Understanding the chemistry of 2D rhodium trihalide solid solutions: tuning of optical properties and nanocrystal deposition

In the search for novel 2D materials with potentially valuable properties, such as a tunable band gap for optoelectronic or catalytic applications, solid solutions hold the potential to significantly expand the inventory of available 2D nanomaterials. In this study, we present for the first time the synthesis of such 2D rhodium trihalide solid solutions: RhBr x Cl3−x and RhBr x I3−x . We use thermodynamic simulations and simultaneous thermal analysis to predict conditions for their rational synthesis and to investigate suitable chemical vapor transport (CVT) parameters for these solid solutions. The evolution of the lattice parameters was investigated by powder x-ray diffraction, showing an isostructural relationship of the synthesized compounds and only minor deviation from Vegard’s law. The optical band gap of these materials can be tuned in an energy range from 1.5 eV (RhCl3) to 1.2 eV (RhI3) by choosing the composition of the solid solution, while the samples also exhibit photoluminescence in similar energy ranges. Ultimately, the successful deposition of bulk as well as ultrathin 2D nanocrystals of RhBr x Cl3−x by CVT from 925 °C to 850 °C is shown, where the composition of the deposited crystals is precisely controlled by the choice of the starting composition and the initial amount of material. The high quality of the obtained nanocrystals is confirmed by atomic force microscopy, high resolution transmission electron microscopy and selected area electron diffraction. For RhBr x I3−x , the CVT from 900 °C to 825 °C is more difficult and has only been practically demonstrated for an exemplary case. According to the observed properties, these novel solid solutions and nanocrystals show a great potential for an application in optoelectronic devices.


Introduction
Among the already discovered and intensely studied classes of 2D materials-such as special element allotropes [1,2], transition metal dichalcogenides [3,4], or MXenes [5,6]-the group of transition metal trihalides with 2D crystal structures hosts numerous compounds with unique and exotic properties, especially when their structures are scaled down to nanometer dimensions. To name just a few, RuCl 3 is featured in countless studies for its potential as a Kitaev quantum spin liquid ground state [7,8], CrX 3 (X = Cl, Br, I) exhibit interesting switches of their magnetic properties during downscaling [9][10][11], or the catalytic activity of TiCl 3 is to improved when downscaled [12].
The group of 2D rhodium trihalides additionally attracted the attention because of their high long-term environmental stability [13,14] compared to similar trihalides [12,15] and the flexible ways to tune their material properties as nanomaterials, e.g. by height depending band gap engineering [16] or doping [17]. Wang et al demonstrated, that the band gap and related properties of RhI 3 can be tuned by the number of stacked layers, making it potentially interesting for optoelectronic applications [14].
Another possibility for adjusting material properties, similar to doping, is the formation of solid solutions. This usually allows certain material properties, e.g. the band gap or the magnetic behavior, to be tuned in a controllable manner between the values of the pure mixed compounds, but sometimes the properties are also improved beyond those of the initial compounds. Based on this concept, expanding the pool of available 2D (nano)materials with tunable properties is highly desirable. Although the fact that the RhX 3 (X = Cl, Br, I) all share the same crystal structure has been known for a long time [18], to the best of our knowledge, no work has yet been published about their solid solutions.
In this study we present the rhodium trihalide solid solutions RhBr x Cl 3−x and RhBr x I 3−x and investigations on structure and some selected physical properties in theory and practice. Prior to the actual experiments we calculate thermodynamic metrics for a rational synthesis approach of the respective solid solutions. Based on the theoretical investigations, we identify the important parameters of the vapor phase chemistry in these systems and derive suitable parameters for chemical vapor transport (CVT) experiments. After the successful rational synthesis of the solid solution material, the structural evolution of the lattice parameters is studied by powder x-ray diffraction (pXRD) and the thermodynamic stability is experimentally investigated by differential scanning calorimetry (DSC) and thermogravimetry (TG). Diffuse reflection and photoluminescence (PL) measurements are used to investigate the evolution of the optical properties (including the optical band gap) of the bulk material. Based on the previously performed simulations, CVT is used for the growth of large bulk crystals, but also for the deposition of ultrathin nanosheets down to the monolayer dimension in the case of RhBr x Cl 3−x . An observed composition enrichment during the CVT process is explained, so that nanocrystals with a desired composition can be selectively deposited. The quality of the deposited nanosheets is investigated by transmission electron microscopy (TEM) and selected area electron diffraction (SAED). Finally, the CVT of RhBr x I 3−x is demonstrated and discussed.

