A Quantitative Analysis of the Laser Sintering of Bismuth Titanate Ceramics

7/28/2019 A Quantitative Analysis of the Laser Sintering of Bismuth Titanate Ceramics

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A quantitative analysis of the laser sintering of bismuth titanate ceramics

Z.S. Macedo a,*, A.C. Hernandes b

a Universidade Federal de Sergipe, Departamento de F sica, C. P. 353, 49100-000 Sao Cristovao, SE, Brazilb Universidade de Sao Paulo, Instit uto de F sica de Sao Carlos, G rupo Crescimento de Cristais e Materiais Ceramicos, Cx Postal 369,

13560-970 Sao Carlos, SP, Brazil

Received 15 February 2005; accepted 9 June 2005

Available online 1 August 2005

Abstract

The aim of this study was to identify the main differences on the kinetic aspects of conventional and laser sintering of bismuth titanate

Bi4Ti3O12. The linear shrinkage, relative density and average grain size of the ceramics were measured for initial, intermediate and final

stages of laser and conventional sintering. It was observed that laser sintering was 10 times faster than the conventional sintering processes.

Also laser sintered ceramics reach 99% density at significantly lower temperatures than that registered for the conventional process.

Theoretical models were fitted to the experimental data in order to determine the kinetic sintering parameters. Remarkable differences were

observed between the activation energy (initial and final stages) and mass transport mechanism (final stage) determined for the laser and

conventional sintering.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Ceramics; Laser sintering; Microstructure

1. Introduction

Sintering is a very important step in ceramic processing,

and can be a determinant to the microstructure and proper-

ties of the produced material. Generally, three stages of

sintering can be distinguished: initial, intermediate and final,

and the kinetics of these stages are studied separately. A

phenomenological equation to describe the densification

during the initial stage as a function of the linear shrinkage

was developed by Coble [1], assuming that the system

temperature remains unchanged and that there is a single or

at least a predominant mass diffusion mechanism during the

initial stage:

YndY

dt Kexp

Q

RT

1

where Y is the linear shrinkage, K is a constant, Q is the

activation energy, T is the absolute temperature, R is the gas

constant and n is the sintering coefficient, which can assume

the value 0, 1 or 2 to represent mass transport mechanism

via viscous flow, volumetric diffusion or diffusion through

grain boundaries, respectively [2].

Cobles model was restricted to isothermal systems, and

was adapted by Woolfrey and Bannister [2] to non-

isothermal sintering yielding the expression:

dY

Y

Q

n 1 R

dT

T22

where Q is calculated by the Dorn method [3]:

Q RT1T2

T1 T2ln Y

1

Y2

3

Eq. (3), combined to the slope of the plots T2dY/ dT vs.

Y, provides the activation energy Q and the sintering

coefficient n for the initial stage.

The theoretical models for the intermediate and final

stages of sintering frequently assume that both grain growth

and densification are associated to the same mechanism of

mass transport, and that there is a single predominant

mechanism occurring in each stage of sintering. In the

0167-577X/$ - see front matterD 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.matlet.2005.06.013

* Corresponding author. Tel.: +55 79 2126809; fax: +55 79 2126807.

E-mail address: [email protected] (Z.S. Macedo).

Materials Letters 59 (2005) 3456 3461

www.elsevier.com/locate/matlet


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isothermal case, the dependency of grain size upon the

temperature obeys the phenomenological equation:

Gn Gn0 K0te Q

RT 4

where K0 is a constant, t is the time interval under a constant

temperature and the sintering coefficient can assume thevalue n = 1, 2 or 3 for mass transport via viscous flow,

volumetric diffusion or grain boundary diffusion, respec-

tively [4].

For the intermediate stage, usually non-isothermal, Eq.

(4) can be modified to provide a kinetic description of grain

growth under constant heating rate (a = dT/ dt), yielding the

expression [4].

GnT GnT0

K0R

aQ

Q

RT

2e

Q

RT 2Q

RT

"

Q

RT0

2

e Q

RT0 2Q

RT0# 5

The above sintering models were employed in this work

to determine the apparent activation energy and the

predominant mechanism of mass diffusion during laser

sintering of bismuth titanate (Bi4Ti3O12BIT). In the last

years, laser technology has been employed in a greatvariety

of processes, as drilling, cutting and soldering [5], direc-

tional solidification applied to the growth of single-crystal

fibers [6,7], surface crystallization and texturing of glasses

[8], sintering of coatings and ceramic bulks [9,10]. As laser

processing is able to produce peculiar microstructure and in

some cases to improve physical properties [10,11], the

understanding of its kinetic is a goal for many researchers.

