Discrete Phase Selection Driven by Evaporation-Induced Off-Stoichiometry in Melt-Grown CsPbBr₃

Abstract

We show that halide evaporation during melt growth of ${\mathrm{CsPbBr}}_3$ on polycrystalline FTO under partially open conditions drives discrete phase selection between the line compounds of the CsBr–PbBr₂ system, producing a sharp ${\mathrm{CsPbBr}}_3/{\mathrm{CsPb}}_2{\mathrm{Br}}_5$ bilayer instead of compositional grading. In situ optical imaging shows that solidification begins with nucleation and lateral growth of a planar ${\mathrm{CsPbBr}}_3$ single crystal while the melt layer is still thick enough to average over the FTO relief. As the crystal thickens, the residual melt then becomes inhomogeneous and unstable, producing a buried porous layer of faceted ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ grains with a characteristic in-plane spacing of 1–10$\mathsf{\mu }\mathrm{m}$). This morphology is consistent with a faceted Mullins–Sekerka-type instability under a non-conservative evaporative boundary condition. Beneath the single-crystal cap, the first-formed faceted islands are large and become progressively smaller as the advancing front approaches the FTO pyramids, while elevated ambient halide partial pressure suppresses the instability, consistent with diffusion–capillarity selection under decreasing residual melt thickness and steepening local gradients, modified by evaporative flux. Oxygen associated with microvoids or the oxide substrate enables a secondary reaction–diffusion pathway forming Pb–Br–O crystallites without altering the primary length scale. These results identify evaporation as an active control parameter coupling phase equilibria and interfacial stability in volatile halide melts. In the buried, porous bilayer morphology observed here, the secondary phases and porosity reduce the active ${\mathrm{CsPbBr}}_3$ volume and are expected to degrade scintillation through increased trapping, nonradiative recombination, and light scattering.

1. Introduction

Halide perovskites, and ${\mathrm{CsPbBr}}_3$ in particular, have emerged as promising scintillator materials because they combine high light yield, short response times, and tunable emission [1,2,3,4,5,6,7]. These advantages, however, are not intrinsic in a simple sense. They depend strongly on the structural and chemical state established during growth. Phase purity, crystalline perfection, and defect chemistry are therefore decisive: wherever secondary phases form, the composition becomes nonuniform, or the microstructure becomes defective, non-radiative recombination and carrier trapping increase, leading to deterioration of scintillation yield and timing [6,7].

In solution-processed films, halide perovskites offer broad compositional tunability. Substitution on the halide and A-site sublattices allows the optical gap, emission energy, carrier transport, and device response to be varied over a wide range [8,9,10,11,12]. Because ion diffusion and precursor intermixing remain active during low-temperature processing, continuous compositional profiles, and graded band-gap structures can be deliberately produced or may arise through interdiffusion [11,13,14,15,16]. This picture, however, is not directly transferable to the melt growth in the CsBr–PbBr₂ pseudobinary system, where the relevant crystalline products are distinct stoichiometric compounds rather than arbitrary off-stoichiometric variants of ${\mathrm{CsPbBr}}_3$.

Solidification morphologies are usually formulated as mass-conserving interfacial transport problems, where heat flow, attachment kinetics, solute diffusion, and capillarity select the morphology and its characteristic length scale [17,18]. In this picture, interfacial perturbations grow when diffusive destabilization overcomes capillary smoothing, producing cellular, dendritic, or, in faceted systems, zigzag morphologies. Direct in situ observations of Si(100) melt growth, for example, show that a planar crystal–melt interface can transform into wavy perturbations and then into zigzag facets at sufficiently high growth velocity [19]. Such descriptions implicitly assume a closed or nearly closed solid–liquid system, in which the local composition evolves mainly by redistribution within the condensed phase rather than by loss to the surrounding atmosphere.

Volatile bromide melts challenge this assumption. In Cs–Pb–Br systems, thermal processing under covered but non-hermetically sealed conditions can be accompanied by non-congruent evaporation of Cs-, Pb-, and Br-containing species, so that the condensed phase exchanges matter with the surrounding vapor/headspace rather than evolving as a strictly closed system [20,21]. Importantly, this volatility is not restricted to ${\mathrm{PbBr}}_2$. Knudsen-effusion mass spectrometry of ${\mathrm{CsPbBr}}_3$ shows that single-source ${\mathrm{CsPbBr}}_3$ evaporation is only partially congruent and is accompanied by CsBr-related vapor species, including ${\mathrm{Cs}}_2{\mathrm{Br}}^{+}$, which was assigned to evaporated (CsBr)_x clusters [20]. These results indicate that heated ${\mathrm{CsPbBr}}_3$ can partially decompose into ${\mathrm{CsBr}}^{-}$ and ${\mathrm{PbBr}}^{2-}$ containing volatile components, which evaporate at different rates and cause both the vapor composition and the residual source composition to evolve with time [20]. Such vapor-driven stoichiometric shifts are also consistent with reports that evaporated ${\mathrm{CsPbBr}}_3$ precursors can produce mixtures of ${\mathrm{CsPbBr}}_3$, ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$, and ${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$ because of composition gradients during evaporation [21].

This complication acquires a specific character in systems governed by line-compound equilibria. In the CsBr–PbBr₂ phase field, ${\mathrm{CsPbBr}}_3$, ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$, and ${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$ are distinct stoichiometric compounds [22,23,24,25]. When evaporation displaces the melt from the nominal ${\mathrm{CsPbBr}}_3$ composition, the perturbation therefore need not be recorded as a continuous compositional gradient. Instead, it may be accommodated by the coexistence of secondary phases or by discrete switching between stoichiometric compounds. Stoichiometric ${\mathrm{CsPbBr}}_3$ growth may persist while the local melt composition remains within the stability range of this phase, but once this condition is no longer satisfied, solidification may switch locally to ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ or ${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$.

