Non-isothermal decomposition kinetics of hydrogarnet in sodium carbonate solution☆

Xiaofeng Zhu ,Ting'an Zhang ,*,Yanxiu Wang ,Guozhi Lu ,Weiguang Zhang ,Cong Wang ,Aichun Zhao

1Key Laboratory of Ecological Utilization of Multi-metal Intergrown Ores of Ministry of Education,School of Materials and Metallurgy,Northeastern University,Shenyang 110819,China

2School of Material Science and Engineering,Taiyuan University of Science and Technology,Taiyuan 030024,China

Keywords:Hydrogarnet Differential scanning calorimetry(DSC)Activation energy Mechanism function Carbonation Alumina

ABSTRACT Carbonation decomposition of hydrogarnet is a signi fcant reaction of the calci fcation-carbonation new method for alumina production by using low-grade bauxite.In this work,non-isothermal decomposition kinetics of hydrogarnet in sodium carbonate solution was studied by high-pressure differential scanning calorimetry(HPDSC)at different heating rates of 2,5,8,10,15 and 20 K·min- 1,respectively.The activation energy(Ea) was calculated with the help of isoconversional method(model-free),and the reaction mechanism was determined by the differential equation method.The calculated activation energy of this reaction was 115.66 kJ·mol- 1.Furthermore,the mechanism for decomposition reaction is Avrami-Erofeev(n =1.5),and the decomposition process is diffusion-controlled.

1.Introduction

As the leader of alumina production in the world,China produced more than 40 million tons of alumina,which accounts for approximately 40%of the global output in 2012[1].However,the lack of bauxite resource,especially high-grade bauxite is in stark contrast to the huge amount of the alumina output in China.More than 65%of bauxite in China is low-grade ore with the mass ratio of Al2O3to SiO2(A/S)below 7,and only 18.5%of bauxite with the A/S higher than 9.It is estimated that the high-grade bauxite will be used up within 10 years in China[2].

Bayer process is the most common method for alumina production both in China and abroad.However,it is not suitable for processing the low-grade bauxite because of the high consumption of caustic alkali and the low recovery of alumina[3].Although the sintering process can be employed for the low-grade bauxite,it is being phased out gradually due to its complex process and high energy consumption.Furthermore,alumina industry in China results in severe environmental problems,due to the huge amount of the red mud with a high alkaline after alumina re fi nery[4].Therefore,an environment-friendly method to ef ficiently utilize the abundance of the low-grade bauxite resources is urgently needed to be developed in China.

In order to produce alumina with low-grade bauxite,a novel calci fication-carbonation method was proposed by our team[5,6].In the calci fication process,silica-containing phase in bauxite is transformed into hydrogarnet,which is a kind of hydroxy aluminosilicate with the general chemical formula of 3CaO·Al2O3·x SiO2·(6-2x)H2O(0＜x＜3).Thereafter,the generated hydrogarnet is decomposed as CaCO3,2CaO·SiO2·n H2O and Al(OH)3through the carbonation process.After that,the Al(OH)3is extracted by NaOH solution at temperature below 373 K.The fi nal red mud is composed of alkali-lean and alumina-lean CaCO3and 2CaO·SiO2·n H2O.This process provides an eco-friendly design for the effective use of low-grade bauxite.The main reactions involved in this process can be presented as:

In previous works,the effect of reaction conditions on calci fication process and transformation of equilibrium phase during the process has been investigated in detail[7-9].However,as a significant intermediate process,the kinetics of carbonation decomposition reaction(Eq.(2))of hydrogarnet is still unclear.

