UDK 546.654.66:621.352.3
Original scientific article/Izvirni znanstveni članek
ISSN 1580-2949 MTAEC9, 42(2)85(2008)
ANALYSIS OF THE TEMPERATURE PROFILES DURING THE COMBUSTION SYNTHESIS OF DOPED LANTHANUM GALLATE
ANALIZA TEMPERATURNIH PROFILOV MED ZGOREVALNO SINTEZO DOPIRANEGA LANTANOVEGA GALATA
Marjan Marinšek
Faculty of Chemistry and Chemical Technology, Aškerčeva 5, 1000 Ljubljana, Slovenia marjan.marinsek@fkkt.uni-lj.si
Prejem rokopisa — received: 2007-10-08; sprejem za objavo - accepted for publication: 2007-12-05
Strontium-, magnesium-, iron-doped lanthanum gallate was prepared by the citrate-nitrate combustion technique. The temperature profiles of the citrate-nitrate metal ions system were measured and analyzed by applying the Boddington method. On the basis of the temperature measurements it was possible to perform thermodynamic and kinetic analysis of the system. The Boddington parameters Tc, u, tr, td, tx, t*, Tad, a, G that are essential for the kinetic analysis were defined by means of calculated X, h, cp values of the combustion system and measured values of p and Q. Arrhenius kinetics was assumed for the determination of the kinetic parameters such as the activation energy Ea, the expotential factor n and pre-expotential factor K0' of the system. The activation energy for the combustion system was determined by the method of combustion-wave propagation velocity to be 34.8 kJ mol-1, by the Boddington method to be 31.8 kJ mol-1 and by the Freeman-Carroll method to be 33.1 kJ mol-1. Key words: lanthanum gallate, self-propagating-high-temperature synthesis, citrate-nitrate combustion process, kinetic analysis, the Boddington method, Freeman-Carrol
Lantanov galat, dopiran s stroncijem, magnezijem in železom, je bil pripravljen po citratno-nitratnem postopku zgorevalne sinteze. Merjeni temperaturni profili sistema citrat-nitrat-kovinski ioni so bili analizirani po Boddingtonovi metodi. Na podlagi izračunanih vrednosti X, h, cp zgorevalnega sistema in merjenih vrednosti p in Q so bili določeni Boddingtonovi parametri Tc, u, tr, td, tx, t*, Tad, a, G, ki so kjučnega pomena za kinetično analizo. Za določitev kinetičnih parametrov, kot so aktivacijska energija Ea, eksponentni faktor n in predeksponentni faktor K0 sistema, je bila predpostavljena Arrheniusova kinetika. Aktivacijska energija je bila določena po metodi hitrosti napredovanja zgorevalnega vala v odvisnosti od temperature z vrednostjo 34,8 kJ mol-1, po Boddingtonovi metodi z vrednostjo 31,8 kJ mol-1 in po Freeman-Carrollovi metodi z rezultatom 33,1 kJ mol-1.
Ključne beside: lantanov galat, zgorevalna sinteza, citratno-nitratni postopek, kinetična analiza, Boddingtonova metoda, metoda Freeman-Carrol
1 INTRODUCTION
Lately, the oxygen ionic transfer in some doped perovskite-type oxides was investigated with special emphasis on the relationship between the oxygen-ion conductivity and the material lattice parameters 1-3. Among the investigated materials gallate ABO3 with A = La was found to have the highest Goldschmidt tolerance factor and correspondingly the highest oxygen ionic conductivity in relation to other A = rare-earth occupations. On the B-site, the maximum specific conductivity and oxygen transfer and the minimum of the activation energy were determined in the case of Ga 4,5. The ionic conductivity properties of perovskites were explained in terms of their structure, i.e., the oxygen ionic conductivity increases with the free volume of the unit cell and decreases with decreasing tolerance factor owing to an increasing distortion of the perovskite structure.