In this context, ${\mathrm{CsPbBr}}_3$ melt growth under covered but unsealed conditions provides a useful model system for examining how evaporation-induced off-stoichiometry influences phase selection during solidification. It also raises a separate question of how substrate topography, such as the pyramidal relief of polycrystalline ${\mathrm{SnO}}_2$ (FTO), perturbs the local morphology of the advancing front. Distinguishing these effects is essential for separating phase selection driven by melt composition from morphology changes associated with substrate-induced thermal or geometrical inhomogeneity.

2. Materials and Methods

2.1. Substrates and Precursor Preparation

Commercial fluorine-doped tin oxide glass substrates, ${\mathrm{SnO}}_2$ (FTO), with a standard size of (25 × 25${\mathrm{mm}}^2$) and a polycrystalline pyramidal surface relief were sequentially cleaned in acetone and isopropanol, rinsed in deionized water, and dried in filtered air. Microcrystalline ${\mathrm{CsPbBr}}_3$ powder was synthesized from equimolar CsBr and ${\mathrm{PbBr}}_2$ precursors, both 99.999% trace-metal basis, following the solution route of Stoumpos et al. [4,26]. The powder was spread homogeneously onto the FTO surface by gentle sieving and leveled with a clean blade, yielding continuous coverage without solvent or binder [Figure 1c]. The areal loading was adjusted such that melting and coalescence produced a film of several tens of micrometers thick over the pyramidal FTO relief [Figure 1d].

2.2. Melt Recrystallization and In Situ Optical Imaging

Melting experiments were carried out in ambient air using a type 3A muffle oven (Simon Müller, Berlin, Germany) with a compact cylindrical heating volume of approximately 95 mm in diameter and 85 mm in height [Figure 1a,b]. The substrate temperature was monitored by an internal thermocouple connected to an LTR 2500 laboratory temperature controller, (Juchheim GmbH & Co. KG, Bernkastel-Kues, Germany). Samples were heated to the melt dwell temperature, held until complete liquefaction and wetting of the FTO relief were achieved, and subsequently cooled slowly to room temperature [Figure 1e].

The reported temperature corresponds to the nominal furnace/controller temperature. No additional thermocouple was placed directly at the sample or melt/substrate interface; therefore, the exact local melt temperature may differ from the recorded furnace temperature.

In situ optical imaging of the melting and solidification sequence was performed in top-view geometry using a Jiusion handheld USB microscope (Jiusion, Shenzhen, China) mounted above a viewport. Video frames were recorded at fixed exposure under diffuse white LED illumination located outside the hot zone to minimize thermal-emission artifacts. Frame timestamps were synchronized with the oven temperature log. Because the oven was covered but not hermetically sealed, volatile halide species could exchange with the ambient headspace during the thermal cycle. Here, covered but unsealed ambient air means that the sample was physically covered, but the enclosure was not gas-tight. Oxygen and moisture partial pressures were not measured and may vary with the laboratory and furnace environment. The solidified samples were transferred to dry storage and characterized without further post-treatment.

2.3. Evaporative Boundary Condition

The net evaporative flux of a volatile species (i) at the melt/gas surface was described by the Hertz–Knudsen relation,

$$J_{\mathrm{ev}}={\alpha }_i{\displaystyle \frac{p_{i,\mathrm{eq}}\left(T\right)-p_i}{\sqrt{2\pi m_i{k}_{\mathrm{B}}T}}}$$

(1)

where ($J_{\mathrm{ev}}$) is the net evaporation flux, (${\alpha }_i$) is the evaporation coefficient, ($p_{i,\mathrm{eq}}\left(T\right)$) is the equilibrium vapor pressure at temperature (T), ($p_i$) is the partial pressure in the headspace, ($m_i$) is the molecular mass, and ($k_{\mathrm{B}}$) is the Boltzmann constant. This expression was used to describe the non-conservative boundary condition at the open melt/gas interface. Order-of-magnitude estimates were based on the literature vapor-pressure data and Knudsen-effusion measurements cited in the main text.

2.4. X-Ray Diffraction

X-ray diffraction was performed on the as-recrystallized surface using a PANalytical Empyrean diffractometer, (Malvern Panalytical, Almelo, The Netherlands) in Bragg–Brentano reflection geometry. $(\theta$–$2\theta )$ scans were collected in the range of ($10°$–$70°$) and plotted on a logarithmic intensity scale. Phase assignment was based on database matching in HighScore, with peak fitting restricted to the dominant ($29°$–$33°$) region. The main reflections were assigned to orthorhombic ${\mathrm{CsPbBr}}_3$ and ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$; weaker features were evaluated within the instrumental detection limit. Because the recrystallized films are single-crystalline or strongly textured, the measured intensities do not satisfy powder-statistical requirements, and Rietveld refinement was not applied.

2.5. Scanning Electron Microscopy and Microanalysis

2.5.1. SEM Imaging Geometry and Sample Preparation

Main SEM imaging was performed on a JEOL JSM-7610F (JEOL Ltd., Akishima, Tokyo, Japan) operated at 5–15 kV. Cross sections were prepared by mechanical cleavage of delaminated films. Both the top surface and the FTO-facing side of the delaminated film were examined to distinguish the free-surface morphology from the buried morphology formed near the substrate. Layer thicknesses were measured from calibrated cross-sectional SEM micrographs and reported as mean (±) one standard deviation.

