# Liquid-Like Interfaces Mediate Structural Phase Transitions in Lead Halide
Perovskites

Connor G. Bischak  These authors contributed equally to this work.  Department
of Chemistry, University of California, Berkeley, CA 94720.  Minliang Lai
These authors contributed equally to this work.  Department of Chemistry,
University of California, Berkeley, CA 94720.  Dylan Lu  Department of
Chemistry, University of California, Berkeley, CA 94720.  Zhaochuan Fan
Department of Chemistry, University of Utah, Salt Lake City, Utah 84112.
Philippe David  Department of Chemistry, University of Utah, Salt Lake City,
Utah 84112.  Dengpan Dong  Department of Materials Science and Engineering,
University of Utah, Salt Lake City, Utah 84112.  Hong Chen  Department of
Chemistry, University of California, Berkeley, CA 94720.  School of
Environmental Science and Engineering, Southern University of Science and
Technology, Shenzhen, Guangdong, China.  Ahmed S. Etman  Department of
Materials and Environmental Chemistry (MMK), Stockholm University, SE 106 91
Stockholm, Sweden.  Department of Chemistry, Faculty of Science, Alexandria
University, Ibrahimia, 21321 Alexandria, Egypt.  Teng Lei  Department of
Chemistry, University of Utah, Salt Lake City, Utah 84112.  Junliang Sun
College of Chemistry and Molecular Engineering, Peking University, Beijing
100871, China.  Michael Grünwald  Department of Chemistry, University of Utah,
Salt Lake City, Utah 84112.  David T. Limmer  Department of Chemistry,
University of California, Berkeley, CA 94720.  Materials Sciences Division,
Lawrence Berkeley National Laboratory, Berkeley, CA 94720.  Kavli Energy
NanoScience Institute, Berkeley, CA 94720.  Peidong Yang  Corresponding Author
<EMAIL_ADDRESS> Department of Chemistry, University of California,
Berkeley, CA 94720.  Materials Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, CA 94720.  Kavli Energy NanoScience Institute, Berkeley,
CA 94720.  Department of Materials Science and Engineering, University of
California, Berkeley, CA 94720.  Naomi S. Ginsberg  Corresponding Author
<EMAIL_ADDRESS> Department of Chemistry, University of California,
Berkeley, CA 94720.  Materials Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, CA 94720.  Department of Physics, University of
California, Berkeley, CA 94720.  Kavli Energy NanoScience Institute, Berkeley,
CA 94720.  Molecular Biophysics and Integrative Bioimaging Division, Lawrence
Berkeley National Laboratory, Berkeley, CA 94720.

###### Abstract

Microscopic pathways of structural phase transitions are difficult to probe
because they occur over multiple, disparate time and length scales. Using in
situ nanoscale cathodoluminescence microscopy, we visualize the thermally-
driven transition to the perovskite phase in hundreds of non-perovskite phase
nanowires, resolving the initial nanoscale nucleation and subsequent mesoscale
growth and quantifying the activation energy for phase propagation. In
combination with molecular dynamics computer simulations, we reveal that the
transformation does not follow a simple martensitic mechanism, and proceeds
via ion diffusion through a liquid-like interface between the two structures.
While cations are disordered in this liquid-like region, the halide ions
retain substantial spatial correlations. We find that the anisotropic crystal
structure translates to faster nucleation of the perovskite phase at nanowire
ends and faster growth along the long nanowire axis. These results represent a
significant step towards manipulating structural phases at the nanoscale for
designer materials properties.

††preprint: AIP/123-QED

Transformations between different crystal structures shape the properties of
solids from the smallest nanocrystals to the interior of planets. Structural
phase transitions occur through complex microscopic mechanisms that span
several time and length scales. Hanneman et al. (1964); Tolbert and Alivisatos
(1994); Murakami et al. (2004); Grünwald et al. (2006); Khaliullin et al.
(2011); Narayan et al. (2016) These microscopic pathways differ markedly from
material to material because of the highly anisotropic nature of crystals. At
two extremes are martensitic and diffusive transformations. Whereas
martensitic transformations involve elastic deformations in each unit cell and
can be extremely fast, diffusive transformations occur when the required
atomic reorganization is substantial and are therefore typically much slower.
Despite the availability of many compatibly slower characterization tools
(e.g. in situ X-ray diffraction (XRD) Hanneman et al. (1964); Tolbert and
Alivisatos (1994); Murakami et al. (2004) or transmission electron microscopy
(TEM)Zheng et al. (2011); Lin et al. (2014)) the mechanistic dynamics of
diffusive solid-solid phase transitions have remained elusive. To span the
substantial structural mismatch during the transition, the presence of
incoherent, disordered interfaces between phases has been hypothesized in a
handful of systems—directly observed only in colloidal models,Peng et al.
(2015) simulated in ice-clathrate Nguyen et al. (2015) and tungsten Barmak et
al. (2017) systems, and suggested as mechanistic features in binary metal
alloys under the framework of “massive transformations.”Howe et al. (2002);
Aaronson (2002); Yanar et al. (2002) Due to the rugged free energy landscapes
of non-trivial atomic rearrangements, the analysis of structural
transformations via computer simulations is also challenging because one must
incorporate time scales of not only atomistic fluctuations and macroscopic
collective reorganizations but also those of processes occurring on scales
that are intermediate to these disparate ones, such as diffusion.

