# Enhanced Electromagnetic Wave Absorption in Mapbi3 Hybrid Perovskite Through a Defect-Tunable Green Synthesis

Yihui Cai, Dominique Bégin, Christophe Lefevre, Charles Sidhoum, Erik Elkaïm, Pascal Boulet, Pierre Desgardin, Marie-France Barthe, Ricardo Helm, Werner Egger, et al.

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To cite this version:

Yihui Cai, Dominique Bégin, Christophe Lefevre, Charles Sidhoum, Erik Elkaïm, et al. "Enhanced Electromagnetic Wave Absorption in Mapbi3 Hybrid Perovskite Through a Defect-Tunable Green Synthesis." Small Structures, 2025, 6 (9), pp.2500066. 10.1002/sstr.202500066. hal-05216863

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# Enhanced Electromagnetic Wave Absorption in $Mapb_i_3$ Hybrid Perovskite Through a Defect-Tunable Green Synthesis

Yihui Cai, Dominique Begin,* Christophe Lefevre, Charles Sidhoum, Erik Elkaim, Pascal Boulet, Pierre Desgardin, Marie-France Barthe, Ricardo Helm, Werner Egger, Maik Butterling, Andreas Wagner, Vasiliki Papaefthimiou, Spiros Zafeiratos, Damien Cianferani, Loic Mager, Ovidiu Ersen, Catherine Corbel, Clément Sanchez,* and Sylvie Begin-Colin*

Defect engineering and structure-property relationship understanding in meth-
ylammonium lead iodide (MAPI) hybrid perovskites (HPs) attract significant
scientific interest, as synthesis-related defects may strongly influence intrinsic
properties. We have explored a green solvent-free synthesis—mechanosynthesis
—leading to large quantities of MAPI powder with tuneable defect density
suitable to study MAPI as an electromagnetic wave absorbing (EMWA) material.
A dielectric loss enhancement was revealed at 11.4 GHz (X-band) for 4 h-ground
MAPI powders (MAPI4h), compared to 30 min-ground powders (MAPI30) when
the particle size was <20 µm. MAPI powders display a fractal microstructure
with agglomerates of clusters of (nano)grains (≈80 nm for MAPI4h), consisting
further of oriented smaller nanograin (5–10 nm) clusters. A strong reabsorption
in smaller particles was evidenced due to a surface-defective layer. MAPI4h was
shown to display a more surface-defective layer with a higher defect density
gradient from surface to (nano)grains core and unique open defects different
from those in solution-processed MAPI. These vacancy-type surface defects
would enhance dipole polarization by stabilizing methylammonium dipoles,
thereby increasing permittivity. The improved dispersion of MAPI particles
(<20 µm) in polymeric matrixes enhanced the surface effects and effective
interactions with electromagnetic waves. This study demonstrated the potential
of this green synthesis for producing large amount of HPs and tuning defects,
opening new avenues for HPs EMWA application.

**1. Introduction**

In the past decades, 3D hybrid perovskites (HP) have emerged as a key player in optoelectronic applications and, beyond the traditional photovoltaic applications, have also other great potentials as light- ing emitting diodes, photocatalysts and photodetectors, leading to more efficient, low-cost and flexible photonic devices.[1,2] Moreover, it has been recently demon- strated that they could be used as electro- magnetic wave (EMW) absorbing materials (EMWAMs).[3–10] EMWAMs are important components in many military and civilian applications to reduce radar- equivalent signatures and limit electro- magnetic interference from various devi- ces (communication systems such as cell phones, wireless local area networks, sat- ellite broadcasting systems, etc.). Indeed, the ever-increasing use of electronic devi- ces has led to ever-greater electromagnetic pollution. In addition, the need is more and more increasing in the civilian sector with the advent of fifth generation wire- less communication. In situations

Y. Cai, D. Begin, V. Papaefthimiou, S. Zafeiratos, S. Begin-Colin
Institut de Chimie et Procédés pour l'Energie
l'Environnement et la Santé (ICPEES)
UMR-7515
CNRS-Université de Strasbourg
25 rue Becquerel, 67087 Strasbourg, France
E-mail: dominique.Begin@unistra.fr; sylvie.Begin@unistra.fr

The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/sstr.202500066.