2.5.2. SE and BSE Imaging

Low-voltage secondary-electron imaging at 5 kV was used to resolve surface topography, terraces, and inverted steps. Backscattered-electron imaging at 15 kV was used for phase discrimination by Z-contrast and to guide EDX point, line, and map analyses. The abrupt ${\mathrm{CsPbBr}}_3/{\mathrm{CsPb}}_2{\mathrm{Br}}_5$ layers were therefore evaluated both morphologically and by SEM-BSE contrast.

2.5.3. EDX Point, Line, and Map Analysis

EDX analysis was performed on the JEOL JSM-7610F. Point spectra and line scans were used to determine Cs, Pb, and Br stoichiometries in at% across the ${\mathrm{CsPbBr}}_3/{\mathrm{CsPb}}_2{\mathrm{Br}}_5$ boundary, within the compact and porous ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ regions, and on secondary Pb–Br-rich crystallites. Quantification was restricted to Cs, Pb, and Br; O was treated qualitatively because of the limitations of EDX for light-element quantification.

2.5.4. SEM-BSE Contrast Estimation

BSE contrast was estimated using a Reimer–Castaing summing procedure to support phase assignment in SEM-BSE images. For each element (i), the elemental backscattering coefficient was calculated as:

$$\eta \left(Z_i\right)=-0.0254+0.016Z_i-1.86\times {10}^{-4}{Z}_i^2+8.3\times {10}^{-7}{Z}_i^3,$$

(2)

where ($Z_i$) is the atomic number of element (i). For a compound, ($n_i$) is the stoichiometric coefficient of element (i), and ($A_i$) is its atomic weight. The molecular weight of the compound is

$$M=\sum _j{n}_j{A}_j,$$

(3)

where the index (j) runs over all elements in the formula unit. The mass fraction of element (i) is then

$$c_i={\displaystyle \frac{n_i{A}_i}{M}}={\displaystyle \frac{n_i{A}_i}{{\sum }_j{n}_j{A}_j}}.$$

(4)

The weighted BSE contribution of element (i) is

$$p_i=c_i·\eta \left(Z_i\right),$$

(5)

and the effective BSE coefficient of the compound is obtained by summing all elemental contributions:

$${\eta }_{\mathrm{HR}}=\sum _i{p}_i=\sum _i{c}_i·\eta \left(Z_i\right)$$

(6)

Table 1. Detailed calculation of the Reimer-Castaing effective SEM-BSE coefficients for candidate phases. For each element (i), ($Z_i$) is the atomic number, ($n_i$) is the stoichiometric coefficient, ($A_i$) is the atomic weight, ($c_i=n_i{A}_i/{\sum }_j{n}_j{A}_j$) is the mass fraction, ($\eta \left(Z_i\right)$) is the elemental Reimer coefficient, and ($p_i=c_i·\eta \left(Z_i\right)$) is the weighted elemental contribution. The total row gives (${\eta }_{\mathrm{HR}}={\sum }_i{p}_i$), used here only as a relative BSE contrast indicator.

Phase	Element	${\mathit{Z}}_{\mathit{i}}$	${\mathit{n}}_{\mathit{i}}$	${\mathit{A}}_{\mathit{i}}$	${\mathit{c}}_{\mathit{i}}$	$\eta \left(Z_i\right)$	${\mathit{p}}_{\mathit{i}}$	${\eta }_{\mathbf{HR}}$
PbO	Pb	82	1	207.200	0.9283	0.5181	0.4809	0.4871
	O	8	1	15.999	0.0717	0.0853	0.0061
${\mathrm{Pb}}_8{\mathrm{O}}_7{\mathrm{Br}}_2$	Pb	82	8	207.200	0.8591	0.5181	0.4451	0.4784
	O	8	7	15.999	0.0580	0.0853	0.0050
	Br	35	2	79.904	0.0828	0.3426	0.0284
${\mathrm{Pb}}_4{\mathrm{O}}_3{\mathrm{Br}}_2$	Pb	82	4	207.200	0.7995	0.5181	0.4142	0.4710
	O	8	3	15.999	0.0463	0.0853	0.0039
	Br	35	2	79.904	0.1542	0.3426	0.0528
${\mathrm{Pb}}_3{\mathrm{O}}_2{\mathrm{Br}}_2$	Pb	82	3	207.200	0.7642	0.5181	0.3959	0.4666
	O	8	2	15.999	0.0393	0.0853	0.0034
	Br	35	2	79.904	0.1965	0.3426	0.0673
${\mathrm{Pb}}_2{\mathrm{OBr}}_2$	Pb	82	2	207.200	0.7021	0.5181	0.3638	0.4588
	O	8	1	15.999	0.0271	0.0853	0.0023
	Br	35	2	79.904	0.2708	0.3426	0.0928
Pb(OH)Br	Pb	82	1	207.200	0.6813	0.5181	0.3530	0.4475
	O	8	1	15.999	0.0526	0.0853	0.0045
	H	1	1	1.008	0.0033	0.0076	0.0000
	Br	35	1	79.904	0.2627	0.3426	0.0900
${\mathrm{PbBr}}_2$	Pb	82	1	207.200	0.5646	0.5181	0.2925	0.4417
	Br	35	2	79.904	0.4354	0.3426	0.1492
${\mathrm{CsPb}}_2{\mathrm{Br}}_5$	Cs	55	1	132.905	0.1404	0.4471	0.0628	0.4341
	Pb	82	2	207.200	0.4377	0.5181	0.2267
	Br	35	5	79.904	0.4220	0.3426	0.1445
${\mathrm{Pb}}_2$(${\mathrm{CO}}_3$)${\mathrm{Br}}_2$	Pb	82	2	207.200	0.6534	0.5181	0.3385	0.4324
	C	6	1	12.011	0.0189	0.0585	0.0011
	O	8	3	15.999	0.0757	0.0853	0.0065
	Br	35	2	79.904	0.2520	0.3426	0.0863
${\mathrm{CsPbBr}}_3$	Cs	55	1	132.905	0.2292	0.4471	0.1025	0.4292
	Pb	82	1	207.200	0.3574	0.5181	0.1851
	Br	35	3	79.904	0.4134	0.3426	0.1416
${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$	Cs	55	4	132.905	0.4364	0.4471	0.1951	0.4180
	Pb	82	1	207.200	0.1701	0.5181	0.0881
	Br	35	6	79.904	0.3935	0.3426	0.1348
CsBr	Cs	55	1	132.905	0.6245	0.4471	0.2792	0.4079
	Br	35	1	79.904	0.3755	0.3426	0.1286
${\mathrm{SnO}}_2$	Sn	50	1	118.710	0.7877	0.4259	0.3355	0.3536
	O	8	2	15.999	0.2123	0.0853	0.0181

