9３mol％イットリアドープジルコニア粉末の初期焼結メカニズム：アルミナの効果
松

井

光

二

Initial Sintering Mechanism of 3 mol％ Yttria−doped Zirconia
Powder: Effect of Alumina
Koji MATSUIThe sintering behavior of 3 mol％ Y2O3-doped ZrO2 powders with and without a small amount of Al2O3 wasinvestigated to clarify the effect of Al2O3 on the initial sintering mechanism.
compact was measured under constant rates of heating (CRH).
remarkably increased by a small amount of Al2O3.

The shrinkage behavior of a powder

The shrinkage rate of a powder compact was

The activation energies of diffusion at the initial sintering

stage were determined by analyzing the shrinkage curves.

The activation energy of a powder compact with

Al2O3 was lower than that of a powder compact without Al2O3.

The diffusion paths of material transport at theinitial sintering stage were determined using the analytical equation that is applicable to the CRH data.

This

analytical result showed that Al2O3 changed the diffusion path from grain boundary (GBD) to volume diffusions(VD).

It is, therefore, concluded that Al2O3 enhances the sintering rate because of a decrease in the activationenergy with the GBD → VD change at the initial sintering stage.

This enhanced sintering mechanism isreasonably explained by the segregated dissolution of Al2O3 at Y-TZP grain boundaries.

ceramic powders has been investigated by many

１．Introduction

researchers, and several sintering-rate equations used

Yttria-stabilized tetragonal zirconia polycrystal (Y-for the kinetic analysis at the initial sintering stage have

TZP) has been known as an important structural

been reported.1)-9)

ceramic, with excellent mechanical properties such asrate equation (Eq. (1)) that is applied for the initialhigh strength and fracture toughness, and used forsintering stage taking into account simultaneous grain-

products of the optical fiber connector, grinding media,

boundary (GBD) and volume diffusions (VD) by

and precision parts.

assuming the two-sphere shrinkage model.

Hydrolysis is well known as theindustrial manufacturing process for Y-TZP powder.

Johnson1) has derived the sintering-

1.03△ L 2.06 d（ΔL ／L 0）
V ΔL ／L0 ）〜 2.63γΩD（
3
＝
dt
kT
0
0.7γΩ・bDB
（1）
＋
kT 4

（L ）

The appearance of Y-TZP with the higher characteristic
and reliability is desired to spread the zirconia-productmarket and to propel a new application development.
To develop new Y-TZP powder with high quality which

Here, ΔL ( ＝L 0−L ) is the change in length of theis excellent in the sintering characteristic by the

specimen, L0 the initial length of the specimen, γ thehydrolysis process, it is important to analyze the effectsurface energy, Ω the atomic volume, bDB the GBD

of various additives on the sintering mechanism of Y-

coefficient (b is the effective grain-boundary width), Dv
the VD coefficient, t the time, T the absolute

TZP powder.
So far, the initial stage of sintering on various

temperature, k the Boltzmann s constant, and

（ 9 ）

the

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TOSOH Research ＆ Technology Review Vol.51（2007）

n the grain size power law ( n =3: VD, n =4: GBD).

particle radius.
2)

Using Eq. (1), Young and Cutler have derived theUsing shrinkage data measured at different heating

sintering-rate equations (Eqs. (2) and (3)) that canrates, the Q can be determined from the slope of thequantitatively analyze the densification behavior at the

Arrhenius-type plot of ln[T(dT/dt)(dρ/dT)] versus

initial sintering stage measured under constant rates of

1/T at same density, under a constant grain size.

heating (CRH).

determined Q corresponds to that either for GBD or for（
d ΔL ／L 0）
2.14γΩbD0BRT 1/3 Q
〜
exp
＝
k 4cQ
dT
3RT 2
Q
（2）
−
3RT

（

）（

）

（

）

d（ΔL ／L 0）
5.34γΩD 0VRT 1/2 Q
〜
exp
＝
k 4cQ
dT
2RT 2
Q
（3）
−
2 RT

（

）（

）

（

）

The

VD, because it is very difficult to experimentally
determine the GBD- and VD-paths from Eq. (6).

