Gas-bubble formation of ruby single crystals by floating zone method with an infrared radiation convergence type heater

664

Journal of Crystal Growth 71 (1985) 664-672 North-Holland, Amsterdam

GAS-BUBBLE FORMATION OF RUBY SINGLE CRYSTALS BY FLOATING ZONE METHOD WITH AN INFRARED RADIATION CONVERGENCE TYPE HEATER

Masatoshi SAITO Suwa Seikosha Co., Ltd., Suwa-shi, Nagano, Japan Received 4 November 1984; manuscript received in final form 4 February 1985

The incorporation of bubbles in ruby single crystals grown by the floating zone method with an infrared radiation convergence type heater was investigated by the Experimental Design Method. The effect of experimental parameters when making specimens or pulling ruby single crystals on bubble formation was analyzed to obtain bubble-less ruby single crystals. It was found that crystal diameter, growth rate, atmosphere during the growth of crystals and sintering conditions had a large influence on bubble formation. These parameters were effective in reducing the bubble density. The model proposed that gas constituents were being rejected from the solidified melt at the interface was consistent with experimental results.

1. Introduction

Bubbles which are often observed in oxide single crystals made by the floating zone method are similar to those in crystals grown by the Czochralski method, and are one of the important problems to solve to improve single crystal quality. There have been several reports on the mechanisms involved in bubble formation during Czochralski growth. For example, Miyazawa [1] theorized that bubbles are due to the capture of gas bubbles displaced from the melt adjacent to the interface where the bubbles nucleated homogeneously. Cockayne [2] theorized that bubbles were caused by the segregation of dopant impurities and/or gaseous impurities associated with cellular growth caused by constitutional supercooling. Kobayashi [3] concluded that bubbles were heterogeneously formed at the interface because of the rejected gas into the melt from the solidified melt. Their common conclusion was that the crystal growth rate was the primary factor in bubble formation, but the discrepancies in their studies have not been settled yet. No detailed reports on bubble formation in the floating zone method exist. This paper proposes a mechanism which is responsible for bubble formation in the floating

zone method using an infrared radiation convergence type heater, and reports experimental results done by an Experimental Design Method [4,5] concerning the possible parameters influencing the bubble reduction. The sintering conditions of the starting material, crystal growth rate, crystal diameter and atmosphere in which the crystals grow were demonstrated to be the most important parameters effecting bubble formation. The mechanism is discussed from the point of view that when the melt solidifies, the gas constituent rejected into the melt exceeds the concentration limit necessary for bubble-embryos to nucleate. Bubbles will nucleate homogeneously close to the interface. It was shown that certain features of the microstructure in the sintered specimens, especially porosity, were closely related to bubble formation.

2. Experimental

2.1. Preparation of specimens Specimens were prepared by a conventional ceramic method, this standard procedure is shown schematically in fig. 1. The alumina powder used was a type of a-A1203 or 7-A1203, with a purity of 99.99%. The concentration of dopant, chromium

0022-0248/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

665

M. Saito / Gas-bubb&formationofruby sing& crysta~

~a dMATERIALs '1 ain_Al203 ~

(i)/

opant-Cr203[ ~ R E F I R I N ~ dditive-MgOl

~ETTING

~a~s~

J

l

THE F.Z.~SINTERIN~-~RESSINq

~UL~ING]-~IN

~uasAcE

/

1600°C

(3)

Fig. 1. Ruby sin~e crystal processing flow chart.

1600°C

1600°C 15hrs

~

Heating rate;lOO°C/hr

Cooling;air cooling

Table 1 Orthogonal arrays of a strength called L8

Fig. 2. Temperature and time profilein sintering.

No.

this study the crystal growth rate was varied from 0.5 to 4 mm/h. The rotation rate ratio either in the same direction or in the opposite direction (between the rotation speed of an axis holding a sintered specimen and that holding a growing crystal) was changed from 1.0 to 2.0. The atmospheres used during crystal growth were either air, argon (purity 99.99%), or nitrogen.

Factor Growth rate Line 1

Crystal diameter Line 2

Atmosphere Line 3

1

1

1

1

2 3 4 5 6 7 8

1 1 1 2 2 2 2

1 2 2 1 1 2 2

1 2 2 2 2 1 1

Table 2 Orthogonal arrays of strength called L16

oxide, was fixed at about 1.0 wt%, and 0.1 wt% magnesium was also added. Alumina powder was prefixed at 1300°C for 2 h in an atmosphere of air or in a vacuum of 1.0 × 10 -5 Torr. The sintering patterns are shown in fig. 2. The apparatus, made by Nihon Electric Company Ltd., was used for the FZ growth of ruby single crystals and is illustrated in fig. 3. This apparatus is powered by two 3.5 kW halogen lamps and can be used to grow single crystals whose melting temperature are below 2150°C. In

No.