The differential scanning calorimetry(DSC)technique is widely used to determine the kinetics of reactions[10,11],curing[12],crystallization[13]and thermo-decomposition[14-16].As reported by BAO et al.[10,11],a high-pressure DSC was used to determine the kinetics of gibbsite,boehmite and diaspore dissolving in caustic solution.Mechanism functions and kinetic parameters were featured by model- fitting method.SULTANIA et al.[12]studied the cure kinetics of vinyl ester-styrene system by non-isothermal DSC at four different heating rates(2.5,5,7.5,10 K·min-1),and obtained the apparent activation energy(Ea)of curing process by isoconversional method.Their results indicated that there is a good agreement between experiment and model.

In this paper,the decomposition kinetics of hydrogarnet in sodium carbonate solution was studied by means of a high-pressure differential scanning calorimetry(HP-DSC).The isoconversional and differential equation methods were used to analyze the DSC curve data.Furthermore,the apparentactivation energy was calculated and the mostprobable mechanism of this reaction was proposed.

2.Materials and Methods

2.1.Preparation and characterization of materials

The hydrogarnet used in this experiment was synthesized by hydrothermal synthesis in a 2 L scale autoclave with a magnetic stirring.The materials for preparing hydrogarnet were analytical reagent CaO,NaOH,Al(OH)3,and Na2SiO3·9H2O(Sinopharm Chemical Reagent Co.,Ltd,China).1 L sodium aluminate solution with concentration of 240 g·L-1Na2O and 197 g·L-1Al2O3was prepared as the hydrothermal medium,which was subsequently mixed with 50 g CaO and 25 g Na2SiO3·9H2O(SiO25 g·L-1)and reacted in the autoclave at 513 K for 4 h.Then,the product was filtered and washed with distilled water to weak alkaline,and dried in an oven at353 Kfor8 h.The percentages ofoxides ofsample,as determined by X-ray fluorescence(XRF),are shown in Table 1.The mineralogy of sample was characterized by X-ray diffraction(XRD,D8 ADVANCE ofBrukercompany,40 kV,40 mA,CuKα,2θ10°-90°,increment 0.0095°)as shown in Fig.1.

Table 1 Chemical composition of the synthesized hydrogarnet

Fig.1.XRD patterns of sample prepared by hydrothermal synthesis.

Fig.1 proves that the hydrogarnet is synthesized successfully.The data in Table 1 show thatthe mass percentagesofoxidesofcalcium,aluminum and silicon are 40.09%,25.80%and 4.69%,respectively.The molar ratio of CaO:Al2O3:SiO2is 2.83:1:0.31,which corresponds to the stoichiometry of 2.83CaO·Al2O3·0.31SiO2·5.38H2O.

2.2.DSC measurements

The DSC measurements were performed with a high-pressure DSC(204HP,NETZSCH,Germany).Dry argon was used as the purge gas at a rate of 20 ml·min-1,and a baseline was obtained with DSC crucible first.The mixture of prepared hydrogarnet and saturated sodium carbonate solution was sealed in a gold crucible with a stainless steel cap at the heating rate of 2,5 and 10 K·min-1when the DSC was performed.The Proteus Software was used to collect and analyze the DSC data.

2.3.Calculation of kinetic parameters

According to non-isothermal kinetics theory,the general decomposition reaction rate can be expressed by[17]:where α is the reaction fraction,k(T)is the rate constant,f(α)is the differential mechanism function,T is the absolute temperature,Eais the apparent activation energy,A is the pre-exponential factor and R is the universal gas constant(R=8.314 J·mol-1·K-1).

When a sample is heated at a constant rate under non-isothermal conditions,β=d T/d t,and Eq.(3)is modi fied as follows:

Taking the logarithm of Eq.(4)and the Friedman-Reich-Levi equation can be described as follows[18]:

The Friedman-Reich-Levi method is considered as one of the most reliable isoconversional methods to calculate activation energy(Ea)of reactions without preselecting a reaction model[19].By this method,activation energy can be evaluated from the slope of linear fitting ln(βdα/d T)against T-1under a given value of reaction fraction(α).