The oxygen ionic conductivity of lanthanum gallates can be improved with appropriate doping owing to the generation of oxygen vacancies. Among the dopands Sr (A-site dopand) and Mg (B-site dopand) additions (La0.9Sr0.1Ga0.8Mg0.2O3-x) were found to have a profound
effect on increasing the oxygen ionic conductivity -LSGM 6. If Ga in La0.9Sr0.1(Ga1-yMy)0.8Mg0.2O3-x is further substituted by a transition metal (M = Cr, Mn, Fe, Co), the electrical properties of LSGM can be further modified. When doped with amounts y < 0.1 of Fe or Co, gallates exhibit oxygen ionic conductivities twice that of LSGM7, which enables these materials to be used as medium-temperature electrolytes. With increasing dopant concentration both the exchangeable oxygen and the p-type electrical conductivity increase, which is of interest for applications as mixed conductors.
Doped lanthanum gallates are usually prepared either from the corresponding oxides with a solid-state reaction at high temperatures 8,9, or with self-propagating high-temperature synthesis (SHS) 10. Such solid-state reactions are diffusion controlled and time consuming, while the resulting powders may show a certain degree of compositional inhomogeneity. In contrast, a combustion synthesis or a self-propagating high-temperature synthesis (SHS) provides an attractive practical alternative to conventional methods. The combustion process involves the decomposition of a redox system, which then proceeds as a self-sustaining front throughout the
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reactant gel mixture. The reaction conditions and the large amount of heat evolved during the reaction enable the direct production of a large number of single or multicomponent crystalline and homogeneous powders that have a narrow particle size distribution 11. From the variety of possible redox systems, a combustion mixture based on the citrate-nitrate combination can be potentially applied for the production of larger quantities of mixed oxides owing to its relatively non-violent combustion 12.
The theoretical physical models that explain, simulate and predict SHS reaction phenomena are based on energy and mass balances 13. In the case where the reaction rate is used to calculate the kinetic parameters of the reaction, several mathematical models have been developed. In this respect the Boddington method 14 is particularly valuable because calculations of the kinetic parameters and the preliminary thermal conductivity determinations are not necessary. Moreover, the Boddington method is not based on a specific kinetic model but predicts the same kinetic behaviour of the system at a certain value of the reactant-to-product conversion. The origin of the Boddington method is thus a mathematical analysis of the measured temperature profiles of the combustion system with respect to the heat-balance equation utilized. The Boddington method employs the following heat-balance equation:
k d T — CppdT + 0(T, n)-h(T - T0) = 0	(1)
dx	dt
In the above equation Cp is the heat capacity of the product, p is its density, k is the thermal conductivity, <&'(T,q) is the rate of heat generation, h is an axial heat-transfer coefficient, T is the temperature, t is the time and x is the coordinate of wave propagation (the radiant heat losses are assumed to be negligible). The result of a combustion temperature profile according to the Boddington method is the calculation of the previously mentioned parameters, which finally enables a determination of the activation energy for the combustion reaction.
When the data on the fraction reacted n vs. T or t are accessible, several approaches are available for the kinetic analysis. A particularly interesting approach to kinetic parameter determination, because of its simplicity, is the Freeman-Carroll method 15. This method is based on Arrhenius kinetics and utilizes the following kinetic function:
^ = K 0 expl 1(1 - n)"
dt
RT
(2)
where Ko' is a constant and n is an exponential factor in a function of the kinetic order.
In the present work, a citrate-nitrate (fuel-oxidant) combustion synthesis method was employed to produce Lao.85Sro.1(Gao.9Feo.1)o.8Mgo.2O3-ô (LSGFM) To our knowledge, this is the first time that combustion synthesis was
chosen for doped-LSGM preparation. The citrate-nitrate system was chosen due to its non-violent nature and because fine-doped LSGM-based perovskites have potential uses in the previously mentioned applications. For the chosen combustion system a complete Bodding-ton analysis was also performed.
