Solubility and dissolution kinetics of GaN in supercritical ammonia in presence of ammonoacidic and ammonobasic mineralizers

Journal of Crystal Growth 479 (2017) 59–66

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Solubility and dissolution kinetics of GaN in supercritical ammonia in presence of ammonoacidic and ammonobasic mineralizers Saskia Schimmel a,⇑, Martina Koch a, Philipp Macher a, Anna-Carina L. Kimmel b, Thomas G. Steigerwald b, Nicolas S.A. Alt b, Eberhard Schlücker b, Peter Wellmann a a b

Materials Department 6, Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Martensstraße 7, 91058 Erlangen, Germany Institute of Process Machinery and Systems Engineering, Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Cauerstraße 4, 91058 Erlangen, Germany

a r t i c l e

i n f o

Article history: Received 10 December 2016 Received in revised form 10 July 2017 Accepted 25 September 2017 Available online 27 September 2017 Communicated by T.F. Kuech Keywords: A1. Solubility A1. Solvents A2. Growth from solutions A2. Ammonothermal crystal growth A2. Solvothermal crystal growth B1. Gallium compounds

a b s t r a c t Solubility and dissolution kinetics of GaN are investigated, as they represent essential parameters for ammonothermal crystal growth of GaN. In situ X-ray imaging is applied to monitor the dissolving crystal. Both ammonoacidic and ammonobasic conditions are investigated. Compared to NH4F, the dissolution is generally much slower using NaN3 mineralizer, leading to a much longer time needed to establish a saturated solution. The solubility of GaN at 540 °C and 260 MPa in supercritical ammonia with a molar concentration of NaN3 of 0.72 mmol/ml is determined to be 0.15 ± 0.01 mol%. This suggest a severe refinement of raw gravimetric literature data also for alkali metal based mineralizers, as we reported previously for ammonium halide mineralizers. The order of magnitude is in good agreement with refined gravimetric solubility data (Griffiths et al., 2016). The apparent discrepancy between the literature and this work regarding the temperature range in which retrograde solubility occurs is discussed. A possible reason for the occurrence of retrograde solubility at high temperatures is described. The paper is complemented by a section pointing out and partially quantifying potential, reactor-material-dependent sources of errors. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction Ammonothermal crystal growth of GaN is a promising approach for the production of native GaN substrates on an industrial scale [1]. Native GaN substrates allow for the further improvement of performance and lifetime of GaN-based optoelectronic and electronic devices [2]. The ammonothermal crystal growth method is based on the dissolution of GaN in the temperature zone with higher GaN solubility and seeded growth from the supersaturated solution in the lower solubility zone [2], thus, the solubility of GaN is very important for both scientific understanding and technological optimization of the process. Furthermore, knowing how the solubility of GaN changes with temperature and pressure is expected to contribute to understanding the chemical and physical mechanisms governing dissolution. In the long run, identifying the underlying chemo-physical processes may allow for optimizing the selectivity of the mineralizer to maximize the normalized solubility of the nitride while minimizing the solubility of the reactor materials. Comparable attempts have been made using other

⇑ Corresponding author. E-mail address: [email protected] (S. Schimmel). https://doi.org/10.1016/j.jcrysgro.2017.09.027 0022-0248/Ó 2017 Elsevier B.V. All rights reserved.

supercritical fluids (e.g. CO2) for which the deviating dependency of the solubility of different solutes on pressure and temperature is comparably well understood [3]. Despite the importance of knowing and tuning the solubility, literature data are both scarce and scatter in the order of magnitude range [4–9]. We have previously reported a novel method for investigating the solubility using in situ X-ray imaging [4]. In this work, more comprehensive information on the dissolution of GaN in presence of ammonium fluoride (NH4F) and sodium azide (NaN3) mineralizers will be presented. Information on the kinetics of dissolution and saturation of the solution will be given. The obtained solubility data will be discussed with respect to literature. In addition, potentially remaining sources of errors are analyzed semi-quantitatively.

