Data-Driven Mapping of the Cesium Cadmium Bromide Phase Space Utilizing a Soft-Chemistry Approach

Abstract

Soft-chemistry techniques provide a versatile approach to synthesizing inorganic materials under mild conditions, enabling access to compositions and structures that are challenging to achieve through traditional thermodynamically driven solid-state methods. However, these solution-based routes often result in phase competition, requiring precise control over reaction conditions to achieve selective product formation. While one-variable-at-a-time (OVAT) approaches have traditionally been used for phase selection, data-driven strategies are emerging as more efficient methods for navigating complex synthetic spaces. Ternary metal halides, such as cesium cadmium bromides (Cs–Cd–Br), are of growing interest due to their potential in wide and ultrawide band gap applications. Unlike the well-studied cesium lead halide phases, the compositional diversity and solution-based synthesis of ternary Cs–Cd–Br phases remain largely unexplored. This study systematically investigates the synthetic phase space of the Cs–Cd–Br system by constructing a data-driven phase map. Using a common set of precursors and a standardized experimental procedure, we successfully synthesize all four known Cs–Cd–Br phasesCsCdBr₃, Cs₂CdBr₄, Cs₃CdBr₅, and Cs₇Cd₃Br₁₃each exhibiting distinct structures, morphologies, and optical properties. Our findings highlight the potential of soft-chemistry methods for expanding the library of ternary metal halides and provide key insights into the thermodynamic and kinetic factors governing phase formation.

Introduction

Solution-phase soft chemistry (chimie douce) methods have emerged as an effective strategy for synthesizing inorganic materials with controlled structures and compositions. Unlike traditional solid-state synthesis, which is primarily governed by thermodynamic factors such as temperature, pressure, and composition, chimie douce methods introduce additional kinetic control through variables such as precursor reactivity. This flexibility gives access to a wider swath of the material phase spaceincluding metastable structures that do not exist on thermodynamic phase diagrams. − However, the inherent complexity of chimie douce methods can also make them difficult to control and result in the simultaneous formation of multiple phases, making it challenging to isolate a single, phase-pure material in a targeted fashion. Using the traditional one-variable-at-a-time (OVAT) approach for phase control in various materials, such as metal chalcogenides − and pnictides, − has proven time- and labor-intensive, since it is extremely hard to capture optimal conditions in a high-dimensional space by one-dimensional (1D) movements. For example, our effort in isolating four nickel sulfide compositions (i.e., Ni₃S₄, NiS, Ni₉S₈, and Ni₃S₂) required years of iterative tuning of precursor reactivity, temperature, and stoichiometry. In contrast, data-driven methods can efficiently navigate these complex phase spaces by revealing the interactions among multiple variables, thereby rapidly reaching conditions that isolate pure phases, as demonstrated in our studies on binary copper selenide and cobalt oxide systems. ,

Chimie douce methods have proven especially fruitful for the synthesis of ternary all-inorganic metal halides with diverse compositions and structures, expanding their applications in light-emitting diodes, photodetectors, lasers, and deep-ultraviolet optoelectronics. Early research on cesium lead halide perovskites (CsPbX₃, where X = Cl, Br, I) utilized the hot injection synthesis of cesium oleate and lead halides (PbX₂) in the presence of amine and carboxylate ligands. In that synthesis, PbX₂ served as both lead and halide sources, coupling the Pb/X ratio and impeding access to other ternary stoichiometries. , The introduction of exogenous organic halide sources (i.e., benzoyl and phenacyl halides) as an independent halide source resolved this limitation, allowing for the synthesis of multinary lead halides with tunable compositions. ,

As a variant of cesium lead halides, the cesium cadmium halides (Cs–Cd–X) have attracted interest due to their ultrawide (>3.4 eV) or wide (>2.0 eV) band gaps and unique optoelectronic properties. − The ternary Cs–Cd–Cl, Cs–Cd–Br, and Cs–Cd–I materials families have been synthesized via various methods, including solvent evaporation, , ball milling, and Bridgman–Stockbarger crystal growth. However, chimie douce synthetic routes to these materials remain underexplored, particularly regarding how to access multiple phases using a common set of precursors and reaction conditions. Toward this end, Schaak et al. reported the synthesis of three distinct Cs–Cd–Cl compositions by the reaction of cesium oleate with CdCl₂, finding that the key phase determining variable was the rate of cesium oleate precursor injection that controlled the local Cs/Cd concentration upon nucleation.