2 EXPERIMENTAL PROCEDURE
Lao.85Sro.1(Gao.9Feo.1)o.8Mgo.2O3-x+<5 perovskite was prepared with a modified combustion synthesis based on the citrate-nitrate redox reaction. The starting substances for the reactive gel preparation were La(NO3)3-6H2O, Sr(NO3)2, Ga(NO3)3-1oH2O, Mg(NO3)2-6H2O, Fe(NO3^ 9H2O, C6H8O7 H2O, and nitric acid (analytical reagent grade). La(NO3)3-6H2O (3.ooo g), Sr(NO3)2 (o.173 g), Ga(NO3)3-1oH2O (2.559 g), Mg(NO3)2-6H2O (o.417 g), Fe(NO3)3-9H2O (o.263) and C6H8O7H2O (2.394 g) were dissolved separately with minimum additions of water in amounts that ensured the desired final composition. Aqueous solutions were mixed and HNO3 (aq. 65 %, 1.25 mL)) was added to ensure the initial citrate/nitrate molar ratio of o.18. With the aim to obtain kinetic parameters from the temperature profile measurements, the reaction system was then diluted with different additions of a-A^O3 (from o % A^O3 up to 5 % A^O3 in the dry reactive mixture). A suspension (mixed nitrate solution with Al2O3 addition) was kept over a water bath at 6o °C under vacuum (5 mbar) until it transformed into a bright fragile xerogel.
The dried and diluted gels were gently milled and homogenized in an agate mortar and subsequently uniaxially pressed (17 MPa) into pellets (16 mm in diameter, height «3o mm). The pellets were ignited at the top to start a self-sustaining combustion reaction producing doped LSGM perovskite. If the additions of Al2O3 exceeded 5 % the combustion system did not react in a self-sustaining mode.
The temperature profiles of the burning tablets were measured using an optical pyrometer (Ircon, model IPE 14o, based on sample brightness) with a measuring range from 5o to 12oo °C and a very quick response time (1.5 ms). The accuracy of the optically measured temperature was ±2.5 °C below 4oo °C and ±o.4 % of the measured value (in °C) above 4oo °C. Since the measured systems were all ceramics with unknown exact emissivities, the emissivity was set to o.85 and was kept constant for all the measurements. This value is close to the cited emissivities of ceramic products and Al2O3 in the measured temperature range. The temperature profiles of the reaction systems were measured from a distance of 1o cm with a space resolution of temperature measurements (the size of the measured spot on the sample surface) of o.3 mm. Prior to the Boddington kinetic analysis, the experimentally measured temperature profiles were smoothed in the zone of rapid temperature change. The smoothing procedure is essential because
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Figure 1: Self-sustaining citrate-nitrate reaction for La0.85Sr0.1(Ga0.9Fe0.1)0.8Mg0.2O3-x+<5 preparation Slika 1: Napredovanje zgorevlne sinteze v sistemu za pripravo La0,85Sr0,1(Ga0,9Fe0,1)0,8Mg0,2O3-x+<5
the measured values may oscillate around an average value, which makes the analysis of the temperature profile difficult. Slight temperature oscillations were ascribed to the surface roughness and to the synthesized material porosity.
3 RESULTS AND DISCUSSION
Combustion synthesis is a relatively new approach to doped-gallate preparation, i.e., gallates are normally prepared via a solid-state reaction. Very few reports are found in the literature describing lanthanum-gallate-based materials prepared via a combustion route 16,17 and none deal with citrate-nitrate-derived doped lanthanum gallates.
One of the reasons why citrate-nitrate combustion synthesis for doped gallates preparation was neglected is that the preparation of pure lanthanum gallate is practically impossible. Regardless of the citrate/nitrate (c/n) molar ratio used (from fuel-lean 0.13 < c/n < 0.25 to fuel-rich mixtures 0.25 < c/n < 0.33) or small additions of various fuels (e.g. urea), the heat evolved during the combustion was not sufficient to trigger a self-sustaining combustion reaction. Only if dopand elements (Fe or Co) that are known for their catalytic activity towards citrate-nitrate combustion are added to the fuel-lean initial mixture (c/n = 0.18) can the self-sustaining combustion be achieved (Figure 1). Such a system was then the basis for the Boddington kinetic analysis.
