Microwave sintering of hydroxyapatite ceramics. Fang et al.: Microwave sintering of hydroxyapatite...

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Microwave sintering of hydroxyapatite ceramics Yi Fang, Dinesh K. Agrawal, Delia M. Roy, and Rustum Roy Materials Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802-4801 (Received 23 June 1993; accepted 7 September 1993) Hydroxyapatite ceramics have been fabricated by microwave sintering in a 500 W microwave oven. Circular-plate specimens of various green densities were sintered in the oven at 1200 and 1300 °C, for 5, 10, and 20 min, respectively. Ceramics with density up to 97% of the theoretical were obtained. Density, grain size, microstructure, and strength of the ceramics sintered by microwave and by conventional methods were compared. The results show that microwave sintering of hydroxyapatite is not only highly efficient in saving time and energy, but can also improve the microstructure and thus enhance mechanical strength of the ceramics. I. INTRODUCTION That the microwave-transparent ceramics such as A12O3 and SiO2 could be melted and sintered by a microwave field was a surprising finding. Using gels of such materials, Roy, Komarneni, and Yang1-2 first showed that extraordinary rates of temperature increase (hundreds of degrees per min) could be attained by microwave heating of such materials. Since then, micro- wave processing has become a new technique to sinter ceramics. In microwave sintering, heat is generated within the materials instead of being transferred from outside as in conventional sintering. Sutton3 has shown how microwave sintering is a volumetric heating process and, thus, makes it possible to reduce or minimize thermal gradients inside the materials being processed. This fundamental feature of microwave processing offers one a unique technique to process a variety of ma- terials (especially those which are difficult to process by conventional methods), to save energy and time, and to obtain improved physical or mechanical prop- erties. Microwave sintering is very promising and seems far more powerful than previously expected. However, this technique is still in an early or exploratory stage of development. In this case, we have studied a new composition involving P2O5, i.e., hydroxyapatite (HAp) [Ca10(PO4) 6(OH) 2], a material that has been investigated for years for biomedical applications. II. EXPERIMENTAL A. Material HAp powder was prepared by the hydrolysis of brushite, CaHPO4 2H2O (J.T. Baker Chemical Co., Phillipsburg, NJ), followed by a ripening process4 with 60 wt. % CaCl2 2H2O (Mallinckrodt, Inc., Paris, KY) of the HAp being ripened. The ripened HAp was dried at 90 °C in a ventilated oven and then ground to -325 mesh followed by firing at 500 °C for 24 h before pellet com- paction. The BET surface area of this powder was found to be 47.4 m2 /g. Powder x-ray diffraction (XRD) by a Scintag diffractometer (Scintag Inc., Sunnyvale, CA) confirmed that the material was pure HAp of low crys- tallinity. With no binder, pellets of 12.7 mm (0.5 in.) diameter were made at uniaxial pressures from 35 to 351 MPa to get various green densities. Two 19.05 mm (3/4 in.) diameter pellets, on which the patterns of a dime were pressed, were used to test the uniformity of shrinkage during microwave sintering. B. Setup A 500 W, 2.45 GHz commercial microwave oven (Model JE43, GE Co.) was used for the sintering experi- ments. The arrangements inside the oven are schemati- cally shown in Fig. 1. Samples were stacked in layers at the center of a vertically placed porous zirconia cylinder (Zircar Products, Inc., Florida, NY) (28 mm ID, 51 mm OD, and 30 mm in height), which was placed on a thick Fiberfrax (Fiberfrax, Harbinson-Carborundum FIG. 1. Schematic showing the arrangements in the microwave sin- tering cavity: (1) thermocouple, (2) zirconia cylinder, (3) pack of samples, (4) thermal insulating fibers, (5) power level control, and (6) time control. 180 J. Mater. Res., Vol. 9, No. 1, Jan 1994 © 1994 Materials Research Society

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Microwave sintering of hydroxyapatite ceramicsYi Fang, Dinesh K. Agrawal, Delia M. Roy, and Rustum RoyMaterials Research Laboratory, The Pennsylvania State University, University Park,Pennsylvania 16802-4801

(Received 23 June 1993; accepted 7 September 1993)

Hydroxyapatite ceramics have been fabricated by microwave sintering in a 500 Wmicrowave oven. Circular-plate specimens of various green densities were sintered in theoven at 1200 and 1300 °C, for 5, 10, and 20 min, respectively. Ceramics with density upto 97% of the theoretical were obtained. Density, grain size, microstructure, and strengthof the ceramics sintered by microwave and by conventional methods were compared.The results show that microwave sintering of hydroxyapatite is not only highly efficientin saving time and energy, but can also improve the microstructure and thus enhancemechanical strength of the ceramics.

