Grain growth kinetics of Li3PO4-doped calcium carbonate

__ .__ i ii!!3

s

SOLID STATE

ELSEVIER

Solid State Ionics 101-103

IONICS

(1997) 517-525

Grain growth kinetics of L&PO,-doped F. TCtard”, D. Bernache-Assollant,

calcium carbonate

E. Champion,

P. Lortholary

Laboratoire de MatPriaux CPramiques et Traitements de Surface, URA CNRS 320. 123 Av. A. Thomas, 87060 Limoges Cedex. France

Abstract Grain growth mechanisms of calcium carbonate doped with lithium phosphate were determined. With small lithium phosphate addition, an abnormal needle-like grain growth was observed. Addition of the dopant as solid solution in calcite follows the equation: Li,PO, - c”coJ + 3(Li,+)+ + V~;I+ + (PO:-)& #. In slightly higher quantities (2 wt.%) above the solubility limit of Li,PO,, a second phase segregated at the grain boundaries. Whatever the thermal treatment (temperature, CO, partial pressure), the grain distribution was self-similar (G(t)/&))= time independent) and followed a single log normal law. The grain growth kinetics can be described by the equation: dcldt=k(c _’ -CT ‘). The grain growth was controlled by the mobility of the second phase. Kewwrds:

Grain growth; Calcium

Materials: Li,PO,;

carbonate;

Self-similar

distribution

CaCo, -

1. Introduction Calcite (CaCO,) transforms into CaO at 600°C in air (PC0 = 300 Pa) and at 890°C under 100 kPa of CO,. Its*densification requires therefore, the use of a stabilising pressure and sintering aids. Fujikawa [l] as well as Olgaard [2] succeeded in densifying up to 96% using hot isostatic pressing. Yamasaki [3] used a hydrothermal hot pressing technique. Yamamoto [4] and Komatsu have defined optimum hot pressing conditions between 600 and 700°C. All these studies underline the difficulty to sinter calcite due to its easy decomposition. Urabe [5] was interested in the pressureless sintering of CaCO, in the presence of LiF. He remarked that swelling appeared during sintering. *Corresponding [email protected].

author.

Fax:

+ 33

5-5545-7586;

e-mail:

0167.2738/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SO1 67-2738(97)00154-9

A theoretical study of calcium carbonate grain growth in the presence of lithium phosphate additive will be presented here, in order to understand its densification process. Reactivity of the system CaCO,-Li,PO, is followed by thermogravimetric and dilatometric measurements as well as differential thermal analysis. Particular sintering conditions were obtained (temperature, CO, atmosphere, additive concentration). Studies of grain growth kinetics allowed the precise definement of the mechanisms responsible for the growth.

2. Experimental 2. I. Starting

procedure

products

Calcium carbonate and lithium supplied by Aldrich Company.

phosphate

were

518

F. T&z-d et al. I Solid State tonics 101-103

Composition given by the supplier is: 40.04 wt.% of calcium corresponding to 99.995% pure calcite. We measured the agglomerate size between 0.6 to 30 pm (Micromeritics particle sizer). Average particle size was 2 pm. Specific surface area measured by the BET method (3 points) was 1 m*/g. Lithium phosphate was 99.99% pure. Average size estimated by SEM was 0.4 pm.

(1997) 517-525

After sintering, the samples were polished to obtain a mirror like surface (Diamond spray 1 pm). Grain boundaries were revealed by thermal etching at 600°C during 2 min under 100 kPa of CO, pressure. Grain size analysis was done using photos from scanning electronic microcopy (Philips XL30). Image analysis was performed using Optilab 2.6 software of Graftek. 2.3. Grain size measurement

2.2. Apparatus

and experimental

conditions

The two powders (CaCO,, Li,PO,) were mixed in pure ethanol. The mixture was performed in an alumina jar during 15 min. The powder was then dried in an oven at 100°C. Discs of 10 mm diameter were uniaxially pressed under a pressure of 125 MPa. Densities were obtained by the Archimedes method (precision: 20.5% of relative density). Theoretical density of the mixture was calculated using the mixture law, theoretical density of CaCO, and Li,PO, being 2.710 g/cm’ and 2.456 g/cm3, respectively. Densities of cold pressed samples were 60% of the theoretical. Thermogravimetric and differential thermal analysis were performed, respectively, using a Setaram B85 microbalance (precision+ 10 pg) and Netzch STA409 equipment. Dilatometric measurements were performed using a SETARAM TMA92 dilatometer. The heating rate was kept at lO”C/min. To obtain a network of points, grain growth as a function of time, the samples were sintered in the microbalance furnace. The furnace is brought to the desired temperature one hour before the sample introduction inside the microbalance. Sample introduction and removal from the hot zone takes about 1.5 min. For pressures lower than atmospheric pressure, the pressure was regulated with CO, dynamic partial vacuum. The atmosphere furnace was only fitted with CO,, whatever the furnace pressure. Table 1 Mean grain size for different