© 2025 The Author(s). Small Structures published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/sstr.202500066

C. Lefevre, C. Sidhoum, D. Cianferani, L. Mager, O. Ersen, S. Begin-Colin
Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS)
UMR-7504
CNRS-Université de Strasbourg
23 rue Loess, 67034 Strasbourg Cedex 2, France

E. Elkaim
Synchrotron SOLEIL
L'Orme des Merisiers
Départementale 128, 91190 Saint-Aubin, France

P. Boulet
Centre de compétences XGamma (Diffraction-Diffusion-Imagerie X et Spectroscopie Mossbauer)
Institut Jean Lamour (UMR CNRS 7198)
2 Allée André Guinier, 54011 Nancy, France
involving complex EM wave patterns, EMWAMs need to exhibit frequency selective properties enabling selective absorption of EMW to reduce EM wave interferences. This widespread electromagnetic pollution and the significant disruptions induced by electronic systems lead to a great deal of research attention into EMWAMs.[¹¹⁻¹⁶]

Many kinds of electromagnetic wave absorbers have been thus elaborated and they can be categorized into two groups based on the type of loss they exhibit: magnetic and dielectric loss materials. The EMWAMs work by absorbing the energy from the radiation and converting it into heat, which is then dissipated into the environment. Various composites are thus currently developed, but there is still a long way to go to obtain EMWAMs over a wider frequency range, with a more tuneable conductivity, more adaptable permittivity and permeability, a lower density, an easy and unexpensive production/shaping and a good environmental stability. In particular, the complex permittivity and complex permeability of a material, reflecting the dissipation of energy by the material, are two key parameters that play an important role in understanding the absorption mechanism of electromagnetic waves. The traditional EMWAMs are generally doped ferrites, carbon-based materials, ceramics conducting polymers, MOF's, POM's, etc.[¹¹⁻¹⁴] Composites materials combining a magnetic material and a dielectric one have been reported to play a significant and effective role in breaking the “bottleneck” to develop high-performance materials for EMW absorption.[¹¹,¹²,¹⁴,¹⁵] The most studied EMWAMs at present are composites based on magnetic nanomaterials such as ferrite or iron alloys and carbonaceous materials such as carbon nanotubes as the dielectric component, but recently hybrid perovskites (HPs) have shown very promising properties for this application. Indeed, the intrinsic properties of HPs, which exhibit a very high charge carrier mobility, combined with the fact that they are complex dielectric

materials exhibiting a broad range of polarization mechanisms (due to added optical, ionic, dipolar and charge contributions), make HPs promising dielectric loss materials for EMW absorption.[³⁻⁵,⁹,¹⁷] However, the application of HPs as EMWAMs has been scarcely studied.[³⁻¹⁰]

One main barrier to their study as EMWAMs is certainly the high required amount of powders to make EMW absorption tests. Indeed, the elaboration of composite “bands” (HPs powders dispersed in a polymeric matrix) for EMW absorption measurements needs quite a high quantity of powders. When chemical routes may face some composition, solvent based intermediary compounds and also scaling-up issues, an environmentally friendly (solvent-free) and energy-efficient solid-state method: mechanosynthesis (MS), recently appeared as a green alternative route to elaborate high amount of HP powders.[¹⁸⁻²⁶] For example, the classic HP methylammonium lead iodide (MAPI) is obtained by the high energy ball-milling of a stoichiometric mixture of precursor powders and such a sustainable approach leads to the formation of a rather high quality MAPI phase in large amount (several grams) after short grinding time.[²⁷]

Furthermore, the defects have been shown to have an impact on their performance as EMWAMs.[¹⁰,²⁸] In the very few research works involving HPs, they were mostly combined with carbon materials to enhance the HPs conductivity and their EMWA performance was related to the defects generated at the interface between HPs and carbon materials.[⁶,⁹] We demonstrated recently that long ball-milling times introduced defects in HPs powders[²⁷] and thus MS would appear as a good way to tune the amount of defects and study their impact on the HPs-based EMWAMs performance. Meanwhile, the defect in HPs has been a frequently spoken hot topic[²⁹⁻³⁴] without being fully and deeply investigated in optoelectronic applications and rarely/not often related to the observed properties. Indeed, due to the soft lattice nature, MAPI has higher defect and strain tolerances as well as structural distortion tolerance. However, the ion migration and lattice dynamic of MAPI play an important role on their properties. These factors are closely correlated to optical properties and device performance.[³⁵⁻³⁷] Therefore, the analysis of the defects and the structural characterization of HP remain an active and challenging domain of research, and require the combination of several characterization techniques to provide a complete view of the relationship between intrinsic structure and properties.