reports the calculation for each candidate phase, listing the element, (Z_i), stoichiometric coefficient ($n_i$), atomic weight ($A_i$), mass fraction ($c_i$), elemental Reimer coefficient ($\eta \left(Z_i\right)$), and weighted contribution ($p_i=c_i·\eta \left(Z_i\right)$). The total row gives (${\eta }_{\mathrm{HR}}$). These values support, but do not by themselves determine, phase assignment because measured BSE intensity also depends on topography, crystallite size, edge effects, detector geometry, beam energy, and crystal orientation.

2.5.5. Cathodoluminescence Imaging

Panchromatic CL imaging was performed at 5 kV on a Tescan Vega II (Brno, Czech Republic) equipped with a tungsten thermionic source. SE reference images were recorded from the same regions to correlate with luminescence contrast with morphology and phase distribution, and compare the radiative response of ${\mathrm{CsPbBr}}_3$ and ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ regions.

2.5.6. TOF-SIMS Light-Element Mapping

TOF-SIMS measurements were carried out on a Zeiss Crossbeam Auriga (Carl Zeiss NTS GmbH, Oberkochen, Germany) equipped with a TOFWERK TOF-SIMS system (TOFWERK AG, Thun, Switzerland). Negative-ion maps were acquired for (${\mathrm{C}}^{-}$) at (m/z = 12), (${\mathrm{O}}^{-}$) at (m/z = 16), and (${\mathrm{OH}}^{-}$) at (m/z = 17). These channels were used to complement EDX and assess the spatial distribution of carbon-, oxygen-, and hydroxyl-containing species near Pb–Br-rich secondary features.

2.6. Thermodynamic Phase Diagrams

For interpretation of phase selection, the CsBr–PbBr₂ binary phase diagram, including the peritectic region near 560–570 (°C), and the ${\mathrm{PbBr}}_2$–PbO binary system were used as thermodynamic references. These diagrams were used to relate the observed ${\mathrm{CsPbBr}}_3$, ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$, ${\mathrm{PbBr}}_2$–rich, and Pb–Br–O phases to the expected compositional pathways during evaporation, decomposition, precipitation, and late-stage reaction at the FTO-facing side.

3. Results

3.1. Non-Conservative Boundary Conditions Established by Halide Evaporation

Figure 1e shows the temperature-time profile together with in situ optical frames of the melting and recrystallization sequences. Upon heating, the powder bed evolves from solid to solid + liquid and finally to a continuous liquid film; upon cooling, the sequence reverses as the advancing solidification front wets the pyramidal FTO relief.

Because the oven was covered but not hermetically sealed, the melt remained in continuous exchange with the ambient headspace. Evaporation from heated ${\mathrm{CsPbBr}}_3$ is only partially congruent: Knudsen-effusion mass spectrometry shows CsBr-related vapor species, including (CsBr)_x clusters detected through ${\mathrm{Cs}}_2{\mathrm{Br}}^{+}$, together with ${\mathrm{PbBr}}_2$–containing volatiles, so that both the vapor composition and the residual condensed source evolve with time [20]. ${\mathrm{PbBr}}_2$ also has a measurable vapor pressure in this temperature range [27], and evaporation of ${\mathrm{CsPbBr}}_3$ precursors has been reported to yield mixtures of ${\mathrm{CsPbBr}}_3$, ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$, and ${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$ because of composition gradients during evaporation [21]. In our setup, visible salt condensate on the oven cover after high-temperature operation provides direct evidence for halide loss, consistent with previous reports of volatile halide transport in ${\mathrm{CsPbBr}}_3$-based processing [23,28].

Together, these observations show that solidification proceeds under a non-conservative boundary condition at the melt/gas interface. The melt therefore cannot be treated as a closed CsBr–PbBr₂ system: its local composition is governed not only by diffusion, phase equilibria, and interface motion, but also by continuous evaporative mass loss to the headspace.

3.2. Evidence for Discrete Phase Selection

X-ray diffraction reveals the structural response to evaporation-induced compositional drift (Figure 2). The ($10°$–$70°$) scan identifies orthorhombic ${\mathrm{CsPbBr}}_3$ as the dominant phase and ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ as the principal secondary phase, as confirmed by fitting the intense ($29°$–$33°$) region [23,24,25,26,29,30,31]. No separate off-stoichiometric ${\mathrm{CsPbBr}}_3$ phase is detected within the experimental resolution. Weak near-background reflections may originate from minor ${\mathrm{Pb}}_2$(${\mathrm{CO}}_3$)${\mathrm{Br}}_2$-type secondary crystallites, but this assignment remains tentative and is discussed in Section 3.5.

Because the recrystallized film is single-crystalline or strongly textured, the XRD intensities were used only for qualitative phase identification and not for quantitative phase-fraction analysis.