The equivalent disc diameter is chosen as a parameter for size evaluation. Sampling representation is a key parameter which controls the measurement reproducibility and conditions its precision. We looked for the minimum number of measurements required for an acceptable precision. Results in Table 1 show that for more than 150 grains, the average grain size measurement is good. In a general way, measurement done over 200 grains gives an error of t3%. Each value is taken from two or three different images of the same sample.

3. Results and discussions 3.1. Choice

qf sintering parameters

In the beginning, we studied the behaviour of mixture (CaCO,-Li,PO,) at different temperatures. 3.1.1. Li,PO,-CaCO,

reaction under 100 kPa

co2 A study was undertaken for 100 kPa CO, pressure, which corresponds to CaCO, decomposition, theoretically at 890°C. Thermogravimetric analysis (Fig. 1) of pure CaCO, shows that the decomposition reaction occurs at 890°C. For mixtures containing 2 or 8 wt.% of Li,PO,, a slight decomposition of CaCO, in the presence of Li,PO, is observed.

sampling

Number of grains

819

565

250

150

100

50

D (pm)

3.60

3.55

3.49

3.48

Relative deviation of D

reference

1.4%

2.9%

3.3%

3.42 4.8%

3.45 4.0%

F. TPtard et al. I Solid State Ionics 101-103

Relative weight loss (%)

519

(1997) 517-525

2% L&PO4100kPa CO2 _-D,~rsnt,* -Shrinkage

0.0

-1.6

-2.6 Sal

i

’

2ha

460

do

do

Temperature (OC) Fig. 1. Relative weight loss of CaCO, additive, under 100 kPa CO,.

600

700

So0

sm

Temperature (‘C)

Fig. 2. Sample shrinkage

as a function

of temperature.

with and without Li,PO,

Differential thermal analysis of mixtures CaCO,Li,PO, at 100 kPa CO, pressure reveals an endothermic peak at 740°C. This peak is not observed for pure CaCO,. This could be due to a liquid phase formation at this temperature. 3.1.2. Sintering conditions Dilatometric studies show that sintering densification of CaCO, with L&PO, (2 or 8 wt.%) takes place between 600 and 765°C (Fig. 2). Above 765°C swelling takes place. In this temperature range, a minimum at 745°C is observed over the densification kinetics. This minimum which corresponds to the DTA peak, determines the transition between solid and liquid phase sintering. A slight decomposition (less than 0.1 wt.%) coupled with the presence of liquid phase, is responsible for the production of pores of 100 pm size. Liquid phase does not allow the decomposition gas to be removed from the structure, which brings about an increase in volume (swelling). To obtain higher than 95% densification with less than 10 h dwell time, the sintering temperature range was reduced to 700-730°C. Variation of Li,PO, percentage and CO, pressure was then studied. Li,PO, percentage was varied between 0.5 and 8 wt.%. CO, pressure was varied between the stabilisation limit to 100 kPa.

3.1.3. In$uence of Li,PO, percentage over the microstructure Sintering was done at 700°C with different Li,PO, percentages, during 15 h under minimum CO, pressure (4 kPa). Sample densities after sintering are given in the Table 2. It can be noted that lithium phosphate improves the densification and final relative density in an important manner. Only 0.5 wt.% addition of L&PO, is sufficient to obtain 94% densification whereas without dopant, the relative density remains at only 60%. An addition of 8 wt.% allows it to reach densification as high as 98.7%. Doping agent percentage influences to a great extent the microstructure of sintered samples. In fact, the dopant also activates the crystalline growth (Fig. 3). Without a doping agent, the grain size remains constant at 1.76 p,m, whereas a small addition of dopant (0.5 wt.%) is sufficient to multiply this value by a factor of 23. Anyhow, still higher quantities of dopant limits the grain growth and the limiting size is around 9 pm for sintering temperature of 700°C during 15 h. Lithium phosphate plays therefore a multiple role. In small quantities it activates, in the form of solid solution, the grain growth as well as densification kinetics. In relatively higher quantities (>2 wt.%), in the form of precipitates, it reduces the grain growth. The effect of second-phase particles on grain growth of calcite marbles was investigated by Ol-

F. Te’tard et al. I Solid State Ionics 101-103 (1997) 517-525

520 Table 2 Influence

of Li,PO,

wt.% on sintering

wt.% Li,PO, Density (g/cm’) Relative density (%) Grain size (pm)

of CaCO,

0% 1.626 60.0 1.76?0.03

(7OO”C, 15 h, P(CO,)=4

kPa)

0.5%

1%

2%

8%

2.540 93.7 40.6?0.8

2.570 94.9 20.9+0.4

2.622 96.0 10.2+0.2

2.652 98.7 9.0-t-0.2

gaard [6], Mas [7] and Joesten [8]. They showed that a small amount of particles could inhibit grain growth and produce a stable maximum grain size.