General remarks
For all experiments the following fused silica (ilmasil PN, qsil, max. 45 ppm OH content) ampoules were used: one-chamber ampoules (temper experiments, CVT for bulk crystal growth): 11 cm long, 1 cm inner diameter, 7.8 ml volume. Two-chamber ampoules (CVT experiments with substrates): 12 cm long, 1 cm inner diameter, 0.5 mm narrow diameter, 9.4 ml volume. For introducing elemental bromine into an ampoule, liquid bromine was carefully sealed in a mark-tube capillary (Hilgenberg GmbH) and transferred into an ampoule. The ampoule was sealed at a pressure of ∼3×10 −3 mbar. Afterwards the capillary was carefully damaged by slight heating or shaking to release the bromine. For the synthesis of iodine containing samples, an excess of iodine was applied. These ampoules, containing elemental iodine, were cooled with liquid nitrogen before applying vacuum to prevent sublimation.
Tempering was performed in a standard muffle furnace. CVT experiments were conducted in a twozone furnace (LOBA, HTM Reetz GmbH) with a heating rate of 10 K min −1 . No inverse cleaning transport was performed before the deposition, since an exothermal Rh transport could occur at elevated temperatures [19]. The given transport durations started when the source reached the target temperature. After the transport, the ampoules were quenched starting from the source to condense the vapor phase.

Synthesis of RhX 3 and solid solutions
RhCl 3 (48.6%-49.2% Rh, Acros Organics) was used without further purification. RhBr 3 was synthesized by sealing ∼1 mmol Rh powder (99.95% metal basis, Alfa Aesar) together with liquid bromine (99.6%, Acros Organics) and tempering it at 600 • C for 100 h. The amount of bromine excess was chosen to result in an overpressure of 1 bar at the target temperature for a complete reaction.
RhI 3 was prepared following Commerscheidt [20], tempering Rh powder with iodine (double sublimed, analytical grade, Merck) at 600 • C for 100 h. The amount of iodine was chosen to result in an overpressure of 2 bar at the target temperature. After the tempering, the excess iodine was removed by sublimation at 200 • C.
Solid solution material was synthesized by sealing RhCl 3 , Rh powder (RhBr x Cl 3−x ) and a bromine capillary (RhBr x Cl 3−x ) or Rh powder, elemental iodine and a bromine capillary (RhBr x I 3−x ). The specific amounts of compounds were based on the amount of bromine in the capillary and the desired composition, while applying a bromine and respectively iodine excess of 0.026 mmol·ml −1 with respect to the ampoule volume. This excess should result in a halogen pressure of 1 bar each during the tempering for 100 h at 650 • C, assuming complete solid solution formation and neglecting the formation of interhalogen compounds.

Preparation of substrates
For the deposition experiments of nanocrystals, sapphire (0001), Si/SiO 2 (100) with initially 300 nm thermal oxide, yttria-stabilized zirconia (111) (9.5 mol% Y 2 O 3 ), α-SiO 2 (10-10) and SiO 2 -glass substrates were used. All substrates were purchased from Crystal GmbH and were one-side polished. Substrates were spin-coated with photoresist and cut into equal pieces with dimensions of 5.0 × 3.3 × 0.5 mm 3 . The photoresist was removed with acetone and the substrates were cleaned by ultrasonic treatment in distilled water for 15 min. Afterwards the substrates were rinsed again with distilled water and excess liquid removed with compressed nitrogen.
Si/SiO 2 substrates were tempered in air for 2 h at 1050 • C to passivate remaining unoxidized Sisurfaces before the CVT experiment.

CVT experiments
CVT was performed by sealing the designated amount of material at the source side of an ampoule, while respectively placing the substrate at the sink side before sealing. If not stated otherwise, CVT experiments were performed without additional bromine. For experiments involving RhI 3 , additional iodine was added to suppress the decomposition. The bulk crystal growth was performed in temperature ranges from 850 • C to 950 • C source temperature with 750 • C-850 • C sink temperatures, while the transport rate increases with the mean temperature, but stays below ∼0.3 mg h −1 for our ampoule geometry, depending on the source composition. If not stated otherwise, nanosheet growth experiments of RhBr x Cl 3−x were performed with 0.1 mmol of starting material, a transport duration of 30 min for a temperature gradient of 925 • C → 850 • C and using sapphire substrates for the systematic experiments. The featured CVT of RhBr x I 3−x was realized using 0.35 mmol starting material with x = 2.5 and additional 0.6 mmol iodine, applying a transport from 900 • C → 825 • C for 5 h. Here, high total pressures inside the ampoule during the experiment (∼10 bar) are to be expected.