Cross-sectional SEM shows a layered structure composed of an (80–100$\mathsf{\mu }\mathrm{m}$) ${\mathrm{CsPbBr}}_3$ top layer, a (10–20$\mathsf{\mu }\mathrm{m}$) compact ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ interlayer, and a porous ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ sublayer conforming to the FTO relief [Figure 3a,b]. These layers are clearly distinguished in SEM-BSE images by Z-contrast. Panchromatic CL imaging shows strong luminescence quenching in the ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ region [Figure 3c], consistent with the weak radiative response expected for this phase [32,33]. EDX point spectra from the upper crystal give the expected (1:1:3) Cs:Pb:Br ratio, with no detectable O or Sn, confirming that the cap is chemically consistent with ${\mathrm{CsPbBr}}_3$ (Figure A2). Based on this cross-sectional morphology, ${\mathrm{CsPbBr}}_3$ remains the dominant phase by thickness, whereas ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ forms a significant FTO-facing fraction. This estimate should be regarded as semi-quantitative rather than as a true volume fraction, because the lower ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$-rich region is porous and laterally non-uniform.

EDX line scans across the ${\mathrm{CsPbBr}}_3/{\mathrm{CsPb}}_2{\mathrm{Br}}_5$ boundary show an abrupt compositional jump without a resolvable graded region [Figure 3d,e]. Point spectra acquired from laterally adjacent domains at the FTO-facing side show the same discreteness: the compositions correspond either to (1:1:3) ${\mathrm{CsPbBr}}_3$ or to (1:2:5) ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$, with no intermediate stoichiometries (Figure A3), indicating that the transition is abrupt rather than compositionally graded within the spatial resolution of SEM-EDX.

In the CsBr–PbBr₂ pseudobinary representation, two limiting pathways can explain the formation of ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$:

• In the first pathway, selective CsBr evaporation directly shifts ${\mathrm{CsPbBr}}_3$ toward the ${\mathrm{PbBr}}_2$-richer line compound:

$$2CsPbB{r}_3\to CsP{b}_{2}B{r}_5+CsB{r}_{\mathrm{evap}}$$

(7)

If this CsBr-loss process occurs broadly through the residual melt, it may produce a more distributed compositional shift. However, because ${\mathrm{CsPbBr}}_3$ and ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ are line compounds, this does not necessarily lead to a graded ${\mathrm{CsPbBr}}_3$ solid solution; instead, the phase response is still expected to occur by switching from ${\mathrm{CsPbBr}}_3$ to ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ once the local stability limit is crossed.

• In the second pathway, CsBr evaporation is accompanied by local accumulation or precipitation of ${\mathrm{PbBr}}_2$-rich residual material, particularly at the FTO-facing side, as supported by the observed traces of ${\mathrm{PbBr}}_2$ on FTO. This ${\mathrm{PbBr}}_2$-rich material can subsequently react with adjacent ${\mathrm{CsPbBr}}_3$ to form ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$:

$$CsPbB{r}_3+PbB{r}_2\to CsP{b}_{2}B{r}_5$$

(8)

This second pathway provides a natural explanation for the abrupt ${\mathrm{CsPbBr}}_3/{\mathrm{CsPb}}_2{\mathrm{Br}}_5$ boundary observed by SEM-EDX, because the reaction is localized where ${\mathrm{PbBr}}_2$-rich residual material is available. Thus, the first pathway explains the overall evaporation-driven shift toward ${\mathrm{PbBr}}_2$-richer conditions, whereas the second pathway better explains the spatial localization and sharpness of the FTO-facing transition. The absence of ${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$, located on the CsBr-rich side of the phase field, further supports a net shift toward ${\mathrm{PbBr}}_2$-rich rather than CsBr-rich conditions. The system therefore accommodates evaporation-induced off-stoichiometry by switching between line compounds, $CsPbB{r}_3\to CsP{b}_{2}B{r}_5$, rather than by forming a resolvable graded ${\mathrm{CsPbBr}}_3$ solid solution.

3.3. Emergence of a Faceted Instability at the Buried Interface

Beyond discrete phase selection, the delaminated films reveal a faceted instability localized at the FTO-facing side. In situ optical imaging shows that solidification begins by nucleation and lateral growth of a planar ${\mathrm{CsPbBr}}_3$ front while the melt is still thick (Figure 1). In this stage, the advancing front is effectively screened from the pyramidal FTO relief. As the ${\mathrm{CsPbBr}}_3$ cap grows and the residual melt thins, the FTO topography imposes stronger local variations in melt thickness, interface curvature, and thermal gradient. These perturbations provide the geometric trigger for the FTO-facing instability. Thus, the FTO relief is not interpreted as a direct template that fixes the terrace spacing. Instead, it acts as a local geometrical and thermal perturbation that becomes important only during the final thin-melt stage, when the residual liquid can no longer screen the pyramidal substrate topography.

The morphology was accessed by mechanical delamination of the recrystallized film (Figure 4). BSE imaging shows the delaminated ${\mathrm{CsPbBr}}_3$ film and exposed FTO surface [Figure 4a], residual material remaining on FTO [Figure 4b], and the FTO-facing side of the flipped film [Figure 4c]. This side consists of coarse and fine ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ grains decorated by sub-$\mathsf{\mu }\mathrm{m}$ Pb–Br–O secondary crystallites. The secondary crystallites are discussed separately in Section 3.5.

Low-voltage SE imaging resolves the faceted topography of this region (Figure 5). Coarse ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ grains contain broad inverted steps, whereas smaller grains show steeper and more closely spaced terraces [Figure 5a,b]. The corresponding height map confirms that the contrast is dominated by terrace-like height modulation rather than by compositional variation [Figure 5d]. EDX point spectra from the compact base and from internal grains of the porous layer give the same (1:2:5) ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ stoichiometry (Figure A4). Thus, the coarse-to-fine hierarchy is primarily morphological, not compositional.

