) stoichiometry were investigated after periods of isothermal and non-isothermal heat treatments at different temperatures. Analysis of the 23Na quadrupolar coupling parameters has identified the early reaction product in all cases as crystalline Na2SiO3. In the non-isothermal experiment, this reaction is preceded by an early silica-rich melt phase formed around 850oC. The early reactions are controlled by solid-state Na+ diffusion across the reaction zone in the grain interface layer. Crystalline Na2SiO3 precipitates in the interface layer, increasing its thickness between the Na2CO3 and the SiO2 grains and slowing down the rate of Na+ migration. This creates a secondary phase, which is temperature dependent. At low temperatures, where Na+ migration is impaired, the production of Na2SiO3 ceases and silica-richer phases are precipitated. In the case of the sodium disilicate batch, where excess SiO2 is present, a secondary reaction of Na2SiO3 with SiO2 forming a glassy phase is observed. A transient carbon-bearing phase has been identified by 13C NMR as a NaCO3- complex loosely bound to bridging oxygens in the silicate network at the SiO2 grain surface.


Chemical reactions involving powdered batches are subject to a number of physical constraints that cause a deviation from equilibrium chemistry. Such reactions can be purely solid-state, in which case diffusion across the boundary layer or interface between the grains plays a major role as well as the malleability of the reactant grains as it determines the active surface area, i.e. the actual contact cross section between adjacent reactant grains. Alternatively, a reactant or a product phase produced by a solid-state reaction may melt, leading to a solid-liquid interface reaction controlled by diffusion as well as surface tension and wetting of the remaining grains by the liquid formed. As a consequence, these physical constraints will determine whether the reaction is kinetically or thermodynamically controlled. This investigation focuses on the role grain surfaces and interfaces play in batch melting reactions of glass-forming silicate batches. The term interface layer will be used to describe the reaction zone near the surface of the quartz grains in which Na+ diffusion may take place.

MAS NMR is well suited to investigate the reaction products of a sodium silicate glass batch because it not only gives quantitative information on the reaction product formed but also structural information on the local environment of the probe nuclei as the progressive change from batch to glass takes place. Therefore, a multinuclear MAS NMR approach using 29Si, 23Na and 13C MAS NMR has been used in this study as a quantitative technique to investigate the intermediate crystalline and amorphous phases formed during the reaction of Na2CO3 and SiO2 to produce a glass.


Non-isothermal batches
Metasilicate batch mixtures were prepared using 13C-enriched Na2CO3. 0.15 wt-% of Fe2O3 was added to speed up 29Si relaxation in all product phases. Samples were quenched from 700, 850, 950, 1090, and 1300oC.

Isothermal batches
Three isothermally heated batches were prepared: metasilicate at 700oC and disilicate at 775 and 850oC, all for varying times. These were not 13C enriched. Again, Fe2O3 was added.

NMR parameters
23Na 29Si 13C
resonance frequency105.8 79.5 100.6 MHz
MAS rate 15 5 10 kHz
flip angle 7.5 30 15 deg
recycle delay 1 * 800 s
reference 1M NaCl aq. TMS TMS
*) Since the Fe2O3 is only incorporated into the reacted or melted phases of the samples, the Fe ions have virtually no effect on the spin-lattice relaxation of the 29Si nuclei in SiO2. Therefore, the relaxation time, T1, in product phases is reduced due to spin diffusion to the paramagnetic centers followed by nuclear-electronic dipolar relaxation. Hence, by employing a suitably short recycle delay the NMR detection is selective to the newly formed phases since the 29Si nuclei in raw SiO2 do not have sufficient time to relax between scans. In order to observe the SiO2 resonance, a delay of 400s has been used in some experiments, but even then the SiO2 intensity is attenuated relative to the other resonance lines.

