Journal of Crystal Growth 130 (1993) 233237 NorthHolland
,o . . . . . o, C M Y S T A L Q I R O W T H .U
Measurement of the distribution coefficient of neodymium in cubic ZrO., H. RiSmer, K.D. L u t h e r and W. Assmus Physikalisches bzstitut, J.W. Goethe Universitiit Frankfurt/M, RobertMayerStrasse 24, DW6000 Frankfurt/M, Germany Received 14 July 1992; manuscript received in final form 10 November 1992
The incorporation of solute elements into single crystals has been examined for many years. In this paper we investigate the distribution coefficient of Nd20 3 in cubic stabilized zirconiumdioxide crystals. The distribution coefficient is measured as a function of the growth velocity. The validity of the BurtonPrimSlichter theory [J A. Burton, R.C. Prim and W.P. Slichter, J. Chem. Phys, 21 (1953) 1987] for the system zirconium dioxide/yttrium oxide is confirmed by the experimental results. The value for the equilibrium distribution coefficient is evaluated as k o = 0.426.
1. Introduction With the development of the skullmelting technique it has become possible to grow large cubic zirconium dioxide crystals (Aleksandrov et al. (1978)) [1]. This material is of great industrial interest especially as diamond imitation. By doping the crystals, various colourings can be obtained. An unsolved problem is the inhomogeneous distribution of the dopants in the bulk crystals. Therefore the knowledge of the distribution coefficients is important.
2. Growth technique Zirconium dioxide is a material with a melting point of about 2750°C. The crystals are grown with the skullmelting technique. This technique eliminates reaction and contamination encountered in crystal growth using crucibles. A detailed description of the skull method is given by Aleksandrov et al. [1]; in the following we only give a brief overview. We use a crucible with watercooled copper fingers. The heating is performed by absorption of RF energy. Zirconium dioxide powder, which
is filled into the crucible at the beginning, is an insulator at room temperature and a conductor at higher temperature. Therefore it can be heated by eddy currents only at high temperatures. To start the heating process, zirconium metal is embedded into the powder and couples directly to the highfrequency field. The hot metal increases' the temperature of the surrounding powder, decreases its electrical resistivity and the RF energy couples directly with the hot powder. Now the material can be heated to the melting temperature. The powder next to the watercooled walls remains cold and is therefore transparent for the RF energy. This powder forms the "container". While the input power is reduced and the crucible is slowly pulled out of the R F field, the crystals start to grow. We are able to control this process by a programmer. Therefore the growth parameters and results are reproducible.
3. Experiments and results To determine the real growth velocity of the crystals, many growth experiments with different parameters are performed. During crystallization the melt is doped in defined steps to mark the
00220248/93/$06,00 © 1993  Elsevier Science Publishers B.V. All rights reselved
H. RSmer et al. / Measurement of distribution coefficient of Nd in cubic ZrO 2
234
Fig. 1. Cubic zirconium dioxide single crystal with marked crystallization front.
front of crystallization at different times. We use several dopants (especially 3d and 4f oxides) which cause various absorption bands in the visible spectra and therefore the crystals show differently coloured sections. An example of such a crystal, where the front of crystallization is marked twice, is shown in fig. 1. After measuring the length of the coloured sections~ we can calculate the real growth velocity of the crystals which may be different from the lowering speed. We are able to vary the growth velocity for different charges from 4 to 14 mm/h with an accuracy of + 1 mm/h.
0
5000
0
4200
0
3400
Pure cubic zirconium dioxide has a calcium fluoride type structure only at high temperature. While adding Y203 in the range of 8 to 35 mol%, the cubic phase can be stabilized down to room temperature. In these examinations we always use 12 tool% Y203 to stabilize the cubic phase. The undoped crystals are colourless and show good transparency in the visible range and a steplike increase of the absorption towards the ultraviolet region. The energy gap, which depends on the yttrium and oxygen concentration, is in the range of 4 eV. While doping the crystals with different elements (especially rare earth oxides), absorption bands in the visible region appear. The intensity of these bands is a function of the dopant concentration (LambertBeer law). Crystals from growth experiments, where the whole melt is crystallized and the growth velocity is not constant, often show inhomogeneities in concentration along the growth direction. Deviation of the distribution coefficient from 1 and dependence of the distribution coefficient on growth velocity cause these variations. The investigation of these relations for the system ZrO2/Y203 at which the liquid phase is doped
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Fig. 2. Absorption spectrum of Nd ~ * in ZrO 2/Y203.