The

Qs for causing sintering related to Al2O3, zirconia (with
Y2O3), and two-phase Al2O3/zirconia (with Y2O3) were
estimated using Eq. (6).3), 4)
In this way, the sintering-rate equations that are used
for CRH techniques can experimentally determine only

Here, Eqs. (2) and (3) are used for GBD and VD,

the Q for causing diffusion. However, the diffusionc is the heating rate (dT/dt), R the gas

path of material transport was experimentallyrespectively.

constant, and Q the activation energy. D 0B and D 0V

determined by analyzing the isothermal shrinkage

represent the constant terms that are given by Eqs. (4)process so far because those cannot be determined byand (5), respectively,

CRH techniques. 5), 6)

research of the zirconia-sintering mechanism, theＱ
bDB ＝ D0B exp − RT（）
Ｑ
D ＝ D exp（− RT ）
V

（4）
（5）

0V

effects of various additives on the initial sintering stage
have not been clarified in previous papers.

clarify the role of Al2O3 which is one of the additives.

the Q can be estimated from the slope of the plot ofln[Td(ΔL/L0)/dT] or ln[TFrom theindustrial standpoint, it is particularly important toUsing shrinkage data measured by CRH techniques,
5/3

On the other hand, for the

3/2d(ΔL/L0)/dT] versus

In the present study, the author derived the analysis
method used for CRH techniques by which not only the

1/T (GBD- or VD-type plot) by assuming GBD or VD.

Q but the diffusion path of material transport at the

The Qs at the initial sintering stage in yttria-stabilized

initial sintering stage can be determined experimentally,

zirconia and Al 2O 3 were estimated by this analysis

and applied that method in order to examine the initial2)

sintering mechanism of Y-TZP powder with and without

method.

Wang and Raj3), 4)

have derived the sintering-ratea small amount of Al2O3.

The effect of Al2O3 on theequation of Eq. (6) used for the quantitative analysis ofinitial sintering stage of Y-TZP powder produced by theshrinkage data measured by CRH techniques, notinghydrolysis process (i.e., Tosoh s zirconia process) wasthat the sintering-rate equation in general can be

determined based on the present analytical results.

separated into temperature-dependent, grain-sizedependent, and density-dependent quantities:dT
ln T dtdρ
dT

２．Experimental procedure

Q＝− RT ＋ ln［ f（ρ）］［ （ （） ）］CγV 2 ／3−n ln d （6）
Ｒ

［

＋ ln

］

［1］Specimen preparation
3 mol％ (5.2 mass％) Y-TZP powders with andHere, ρ is the density, f(ρ) a function only of density,

without 0.25 mass％ Al 2 O 3 produced by Tosoh s

C a constant, V the molar volume, d the grain size, andzirconia process (TZ-3Y and TZ-3YE grades, Tosoh,

Table１

Specimen
3Y
3YE

Chemical composition and characteristic of Y−TZP powder
Chemical composition
Y2O3
Al2O3
(mass％) (mass％)
5.2≦0.0055.2
0.25

Powder characteristic
Crystallite size Specific surface
2（nm）
area（m ／g）
28
15
28
15

（ 10 ）

東ソー研究・技術報告 第51巻（2007）

Tokyo, Japan) were used as starting raw materials(Table I).

Both 3Y and 3YE had nearly the same

11

３．Derivation

The 3Y and 3YE powders were

Using CRH techniques, the concept of the analysis

pressed uniaxially into a disk under 70 MPa. The

method that is able to determine the diffusion path ofresulting powder compacts were sintered at 1100-

material transport at the initial sintering stage is

1500℃ for 2 h in air (heating rate 100℃/h).

derived as follows.

characteristics.

When Eq.(1) is transformed by thedifferent viewpoint from the derivation procedure thatis reported by Young and Cutler, 2) the following［2］Density and grain-size measurements
The density of sintered bodies was mainly measured
using the Archimedes method.

However, in the casesintering-rate equation can be derived by treating
separately GBD and VD (Appendix).

of the sintered bodies with relative densities of < 80％,
Scanning electron microscopy (SEM; Model S-4500,

dT

dρ

Q

［ （ dt （）dT ）］＝− RT ＋α or αln T

the density was calculated from the weight and the size.