According to the Cs–Cd–Br ternary phase diagram on Materials Project, four thermodynamically accessible compositions exist along the CsBr–CdBr₂ tie line: CsCdBr₃, Cs₂CdBr₄, Cs₃CdBr₅, and Cs₇Cd₃Br₁₃ (Figure a,b). The hexagonal CsCdBr₃ phase (P6₃/mmc) consists of face-sharing [CdBr₆] octahedra forming one-dimensional [CdBr₃] chains, which are hexagonally packed and separated by 12-coordinate Cs⁺. The orthorhombic Cs₂CdBr₄ phase (Pnma) features isolated [CdBr₄] tetrahedra surrounded by 8- or 9-coordinate Cs⁺. The tetragonal Cs₃CdBr₅ phase (I4/mcm) also contains isolated [CdBr₄] tetrahedra, but with a different packing arrangement among 8- or 10-coordinate Cs⁺. The tetragonal Cs₇Cd₃Br₁₃ (I4/mcm) phase uniquely combines both chains of corner-sharing [CdBr₆] octahedra and isolated [CdBr₄] tetrahedra, with Cs⁺ in 8- or 9-coordinate geometries. The energy of formation above the convex hull for all four phases ranges from 0 to 0.004 eV/atom, indicating good thermodynamic stability and synthetic accessibility. Notably, the CsCdBr₃ and Cs₂CdBr₄ phases are not isostructural to their chloride counterparts reported by Schaak et al. Of the possible phases within the ternary Cs–Cd–Br materials family, CsCdBr₃, , Cs₂CdBr₄, Cs₇Cd₃Br₁₃, ,, and more recently the Cs₃CdBr₅ phases have been made with either hydrothermal, ball milling, or limited hot injection reactions using cesium oleate, cadmium oxide or cadmium acetate, and halide sources such as hydrobromic acid. , To this point, there is not a cohesive chimie douce synthesis strategy for accessing all four Cs–Cd–Br phases from a common set of precursors and reaction conditions. The thermodynamic stability of all four ternary phases determined their tendency to evolve simultaneously, leading to a highly complex phase space with numerous possible combinations. That is, the subsets of the four ternary phases, along with the binary CsBr and CdBr₂, can theoretically yield up to 2⁶ = 64 unique phase combinations. Moreover, controlling the ternary precursor composition requires managing at least three independent degrees of freedom, further increasing the number of variables that must be investigated. This inherent complexity renders phase selection and synthetic control virtually impossible through traditional OVAT approaches, necessitating a more systematic exploration of the experimental variable space.

1.

(a) Crystal structures of hexagonal CsCdBr₃ (coded: A), orthorhombic Cs₂CdBr₄ (coded: B), tetragonal Cs₃CdBr₅ (coded: C), and tetragonal Cs₇Cd₃Br₁₃ (coded: D). Cesium (Cs⁺) cations are teal, cadmium (Cd²⁺) cations are purple and surrounded by purple polyhedra, bromine (Br^–) anions are brown. (b) A pseudobinary phase diagram showing the presence of the four Cs–Cd–Br compositions as linear combinations of CsBr and CdBr₂. (c) Coded and color identifiers for each of the 20 unique phases or phase combinations observed in this study.

In this work, we employed data-driven methods to systematically explore the chimie douce synthesis of ternary Cs–Cd–Br materials. Using the theories of statistical design of experiments (DoE), we efficiently sampled the synthetic space using a minimal number of experiments. The construction of multidimensional synthetic phase maps allowed for the isolation of all four known stoichiometries of Cs–Cd–Br despite the complexity of the ternary phase spacewhere some phases were isolated in only one or few experiments in the whole study. The phase maps also provided insights into thermodynamic and kinetic factors governing phase selection and reactivity, which can potentially be applied to the synthesis of other metal halide materials. This study highlights the power of data-driven strategies in more complex materials systems, paving the way for more efficient synthetic exploration using small data sets.