In this work, we have mechanosynthesized MAPI powders by varying the milling time to tune the defect level, sieved them in different particle size ranges and dispersed them in a polymer matrix. EMWA measurements demonstrated an enhanced EMWA at X band region (8.2-12.4 GHz) with MAPI powders ground for 4 h with sizes smaller than 20 microns, which was never reported for mechanosynthesized MAPI alone. The structural characterizations have evidenced a fractal microstructure of powders consisting in agglomerates of clusters of (nano)grains (≈80 nm for MAPI4h), themselves made of oriented smaller-nanograins (5–10 nm). Photoluminescence (PL) measurements demonstrated a decrease of the reabsorption phenomenon with grinding time, highly related to the surface state considering grain size characteristics. To further probe the defect density, combined techniques such as positron annihilation lifetime spectroscopy (PALS), X-Ray photoelectron spectroscopy (XPS) and EDXS-HRTEM were carried out. These combined characterization

P. Desgardin, M.-F. Barthe
Conditions Extrêmes et Matériaux: Haute Température et Irradiation
(CEMHTI)
UPR-3079
CNRS
3A rue de la Férollerie, 45071 Orléans cedex 2, France

R. Helm, W. Egger
Institut für Angewandte Physik und Messtechnik
Universität der Bundeswehr München
Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany

M. Butterling, A. Wagner
Helmholtz-Zentrum Dresden-Rossendorf
Bautzner Landstraße 400, 01328 Dresden, Germany

C. Corbel
LSI, CEA/DRF/IRAMIS, UMR7642
CNRS, Ecole polytechnique
Institut Polytechnique de Paris
91120 Palaiseau, France

C. Sanchez
Collège de France, LCMCP, UMR 7574 CNRS
Sorbonne Université
4 Place Jussieu, 75005 Paris, France
E-mail: clement.sanchez@sorbonne-universite.fr

C. Sanchez
University of Strasbourg Institute for Advanced Study (USIAS)
5 allée du Général Rouvillois, 67083 Strasbourg, France
techniques pointed to important increase of surface vacancies
defect concentration and of surface defective layer depth in
(nano)grains with extended milling time and especially to unusual
defects (PALS measurements). All the results showed that, apart
from conventional methods, defect engineering could be achieved
by this green approach, which appears thus as a very suitable and
promising strategy to design surface defective hybrid perovskite
displaying highly efficient EMW absorbing properties.

**2. Result and Discussion**

**2.1. Electromagnetic (EM) Wave Absorption Properties of
Mechanosynthesized (MS) MAPI**

MAPI powders were prepared under our standard synthesis con-
ditions with a grinding time of 30 min (named MAPI30) and
with an extended grinding time of 4 h (named MAPI4h). They
were sieved into different size ranges using sieves of different
granulometries (200, 100, 50 and 20 µm), dispersed in a silicone
matrix and shaped in bands of measured thickness (Figure S1A,
Supporting Information). To obtain a homogeneous dispersion
of powders within the silicone band with a small band thickness,
the first experiments have been performed by sieving the pow-
ders below 50 µm, which is a relative median sieving size accord-
ing to the used sieves and often used with such MS powders.[26]
The thickness of both bands was 646 and 604 µm for powders
ground for 30 min and 4 h respectively. The SEM image of
the cross-section of the band in Figure S1B, Supporting
Information, showed the homogeneous dispersion of the
MAPI powder within the silicone matrix.

The electromagnetic wave absorption capacity of both MAPI
powders was investigated by analysing the electromagnetic
parameters notably the complex relative permittivity ε<sub>r</sub>
(ε<sub>r</sub> = ε' - jε'') and permeability μ<sub>r</sub> (μ<sub>r</sub> = μ' - jμ'') over frequency
range from 8 to 13 GHz. No significant difference was observed
on both real (ε') and imaginary (ε'') part of permittivity of stan-
dard sieved MAPI30 samples: they remained quite flat around
4.7 and 0.1 respectively (Figure 1A). These ε' and ε'' values
are close to the reported values from Zhang et al.<sup>[3]</sup> with 50 wt%