2. Experimental Regarding the autoclave and the X-ray imaging equipment, the experimental setup was almost identical to the one used in our previous study [4]. However, a few changes to the setup and experimental procedure were made as described in the following. Ammonia was purified using a gas purifier (MicroTorr MC190-702F) and no

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changes to the fill level were made once the heating process had been started. In addition, the autoclave was not connected to any metal tubes except the unavoidable connections to burst disc, pressure transmitter and hand valve. This eliminates thermal conduction via the metal tube connection from the hand valve to the filling setup, which otherwise represents an avoidable heat sink. A separate, unlined optical cell (12.2 ml including head assembly) was used for the ammonobasic experiments whereas an optical cell equipped with a platinum liner (10.9 ml including head assembly) was used for ammonoacidic experiments. Temperature and pressure were continuously recorded (1.2 values per second) except for one experiment for which the data had to be documented by hand (data points in Fig. 3). Fill levels are given with regard to the density of ammonia at
33.331 °C and 1.013 bar. The solubility was calculated based on the dissolved volume in the saturated solution i.e. using the remaining crystal volume as determined from the X-ray image and the initial volume at the beginning of the experiment. In case of the experiments using NaN3 mineralizer, we found that the dissolution is a very slow process even at high temperatures and pressures. Therefore it was more accurate to use the in situ X-ray images for determining the appropriate duration of the experiment as well as for investigating dissolution kinetics but use the mass of the remaining crystal for solubility determination. Prior to gravimetric measurements after the ammonothermal experiments, the samples were cleaned in a 25% HCl solution for at least 3 h. Mass change of the samples were investigated using a laboratory balance (Mettler Toledo AB204). A scanning electron microscope (SEM, Jeol 6400), energy dispersive X-ray fluorescence (EDX, Oxford Inka) and an optical microscope were used for investigation of untreated and ammonothermally etched sample surfaces. For estimating the potential errors introduced by inner surfaces of the autoclaves acting as Ga sinks or sources, crystal mounts which had been used in several ammonobasic (uncoated Inconel 718) or ammonoacidic (Au coated Inconel 718) experiments were investigated as a sample surface of the inner surfaces of the reactor. Both SEM (Jeol JSM-7610F) and EDX (Oxford, Aztec) measurements were used for characterization of the crystal mounts. Untreated crystal mounts were investigated as reference samples. Average measured mass fractions of Ga were used to estimate the total amount of Ga that is present in the inner surface layers of the autoclave parts. For approximately calculating the volume of the Ga-containing surface layers of uncoated Inconel 718, a penetration depth of 3 mm was assumed based on the EDX measurements on Inconel 625 cross sections by Griffiths et al. [9]. Together with the density of Inconel 718 and the measured mass fractions at the surface of the crystal mounts, this allowed to roughly estimate the total amount of Ga that may be taken up or released by uncoated Inconel 718 autoclave parts. To investigate the relevance of this effect also in the ammonoacidic experiments, gold coated crystal mounts were also investigated using EDX measurements (samples used for experiments with NH4F mineralizer as well as untreated reference samples). 3. Results and discussion A few general observations will be described and discussed first, followed by a detailed discussion of the results with regard to various parameters that potentially influence GaN dissolution kinetics, GaN solubility, or both of them. 3.1. General observations The solubility of GaN is known to be governed by the mineralizer, thus, the question arises at which conditions the mineralizer