Characterization
Scanning electron microscopy (SEM) was performed with a 'FEI Nova NanoSEM 200' (FEI company) with an Everhart-Thornley detector with 15 kV acceleration voltage. Energy-dispersive x-ray spectroscopy (EDX) was performed with a QUANTA 200/400 (AMATEX) with 51.2 µs amp time, 50 s measurement time and 15 kV acceleration voltage, using the software 'Genesis Spectrum' version 6.32 for quantification. All samples were placed on conductive carbon tape. In case deposited crystals on the nonconductive substrates were investigated, the sample was sputtered with carbon (∼90 nm) with a Carboncoater EMITECH K450 (Emitech group, twisted carbon yarn of 1 mm diameter and 0.7 g m −1 , PLANO GmbH) before the investigation.
To increase the precision of the EDX quantification results for the solid solution samples, a calibration of the Rh-L, Cl-K, Br-L and I-L peak ratios was performed with the help of pure RhCl 3 , RhBr 3 and RhI 3 . The composition of each sample was calculated by averaging five measurements of different areas or crystals. The values of x for the solid solutions were calculated by comparing the determined amounts of the halogens, expecting a Rh:X ratio of 1:3. Because of inseparable overlapping of the Al-K and Br-L peak, the EDX quantification of deposited crystals when using sapphire substrates was performed by using material that was deposited on the ampoule walls next to the substrate.
Atomic force microscopy (AFM) measurements were performed with a 'Dimension icon' (Bruker), using a Si single crystal cantilever in tapping mode with 0.3 Hz scan rate. Data analysis was performed using 'Nanoscope Analysis' version 1.8.
Diffuse-reflectance spectroscopy was performed on as-synthesized powder for all solid solution samples and RhI 3 , as well as grinded crystals obtained from CVT experiments for RhCl 3 and RhBr 3 . For the measurements a 'Shimadzu UV-3101PC Spectrometer' with an attached multi-purpose large-sample compartment 'MPC-3100' was used. The samples were pressed onto BaSO 4 pellets before the measurements. The obtained reflectance data were transformed with the Kubelka-Munk function and fitted according to the Tauc-plot method with γ = 2 for indirect and allowed transition band gaps [22,23].
PL measurements were performed at room temperature on similar samples like the diffuse reflection spectroscopy, using a microscope of home design and laser excitation at 488 nm (Omicron PhoxX diode laser). PL detection was realized using a 'Kymera 328i' spectrograph (Andor) and two detectors: a 'Newton 920' CCD camera (Andor) for visible and an 'iDus' 1.7 µm InGaAs camera (Andor) for near infrared range, both calibrated versus black body radiation. Due to the PL signal crossing the detection ranges of both detectors, the measurements of both detectors were merged at 920 nm for the final spectra.
For TEM preparation, overgrown substrates were ultrasonicated in 500 µl ethanol for 1 min and several drops of the resulting dispersion pipetted onto a lacey-carbon copper grid (Science Services GmbH, 200 mesh), so that multiple nanosheets were transferred to the grid. TEM investigation was performed with a 'FEI Titan 3 80-300' electron microscope operated at 300 keV acceleration voltage. Aberrationcorrected high resolution TEM (HRTEM), as well as SAED were carried out to observe the local crystal structure until atomic resolution. The software package 'Single-Crystal Version 3.1.5' (Crys-talMaker Software Ltd, UK) was used for indexing the SAED pattern with the corresponding structure model.
An expanded version of 'TRAGMIN 5.1' [24] was used for thermodynamic simulations. The expansions allowed calculations for gapless solid solutions under the assumption of ideal mixing behavior. The used thermodynamic data and a discussion of the same are given in the supplementary information (SI) section S1 and table S1. The external parameters (volume, amount of material) were chosen according to the actual performed experiments, including 5 × 10 −9 mol H 2 O and 1 × 10 −9 mol Ar traces.