The characteristic lateral spacing of the faceted features is (1–10$\mathsf{\mu }\mathrm{m}$), much smaller than the total film thickness, $\lambda \ll h\approx 100\mathsf{\mu }\mathrm{m}$.

Together with the absence of hexagonal or roll-like planforms, this scale separation argues against a hydrodynamic convection origin. Instead, the stepped faceted morphology is consistent with a diffusion-controlled solidification instability of Mullins–Sekerka type, modified by anisotropic interface kinetics [17,18]. In this picture, diffusion–capillarity competition selects the spacing, while crystallographic anisotropy produces the faceted terraces of Figure 5c.

3.4. Coarse-to-Fine Evolution of the FTO-Facing Morphology

The spatial evolution of the FTO-facing microstructure provides an additional constraint on the growth mechanism. Beneath the ${\mathrm{CsPbBr}}_3$ single-crystal cap, the ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ grains are coarse and exhibit large, widely spaced inverted steps. Closer to the FTO relief, where the residual melt was thinner during the final stage of solidification, the grains become smaller and the terraces become steeper and more closely spaced [Figure 5a,b,d]. This trend is consistent with growth under a decreasing effective transport length. In a diffusion-limited description,

$${\ell }_D\sim {\displaystyle \frac{D}{R}}$$

(9)

where (D) is the relevant diffusivity and (R) is the local interface velocity. As the melt thins, local variations in (R), interface curvature, and the thermal gradient imposed by the pyramidal FTO surface becomes stronger, favoring a finer faceted morphology.

The same interpretation is consistent with the sensitivity of the porous faceted microstructure to the openness of the melt/gas boundary. Conditions that reduce evaporative exchange with the headspace suppress the porous, faceted morphology, whereas stronger evaporative loss promotes it. This behavior links the instability to evaporation-induced compositional drift, rather than to a purely geometrical imprint of the substrate.

The compact ${\mathrm{CsPbBr}}_3$ cap thickness does not set the characteristic in-plane spacing, and the FTO relief does not act as a direct template with a fixed pitch. Instead, the substrate topography localizes and perturbs the final solidification front, while the selected morphology is governed by transport, capillarity, faceted interface kinetics, and the evaporative boundary condition.

3.5. Secondary Light-Element Chemistry in Confined Microenvironments

Sub-$\mathsf{\mu }\mathrm{m}$ rice-shaped crystallites decorate the porous ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ region at the FTO-facing side [Figure 4c and Figure 6]. EDX maps show that these features are Pb–Br-rich and locally enriched in O, with weaker C and F signals (Figure 6). The C and F signals are minor and are, therefore, treated as trace contributions. Point spectra give ($\mathrm{Pb}\approx 1$) and no detectable Cs, excluding ${\mathrm{CsPbBr}}_3$ and ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ and indicating a secondary Pb–Br phase containing light elements (Figure A5). Negative-ion TOF-SIMS maps confirm that (${\mathrm{C}}^{-}$), (${\mathrm{O}}^{-}$), and (${\mathrm{OH}}^{-}$) are concentrated in the same reacted regions (Figure 7).

The phase assignment is constrained but not unique. The rice-shaped crystallites are compatible with a ${\mathrm{Pb}}_2$(${\mathrm{CO}}_3$)${\mathrm{Br}}_2$-type phase, based on their morphology, Pb–Br-rich composition, C signal, weak near-background XRD features, and calculated BSE coefficient, which is higher than that of ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ [Figure 4f]. Nanowire-like crystallites with ($\mathrm{Pb}:\mathrm{Br}atomicratio\approx 1:1$) are additionally compatible with Pb(OH)Br-type phases. Lead oxybromides such as ${\mathrm{Pb}}_2{\mathrm{OBr}}_2$ also remain possible, because the ${\mathrm{PbBr}}_2$–PbO phase diagram contains stable Pb–O–Br compositions near the measured Pb ratio (Figure A1) [34,35]. We, therefore, denote these products as Pb–Br–O secondary phases. Local diffraction, micro-Raman spectroscopy, or TEM-based analysis would be required for definitive identification.

Their formation is consistent with late-stage enrichment of ${\mathrm{PbBr}}_2$-rich residual material. CsBr loss and partial melt decomposition shift the system from ${\mathrm{CsPbBr}}_3$ toward ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ and finally toward ${\mathrm{PbBr}}_2$-rich compositions. The residual fragments on FTO record this sequence, with ${\mathrm{PbBr}}_2$-rich material near the substrate and ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ above (Figure A6). Because ${\mathrm{PbBr}}_2$-rich material is denser than the ${\mathrm{CsPbBr}}_3$-rich melt, it may precipitate at the FTO-facing side during the final solidification stage. Reaction of this residual material with O-, OH-, or carbonate-containing species can then produce the observed Pb–Br–O crystallites in confined voids or pockets.

These reactions are secondary to the primary faceted solidification instability. They decorate the internal porous FTO-facing morphology and record the chemistry of the last residual liquid, but they do not set the grain or terrace spacing.

3.6. Mechanistic Constraints

The observations constrain the mechanism to a coupled sequence. First, the covered but non-hermetic geometry imposes a non-conservative melt/gas boundary. Second, evaporation and partial decomposition shift the CsBr–PbBr₂ balance toward ${\mathrm{PbBr}}_2$-rich conditions, producing discrete line-compound selection, $CsPbB{r}_3\to CsP{b}_{2}B{r}_5$.