I. INTRODUCTION

That the microwave-transparent ceramics such asA12O3 and SiO2 could be melted and sintered by amicrowave field was a surprising finding. Using gelsof such materials, Roy, Komarneni, and Yang1-2 firstshowed that extraordinary rates of temperature increase(hundreds of degrees per min) could be attained bymicrowave heating of such materials. Since then, micro-wave processing has become a new technique to sinterceramics. In microwave sintering, heat is generatedwithin the materials instead of being transferred fromoutside as in conventional sintering. Sutton3 has shownhow microwave sintering is a volumetric heating processand, thus, makes it possible to reduce or minimizethermal gradients inside the materials being processed.This fundamental feature of microwave processing offersone a unique technique to process a variety of ma-terials (especially those which are difficult to processby conventional methods), to save energy and time,and to obtain improved physical or mechanical prop-erties. Microwave sintering is very promising and seemsfar more powerful than previously expected. However,this technique is still in an early or exploratory stageof development. In this case, we have studied a newcomposition involving P2O5, i.e., hydroxyapatite (HAp)[Ca10(PO4)6(OH)2], a material that has been investigatedfor years for biomedical applications.

II. EXPERIMENTAL

A. Material

HAp powder was prepared by the hydrolysis ofbrushite, CaHPO4 • 2H2O (J.T. Baker Chemical Co.,Phillipsburg, NJ), followed by a ripening process4 with60 wt. % CaCl2 • 2H2O (Mallinckrodt, Inc., Paris, KY) ofthe HAp being ripened. The ripened HAp was dried at90 °C in a ventilated oven and then ground to -325 mesh

followed by firing at 500 °C for 24 h before pellet com-paction. The BET surface area of this powder was foundto be 47.4 m2/g. Powder x-ray diffraction (XRD) bya Scintag diffractometer (Scintag Inc., Sunnyvale, CA)confirmed that the material was pure HAp of low crys-tallinity. With no binder, pellets of 12.7 mm (0.5 in.)diameter were made at uniaxial pressures from 35 to351 MPa to get various green densities. Two 19.05 mm(3/4 in.) diameter pellets, on which the patterns of adime were pressed, were used to test the uniformity ofshrinkage during microwave sintering.

B. Setup

A 500 W, 2.45 GHz commercial microwave oven(Model JE43, GE Co.) was used for the sintering experi-ments. The arrangements inside the oven are schemati-cally shown in Fig. 1. Samples were stacked in layersat the center of a vertically placed porous zirconiacylinder (Zircar Products, Inc., Florida, NY) (28 mm ID,51 mm OD, and 30 mm in height), which was placedon a thick Fiberfrax (Fiberfrax, Harbinson-Carborundum

FIG. 1. Schematic showing the arrangements in the microwave sin-tering cavity: (1) thermocouple, (2) zirconia cylinder, (3) pack ofsamples, (4) thermal insulating fibers, (5) power level control, and(6) time control.

180 J. Mater. Res., Vol. 9, No. 1, Jan 1994 © 1994 Materials Research Society

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Corp., Niagara Falls, NY) cushion, and then covered allaround with a layer of Fiberfrax thermal insulation fibers.

C. Temperature measurement

An alumina-sheathed, Pt foil-shielded, tip-open Pt-PtlORh thermocouple was inserted from the left wallof the oven to monitor the temperature of the samplesduring sintering. The thermocouple was so arranged thatthe tip was only about 2 mm away from the surface ofa sample.

The microwave interference with the temperaturemeasurement was usually noticed at low temperatures,but once coupling had started (i.e., zirconia and speci-mens began to absorb microwave effectively) the tem-perature readings got stable. In the former case, thetemperature readings were recorded by momentarilyswitching off the power supply to the microwave oven.The response time was less than 3 s.