Factor Crystal diameter

Growth rate

Rotation ratio

1

1

4

1

2 3 4

2 3 4

3 2 1

2 3 4

13 14 15 16

4 3 2 1

3 4 1 2

3 4 3 2

Table 3 Orthogonal arrays of strength modified L8 No.

Factor Prefiring

Sintering pattern

Line 2

Line 3

Line 4

Line 5

Material

Atmosphere in sintering

Line 6

Line 7

1

1

1

1

1

2 3

1 2

2 1

2 2

2 2

4

2

2

5 6 7

3 3 3

3 3 3

1 1

1 2

2 2

1 1

8

3

3

1

2

M. Saito / Gas-bubbleformation of ruby single crystals

666

2.2. Assignment of experimental parameters by experimental designs

Table 5 Analysis of variance on bubble density in ruby single crystals corresponding to table 2

The Experimental Design Method [4,5] was used to carry out experiments more efficiently. In tables 1 - 3 orthogonal arrays of strength are shown. Table 1 shows the so-called L8 (23). The first line represents the growth rate, for instance, 1 represents 0.5 m m / h and 2 represents 4 m m / h . The second line represents the crystal diameter, 1 represents 4 mm in diameter and 2 represents 8 mm in diameter. The third line represents atmospheres during the growth of crystals: 1 represents nitrogen and 2 represents argon. The residuary lines represent the error term. The experimental parameters were also assigned to both table 2 and table 3.

Factor

SS

DF

MS

P (%)

Crystal diameter Growth rate Rotation ratio Error

27.4 98.0 15.1 22.3

3 3 3 6

9.13 32.7 5.03 3.72

10.0 53.4 2.4 34.2

Table 6 Analysis of variance on bubble density in single crystals corresponding to table 3 Factor

SS

DF

MS

P (%)

Play term Material Prefiring Sintering pattern Atmosphere in sintering

15.0 31.1 9.38 1.51 23.9

1 1 2 2 1

15.0 31.1 4.69 0.755 23.9

18.5 38.4 11.6 1.9 29.6

3. Results

The analysis of the variance tables are listed in tables 4-6. In table 4 it is seen that of the factors contributing to the bubble diameter, the growth rate is greater than the crystal diameter which in turn is greater than the atmosphere. Likewise with respect to the bubble density as shown in table 2, the growth rate is greater than the crystal diameter which in turn is greater than the rotation ratio. The contribution of the rotation ratio is extremely small. Therefore, varying the rotation ratio will not effect the bubble reduction. The crystal diameter dependence of bubble density and diameter is shown in fig. 4. The crystal growth rate dependence of bubble density and diameter is shown in fig. 5. A small crystal diam-

Sintered /~Material

Ilill

Melted ~/// ~

zooe

\j..logen

Growing ~ Crystal

\ / III~ k/ I [i[ I ~ ~-~ I IIll /

~

~

Ellipsoid Mirror Rotating and Moving axis

Fig. 3. Schematic illustration of the floating zone system with an infrared radiation convergence type heater cross section.

10 -2

10 3

1.2

6.0

o k

o

>. 4~ -M 4.0 Table 4 Analysis of variance on bubble diameter in ruby single crystals corresponding to table 1

0.8

0

o.4

2.0 Factor

SS

DF

MS

P (%)

Growth rate Crystal diameter Atmosphere Error

20.2 13.0 12.3 0.215

1 1 1 4

20.2 13.0 12.3 0.0539

44.1 28.3 26.8 0.8

SS: sum of squares; DF: degree of freedom; MS: mean square; P: contribution.

~

m ~.

I

I

4

Crystal

I

8

I

I

12

D i a m e t e r (rfgn)

Fig. 4. Crystal diameter dependence of bubble density and diameter.

M. Saito / Gas- bubble formation of ruby single crystals 10 3

I

I

I

667

-2

0, I

i0

6.0

1.2

W

I

0.8

~4.0

•

40 0

40 ¢:

0 0

0.4

2.0

O ~q n

Fig. 8. As-grown ruby single crystal pulled to the [a] axis (mm grid).

m

1.0

2.0

3.0

4.0

Crystal Growth Rate(mm/hr) Fig. 5. Crystal growth rate dependence of bubble density and diameter.