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H. RSmer et aL / Measurement of dist.~.bution coe~cient of Nd i. cubic ZrO,
use a Lambda16 spectrophotometer (PerkinElmer) for the absorption measurements. To determine the concentration we observe the most intensive absorption band of neodymium oxide at 590 nm because of signal/noise ratio (fig. 2). A E S measurements are done to calibrate the extinction coefficient and to check for our system the validity of the LambertBeer law E = a c s d ( E = extinction, a = extinction coefficient, cs= concentration of Nd 3÷ in the crystal, d = thickness). The results are shown in fig. 3, in which the extinction E is normalized to a thickness of 1 mm. The extinction coefficient a = 0.179 + 0.005 mol%  t is obtained as a result of these experimental data. Fig. 4 shows the concentration profiles of some experiments with different rates of crystallization. At the beginning and at the end of the crystals, large fluctuations in concentration caused by fluctuations in growth velocity can be observed. In these regions the growth velocity is very, difficult to control. Spontaneous nucleation, the influence of the crucible bottom which absorbs itself RF energy, and the influence of radiation loss at the top of the cnmihle are the main reasons for this. In the centre of the crucible the growth velocity, and therewith the dopant concentration, is
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Nd 3+ concentration [mol%] Fig. 3. Optical extinction versus Nd3+ concentration in cubic zirconium dioxide (the concentration calculations are based on the cation concentrations).
with 1.2265 wt% N d 2 0 3 is the topic in the following. The crystals, which are grown with defined growth velocity (v) in the range of 4 to 14 m m / h , are cut in parallel plates with a thickness of about 2 mm along the growth direction and polished with diamond paste with particle size of down to 3 txm. Then the Nd3+ion concentration is measured by optical absorption in steps of 1 mm. We
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Fig. 4. Nd3+ concentration profiles for crystals grown with different growth velocities.
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H. R&ner et al. / Measurement of distribution coefficient of Nd in cubic ZrO 2
230
nearly homogeneous. We use this region for our investigations. In general the effective distribution coefficient is defined as the ratio of the solute concentration in the solid phase to the solute concentration in the liquid phase. Cubic zirconium dioxide is a solid solution which consists of Zr 4+ ions and y3+ ions with a distribution coefficient of about 1.09 (given by Aleksandrov et al. [1]). Therefore the effective distribution coefficient for Nd 3+ ions in this system has to be defined exactly as: [Nd3+] [Zr4+ ]
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[y3+ ] + [Nd3+ ] ,,
+
k off 
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[Nd3+] [ Zr4+l + [ Y ' + ] + [ Nd3+]
Table 1 Growth velocity and effective distribution coefficient for different growth experiments
v (mm/h)
ker[
4 4 6 6 8 8 10 10 12 12 14 14
0.51 +0.016 0.52 + 0.025 0.54t0.013 0.54 + 0.013 0.61 + 0.025 0.60 + 0.03 0.63 :t: 0.006 0.68 + 0.038 0.68+0.019 0.65:1:0.013 0.73 + 0.06 0.70 + 0.06
" ,
The sum of the ions in the solid and in the liquid phase is supposed to be equivalent, which results in a systematic error smaller than 0.5%. Because the quantity of melt is large compared to the quantity of the solid phase, we can assume the concentration of the dopant in the melt to be constant. With these assumptions the effective distribution coefficient can be calculated as a function of growth velocity. This relation and the experimentally obtained values are shown in fig. 5 and table 1.
We assume the BurtonPrimSlichter (BPS) theory to be valid for our system. The BPS equation [2] is: k0 keff =
ko)
k 0 + (1 
exp(va/D)
'
where 8 is the boundary layer thickness and D is the diffusion coefficient. This equation is solved graphically (fig. 6) with the parameters kef f and v. With regard to the limited accuracy of the measurements, the curves intersect in one point, as one would expect if the
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Fig. 5. Distribution coefficient as a function of the growth velocity.
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il~,,. 6. Graphic solution of the BPS equation. Each curve belongs to a different growth velocity (in ram/h): (1) 4: (2) 6; 13) 8; (4) 10: {5) 12: (6i 14.
H. R6mer et al. / Measurement of distribution coe~cient of Nd in cubic ZrO:
BPS theory is valid. As a result from the linear regression at which growth velocit3' c against In(1/k~ff 1) is plotted, we obtain k 0 = 0.426 + 0.013 and t~/D = (3,1 + 0.2) × 103 s / c m . These values are conformable to the graphic solution. The diffusion coefficient for the system is unknown, but typical values for D in melts are in the order of 5 x 10 5 cm2/s. With this assumption we can estimate the thickness of the boundary layer at the liquidsolid interface, where the transport of the dopants by diffusion is large compared to convection. We get ~ ~ 1 mm, which seems to be a realistic estimation for the system.
~7
Acknowledgement We thank D. Swarovski & Co. for executing the AES measurements and financial support of this work.
References [1] V.I. Aleksandrov, V.V. Osiko, A.M. Prokhorov and V.M. Tatarintsev, in: Current Topics in Materials Science, Vol. 1, Ed. E. Kaldis (NorthHolland, Amsterdam, 1978) p. 421. [2] J.A. Burton, R.C. Prim and W.P. Slichter, J. Chem. Phys. 21 (1953) 1987.