Tricalcium phosphate (TCP), Ca3(PO4)2, was used toevaluate the validity and accuracy of the thermocouple-temperature-measurement method used in the currentmicrowave experiments. TCP exists in two crystallineforms: a-TCP (high-temperature form) and /3-TCP(low-temperature form). The transition of /3-TCP toa-TCP starts at about 1125 °C and the process issluggish. /3-TCP will transform completely to a-TCPif the temperature is sufficiently greater than 1125 °C orif kept above the transition temperature for a sufficientlylong time. Although a-TCP is a high-temperature form,it can also metastably exist at room temperature even inregularly cooled samples. Therefore, by comparing therelative amounts of TCP phases in the sample of /3-TCPheat-treated by conventional and microwave methodsat temperatures around the transition temperature, anaccurate temperature of microwave-heated samples canbe determined indirectly.

For this purpose, the following experiments wereconducted. Three pellets of lab-synthesized /3-TCP werestacked one over another inside the porous zirconiacylinder in the microwave setup, with the thermocouplelocated at a distance of about 2 mm from the pellet inthe middle (Fig. 2). The rest of the arrangement wasidentical to that used for HAp sintering. The sampleswere heated by microwave irradiation at 1125 ± 10 CCfor 15 min, then cooled to room temperature. Anotherset of three pellets was sintered (one pellet per run) ina conventional furnace for 15 min at 1100, 1125, and1150 °C, respectively, then air-quenched to room tem-perature. XRD was carried out on all samples sinteredby these methods for phase identification.

D. Sintering

Six multisample runs (six HAp pellets with greendensities ranging from 32.6 to 51.4%, stacked in two

3

1r̂ ulllf

11111ill 1

FIG. 2. Schematic showing of relative positions of thermocoupleand /3-TCP pellets during the temperature measurement calibration:(1) thermocouple, (2) porous zirconia, and (3) TCP pellets.

layers in each run) of microwave processing were car-ried out for 5, 10, and 20 min at 1200 and 1300 °C,respectively. The two pellets with the dime-patternswere microwave sintered at 1200 °C for 7 min to checkthe uniformity of shrinkage. During the sintering, themicrowave oven was set at the full power level (500 Woutput), and the temperature was controlled manually byon-and-off operations of the power supply. After eachrun, the system was allowed to cool naturally to roomtemperature. For comparison, conventional sintering ofthe same material was also carried out at the sametemperatures (2 h soaking at each sintering temperature,with heating and cooling rates of 5 °C per min) in a 5 kWprogrammable box furnace (Model 51524, Lindberg,Watertown, WI).

E. Characterization

Density, grain size, microstructure, and strength ofthe sintered pellets were studied. Density was determinedby direct measurement of the geometric size and weightof the specimens. Grain size was measured on the micro-graphs of the as-sintered surfaces. Microstructure wasexamined on the fracture surfaces with the scanning elec-tron microscope (SEM) (SEM, ISI 130, Akashi BeamTechnology Corp.) Phase compositions were identifiedby XRD. The tensile strength was measured by thediametral-compression test5 in a MTS810 (Material TestSystem, MTS System Corp., Minneapolis, MN) with acrosshead speed of 0.051 mm (0.002 in.) per min.

111. RESULTS AND DISCUSSION

A. Temperature measurement

Figure 3 shows the XRD patterns of six TCP sam-ples processed in this study. As can be seen, conven-tionally, the sample sintered at 1100 °C remained pure/3-TCP [Fig. 3(a)l]; a-TCP appeared as a minor phaseat 1125 °C [Fig. 3(a)2] and as a major phase at 1150 °C[Fig. 3(a)3]. These results indicate that in conventionalheating, the phase transition from fi- to a-TCP startedat about 1125 °C when soaked for 15 min, and substan-tially transformed at 1150 °C. In contrast, in the case of

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3. 1150 °C 3. top

2. 1125 °C

\JLJL-tJ

1. 1100°C

JL20 30

20, degrees

(a)

40

L Ji. ki i i

2. middle1 2. mid

1. bottom

20 3026, degrees

(b)

40

FIG. 3. XRD patterns (CuKa) of /3-TCP samples used to calibrate temperature measurement, (a) Conventionally sintered for 15 min attemperatures indicated, (b) Microwave sintered at 1125 ± 10 °C for 15 min (pellet positions are indicated). (•) a-TCP. Unmarked peaks: /3-TCP.