3.2. Grain growth kinetics 3.2.1. Abnormal growth (low Li,PO, concentration) For a dopant concentration of 0.5 wt.%, the microstructure shows an abnormal growth of some CaCO, grains. These grains of about 200 km diameter are surrounded by 40 km grains. Some grains are twinned. Fig. 4 shows the needle-like grain growth of calcite sintered at 700°C in the presence of 0.5 wt.% Li,PO,, during 15 h. For a dopant concentration of 0.5 wt.%, the cumulative grain size distribution (normalised by the mean grain size D,,,, ) is not similar to those samples containing 0, 2 and 8% Li,PO, (Fig. 5). The overall size distribution is strongly dispersed for large grain size, characteristic of duplex microstructure. The proportion of large sized grains is almost 10% (size 2.5 times larger than the average size) with 0.5% dopant addition and less than 1% with 2 or 8% Li,PO,. Addition of lithium [9] and phosphate [ 10,l l] ions was shown in natural calcite single crystals. Lithium ion is placed at the interstitial sites between alternative carbonate and calcium layers, perpendicular to the C-axis. The presence of lithium induces a selective stabilisation [ 121 of (001) calcite planes. This was demonstrated by X-ray diffraction on the polished surface of dense samples (Fig. 6). The diffraction pattern shows that (0 0 6) and (0 0 12) plane intensity is multiplied by 10. This proves that the grain growth takes place along the C-axis. The following mechanism of dopant incorporation can be proposed:

taco,

L&PO,

+

3(Li:)+

+ V:~Z+ + (PO:-)c,:-.

(1)

It can be deduced from this reaction that the formation of a solid solution with Li,PO, increases the concentration of Ca vacancies in the structure. The dopant therefore favours the sintering through an increase of Ca vacancies, Ca diffusion therefore is the limiting factor during the sintering of CaCO,. The same results were presented by Farver [ 131 who showed through a study of calcium diffusion in calcite that Ca diffusion was the limiting factor during sintering (slowest diffusion rate). 3.2.2. Normal growth (high Li,PO, concentration) A systematic study of CaCO, grain growth in the presence of 2 wt.% of Li,PO, was done while varying the temperature and CO, partial pressure. In the case of normal growth, the kinetic laws goveming the grain growth are of the form: G”‘-G;=kt

(2)

where G is the average grain size at time t, G, is the initial grain size, k is a constant and m is a whole number whose value depends upon the diffusion mechanism which is responsible for sintering. In this hypothesis, the granulometric distribution must be similar, for any period of time. Thus the normalized distribution should be invariant as a function of time [ 141. Some authors [ 15,161 were able to show experimentally the self-similarity of grain size distribution as a function of time. This self-similarity is a result of invariance as a function of time, of each grain class (with a ratio x=DID, as constant). Thus for x= 1 the grain percentage is constant, equal to 5.6%, whatever the time may be. Fig. 7a shows the grain distribution obtained at

F. TPtard et al. I Solid State Ionics 101-103

(4

(1997) 517-525

Fig. 4. Microstructure Li,PO 4’

521

of a sintered

sample at 700°C with 0.5%

Cumulative frequency in number 1.0

0

1

2

Fig. 5. Influence of Li,PO, granulometric distribution.

Fig. 3. Microstructure of a sample sintered at 700°C P(C01)=4 kPa) with different additive concentration.