starts to dissolve or decompose and can be transported to the GaN crystal. In our previous study [4] we suspected that NH4F might be partially released if the fill level is adjusted at 150 °C because NH4F decomposes at 100 °C to NH3 and HF under ambient conditions. However, in an experiment with less than 5% fill level resulting in a maximum pressure of about 2 MPa and a maximum temperature of 500 °C, NH4F was recovered unchanged after the experiment. This indicates that an ammonia atmosphere hinders thermal decomposition of NH4F even at temperatures as high as 500 °C. However, we did observe dissolution of GaN with NH4F mineralizer at lower temperatures if supercritical conditions were reached. This suggests that NH4F dissolves in ammonia but does not decompose thermally under ammonothermal conditions. In another experiment with very low fill level (below 10%, resulting in 16 MPa at 569 °C), no dissolution of GaN was observable despite no residual NH4F was visible in the autoclave postrun. According to the above-mentioned observations, NH4F presumably vanished by dissolution and complete removal upon venting the autoclave post-run. The observation that NH4F dissolution does not necessarily lead to GaN dissolution suggests that the onset of GaN dissolution is rather governed by the reaction of NH4F with GaN (i.e. formation of soluble complex ions) than by dissolution of the mineralizer. 3.2. Process window for GaN dissolution The process window in which GaN dissolution is observed varies strongly with mineralizer species. An overview gathered from our experiments is presented in Table 1, indicating that if NaN3 is used significantly higher pressure is needed whereas in presence of NH4F, GaN dissolution begins relatively close to the critical point. The dissolution of GaN in pure supercritical ammonia was also investigated. This confirmed that either the solubility of GaN in pure supercritical ammonia is negligibly low or the reaction kinetics are significantly slower than in presence of mineralizers. No alteration of the surface and no measurable mass loss were observed within 34 h at 138 MPa at 530 °C. Despite the relatively low pressure of this experiment, the negligible dissolution of GaN can be attributed to the absence of a mineralizer because in another experiment with even lower pressure and similar temperature (92 MPa bar, 540 °C, 24 h) a small but clearly measurable amount of GaN was dissolved. 3.3. Dissolution kinetics Three phases of the experiment could regularly be distinguished, regardless of the mineralizer used. These correspond to (i) no dissolution until above mentioned minimum parameters were reached, (ii) a time period with relatively fast dissolution and (iii) a time period with no or extremely slow further dissolution corresponding to a saturated solution as elaborated in [4]. Fig. 1 shows a typical set of X-ray images for run times between 0 and 145 h and is taken from the same experiment as the graph on crystal dissolution kinetics and experimental parameters shown in Fig. 2. Range III from the description in [4] could be changed

Table 1 Overview of minimum pressure, temperature and pressure required to dissolve GaN. The NaN3 data are from two separate experiments whereas the NH4F data are from one experiment. The errors mostly originate from the time interval of in situ X-ray imaging i.e. dissolution may begin between two measurements. Mineralizer species

Minimum temperature/°C

Minimum pressure/MPa

NH4F NaN3

Below 220 ± 10 Below 299 ± 10

Below 21 ± 5 Below 92 ± 5

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Fig. 1. Direct insight into ammonothermal autoclave by in situ X-ray imaging, showing dissolution of a GaN crystal over time.

Fig. 2. Kinetics of GaN dissolution under ammonobasic conditions using 3 mol% NaN3 mineralizer (molar concentration: 0.72 mmol/ml).

Fig. 3. Kinetics of GaN dissolution under ammonoacidic conditions using 11 mol% NH4F mineralizer (molar concentration: 0.76 mmol/ml). Lines connecting temperature and pressure data are only a guide to the eye.

from slow further dissolution by mass transport and deposition to virtually no further dissolution after saturation of the solution by disconnecting the head assembly from the ammonia filling line, i.e. by removing an unwanted heat sink. This modification in the setup also eliminated crystallization of reaction products in the filling tube. This observation further confirms that mass transport and deposition are negligibly low in the experiments presented in this work. A logistic fit was found to work well for fitting the remaining GaN volume over time. The logistic fit describes a saturation process with one of the resources for growth being limited; in case of our experiments, the dissolved volume saturates as the solubility limit is approached. In this work, this fit is used for a more precise determination of the dissolved volume at the solubility limit. The reaction kinetics were found to depend strongly on the mineralizer used. This can be seen from a comparison of Fig. 2 and Fig. 3 showing the dissolution over time in presence of NaN3 and NH4F, respectively.