Here we reveal the mechanism of a non-martensitic, massive structural
transformation on the nanoscale by exploiting differences in
cathodoluminescence (CL) emission of different crystal structures and by
realizing multiscale simulations that include molecular dynamics (MD) and
coarse-grained models. With in situ scanning electron CL imaging, we follow a
thermally induced structural transformation in CsPbIBr2 nanowires with
exquisite temporal and spatial resolution over a large field of view, allowing
the simultaneous characterization of the nucleation and growth kinetics in a
statistically significant number of single particles. The multi-scale nature
of our experimental observations and modeling enables us to determine the
microscopic mechanisms of the structural transformation. We find that both
nucleation and growth are characterized by strongly anisotropic kinetics and
that the boundary between crystal structures is propagated by activated ion
diffusion through a liquid-like interface. Despite the overall disorder of the
interface, long-range anionic charge density correlations are observed, which
promote the crystallographic registration of the two crystal phases. Our
observations provide an unprecedented view of the complex dynamic pathways by
which two distinct crystal structures interconvert.

Figure 1: Cathodoluminescence (CL) imaging of the LT-CsPbIBr2 to HT-CsPbIBr2
phase transition in nanowires. (A) Schematic of the LT-CsPbIBr2 and HT-
CsPbIBr2 phases. (B) Photoluminescence spectra of LT-CsPbIBr2 and HT-CsPbIBr2
nanowires. (C) Schematic of the CL imaging apparatus. (D) SE image of the full
field-of-view of the measurement containing $\sim$150 individual nanowires. CL
images (E) before and (F) after the phase transition. (G) Magnified view
showing individual nanowires. (H) An example time series of SE and CL images
of a single nanowire during the phase transition at 163 °C. The white circle
indicates one of two nucleation events in the nanowire, and the dotted white
line marks the corresponding phase boundary as it migrates along the length of
the nanowire. (Adjacent snapshots are separated in time by 6 seconds.)

Mixed halide perovskites are promising semiconductor materials for
optoelectronicsDeschler et al. (2014); Eperon et al. (2016); McMeekin et al.
(2016) and are an ideal platform for investigating solid-solid phase
transitions. Much like CsPbI3,Sharma et al. (1992); Stoumpos et al. (2013);
Eperon et al. (2015); Lai et al. (2017) the metal halide perovskite material,
CsPbIBr2, undergoes a thermally-driven phase transition from a low temperature
non-perovskite phase (LT-CsPbIBr2) to a high temperature perovskite phase (HT-
CsPbIBr2) upon heating (Figure 1A) and remains kinetically-trapped in the HT-
CsPbIBr2 phase upon rapid cooling. This phase transition contributes to the
instability of perovskite photovoltaicsEperon et al. (2015); Yi et al. (2016)
and has been utilized for generating nanoscale p-n heterojunctions Kong et al.
(2018) and thermochromic smart window technologies. Lin et al. (2018) Despite
much interest, the mechanism of this phase transition has not been explained.
In contrast to structurally similar perovskite phases known to
interconvert,Dobrovolsky et al. (2017); Quarti et al. (2016) LT-CsPbIBr2 and
HT-CsPbIBr2 are not related by simple elastic deformations. Transitions
between these structurally dissimilar lattices thus require a more complex
rearrangement of atoms, suggesting the possibility to observe a massive
transformation and to evaluate how the anharmonic, soft, and ionic nature Zhu
et al. (2016) of the material affects its dynamics. Additionally, the density
of the material increases by approximately 7% during the transition,
suggesting that disparate interfacial energies and lattice strain could play
an important role in nucleation and growth. Crucial to this study, the LT-
CsPbIBr2 phase has an indirect band gap, resulting in low photoluminescence
(PL) emission, whereas the direct bandgap HT-CsPbIBr2 phase exhibits bright PL
emission (Figure 1B). This large difference in emission intensity produces
strong contrast differences between the two structures during CL imaging and
allows us to accurately track the progress of the phase transition.