Third, during the final thin-melt stage, the FTO relief localizes a faceted instability at the FTO-facing side, expressed as a coarse-to-fine grain and terrace hierarchy. Finally, ${\mathrm{PbBr}}_2$-rich residual material reacts locally with O-, OH-, and C-containing species to form Pb–Br–O secondary crystallites.

The candidate mechanisms are compared in

Table 2. Candidate models for the FTO-facing faceted microstructure. Epitaxial growth models are excluded a priori because the observed morphology develops in the recrystallized melt film rather than by vapor-phase epitaxy.

Model	Expected Signature	Assessment
Spinodal dewetting (ultrathin film)	Holes, rims, coarsening, non-faceted morphology	Unlikely: the melt is thick, the structures are faceted, and no rim–hole morphology is observed.
Nucleation-limited solidification	Broad, stochastic island spacing and orientation distribution	Unlikely: the morphology shows an ordered grain/terrace hierarchy rather than random nucleation.
Substrate-templated geometric focusing	Features pinned to the substrate relief with spacing fixed by the FTO pitch	Unlikely: the FTO relief localizes the morphology but does not alone define the spacing.
Marangoni/Bénard convection	Hexagonal or roll-like cells with wavelength comparable to the liquid thickness	Unlikely: no roll/cell planform is observed and the spacing is much smaller than the film thickness.
Reaction–diffusion (oxidation/ precipitation)	Local O-, OH-, or C-containing Pb–Br secondary crystallites appearing late and locally	Secondary: explains the Pb–Br–O crystallites but not the primary grain or terrace spacing.
Faceted Mullins–Sekerka with evaporation-induced undercooling	Micrometer-scale faceted pattern selected by diffusion–capillarity balance and modified by open-boundary mass loss	Consistent: explains the faceted morphology, coarse-to-fine hierarchy, and coupling to evaporation-driven ${\mathrm{PbBr}}_2$-rich conditions.

. Spinodal dewetting and nucleation-limited solidification can be excluded because they do not reproduce the thick-melt geometry, crystallographic faceting, and ordered terrace hierarchy. Pure substrate templating and Marangoni/Bénard convection is also unlikely: the first would lock the spacing to the FTO pitch, whereas the second would generate roll or cellular platforms with wavelengths comparable to the liquid thickness. Reaction–diffusion chemistry is present but secondary; it accounts for the local Pb–Br–O crystallites without setting the primary grain or terrace spacing.

The mechanism most consistent with the observations is a faceted Mullins–Sekerka-type solidification instability modified by evaporation-induced compositional drift. Diffusion and capillarity select the characteristic length scale, anisotropic interface kinetics produce faceting, and the open evaporative boundary shifts the melt toward ${\mathrm{PbBr}}_2$-rich line-compound equilibria [17,18]. Thus, the FTO relief perturbs and localizes the instability, but the primary pattern is governed by transport, capillarity, and evaporative boundary conditions rather than by hydrodynamic flow or direct geometrical templating.

4. Discussion

Our results show that slow cooling of a ${\mathrm{CsPbBr}}_3$ melt on polycrystalline ${\mathrm{SnO}}_2$ (FTO), under covered but non-hermetic conditions, produces an open-boundary solidification regime in which evaporation, discrete phase selection, and faceted interfacial instability are coupled.

The key condition is non-conservative mass loss at the melt/gas surface. Evaporation of Cs–Br-related, ${\mathrm{PbBr}}_2$-containing, and Br-containing species changes the local CsBr–PbBr₂ balance during solidification. In a line-compound system, this drift is not accommodated by continuous off-stoichiometry of ${\mathrm{CsPbBr}}_3$. Instead, the phase response is discrete from ${\mathrm{CsPbBr}}_3$ to ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$, corresponding to reduced CsBr activity and/or relative ${\mathrm{PbBr}}_2$ enrichment. This distinguishes the present case from the classical Mullins–Sekerka problem, where the interface is usually treated with conserved mass transport and continuous compositional variation [17,18].

The instability appears when the residual melt becomes thin. During the early stage, the melt thickness is sufficient to screen the advancing front from the pyramidal FTO relief, allowing lateral growth of a planar ${\mathrm{CsPbBr}}_3$ single-crystal cap. As solidification proceeds, the liquid layer thins and the FTO relief imposes local variations in melt thickness, curvature, and thermal gradient. At the same time, evaporation and partial decomposition shift the remaining liquid toward ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ and ${\mathrm{PbBr}}_2$-rich compositions. The resulting FTO-facing morphology consists of coarse ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ grains with broad inverted steps, followed by finer grains with steeper and more closely spaced terraces. This coarse-to-fine evolution is consistent with a decreasing effective diffusion length.

${\ell }_D\sim {\displaystyle \frac{D}{R}}$, a leading to a morphology consistent with a Mullins–Sekerka-type instability modified by an anisotropic interface kinetics and by the evaporative boundary condition.

The proposed evolution is summarized schematically in Figure 8. In step 1, small nuclei form while Cs–Br-related species evaporate from the melt. In step 2, lateral growth produces a ${\mathrm{CsPbBr}}_3$ cap, while the lower melt shifts toward ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ formation because of reduced CsBr activity and/or relative ${\mathrm{PbBr}}_2$ enrichment. In step 3, as the residual melt thins, temperature-gradient inhomogeneities imposed by the pyramidal FTO relief promote a more polycrystalline and porous ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ morphology at the FTO–facing side. In step 4, after final melt consumption, voids and ${\mathrm{PbBr}}_2$-rich residual pockets remain between grains, where local reaction with O-, OH-, or carbonate-containing species produces Pb–Br–O secondary crystallites.