Results - non-isothermal batches

Fig. 1.
Fig. 1: a) 29Si MAS NMR spectra of the non-isothermal batch heated at 10 K min-1 to the specified temperatures. b) A spectrum of the sample quenched at 850oC, acquired with a shorter recycle delay than in (a), together with Gaussian fit components.
The 29Si quartz resonance is located at -107ppm. Progressive heat treatment promotes the formation of a second narrow line at -77ppm. This resonance possesses a chemical shift that is expected for crystalline Na2SiO3. The growth of this crystalline Q2 line is accompanied by a reduction in the intensity of the SiO2 or crystalline Q4 line at -107ppm. The spectrum of the sample quenched from 850oC was acquired with a delay of 400s between consecutive data acquisitions, therefore allowing a partial relaxation of the 29Si nuclei in SiO2. This spectrum of the 850oC sample was acquired using a 25s delay and 4500 averaged spectra. The signal to noise is improved and all the reaction products can be identified. However, the SiO2 peak has lost intensity due to the long 29Si T1 relaxation time in pure unreacted SiO2. A broad resonance peak centered at about -90ppm is attributed to glassy Q3.

Fig. 2.
Fig. 2: a) 23Na MAS NMR spectra of the non-isothermal batch heated at 10 K min-1 to the specified temperatures. b) The spectrum of the sample quenched at 850oC after subtraction of the spectrum of the raw material, Na2CO3.
The 23Na spectrum of the unheated sample (i.e. Na2CO3 spectrum) is characterized by two peaks in the range 10ppm to -55ppm. These are due to two crystallographic Na+ sites in Na2CO3. A peak emerges at about 19ppm and the Na2CO3 contribution diminishes as heat treatment progresses. The quadrupole parameters of the new peak compare well with published values for crystalline Na2SiO3 prepared by devitrification. The spectrum of the sample heated to 950oC is characterized by only one peak, which is due to Na2SiO3; therefore Na2CO3 is no longer present. However, a broad line re-emerges in the range 10 to -40ppm in the spectrum of the sample heated to 1090oC. The smoothed and slightly broadened lineshape signifies a glassy component. This glassy phase is also evident in the corresponding 29Si spectrum (cf. Fig. 1a). A closer inspection of the 23Na spectrum of the sample heated to 850oC reveals a slight change in the lineshape between -5ppm and -15ppm compared to spectra of the unheated sample and the sample heated to 700oC. This is clearly visible when the Na2CO3 component of the spectrum is subtracted (using the narrow Na2CO3 resonance line to scale the contribution). The difference spectrum highlights a broad component between about 0ppm and -40ppm, similar to that seen in the spectrum of the sample heated to 1090oC. Therefore, a glass phase is formed in the sample heated to 850oC, which subsequently disappears by 950oC followed by the formation of a new glass phase in the sample heated to 1090oC.

Fig. 3.
Fig. 3: 13C MAS NMR spectra of the (13C-enriched) non-isothermal batch heated at 10 K min-1 to 700oC and 850oC. The spectrum of the raw batch (RT) is shown for comparison. At higher temperatures, no 13C signal is observable.
The 13C resonance of Na213CO3 has a peak maximum at 170.7ppm and a full width at half magnitude (FWHM) of 0.4ppm. The sample heated to 700oC shows no change in line shape or position. However, the spectrum of the sample heated to 850oC shows an additional peak at 172.1ppm with an FWHM of 0.7ppm. The relaxation of both lines is very slow; complete relaxation of the raw material's contribution was not observed after 9 hours. Therefore, a quantitative analysis of the relative strength of the two peaks is not possible. However, the T1 value of the peak at 172.1ppm is 200s. This indicates that the 13C nuclei are in closer proximity to the paramagnetic ions that facilitate the 13C nuclei to dissipate their energy and hence reduce the T1 time. No 13C signal is detectable in samples heated beyond 850oC.

Results - Isothermal metasilicate batch

Fig. 4.
Fig. 4: 23Na MAS NMR spectra of isothermal metasilicate batch reacted at 700oC for the periods indicated.
The 23Na MAS NMR spectra (left) of the Na2CO3--SiO2 series of samples isothermally heated at 700oC (M700) show the onset of crystalline Na2SiO3 formation after 20min as identified by the resonance line centered near 20ppm. The growth of the Na2SiO3 peak is observed with increasing heat treatment at the expense of the Na2CO3 contribution. However, there is a significant difference in the 23Na MAS NMR lineshape of the sample heated for 41 hours, with a broadening at the base of the resonance lines. Subtracting the Na2CO3 contribution from this lineshape (using the narrow Na2CO3 resonance line to scale the contribution) as illustrated below can separate this additional component. The difference spectrum clearly shows the resonance line of Na2SiO3, together with an additional resonance line centered near -10ppm, which is distinctly narrower than the glassy residual phase found in the non-isothermal experiment (cf. Fig. 1b). This indicates that changes of the local environment surrounding some 23Na atoms occur only after 41hr of heating.