While with ammonium fluoride dissolution began rapidly when minimum necessary process parameters were reached, GaN dissolution started less abruptly if NaN3 was used. This was observed in various experiments with different final pressure (i.e. ammonia density) and temperature. In a series of experiments using NaN3 mineralizer, also the amount of mineralizer (and its concentration) was varied and dissolution kinetics remained similar. Thus, the faster dissolution in the NH4F experiments is most likely not an effect of the higher mineralizer concentration. The deviation of mineralizer concentration between acidic and basic experiments originates mostly from using higher fill levels for most of the ammonobasic experiments. Note that unless working with an excess of mineralizer (i.e. a saturated solution of the mineralizer in ammonia), the molar concentration of the mineralizer (i.e. total amount of mineralizer normalized to the reactor volume) is expected to be more relevant to GaN solubility than the molar ratio of mineralizer and ammonia. The reason is that the solubility of the mineralizer in ammonia probably varies with the ammonia den-

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sity. This is expected because the relative permittivity increases with increasing density and a high relative permittivity favors the dissolution of ionic compounds [10,11]. Therefore, if an excess of mineralizer is present then increasing the amount of ammonia may lead to an increase of the amount of mineralizer dissolved. No signs of a liquid being present on the bottom of the autoclave were observed in our experiments (as reported if working with excess mineralizer [9]), suggesting that the mineralizer was fully dissolved. The molar concentration of the two experiments shown in Fig. 2 and Fig. 3 is very similar: 0.72 mmol/ml for the NaN3 experiment and 0.76 mmol/ml for the NH4F experiment. It is not yet known whether the observation of differing dissolution kinetics holds for ammonobasic and ammonoacidic mineralizers (potentially azides and amides) in general. It is also not yet clear whether the delay in time in case of NaN3 is due to the reaction of NaN3 to the actual mineralizer NaNH2. In the pressure over temperature chart during the dissolution experiments, no spikes in pressure have been observed, suggesting that there is no sudden decomposition of a large proportion of NaN3 in our experiments.

ent crystal faces, which is confirmed by the change of crystal dimensions over time revealed by evaluation of the in situ X-ray images. For both ammonoacidic conditions (NH4F) and ammonobasic conditions (NaN3), virtually no difference between dissolution velocity in m- and a-directions were observed whereas the cdirection showed clearly different dissolution velocities (see Figs. 5a and 5b). This is in accordance with very similar surface energies for m- and a-planes whereas the surface energy of the c-planes and semipolar planes are significantly larger [12]. The similarity of the dissolution velocities of m- and a-planes also in presence of NaN3 is important for correctly estimating the dissolution in the third dimension for calculating the remaining crystal volume if the solubility is determined directly from the X-ray images. The dissolution velocities of both nonpolar and polar crystal faces are significantly lower with NaN3 compared to NH4F. Typical values are given in Table 2. 3.5. Solubility

3.4. Dissolution kinetics of different crystal faces For both ammonoacidic (NH4F) and ammonobasic (NaN3) conditions, anisotropic etching was clearly observed by SEM investigation of the samples after the dissolution experiments (see Fig. 4). This suggests that the dissolution velocities are different for differ-

a) 396 °C, 268 MPa, 2.0 mol%, 24 h

As elucidated already in our previous paper [4], the saturation observed in the dissolved volume over time plot indicates the saturation of the solution and thus, the respective dissolved volume can be used to determine the solubility of GaN. Solubility data for both ammonoacidic and ammonobasic conditions obtained in

b) 299 °C, 262 MPa, 2.4 mol%, 24 h

Fig. 4. SEM images of GaN sample surfaces investigated after ammonobasic dissolution experiments. Faceting indicates anisotropic etching. Remains of surface damage resulting from wire sawing are observed if only a small amount of GaN was dissolved (spallation-like features in b)).

a) Experiment NaN3-1

b) Experiment NaN3-2

Fig. 5. Dissolution kinetics of different crystal faces using NaN3 mineralizer. Note that the shown scale range in each of the figures is identical within one figure in order to ensure optical comparability of the corresponding slopes representing the dissolution velocities.

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Table 2 Dissolution velocities for different mineralizers and crystallographic directions from experiments with comparable process parameters as given in the table (two experiments per mineralizer, each of them yielding dissolution velocities of two crystallographic directions). The data are based on measuring the distance between the respective crystal faces, thus, the value for c-direction represents an average between potentially deviating values for (0 0 0 1) and (0 0 0
1) faces. Note that what is seen macroscopically as c-planes consists of numerous facetted etch hillocks on a microscopic scale. These etch hillocks in turn are terminated by semipolar crystal faces. Experiment

NH4F-1

NH4F-2

NaN3-1

NaN3-2

Temperature [°C] Pressure [MPa] n(mineralizer) [mmol] c-direction [mm/h] m-direction [mm/h] a-direction [mm/h]

500 124 8.1 60 300 –

550 133 8.1 30 – 300

445 268 7.0 26 – 6

396 268 7.1 – 6 7

this study by in situ monitoring of the saturation of the dissolution are shown in Figs. 6 and 7. The data are given with respect to the autoclave inner volume, the amount of ammonia and the amount of mineralizer, respectively. The purpose is to gain a better overview of potentially relevant parameters.