Thermodynamic calculations
A comprehensive understanding of the thermodynamic equilibria and the vapor phase composition in the Rh-X systems is essential in order to carry out a rational and successful synthesis of the solid solutions and, based on this, to realize CVT of the rhodium halides. A discussion of the thermodynamic data used for this work is presented in the SI section S1. The datasets are based on the works of Bell et al [25], Görzel and Glaum [26], as well as Commerscheidt [20,27], and are combined with results from our own experiments to present a consistent description of the relations in these chemical systems.
In the Rh-X (X = Cl, Br, I) systems, the only nontrivial stable phases known to exist are the trihalides. Since RhCl 3 (s), RhBr 3 (s) and RhI 3 (s) are isostructural, the formation of solid solutions by combining them should be possible, keeping some limitations regarding the size compatibility of the mixing anions in mind. All of them also start to decompose into Rh (s) and the halogen at elevated temperatures, while the temperature at which a significant decomposition starts decreases from RhCl 3 , see also section 3.2 about DSC/TG measurements: (1) Besides this decomposition, stable Rh-containing vapor species are of special interest regarding the synthesis and especially a potential CVT of the materials. Simulated partial pressures for temperature ranges from 500 • C to 1200 • C for the pristine trihalides can be found in the SI figure S1, while the ones for an exemplary RhBr x Cl 3−x and RhBr x I 3−x solid solution with x = 1.5 are displayed in figure 1.
In the Rh-Cl system, the stable Rh-containing vapor species RhCl 2 (g) and RhCl 3 (g) start to form in significant amounts above RhCl 3 (s) at temperatures above the decomposition temperature (∼800 • C). This means that for CVT experiments without the addition of excess Cl, a (at least partial) decomposition will always occur (figure S1(a)). The simulations predict that in the Rh-Br system RhBr 2 (g) and RhBr 3 (g) form partial pressures that could potentially allow for vapor transport processes to occur at temperatures around 900 • C. In contrast to the Rh-Cl system, RhBr 2 (g) is supposed to be the dominant Rh-containing vapor species, while also the corresponding pressure of Br 2 (g) is much higher, due to the lower stability of RhBr 3 (s) compared to RhCl 3 (s) (figure S1(b)). The derived stability of RhI 2 (g) and RhI 3 (g) predicts that potentially transport relevant pressures could be reached around 1100 • C (figure S1(c)). However, at such temperatures, the total equilibrium pressure above RhI 3 (s) is supposed to be above 20 bar. Such conditions are not safe for common experimental setups to operate. Still, with special equipment, potentially a CVT of RhI 3 (s) might be possible, in case the predicted vapor species really exist.
The situation of chemical equilibria at elevated temperatures becomes more complex for the solid solutions. Besides the appearance of mixed interhalogen vapor species like BrCl (g) or hypothetical bihalide ones like RhClBr (g), the decomposition behavior and the partial pressures of transport relevant vapor species depend on the composition of the solid solution, since the chemical potentials of the anionic elements are also composition dependent, see SI figure S1(d). In the case of RhBr x Cl 3−x , Rh-containing species with relevant pressures for CVT are predicted above ∼925 • C for all possible compositions (figure S1(d)). However, depending on the total amount of elements and their respective ratios, the actual composition of the solid solution at elevated temperatures can be significantly different from the initial composition at e.g. room temperature. This is caused by incongruent decomposition, reasoned by the large differences in the stabilities of Cl 2 (g) and Br 2 (g), compared to RhCl 3 (s) and RhBr 3 (s). Therefore, the total amount of bromine (including bromine The initial elements for the simulation were chosen to result in 1 mmol solid solution with x = 1.5 for, using the other parameters as described in section 2.5. Note, that the actual composition of the solid solutions is temperature dependent due to incongruent decomposition. The grey area highlights partial pressures that are too low for significant contribution to transport phenomena. Only condensed phases with an amount greater than 10 −7 mmol are displayed at the bottom. containing species) in the vapor phase is generally larger than the amount of chlorine, altering the composition of the solid solution. With respect to CVT experiments, this might lead to differences between the initial starting and the deposited composition of the solid solution, especially when smaller amounts of material are used.
The situation is similar for RhBr x I 3−x , while here the partial pressures for Rh-containing vapor species are generally far lower, potentially just allowing CVT for source temperatures higher than ∼950 • C, again depending on the specific composition. Similar to binary RhI 3 , the total pressure at such a high temperature can exceed 10 bar due to the significant decomposition, but is lower than for pure RhI 3 due to the stabilization of the solid solution by combination with the more stable RhBr 3 and the entropy of mixing. This strong decomposition makes it practically unavoidable to use excess iodine for the synthesis and potential CVT.