Fig. 5.
Fig. 5: 23Na MAS NMR spectra of a) isothermal metasilicate batch reacted at 700oC for 41h and b) of the raw material, Na2CO3. c) difference spectrum, i.e. the batch spectrum after subtraction of the contribution from unreacted raw material.

Results - isothermal disilicate batches

Fig. 6.
Fig. 6: 23Na MAS NMR spectra of isothermal disilicate batch reacted for the periods indicated at a) 775oC and b) 850oC.
The 23Na MAS NMR spectra of the Na2CO3--2SiO2 mixture heated at 775oC (D775) show that crystalline Na2SiO3 is produced at a substantially increased rate -- it is already detectable after 5min of heating. Na2CO3 is fully reacted after 60min leaving only crystalline Na2SiO3 and the remaining SiO2.

At 850oC (D850 series), i.e. near the melting point of Na2CO3, the time scale of the reaction is much shorter than in the previous experiments. After only 20s, 5mol-% crystalline Na2SiO3 has formed. The reaction between SiO2 and Na2CO3 continues until all the Na2CO3 has reacted and only Na2SiO3 and the excess SiO2 are left. The complete reaction of Na2CO3 takes only about 140s. The spectral line shapes of the samples heated up to 140s are identical to those of the D775 series. On further heating, a broad line appears after 300s close to the position of the original Na2CO3 resonance. The intensity increases with heating time at the expense of the crystalline Na2SiO3 resonance line. The new line centered near -15ppm is very broad and, therefore, due to an amorphous phase.

Fig. 7:
Fig. 7: 29Si MAS NMR spectrum of isothermal disilicate batch reacted at 850oC for a) 5min and b) 35min with model fits comprising crystalline SiO2 and Na2SiO3 and amorphous Na2O · 2 SiO2 components.
29Si spectra of the D850 samples are fitted with Gaussian components. The sharp resonance lines positioned at -77ppm and -107ppm are due to crystalline Na2SiO3 and SiO2, respectively. In addition, after 5min of heating, there is a broad line between the crystalline peaks due to the formation of a melt. This peak can be fitted with one Gaussian component positioned near -90ppm, which is at a chemical shift position expected for Q3 species. The intensity of the broad component is considerably greater in the spectrum obtained after 5min of heating, indicating an increased amount of glassy phase. It is also apparent that three Gaussian components are needed to fit the glassy component positioned at -78ppm, -90ppm and -106ppm. These relate to chemical shifts expected of Q2, Q3, and Q4 species, respectively. These glass phases match those observed in the 23Na MAS NMR spectra.

Discussion - non-isothermal batches

29Si experiments using a 400s delay show no contribution from SiO2 in the sample heated to 950oC. This proves that all the SiO2 has reacted and only crystalline Na2SiO3 is present by 950oC. The formation of an increasing amount of glassy phase is observed as the sample is heated past the melting temperature of Na2SiO3. The sample heated to 1300oC illustrates the broadening of the resonance line due to the greater range of bond angle distribution in the glassy Na2SiO3 structure compared to the crystalline equivalent. Some crystalline Na2SiO3 remains at 1300oC and is clearly seen as a narrow peak on top of the broad resonance peak in the bottom trace of Fig. 1a.

A fully quantitative analysis of the 29Si spectra containing unreacted SiO2 is not possible due to the 29Si in the SiO2 not fully relaxing. This manifests itself by attenuating the SiO2 peak intensity in the spectra. Full relaxation of the 29Si nuclei in all phases present was only observed for the sample heated to 1300oC, making a quantitative analysis possible. Hence, the amounts of various Qn species were determined together with the amount of crystalline Na2SiO3. The 23Na spectra were used to determine the quantity of the various phases present for the remaining spectra, where full 29Si relaxation was not observed.