(15 h,

II/i_

4

percentage

on

5

the

6

normalized

700°C under 4 kPa CO, pressure, for sintering time between 5 min and 15 h. Fig. 7b shows the conservation of grain size distribution or self-similarity. The CaCO, grain growth is therefore normal under these experimental conditions. All grain distributions follow the same curve, independent of time (5 min to 15 h) and temperature (700, 710, 720°C). Once an important number of results belonging to the same population are obtained, the distribution law can be studied using the estimation of centered moments of the order from 1 to 4. In order to

F. Tbtard et al. I Solid State Ionics 101-103

522

(006)

40

30

50

60

280

70

Fig. 6. XRD of a sample sintered at 7OO”C, with 0.5% Li,PO,, during 15 h. (0: standard peak intensity from calcite XRD JCPDS no. 5-586).

demonstrate that the distribution follows a log-normal law, a variable change z = In(G) was affected to facilitate the data treatment. We pose Z,,, =ln(G). So for a given distribution the calculation of pr, is:

i

n;(ln(G,)

- In(G))” n

2 =

ni(1n(2))p

GT

&) = ~

exp[ -;

(ln(~~~)].

(4)

(3)

n

where ni is the number of grains having size G,, IZ is the total number of grains and q is the number of classes (q = 50). The 4 moments are identical for the 51 distributions (700, 710, 720°C at different time and for

J.

different pressure). The average values of the centered moments are summarised in Table 3. From the values of the four moments it is possible to establish the distribution law using Pearson coefficients. Two coefficients (p, and p,> characterise the form of the size distribution. The skewness (p, = ( p(L: lpi)) measures the asymmetry of the distribution relative to its mean and the degree of peakedness is given by the kurtosis (/3, =( ,u~//_L~)). The results obtained are approached from theoretical value p, = 0.00 and p, =3.00. Symmetry and normality tests allowed the validation of the normal distribution. The Pearson coefficients were earlier employed by Sequiera [ 171 to characterise the distribution of precipitates. The experimental distribution in logarithmic coordinates is attributed to a gaussian. The law for abscissa x=(GIG) is therefore a log-normal law:

Some authors [ 18,191 have shown that log-normal law can be used in the case of sintered materials. The distribution function in Fig. 7 is established using calculated moments ,u, and ,+ of Table 3. The invariance as a function of time of the function g

,=I

Pp =

(1997) 517-525

. ...,!

Table 3 Values of the centered

moments

of granulometric

distributions

Centered moments &cL.=(-=Z,)” Average Standard deviation

-0.11 0.03

0.19 0.04

0.00 0.03

I

10

?

DO

a)

b)

Fig. 7. Conservation

of grain size distribution

at 700°C 4 !cPa CO, pressure (experimental

points and theoretical

curve)

0.11 0.05

F. TAard et al. I Solid State lonics IO1-103

where C is a constant and D is a diffusion coefficient. The value of m was varied between 1 to 4. The grain growth rates dGldt were plotted as a function of 1 /G”-‘. The regression straight lines are best adjusted to a value of m = 2 (Table 4). The correlation coefficients are more superior than 0.99. The kinetics established with m = 2 (Fig. 9) give a critical grain size which limits the grain growth. This critical diameter has an average value of 12 Km.

allows the separation of the variables grain size and time. The distribution function f(G,t) can therefore be represented as the product of the two functions: f(G,t) = g ; X h(t) ( >

523

(1997) 517-525

(5)

where the function g((G/G)) characterises the initial distribution of grains and the function h(t) gives the evolution of grain growth independently of the grain size. This implicates that the knowledge of grain growth kinetics from the mean grain size (G=G) allows also the description of the kinetics as a whole. In fact for a given ratio (here x = 1) the function h(t) will be studied. The similarity of the distribution as a function of time (function g) induces also the knowledge of the function J for all diameters.

Table 4 Evolution alG”-‘+b

of correlation

Temuerature

(“C)

m=l m=2 In=3 in=4

3.2.3. Growth mechanisms Samples were sintered at temperatures between 700 and 720°C for dwell times varying between 5 min and 5 h, for different CO, pressures. The curves showing the growth kinetics were established from the granulometric distribution (at least 500 grains), as a function of time, temperature and CO, pressure. The CO, pressure apparently does not affect the grain growth in an important manner (Fig. 8). To establish the growth laws, the growth rate evolution as a function of grain size was determined. The growth laws can be described under a derived form:

coefficients

for the equation

dGldr=

700

710

720

0.8955 0.9974 0.9914 0.9850

0.9505 0.9910 0.9897 0.9777

0.9504 0.9930 0.9753 0.9352

5 0 4

dG -=dt

l/G

CD (6)

Grn-’ G(lrm)

Fig. 9. Grain growth kinetics (m=2)

C(IM)

0.s

~JUU-‘) as a function

G(rp)

i.s

0.S

1.s

2.0

Time (Is)

Fig. 8. CaCO,

grain growth with 2% Li,PO,

at different

The00 temperatures

(700, 710, 720°C).

of grain size.