10 3 ~6.0

10 - 2 1.2

g

I

~ 4.0

0.8

40 0)

0.4

~

O O

~2.0 .n

I

I

Ar

N2 Atmo

n ,gl

I

Air

sphere

Fig. 6. Atmosphere dependence of bubble density and diameter.

eter and a small growth rate have a strong effect on the bubble reduction. The atmosphere dependence of bubble density and diameter is shown in fig. 6. An atmosphere of argon gas has a large influence on the reduction of bubbles. In the contribution to the bubble density, the starting material is contributing more than the. atmosphere used during sintering. Fig. 7 shows that by using 7-A1203 and an atmosphere of vacuum during sintering, ruby single crystals with small bubble density can be obtained. Fig. 8 illustrates a ruby single crystal, 10 mm in diameter, grown at a rate of 1 m m / h . The typical bubble distribution of ruby single crystals in this study is shown in fig. 9. Bubbles are likely to gather near the center of the crystals and the bubble density becomes smaller further away from the center. The statistically presumed value when com-

Material

~~

7-A1203

a-A1203

!

i

o

•

~

,

Vacc~m

Air

Sintering Atomosphere Fig. 7. E f f ~ t o f m a t e f i a l a n d s i n t e f i n g a t m o s p h e ~ denNty.

onbubble

Fig. 9. Typical bubble distribution of a ruby single crystal.

668

M. Saito / Gas-bubbleformationof rubysinglecrystals

bined with effective parameters, such as crystal growth rate, crystal diameter, atmosphere during the growth run, materials and atmosphere during sintering, becomes zero. In fact, experiments carried out using the best combination of parameters have yielded bubble-free ruby single crystals which were comparatively large in size.

4. Discussion

4.1. Bubble nucleation site Under equilibrium conditions the relations between specific free energies are generally given as follows [6]: OsG >> OsL, Os~ >- OLC,,,

(1)

where OSL, OS• and OLG are the specific free energy between the solid and the liquid phase, between the solid and the gas phase, and between the liquid and the gas phase, respectively. Eq. (1) means that the bubble surface energy increases when bubbles touch the interface. Accordingly, it is deduced that the interface is not an effective heterogeneous nucleation site for bubble formation. However, bubbles will be formed close to the interface because of the condensation of gaseous elements rejected into the melt layer near the interface during solidification. Therefore, if the growth rate of the crystal is higher than that of the bubble or if the interface has a cell wall structure [2], it is still easier for bubbles to be included in the crystal.

was shown to have little effect on the bubble formation so that rotation appears to play a very small part in the bubble formation. Therefore, in order to simplify the problem of calculating the gas constituent distribution in the melt, we assume that convection is negligible. A simplified floating zone model is shown in fig. 10. We will also make the following assumptions: (1) Gas is released in the melt adjacent to the interface when the melt solidifies. The solubility of the gas constituent is smaller in the crystal than in the melt [12,13]. (2) The interface separating the solid and the liquid is plane and perpendicular to the z axis. (3) The melted zone is cylindrical (r, q~, z). (4) The amount of rejected gas from the melt surface into the outside is proportional to the gas constituent in the melt near the surface. (5) The concentration of gas constituent in the melt is direction symmetric. Under these assumptions, the gas constituent distribution in the melted zone is expressed [14,15]

as: 0CL DV2Cc = Ot°

(2)

It is transformed into a coordinate system which moves with the interface

OCL = D ( 1 0t

O r OCL + _02CL _ R OCL ) °--~-r 0 Oz2 + 0z ° ,

r0 ~

(3)

where C L is the concentration of gas constituent in the melted zone, D is the diffusion coefficient, R

4.2. Effect of crystal diameter and growth rate 4.2.1. Mathematical analysis From table 2 the rotation ratio is seen to be insensitive to the bubble formation, since the contribution rate is very small. There were many reports on the effect of forced convection, caused by crystal rotation in the Czochralski method, on bubble formation [7-10]. On the other hand, Kobayashi [9] showed the mathematical analysis for forced convection in the FZ method by solving the Navier-Stokes equation. However, from the experimental results in this study the rotation ratio

Material

Crystal fro _

Fig. 10. Simplifiedmodel in this study for mathematicalanalysis.