Thermochemical and thermodynamic investigations
Similar to the parent compounds, all investigated solid solution samples are stable in atmospheric conditions and show no signs of any degradation or surface oxidation even after several months exposed to air (see figure S12).
In order to increase the accuracy of the thermodynamic simulations and to investigate the possibility of non-ideal mixing behavior of the studied solid solutions, DSC/TG measurements were performed on the pristine RhX 3 (s) compounds and exemplary solid solution compositions (x = 1.2 and 2.0 for RhBr x Cl 3−x and x = 1.5 for RhBr x I 3−x ). The RhCl 3 and RhBr 3 samples used for the DSC/TG consisted of grinded, purified crystals obtained by CVT. For the measurements of the solid solutions, as synthesized powder was used. The results are graphically displayed in SI figure S3.
All DSC/TG measurements confirmed the purity of the investigated samples. Since the decomposition of all samples to Rh (s) occurs at temperatures, where the released vapor is completely dominated by the halogens (see section 3.1, figure 1 and SI figure S1), the released heat of decomposition can be assigned to the decomposition in reaction (1) for RhX 3 (s) or reactions (2) and (3) for the solid solutions: Using this information together with thermodynamic data of the well-known product species allows for the determination of the heat of formation of the RhX 3 and solid solution samples. A more detailed discussion of the DSC/TG results can be found in SI section S3, while the calculated enthalpies are given in SI  [30]). For the solid solutions, the results suggest a small exothermal enthalpy of mixing for the investigated samples of about −11 to −16 kJ·mol −1 . However, due to experimental difficulties, these values are close to the estimated experimental error of these measurements.

Structural investigation
The synthesized parent compounds and their solid solutions were investigated by pXRD to check for potential impurities (such as elemental Rh) and to further identify possible deviations from ideal structural mixing behavior by comparison with Vegard's law. The unmanipulated diffraction pattern compared with the fitted refinement results can be found in the SI figures S4 and S5. For all samples, all observed reflections could be assigned to the respective phase with the monoclinic space group C2/m, while no impurities or reflection splitting were detected, thus confirming a successful synthesis. This also confirms that the stacking order at room temperature of the solid solutions remains similar to the RhBr 3type of the parent compounds. Figure 2  To make a comparison of the refined lattice parameters with Vegard's law, the composition of each sample was determined by calibrated EDX analysis. The results are shown in SI figure S6 and the values are given in table S4. The intra-layer defining lattice parameters a and b follow Vegard's law quite well, while for the interlayer ones (c, β, interlayer distance [ILD]) a small but systematic deviation from linear dependency is observed for the RhBr x Cl 3−x mixtures, which is commonly observed in anionic solid solutions of 2D materials [31][32][33]. For RhBr x I 3−x samples on the other side, similar trends of the different lattice parameters are present. However, for the RhBr x I 3−x sample with x = 1.5, the results show a deviation from linear behavior for a and b towards slightly smaller values, while the other parameters follow Vegard's law. A special case that would explain this observation would be the occurrence of partial or complete ordering of the anions for this specific composition. However, the pXRD pattern does not show any signs of symmetry breaking or additional reflections that would indicate the formation of a superstructure. To investigate this issue more deeply, further studies could potentially investigate the course of lattice parameters in this specific range of the RhBr x I 3−x composition to follow the course of lattice parameter changes with greater resolution.
As all calculated a √ 3: b ratios are equal to 1 within the expectable range of error (table S4), this further proves that the hexagonal arrangement of the Rh-cations also remains intact for all investigated samples.

Optical measurements
Previous work of Wang et al demonstrated that the band gap of RhI 3 nanosheets can be tuned with their height in the few-layer regime [14]. Such behavior is potentially interesting for optoelectronic nanoscale applications. However, since to area of potential band gap tuning in nanoscale dimension is determined by the band gap of the bulk material, the possibility of adjusting the properties of such bulk material is also highly desirable. To investigate, if such a band gap tuning is possible already for the bulk material in the solid solutions, the optical band gap of the synthesized powder material was investigated by diffuse reflection spectroscopy. The determined optical band gaps are shown in figure 3(a). The results show that for small amounts of Br in the RhBr x Cl 3−x solid solution, the optical band gap remains stable at ∼1.51 eV and drops significantly to 1.40 eV for x = 0.64, while then remaining stable in this energy range up to pure RhBr 3 .  The first reduction of the optical band gap is visible to the naked eye due to the color change of the solid solution powder. For RhBr x Cl 3−x , the color of the solid solution darkened starting from wine red of pure RhCl 3 to x = 0.4 (figure 4(a)), while remaining black for all other synthesized compositions ( figure 4(b)), including the whole RhBr x I 3−x series. For the solid solution of RhBr 3 and RhI 3 on the other side, the band gap further decreases in a linear relation with x down to ∼1.17 eV for x = 0.79 and RhI 3 . Our value of the optical band gap for RhI 3 is close to the 1.1 eV reported by Wang et al for 18 layers of RhI 3 , which is the thickest sample that they reported [14]. These results show that the optical band gap of the bulk material system can be tuned in an energy range from 1.5 eV (RhCl 3 ) to 1.2 eV (RhI 3 ) (near infrared range) by simply controlling the mixing ratio of the anions in the solid solution.
A similar conclusion follows from the complementary PL measurements. Upon laser excitation at 488 nm, all samples of the RhBr x Cl 3−x series showed near infrared emission consisting of one slightly asymmetric band (see figure 3(b) for a representative example), with the shape well described by a bigaussian function (see SI figure S8). Similar spectra were recorded for the RhBr x I 3−x series, which however showed a fast drop of the PL intensity with the increase of the iodine content, whereas the emission of pure RhI 3 was too weak for a reliable measurement. The PL bands exhibited a systematic narrowing from RhCl 3 to RhBr 3 to RhBr 0.8 I 2.2 , whereas the variation of the PL peak position with the sample composition paralleled that of the optical band gap in diffuse reflectance measurements (see figure 3(a)).
In addition to this tuning of the bulk material property, the optical properties, respectively the band gap and potentially also the PL energy, could be additionally fine-tuned when the materials get down scaled to few-layer dimensions, like it was demonstrated for RhI 3 [14]. This would open up additional application related opportunities in e.g. optoelectronics, using ultrathin nanocrystals of these materials. Nevertheless, additional research is needed to investigate these property tuning abilities in the case of the solid solution nanomaterials.