The aim of the present study is to use simple models to

identify the main differences on the kinetic aspects of

conventional and laser sintering of Bi4Ti3O12.

2. Experimental

Single-phase Bi4Ti3O12 powder with average particle

size of 1 Am was obtained via solid-state reaction. The

details of the production and verification of the crystalline

structure are detailed elsewhere [11,12]. The calcined

powders were mixed with a binder solution of poly(vinylalcohol) (PVA, with a concentration of 0.1 g/mL), and

conformed by uniaxial pressing into the form of pellets 6

mm in diameter and 2 mm thick. Green ceramics presented

relative density of 55T5%.

The sintering process used a continuous CO2 laser

(Model 57-1, Synrad) as the main heat source. The beam,

with a spot diameter of 4.0T0.5 mm, was fixed on the

ceramic surface. Before irradiation, the samples were pre-

heated with an electric heater up to 350 -C with a heating

rate of 50 -C/min. The heater temperature was kept

constant, and then the ceramic was irradiated by the CO2laser. The laser power was raised at a linear rate of 2.7 W/

min, up to 5 W, kept for 5 min and then raised again at the

same rate up to a power that will be called Pmax. After

irradiating the first face, the whole process was repeated for

the other side. During the power ramp of 2.7 W/min, the

measured heating rate was 45 -C/min. The choice of this

rate was based on several tests to determine the maximum

heating rate for damage-free sintering, since it was observedthat heating rates above 45 -C/min resulted in crack

development during the laser sintering.

The temperatures were monitored throughout the laser

sintering with Type S thermocouples (0.25 mm diameter)

positioned on the ceramic surface. The center as well as the

edge of the irradiated surface was monitored, in order to

determine the average temperature that was used in this

study. To evaluate the experimental error in temperature, we

monitored the temperature of melting under laser irradiation

for the materials Bi4Ti3O12 (Tm=1200 -C) and Bi4Ge3O12(Tm=1050 -C), previously verified through differential

thermal analysis. An error ofT

20-

C was observed in thetemperature measured with the thermocouple, which is

comparable to the errors normally observed in conventional

furnace.

The density, linear shrinkage and average grain size were

determined as a function of Pmax and the sintering period.

The density was measured by geometrical and Archimedes

method [10] and the grain sizes were measured from

Scanning Electron Microscopy (SEMZeiss DSM960)

images, using the intercept linear method, ASMT procedure

E112-95.

Reference samples were submitted to conventional

sintering in electric furnace and also to dilatometric

measurements (dilatometer NETZSCH402 PC) per-

formed under synthetic air flow at heating rates of 5 -C/

min and 10 -C/min, in a temperature interval from 25 -C to

300 400 500 600 700 800 900 1000 1100

-20

-15

-10

-5

0

30 watts

15 watts

0 watts

Laser sintering:Heating rate 45 C/min

Furnace sintering:Heating rate 5 C/min

Heating rate 10

C/min

Y(L/L0

)(%)

Temperature (C)

Fig. 1. Linear shrinkage as a function of the sample temperature for laser

sintering (heating rate of 45 -C/min) and reference samples (heating rates of

5 -C/min and 10 -C/min). Some values of Pmax are indicated on the curve

corresponding to the laser sintering. Laser sintering data correspond to the

relative shrinkage of diameter and thickness measured for at least 5 sintered

ceramics, and the error bars correspond to the average standard deviation.

The reference measurements were performed in dilatometer with an error

lower than 1%.

Z.S. Macedo, A.C. Hernandes / Materials Letters 59 (2005) 3456 3461 3457


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1100 -C. The relative density was calculated from the linear

shrinkage ( Y=DL /L0) and theoretical density (q0), throughthe expression q=q0 / (1 Y)

3. The grain size of these

samples was also monitored, in order to perform kinetic

analysis.

3. Results and discussion

3.1. Linear shrinkage

One remarkable feature of laser sintering observed in this work

was the beginning of linear shrinkage at temperatures much smaller

than that observed in conventional sintering. Fig. 1 presents the

linear shrinkage as a function of the temperature for all the samplesstudied. It can be observed that the linear shrinkage of the laser

heated samples (heating rate of 45 -C/min) starts at temperatures

lower than 600 -C, while the furnace sintered ceramics (heating

rates of 5 and 10 -C/min) begins to shrink at 850 -C. Similar

behavior has been reported for microwave sintering, which also

employs high heating rates [13,14]. This behavior was also

confirmed in the present work when the samples were measured

in dilatometer under two different heating rates of 5 -C/min and 10

-C/min. It was observed that the linear shrinkage occurred at a

slightly lower temperature when the higher heating rate wasemployed.

