Article pubs.acs.org/crystal
Rapid Growth in Solution of a Solid Solution under Stationary Conditions Julien Leroudier, Julien Zaccaro,* Jérôme Debray, Patricia Segonds, and Alain Ibanez Institut Néel, CNRS & Université Joseph Fourier, UPR 2940, 25 av. des Martyrs, BP 166, 387042 Grenoble Cedex 09, France ABSTRACT: Using a rapid transport method (RTM), homogeneous crystals of intermediate compositions of the DKDP solid solution (K(H(1−x)Dx)2PO4) have been rapidly grown at constant temperatures and supersaturations. X-ray diffraction topography asserted their high crystal quality, without disorientation between growth sectors, striation, or growth bands. Micro-Raman spectroscopy showed homogeneous isotopic compositions without any drift, fluctuations, or sector segregations. These results confirm that RTM is perfectly adapted to the rapid growth of intermediate compositions of solid solutions or doped crystals.
1. INTRODUCTION Rapid growth in solution is well established for pure compounds such as KH2PO4 (KDP)1−3 or organic molecular crystals.4 However, this method labeled temperature lowering method (TLM) relies on varying the growth temperature to keep the solution supersaturated. However, the varying growth temperature or even supersaturation can prove detrimental to the growth of intermediate compositions of solid solutions or doped crystals. Indeed, the partition (segregation) coefficient between crystal and solution may vary with the supersaturation and temperature5,6 through several different processes like the diffusion of the entities, their adsorption−desorption from the growth faces, the size of the boundary layer, or the energy of formation of the associated defects. Thus, as the temperature is lowered in TLM, the growth mechanisms are altered and the resulting chemical inhomogeneities can in turn lead to tensions in the grown crystals resulting in a higher defect density. This is why constant temperature growth methods7−9 have always been regarded as more favorable for the growth of homogeneous crystals.10 In addition to chemical homogeneity, they allow to grow crystals at lower temperatures, which are beneficial for the optical properties such as the laser damage threshold.11,12 Recently, we have implemented a method13 that improves the inhibition of the nucleation compared to that used for the TLM.14 This allowed us to operate a Walker−Kohman type method7 in a rapid growth regime. Our rapid transport method (RTM) is based on the transport of the solution between two zones kept at constant temperatures, but different from one another. One is the saturation zone holding microcrystals of solute as nutrient, the other is the growth zone where the single crystals are grown (Figure 1). After demonstrating that this method allows to rapidly grow, under stationary conditions, high quality crystals for a pure © 2013 American Chemical Society
Figure 1. Rapid transport method setup used for the rapid growth under stationary conditions. It consists of two double jacketed reactors (saturation and growth), peristaltic pumps to ensure a stationary solution flow, and a continuous ultrasound-filtration unit. For details, see ref 13.
compound,13 we have tested its ability to produce homogeneous crystals in the case of intermediate compositions of a solid solution. For that purpose, we have selected the K(H(1−x)Dx)2PO4 (DKDP) solid solution as a case study. Indeed, in addition to the question of isotopic homogeneity, the stable phase of the DKDP solid solution is tetragonal only below a limit temperature that decreases with increasing deuterium concentrations.15 Such phase transition with temperature in solid solutions can set an upper limit to the applicable growth temperature and thus reduce the applicability of the TLM method. Using RTM, however, one can rapidly grow crystals of constant compositions, with high D Received: April 18, 2013 Revised: June 13, 2013 Published: June 21, 2013 3613
dx.doi.org/10.1021/cg400586r | Cryst. Growth Des. 2013, 13, 3613−3620
Crystal Growth & Design
Article
fixed on a platform. After a limited dissolution, the temperature of the growth zone was lowered to reach the desired growth temperature, while the temperature difference with the saturation zone generated the supersaturation. Both temperatures and the solution flow from one zone to the other were kept constant throughout the growth run to achieve stationary growth conditions. The solution flow from one zone to the other was set high enough to ensure that, even at the end of the growth run, the solute consumed by the growth only amounted to a fraction of the quantity in excess in the solution. This was ascertained by measurements of the achieved growth rates, which were found perfectly constant throughout the growth runs (see ref 13). With growth temperatures close to room temperature, depending on the seed orientation and the supersaturation applied, different growth rates Rc have been obtained. They were determined from snapshots of the growing crystal recorded with a CCD camera equipped with a macro lens. It allowed measuring the position of the crystal apex within 0.2 mm every 30 min. The stationary growth rates were derived from the slope of the apex position as a function of time with an associated error of about 0.1 mm/d. 2.2. Characterizations. Several characterizations of the powders used as nutrient, and the grown crystals were undertaken. For the nutrient, the phases synthesized and the isotopic compositions obtained had to be determined. For the grown crystals, the growth mechanism involved was identified from surface microscopies observations, the isotopic composition homogeneity was determined, and the crystal quality was ascertained by two methods. 