CVT and nanosheet deposition of RhBr x Cl 3−x
Based on the calculations described in section 3.1, the CVT of RhCl 3 , RhBr 3 , RhBr x Cl 3−x and RhBr x I 3−x were conducted, while transport for RhI 3 was not successful. For the pure RhCl 3 and RhBr 3 , we observed a transport for T source ⩾ 850 • C, which is in good agreement with the simulation results. The successful transport of RhBr 3 without the addition of an external transport agent indirectly proves the existence and stability of RhBr x (g) vapor species, as predicted with the estimated thermodynamic data and simulations. However, the predicted transport dominance of RhBr 2 (g) over RhBr 3 (g) in this case, in contrast to the transport of RhCl 3 , cannot be verified without further experiments. For the RhBr x Cl 3−x solid solution, a transport only occurred for T source > 900 • C. Larger bulk crystals of these materials were obtained by using enough material and longer transport durations, whereas flat crystals with lateral dimensions of several mm 2 could easily be obtained, like the ones displayed in figures 4(a) and (b).
For the deposition of nanosheets, an optimization of the transport parameters was performed, while also testing different kinds of substrates. While the YSZ and Si/SiO 2 substrates started to decompose at such high temperatures and were excluded from further experiments, the other investigated substrates did not show significant differences in their results, so the following systematic experiments were performed with sapphire (0001) substrates. Even though the transport rate in this system is also depending on the composition, transports from 925 • C to 850 • C for transport durations around 30 min were generally found to give the best reproducible results for all compositions of RhBr x Cl 3−x . Examples of such as-grown nanosheets are displayed in figure 5. These crystals show sharp edges and appear pale blue, whereas the color saturation decreases with height. Crystals with heights >∼100 nm appear intensely colored within the full visible spectrum. This behavior is similar to the chromium trihalides [10,34], but seems to be even more pronounced in this system. With this set of parameters, regularly nanosheets with heights of about 5-30 nm were obtained, while in some cases few-layer crystals and even monolayers were found, as presented in figures 5(g) and (h). Most of the nanosheets show areas with lateral dimensions of several µm 2 . The homogeneity of such deposited crystals was confirmed by EDX measurements and mapping, whereas exemplary results can be found in the SI figures S9 and S10. Similar to the synthesized powder material, the bulk crystals as well as the deposited nanosheets show degradation even after several months stored at ambient conditions (see figure S12), which makes them interesting for various kinds of potential applications.
To further investigate the quality and crystallinity of the deposited nanosheets, HRTEM and SAED were performed on exemplary RhBr 1.5 Cl 1.5 nanosheets, with representative results displayed in figure 6. The highly periodic hexagonal arrangement of atoms in the HRTEM images in figures 6(c) and (d) indicates high crystallinity. The perfect match of the experimental SAED along the [001] zone axis ( figure 6(b)) with the simulated pattern strongly the proposed crystal structure and confirm the high sample quality of the deposited material. The slight stretching in the atomic contrast visible in figure 6(d) from top-left to bottom right can be associated to a slight bending of the crystal and displays the stacking of the layers in the structure. This bending was most likely introduced during the transfer process of the crystals to the TEM grid.
To ensure a deposition of nanosheets with a predictable composition, several experiments were performed to investigate the occurring decomposition of the source material at the growth temperatures as well as possible enrichment effects during the transport by EDX measurements. In figure 7 the relations between starting composition, the composition of the source material during the experiment and deposited composition are displayed. The sink composition of one experiment was determined by averaging five measurements of different deposited crystals, while for the source material leftover powder after the experiment was mixed and five measurements averaged.
For all experiments with the same starting material and amount, the deposited sink compositions were practically identical, proving the reproducibility of the presented method. As the simulations suggested, when the solid solution starting material with a specific composition is heated up to the source temperature (in this case 925 • C), a significant and incongruent decomposition occurs. Since for the nanosheet growth experiments, only trace amounts of material were actually deposited in the sink and the ampoules were quenched after the transport duration of 0.5 h, the determined composition of remaining source material after the experiment can be assumed to be the source composition during the experiment. Due to the decomposition, for Br-rich starting materials, most of the remaining material in the source was Rh (s) and only minor amounts of solid solution were left after the experiments. This significantly increasing the error for the determination of the leftover solid solution composition due the reduced concentrations of Cl and Br. However, the errors of the determined solid solution composition in the source significantly decrease with increasing Cl-amount of the starting material due to the increasing stability of the solid solution, thus more remaining solid solution in the source.   means that actually no enrichment during the transport occurs, so that the difference in composition between the used starting material and the deposited sink material is determined by the initial incongruent decomposition of the material.
The experiments with starting materials of highest Br-content (x = 2.47 and 2.82) resulted in no deposition for a source temperature of 925 • C and 0.1 mmol starting material. Here, the source material after the experiment was found to be almost pure Rh (s) with barely detectable traces of Br, that most likely condensed in the form of RhBr 3 (s) during the quenching. Since no transport was observed in these cases, this means that the amount of material was too small to reach equilibrium pressures of Cl 2 (g) and Br 2 (g) above the solid solution to be reached by the decomposition. Thus, the partial pressures of Rh-containing vapor species did not reach values high enough for CVT or nucleation to occur.
Interestingly, when pure RhBr 3 (s) is used as starting material, 0.1 mmol are enough for a deposition to take place. The explanation for this can be found in the fact, that in the case of the solid solution experiments chlorine is present in the system and is absent for the pure RhBr 3 (s) transport. The presence of chlorine results of the formation of the stable interhalogen BrCl (g), draining significant amounts of both halogens from the equilibria and ultimately resulting in increased amounts of decomposed solid solution.
Since especially for the starting materials with high Br-amount the composition shift caused by the decomposition is large, no samples with x > 1.5 were possible to grow with just 0.1 mmol starting material at 925 • C source temperature. However, since the reason for the decomposition is the formation of a specific amount of vapor species for reaching the equilibrium conditions, the resulting composition of the source material and therefore also of the deposited material should be controllable by increasing the amount of starting material. To prove this, experiments for samples of x = 1.59 and 2.83 with more than 0.1 mmol starting material were conducted. The results are displayed in SI figure S11, showing indeed that compositions with 1.5 ⩽ x ⩽ 3 can be obtained by using more than 0.1 mmol starting material and that the solid solution composition in source and sink approaches the initial composition of the starting material with increasing amount. Therefore, it is not only possible to fine tune the deposited composition by proper adjustment of the amount of starting material, but also to grow nanosheets with x > 1.5. Overall, nanosheets with a controllable composition within the whole solid solution range are accessible, opening up the possibility for future systematic and detailed investigation about the property changes, e.g. in regard to the band gap, when downscaling these 2D materials to nanoscale dimensions.
Theoretically, also a reduction of the ampoule volume would decrease the composition shift caused by the decomposition, since fewer amounts of vapor species would be required to reach equilibrium conditions. Experiments that tried to counteract the strong decomposition by introducing additional amounts of Br inside capillaries to the nanosheet growth experiments were not successful. Investigation of the residue source material showed that the special glass of the capillaries did not withstand the corrosive atmosphere at such high temperatures. This most likely altered the chemical composition of the vapor phase during the experiment, so that the transport conditions changed in an unpredictable way that did not result in CVT to occur. However, when additional Br (and/or Cl) could be added to the ampoule in a consistent way, e.g. using Br-capillaries made of more resilient glass, the decomposition of the solid solution material should be avoidable and could potentially increase the reaction economics.