We use CL imaging with in situ heating to monitor the phase transition
kinetics of CsPbIBr2. CL microscopy uses a focused, scanning electron beam to
excite the sample of interest, and the emitted light is collected by a
parabolic mirror and directed to a detector to form an image (Figure 1C). It
has been used to image steady-state properties Lai et al. (2017); Kong et al.
(2018); Bischak et al. (2015); Dou et al. (2015); Dar et al. (2017);
Ummadisingu and Grätzel (2018) and dynamic processesBischak et al. (2017,
2018) of metal halide perovskites. Similar to with CsPbI3 nanowires, single-
crystal LT-CsPbIBr2 nanowires were synthesized with the edge-sharing
octrahedral chains oriented along the long axis of the nanowires, as confirmed
by continuous rotation electron diffraction (cRED) (Figure S1). Using CL
microscopy, we measure a large field-of-view containing tens to hundreds of
these CsPbIBr2 nanowires to build up statistics on nucleation and growth
kinetics. A secondary electron (SE) image of a typical field-of-view is shown
in Figure 1D, containing $\sim$150 nanowires that are monitored
simultaneously; CL images showing the nanowires before and after the phase
transition are shown in Figure 1E and Figure 1F, respectively. The evolution
of the nanowires from the LT-CsPbIBr2 to the HT-CsPbIBr2 phase from this
larger field-of-view is depicted in Figure S2 and Movie S1. We select
individual nanowires from this larger field-of-view (Figure 1G) and measure
phase propagation rates. Figure 1H shows a time series of simultaneously
acquired SE and CL images that illustrate the evolution from LT-CsPbIBr2 to
HT-CsPbIBr2 in a single nanowire upon heating. Although no changes are obvious
in the SE images, the CL images initially show a nanowire entirely composed of
LT-CsPbIBr2 followed by nucleation of the bright HT-CsPbIBr2 phase at the
nanowire ends and phase propagation along the length of the wire until the
wire is completely converted to HT-CsPbIBr2. Temperature-dependent in-situ
X-ray diffraction (XRD) before and after the phase transition confirms the
presence of the two phases (Figure S3).

Figure 2:  Energetics of perovskite phase propagation. (A) Histograms of the
propagation rate of three different populations of nanowires heated at three
different constant temperatures, 163 °C (purple), 177 °C (orange), and 182 °C
(green). The insets show a characteristic nanowire at each temperature with a
countdown time axis for full conversion into the perovskite phase shown at the
top. (B) An Arrhenius plot of experimental and MD simulation data. Red points
correspond to the experimental propagation rate of different nanowire
populations measured at different temperatures, where the units of k are m/s,
also shown in the inset; from the simulation data, light blue points indicate
growth rates of <100> HT-CsPbBr3 along the wire axis, as observed in c-RED and
SAED (Figure S1), and dark blue points indicate growth rates of <110> HT-
CsPbBr3 along the wire axis. The solid red line is the linear fit to the
experimental data (210 $\pm$ 60 kJ/mol), and the solid blue line is the linear
fit to the simulation data (140 $\pm$ 80 kJ/mol). The red and blue shaded
regions show the 95% confidence interval of the experimental and simulation
fits, respectively, with the overlapping (mauve) region showing the overlap
between these two regions. While the <110> HT-CsPbBr3 plane is not observed to
be transverse to the wire axis in SAED, the growth rates thus obtained are
statistically indistinguishable and further constrain the fit to simulation
data. See Figure S16 for further details. (C) Snapshots from the MD simulation
of phase propagation as a function of time at 267 °C, showing the disordered
interface between the LT-CsPbBr3 and HT-CsPbBr3 phases. (D) Charge density
profiles from the MD simulation at 267 °C, obtained by projecting ion
positions onto the direction of the wire axis. Data are averaged over a 50 ns
time window.

The combination of the nanowire geometry and the high spatial resolution of CL
imaging allows for a quantitative analysis of the phase propagation rates
along the length of the nanowire. Taking advantage of the ability to probe the
phase transition dynamics in many CsPbIBr2 nanowires simultaneously, we
provide a statistical analysis of the HT-CsPbIBr2 phase growth rate as a
function of temperature. We record the phase propagation dynamics of a
population of nanowires at temperatures ranging from 163 to 182 °C (Figure
S4). We first rapidly increase the stage temperature to a specific value to
initiate the phase transition and then maintain a constant temperature to
measure the phase propagation rate (see Supplementary Information and Figure
S5 for more details). Figure 2A shows the distribution of phase propagation
rates at three different temperatures with typical time series of individual
nanowires shown in the inset. At 163 °C, 177 °C, and 182 °C, we observe
average propagation rates of 3.1 $\pm$ 0.2 nm/s, 11 $\pm$ 1 nm/s, and 33 $\pm$
3 nm/s, respectively. This strong temperature dependence suggests that phase
propagation is controlled by thermally activated microscopic processes.
Indeed, we find that the propagation rate as a function of temperature
exhibits Arrhenius-like behavior with an activation energy of 210 $\pm$ 60
kJ/mol (Figure 2B)— 50$\times$ the scale of a typical thermal fluctuation
($k_{\rm B}T$). (Uncertainty provided represents 95% confidence interval.)
Given this substantial energetic barrier, there must be a significant
compensating increase in entropy for interphase boundary propagation to
proceed at the observed rates.