Results and Discussion

To synthesize the Cs–Cd–Br materials, we injected an organic Br source directly into a solution of CdO and Cs₂CO₃ in the presence of oleic acid, oleylamine, and octadecene. The precursors were intentionally chosen so that the cadmium, cesium, and bromide sources were decoupled from one another, allowing for more flexible compositional tunability. One of the steps in the reaction scheme, where the CdO precursor solution was heated to 220 °C to allow for dissolution and activation of Cd²⁺, was inspired by Pradhan’s work on Cs₂CdBr₄ and Cs₇Cd₃Br₁₃. , More information on the complete procedure used to synthesize phase-pure materials can be found in the Experimental Section. To construct the Cs–Cd–Br phase map, the first step was to set the bounds of the experimental variable space. The key variables selected for this study were: (1) organic Br precursor reactivity, (2) reaction temperature, (3) ligand ratio of oleylamine-to-oleic acid (OAm/OAc), (4) Cs/Cd precursor ratio, and (5) Br/Cd precursor ratio. Preliminary experiments were performed to set the experimental boundaries (Table ). The choice of variables was based on a few exploratory reactions that utilized the reaction scheme discussed above, where all the variables were shown to affect the resulting phase(s) of the material products. The boundaries were set based on the higher and lower amounts that resulted in mostly ternary products. Reactions outside these bounds often yielded mostly binary CsBr or CdBr₂, which were not desirable. The organic Br precursor reactivity is a categorical variable defined by the different structures of benzoyl bromide (PhC­(O)­Br) and phenacyl bromide (PhC­(O)­CH₂Br). Since phenacyl bromide has a lower boiling point (∼140 °C) than benzoyl bromide (∼220 °C), its experimental matrix was assigned a lower temperature range. The oleylamine-to-oleic acid ligand ratio was defined by their fractions in a fixed 2.5 mL ligand mixture. It was found that the formation of ternary phases required at least 0.5 mL (20 vol %) of both oleylamine and oleic acid, indicating their importance in converting the CdO precursor into reactive Cd²⁺ complexes. The precursor ratios were controlled using two independent variables to account for the system’s degrees of freedom (D.F. = 3). While the overall precursor concentration (D.F. = 1) was fixed by the CdO precursor amount, the Cs/Cd and Br/Cd ratios were independently varied to ensure full coverage of the possible ternary compositions. The bounds of these ratios were carefully set to prevent the exclusive formation of CsBr or CdBr₂ across the variable spacehigh Cs/Cd ratios favored CsBr formation, while low Cs/Cd ratios led to CdBr₂ formation. For statistical consistency, the amount of CdO precursor, reaction time (3 min posthalide injection), and total reaction volume were kept constant across all reactions. Additionally, all X-ray diffraction (XRD) data were collected within 2 h of synthesis to minimize the effects of possible postsynthetic transformations.

1. Bounds of the Experimental Space.

bound	temperature (°C)	ligand ratio (OAm/OAc)	Cs/Cd ratio	Br/Cd ratio
high (+1)	300 (benzoyl bromide)	4:1	3:1	7:1
	280 (phenacyl bromide)
low (−1)	120 (benzoyl bromide)	1:4	1:1	1:1
	100 (phenacyl bromide)

After the variable bounds were set, we utilized common screening and optimization matrices in DoE to define our reaction conditions. These matrices were designed to be orthogonal with evenly distributed points, allowing for an efficient and systematic exploration of the high-dimensional experimental space by performing a minimal number of experiments. − The organic Br precursor was a categorical variable with two discrete molecular structures, while the other four numerical variables were continuously tuned within their respective bounds. Therefore, two parallel phase maps were constructed, corresponding to the two organic Br precursors. Phase outcomes were assessed by powder X-ray diffraction (PXRD), though relative phase quantities were not considered for experimental expediency. Additionally, phase mixtures containing more than three phases were not considered, as the presence of a fourth minor phase would be difficult to interpret from XRD patterns of low symmetry structures. The experimental conditions and resulting phase outcomes of all reactions are provided in Tables S1–S7, with their resulting XRD patterns included in Figures S5–S31. All the observed phase combinations were color- and letter-coded, as shown in Figure c.