microwave processing at 1125 ± 10 °C, the pellet locatedat the bottom of the stack remained /3-TCP [Fig. 3(b)l],the middle pellet contained only a trace amount ofa-TCP, and /3-TCP was still the major phase in thetop pellet [Fig. 3(b)3]. Table I lists the intensity ratio(using intensity of d = 2.909 A for a-TCP, and d =2.880 A for /3-TCP) of the characteristic reflections inthe XRD patterns. As can be seen, the middle pelletsintered by microwave at 1125 ± 10 °C is compara-ble in the a//3 intensity ratio to that of the sampleconventionally sintered at 1125 °C, while the top pelletshows a higher a//3 ratio than the one conventionallysintered at 1125 °C, but obviously much lower than thatsintered at 1150 °C. The bottom pellet was the same asconventionally sintered at 1100 °C (no trace of a-TCP).Considering the temperature deviation of ±10 °C in themicrowave sintering, the measured temperature (on themiddle pellet) was in excellent agreement with the ex-pected value. Thus, the validity and accuracy of thetemperature measurement with the thermocouple in thecurrent microwave processing is confirmed.

B. Sintering process

Figure 4 shows the temperature-time curves of thesix sets of HAp specimens sintered by microwave pro-

cessing. The run at 1200 °C for 5 min was irregular;therefore, the results of this run are not included here.As can be seen, each curve has three parts, correspondingto three stages: heating, soaking, and cooling. The sharptemperature increase in the heating curve is characterizedby the phenomenon of thermal runaway. It is wellknown that zirconia is a microwave absorber, so thatthe zirconia cylinder played a dual role during themicrowave heating: (i) a thermal insulator and (ii) apreheater. Furthermore, since the amount of HAp (lessthan 6 g per run) used in the sintering was much less thanzirconia (about 20 g), it is proposed that the zirconiacylinder triggered thermal runaway. To confirm this,and to determine the role of Fiberfrax insulation, two

TABLE I. Intensity ratio of a-TCP (d = 2.909 A) to jS-TCP(d = 2.880 A) in the /3-TCP after firing under different conditionsfor temperature measurement calibration.

1150 °C

1.769

Conventional15 min

1125 °C

0.172

1100

0

°C

Microwave 112515 min

Top

0.282

Middle

0.111

± 10 °C

Bottom

0

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U

0 10 20 30 40 50 60

Time, min

(a)

0 10 20 30 40 50 60

Time, min

(b)

FIG. 4. Temperature-time curves in the microwave sintering of HAp at (a) 1200 °C and (b) 1300 °C. Sintering time: (A) 5 min, (—) 10 min,and (• • •) 20 min.

blank tests were carried out. With only the Fiberfrax(no sample or zirconia cylinder), temperature rose onlyto 369 °C after a 60 min irradiation, while thermalrunaway was noticed at 21 min in a test with both theFiberfrax and the zirconia cylinder. This confirms thatonly the zirconia cylinder played a key role in triggeringthermal runaway in the current microwave sintering.At low temperature, HAp absorbed little microwaveand was heated up by the zirconia which was firstheated up by microwave energy. When temperature wassufficiently high, both zirconia and HAp would absorbmicrowave more efficiently; thus, the sintering of theHAp samples was a complex result of both direct andindirect microwave heating.

C. Uniformity

Although having experienced high-rate heating(thermal runaway) and cooling (in the first few minof cooling the cooling rate was high), the HAp pelletsdid not show any cracks after microwave sintering. Asshown in Fig. 5, all the details of the coin-patternshave been uniformly reduced on the sintered HAppellets after 7 min microwave sintering at 1200 °C.This indicates that under proper conditions microwavesintering will not introduce any distortion in the shapeof the specimens. The uniform shrinkage should beattributed to the volumetric heating, good thermalinsulation, and the small size of the specimens.

D. Sintered density

Figure 6 shows the relative densities of the 10 minmicrowave sintered pellets versus the corresponding

green densities. The values of the conventionallysintered pellets were also plotted in the same graph forcomparison. It can be seen that at the same temperature,higher densities were achieved in the microwave sinteredpellets, and this is more obvious when green density washigh (typically over 45%). Generally, the densificationof ceramics in a solid-state sintering is a process ofshrinkage of the compact or decrease of porosity.Although quite a few mass transfer processes take placesimultaneously during sintering, "only transfer of matterfrom the particle volume or from the grain boundary be-tween particles causes shrinkage and pore elimination",6

FIG. 5. Photograph showing the uniform shrinkage of microwave-sintered HAp pellets. The dime-patterns on the green pellets (large)have been uniformly reduced to the sintered pellets (small) bymicrowave sintering at 1200 °C for 7 min.