Figure 3:  Perovskite phase nucleation and anisotropic growth from experiment
and simulation. (A) Plot of observed nucleation events as a function of time
for nucleation at nanowire ends (teal), and nucleation at nanowire sides
(blue). (B) A time series of CL and SE images of a single nucleation event at
the end of a nanowire. (C) A time series of CL and SE images of a single
nucleation event at the side of a nanowire. An outline of nanowire from the
corresponding SE image is shown in the CL images in B and C. (D) Plot of
nucleation probability (P($\tau$)) as a function of time for nucleation at
nanowire ends (teal) and nanowire sides (blue) as a function of time from
simulations. (E) A time series showing a single nucleation event at the
nanowire end from simulations. (F) A time series showing a single nucleation
event at the nanowire side from simulations.

To reveal the microscopic mechanism of phase propagation, we use electronic
structure calculations to parameterize a classical force field for CsPbBr3
crystals, which we use as a proxy for the structurally similar mixed halide
perovskite studied experimentally (see Table S1 and Table S2, Figure S6 and
Figure S7, and the Supplementary Information). We employ this force field in
MD simulations. We start our simulations from configurations that include
planar interfaces between the LT-CsPbBr3 and HT-CsPbBr3 phases, employing the
relative crystallographic orientations suggested by single area electron
diffraction (SAED) ((100) LT-CsPbBr3 abutting (100) HT-CsPbBr3), as seen in
Figure 2C. We considered additional interfacial possibilities, such as (110)
LT-CsPbBr3 planes abutting (100) HT-CsPbBr3, described further in the
Supplementary Information. In several long MD simulations at temperatures of
227 °C, 247 °C, and 267 °C we consistently observe growth of the HT-CsPbBr3
phase, in agreement with experiments (see Figures S8-S10 and Supplementary
Information). (Phase propagation was intractably slow in simulations at lower
temperatures.) Propagation rates estimated from at least three independent
simulations for each aforementioned interface at each temperature are plotted
in Figure 2B. An Arrhenius-type analysis of these data yields an activation
energy of 140 $\pm$ 80 kJ/mol, in good agreement with experiments.

The simulations reveal the formation of a structurally disordered, liquid-like
interfacial layer as the origin of the compensating increase in entropy
hypothesized from the experiments as necessary to achieve the observed
interphase boundary propagation rates. Large energetic barriers to phase
propagation, as measured in our experiments and simulations, can be
interpreted as describing activated ion diffusion events between
stoichiometrically different coordination environments. Growth of the HT-
CsPbBr3 structure proceeds via diffusion of ions across this amorphous
interface (Figure 2C and Movie S2).Peng et al. (2015) Due to the marked
structural differences of the two phases, growth cannot proceed layer-by-
layer. In particular, (100) layers of HT-CsPbBr3 have a different ionic
composition than (100) layers of LT-CsPbBr3. Completion of a new layer of HT-
CsPbBr3 thus requires the recruitment of ions from at least two (100) layers
of LT-CsPbBr3.

Despite the mediating liquid-like region between the two phases, using SAED we
find the same crystallographic orientation of the HT phase in all nanowires
probed. This can be understood by separately computing the distribution of
each species of ion within the disordered region in the molecular simulations
(Figure 2D). Interestingly, we find that, while the positions of the cations
are essentially uniform, the positions of the halides remain correlated across
the entire liquid-like interface. These correlations manifest as oscillations
in the halide density distribution, shown in Figure 2D, and act to template
the formation of the growing HT phase, ensuring its crystallographic
orientation despite the overall incoherent interface. These persistent anionic
density correlations are reminiscent of those templating the association of
metal nanoparticles in dense ionic solutions.Zhang et al. (2017)

In our experiments, we observe nucleation of the HT-CsPbIBr2 primarily at
nanowire ends; a minority of wires also displays nucleation along the lateral
surface. Preferential nucleation on nanowire ends is evident from Figure 3A,
which shows a histogram of all nucleation events in 100 nanowires as a
function of time, observed at 163 °C (see Supplementary Information and Figure
S11 for more details). Here, time zero is defined by the image frame in which
we first observe a single HT-CsPbIBr2 phase pixel above the LT-CsPbIBr2
background CL intensity threshold. The distributions of end and side
nucleation events are clearly different; the earlier peak of the end
nucleation distribution indicates faster nucleation at nanowire ends than
sides. To extract a nucleation rate at each of the nanowire ends and sides, we
examine distributions of waiting times, which are exponentially distributed,
as expected for an independent, reaction limited process. We find that
nucleation at nanowire ends occurs with a rate of 0.045 s-1, whereas
nucleation at wire sides occurs with a rate of 0.013 s-1 (Figure S12). The
nucleation rates at early times are consistent with those inferred at latter
times using an Avrami analysis,Chaikin (2000) accounting for a constant rate
of growth measured independently (see Supplementary Information for details).
The inset of Figure 3A shows CL and SE images of part of a single nanowire
after nucleation occurred at the end and side of the nanowire. Time series of
the CL and SE images of the nuclei growth at the nanowire end and nanowire
side are depicted in Figure 3B and 3C, respectively (Movie S3 and S4).
Additional nucleation events are shown in Figure S13. Nucleation at the
nanowire end leads to the new phase expanding until it occupies the full width
of the nanowire and then propagating along the long axis of the wire (Figure
3B). Because axial growth can occur in two opposite directions, new regions of
HT-CsPbIBr2 formed on the nanowire side are seen to clearly grow
asymmetrically with a faster growth rate along the long axis of the nanowire
(Figure 3C). By analyzing the extent to which the perovskite phase is circular
in the image frames at early times, we find that nucleation at the nanowire
sides results in a more anisotropically-shaped perovskite phase volume with
faster growth along the length of the wire (Figure S14).