Fig. 6. Overview of dissolved amount of GaN per reactor volume (including head assembly) obtained in this study by observing the saturation of the solution by in situ X-ray imaging, including both data for acidic and basic experiments. The ammonobasic data have been obtained from the experiments also used in Figs. 2 and 5, respectively.

In case of the solubility given with respect to the amount of mineralizer, the total amount of mineralizer filled into the autoclave is used. Ideally, only the dissolved amount of mineralizer that contributes to the dissolution of GaN should be used instead, however, this is currently hindered by the lack of solubility data for the mineralizer itself under the respective process conditions. Baser et al. have recently reported a promising technique for measuring mineralizer concentrations in a saturated solution [13], however, data for the parameter range applied in our study are not yet available. Griffiths et al. have pointed out that a Na-rich liquid phase seems to be present in their growth and solubility experiments at the bottom of the autoclave, suggesting that a molar ratio of NH3:Na = 20:1 leads to exceeding the solubility of the mineralizer (presumably present as NaNH2) under the respective process conditions [9]. The molar ratio employed in the here presented work ranges from NH3:NaN3 = 33:1 to NH3:NaN3 = 50:1. Together with the fact that we (in contrast to Griffiths et al. [9]) did not observe any signs of a liquid being present at the bottom of the autoclave during the experiments this suggests that in the here presented study the mineralizer was fully dissolved. Thus calculating normalized solubility values using the full amount of mineralizer is likely to be justified if full conversion of NaN3 to NaNH2 is assumed. Our results obtained by in situ X-ray imaging suggest that the solubility of GaN under ammonothermal conditions is significantly lower than generally reported in conventional gravimetric literature [6,8,14,15] i.e. based on the mass change of GaN granules measured after the experiment. This holds for both ammonobasic and ammonoacidic mineralizers. However, there are no literature values for GaN solubility in presence of NH4F mineralizer (the presumably most comparable mineralizer for which such data exist is NH4Cl [6,8]). In case of ammonobasic mineralizers, data for NaNH2

Fig. 7. Overview of GaN solubility obtained in this study by observing the saturation of the solution by in situ X-ray imaging, including both data for acidic and basic experiments. The solubility is given as percentage of substance amount (left) and as normalized solubility (right). The ammonobasic data have been obtained from the experiments also used in Figs. 2 and 5, respectively.