In order to obtain a reliable value,the activation energy Eawas determined by the isoconversional method(Friedman-Reich-Levi),which avoids the choosing of mechanism function.Herein,the differential equation method of non-isothermal kinetics was applied to study the reaction mechanism of the decomposition reaction,and it can be presented as follows[20]:

where f(α)is a differential expression for mechanism functions listed in Table 2.

3.Results and Discussion

3.1.XRD analysis of decomposition products

In order to characterize the product after decomposition of hydrogarnet by sodium carbonate solution,6 g synthesizedhydrogarnet was added to a 200 ml saturated sodium carbonate solution and the reaction mixture was stirred at 350 rpm at 343,353 and 363 K in a water bath for 1.5 h.Then the reactants were filtered under vacuum,washed by distilled water,and dried at 353 K for 8 h.Fig.2 shows the XRD patterns of decomposition products at different temperatures.It indicates that the mineralogy of decomposition at different temperature is essentially the same,mainly composed of calcium carbonate,and hydrogarnet can also be found in XRD patterns due to incomplete decomposition.It is noted that the hydrated calcium silicate(2Ca O·SiO2·n H2O)is not found in the products,which may be formed as an amorphous phase with low crystallinity[21].

Table 2 Mechanism functions of differential equation

Fig.2.XRD patterns of decomposition products at different temperatures.

3.2.Calculation of activation energy(Ea)

The DSC curves of at six different heating rates(2,5,8,10,15 and 20 K·min-1)are shown in Fig.3.It can be seen from the curves that the thermal effects of reaction are more obvious under a higher heating rate.Simultaneously,the peaks of thermal effects broaden with an increased heating rate,which might be resulted from the reduced resolution[22].According to Fig.3,the reaction temperature range is significantly dependent on the heating rate,and the peak endothermic temperature(Tmax)shifts to a higher temperature region as the heating rate rises.

Fig.3.DSC curves at differentheating rates of 2,5,8,10,15 and 20 K·min-1,respectively.

By integrating the DSC curve[23],the fractional conversion as a function of temperature is obtained and shown in Fig.4.All the T-α curves atdifferentheating rates show a S-shape,and it shifts to a higher temperature region with an increased heating rate,which mightbe due to the K(T)and f(α)varying simultaneously under non-isothermal conditions[12].The isoconversional temperatures at six different heating rates were obtained from the crossover point of fractional conversion curves.

Fig.4.Fractional conversion as a function of temperature at different heating rates of 2,5,8,10,15 and 20 K·min-1,respectively.

By meaning of Friedman-Reich-Levi method,the diagrams of ln(βdα/d T) ～ T-1for the decomposition reaction were showed in Fig.5.The slopes,activation energy,residual standard deviation(S)and correlation coef ficients(R2)of each line with different degrees of conversion α were listed in Table 3.It can be seen that the activation energy changed in the range of 133.10 kJ·mol-1to 93.19 kJ·mol-1at different conversion α between 0.2 and 0.8.In solid-state reactions,the variation of activation energy with the degree of conversion α may be caused by the heterogeneous nature of sample under nonisothermalconditions[24].The average activation energy ofthe decomposition reaction was 115.66 kJ·mol-1,and itwillbe subsequently used as a criterion to determine the reaction mechanism.

Fig.5.ln(βdα/d T α,i) againstof Friedman-Reich-Levi method in the interval 0.2＜α＜0.8.

Table 3 The values of slopes,activation energy,residual standard and correlation coef ficient at different degrees of conversionα

3.3.Determination of the reaction mechanism function

For the thermal analysis kinetics,the extent of a chemical reaction can be measured by its thermal effects.This can be presented as a=Ht/ H0,where H0is the totalheateffectof a reaction,Htis the heateffects ata transienttime t,in the non-thermalprocess,Ti=T0+βt.Therefore,dα/d T is easy to be expressed as:

Ti,αand d Ht/ d t can be obtained from the DSC curve,thus the corresponding dα/d Tican be calculated as shown in Fig.6.Due to thatthere is a linear relationship between the left part of Eq.(6)and 1/T for each mechanism function listed in Table 2,Eq.(6)could be solved by the iterative method[10].