B

V

（8）

where
2.14γΩD 0B− 41nk
5.34γΩD 0V
αV＝ ln［ f（
］＋ ln
− 31n
V ρ）
k

Hitachi, Tokyo, Japan) was used to measure theαB＝ ln［ f（］＋ ln［B ρ）

average grain sizes of the sintered bodies. SEM］］［

specimens were polished with 3 μm diamond paste,

（9）
（10）

and then thermally etched in air for 1 h at a temperature

Here, αB - and αV -terms are used for GBD and VD,

lower by 50℃ than the sintering temperature of each

respectively.

specimen. The average grain size was measured by thedensity of GBD and VD, respectively.

Planimetric method.

10)fB(ρ) and fV(ρ) are functions only of
The Q at theinitial sintering stage can be experimentally determinedin the same analytical procedure as that reported by
Wang and Raj, 3) because the form of Eq. (8)［3］ Analysis of sintering behavior
The 3Y and 3YE powders were pressed uniaxiallycorresponds to that of Eq. (6).

Using the slope S1 of

into a cylindrical disk under 70 MPa, and afterwards

the Arrhenius-type plot of ln[T(dT/dt)(dρ/dT)] versus

pressed isostatically at 200 MPa. The size of the

1/T at same density, the Q is expressed by Eq. (11).

resulting powder compacts was 6 mm○／×15 mm. The

Q ＝− RS 1

shrinkage of the powder compacts with sintering was（11）measured using a dilatometer (Model DL9700, ULVAC-

On the other hand, using the slope S2 of the GBD- or

RIKO, Yokohama, Japan). The shrinkage measurements

VD-type plot determined by applying Eqs. (2) and (3),by CRH techniques were performed in the range fromthe apparent activation energy (Q/m) is expressed as

room temperature to 1500℃ at heating rates of 5, 10,Qm ＝− RS 2

15, and 20℃/min in air. When the temperature（12）

reached 1500℃ , the CRH measurements were

Here, m is the order depending on the material-

terminated. The dilatometer was calibrated usingtransport path (m=2: VD, m=3: GBD).

sapphire as a standard specimen. Using the thermaland (12) are derived using Eq. (1) as the starting

expansion coefficient of Y-TZP,11) thermal expansions ofequation.

Hence, the Q in Eq. (11) is equal to that in

the specimens were corrected from the observed

Eq. (12).

Combining Eqs. (11) and (12), one obtains

shrinkages.

Assuming isotropic shrinkage to powder

S1
Q
m＝
＝
S2
（Q ／m ）

compact, the density ρ(T) at a given temperature T isgiven by the following equation3) :

Lf

f

（13）

Equation (13) implies that, using both sintering-rateequations of Eqs. (8) and (2)-(3), the diffusion path of3（L（T ））ρ

ρ（T ）＝Both Eqs. (11)（7）

material transport at the initial sintering stage can be

Here, Lf and L(T) are the final length and the length atdetermined experimentally by CRH techniques.

a T of the specimen, respectively. ρf indicates the final

Taking into account the application range of Eq. (1), thedensity measured by the Archimedes method. Theρ

present analyses should be performed at the fractional(T) at a given temperature was calculated using Eq. (7).

shrinkages of < 〜4 %.

（ 11 ）

Wang and Raj pointed out that

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TOSOH Research ＆ Technology Review Vol.51（2007）

the exact Q can be estimated under a constant density
3)

Planimetric method. As shown in Fig.1, the relationships

When the fractional shrinkages of <between the average grain size and the sintering〜4 % is satisfied, the influences of density and particle

temperature were approximately plotted onto the same

size on the Q and Q/m are negligibly small.

curve for 3Y and 3YE.

and particle size.

These experimental results

showed that a small amount of Al2O3 doped in Y-TZP
powder increased the sintering rate remarkably,

４．Results and discussion

whereas the grain-growth process was hardly affected［1］Densification and grain growthat the hold time of 2h in the present sintering profile.