Fig. 8.
Fig. 8: a) Abundance of crystalline and glassy phases in non-isothermal batch as a function of temperature reached based on the Qn speciation derived from 29Si experiments. b) The reaction path reconstructed from the evolution of 29Si and 23Na spectra. See text for details.

The bar chart shows the contributions (mol-%) of the different phases in the sample as a function of time determined from the 29Si and 23Na spectra. The occurrence of a Q1 species in the 1090oC sample, which unbalances the average fraction of non-bridging oxygens suggests that a small amount of unreacted quartz has not been detected. The upper limit of this contribution, whose exact line width is difficult to determine due to the low signal-to-noise, is 14%, corresponding to 7% unreacted quartz. The schematic above illustrates the possible reaction path and intermediate compounds formed on heating of the Na2CO3--SiO2 mixture.

At 700oC a solid-state reaction between SiO2 and Na213CO3 begins to form crystalline Na2SiO3. This is evident in the 29Si spectrum with the line appearing at -77ppm and from the 23Na spectrum with the line appearing at about 19ppm attributed to Na2SiO3. The formation of Na2SiO3 increases as a function of heating at the expense of the SiO2 and Na2CO3. This is observed in both 29Si and 23Na spectra with a decrease in the relative intensities of the SiO2 and Na2CO3 lines, respectively. The first occurrence of a glass phase is observed at 850oC, therefore indicating the formation of a silicate melt. This relates to the broad peak in the 29Si spectra centered at -90ppm (Q3) corresponding to the chemical composition of Na2O · 2 SiO2. The formation of this glass phase could be due to the melting of an equivalent crystalline phase, further reaction of the Na2SiO3 with SiO2, or a reaction of a liquid film of Na2CO3 wetting the quartz grains. Crystalline Na2Si2O5 melts at 874oC, therefore it is thermodynamically possible for this compound to precipitate following the reaction of SiO2 and Na2CO3 between 700oC and 850oC. This would then melt when approaching its actual melting point, producing the glass phase observed after quenching. However, as no solid silica-rich intermediate product is directly observed, it is more likely that a reaction at the interface of the crystalline Na2SiO3 and SiO2 grains leads to the formation of glassy Na2O · 2 SiO2. This glass phase then disappears at higher temperatures and is replaced by other glass phases. By 950oC, both SiO2 and Na2CO3 have fully reacted since the SiO2 signal at -107ppm has disappeared from the 29Si spectra and no Na2CO3 contribution is present in the 23Na spectra. The sample is composed only of crystalline Na2SiO3 at 950oC. The silicate glass (Na2O · 2 SiO2) observed in the 850oC sample is no longer present. This indicates a reaction of Na2O · 2 SiO2 with Na2CO3 to form crystalline Na2SiO3, which is the thermodynamically stable product at this temperature. A significant change in the 29Si spectra appears above the melting point of Na2SiO3, at 1090oC. A broad resonance peak due to a glass phase is observed corresponding to the melting of the crystalline Na2SiO3 structure. The broadness of the peak reflects the disordered environment of the 29Si atoms in the newly formed melt/glass. By 1300oC, virtually all of the crystalline Na2SiO3 has melted to form a homogeneous Q2 glass.