With an initial value(＞0)for Ea, the left side of Eq.(6)can be calculated for each dα/d Ti. Then,a new Eacan be obtained by linear least square method from the slope and A from the intercept of Eq.(6).Take the new Eaas the initialvalue and do iteration.The calculating process is shown as follows[20]:

Fig.6.dα/d Ti as a function of temperature at a heating rate of 2 K·min- 1.

Eq.(6)can be presented as:

where a=-Ea/ R,b=ln(A/β)and L is the number of data point.

Eq.(10)can be solved by the least squares method through the following equation:

29 dα/d Tipoints shown in Fig.6 were used to analyze the 29 mechanism functions listed in Table 2,and the results have been summarized in Table 4.It was found that six mechanism functions(No.18,19,20,25,26,27)yield invalid values through the iteration process.The reaction mechanism function was determined by matching the activation energy calculated via isoconversional method and correlation coef ficient of linear fit is more than 0.98.It can be found that only function No.10 with the value of Ea111.97 kJ·mol-1and correlation coef fi cient 0.9816 can satisfy both requirements,which indicated that it should be the most probable mechanism function for the decomposition reaction.Function No.10 is anucleation-growth mechanism derived by Avrami-Erofeev equation(n=1.5),f(α)=(3/2)(1- α)[-ln(1- α)](1/3),Pre-exponential constant is 1.5933×1017s-1.For this decomposition process,the calculated reaction order n is 1.5,which means the decomposition of hydrogarnet in sodium carbonate solution should be occurred in the presence of amorphous phase,and the process is controlled by diffusion[25].

Table 4 Kinetics parameters of hydrogarnet decomposed by sodium carbonate solution calculated by 29 differential mechanism functions

For this reaction,the amorphous phase can be attributed to the generation of hydrated calcium silicate(2CaO·SiO2·n H2O)as a product,which was not detected in the XRD patterns(Fig.2).On the other hand,the diffusion mechanism can be interpreted thaton the decomposition ofhydrogarnet,a solid layerofCaCO3was formed,and covered on the surface of hydrogarnet particles.For further reaction,the CO32-ions have to diffuse in through the solid layer of CaCO3,therefore,the hydrogarnet cannot be decomposed completely,and can be detected in the XRD patterns(Fig.2).

Based on the values of activation energy and reaction mechanism,the kinetic equation of this reaction can be described as:

which is a diffusion-controlled mechanism.

4.Conclusions

(1)The hydrogarnet was synthesized in the CaO-SiO2-Na Al(OH)4-H2O system by hydrothermal method in laboratory conditions,and the synthesized products were characterized by chemical analysis and X-ray diffraction.The results indicated that synthesized hydrogarnet had the stoichiometry of 2.83CaO·Al2O3·0.31SiO2·5.38H2O.After decomposition by sodium carbonate solution at different temperatures,the products were mainly composed of calcium carbonate and unreacted hydrogarnet.The hydrated calcium silicate was not detected by XRD maybe due to the formation of the amorphous phase.

(2)The high-pressure DSC technic was used to investigate the kinetics of hydrogarnet decomposed by sodium carbonate solution.Measurements at six different heating rates provided a determination of Eaby the Friedman-Reich-Levi isoconversional method,and the average activation energy of the decomposition reaction was 115.66 kJ·mol-1.The reaction mechanism function was selected from 29 types of differential equations,which can be presented as f(α)=(3/2)(1- α)[-ln(1- α)](1/3)derived by Avrami-Erofeev equation.The reaction mechanism indicated that the decomposition of hydrogarnet in sodium carbonate solution should occur in the presence of amorphous phase,and the reaction is diffusion-controlled mechanism.