To confirm citrate-nitrate combustion as an appropriate synthesis route for LSGFM preparation, the final ash product, as well as the intermediate products, was submitted for XRD analysis (Figure 2). Intermediates were prepared by careful heating of small amounts of the initial xerogel in air up to a predetermined temperature. According to Figure 2 it is apparent that the intermediate precursors were amorphous at temperatures below 740 °C. At higher temperatures some crystalline phases appeared. The main crystalline phase found in intermediates treated above 740 °C was identified as the perovskite La0.895Sr0.105Ga0.8Mg0.2O3-<5. Additionally, only traces of residual secondary phases
SrLaGa3O7 and SrLaGaO4 were found with XRD. If the intermediate preparation temperatures ware increased, the secondary phases were almost completely dissolved in the LSGFM perovskite structure. The relatively low amounts of secondary phases in the intermediates prepared above 740 °C make, in our opinion, the combustion synthesis favourable when compared to preparation processes that are based on the diffusion of components in the solid state (in the latter case the amount of secondary phases is normally greater).
The entire range of as-measured temperature profiles for the chosen citrate-nitrate combustion system with different additions of Al2O3 diluting agent (!) are shown in Figure 3. Altering the amount of diluting agent influences many parameters pertaining to the combustion reaction, such as the wave velocity and the combustion temperature, as summarized in Table 1. According to the results in Figure 3 and Table 1, a greater addition of diluting agent lowers the peak combustion temperature, as well as the rate of propagation of the combustion reaction. However, the general shape of the temperature profile did not change with any variation in the amount of diluent. Another interesting fact is the relatively rapid
Figure 2: XRD patterns of intermediates and as-synthesized LSGFM Slika 2: Rentgenogrami vmesnih produktov ter LSGFM sintetizira-nega materiala
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product cooling. The samples cooled down from their peak temperature to 50 °C in approximately 40-60 s. The fast cooling was ascribed to the very porous structure formed after the combustion (Figure 1). The determination of the parameters' peak combustion temperature (Tc) and the combustion propagation velocity (u) is essential for the wave-velocity analysis. For the activation-energy calculation the following equation was utilized:
2	C R ' X
ur (1 - X) = f(n)K 0 a~L R exp
T c	Q0 E

where f(q) is a function that depends on the kinetic order of the reaction, a is the thermal diffusivity of the product, Cp is the heat capacity of the product, Q0 is the heat of reaction for an undiluted system, X is the weight fraction of diluent, E is the activation energy, R is the general gas constant and K0 is a constant. As the parameters u and Tc are altered if the reaction system is diluted with an inert substance, the activation energy can then be calculated from the slope in the plot of ln ((1-X)0'5(u/Tc)) vs. 1/Tc. From the best-fit linear slope of the experimental combustion parameters, an apparent combustion activation energy of 34.8 kJ/mol was calculated (Figure 4).
Table 1: Reaction parameters of citrate-nitrate SHS systems Tabela 1: Parametri citratno-nitratne zgorevalne reakcije
X/wt	Tc/K	u-103 /(cm s-1)	(dT/dt) /K-s-1	(3T/3xt) /K-cm-1
0	907.2	18.33	177	9655
0.01	871.5	19.71	149	7557
0.02	834.6	17.07	146	8552
0.03	725.5	12.17	129	10596
0.04	715.7	9.09	103	11329
0.05	700.5	7.63	96	12575
In order to obtain kinetic information from the temperature profiles, a variety of calculations were
Figure 3: Measured temperature profiles of citrate-nitrate SHS systems with different additions of diluent
Slika 3: Merjeni temperaturni profili citratno-nitratnega sistema z različnimi dodatki sredstva za redčenje
performed on the basis of the experimental data. First, the temperature profiles in the zone of rapid temperature change were smoothed. From the smoothed version of the temperature profiles, the first and the second derivatives dT/dt and d2T/dt2 of each smoothed profile were calculated. The peak value in the plot of dT/dt vs. t corresponds to the maximum heating rate achieved during the reaction. If this value were divided by the measured wave-velocity value (u), the maximum thermal gradient (ôT/ôx)max in the propagating coordinate could be calculated (Table 1).