We develop a phenomenological model to describe both the preferential location
of nucleation sites at the wire end as well as the anisotropic growth rate at
the nanowire side (see Figure S15 and Supplementary Information for additional
details). Specifically, we use a simple lattice model of crystal growth with
anisotropic bond and surface energies that are greater along the long axes of
the wire compared to the short axes. This model phenomenologically accounts
for the anisotropy in lattice orientations of the HT-CsPbIBr2 and LT-CsPbIBr2
phases. The lattice is initialized in the pure LT-CsPbIBr2 phase and is
instantly quenched to favor the HT-CsPbIBr2 phase. Figure 3D shows two
distributions of nucleation events at nanowire ends and nanowire sides from
the model, which qualitatively matches our experimental results, suggesting
that preferential nucleation at nanowire ends is caused by the tendency to
minimize interfacial energies between the two phases. Two time series of
simulation snapshots of end and side nucleation are shown in Figure 3E and 3F.
Growth from the nanowire end proceeds almost isotropically, whereas growth on
the nanowire side occurs anisotropically due to the alternation between
octahedral double chains and gaps in between them. Specifically, growth occurs
at a faster rate in the direction of the lead-halide octahedral chains (i.e.,
along the wire axis); growth in perpendicular directions is noticeably slower.
Our MD simulations confirm these anisotropic growth rates: Interfaces
involving (010) and (001) layers of LT-CsPbBr3, which are parallel to the
nanowire axis, display slower average phase propagation compared to orthogonal
(100) layers (Figure S6).

The kinetic pathways of the structural phase transition are also apparent in
the morphology and photophysical properties of the resulting HT-CsPbIBr2
nanowires. In some cases, when the nanowire is not uniformly contacting the
substrate, changes in the nanowire morphology are evident upon the formation
of the perovskite phase. As the phase transition proceeds, lattice stress
associated with the 7% increase of nanowire volume results in nanowire bending
and expansion (Figure S7). Additionally, HT-CsPbIBr2 nanowires with multiple
nucleation sites sometimes display dark regions where two phase boundaries
meet (Figure S8), suggesting the formation of grain boundaries with suppressed
emission due to a high defect concentration.

Through in situ dynamical CL imaging and multiscale modeling of the LT-
CsPbIBr2 to HT-CsPbIBr2 structural phase transition we have uncovered the
mechanism for a complex, non-martensitic structural transformation. The
measured activation energy for phase propagation is consistent with a
disordered interface between the two phases through which ions must diffuse,
as observed in MD simulations. This liquid-like interface is far from the
melting point of the involved solids and presents strong anion density
correlations, which we suspect as being responsible for the fixed
crystallographic orientation of the nascent perovskite phase within the
nanowire that is observed in SAED. The spontaneous formation of an incoherent
interface suggests that an ordered solid-solid interface between these two
structurally dissimilar phases is thermodynamically less favorable than the
sum of LT-CsPbIBr2-liquid and HT-CsPbIBr2-liquid interfaces, plus the
concomitant enthalpy required to disorder the interfacial layer, even when
such liquid-like configurations are not stable by themselves. Our findings are
yet another manifestation of the liquid-like dynamics that have been observed
in these highly anharmonic metal halide perovskite lattices that result from
the inherent low cohesive energy of their ionic bonds, in contrast with
traditional behaviors of covalent semiconductors.

Our results suggest that similar diffusive mechanisms might occur in a large
range of materials, including other perovskite materials, that crystallize in
structures that do not share simple epitaxial interfaces. The experimental
method for observing dynamic structural changes introduced in this work could
also be extended to other systems, such as 2D transition metal
dichalcogenidesTongay et al. (2012); Bediako et al. (2018) and metal organic
frameworks (MOFs),Silva et al. (2010); Cui et al. (2012) in which a change in
the luminescence intensity or wavelength accompanies a structural change. We
expect that similar in situ monitoring of phase transitions will significantly
aid our ability to characterize phase behavior, enabling quantitative
comparison to theoretical results and creating opportunities to manipulate
solids and their properties on the nanoscale.