The brief appearance of a second peak in the 13C spectrum at 850oC and its much shorter relaxation time in comparison to that of the reactant points to the fact that this contribution is due to a transient phase that exists only for a short time immediately before the 13C is released as CO2. The only source of paramagnetic ions is 0.15wt% Fe2O3 introduced into the sample to reduce the T1 value of the reaction products. These Fe2O3 particles would therefore be in contact with the SiO2 and Na2CO3 grain surfaces. Hence, the interaction of the 13C nuclei with paramagnetic centers suggests that the resonance at 172.1ppm is due to 13C nuclei in the interface layer. The change in chemical shift associated with this resonance line indicates that the 13C chemical environment in this phase is somewhat different to that in the bulk Na2CO3 due to interactions of the carbonate with the silicate network. Molecular CO2 can be ruled out as a possible origin of the peak since its line would occur at 125ppm. High-pressure CO2 saturation studies also describe a resonance peak in the range 171ppm to 175ppm, which is being related to a Na-carbonate ionic complex, i.e. a structural unit where the Na+ is more closely connected with one of the carbonate ion's oxygen atoms, resulting in a reduced coordination number of the Na+ ion. The formation of such complexes has also been concluded from Raman spectra of albitic and anorthic glasses. Calculated 13C NMR shielding values for various carbonate complexes in alumosilicates predict resonance peaks positioned between 155ppm and 175ppm. At the lower end of the scale, peaks are assigned to CO2 molecules attached to a bridging oxygen in the silicate network, while medium-range shifts correspond to carbonate ions forming part of the network themselves, i.e. where the carbonate oxygens are bridging oxygens connected to silicon neighbors. Values above the position of Na2CO3 itself are again ascribed to NaCO3- complexes with reduced sodium coordination number. Therefore, the line observed here at 172.1ppm is due to NaCO3- complexes incorporated in the interface layer which bond loosely to a bridging oxygen of the silicate network at the SiO2 surface. CO2 solubility is negligible unless under geological pressures. In this study, no external pressure is applied. However, the ready supply of excess CO2 from the decomposing Na2CO3 constitutes a driving force for CO2 to dissolve temporarily in the silicate as NaCO3- complexes by biasing the thermodynamic equilibrium. This dissolved CO2 is immediately released as soon as the CO2 supply is exhausted and the thermodynamic equilibrium reinstated.

Discussion - Isothermal batches

Fig. 9.
Fig. 9: Fraction of raw material, Na2CO3, reacted vs. time for isothermal metasilicate batch at 700oC (M700).
Fig. 10.
Fig. 10: Fraction of raw material, Na2CO3, reacted vs. time for isothermal disilicate batch at 775oC (D775). Note the much shorter time scale than in M700 (left).
Fig. 11.
Fig. 11: Fraction of crystalline metasilicate present in isothermal disilicate batch vs. time at 850oC (D850). The buildup (full squares) and decay (open circles) of the intermediate product take place on two different time scales.
The progress of the reaction of the isothermal batches is monitored by analyzing the quantitative 23Na spectra. The reaction of metasilicate batch at 700oC (M700, above left) is deceleratory and only about 60% of the Na2CO3 has reacted after 41 hours.

The reaction of disilicate batch at 775oC (D775, above) proceeds in approximately linear fashion until all Na2CO3 is consumed after about 1 hour. The product is metasilicate, with excess quartz remaining after the end of the reaction.

In disilicate batch at 850oC (D850, left), the reaction proceeds in a second step. Metasilicate is merely an intermediate product in this case; it reacts with the excess quartz by forming a glass. The buildup and decay of crystalline Na2SiO3 occur on two different time scales.

The formation of crystalline Na2SiO3 from the reaction of SiO2 and sodium carbonate is common between both the initial Na2CO3--SiO2 and Na2CO3--2SiO2 samples. The rate of reaction increases with temperature, but the initial reaction product is independent of temperature in the temperature range studied. The reaction rate is very slow for series M700 with only the formation of Na2SiO3 being observed. Only after 41 hours of heating, first indications appear of a change of some 23Na product environments away from undistorted metasilicate type. The deceleratory reaction kinetics indicates that the reaction is diffusion-limited. The reaction product is formed at the point of contact between the SiO2 and the Na2CO3 grains; if the reaction is to continue, the mobile sodium ions must be transported across the increasing layer of product. The amount of Na+ diffusing from the Na2CO3 and depolymerizing the SiO2 will be decreasing as the Na2SiO3 layer increases in thickness. The transport of Na+ towards the SiO2 will become too slow for the production of Na2SiO3 to continue. Due to the Na+ concentration gradient caused by the diffusion through the increasing interface layer, there will not be a sudden change in the reaction product from Na2SiO3 to Na2Si2O5 as we have shown recently by in-situ 23Na NMR.