3.2. Grain size and density

Fig. 2 presents the temperature and density as a function of the

laser power and irradiation time. The relative density of BIT

ceramic bodies reached 88% during the heating step and 99% after

5 min under constant power of 30 W. Fig. 3 illustrates the

microstructure evolution during laser sintering. From the micro-

graphs, some differences in grain size and porosity between the

center and the edge of the pellets during the intermediate stage of

the sintering can be observed. This non-homogeneity in micro-

structure was due mainly to the Gaussian profile of the laser beam,

which induces higher temperatures in the center than in theperipheral region of the irradiated surface. However, the edge of

the surface was heated either by the laser irradiation and heat

conducted from the central part, and a good homogeneity was

reached at the final stage of sintering (see Fig. 3).

Fig. 4 presents the density evolution of the reference samples,

sintered in electric furnace. One can observe that the density is

enhanced from 50% to 90% as the temperature is raised from 870

-C to 1050 -C, and that after 2 h at 1050 -C the ceramic reached

0 5 10 15 20 25

50

60

70

80

90

1002010 3030550

Power (W)

relativedensity(%)

Time (min)

300

400

500

600

700

800

900

Temperature

Fig. 2. Relative density and temperature of laser sintered Bi4Ti3O12ceramics, as a function of time and laser power.

0 60 120 180 240

50

60

70

80

90

100

rel

(%)

time (min)

0

200

400

600

800

1000

120 180 24096

98

100

Temperature(C)

Fig. 4. Relative density and temperature of the ceramics sintered in electric

furnace, as a function of time, obtained from dilatometric analysis, in

synthetic air atmosphere. The heating rate was 10 -C/min.

Fig. 3. SEM images of the center and edge of Bi4Ti3O12 ceramics in the initial, intermediate and final stages of laser sintering.

Z.S. Macedo, A.C. Hernandes / Materials Letters 59 (2005) 3456 34613458


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relative density of 99%. The microstructure ofthe ceramics during

the sintering in electric furnace, presented in Fig. 5, is similar to

that observed during laser sintering, but with larger grains at the

final stage.

Fig. 6 presents the average grain size and density as functions

of the processing time and mean temperature, for both proceduresstudied. At the beginning of the holding period, which corresponds

to the isothermal final stage, the ceramic densities for both

processes are the same (near 90%), but the laser sintered have

larger grains (4 Am) than the conventionally sintered (2.5 Am).

In the final sintering stage, both samples reached the same density

(99%) but the laser processing resulted in grains 50% smaller.

Large error bars are due to the exaggerated growth of some grains

in both processes.

3.3. Sintering kinetics

The Woolfrey Bannister model was applied to the non-

isothermal first stage. According to Eq. (2), the diagram of

T2dY/ dT vs. Y is a straight line if the grain size remains unaltered

and the superficial diffusion is negligible. The slope of this graph is

Fig. 5. SEM images of Bi4Ti3O12 ceramics heated in electrical furnace.

0 10 20 30 400

2

4

6

8

10

grain size(a)

Average temperature (C)

Average temperature (C)

860860860640350

Time (min)

averagegrainsize(m)

50

60

70

80

90

100

densityrelativeden

sity(%)

0 60 120 180 2400

2

4

6

8

10

Time (min)

averagegrains

ize(m)

grain size

50

60

70

80

90

100

relativedensity(%)

density

(b)

1050105077020

Fig. 6. Average grain size and density of the BIT ceramics, as a function of

sintering time and temperature: (a) laser sintering; (b) furnace sintering. For

the laser sintering ceramics, the temperature is an average of the values

taken at different points of the irradiated surface.

0 5 10 150.0

0.5

1.0

(a)

T2dY/dT

(.103)

T2dY/dT(.103)

|Y| (%)

0 5 10 15 20

0

1

2

3

4

(b)

|Y| (%)

Fig. 7. Diagrams used for the analysis of initial stage of sintering, using

WoolfreyBannister model. Only the points corresponding to the linear

region were used in the analysis. (a) laser sintering; (b) furnace sintering

under 5 -C/min.



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Q / (n + 1)R and the activation energy can be obtained from the Eq.