Figure demonstrates the stepwise construction of our phase maps using the benzoyl bromide precursor as an example. Alternative views of the variable space are available in Figure S33 to visualize the dispersion of data points. To preliminarily evaluate the four continuous experimental variables at their high (+1) and low (−1) boundary levels, we conducted a 2-level full-factorial design with 2⁴ = 16 reactions for each of the organic Br precursors (Figure a). Triplicate center points were carried out for error estimation. Phase-pure CsCdBr₃ and Cs₃CdBr₅ were observed in both benzoyl bromide and phenacyl bromide screening matrices (Tables S1 and S2). The center-point triplicates (Tables S1 and S2, reactions #17–19) yielded reproducible results (Figures S5 and S18), confirming the reproducibility of our experimental protocols. However, Cs₂CdBr₄ and Cs₇Cd₃Br₁₃ only appeared as a fraction of the product in a few benzoyl bromide reactions, including the center point (Table S1), necessitating further exploration within the experimental variable space. Notably, the initial phenacyl bromide screening matrix (Table S2) did not yield any Cs₂CdBr₄ or Cs₇Cd₃Br₁₃, even in combination with other phases.

2.

Stepwise construction of the multidimensional phase map leading to the synthesis of all four Cs–Cd–Br phases when utilizing benzoyl bromide as the organic Br precursor. The experimental variable space is visualized using the three most important variables, with overlapping data points stacked vertically to show outcomes with high (top) and low (bottom) Br/Cd precursor ratios. Colored dots correspond to pure Cs–Cd–Br phases while gray dots indicate mixed phases. (a) The initial 2⁴ full-factorial matrix, leading to phase-pure CsCdBr₃ (A) and Cs₃CdBr₅ (C), and the gray cube showing the bounding of the experimental variable space. (b) The addition of a secondary Doehlert matrix, leading to phase-pure Cs₂CdBr₄ (B). (c) The addition of reactions at a lower temperature (indicated by the black square), leading to phase-pure Cs₇Cd₃Br₁₃ (D).

Based on the outcomes of experiments defined by the full factorial screening matrices, we employed secondary Doehlert matrices (Figure b), which are known to be efficient in sampling the inside of variable spaces at evenly distributed points (Tables S3 and S4). These matrices were oriented such that the most important variables were evaluated at the greatest number of levels. A feature ranking algorithm based on χ² tests was applied to the benzoyl bromide factorial matrix, identifying the variables in order of importance; that is, temperature, oleylamine-to-oleic acid ligand ratio, Cs/Cd precursor ratio, and Br/Cd precursor ratio (Figure S4). Consequently, the four-dimensional (4D) Doehlert matrix was aligned to assess these variables at 7, 7, 5, and 3 levels, respectively. The Doehlert experiments yielded new phase combinations, including phase-pure Cs₂CdBr₄ synthesized with both organic Br precursors. However, Cs₇Cd₃Br₁₃ was still observed only as a phase fraction in a few experiments with exclusively benzoyl bromide and was completely absent in all reactions using phenacyl bromide (Tables S1–S4).

Suspecting that Cs₇Cd₃Br₁₃ might be a kinetically favored phase under these reaction conditions requiring lower temperatures for stabilization, we further extended our lower boundary condition with benzoyl bromide to 60 °C, beyond the initial lower bound (coded value = −1.67). Indeed, one reaction at this temperature yielded phase-pure Cs₇Cd₃Br₁₃, while only two out of ten other conditions at 60 °C produced it as a minor phase fraction. This result underscored the complexity of the Cs–Cd–Br materials system, highlighting the limitations of traditional OVAT approaches in achieving phase-pure products in a high-dimensional synthetic space. In contrast, further lowering the temperature <100 °C for phenacyl bromide did not result in the observation of the Cs₇Cd₃Br₁₃ phase. Therefore, the lower bound of the phenacyl bromide experimental space was maintained at 100 °C.