Figure１ shows the change of relative densities of 3Yand 3YE with sintering temperature. The relative［2］Densification behavior at the initial sintering
stage

density of 3YE (including 0.25 mass％ Al 2 O 3 ) was
higher than that of 3Y (including no Al 2O3) at lower

To probe the effect of Al2O3 on the sintering rate, theFigure２shrinkage behavior of powder compacts of 3Y and 3YEshows SEM micrographs of the polished and etchedin the course of heating was analyzed by a dilatometricsurface of 3Y and 3YE sintered at 1300 and 1500℃.

method. Figure 3 shows the change of the shrinkage

The grain sizes of both 3Y and 3YE increased as thein the course of 5℃/min heating. As seen in Fig. 3(A),sintering temperature increased. To analyze

the starting temperatures of shrinkage was 〜1000℃,

quantitatively the grain-growth behavior, the averageand nearly equal for 3Y and 3YE.

grain sizes of 3Y and 3YE were determined by thethe shrinkage of 3YE clearly increased more than thattemperatures, and attained 99.6％ at 1350℃.

Using the shrinkage curves in Fig. 3(A), the

1.0

90

0.8

80

0.6

70

0.4

60

0.2

50
1100

1200

1300

1400

temperature changes of the relative density ( ρ) and
Average grain size［μm］

Relative density［％］of 3Y.
100

Beyond 〜1150℃,

3Y−1300℃

3YE−1300℃

3Y−1500℃

3YE−1500℃

0.0
1500

Temperature［℃］
1μm

Changes of relative density and average grain
size in 3Y and 3YE with sintering temperature.
（○）and（□）are 3Y and 3YE, respectively.

100

0
−5
−10
3YE

3Y

−15
−20
−25
900 1000 1100 1200 1300 1400 1500
Temperature［℃］

Fig.３

Fig.２

SEM micrographs of 3Y and 3YE sintered at1300 and 1500℃

0.35

（B）

（C）

0.30

90
80
3YE

3Y

70
60

dρ／dT［℃−1］（A）

Relative density（ρ）［％］

5
Expansion［％］

Fig.１

0.25

3YE

0.20
0.15
0.10

3Y

50

0.05

40
900 1000 1100 1200 1300 1400 1500
Temperature［℃］0.00
900 1000 1100 1200 1300 1400 1500
Temperature［℃］

Temperature dependence of shrinkage, relative density（ρ）, and densification rate（dρ／dT ）of 3Yand 3YE in the course of heating（5℃／min）.（○）and（□）are 3Y and 3YE, respectively.

（ 12 ）

東ソー研究・技術報告 第51巻（2007）

13［3］CRH shrinkage analysis

the densification rate (dρ/dT) were determined by Eq.

To analyze the effect of Al 2 O 3 on the dρ /d T(8) (Fig. 3(B) and (C)). The ρ of 3YE was clearlyhigher than that of 3Y at temperatures of > 〜1150℃.

quantitatively, the Q at the initial sintering stage was

The dρ/dT of 3YE increased more rapidly than that ofdetermined by applying Eq. (8) to the above results.

3Y when the temperature exceeded 〜1120℃, and theEquation (8) can be applied in the following way.

temperature of peak maximum of the dρ/dT curve ofdifferent values of dT/dt of 5, 10, 15, and 20℃/min, the3YE shifted to a lower temperature than that of 3Y.

values of T and dρ/dT at the same ρwere determined,

Figure 4 shows the temperature dependence of the dρ

respectively, and their values were plotted as the/dTs of 3Y and 3YE measured at 5-20℃/min heating

Arrhenius-type plot of T(dT/dt)(dρ/dT) against 1/T

rates.

(Fig. 5).

The dρ/dT curves of both 3Y and 3YE shifted

For

The Q at each ρ was determined from theto a higher temperature, as the heating rate increased.

slope of the straight line in the Arrhenius-type plot.

The shift of the dρ/dT curve of 3YE with the increase

The value ofαB - or αV -term was also determined fromin heating rate was greater than that of 3Y.

the intercept of the straight line in the plot.

The

Here, thepresent results indicate that Al 2O 3 doped in Y-TZP

present analysis was performed at the fractional

powder increased the dρ/dT remarkably in the low-shrinkages of < 〜4％ (namely, corresponding to the ρtemperature range of < 〜1300℃.

range of 54％ and below), which satisfy the range of the

0.35

0.35

3YE

3Y
0.30
dρ／dT［℃−1］dρ／dT［℃−1］

0.30
0.25
0.20
0.15

0.25
0.20
0.15

0.10

0.10

0.05

0.05
0.00

0.00

900 1000 1100 1200 1300 1400 1500
Temperature［℃］

900 1000 1100 1200 1300 1400 1500
Temperature［℃］

Fig.４

Temperature dependence of densification rate（dρ／dT ）of 3Y and 3YE atvarious heating rates.（○）,（□）, and（△）are 5, 10, and 20℃／min,
respectively. The data measured at a 15℃／min heating rate were also
obtained in the similar manner.