2.2.1. X-ray Powder Diffraction. To control that the DKDP powders synthesized were purely of the tetragonal phase, we used Xray powder diffraction (XRPD). For each batch of synthesis, diffraction patterns were recorded using a Siemens D5000 diffractometer in Bragg−Brentano geometry using the Co Kα̃ radiation (Fe filtered) emitted from a sealed tube. The crystal phases obtained were identified by a Rietveld analysis of the XRPD patterns using the Fullprof Suite software.16 2.2.2. Micro-Raman Spectroscopy. Several methods can be used to determine the deuterium content, Xc, of DKDP crystals such as Curie Temperature Tc measurement17 and thermogravimetry.18 Unfortunately, these methods require sampling the analyzed crystal, which renders impossible to accurately determine the concentration profile in a bulk crystal. Micro-Raman spectroscopy, however, only collects the intensity scattered from the confocal volume, which is only a few micrometers in size and is located several hundreds of micrometers away from the objective, at the working distance. This is why we used micro-Raman spectroscopy to determine the deuterium content of the as-grown DKDP bulk crystals. We relied on this technique also for the determination of the isotopic composition of the powders synthesized to be used as nutrient. For DKDP, it has been shown that the position of the asymmetrical P(OD)2 stretching vibration (ν1, located around 880 cm−1)19 exhibits a linear dependency to the proton/deuterium substitution:20
concentrations and the case of DKDP, at temperatures maintained below that limit. We report here the results obtained using RTM for rapid growth under stationary conditions of several intermediate isotopic compositions of the DKDP solid solution, namely, deuterium contents in the crystals hereafter noted Xc = 0.85, 0.73, and 0.60. The conditions to reproducibly obtain homogeneous crystals of fixed compositions were determined, and the corresponding growth mechanism involved was identified from surface microscopy (optical profiler and ex situ atomic force microscopy (AFM) measurements). The crystals quality was revealed by X-ray diffraction topography and optical characterizations, while their isotopic composition homogeneity was demonstrated by micro-Raman spectroscopy.
2. EXPERIMENTAL SECTION 2.1. Elaboration. In order to rapidly grow homogeneous single crystals by RTM, maintaining constant temperature and supersaturation is necessary but not sufficient. One also has to preserve the composition of the growth solution. For this, it is mandatory to have a nutrient of the same phase and composition as the growing crystal. Hence, it has been essential to be able to synthesize tetragonal DKDP microcrystalline powders of controlled isotopic composition to be used as nutrient and to prepare the growth solution. 2.1.1. Starting Material Synthesis. In order to obtain such microcrystalline powders of controlled isotopic composition, DKDP was prepared by dissolution of high purity KDP ( 1, Graham’s, Maddrell’s, or Kurrol’s salts). Their formation begins around 180 °C for pure KDP (Xc = 0) at normal pressure,24 but one can reasonably assume that this temperature is lowered when, like in our syntheses, the pressure is reduced and the deuterium content increased. So, while the tetragonal phase is the stable one at room temperature for most intermediate compositions of the DKDP solid solution, for high deuterium contents synthesized under reduced pressure, some metastablehigh temperature phases along with polyphosphates may be present. On the basis of the recorded XRPD patterns, like the one shown in Figure 2, these two parasitic phases were avoided during evaporation, even for deuterium content as high as Xc = 0.84 and reduced pressure. Indeed, if the evaporation temperature (especially at the end when the salt is practically dried) did not exceed 110 °C at normal pressure and 90 °C at 4 mbar, no diffraction peaks other than those pertaining to the tetragonal (I4̅2d) phase were observed (see the difference between the experimental and the Rietveld calculated patterns Iobs − Icalc curve, blue line bottom of Figure 2). The reduced pressure of 4 mbar allowed to drastically reducing the evaporation time from 3 to 4 days, for normal pressure, to 2 h for 500 g of initial homogeneous solution. The achieved yields of DKDP salt of pure tetragonal phase were above 99%. The isotopic composition of the synthesized salts were determined by micro-Raman spectroscopy using the position of the asymmetrical P(OD)2 stretching vibration, ν1. It has been demonstrated25 that in the 25−70 °C range, the isotopic composition of DKDP crystals Xc is only but slightly dependent on the temperature at which they are grown and mainly depends on the solution deuterium content noted Xs. For our syntheses, the solutions deuteration level Xs is fixed by the D2O/H2O/KDP ratios engaged and writes: Xs =
Figure 3. Logarithm scale of the solubility limits S (in mole fraction) as a function of the inverse of the temperature (in K−1). Data points, measured solubility limit of DKDP salt with Xc = 0.73 in a solution of Xs = 0.8; solid line, linear regression; dashed line, calculated KDP (Xc = 0) solubility limit from ref 2; dash−dotted line, calculated DKDP solubility limit from ref 2.