The powder XRD patterns and scanning electron microscopy (SEM) images of the four phase-pure Cs–Cd–Br materials are given in Figure . The XRD patterns were phase matched with standard patterns from the Inorganic Crystal Structure Database (ICSD), illustrating the phase purity of the products. It was found that CsCdBr₃ adopted a roughly spherical morphology, with an average particle diameter of ∼600 nm that varied greatly from ∼430 to 860 nm. Cs₂CdBr₄ and Cs₃CdBr₅ exhibited short rod or platelet morphologies. The Cs₂CdBr₄ rods tended to be more anisotropic with average dimensions of ∼120 nm by ∼630 nm (aspect ratio = 5.04) while the Cs₃CdBr₅ platelets had average dimensions of ∼320 nm by ∼660 nm (aspect ratio = 2.06). In contrast, Cs₇Cd₃Br₁₃ formed thin rods or ribbons that were highly anisotropic (dimensions varied greatly but were on average ∼300 nm by tens of microns). Ultraviolet–visible-near infrared (UV–vis–NIR) diffuse reflectance spectroscopy was performed to measure the optical band gaps of the materials using the Kubelka–Munk function (Figure S2). From Tauc plot analysis, and assuming direct band gaps, Cs₂CdBr₄ and Cs₃CdBr₅, which possessed a slight yellow tint, exhibited band gaps of 2.41 and 2.36 eV, respectively. CsCdBr₃ and Cs₇Cd₃Br₁₃, appearing white, had larger band gaps of 3.46 and 3.10 eV, respectively (Figure S2). These results classify Cs₂CdBr₄, Cs₃CdBr₅, and Cs₇Cd₃Br₁₃ as wide-band gap materials, while CsCdBr₃ falls into the ultrawide-band gap category.

3.

Powder XRD patterns and SEM images of phase-pure (a) CsCdBr₃, (b) Cs₂CdBr₄, (c) Cs₃CdBr₅, and (d) Cs₇Cd₃Br₁₃. Scale bars represent 1 μm in all cases.

With results from all the reactions in Tables S1–S6, a multidimensional synthetic phase map was constructed for each organic Br precursor to analyze the reaction chemistry (Figure ). The maps are visualized using the three most statistically significant variables on phase outcometemperature, oleylamine-to-oleic acid ligand ratio, and Cs/Cd precursor ratioidentified through a feature ranking algorithm using χ² tests (Figure a,b). Additional visualizations of the phase maps are provided in Figure S3 to display the frequency distribution of different phase combinations and their corresponding variable sets.

4.

Phase maps (left) and importance scores (right) ranking the significance of different experimental variables for reactions with (a) benzoyl bromide and (b) phenacyl bromide. The experimental variable space in the phase maps is visualized using the three most important variables ranked by the importance scores, with overlapping data points stacked vertically to show outcomes with high (top) and low (bottom) Br/Cd precursor ratios.

For both benzoyl bromide and phenacyl bromide, oleylamine concentration and temperature emerged as the most influential variables. This can be attributed to the role of oleylamine in promoting halide release via its reaction with the organic halide precursor. Both acyl halides (benzoyl bromide), and α-halo ketones (phenacyl bromide), are known to react with nucleophiles, such as amines, leading to the release of hydrohalic acids. − , The main difference between these two compounds is the additional methylene (−CH₂−) group between the bromine and carbonyl in phenacyl bromide, which leads to distinct halide release mechanisms: benzoyl bromide undergoes nucleophilic substitution via an S_N1 mechanism, while phenacyl bromide follows an S_N2 pathway. , Consequently, benzoyl bromide releases halide more readily, even at room temperature. As shown in Figure a, benzoyl bromide facilitated binary or ternary metal halide phase formation at temperatures as low as 60 °C. In contrast, phenacyl bromide exhibited no reaction (coded as T, Figure b) at 100 °C when both oleylamine-to-oleic acid ligand ratio and Cs/Cd precursor ratio were at their lowest levels, indicating its lower reactivity and greater dependence on oleylamine concentration. While the halide release mechanism differs between benzoyl bromide and phenacyl bromide, both organic Br precursors provide more controlled halide release than aliphatic acyl halides due to stabilization by π-overlap in the ground state, allowing for fine-tuned composition control. , Temperature also plays a crucial role in balancing kinetic and thermodynamic factors, influencing reaction pathways through volatilization (benzoyl bromide bp = ∼220 °C; phenacyl bromide bp = ∼140 °C) or C–Br bond cleavage driven by increased thermal energy. Notably, the Br/Cd precursor ratio had the least effect on phase determination, suggesting that Br activation is more strongly influenced by temperature and ligand ratio than by the Br-to-metal precursor ratio, which is a nonintuitive result that is only revealed through the data-driven approach.