Then a complete Boddington analysis 14 of the temperature profiles obtained was performed, including the calculations of tr and td (the rise time of a general adiabatic fore-wave and the remote decay time, respectively) in order to determine the two other values tx (thermal relaxation time) and t* using the relationships tx = td - tr and 1/t* = 1/tr - 1/td. The parameters tx and t* include the thermodynamic values and can be further expressed as t* = a/u2 and tx = pCp/h, where a represents the effective thermal diffusivity (Table 2).
Table 2: Experimentally determined parameters of the Boddington analysis for the citrate-nitrate combustion
Tabela 2: Parametri citratno-nitratne zgorevalne reakcije določeni z Boddingtonovo metodo
X/wt	tr/s	td/s	tx/s	t*/s	Tad/K	a-103 /cm2-s-1
0	2.579	11.274	8.695	3.343	1392	1.124
0.01	2.369	12.005	9.636	2.951	1319	1.147
0.02	2.968	13.351	10.383	3.817	1296	1.113
0.03	2.952	13.850	10.898	3.752	1271	0.556
0.04	4.625	14.327	9.701	6.831	1222	0.565
0.05	5.733	15.432	9.698	9.124	1093	0.532
The temperature rise of the combustion system without heat losses, the value Tad (Table 2), was calculated by integrating the temperature profile, as described in 18. If the combustion system is under adiabatic
Figure 4: Wave-velocity analysis for combustion-derived LSGFM with different additions of Al2O3
Slika 4: Analiza hitrosti napredovanja zgorevalnega vala za sintezo LSGFM ob različnih dodatkih Al2O3
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conditions, the value of Tad. should be close to the value of Tc. However, if data from Tables 1 and 2 are compared, Tad. and Tc differ substantially. One reason for this is the incompletely adiabatic conditions during the reaction, i.e., during the citrate-nitrate combustion some volatile products are also formed19, carrying off a certain amount of heat. This implies that Eq. (1) should be changed in such a way as to describe the heat balance of the citrate-nitrate combustion, also taking into account the heat losses due to hot-gas formation. Nevertheless, the proposed Boddington heat-balance equation can still be used for the kinetic analysis and for the estimation of the n vs. T (or t) relationship (Figure 5). The function n vs. t was calculated in accordance with the following re-arranged Boddington heat-balance equation:
G = t—1 (T - To) + dT/dt -1 * d2 T/dt2
Since G also equals tad(ßrj/dt), it was possible to calculate the reaction rate by dividing the values of G by the adiabatic temperature rise. Finally, by integrating the experimentally determined reaction rate, the fraction reacted n was calculated.
The calculated n vs. t data showed that the citrate-nitrate combustion is a relatively rapid process. In an undiluted sample the elapsed time interval from 1o % conversion to 9o % conversion was approximately 4.1 seconds, or, expressed in distance, equal to o.75 mm.
The kinetic parameters obtained were used to calculate the activation energy of the citrate-nitrate combustion process. Due to the dependence of the T-n relationship on inert diluent additions 14, the activation energy could be calculated by plotting the experimentally determined values of dn/dt vs. the reciprocal of the absolute temperature at a fixed value of n. The magnitude of the slope in such a diagram should equal -E/R. The temperature dependence of the reaction rate at
Figure 5: Temperature profile and time dependence of the fraction reacted for the undiluted sample
Slika 5: Merjeni temperaturni profil ter izračunana stopnja konverzije za pripravo LSGFM v neredčenem sistemu
Figure 6: Temperature dependence of the reaction rate ln (dT/dt) for different values of n in the citrate-nitrate combustion system Slika 6: Temperaturna odvisnost reakcijske hitrosti ln (dT/dt) pri različnih vrednostih n v citratno-nitratnem zgorevalnem sistemu
different n values is shown in Figure 6. From this it is evident that the slopes of the middle data sets (from n = o.4 to n = o.8) agree fairly well with each other. On the other hand, the slopes at lower values of n (from n = o.1 to n = o.3) and the slopes at the highest n values (n = o.9) exhibited different (normally slightly lower) values compared to the middle data sets. Taking into account only the slopes of the middle data sets, the activation energy of 31.8 kJ/mol was deduced for the citrate-nitrate combustion system.