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100

90

C/3

80

70

6030 35 40 45 50 55

Green density, %

FIG. 6. Relative density (% theoretical) of HAp ceramics sintered by(1) microwave/1300 "C/10 min, (2) microwave/1200 "C/10 min,(3) conventional/1300 °C/2 h, and (4) conventional/1200 °C/2 h.

so that it can be suggested that grain boundary diffusionbetween the HAp particles was substantially enhancedduring the microwave sintering. The grain boundarydiffusion can effectively take place only after theparticles are necked (in contact) and at a sufficienttemperature (to overcome the energy barrier). In thepellets of low green density, the number of contactingpoints is limited. As the green density increases, thenumber of particles in contact correspondingly increasesso that sintered density also increases in both microwaveand conventional sintering (Fig. 6), but the increase inthe microwave sintered samples is more obvious thanthat in the conventionally sintered samples. Since themicrowave sintering took a much shorter time (<10% ofthe time of the conventional sintering), it can be furthersuggested that the densification rate (through boundarydiffusion) in the microwave sintering process was muchhigher than in the conventional sintering. The volumetricheating in the microwave sintering is a consequence ofa series of losses. The principles of microwave sinteringhave been reviewed by Sutton.3 When microwaves

penetrate and propagate through a dielectric material,the internal fields generated within the affected volumeinduce translational motions of free and bound chargesand rotate charge complexes such as dipoles. The resis-tance of these induced motions due to inertial, elastic,and frictional forces, causes losses and attenuates theelectric field. As a consequence of these losses, volumet-ric heating results. These principles should be applicableto the microwave sintering of HAp also. In particular,the hydroxyl in the HAp structure might have playedan important role in causing losses and enhancingdensification in the microwave sintering of HAp.

E. Grain size and microstructure

Figure 7 shows the SEM photographs of the as-sintered surfaces of some pellets. The morphology dif-ference in the HAp pellets sintered at 1200 °C can beclearly seen. Compared with the conventionally sinteredsample (a) in which the entire area of the as-sinteredsurface is rough and uneven, the grains are angular withboundaries shown by the straight lines; the microwavesintered ones (b, d) show unique features: the entirearea looks flat and smooth. Since the driving force forthe densification of solid-phase sintering is the decreasein surface area and the lowering of the surface freeenergy by the elimination of solid-vapor interfaces,7 therough and uneven as-sintered surfaces correspond to ahigher residual surface area and imply a lesser degreeof sintering.

Table II shows a comparison between the averagegrain size of the microwave sintered and the conven-tionally sintered HAp samples. The grain size of the1200 °C conventionally sintered pellets is close to thatof microwave sintered one at the same temperature. Forthe pellets sintered at 1300 °C, the grain size of both mi-crowave and conventionally sintered samples increasedsubstantially, but the grains in conventionally sinteredsample were much larger. In addition, the abnormal graingrowth was pronounced in the conventionally sinteredpellet, but was less obvious in the microwave sinteredone. The relatively suppressed grain growth is attributedto the shorter sintering time and a more effective densifi-cation process during microwave sintering. A few SEMphotographs of the fracture surfaces are shown in Fig. 8.The lower total porosity and finer pore size are obviousin the HAp sintered by microwave at 1200 °C [Fig. 8(b)]compared with that conventionally sintered at the sametemperature [Fig. 8(a)], while the features of a fracturesurface of the microwave and conventionally sinteredHAp at 1300 °C are similar [Figs. 8(c) and 8(d)].

F. Phases

Some white particles along the grain boundariesare visible in the micrograph of the as-microwave-

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i -

I • > < . . '5 [Jin (b)

ifei] 10 I! Ill (d) 5 urn

FIG. 7. SEM micrographs showing the as-sintered surface of HAp sintered: (a) conventionally/1200 °C/2 h, (b) microwave/1200 °C/10 min,(c) conventionally/1300 °C/2 h, and (d) microwave/1200 °C/20 min.

sintered surface [Fig. 7(d)], which are believed to bea—TCP produced by a partial decomposition of HAp.XRD analysis on the sintered samples confirmed theexistence of a-TCP as a minor phase, but, still, HApwas the major. To prevent the decomposition of HAp,either lower processing temperature should be used orsome special precautions should be taken. Sinteringunder special atmosphere or using HAp of high thermalstability are the examples of the latter.