(3). Fig. 7 presents T2dY/ dT as a function of Y for laser sintering

with heating rate of 45 -C/min and furnace sintering under heating

rates of 5 -C/min. The points belonging to the linear part of these

graphs were used to obtain the activation energy for the first stage

of sintering, which were Q =86 kJ/mol for laser sintering and

Q =257 kJ/mol for furnace sintering. The activation energy wasalso calculated for furnace sintering under 10 -C/min (graph not

shown), and the determined value was Q = 274 kJ/mol. The smaller

activation energy of laser sintering is related to the fact that the

linear shrinkage begins at temperatures much lower than the

corresponding temperature for furnace sintering. It is also possible

that the temperature gradient induced by superficial laser irradi-

ation causes an enhancement of mass transport at this stage.

Fig. 8 presents the results obtained from the fitting of the

average grain size as a function of the temperature (Eq. (5)) during

the intermediate stage of sintering. The fitting considers a constant

heating rate (here called a). The heating rates employed were

a = 10 -C/min (0.17 K/s) for the conventional sintering and a = 45

-C/min (0.75 K/s) for the laser sintering. The sintering parameters

obtained were Q =115T1 kJ/mol and n =2 for laser sintering andQ =119T2 kJ/mol and n =2 for conventional sintering, showing

that laser sintering is as efficient as furnace, in a shorter timescale.

This reduced timescale will prove to be advantageous also in the

final stage of sintering, as we will see below.

The transport mechanism and apparent activation energy for the

isothermal stage were analyzed from Eq. (4), using as starting

parameters the values of Q and n determined for the intermediate

stage. Fig. 9a and b present the fitting curves and the obtained

values forQ and n. For this study, the final stage of laser sintering

was prolonged to 12 min, in order to get further information about

the grain growth under laser irradiation. The activation energy

determined for laser sintering ( Q =312T2 kJ/mol) at this final

stage was higher than that calculated for the conventional process

( Q =281T1 kJ/mol). The period of isothermal stage is markedly

shorter for laser sintering, compared to conventional sintering, and

it can be a determinant feature to avoid grain growth. The

parameter n assumed values of 3 for laser sintering and 2 for

conventional sintering.

4. Conclusions

The laser sintering kinetics of Bi4Ti3O12 was analyzed

and compared to the kinetics of the conventional sintering in

electrical furnace. The obtained results presented remark-

able differences in the starting temperature of linear

shrinkage, activation energy (initial and final stages) and

mass transport (final stage). Under a heating rate of 45 -C/

min, the laser sintering was completed 10 times faster than

the conventional process. In the initial stage, the low

activation energies can explain the beginning of linear

600 700 800 900 10000

2

4

6

(a)

Averagegrainsiz

e(m)

Temperature (K)

Q = 115 1 kJ/moln = 1.9

800 1000 12000

2

4

6(b)

Averagegrainsize(m)

Temperature (K)

Q = 119 2 kJ/mol

n = 1.8

Fig. 8. Grain growth under constant heating rate (intermediate stage). (a)

Laser sintering under 0.75 K/s; (b) furnace sintering under 0.17 K/s.

0 120 240 360 480 600 720

2

4

6

8

10

12

(a)

Averagegra

insize(m)

time (s)

Q = 312 2 kJ/mol

n = 3

0 1200 2400 3600 4800 6000 7200

2

4

6

8

10

12

(b)

Averagegrainsize

(m) Q = 281 1 kJ/mol

n = 2

time (s)

Fig. 9. Isothermal grain growth at final stage. (a) Laser sintering; (b)

furnace sintering.

Z.S. Macedo, A.C. Hernandes / Materials Letters 59 (2005) 3456 34613460


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shrinkage and densification at temperatures much lower for

laser sintering than for conventional sintering. In the

intermediate stage the energy was approximately the same

for laser and conventional sintering. The values of Q

calculated in this paper for the intermediate stage agree with

the value Q = 22 kcal/mol (92 kJ/mol) found by German and

co-workers [15] for the sintering of submicronic Bi4Ti3O12.During the final stage, both laser and conventionally

sintered ceramics have similar densification, but the conven-

tional process results in higher grain growth. For this stage

the activation energy of laser sintering was higher than that

from conventional process. Taking into account the values

n=2 for conventional sintering and n=3 for laser sintering,

meaning mass transport via volumetric diffusion and grain

boundary diffusion respectively, we can conclude that grain

boundary diffusion promotes high densification and low

grain growth. The role of temperature gradient on the mass

diffusion during laser sintering is also under investigation in

our laboratory.

Acknowledgements

The authors would like to thank CAPES, FAPESP, CNPq

and FAP-SE for the financial support.

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A Quantitative Analysis of the Laser Sintering of Bismuth Titanate Ceramics