M. Saito / Gas-bubbleformation of ruby single crystals

is the rate of movement of the interface, Z is a distance measured from the interface into the melt perpendicular to the interface, and r0 is a distance measured from the center of the cylinder into the melt parallel to the interface. The dimensionless variables are introduced to solve eq. (3): CL CCo

f=

L'

ro

'

r=-~,Z= S= D L '

Zo t

'

t=-st°"

(4)

The basic equation may be rewritten in the dimensionless form: a2C F 1 a c .O2C aC 0"-7= ar 2 r ~ +'t-~-z2 + g'-~-z"

OC

(5)

The initial conditions are

c(r, z , 0 ) = l . 0

at

0
(6)

The boundary conditions are

c(r,l,t)=l.O

at

OO, (7a)

DaC

R(1-k)CL

at

z=0and0
aC =KCL - D "~r

at

r=dandO
(7c) where C is the concentration of gas contained in the materials, L is the length of the melted zone, d is the crystal radius, K is the rejection rate of gas constituent near the surface in the melt into the exterior, k is the ratio between the amount of gas constituent remaining in the solidified melt and the amount of gas constituent in the melt at the melting point.

4.2.2. Computational results Eq. (5) is solved under the above initial and boundary conditions using the finite difference equation method. The values used for numerical computations are listed in table 7. The effect of the crystal diameter

669

Table 7 Values of the quantities used for numerical computations

a (mm/h) d (cm) D (cm2/s) K (cm/s) L (cm)

0.5,1.0 0.25, 0.5 1.0 >( 10 -6 0.1 1.0

on the concentration of gas constituent is shown in fig. 11. The concentration of gas constituent in the melt close to the interface increases with crystal diameter. This suggests that bubble formation will occur more readily with an increase of the crystal diameter, which is in fact consistent with the experimental results as shown in tables 4-6. It is necessary therefore to use a specimen of small diameter to grow crystals without bubbles. Another characteristic, as seen in fig. 11, is that the concentration near the center (i.e. r = 0) is higher than that near the surface since the surface acts as a sink where the gas constituent in the melt is released into the exterior. As a result, bubbles are more readily formed near the center of the melt than near the surface as shown in fig. 9. The effect of the crystal growth rate on the concentration of gas constituent is shown in fig. 12. The concentration of gas constituent in the melt close to the interface increases remarkably with the crystal growth rate. This is the reason why the amount of gas constituent rejected into the melt from the solidified melt greatly exceeds that released in the exterior. Therefore, bubble formai

2,0

,

~

1.8 ~ \z=O~

I

i

o.5(cm) 0.25(cm t=O.15

1.41"6~..~z= I..~ 0

1.2 i.0 0.8 0

~

.z=O. 9

.....

~

--_

%

z=O.3 f

I

I

"-,"~ I

I

0.2 0.4 0.6 0.8 1.0 r

Fig. 11. Crystal diameter dependence of gas concentration in the melt.

M. Saito / Gas-bu~& ~rmation ~ ~by smg~ c~smb

670 !

,

1.8 _

,

i

i

a) Type 1

~

1.6

ogo

°9°

o~o

Bubble

1.4

b) Type 2

1.2

z=0.9

..... 0 0 0 0 9

ggg~oo

° 0 0 0 0

oo

oo

ooooo o o o o o o o o o o o o

u i'0 0.8 . . . . .

. jz=0.3

\->~,

"-.

"

0 4 k--0 [5 (mm/hr) I

I

direction.

"'" ""

t=0"17

0.2~ I 0 0.2

grown direction Fig.13.~hematicdiagramof bubbledistributioninthegrowth

0.6 --10(mm/hr) • I

ogo

ooogo o o.ooo.o. .o o ooo~o o.oo.oo.oo .o o

t

0.4 0.6 0.8 i. r

Fig. 12. Crystal growth rate dependence of gas concentration in the melt.

tion easily occurs with an increase in the crystal growth rate, which successfully explains the experimental results in fig. 5. This model gives an explanation for the bubble distribution in the growth direction. Fig. 13 depicts the widely observed bubble distribution. Type 1 is the case of periodical bubble formation. When the concentration of gas constituent in the melt is comparatively low, the concentration decreases instantly with bubble formation. Accordingly, it will take some time to reach the concentration limit

necessary for bubble nucleation. This makes the bubble distribution periodical. On the other hand, type 2 portrays the case of a high concentration in the melt. Bubble formation has little influence on the concentration in the melt to the high concentration. Bubbles are formed continuously in the case of type 2.

4.3. Effect of atmospheres Fig. 6 indicates that argon gas was more effective in the reduction of bubbles than nitrogen gas, and nitrogen gas was more effective than the air. These facts are explained as follows. The chemical reaction equation of oxygen gas in the melt is given as follows. O(liquid) ~ ½0 2,

Fig. 14. Microstructures of sintered materials. (a) ot-Al203 in air; (b) y-AI203 in vacuum.