supersaturations used throughout this article will be, to a good approximation, calculated independently of Xs and Xc using eq 1 and the solubility presented in Figure 3. 3.2.2. Crystal Growth. For the three isotopic compositions selected (Xc = 0.85, 0.73, and 0.60), optically clear crystals of up to 2 inches in size (limited by the size of the growth plateform) have been grown on point seeds at constant temperatures under high supersaturations (σ = 10−23%, Figure 4).
[D2 O] [D2 O] + [H 2O] + [KDP]
Here also, the isotopic composition Xc of the salt synthesized (determined by micro-Raman spectroscopy) was found to only depend on the solution deuteration level Xs. So the behavior presented in ref 25 extends to higher temperatures, up to 110 °C at normal pressure and 90 °C at 4 mbar, and the partition coefficient k can still be described like in ref 25 by k = Xc/Xs = F + (1 − F)Xs with F = 0.534. 3.2. Growth. 3.2.1. DKDP Solubility. The solubility limit S(T) of DKDP (Xc = 0.73) in a solution of deuteration level Xs = 0.8 was determined as a function of the temperature in the 5−45 °C range and was fitted by the standard equation: S(T ) = S∞ e−ΔHdiss/ RT
Figure 4. DKDP crystals grown under stationary conditions from point seeds, viewed along c on millimeter paper. Top row, crystals with Xc = 0.85 grown at σ = 25%; bottom row, from left to right, crystals with Xc= 0.85, 0.73, and 0.60 grown with σ = 10%.
(4)
where ΔHdiss is the dissolution enthalpy. Figure 3 represents the logarithmic scale of the solubility limit (expressed in mole fraction) as a function of the inverse of the temperature (in K−1). The slope of the curve leads to ΔHdiss = 3.46 kcal·mol−1 and the intersect to S∞ = 15.93. The measured solubility limit of DKDP (Xc = 0.73) was found to be significantly higher than that of KDP in H2O at normal pH (see Figure 3) but differs from that of DKDP2 (deuteration level of 0.98) by no more than 3%. As a result, the
The measured growth rates, Rc (Table 1), appear limited when compared with those previously presented in the literature. For instance, in a kinetic regime of growth (solution flow rate of ∼60 cm/s), the growth rate of KDP is Rc ≈ 9 mm/ day at σ = 5−6%.26 The existence of the DKDP monoclinic phase, by narrowing the metastable zone width, reduces the DKDP growth rates when compared with those of KDP in the same conditions15 but not to an extent that would account for the values presented here. Also, the solution flow through the 3616
dx.doi.org/10.1021/cg400586r | Cryst. Growth Des. 2013, 13, 3613−3620
Crystal Growth & Design
Article
regime). We favor the later explanation since, if the mass transport was rapid enough, the very high supersaturations imposed to the bulk solution would reach the steps. Then, the impurity impact would be extremely reduced, no step bunching would occur, and 2D nucleation would be present. Following the analysis presented in ref 28 based on the BCF formalism and considering the most extreme case of an applied supersaturation of σbulk = 30%, one can estimate the supersaturation effectively present at the growing surface. Combining the hillock slopes measured from the surface profile (slope average on the steep, shallow, and intermediate vicinal sectors p = 8.6 × 10−3, Figure 5) and the size of the step source Burger’s vector in unit step heights h determined from AFM images (b⊥ = mh, m = , 2 Figure 6), if one considers a unique dislocation source (source size L = 0) the calculated radius for a critical cluster is rc = 0.63 nm and the corresponding supersaturation σsurf = 7.6%. This last value is further lowered if one is to consider the effect of the dislocation core29 (2L = 2πrhc; inset in Figure 6: hollow core radius rhc = 22.5 nm for m = 2 in agreement with ref 29) or a multiple dislocation source of finite size. The dramatique reduction of the supersaturation from σbulk = 30% to σsurf ≲ 8% at the crystal surface correspond to the formation of a boundary layer. Such layer of lowered supersaturation at the growing interface may occur when flow velocity is too low to establish a regime of forced turbulent convection thus leading to a dominant mass transfer mechanism by natural convection.30 This phenomenon is amplified in our system by the low growth temperature that reduces the diffusion coefficient of the species, by the centered position of the seed on the supporting platform, and by the size of the growth reactor (1 L) that limits the accessible rotation rates (