## Acknowledgments

We thank E. Wong, E. S. Barnard, D. F. Ogletree, and S. Aloni at the Molecular
Foundry for assistance with CL equipment and helpful discussions. CL and
analysis work by C.G.B. and N.S.G. has been supported by STROBE, A National
Science Foundation Science & Technology Center under Grant No. DMR 1548924.
The CL imaging at the Lawrence Berkeley Lab Molecular Foundry and the TEM
imaging at the National Center for Electron Microscopy were performed as part
of the Molecular Foundry user program, supported by the Office of Science,
Office of Basic Energy Sciences, of the U.S. Department of Energy under
Contract No. DE-AC02-05CH11231. C.G.B. acknowledges an NSF Graduate Research
Fellowship (No. DGE1106400), and N.S.G. acknowledges an Alfred P. Sloan
Research Fellowship, a David and Lucile Packard Foundation Fellowship for
Science and Engineering, and a Camille and Henry Dreyfus Teacher-Scholar
Award. Modeling by D.T.L., materials fabrication and characterization by P.Y.
and co-workers is supported under the U.S. Department of Energy, Office of
Science, Office of Basic Energy Sciences, Materials Sciences and Engineering
Division under Contract No. DE-AC02-05-CH11231 within the Physical Chemistry
of Inorganic Nanostructures Program (KC3103). Molecular dynamics simulations
have also been partially supported by the National Science Foundation under
NSF-REU grant CHE-1659579. The support and resources of the Center for High
Performance Computing at the University of Utah are gratefully acknowledged.

## Author Contributions

C.G.B, M.L., D.T.L., M.G., P.Y., and N.S.G. wrote the manuscript. C.G.B.,
M.L., D.Y., D.T.L., P.Y., and N.S.G. conceptualized the experiment. M.L.
synthesized the LT-CsPbIBr2 nanowires and performed the PL and XRD
measurements. C.G.B. performed the CL experiments and analyzed the CL
nucleation and growth data. D.T.L. conceptualized and performed the Ising
model simulations. Z.F., P.D., D.T.L., and M.G. conceived the MD simulations
and analyzed simulation results. Z.F., P.D., D.D., and M.G. developed the
force field and performed MD simulations. A.S.E., J.S., H.C. collecting and
analyzing the continuous rotation electron diffraction (cRED). T.L. performed
the SAED.