The thermochemical pathway is constrained by the CsBr–PbBr₂ and ${\mathrm{PbBr}}_2$–PbO phase diagrams (Figure A1):

$$CsPbB{r}_3\to CsP{b}_{2}B{r}_5\to PbB{r}_2\to P{b}_{2}OB{r}_2\to P{b}_3{O}_{2}B{r}_2$$

The ${\mathrm{PbBr}}_2$-rich residual fragments on FTO (Figure A6) support this sequence. Because ${\mathrm{PbBr}}_2$-rich material is denser than the ${\mathrm{CsPbBr}}_3$-rich melt, it may precipitate near the FTO-facing side during the final stages of solidification, particularly when the upper single-crystalline film partially restricts evaporation from the lower melt. This provides a plausible route from discrete phase selection to the late secondary chemistry.

The secondary Pb–Br–O chemistry is local and subordinate to the primary instability. EDX and TOF-SIMS show that the rice-shaped and nanowire-like crystallites contain Pb, Br, O, OH, and locally C, but the grain and terrace hierarchy is already defined by the ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ morphology. These secondary phases decorate the porous FTO-facing region and record the chemistry of the last residual liquid; they do not set the primary in-plane spacing.

Several limitations remain. The evaporative boundary condition is treated using order-of-magnitude Hertz–Knudsen-type estimates rather than a fully coupled transport model. The EDX profiles bound any transition width only within the spatial resolution of the measurement. The source of the light elements in the secondary crystallites cannot be assigned uniquely; possible contributions include trapped gas, the ${\mathrm{SnO}}_2$ substrate, residual humidity, ${\mathrm{CO}}_2$, and post-growth ambient exposure. The phase identity of the secondary Pb–Br–O crystallites also remains tentative. ${\mathrm{Pb}}_2$(${\mathrm{CO}}_3$)${\mathrm{Br}}_2$-type, Pb(OH)Br-type, and lead oxybromide phases remain plausible if there is a reaction with C or H from the surrounding atmosphere at the processing temperature, and definitive assignment requires local diffraction, micro-Raman spectroscopy, or TEM-based analysis of individual crystallites [36,37].

The results suggest practical control parameters. Increasing (G/R) should stabilize the solidification front. Reducing the evaporation drive, for example, by increasing the halide partial pressure or improving enclosure of the melt should suppress the ${\mathrm{PbBr}}_2$-rich shift and reduce formation of the porous faceted morphology. The FTO relief controls where the instability develops by modulating local melt thickness, curvature, and thermal gradient, but it does not by itself set the characteristic in-plane spacing. Oxygen-, hydroxyl-, and carbonate-containing species control secondary phase formation without determining the primary morphology. A practical route to suppress ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ formation is therefore to reduce the evaporation-driven shift toward ${\mathrm{PbBr}}_2$-rich conditions. A slight excess of CsBr in the starting composition could compensate for partial CsBr loss during heating and solidification, thereby maintaining the local composition closer to the ${\mathrm{CsPbBr}}_3$ stability range. However, this excess must be optimized carefully, because too much CsBr could promote CsBr-rich residues or ${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$ formation. Additional strategies include improving enclosure of the melt, increasing the local halide partial pressure, reducing the dwell time at high temperature, and stabilizing the thermal gradient during cooling.

From an application perspective, suppressing the extended ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ region is more important than eliminating the localized Pb–Br–O crystallites, because ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ reduces the continuous scintillating ${\mathrm{CsPbBr}}_3$ volume, whereas the secondary crystallites are localized and sub-$\mathsf{\mu }\mathrm{m}$ in size.

More generally, these results identify a solidification regime in which open-boundary evaporation and discrete line-compound equilibria jointly control pattern formation. Such behavior should be relevant to other volatile halide and oxide-halide melts where evaporation, phase selection, and interfacial stability remain coupled during cooling.

5. Conclusions

We have shown that slow cooling of ${\mathrm{CsPbBr}}_3$ on polycrystalline ${\mathrm{SnO}}_2$:F (FTO) under covered but non-hermetic conditions produces an open-boundary solidification pathway. Evaporation drives the melt away from mass-conserved behavior and converts compositional drift into discrete phase selection. Instead of forming a continuously off-stoichiometric perovskite, the film separates into abrupt ${\mathrm{CsPbBr}}_3$ and ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ regions, consistent with the line-compound character of the CsBr–PbBr₂ system. At the FTO-facing side, the remaining melt develops a porous, faceted ${\mathrm{CsPb}}_2{\mathrm{Br}}_5$ morphology with inverted-step terraces. The coarse-to-fine evolution of the grains and terraces is consistent with late-stage thin-melt solidification, where the FTO relief enhances local variations in thermal gradient, curvature, and transport length. The morphology is therefore best described as a faceted Mullins–Sekerka-type instability modified by evaporative compositional drift, rather than by hydrodynamic convection or direct substrate templating. Secondary Pb–Br–O crystallites form locally in ${\mathrm{PbBr}}_2$-rich residual pockets at the FTO-facing side. EDX, TOF-SIMS, and BSE-contrast estimates constrain these products to Pb–Br phases containing O, OH, and locally C, with ${\mathrm{Pb}}_2$(${\mathrm{CO}}_3$)${\mathrm{Br}}_2$-type, Pb(OH)Br-type, and lead oxybromide phases remaining plausible. These crystallites record late residual-melt chemistry but do not set the primary grain or terrace spacing. These results identify an open-boundary solidification regime in which evaporation, discrete phase equilibria, and interfacial stability are coupled. Control of halide partial pressure, enclosure, (G/R), film thickness, and substrate relief should therefore provide routes to tune phase selection and buried morphology in volatile halide melts. Future optimization should therefore focus on suppressing CsBr loss through slight CsBr excess, improved enclosure, shorter high-temperature dwell time, and better control of the thermal gradient during solidification.