In the phase maps, we observed a total number of five product phases in various combinationsthe four ternary phases and CsBr (Figure a,b). CdBr₂ was never observed as a side product, likely due to the excess stoichiometry of Cs and Br precursors, as well as the relatively low reactivity of CdO (vide infra) (Figure c). The 47 experimental conditions using benzoyl bromide yielded 18 out of the $\sum _{i=0}^3\left(\begin{array}{l}5\\ i\end{array}\right)=26$ theoretically possible distinct phases or phase combinations (with three or fewer phases). The 48 conditions with phenacyl bromide resulted in only 11, as it failed to produce any Cs₇Cd₃Br₁₃, reducing the total number of possible phase combinations to $\sum _{i=0}^3\left(\begin{array}{l}4\\ i\end{array}\right)=15$ . The presence of approximately 70% of the theoretically possible phases in each matrix underscores the high complexity of the synthetic spacefar exceeding what we observed in our previous work on binary systems. , Most experiments resulted in mixed phases, with pure CsCdBr₃, Cs₂CdBr₄, Cs₃CdBr₅, or Cs₇Cd₃Br₁₃ only observed in one or few reactions per matrix. Due to the large number of classes in the responses, the classification algorithm we previously used to map binary phase spaces tended to overfit and provided limited insights. , To address this, we applied a binary logical classification to visualize phase distributions in the experimental variable space (Figures and ). In these maps, colored dots indicate the presence of a given phase as at least a fraction of the product under corresponding synthetic conditions, while gray dots denote its absence. All phases were clustered in one or a few areas of the variable space, suggesting that their formation was preferred by certain combinations of synthetic parameters.

5.

Phase distributions and trends for (a) CsCdBr₃, (b) Cs₂CdBr₄, (c) Cs₃CdBr₅, (d) Cs₇Cd₃Br₁₃, and (e) CsBr synthesized with benzoyl bromide. The experimental variable space is visualized using the three most important variables, with overlapping data points stacked vertically to show outcomes with high (top) and low (bottom) Br/Cd precursor ratios.

6.

Phase distributions and trends for (a) CsCdBr₃, (b) Cs₂CdBr₄, (c) Cs₃CdBr₅, and (d) CsBr synthesized with phenacyl bromide. Cs₇Cd₃Br₁₃ was not synthesized with phenacyl bromide as the organic Br source. The experimental variable space is visualized using the three most important variables, with overlapping data points stacked vertically to show outcomes with high (top) and low (bottom) Br/Cd precursor ratios.

Among the four ternary Cs–Cd–Br phases and CsBr, the most Cd-rich halide composition was CsCdBr₃, while the most Cd-poor was CsBr (Figure b). The stark contrast in their spatial distributions in the phase maps provides preliminary insights into the formation pathway. For both benzoyl bromide (Figure e) and phenacyl bromide (Figure d), the CsBr phase was localized in regions with high oleylamine-to-oleic acid ligand ratios and high Cs/Cd precursor ratios, whereas CsCdBr₃ was mostly confined to the opposite side, where oleylamine-to-oleic acid ligand ratios and Cs/Cd precursor ratios were both low. The separation likely results from differences in the availability of reactive species in the reaction. In CsBr formation, low oleic acid content likely hindered CdO activation into reactive Cd²⁺ complexes. In one reaction with a high oleylamine-to-oleic acid ligand ratio, a mixture of CsBr and CdO was observed (coded as R), indicating only partial Cd²⁺ activation. On the other hand, the high concentration of oleylamine facilitated organic Br precursor activation, leading to an excess of Br^–. In the absence of sufficient Cd²⁺, Cs⁺ and Br^– preferentially reacted to form CsBr. In contrast, CsCdBr₃ formation was favored in regions with low oleylamine-to-oleic acid ligand ratios, which ensured Cd²⁺ activation while limiting Br^– activation. A near 1:1 Cs/Cd ratio produced a balanced stoichiometry, favoring CsCdBr₃ formation. There was one outlier in the benzoyl bromide phase map where CsCdBr₃ and CsBr coexisted (coded as H), likely due to thermally driven CdO activation at high temperature.

