Article pubs.acs.org/crystal
Chemical Segregation of Titanium in Sapphire Single Crystals Grown by Micro-Pulling-Down Technique: Analytical Model and Experiments A. Nehari,†,‡ T. Duffar,† E.A. Ghezal,‡ and K. Lebbou*,‡ †
SIMAP-EPM, UMR 5266 CNRS, 38402 Saint Martin d’Hères, France Institut Lumière Matière, Université Lyon 1UMR 5306 CNRS, 69622 Villeurbanne, France
‡
ABSTRACT: The micro-pulling-down (μ-PD) process consists in pulling a crystal under a capillary channel placed at the bottom of a crucible. Despite it being limited to rather small liquid volumes, it is used to grow single crystal fibers and shaped crystals of various cross sections, mainly applied industrially for optical applications, such as lasers, optics, or scintillators. Consequently, those crystals should be doped with active elements to fit the target application. Unfortunately, whatever the growth parameters and the dopant type, quite often segregation problems are observed. It is generally believed that chemical partition in μ-PD technique is restricted to the first grown millimeters, but some experiments show that it is not always the case. An analytical onedimensional model is presented, aiming to predict the longitudinal segregation along the growth direction. It is shown that it depends in practice on growth parameters such as capillary length, meniscus height, capillary section, and pulling rate. The characteristic numbers controlling the segregation profile are derived and a parametric study is performed in the case of Ti-doped sapphire single crystal fibers. Ti3+:Al2O3 single crystal fibers oriented along c-axis have been grown under stationary stable growth regime using different pulling rates and the longitudinal chemical segregation has been characterized by photoluminescence. Results are in agreement with the model predictions.
1. INTRODUCTION The micro-pulling-down (μ-PD) technique (Figure 1) has become one of the main methods for production of highquality single crystal fibers.1,2 Various types of novel singlecrystal fibers have been grown by this process with remarkable excellence in diameter control and concentration uniformity. This method is interesting for the production of as-grown fiber
crystals for a broad range of applications, especially lasers and scintillation applications.3−6 It is generally accepted that a hanging meniscus combines capillary stability by die anchoring with positive gravity effect and good liquid homogeneity because of strong Marangoni convection. It results in a more uniform distribution of dopants or solutes in the crystal than in the case of pulling upward methods, such as EFG technique. Incidentally, control of dopant and impurities in the grown crystal is important, which is not a priori obtained because of the well-known chemical segregation linked to solidification.7 In general, the μ-PD fiber growth technique provides quite favorable conditions for axial homogeneous component distribution such as high pulling rate, small solidifying volume and small melt volume separated by the capillary die channel. Additionally, the high axial temperature gradient, as high as 1000 K/cm2, and nearly unidirectional heat flow ensure morphological stability of the growing interface. However, experiments show that homogeneous longitudinal composition is not always obtained. In the present paper, an analytical and experimental study of chemical segregation in micropulling-down process is discussed. Ti3+-doped sapphire crystal fibers (later referred as Ti3+:Al2O3), oriented along c-axis, have been grown under stationary stable growth regime using different pulling rates and the longitudinal chemical segregation has been characterized by photoReceived: September 10, 2014 Revised: October 22, 2014 Published: October 31, 2014
Figure 1. Schematic illustration of the micropulling-down growth process. © 2014 American Chemical Society
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dx.doi.org/10.1021/cg5013582 | Cryst. Growth Des. 2014, 14, 6492−6496
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3. ANALYTICAL MONODIMENSIONAL MODEL OF SEGREGATION Our objective in this section is to derive a model to quantify a priori the concentration variations along the grown fiber axis as a function of the various experimental parameters. The model is monodimensional, that is, the composition in the crystal depends only on the abscissa measured in the growth direction, noted z. Another assumption is that the partition coefficient, linking the equilibrium liquid and solid concentrations CS and CL, k = CS/CL, is constant, which is generally the case in dilute materials. As initial condition, a homogeneous melt is assumed, at composition C0. According to the treatment of chemical segregation presented in chapter 2 of ref 1, two zones are considered close to the solidification interface: the meniscus and the capillary channel. Two extreme cases will be considered: either the convective movements in the meniscus are negligible, then the transport is diffusive, either they are preponderant; the liquid is then assumed homogeneous. When diffusion occurs, conservation of the mass of solute in each of the phases can be written in the frame of the solid−liquid interface:
luminescence measurement. A segregation model is proposed in order to explain the experimental observations.