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do exist [15,16] but have been obtained at very different experimental parameters, i.e. pressures around 76 MPa [16]. Recently, Griffiths et al. have pointed out a number of error sources affecting the raw data of ammonothermal solubility measurements such as the autoclave wall acting as a Ga sink or source in subsequent experiments [9]. Their refined data (i.e. accounting for the reported error sources) support the order of magnitude reported in this work: they report a band of GaN solubility of typically 0.03– 0.10 mol% and our data are in a range of 0.04–0.15 mol%. At present, it is not completely clear to what extent Ga uptake by or release from the autoclave walls also affect the here presented data. Initial investigations to clarify this will be given in the section on not yet adequately quantifiable errors. A more comprehensive investigation is currently under way. While a quantitative comparison to literature data is difficult and questionable due to severely differing experimental parameters as described above, considering the occurrence of retrograde or normal solubility focusing on studies that give internal temperatures measured in the fluid is thought be more instructive. Griffiths et al. have reported that they observe crystal growth in the hot zone at 505 °C with the dissolution zone set to 451 °C (both internal temperatures) in their growth experiments using Na mineralizer [9]. The data are comparable in the aspect that a growth experiment is nominally isobaric and our data have been obtained at approximately constant pressure. In both studies the compound acting as mineralizer is NaNH2 since both NaN3 and Na react to NaNH2. The experimental conditions are therefore relatively well comparable. Thus, there is an apparent discrepancy between their observation of retrograde GaN solubility between 451 and 505 °C and our above shown results indicating normal solubility in the overlapping temperature range from 396 °C to 538 °C. However, given the directly observed slow dissolution kinetics in relation to the relatively short ramp up phase, it also appears unlikely that the normal solubility observed in our experiments is an artifact from crossing lower temperatures upon heating to the examined temperature. As we consider both our measurements and the observation by growth experiments in the literature as trustworthy, the question arises whether it is possible that both are correct despite the apparent discrepancy. Both the literature and our study being correct would imply that the temperature range in which retrograde solubility of GaN occurs can be altered by remaining deviating experimental parameters, i.e. primarily the ratio of NH3:Na and the pressure or ammonia density. It is noteworthy that the phenomenon of retrograde solubility recently has been observed also if specific ammonoacidic mineralizers are employed at high temperatures [17,18]. Previously, retrograde solubility had been observed only if working with ammonobasic mineralizers [15,19] which is presumably due to technical difficulties in reaching high temperatures in conjunction with pressures typically required for ammonothermal growth. The occurrence of a change from normal to retrograde solubility for both ammonobasic and ammonoacidic reaction media suggests that the underlying chemical or physical effect is likely to be rather unspecific. In addition, all ammonothermal mineralizers for which a negative temperature coefficient of GaN solubility (i.e. retrograde solubility) has been reported show the retrograde solubility if the temperatures exceed a mineralizer-specific value. This implies that the underlying unspecific effect is closely related to temperature. It is well known that for the dissolution of ionic compounds in polar solvents both the enthalpy change DH and the product of entropy change and temperature TDS are typically in the same order of magnitude [20]. Therefore, both terms must be considered to determine whether Gibbs free energy is positive or negative at specific conditions [20], i.e. whether the process is endergonic or exergonic. If we assume that the intermediate compounds formed in presence of sodium-based mineralizers are Na[Ga(NH2)4] or

Na2[Ga(NH2)]4NH2, suggesting [Ga(NH2)4]
being the dissolved species according to [21], the formation and decomposition of these intermediates may occur as follows (cryst.: crystalline, diss.: dissolved in ammonia, sc: supercritical):

GaNðcryst:Þ þ Naþ ðdiss:Þ þ NH
2 ðdiss:Þ þ 2NH3 ðscÞ ¢ Naþ ðdiss:Þ þ ½GaðNH2 Þ4 
ðdiss:Þ For large ions with low charge density, DS is typically positive [20,22]. Since the dissolved species in ammonothermal crystal growth are believed to be large complex ions, DS is likely to be positive. The enthalpy change DH is likely to be positive as well due to the large bonding energy of GaN [23] that probably dominates the solvation enthalpy of the intermediate complex ion. If both DH and DS for the above described reaction of GaN dissolution are positive, then DG ¼ DH
T DS becomes negative if a certain temperature is exceeded. A negative DG corresponds to an exergonic reaction. An exergonic reaction will be favored if the surrounding can take up energy released by the reaction. This applies to the cold zone of the autoclave that becomes the dissolution zone in this case. Consequently, the same effect applies to the reverse reaction, i.e. the crystallization of GaN, in the opposite direction. Therefore, the crystallization reaction becomes endergonic at high temperatures and thus is favored in the hot zone of the autoclave at high temperatures. Since the enthalpy contribution of solvation of mineralizer and intermediate as well as the associated entropy changes presumably depend on the properties of the respective ions as well as the solvent density, it is obvious that the absolute temperature at which DG changes its algebraic sign depends on the mineralizer used. This is in good agreement to the literature as for different mineralizers different temperature ranges have been reported for the occurrence of retrograde solubility [9,17,18]. The relevance of both enthalpy and entropy changes imply that the temperature above which retrograde solubility occurs is sensitive to various parameters. The above elaborated consideration on the thermodynamics of intermediate formation and decomposition are in accordance with the fact that an intermediate acting as a transporting species generally shows intermediate thermodynamic stability [24]. The reason is that it needs to be stable enough to form in one area of the reaction chamber but also has to be instable enough to decompose again in another area under moderately different conditions [24]. Those parameters may include pressure, ammonia density and mineralizer concentration which are different in this work and in the crystallization experiments performed by Griffiths et al. [9]. Therefore, there is not necessarily a discrepancy between our results and those reported by Griffiths et al. [9] because the experimental conditions may be not similar enough. Further experiments with experimental conditions as comparable to the literature are needed to verify this conjecture but are beyond the scope of the current study. For ammonothermal crystal growth using NH4F mineralizer, retrograde solubility has been observed in the temperature range of 550–650 °C by Bao et al. [17]. The acidic solubility data of our study are not exactly isobaric and in this aspect not fully comparable to a growth experiment, however, it is interesting that they do show retrograde solubility in the temperature range of 514–572 °C and a normal solubility in the range of 486–514 °C for both the dissolved amount of substance and the normalized solubility (i.e. dissolved amount of GaN divided by amount of mineralizer). This is viewed as a reasonable agreement considering that Bao et al. do not state measuring the temperature directly in the fluid so the actual fluid temperatures may deviate moderately. A deviating behavior of the solubility as percentage of substance amount (mol%) is not surprising since growth experiments are approximately isobaric (within one experiment) but our experiments (from one to another) were not. Our data show that the solubility