The other ternary phases (i.e., Cs₂CdBr₄, Cs₃CdBr₅, and Cs₇Cd₃Br₁₃), with moderate Cs/Cd stoichiometries, predominantly occupied the central region of the phase maps (Figures b,c and b–d). Cs₃CdBr₅, the most Cd-poor ternary phase, frequently coexisted with CsBr, while Cs₂CdBr₄, with the second lowest Cs/Cd, was localized in regions with moderate-to-low oleylamine-to-oleic acid ligand ratios and Cs/Cd precusor ratios, underscoring the importance of these variables in phase determination. Cs₇Cd₃Br₁₃ was unique to the benzoyl bromide system, appearing at the intersection of the Cs₂CdBr₄ and Cs₃CdBr₅ regions. This suggests a possible formation mechanism via 2 Cs₂CdBr₄ + Cs₃CdBr₅ → Cs₇Cd₃Br₁₃. Such a phase conversion was observed postsynthetically, where a two-phase mixture of Cs₂CdBr₄ and Cs₃CdBr₅ converted into Cs₇Cd₃Br₁₃ after 4 days on the benchtop (Figure S32). However, the calculated energy of formation of (2 Cs₂CdBr₄ + Cs₃CdBr₅) is 0.001 eV/atom lower than that of Cs₇Cd₃Br₁₃, suggesting that this transition is not thermodynamically driven. The fact that Cs₇Cd₃Br₁₃ formed in situ only with the benzoyl bromide system underscores the crucial role of precursor chemistry in kinetically controlling the synthesis. To minimize the impact of postsynthetic transformations, we ensured consistent workup procedures for all samples, and all XRD measurements were performed immediately after sample preparation.

Conclusions

By leveraging a data-driven phase map based on statistical DoE, we efficiently explored the high-dimensional and complex chimie douce synthesis of the ternary Cs–Cd–Br phase space. Despite the numerous phase combinations observed (out of the 64 theoretically possible), we successfully identified the precise synthetic conditions required to isolate each of the four known ternary phases. To our knowledge, this represents the first successful synthesis of all four Cs–Cd–Br compositions using a uniform set of precursors and a standardized experimental procedure. Preliminary characterization of the products revealed distinct morphologies and optical properties for each of the structures. Analysis of the phase distributions within the experimental variable space uncovered higher-order interactions among various synthetic parameters, which can be difficult to disentangle using chemical intuition alone. Notably, the Cs₇Cd₃Br₁₃ phase, which was obtained using benzoyl bromide, was entirely inaccessible with phenacyl bromide, highlighting the critical role of precursor reactivity in synthetic phase control. More specifically, it was determined that temperature, ligand ratio, and precursor stoichiometry all significantly influenced phase selectivity by modulating precursor activation and release. These findings underscore the power of data-driven methodologies for both synthetic exploration and understanding of complex multinary systems. We anticipate that chimie douce approaches can be extended to similar metal halide systems, paving the way for more rapidly preparing multinary materials with controlled compositions and optoelectronic properties.

Experimental Section

Materials

Cesium carbonate (Cs₂CO₃, 99.9%) was purchased from Alfa Aesar. Cadmium oxide (CdO, 99%) was purchased from Strem Chemicals. Benzoyl bromide (97%) and phenacyl bromide (98%) were purchased from Thermo Scientific. Oleic acid (OAc, 90% technical grade), oleylamine (OAm, 70% technical grade), and octadecene (ODE, 90% technical grade) were purchased from Sigma-Aldrich. All chemicals were used without further purification. OAc, OAm, and ODE were all dried under vacuum at 120 °C for 3 h, and then under vacuum overnight before use.

The experimental procedures below outline only the specific conditions to synthesize phase-pure compositions from reactions with benzoyl bromide. All reaction conditions were the same for the phenacyl bromide reactions, apart from phenacyl bromide being injected in place of benzoyl bromide.

Synthesis of CsCdBr₃

This is a phase-pure reaction with the synthetic conditions outlined in the benzoyl bromide matrix for reaction #11, found in Table S1. In a 15 mL round-bottom flask, 0.024 g of Cs₂CO₃ (0.075 mmol), 0.0193 g of CdO (0.150 mmol), 0.5 mL OAm, 2 mL OAc, and 4 mL ODE were added then degassed at 120 °C for 30 min. Next, the flask was put under a flowing nitrogen atmosphere and the temperature was raised to 220 °C and allowed to equilibrate at the set temperature for 30 min. Lastly, the temperature was raised to 300 °C and allowed to equilibrate at the set temperature for 30 min. Once at the desired temperature, 97 μL of neat benzoyl bromide (0.82 mmol) was swiftly injected and allowed to react for 3 min, followed by a thermal quench in a water bath.