G. Mechanical strength

Figure 9(a) shows the diametral tensile strengthagainst the sintered density of the HAp ceramics,

TABLE II. Grain size of HAp pellets sintered under differentconditions, ytim.

12001300

°C°C

5 min

2.06

Microwave

10 min

1.053.16

20 min

1.483.39

Conventional

120 min

1.126.52

regardless of the sintering time and temperature.The data for both the microwave and conventionallysintered HAp seem to follow the same density-strengthrelation. The diametral tensile strength of the pelletssintered at 1200 °C was plotted against the greendensity in Fig. 9(b). In this figure, it can be seen thatstarting with the same green density, a microwave-sintered pellet showed a higher strength than theconventionally sintered one: 10 min microwave sinteringachieved higher strength [Fig. 9(b), 2] than the 2 hconventional sintering [Fig. 9(b), 3], and the pelletsby the 20 min microwave sintering led to even higherstrength [Fig. 9(b), 1]. Comparing with Fig. 9(a), itis clear that the enhanced mechanical strength in themicrowave sintered HAp ceramics should be attributedto the higher density achieved by that process.

H. Energy consumption

In addition to the denser microstructure, finer micro-structure, smaller grain size, and the improved me-chanical strength, the economic issue of microwavesintering in terms of both time and energy is very

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JSI

' i f " " " • • . "

FIG. 8. SEM micrographs of the fracture surface of HAp sintered (a) conventionally/1200 °C/2 h, (b) microwave/1200 "C/10 min,(c) conventionally/1300 °C/2 h, and (d) microwave/1300 "C/20 min.

5th,

stre

I

tral

£

70

50

30

10

2oA

ooo

o oA

G

A

i

OQ

O

o ©

J / ° °5 A o

o

I . I .

s60 70 80 90 100

Sintered density, %

(a)FIG. 9 Diametral tensile strength of HAp ceramics (a) versus sintered density: (o) microwave sintered, (A) conventionally sintered; (b) versusinitial green density: (1) microwave/20 min, (2) microwave/10 min, and (3) conventionally/2 h.

30 35 40 45 50

Green density, %

(b)

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important. Figure 10 compares the temperature-time pro-files between microwave and conventional sintering.Taking a typical run at 1200 °C for 10 min with a500 W microwave oven, for example, the microwavesintering process consumed energy only in the heatingand soaking periods, which was about 0.5 h in total,while the conventional sintering process required 10 h(it consumed energy in the cooling cycle also) and afurnace with a minimum of 1 kW power (although a5 kW furnace was used in the current study). Thus, mi-crowave sintering requires only about 5% of the timeand even less energy than in the conventional process.

100 200 300 400

Time, min500 600

FIG. 10. Comparison of temperature-time profiles between micro-wave and conventional sintering of HAp. (1) Microwave sintering.(2) Conventional sintering.

IV. CONCLUSIONS

HAp ceramics have been sintered by microwaveheating. The results show that HAp pellets of certaingreen density can be sintered by microwave irradiationto high densities within a short period of time. Incontrast to conventional method, microwave sinteringof hydroxyapatite consumed much less energy, offeredapparently denser microstructure, finer grain size, andconsequently, improved mechanical strength. Techni-cally, if a microwave oven is adjustable in both powerand frequency, with a combined feedback temperaturecontrolling system, the efficiency of the process shouldbe even higher.

ACKNOWLEDGMENTS

This research was supported by the National Sci-ence Foundation under Contract DMR8812824 and theConsortium on Chemically Bonded Ceramics.

REFERENCES

1. R. Roy, S. Komarneni, and L. J. Yang, J. Am. Ceram. Soc. 68 (7),392-395 (1985).

2. S. Komarneni and R. Roy, Mater. Lett. 4 (2), 107-110 (1986).3. W. H. Sutton, Am. Ceram. Soc. Bull. 68 (2), 376-386 (1989).4. H. Monma and T. Kamiya, J. Mater. Sci. 22, 4247-4250 (1987).5. A. Rudanick, A. R. Hunter, and F. C. Holden, Mater. Res. Stand.

April, 283 (1963).6. W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to

Ceramics, 2nd ed. (John Wiley, New York, 1976), p. 475.7. W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to

Ceramics, 2nd ed. (John Wiley, New York, 1976), p. 469.

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