CVT of RhBr x I 3−x
A CVT of RhBr x I 3−x solid solutions is more difficult than for RhBr x Cl 3−x , due to the much lower stability of RhI 3 at the required elevated temperatures. However, with sufficiently high pressures of iodine and bromine, even here a CVT can be realized. An exemplary transport of RhBr x I 3−x with x = 2.4 (Brrich) was performed with 0.3 mmol starting material and 0.6 mmol iodine excess for 5 h from 900 • C → 825 • C. Although no relevant deposition of material was observed on the substrate, well-shaped crystals with a size of ∼250-1000 µm 2 and a composition of x = 2.55 grew on the ampoule walls in the sink during the transport, see figure 4(c). The size could potentially be increased by simply increasing the transport duration and starting material. Even a deposition of nanosheets on substrates seems conceivable with further transport parameter optimization. However, as the simulations predicted, the main problem for successful CVT in this system is the high required pressures of halogens to suppress the decomposition and to form relevant amounts of transport active Rh-containing vapor species. For compositions with high I-content, very high temperatures and respectively pressures are needed, for which a large excess of starting material or additional halogens, as well as pressure resistant ampoules are required, making experiments in this regard expensive and elaborate. Nevertheless, our experiments and calculations prove the possibility to achieve a successful CVT in the RhBr x I 3−x system and are transferable to other compositions of the solid solution. Further improvement with regard to the transport economics could potentially be achieved by lowering the transport distance and volume of the ampoule, or by finding stable Rh-containing vapor complexes that would allow the Rh-volatilization in this system at lower temperatures.