Synthesis of Cs₂CdBr₄

This is a phase-pure reaction with the synthetic conditions outlined in the benzoyl bromide low temperature reaction #7, found in Table S5. In a 15 mL round-bottom flask 0.024 g of Cs₂CO₃ (0.0749 mmol), 0.0193 g of CdO (0.150 mmol), 0.5 mL OAm, 2 mL OAc, and 4 mL ODE were added then degassed at 120 °C for 30 min. Next, the flask was put under a flowing nitrogen atmosphere and the temperature was raised to 220 °C and allowed to equilibrate at the set temperature for 30 min. Lastly, the temperature was lowered to 60 °C and allowed to equilibrate at the set temperature for 30 min. Once at desired temperature, 124 μL of neat benzoyl bromide (1.20 mmol) was swiftly injected and allowed to react for 3 min, followed by a thermal quench in a water bath.

Synthesis of Cs₃CdBr₅

This is a phase-pure reaction with the synthetic conditions outlined in the benzoyl bromide screening matrix reaction #13, found in Table S1. In a 15 mL round-bottom flask 0.0733 g of Cs₂CO₃ (0.230 mmol), 0.0193 g of CdO (0.150 mmol), 0.5 mL OAm, 2 mL OAc, and 4 mL ODE were added then degassed at 120 °C for 30 min. Next, the flask was put under a flowing nitrogen atmosphere and the temperature was raised to 220 °C and allowed to equilibrate at the set temperature for 30 min. Lastly, the temperature was lowered to 120 °C and allowed to equilibrate at the set temperature for 30 min. Once at desired temperature, 124 μL of neat benzoyl bromide (1.20 mmol) was swiftly injected and allowed to react for 3 min, followed by a thermal quench in a water bath.

Synthesis of Cs₇Cd₃Br₁₃

This is a phase-pure reaction with the synthetic conditions outlined in the benzoyl bromide extra low temp reaction #10, found in Table S5. In a 15 mL round-bottom flask 0.0564 g of Cs₂CO₃ (0.170 mmol), 0.0193 g of CdO (0.150 mmol), 0.85 mL OAm, 1.65 mL OAc, and 4 mL ODE were added then degassed at 120 °C for 30 min. Next, the flask was put under a flowing nitrogen and the temperature was raised to 220 °C and allowed to equilibrate at the set temperature for 30 min. Lastly, the temperature was lowered to 60 °C and allowed to equilibrate at the set temperature for 30 min. Once at desired temperature, 72 μL of neat benzoyl bromide (0.61 mmol) was swiftly injected and allowed to react for 3 min, followed by a thermal quench in a water bath.

Material Purification

The resulting material product from each reaction was first collected by centrifugation of the reaction mixture at 6000 rpm for 5 min. The supernatant was discarded. Next, 5 mL of hexanes was added, and the material was sonicated in solution. Then, 5 mL isopropanol was added, and the solution was vortex mixed and sonicated for 5 s before being centrifuged at 6000 rpm for 5 min. The supernatant was again discarded. Lastly, hexanes were added, and the material was sonicated until the precipitant went into suspension. This suspension was used for further characterization methods.

Characterization

Ultraviolet–visible–near-infrared (UV–vis–NIR) diffuse reflectance spectroscopy was performed on drop-cast colloidal dispersions of the materials with BaSO₄ placed behind and sandwiched between two glass slides. A PerkinElmer Lambda 950 UV–vis–NIR spectrometer with a 150 mm integrating sphere was used to collect the spectral data. Powder X-ray diffraction (XRD) characterization was performed on either a Rigaku Ultima IV or a Rigaku Miniflex powder X-ray diffractometer using Cu Kα radiation (λ = 1.541 Å). Suspensions of the samples were directly drop-cast onto zero-diffraction silicon substrates. Scanning electron microscopy (SEM) was performed on samples drop-cast on copper plates using a Thermo Scientific Apreo 2S field emission scanning electron microscope operating at a voltage of 15 kV.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.5c01137.

• Tables including reaction conditions for benzoyl and phenacyl bromide reactions; additional visualization of phase maps for experimentally determined phases; additional experimental details; powder XRD data for all reactions performed (PDF)

The authors declare no competing financial interest.