8.0

8.0

3YE
dT dρ
In｛T
（−dt
−）
（−
−）［K／min］｝
dT

dT dρ
In｛T
（−dt
−）
（−
−）［K／min］｝
dT

3Y
7.0

6.0

5.0

7.0

6.0

5.0

4.0

4.0
6.8

7.0

7.2

7.4

7.6

104／T［K−1］

Fig.５

6.8

7.0

7.2

7.4

7.6

104／T［K−1］

Arrhenius−type plots for the estimate of activation energies of sintering.
（○）,（□）,（△）,（◇）, and（●）are 50, 51, 52, 53, and 54％ relative densities,
respectively. The data of 50.5, 51.5, 52.5 and 53.5％ relative densities werealso obtained in the similar manner.

（ 13 ）

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TOSOH Research ＆ Technology Review Vol.51（2007）

initial sintering condition without grain growth.

(2) and (3) to the results of the above shrinkage

Figure 6 shows the Q and αB - or αV -term in the ρ

measurements.

range of 50-54％.

In this ρ range, the Qs of 3YE werelower than those of 3Y (Fig. 6(A)).

Equations (2) and (3) were applied in

the following way.

By assuming both GBD and VD in

Determination thethe same fractional shrinkage range as above, theaverage Qs of 3Y and 3YE in the ρ range of 50-54％,

values of Q/m were determined from the slopes of thethe average Q of 3YE was lower than that of 3Y (TableII).

GBD- and VD-type plots, respectively.

Wang and Raj4) reported that the Q for sintering ofAs an example,

the GBD- and VD-type plots for 3Y and 3YE at a 5℃

zirconia with 2.8 mol％ (5.0 mass％ ) Y 2 O 3 was/min heating rate are shown in Fig. 7.

determined using CRH techniques and by applying Eq.

VD-type plots of both 3Y and 3YE revealed nearly linear(6) and was estimated to 615±80 kJ/mol.

relations.

Compared

The GBD- andThe values of Q/m for causing GBD andwith that value, the average Q (688 kJ/mol) of 3Y

VD were estimated as the average of that determined

determined by the present analysis is considered to befrom the GBD- and VD-type plots of each heating rate,

reasonable.

The behaviors of the αB - or αV -term ofrespectively (Table II).

Using the values of average Q

3Y and 3YE also revealed tendencies similar to those of

and Q/m, the orders (m) depending on the diffusion

the Qs (Fig. 6(B)).

path of material transport at the initial sintering stage

According to Eqs. (9) and (10),the low value of αB or αV of 3YE suggests that the γwere determined by Eq. (13) (Table II).

of Y-TZP particles was reduced by Al 2 O 3 -doping.

m of GBD and VD of 3Y were both close to 3, and their

These analytical results revealed that Al2O3 doped in Y-

values of 3YE were both close to 2.

TZP powder decreased the average Q at the initialaccount that the values of m of GBD and VD

sintering stage.

correspond to 3 and 2, respectively, the diffusion paths

The values of
Taking into

It is assumed that the decrease in the average Q

of 3Y and 3YE is assigned to GBD and VD, respectively.

appearing as a result of the present of Al2O3 occurs by

In previous papers, the author analyzed the initial

the change of the diffusion path.

In order to estimate

sintering behavior of Y-TZP powder with and without athe order depending on the diffusion path, the values ofsmall amount of Al 2O 3 by the isothermal shrinkage

Q/m of 3Y and 3YE were determined by applying Eqs.

analysis, and reported that Al2O3 changes the diffusion

80

800

（B）

600

αB− or αV−termActivation energy［kJ／mol］

（A）

400

60

40

20

200

0

0
50

51

52

53

54

Relative density［％］

Fig.６

Table２

50

51

52

53

54

Relative density［％］

Activation energy and αB −or αV −term of 3Y and 3YE at 50−54％ relative
densities.（○）and（□）are 3Y and 3YE, respectively.