## References

## References

  * Hanneman et al. (1964) Hanneman, R. E.; Banus, M. D.; Gatos, H. C. High pressure transition in InSb. _J. Phys. Chem. Solids_ 1964, _25_ , 293–302
  * Tolbert and Alivisatos (1994) Tolbert, S. H.; Alivisatos, A. P. Size Dependence of a First Order Solid-Solid Phase Transition: The Wurtzite to Rock Salt Transformation in CdSe Nanocrystals. _Science_ 1994, _265_ , 373–376
  * Murakami et al. (2004) Murakami, M.; Hirose, K.; Kawamura, K.; Sata, N.; Ohishi, Y. Post-Perovskite Phase Transition in MgSiO3. _Science_ 2004, _304_ , 855–858
  * Grünwald et al. (2006) Grünwald, M.; Rabani, E.; Dellago, C. Mechanisms of the Wurtzite to Rocksalt Transformation in CdSe Nanocrystals. _Phys. Rev. Lett._ 2006, _96_ , 255701
  * Khaliullin et al. (2011) Khaliullin, R. Z.; Eshet, H.; Kühne, T. D.; Behler, J.; Parrinello, M. Nucleation mechanism for the direct graphite-to-diamond phase transition. _Nat. Mater._ 2011, _10_ , 693–697
  * Narayan et al. (2016) Narayan, T. C.; Baldi, A.; Koh, A. L.; Sinclair, R.; Dionne, J. A. Reconstructing solute-induced phase transformations within individual nanocrystals. _Nat. Mater._ 2016, _15_ , 768–774
  * Zheng et al. (2011) Zheng, H.; Rivest, J. B.; Miller, T. A.; Sadtler, B.; Lindenberg, A.; Toney, M. F.; Wang, L.-W.; Kisielowski, C.; Alivisatos, A. P. Observation of Transient Structural-Transformation Dynamics in a Cu2S Nanorod. _Science_ 2011, _333_ , 206–209
  * Lin et al. (2014) Lin, Y.-C.; Dumcenco, D. O.; Huang, Y.-S.; Suenaga, K. Atomic mechanism of the semiconducting-to-metallic phase transition in single-layered MoS2. _Nat. Nanotechnol._ 2014, _9_ , 391–396
  * Peng et al. (2015) Peng, Y.; Wang, F.; Wang, Z.; Alsayed, A. M.; Zhang, Z.; Yodh, A. G.; Han, Y. Two-step nucleation mechanism in solid–solid phase transitions. _Nat. Mater._ 2015, _14_ , 101–108
  * Nguyen et al. (2015) Nguyen, A. H.; Koc, M. A.; Shepherd, T. D.; Molinero, V. Structure of the Ice–Clathrate Interface. _J. Phys. Chem. C_ 2015, _119_ , 4104–4117
  * Barmak et al. (2017) Barmak, K.; Liu, J.; Harlan, L.; Xiao, P.; Duncan, J.; Henkelman, G. Transformation of topologically close-packed $\beta$-w to body-centered cubic $\alpha$-w: Comparison of experiments and computations. _J. Chem. Phys._ 2017, _147_ , 152709
  * Howe et al. (2002) Howe, J. M.; Reynolds, W. T.; Vasudevan, V. K. Static and in-situ high-resolution transmission electron microscopy investigations of the atomic structure and dynamics of massive transformation interfaces in a Ti-Al alloy. _Metall. Mater. Trans. A_ 2002, _33_ , 2391–2411
  * Aaronson (2002) Aaronson, H. I. Mechanisms of the massive transformation. _Metall. Mater. Trans. A_ 2002, _33_ , 2285–2297
  * Yanar et al. (2002) Yanar, C.; Wiezorek, J. M. K.; Soffa, W. A.; Radmilovic, V. Massive transformation and the formation of the ferromagnetic L10 phase in manganese-aluminum-based alloys. _Metall. Mater. Trans. A_ 2002, _33_ , 2413–2423
  * Deschler et al. (2014) Deschler, F.; Price, M.; Pathak, S.; Klintberg, L. E.; Jarausch, D.-D.; Higler, R.; Hüttner, S.; Leijtens, T.; Stranks, S. D.; Snaith, H. J.; Atatüre, M.; Phillips, R. T.; Friend, R. H. High Photoluminescence Efficiency and Optically Pumped Lasing in Solution-Processed Mixed Halide Perovskite Semiconductors. _J. Phys. Chem. Lett._ 2014, _5_ , 1421–1426
  * Eperon et al. (2016) Eperon, G. E. et al. Perovskite-perovskite tandem photovoltaics with optimized bandgaps. _Science_ 2016, aaf9717
  * McMeekin et al. (2016) McMeekin, D. P.; Sadoughi, G.; Rehman, W.; Eperon, G. E.; Saliba, M.; Hörantner, M. T.; Haghighirad, A.; Sakai, N.; Korte, L.; Rech, B.; Johnston, M. B.; Herz, L. M.; Snaith, H. J. A mixed-cation lead mixed-halide perovskite absorber for tandem solar cells. _Science_ 2016, _351_ , 151–155
  * Sharma et al. (1992) Sharma, S.; Weiden, N.; Weiss, A. Phase Diagrams of Quasibinary Systems of the Type: ABX3 — A′BX3; ABX3 — AB′X3, and ABX3 — ABX′3; X = Halogen. _Z. Phys. Chem._ 1992, _175_ , 63–80
  * Stoumpos et al. (2013) Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G. Semiconducting Tin and Lead Iodide Perovskites with Organic Cations: Phase Transitions, High Mobilities, and Near-Infrared Photoluminescent Properties. _Inorg. Chem._ 2013, _52_ , 9019–9038
  * Eperon et al. (2015) Eperon, G. E.; Paternò, G. M.; Sutton, R. J.; Zampetti, A.; Haghighirad, A. A.; Cacialli, F.; Snaith, H. J. Inorganic caesium lead iodide perovskite solar cells. _J. Mater. Chem. A_ 2015, _3_ , 19688–19695