(8)

M. Saito / Gas-bubble formation of ruby single crystals where O is the oxygen element in the liquid. Then the equilibrium constant K is obtained: K = P ~ / 2 / a o,

(9)

where P02 is the pressure of oxygen gas and a 0 is the oxygen activity in the liquid. Eq. (9) satisfies the relation that a 0 ~ 0 as P02 ~ 0 because K is constant under a fixed temperature. As the gas activity in the melt lessens, it is more difficult to form bubbles in the melt. If the external atmosphere is argon gas, and the gas constituent in the melt is oxygen r nitrogen, the activity of oxygen or nitrogen lessens because of P02 or PN2 ~ 0. For the same reason, an atmosphere of nitrogen is more effective in reducing bubbles than air. It is speculated that the gas constituent in the melt will be air. 4. 4. Effect of sintering conditions The different microstructures found between ot-Al20 3 sintered in air and "y-A120 3 sintered in vacuum is shown in fig. 14. The density of sintered v-A120 3 is about the same as that of t~-A120 3. It can be recognized that the porosity is distributed along the grain boundaries, triple points, and in the grains. The grain sizes are not uniform and occur in the wide range of 2 to 80 /~m. On the other hand, ,/-A120 3 does not have as much porosity as a - A l 2 0 3 and t h e grain sizes are almost uniform compared with those of a-A1203 . In fact, using the alumina specimens of v-A1203 and pulling at 1 m m / h , the obvious differences in bubble density appear. The result (i.e. the use of ~,-A1203 and sintering in vacuum has an effect on the reduction of the bubble density in ruby single crystals) is shown in table 3. Therefore, it is considered that a correlation between bubble density and porosity in the sintering materials exists.

5. Conclusion The following conclusions can be drawn from the experimental results and the mathematical analysis: (1) Crystal growth rate, crystal diameter and atmosphere have a great effect on the bubble

671

formation. By keeping the growth rate slow, the diameter small and using an atmosphere of argon gas, crystals without bubbles can be obtained, (2) Materials and sintering atmosphere play an important role in the reduction of the bubble density. It is explained by the difference in the porosity of the specimens. Pores remaining in the matrix appear to play a great role in the bubble formation. (3) Using the best combination of experimental parameters, bubble-less ruby single crystals which are comparatively large in size can be obtained. (4) Bubbles seem to be homogeneously nucleated close to the interface in the melt. The interface does not seem to be a very effective nucleation site for bubble formation. (5) The model of the gas constituent distribution in the melt indicates that the bubble formation in ruby single crystals is due to the surplus gas constituent rejected from the solidified melt in the interface. This is consistent with the results of experiments.

Acknowledgement The author wishes to thank the staff of the Research and Development Division of Suwa Seikosha, Mr. K . Teraishi, Mr. K. Yamada, Mr. H. Miyasaka and Mr. M. Kunugi, for performing the experiments.

References [1] S. Miyazawa,J. Crystal Growth 49 (1980) 515. [2] B. Cockayne, M. Chesswar and D.B. Gasson, J. Mater. Sci. 2 (1967) 7. [3] N. Kobayashi, J. Crystal Growth 54 (1981) 414. [4] R.A. Fisher, Design of Experiments (Oliver and Boyd, 1951). [5] O. Kempthorn, The Design and Analysis of Experiments, (Wiley, New York, 1952). [6] B. Chalmers, Principlesof Solidification(Wiley,New York, 1964). [7] W.E. Langlois, J. Crystal Growth 46 (1979) 743. [8] J.R. Carruthes and K. Nassau, J. Appl. Phys. 39 (1968) 5205. [9] N. Kobayashi, J. Crystal Growth 30 (1975) 177. [10] M. Mihel~6, C. Schr0ck-Pauliand K. Wingerath, J. Crystal Growth 53 (1981) 337.

672

M. Saito / Gas-bubble formation of ruby single crystals

[11] C.E. Chang, J. Crystal Growth 44 (1978) 168. [12] M. Hansen, Constitution of Binary Alloys, 2nd ed. (McGraw-Hill, New York, 1958) p. 587. [13] M. Smialowski, Hydrogen in Steel (Addison-Wesley, Reading, MA, 1961).

[14] V.G. Smith, W.A. Tiller and J.W. Butter, Can. J. Phys. 33 (1975) 723. [15] J.A. Burton, R.C. Prim and W.P. Slichter, J. Chem. Phys. 21 (1953) 1987.