Activation energies, apparent activation energies, and orders depending on diffusion path

Specimen

3Y
3YE

Activation energy（kJ／mol）
Standard
Q
deviation
688
58
605
31

GBD
Q／m
222
259

Apparent activation energy（kJ／mol）
Standard
Standard
VD
Q ／m deviation
deviation
221
5
5
258
4
4

（ 14 ）

Order ondiffusion path（ m ）
GBD

VD

3.1
2.3

3.1
2.3

東ソー研究・技術報告 第51巻（2007）

3.5
GBD−type

In｛T3／2・d（△L／L0）／dT［K1／2］｝

In｛T5／3・d（△L／L0）／dT［K2／3］｝

5.0

15

4.5

4.0

3.5

VD−type

3.0

2.5

2.0

3.0
7.0

Fig.７

7.1

7.2
7.3
104／T［K−1］

7.4

7.0

7.1

7.2
7.3
104／T［K−1］7.4

GBD−and VD−type plots of 3Y and 3YEin the course of heating（5℃／min）.
（○）and（□）are 3Y and 3YE, respectively.

path at the initial sintering stage from GBD to VD.12)-15)dρ/dT of 3YE relates to the solubility of Al2O3 in Y-

The analytical results of 3Y and 3YE agree with these

TZP, and the dρ/dT increases with increasing amountreports.

of dissolved Al2O3.

It is, therefore, clarified that the diffusion

The author has reported that thepath of material transport at the initial sintering stage

microstructure development in 3Y and 3YE during

can be experimentally determined by applying thesintering which was analyzed using high-resolution

present analytical method to CRH experiments.

electron microscopy and nanoprobe X-ray energy

Taking into account the results obtained in thedispersive spectroscopy techniques. 18)-21)

In thesepresent CRH analysis, it is clarified that the role ofanalytical results, it has been showed that noAl2O3 doped in Y-TZP powder changes the diffusion

amorphous layer exists along the grain-boundary faces

path at the initial sintering stage from GBD to VD, andin 3Y and 3YE, but Y 3+ ions segregate at the grain

the dρ/d T remarkably enhances because of theboundaries over a width of 〜10 nm, and in 3YE, Al3+

decrease in the Q with the GBD → VD change.

ions also segregate at grain boundaries over a width of［4］ Al2O3 effectIt is generally known for the comparison in the sameoxide that the Q for causing GBD is smaller than that

〜6 nm.

As shown in Fig. 8, in the 3YE sintered at

1100℃, Al

3+ions have already segregated at grainboundaries, and the segregation of Al3+ ions increases
with increasing sintering temperature.20)

Taking into

Therefore, the Q for VD of Y-TZP

account these reports, it is concluded that as the result

without Al2O3 is assumed to be a value of > 688 kJ/mol,of segregated dissolution of Al 2 O 3 at Y-TZP grainbecause the Q for GBD of 3Y was estimated to 688

boundaries, the diffusion path changes to VD and the Q

kJ/mol by the present CRH analysis.

In the present

for VD is lower than that for GBD of Y-TZP without

results, Al2O3 changed the diffusion path of material

Al2O3. Because the decrease of αV-term of 3YE in Fig.

transport at the initial sintering stage from GBD to VD

6(B) indicates a decrease in the γ of Y-TZP powder,and, contrary to the general tendency above, the Q (605

the segregated dissolution of Al 2O 3 at Y-TZP grainkJ/mol) for VD of 3YE was smaller than that for GBD

boundaries may be considered.

for causing VD.

of 3Y.

These results evidently exhibit that a small

amount of Al2O3 directly affects the diffusion path at theinitial sintering stage of Y-TZP powder.

５．Conclusions

Al2O3 and ZrO2 (without Y2O3) are known to exhibit

In the present study, the author derived thevery limited mutual solubility (〜0.1％ at 1300℃), andanalytical method used for CRH techniques by which

the solubility of Al 2 O 3 in ZrO 2 increases as thethe diffusion path at the initial sintering stage can be16), 17)temperature increases.

Analogizing from thesereports, it is assumed that the behavior of the enhanced

determined experimentally.