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using NH4F mineralizer increases sharply already at moderate pressures, this is in good agreement with growth experiments being performed at moderate pressures in the range of 80– 150 MPa [17,25]. 3.6. Remarks on not yet adequately quantifiable potential sources of errors For investigating the relevance of autoclave parts acting as Ga sinks and sources (as first reported by Griffiths et al. [9]) in our experiments, the total amount of Ga that may be contained in the surface layers of the inner surfaces of the autoclave was estimated as described in the experimental section. The EDX measurements showed an average surface concentration of Ga of 11.8 ± 0.8 wt% (7.6 ± 0.7 at.%). The estimation based on this value showed that for the NaN3 experiments (unlined, uncoated autoclave parts), up to 3 times of the maximum molar amount of GaN that was dissolved within one experiment may have been stored in the exposed autoclave parts. Only part of the total stored amount of Ga is expected to be taken up or released by the autoclave walls within a single experiment, however, not negligible errors must be expected as previously pointed out by Griffiths et al. [9]. It is not feasible to retrospectively quantify these errors for individual experiments of the here presented study. In spite of that, no suspicious trend is seen if looking at the experimental results from a chronological point of view. Gold coated crystal mounts used for ammonoacidic experiments using NH4F showed no detectable amounts of Ga on most measured sample areas (the largest concentration found locally was 0.9 at.%). Therefore, the Au coated surface areas (window mounts and crystal mounts in acidic experiments) apparently do not act as Ga sinks or sources. However, a Platinum liner covers the remaining inner surfaces of the optical cell. An investigation of the Pt liner in terms of potential Ga alloying was not feasible within the here presented work because it cannot be removed from the autoclave nondestructively. Noteworthy, no sodium was found in the EDX measurements of uncoated Inconel 718 crystal mounts exposed to supercritical ammonia with NaN3 mineralizer. Unlike Ga, Na is not taken up by Inconel 718 autoclave parts, which is probably due to the larger size of Na atoms compared to Ga. In gold coated crystal mounts used for ammonoacidic experiments with NH4F mineralizer, however, some of the mineralizer appears to be taken up by the gold coating. This was observed by EDX measurements showing a F concentration of 4.85 ± 1.14 wt% (29.09 ± 4.9 at.%). This suggests that the gold coating may act as a F sink and source in a similar way as Inconel 718 with respect to Ga. In addition to the above discussed potential sources of errors, it is not known whether and to what extent the different construction materials influence the results in other ways, e.g. by acting as a reactant in possible side reactions or by catalytic effects. Clearly, a further investigation of potential sources of error is thus very desirable but requires a study on its own. 4. Conclusions Experimental data on the solubility and dissolution kinetics of GaN in supercritical ammonia in presence of ammonoacidic and ammonobasic mineralizers, namely NH4F and NaN3, have been obtained using in situ X-ray imaging. Governing parameters for solubility of GaN are mineralizer, temperature and pressure. Compared to NH4F, the dissolution is generally much slower using NaN3 mineralizer, leading to a much longer time needed to establish a saturated solution. The solubility of GaN at 540 °C and