2. EXPERIMENTAL SECTION Single-crystal fibers were grown by the micro pulling down technique. A cylindrical iridium crucible, 6 cm3 in volume and insulated with alumina ceramic, was heated inductively by a 25 kW RF generator. The capillary inner and outer diameters were 0.5 and 1 mm. Starting material is pure alumina (RSA Company, purity ≥99.998%) charged with 0.2 wt % TiO2. Fibers of diameters about 1 mm and length up to 1 m were grown along the c-axis with different pulling rates: 0.2 and 5−17 μm.s−1. The atmosphere was 1 bar of pure argon (purity ≥99.998%, an tube inox is used between argon bottle and the growth chamber) to prevent Ir crucible oxidation at low temperature.8 The whole assembly is maintained in a fused silica tube, which allows control of the ambient gas and enables visualization of the grown crystal including the meniscus zone by CCD camera (see Figure 1). The heating and cooling program are automatically controlled using appropriate software.9,10 The sapphire seed crystal is connected to the melt at the bottom of the Ir capillary die, and the heating power is adjusted until a stable meniscus is formed.11 Then the molten zone volume and meniscus length are controlled by careful adjustment of the heater power. Figure 2 shows different Ti3+:Al2O3 fibers with various Ti concentrations. The crystals are transparent and the contrast of the color depends on titanium concentration.
∂C L ∂ 2C L ∂C =D + Uliquid L 2 ∂t ∂Z L ∂Z L
(1)
where D is the solute diffusion coefficient in the liquid and U the fluid velocity. This gives the concentration profile in the liquid in the meniscus or in the capillary, with a boundary layer of the form7 C L = C0 + (C* − C0)e−UliquidZ / D
(2)
with C* the concentration at the interface or at the capillary exit. The geometry in which the system is studied is shown on Figure 3. h is the meniscus height, l capillary length, Dcr crystal Figure 2. Ti3+:Al2O3 single crystal fibers with various Ti concentrations.
Chemical segregations are measured by μ-luminescence characterization, which does not give absolute concentration, but is linearly proportional to its variation. The luminescence spectra were investigated under second Nd3+: YAG harmonic (532 nm) pulsed laser excitation (Spectra Physics Quanta-Ray, GCR130), which deliver pulses of 10 ns duration and 0.1 cm−1 spectral widths. The laser signal is reflected by two mirrors to pass through an optical microscope to excite horizontal surface of about 50 μm of the studied sample. Time resolved spectra acquisition with the following features: delay times and strobe pulse duration: 1 ns to 19 ms; spectral detection range: 200−900 nm were performed after the excitation pulse. The luminescence observed was analyzed by a f-125 monochromator with a grating of 400 and 1200 grooves/mm and detected by an Instaspec V detector, which combines the advantages of a gated intensified charge-coupled device (CCD) camera (calibrated using the standard Hg lamp rays).12 All the measurements were carried out at room temperature, and the analyzed crystals were not polished. The first millimeters are not significant because generally some liquid, from previous crystal growth experiment, remains at the bottom of the crucible and in the capillary. Then the first millimeter of fiber is not representative of the initial segregation of the grown sample.
Figure 3. Simplified geometry of the μ-PD crystal growth process.
diameter, and Dcap capillary inner diameter. The change of meniscus section is neglected. Neglecting the change of density between liquid and solid, a simple relation joins the puling rate V and the fluid mean velocity in the capillary channel ⎛ D ⎞2 U = V ⎜⎜ cr ⎟⎟ ⎝ Dcap ⎠
(3)
3.1. Diffusion in the Meniscus. Generally strong Marangoni convection occurs in the meniscus, which will be considered in the next paragraph. However, if some layer blocks 6493
dx.doi.org/10.1021/cg5013582 | Cryst. Growth Des. 2014, 14, 6492−6496
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Article
Table 1. Physical Parameters Used in the Calculations parameters
D (m2/s)
h (mm)
l (mm)
k
Dcap (mm)
Dcr (mm)
C0 (at %)
V (m/s)
values
5 × 10−9
0.3
1
0.2
0.5
1
0.2
variable
Figure 4. Theoretical profiles of the concentration along the crystal for different values of the growth rate and for the different cases.
surface convection, it may happen, in some rare cases, that diffusive conditions occur in the meniscus. An obvious solution is for very high growth rate, where the boundary layer thickness is smaller than the meniscus height, D/V < h, which simply gives the classical equation of segregation in purely diffusive conditions.13 For slowest growth rates, two cases are considered.
Combining the two diffusion equations, in the meniscus and in the capillary, gives the parameter α14 α=
−
D −V / Dh (e Vk
− 1)
(5)
D D > h and >l V U
D D > h and