To substantiate thevalidity of the derived analysis method, the initial（ 15 ）

16

TOSOH Research ＆ Technology Review Vol.51（2007）

8

8
1500℃
Y2O3 or Al2O3 concentration［mol％］

Y2O3 or Al2O3 concentration［mol％］

1100℃

6

4

2

0

6

4

2

0
−10

−5

0

5

10

−10

−5

Distance from grain−bonudary［nm］
8

5

10

8
1650℃
Y2O3 or Al2O3 concentration［mol％］

1200℃
Y2O3 or Al2O3 concentration［mol％］0Distance from grain−bonudary［nm］

6

4

2

0

6

4

2

0
−10

−5

0

5

10

−10

Distance from grain−bonudary［nm］

−5

0

5

10

Distance from grain−bonudary［nm］

8
Y2O3 or Al2O3 concentration［mol％］

1300℃

6

4

2

0
−10

−5

0

5

10

Distance from grain−bonudary［nm］

Fig.８

Y− and Al−concentration profiles across the grain boundaries in 3YEs sintered at 1100−1650℃.20）（○）and（□）indicate Y and Al, respecitively.

sintering mechanisms of Y-TZP powder with andobtained:

without a small amount of Al 2O 3 were examined by（1）A small amount of Al2O3 doped in Y-TZP powder

applying this method.

The following conclusions were
（ 16 ）

enhanced the sintering rate remarkably, whereas東ソー研究・技術報告 第51巻（2007）17

the grain-growth process was hardly affected at theshown in Eq. (A6), (ΔL/L0)3.06 can be expressed as thehold time of 2h in the present sintering profile.

function of density, FB(ρ).

CRH measurements revealed that Al2O3 doped in（

Y-TZP powder remarkably increased the dρ/dT in

）

（A6）

Differentiating Eq. (A6) with respect to ρ, one obtains

the low-temperature range of < 〜1300℃.
（2）By applying the present analytical method to theEq. (A7).

d ΔL 3.06d＝ dρ F（＝ F'B（ρ）
B ρ）
dρ L 0306
ΔL
d L＝ F'B（ρ）dρ0

CRH shrinkage curves, it is clarified that the Al2O3（

effect on the initial sintering stage changes theincreases the dρ/dT because of the decrease in）（diffusion path from GBD to VD, and remarkably
the Q with the GBD → VD change.

ΔL 3.06＝FB（ρ）
L0）（A7）

Combining Eqs. (A7) and Eq. (A5) gives

This

dρ
Tc dT ＝enhanced sintering mechanism is reasonably

2.14γΩD 0B
1
Q・・exp −
k 4
F'（
RT
B ρ）

（

） （A8）

explained by the segregated dissolution of Al2O3 at

Here, when F' B (ρ) is formally placed as 1/f B (ρ)

Y-TZP grain boundaries.

(namely, F'B(ρ)＝1/fB(ρ)), Eq. (A8) can be expressed（3）The present analytical method derived based onby Eq. (A9).

the sintering kinetics at CRH is very useful for2.14γΩD 0Bdρ
Q
Tc dT ＝ fB（ρ）
・・exp −k 4
RT（determination of the diffusion mechanism at the

Substituting c＝dT/dt into Eq. (A9) and taking

initial sintering stage of ceramic powders.

logarithms, one obtains

Appendix

reported by Johnson. 1)

If the isothermal shrinkage

000.7γΩ・bDB
dt
kT 4

0.7γΩ・bDB

0

4

ΔL 1.032.63γΩDVdt
kT 3（ L ） d（ΔL ／L ）＝
0

0

（A2）

△ L 2.06
0.7γΩ D0B
d（ΔL ／ L0 ）＝
L0
k 4c
exp
（−Ｑ ／RT ）dT
（A3）
・
T

）

ΔL 1.03002.63γΩD 0B
k 3c
exp（−Ｑ ／RT ）dT （A11）・T

Integrating and differentiating Eq. (A11) at the same
conditions as above result inddT

ΔL 2.03（L ） ＝
05.34γΩD0B exp（−Ｑ ／RT ）
（A12）
・
T
k 3c

Integrating Eq. (A3) at the ranges of ΔL/L0=0→ΔL/L0

Here, (ΔL/L0)2.03＝FV(ρ).

and T=T0→T results inequation with respect to ρ leads to

ΔL 3.06

ΔL 2.03
d L＝ F'V（ρ）dρ02.14γΩD 0B T exp（−Ｑ ／RT ）∫T
dt （A4）Tk 4c
0Here, T0 is a room temperature.