The third technique used for the kinetic analysis of the investigated citrate-nitrate system was the Freeman-Carroll method 15. When predetermined dn/dt vs. T data are used, this method enables the activation energy to be determined, as well as the parameters n and Ko' from Eq. (2). First, the parameter n was calculated from the slope in the plot of (A ln (dn/dt))/(A 1/T) vs. (A ln (1-n))/(A 1/T). Then the activation energy and the parameter Ko' of the system were calculated from the plots of ln (dn/dt . 1/(1-n)n) vs. the reciprocal of the absolute temperature. The magnitudes of the slope in such a diagram equal -E/R, while the intercept on the ordinate gives the value of ln Ko' (Figure 7). Parameters n, E and Ko' were determined for the undiluted system, as well as for all systems with various additions of diluent. The average n, Ko' and E values for all the investigated systems were calculated as (o.52, 5.97) s-1 and 33.1 kJ/mol, respectively.
The results of the calculation of the activation energy obtained from wave-velocity measurements (34.8 kJ/mol), the temperature-profile analysis (31.8 kJ/mol) and the Freeman-Carroll kinetic analysis (33.1 kJ/mol) are in good agreement, implying that any of the three techniques described can be used for a determination of the kinetic parameters. However, the good correlation between the E values obtained with different methods is not surprising, because all the methods are based on a similar assumption concerning the kinetic law (the Freeman-Carroll analysis uses data obtained from a
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-60000;--80000 J-
(Aln(l-??)y(Al/r)
0.00087 0.00089 0.00090 0.00092 -L24 —' -1- h-'-'-1-' h -1.26 j-rs -1.28
S -1.3 r
S -1.32 r 4 -1.34:> -1.36:-
a -L38=-
-1.4 T--1.42
j/r/K-'
Figure 7: Determination of n, E and K0 according to the Freeman-Carroll method, demonstration on a sample with ! = 0.01 wt.: a) determination of the parameter n, b) determination of Ko ' and E Slika 7: Določitev n, E in K0 z metodo Freeman-Carroll v sistemu ! = 0,01 a) določitev parametra n, b) določitev Ko' in E
temperature-profile analysis). For a further validation the values of the kinetic parameters should be related to those deduced by applying an analogous or at least a similar method. As is implicit in the model on which the Boddington analysis is based, the processes which govern the rate of conversion are assumed to be chemical reactions and diffusion processes. Using this model all the reactions are treated simultaneously by applying a general function f(rf) that describes sufficiently the time dependence of the conversion equivalent h. The calculated value of the exponent n implies that there are several (at least two) processes that determine the rate of conversion. Either we have more than one reaction, each determined by its own kinetic law, affecting the rate, which leads to an overall exponent value of 0.5, or the diffusion process is the rate-limiting factor. This would also explain the relatively low value of the activation energy.
4 CONCLUSIONS
Sr-, Mg-, Fe-doped lanthanum gallate was prepared for the first time via citrate-nitrate combustion synthesis. This was successful only after the addition of an appropriate amount of a doping element, which is also
catalytically active toward the citrate-nitrate combustion. The main benefits of combustion-derived powders are a single-step process that is relatively quick, and the practical absence of secondary phases in the LSGFM after the synthesis.
A kinetic analysis of the burning system was made using three methods - wave-velocity measurements, temperature-profile analysis and the Freeman-Carroll analysis - all based on the kinetic law. The kinetic parameters obtained with the different methods are in good agreement, meaning that any of the three techniques described can be used for determining the kinetic parameters. The average n and E calculated values («0.5 and 31-35 kJ/mol, respectively) may be denoted as apparent values, and this implies that the diffusion process is the probably the rate-limiting factor.
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