  * Lai et al. (2017) Lai, M.; Kong, Q.; Bischak, C. G.; Yu, Y.; Dou, L.; Eaton, S. W.; Ginsberg, N. S.; Yang, P. Structural, optical, and electrical properties of phase-controlled cesium lead iodide nanowires. _Nano Res._ 2017, _10_ , 1107–1114
  * Yi et al. (2016) Yi, C.; Luo, J.; Meloni, S.; Boziki, A.; Ashari-Astani, N.; Grätzel, C.; M. Zakeeruddin, S.; Röthlisberger, U.; Grätzel, M. Entropic stabilization of mixed A-cation ABX3 metal halide perovskites for high performance perovskite solar cells. _Energy Environ. Sci._ 2016, _9_ , 656–662
  * Kong et al. (2018) Kong, Q.; Lee, W.; Lai, M.; Bischak, C. G.; Gao, G.; Wong, A. B.; Lei, T.; Yu, Y.; Wang, L.-W.; Ginsberg, N. S.; Yang, P. Phase-transition-induced p-n junction in single halide perovskite nanowire. _Proc. Natl. Acad. Sci. U.S.A._ 2018, _115_ , 8889–8894
  * Lin et al. (2018) Lin, J.; Lai, M.; Dou, L.; Kley, C. S.; Chen, H.; Peng, F.; Sun, J.; Lu, D.; Hawks, S. A.; Xie, C.; Cui, F.; Alivisatos, A. P.; Limmer, D. T.; Yang, P. Thermochromic halide perovskite solar cells. _Nat. Mater._ 2018, _17_ , 261
  * Dobrovolsky et al. (2017) Dobrovolsky, A.; Merdasa, A.; Unger, E. L.; Yartsev, A.; Scheblykin, I. G. Defect-induced local variation of crystal phase transition temperature in metal-halide perovskites. _Nat. Commun._ 2017, _8_ , 34
  * Quarti et al. (2016) Quarti, C.; Mosconi, E.; M. Ball, J.; D’Innocenzo, V.; Tao, C.; Pathak, S.; J. Snaith, H.; Petrozza, A.; Angelis, F. D. Structural and optical properties of methylammonium lead iodide across the tetragonal to cubic phase transition: implications for perovskite solar cells. _Energy Environ. Sci._ 2016, _9_ , 155–163
  * Zhu et al. (2016) Zhu, H.; Miyata, K.; Fu, Y.; Wang, J.; Joshi, P. P.; Niesner, D.; Williams, K. W.; Jin, S.; Zhu, X.-Y. Screening in crystalline liquids protects energetic carriers in hybrid perovskites. _Science_ 2016, _353_ , 1409–1413
  * Bischak et al. (2015) Bischak, C. G.; Sanehira, E. M.; Precht, J. T.; Luther, J. M.; Ginsberg, N. S. Heterogeneous Charge Carrier Dynamics in Organic–Inorganic Hybrid Materials: Nanoscale Lateral and Depth-Dependent Variation of Recombination Rates in Methylammonium Lead Halide Perovskite Thin Films. _Nano Lett._ 2015, _15_ , 4799–4807
  * Dou et al. (2015) Dou, L.; Wong, A. B.; Yu, Y.; Lai, M.; Kornienko, N.; Eaton, S. W.; Fu, A.; Bischak, C. G.; Ma, J.; Ding, T.; Ginsberg, N. S.; Wang, L.-W.; Alivisatos, A. P.; Yang, P. Atomically thin two-dimensional organic-inorganic hybrid perovskites. _Science_ 2015, _349_ , 1518–1521
  * Dar et al. (2017) Dar, M. I.; Hinderhofer, A.; Jacopin, G.; Belova, V.; Arora, N.; Zakeeruddin, S. M.; Schreiber, F.; Grätzel, M. Function Follows Form: Correlation between the Growth and Local Emission of Perovskite Structures and the Performance of Solar Cells. _Adv. Funct. Mater._ 2017, _27_ , n/a–n/a
  * Ummadisingu and Grätzel (2018) Ummadisingu, A.; Grätzel, M. Revealing the detailed path of sequential deposition for metal halide perovskite formation. _Sci. Adv._ 2018, _4_ , e1701402
  * Bischak et al. (2017) Bischak, C. G.; Hetherington, C. L.; Wu, H.; Aloni, S.; Ogletree, D. F.; Limmer, D. T.; Ginsberg, N. S. Origin of Reversible Photoinduced Phase Separation in Hybrid Perovskites. _Nano Lett._ 2017, _17_ , 1028–1033
  * Bischak et al. (2018) Bischak, C. G.; Wong, A. B.; Lin, E.; Limmer, D. T.; Yang, P.; Ginsberg, N. S. Tunable Polaron Distortions Control the Extent of Halide Demixing in Lead Halide Perovskites. _J. Phys. Chem. Lett._ 2018, _9_ , 3998–4005
  * Zhang et al. (2017) Zhang, H.; Dasbiswas, K.; Ludwig, N. B.; Han, G.; Lee, B.; Vaikuntanathan, S.; Talapin, D. V. Stable colloids in molten inorganic salts. _Nature_ 2017, _542_ , 328–331
  * Chaikin (2000) Chaikin, P. M. _Principles of Condensed Matter Physics_ ; Cambridge University Press: Cambridge, 2000
  * Tongay et al. (2012) Tongay, S.; Zhou, J.; Ataca, C.; Lo, K.; Matthews, T. S.; Li, J.; Grossman, J. C.; Wu, J. Thermally Driven Crossover from Indirect toward Direct Bandgap in 2D Semiconductors: MoSe2 versus MoS2. _Nano Lett._ 2012, _12_ , 5576–5580
  * Bediako et al. (2018) Bediako, D. K.; Rezaee, M.; Yoo, H.; Larson, D. T.; Zhao, S. Y. F.; Taniguchi, T.; Watanabe, K.; Brower-Thomas, T. L.; Kaxiras, E.; Kim, P. Heterointerface effects in the electrointercalation of van der Waals heterostructures. _Nature_ 2018, _558_ , 425
  * Silva et al. (2010) Silva, C. G.; Corma, A.; García, H. Metal–organic frameworks as semiconductors. _J. Mater. Chem_ 2010, _20_ , 3141–3156
  * Cui et al. (2012) Cui, Y.; Yue, Y.; Qian, G.; Chen, B. Luminescent Functional Metal–Organic Frameworks. _Chem. Rev._ 2012, _112_ , 1126–1162