Conclusions
In the present work, we report about the preparation and characterization of 2D solid solutions in the RhX 3 (X = Cl, Br, I) system, namely RhBr x Cl 3−x and RhBr x I 3−x . The successful synthesis was realized by rational planning and preceding thermodynamic simulations, which were successfully confirmed with respective experiments.
The simulations predicted the dominant vapor species, which are additionally relevant for the CVT and the appropriate conditions for the transports in terms of absolute temperature and temperature gradient. The enthalpies of formation of the pristine RhX 3 (s) and selected solid solution compounds were determined by DSC/TG experiments to further substantiate the results of the thermodynamic simulations. After the synthesis of the solid solution powder material, phase purity and the evolution of the lattice parameters were investigated by pXRD. Only for the ILD, a slight deviation from Vegard's law to higher distances for both solid solutions is observed. One exception seems to exist for RhBr 1.5 I 1.5 , showing a decrease in the intralayer parameters a and b, but not for the ILD. Still, the pXRD measurements show no evidence of nonrandom solid solution formation for all samples. Furthermore, the optical band gap of the synthesized solid solution bulk material was determined by diffuse reflection measurements and consecutive Taucplot. The optical band gap of the bulk material can be tuned in an energy range from 1.5 eV (RhCl 3 ) to 1.2 eV (RhI 3 ) by simply controlling the halogen mixing ratio of the solid solutions, making these materials potentially interesting candidates for optoelectronic applications. Complementary to these results, all samples show also PL at energies close to the observed optical band gaps, but the emission intensity in the RhBr x I 3−x series gradually decreases to almost zero for RhI 3 . Based on the previous simulations, we realized the CVT for the growth of bulk crystals, as well as high quality nanosheets for RhBr x Cl 3−x . The best results for the nanosheet deposition were achieved by transport from 925 • C → 850 • C for 30 min on sapphire (0001) substrates. While the average deposited nanosheets display heights around 5-30 nm and lateral dimensions of several µm, asgrown nanosheets down to the monolayer limit were observed as well. The high quality of the nanosheets was demonstrated by AFM, HRTEM and SAED. Such nanosheets will allow for consecutive future studies about downscaling effects in this solid solution system. We explain the observed differences of the composition of the starting material and the deposited crystals, so that the composition of the deposited material can be precisely controlled by the choice of the starting composition and the used amount of starting material. The CVT of RhBr x I 3−x was demonstrated on an exemplary composition, but is difficult to expand to the general case due to the very high required pressures for the transport to take place. Overall, the demonstrated rational approach on synthesis and high quality nanosheet deposition opens opportunities for continued research among pure RhX 3 bulk and nanosheets samples as well as their solid solutions, which also support a specialized optical property tuning. To further explore the potential of the described solid solutions with respect to possible applications in the (opto)electronic field, future studies should investigate the changes in the (especially optical) properties in greater detail when the nanocrystals are reduced to a few layers. The investigation of other application-relevant properties such as the specific detectivity or the electron mobility of these materials for the use in e.g. sensor or photodetector applications is also necessary to assess the full potential.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.

Funding
The 'Deutsche Forschungsgemeinschaft' is gratefully acknowledged for funding multiple authors: S F received funding from the project 'next2D' , Project Number 437046793. D W received funding from Project Number 417590517, Grant Number SFB 1415. A P received funding from Project Number PO 1602/8-1. Also the financial support from the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter-ct.qmat (EXC 2147, Project-id 390858490) is gratefully acknowledged.

Conflict of interest
The authors declare no conflict of interest.