The reaction in the Na2CO3--2SiO2 batch series heated at 775oC (D775) also produces Na2SiO3 as a reaction product. The reaction comes to completion in about 60min by solid-state reaction with no evidence of the formation of any melt phase. The linear relationship between the Na2CO3 fraction reacted and time indicates that the transport of Na+ ions across the product layer is not decreasing at this temperature. The rate of reaction increases further for the D850 samples. The reaction proceeds in the same manner as with D775 except that complete reaction of Na2CO3 is obtained after 140s of heating. After the Na2CO3 has completely reacted, the production of a silicate melt is observed in the D850 series of experiments. This is evident from both the 23Na and 29Si spectra with the growth of a broad resonance line. The average Qn species in a Na2O · 2 SiO2 glass should be Q3, i.e. n=3, however this does not imply that only Q3 species are expected in the glass. In the D850 sample heated for 35min, about 95mol% of the sample is glassy and there exist Q2, Q3, and Q4, having a weighted average of n=3. The reaction of Na2CO3 in the D850 samples turns deceleratory towards the end of the reaction. This slowing in the rate of reaction of Na2CO3 indicates a change in the reaction mechanism towards diffusion control as soon as the reaction between SiO2 and the crystalline Na2SiO3 begins.


Quantitative information concerning the formation and evolution of intermediate reaction products has been obtained through a multinuclear combination of NMR techniques. Furthermore, MAS NMR, although being essentially a bulk technique, has been used to gain quantitative information involving a spatially restricted interface layer.

Crystalline Na2SiO3 is an early reaction product in both the non-isothermal and isothermal experiments. In the non-isothermal series, evidence of the formation of a Na2O · 2 SiO2 melt at 850oC is obtained. At temperatures of 1090oC and above, the melting of crystalline Na2SiO3 is deduced from the broadening of the 29Si spectra. Na2SiO3 is also the preferred initial reaction product for the isothermally heated samples M700, D775 and D850. It can be concluded that, once the Na2SiO3 layer grows to a critical thickness and the temperature is sufficiently low, the diffusion of Na+ is decreased to such an extent that not enough Na+ will reach the SiO2 to produce more Na2SiO3. This is the case with the M700 series. Silica-richer phases are now being formed in the interface layer between the SiO2 and Na2SiO3, with a pronounced Na+ concentration gradient across the layer. The reaction process of the disilicate and metasilicate samples appears to be a two-step mechanism. The first step for sodium disilicate batch samples is the solid-state reaction between SiO2 and Na2CO3 forming crystalline Na2SiO3. This stage continues until all Na2CO3 has reacted. The second stage is the reaction between the SiO2 and the Na2SiO3 forming the Na2O · 2 SiO2 melt. The second stage of the reaction is considerably slower than the first stage. The first stage is complete after 140s for D850, while the second stage is near completion after 45 minutes. Therefore, the first melt only appears after all the Na2CO3 has reacted. A similar two-stage mechanism can be used to describe the reaction of the metasilicate batch. The first stage is again the reaction of SiO2 and Na2CO3 producing Na2SiO3. This continues until no more Na2SiO3 can be produced due to a critical thickness of Na2SiO3 already formed, preventing sufficient Na+ ions from reaching the SiO2. The second stage sees the production of Na2O · 2 SiO2 at the SiO2 grain interface layer. Also there will be a significant Na+ concentration gradient between pure Na2O · SiO2 and pure Na2O · 2 SiO2 layers. In both cases the reaction product and rate of formation is controlled by the diffusion of Na+.

The 13C MAS NMR experiments have revealed a carbonate species that exists at the Na2CO3 grain boundary, i.e. at the reaction interface between SiO2 and Na2CO3. The observed additional peak at 172.1ppm for the 850oC sample relates to a carbon species located in the interface layer between the Na2CO3 and SiO2 grains. This species is similar to the Na-carbonate complex that was observed in studies of CO2 dissolution in melts at high pressure. This species is a transient reaction state on the Na2CO3 grain boundary during atomic rearrangements as the reaction proceeds before release of the CO2 in molecular form. This interpretation is supported by the shorter T1 value of this carbonate species due to its being in closer proximity to a Fe3+ paramagnetic center, and by the change in its chemical shift.

Acknowledgements. ARJ and RW thank Dominique Massiot (Centre de Recherche sur les Matériaux à Haute Température, Orléans) for discussion and for the use of the Dmfit software. ARJ would like to thank the UK Engineering and Physical Sciences Research Council and Pilkington plc for a PhD studentship from the Collaborative Awards in Science and Engineering scheme.
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