The differentiation of（（

ΔL 3.06
2.14γΩD0B exp（−Ｑ ／RT ）
（A5）
＝
・
L0
T
k 4c

）

Since the ΔL/L 0 is correlated with the density, as

The differentiation of this

）

（A13）

Substituting Eq. (A13) into Eq. (A12) results in

Eq. (A4) with respect to T gives

d
dT

（A10）

（ L ） d（ΔL ／L ）＝

becomes0（9）results indT

Substituting Eq. (4) into Eq. (A2) (i.e., eliminating bDB)（L ） ＝］− 41nSubstituting dt＝dT/c and Eq. (5) into Eq. (A10)

one obtains the following equation.
02.14γΩD 0B
k

VD, Eq. (1) can be expressed as Eq. (A10)(namely, dt＝dT/c) into Eq. (A1) and eliminating dt,△ L 2.06（8）

B

If the isothermal shrinkage process proceeds only at（A1）

Substituting the differential equation of heating rate

（ L ） d（ΔL ／L ）＝ kT cQ

αB＝ ln［ f（］＋ ln［B ρ）

expressed as Eq. (A1).

△ L 2.06

dρ

where

process proceeds only at GBD, Eq. (1) can be（ L ） d（ΔL ／L ）＝dT［ （ dt （）dT ）］＝− RT ＋α

ln T

Eqs. (8)-(10) can be derived as follows, using Eq. (1)（） （A9）

5.34γΩD 0Vdρ
Q
Tc dT ＝ fV（ρ）
・・exp −
k 3
RT（Here, fV(ρ)＝1/F'V(ρ).

） （A14）

Substituting c＝dT/dt into

Eq. (A14) and taking logarithms, one obtains（ 17 ）

18

TOSOH Research ＆ Technology Review Vol.51（2007）

dTdt16）S.N.B.Hodgson, J.Cawley, M.Clubley, J. Mater.

dρQdT ＝− RT ＋αV［ （ （） ）］

ln T

（8）

Process. Tech., 92-93, 85(1999).
17）Edited by H.M.Ondik and H.F.McMurdie,

where

αV＝ ln［ f（］＋ ln［V ρ）

5.34γΩD 0V
k

Phase

Diagrams for Zirconium and Zirconia Systems, ;］− 31n （10）p 63 (Fig. Zr-084), Am.Ceram.Soc., Ohio, 1998.
18）K.Matsui, H.Horikoshi, N.Ohmichi, M. Ohgai,
H.Yoshida, and Y.Ikuhara, J.Am.Ceram.Soc .,Acknowledgement86(8), 1401(2003).

The author would like to express his sincere thanks to19）K.Matsui, N.Ohmichi, M.Ogai, H.Yoshida, andProfessor Junichi Hojo, Kyushu University, for his

Y.Ikuhara, J.Ceram.Soc.Jpn, 114(3), 230(2006).

valuable advice in this work.

20）K.Matsui, N.Ohmichi, M.Ogai, H.Yoshida, andY.Ikuhara, J.Mater.Res, 21(9), 2278(2006).
21）K.Matsui, H.Yoshida, and Y.Ikuhara, Mater. Sci.

Reference

Forum, 558-559, 921(2007).

１）D.L.Johnson, J.Appl.Phys., 40(1), 192(1969).
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５）D.L.Johnson and I.B.Cutler, J.Am.Ceram.Soc .,46(11), 541(1963).
６）D.L.Johnson and I.B.Cutler, J.Am.Ceram.Soc .,46(11), 545(1963).
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11） Edited by T.Yamaguchi and H.Yanagita,

Enjiniaringu Seramikkusu,; pp.22-25, Gihodo,

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M.Uehara,

N.Enomoto,andJ.Hojo,J.Ceram.Soc.Jpn ., 112(5, Supp. 112-1, PacRim5
Special Issue), S343(2004).
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14）K.Matsui, A.Matsumoto, M.Uehara, N.Enomoto,and J.Hojo, J.Am.Ceram.Soc., 90(1), 44 (2007).
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（ 18 ）

東ソー研究・技術報告 第51巻（2007）

著者

氏名 松 井 光 二
Koji MATSUI入社 昭和61年 4 月 1 日
所属 東京研究所
新材料・無機分野
主席研究員（ 19 ）

19