524

F. Tktard

et al. I Solid State Ionics

This value is related to the L&PO, percentage (Table 1). A sintering of 15 h at 700°C allows the confirmation that the critical grain size is 10 pm with 2% Li,PO,. In fact the grain boundary blocking by the precipitates could be explained by the Zener [20] approach. The critical size depends upon the volume fraction (f) of the particle and its size (r) according to the formula: G, = r/J: With 2 wt.% Li,PO,, the dopant is in excess and it is found in the form of precipitates at the grain boundaries (Fig. 10). The average radius of Li,PO, grains is 0.2 pm. With a precipitate volume fraction of about 2%, a critical size of CaCO, grains of nearly 10 pm is experimentally observed. The growth kinetics between 700 and 720°C follows a law of the type:

Integration of the kinetic lowing expression: G,-G In

7=zt

equation

101-103

(1997)

517-525

this law is well adapted to the grain growth curve (Fig. 8). The Eq. (7) represents the interaction between the grain boundary movement and mobile impurities. Studies [21,22] have shown that the impurities diffuse at the grain boundaries in a correlated manner. Burke [23] has already described the grain growth of the form in Eq. (8). The dopant while segregating to the grain boundary, reduces its mobility (blocking effect):

uJ

+Mj(Fj

-F,)

where IV, is the mobility of grain boundary, F, and force of the grain boundary and the particles, respectively. Hillert [24] gives the following equation:

F, are the driving

gives the fol-

k

(8)

with G=G, at t=O. The integrated law [Eq. (S)] is verified by using constants k, G,, obtained experimentally for each temperature. For G,, a value of 1.8 km was chosen (initial CaCO 3 grain size). It can be observed that

where (Y is a geometrical constant without dimension, z depends upon the number of particles per unit volume and the second phase particle size. Anderson [25] has retaken this model and generalised it. From the slopes of the derived straight lines at different temperatures shown on Fig. 9, the activation energy of the grain growth rate can be estimated, which is almost 380270 kJ/mol.

4. Conclusion

Fig. 10. Grain boundary phase.

blocking

by the presence of a secondary

Lithium phosphate has a multiple role in the sintering of CaCO,, influencing the densification and the grain growth. Lithium phosphate in the form of solid solution (under 1 wt.%) activates both the densification and the grain growth of calcium carbonate. The dopant in the form of solid solution, increases calcium vacancies concentration and activates the grain growth and densification during sintering. The normal growth of calcite grains in the presence of a small excess of Li,PO, (> 1 wt.%) was defined by the self-similarity of granulometric distribution. The granulometric distribution follows a log-normal law. The laws governing the grain growth give rise to a critical grain size of calcite

F. T&lard et al. I Solid State Ionics

grains. Segregation of the doping agent at the grain boundaries reduces the grain growth. The CO, partial pressure does not affect the grain growth. Near theoretical densities of sintered samples, were obtained with pressureless sintering.

101-103

(1997)

[lOI R.A. Serway, 4098.

517-525

525

S.A. Marshall,

1111 M. Ishikawa, A. Sawaoka, 8 (1982) 247.

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M. Ichikuni,

Phys. Chem. Miner.

[I21 S. Rajam, S. Mann, J. Chem. Sot. Chem. Commun. 1789.

(1990)

[I31 J.R. Farver, R.A. Yund, Contrib. Mineral Petrol. 123 (1996) 77.

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[I41 W.W. Mullins, J. Vinals, Acta Metall. 37(4) (1989) 991. [I51 B.D. Gaulin, S. Spooner, Y. Morii, Phys. Rev. Lett. 59 (1987) 668. [IhI D.J. Srolovitz, M.P. Anderson, Metall. 32(9) (1984) 1429.

G.S. Grest, P.S. Sahni, Acta

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J.S. Pedersen,

[I81 F.M.A. Carpay, S.K. Kurtz, Mater. Sci. Res. 11 (1978) 217. L191 J. Ricote, L. Pardo, Acta Metall. 44(3) (1996) 1155. to C.S. Smith, 1201 C. Zener, Private communication Amer. Inst. Min. (Metall.) Eng. 175 (1949) 15.

Trans.

u-11 R.J. Brook, Scripta Metall. 2 (1968) 375. WI G.N. Hassold, D.J. Srolovitz, Scripta Metall. 32( 10) (1995) 1541. E31 J.E. Burke, (1949) 73.

Trans.

Amer.

Inst. Min.

(Metall.)

1241 M. Hillert, Acta Metall. 13 (1965) 227. D51 I. Anderson, 0. Grong, Acta Metall. Mater. 2673.

Eng.

43(7)

180

(1995)