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260 MPa in supercritical ammonia with a molar concentration of NaN3 of 0.72 mmol/ml is 0.15 ± 0.01 mol% (molar concentration based on the volume of the fluid in supercritical state), corresponding to a normalized solubility of 0.050 ± 0.001 mol GaN/mol NaN3. Using NH4F mineralizer with a molar concentration of 0.76 mmol/ ml, the solubility of GaN at 570 °C and 50 MPa was determined to be 1.03 ± 0.01 mol%, corresponding to a normalized solubility of 0.092 ± 0.001 mol GaN/mol NH4F. Note that increasing GaN solubility by increasing the amount of mineralizer is only feasible until the solubility limit of the mineralizer itself is reached because undissolved mineralizer cannot contribute to the dissolution of GaN. The solubility data reported in this work differ greatly from unrefined gravimetrically obtained literature data previously reported by different groups, however, the experimental parameters to conventional gravimetric solubility studies are not well comparable. However, the order of magnitude obtained by in situ X-ray imaging is in reasonable agreement to refined gravimetrically obtained solubility data recently published by Griffiths et al. [9] which account for a number of previously unreported error sources in conventional gravimetric measurements. Supplementary investigations on the effect of the autoclave walls acting as a Ga sink or source are currently under way. The ammonoacidic data are in good agreement with the observation of retrograde solubility in growth experiments by Bao et al. [17]. The ammonobasic data do not show the retrograde solubility that is reported in the crystal growth literature, however, this apparent deviation may be due to deviating experimental parameters that may lead to a shift of the temperature above which the solubility exhibits a negative temperature gradient. The shift from normal to retrograde solubility is thought to originate from the dissolution reaction turning from an endergonic to an exergonic process at high temperatures due to the increased importance of entropy-related effects at high temperatures. The presented results and the method are believed to pave the way for substantial progress in both scientific understanding and further technological development of ammonothermal crystal growth. Acknowledgements Financial support by German Research Foundation (DFG) under contract number WE2107/6-2 (FOR1600) is gratefully acknowledged. In addition, we would like to thank E. Meissner and Freiberger Compound Materials GmbH for HVPE-GaN samples, U. Künecke and M. Schuster for assistance with EDX and SEM investigations, S. Eichner for assistance with ammonothermal dissolution experiments and D. Jockel for fruitful discussions. Special thanks to Rainer Niewa as well as the reviewer for thoroughly reading the manuscript and fruitful discussions. References [1] T. Fukuda, D. Ehrentraut, Prospects for the ammonothermal growth of large GaN crystal, J. Cryst. Growth 305 (2007) 304–310, https://doi.org/10.1016/j. jcrysgro.2007.04.010. [2] D. Ehrentraut, E. Meissner, M. Bockowski (Eds.), Technology of Gallium Nitride Crystal Growth, 2010, https://doi.org/10.1007/978-3-642-04830-2. [3] S.N. Reddy, G. Madras, Semi empirical models for selectivity of supercritical carbon dioxide for solid mixtures, Sep. Purif. Technol. 89 (2012) 181–188, https://doi.org/10.1016/j.seppur.2012.01.029. [4] S. Schimmel, M. Lindner, T.G. Steigerwald, B. Hertweck, T.M.M. Richter, U. Künecke, et al., Determination of GaN solubility in supercritical ammonia with NH4F and NH4Cl mineralizer by in situ x-ray imaging of crystal dissolution, J. Cryst. Growth 418 (2015) 64–69, https://doi.org/10.1016/j. jcrysgro.2015.02.020. [5] V. Avrutin, D.J. Silversmith, Y. Mori, F. Kawamura, Y. Kitaoka, H. Morkoc, Growth of bulk GaN and AlN: progress and challenges, Proc. IEEE. 98 (2010), https://doi.org/10.1109/JPROC.2010.2044967.

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