MAPI synthesized by precipitation method mixed with paraf-
fin in a toroidal shape (ε' ≈ 4 and ε'' ≈ 0.1). Using a mixture
of MAPI powders obtained from solvent approach and paraffin
(MAPI:paraffin ratio = 2:3), Zhang et al.[6] and Yu et al.[10] also
obtained similar values (ε' ≈ 3 and ε'' close to 0) under the fre-
quency range of 8–13 GHz, while Guo et al.[5] with cylindrically
compacted mixture of MAPI powder (pulverized from single
crystal) and paraffin in a mass ratio of 3:1 obtained a higher
ε' value staying around 8 at the same frequency range. The cal-
culated dielectric loss tangent (tan(ε<sub>r</sub>) = ε''/ε') (Figure S2A,
Supporting Information) also showed no obvious changes.
The low value of permittivity showed the insulating nature
and the low dielectric polarization of the MAPI30 sample. By
contrast, MAPI4h sample exhibited a strong and distinct reso-
nance in the real and imaginary part of permittivity at
11.4 GHz (Figure 1A) as well as a remarkable resonance peak
on dielectric loss tangent at the same position (Figure S2A,
Supporting Information). Thus, MAPI4h (<50 μm) displayed a
high dissipative ability at frequencies between 11 and 12 GHz,
which was for the first time observed here in mechanosynthe-
sized MAPI alone. To the best of our knowledge, only Zhang
et al.[6] reported on a dielectric loss between 14 and 15 GHz with
MAPI synthesized by a solvent method in another measurement
configuration. Figure 1B showed the real (μ') and imaginary (μ'')
part of the complex permeability. Both MAPI30 and MAPI4h
samples presented non-magnetic characteristics: μ' and μ''
stayed almost constant at around 1 and 0, suggesting that there
was almost no magnetic loss from 8 to 13 GHz (the magnetic loss
tangent (tan(μ<sub>r</sub>) = μ''/μ') is given in Figure S2B, Supporting
Information).

From magnetic measurements, a very weak ferromagnetic sig-
nal was observed (Figure S3, Supporting Information), which
might be related to the defect-induced ferromagnetism as
reported by Sil et al.[38] but also to a possible contamination from
steel ball milling tools. However, the very weak magnetic signal
made it difficult to attribute them to the observed magnetic loss
(Figure S3, Supporting Information). Moreover, electron para-
magnetic resonance measurements were also carried out and
no paramagnetic signals were noticed in all the samples.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Real and imaginary parts of the A) permittivity and B) permeability of MAPI30 and MAPI4h (powder size < 50 µm).</figcaption></figure>
A magnetic loss may be due to the eddy current effect and resonance mechanisms (exchange resonance and natural resonance). [5] the eddy current loss (C₀): C₀ = μ''(μ')⁻²f⁻¹, was calculated (Figure S4, Supporting Information) and remained unchanged, confirming no magnetic loss in our samples.

Considering the original EMWA behaviour of MAPI4h by comparison with MAPI30, we attributed at first the large difference in EMWA between MAPI30 and MAPI4h powders sieved below 50 µm to the difference in their defect level. Indeed, in our previous report, [27] we demonstrated that an extended ball-milling introduced large amounts of defects to MAPI due to the energetic collisions and the repeated welding and fracturing mechanisms during the MS process in agreement with other reported results. [39,40] Such impact of defects would be in agreement with Quan et al. [41] who reported that for EMWAMs, defects could tolerate higher charge carrier concentrations and thus behave as dielectric polarization centers, inducing polarization relaxation, which plays an important role in the EMWA mechanism.

In general, the main contributions to dielectric polarization are molecular (or dipole) polarization, atomic polarization, ion polarization, space charge polarization and electron polarization. [42,43] Atomic polarization and electron polarization cannot be avoided in the wave frequency range that we used (8-13 GHz in this study) but they do not play an important role and contributed less compared to ionic polarization and dipolar polarization. Ionic polarization could not be found at the used frequency range in this study. Thus, mainly molecular (or dipole) polarization would be expected to dominate the dielectric polarization process. [41,44,45] The relaxation loss in MAPI4h (<50 µm) sample was thus further evaluated by the Debye equation as follows [41]

$$ (\epsilon' - \frac{\epsilon_s + \epsilon_\infty}{2})^2 + (\epsilon'')^2 = \left(\frac{\epsilon_s - \epsilon_\infty}{2}\right)^2 \quad (1) $$

where, ε_s is the static dielectric constant, and ε_∞ is the dielectric constant at infinite frequency.

By plotting ε' versus ε'', a well-defined Cole-Cole circle was observed in MAPI4h (size < 50 µm), while no distinct Cole-

Cole semicircles was noticed in MAPI30 (size < 50 µm). This supported strongly the presence of a polarization relaxation process, particularly dipole polarization relaxation, when MAPI powders were submitted to an extended ball milling time (Figure 2).

To evaluate a possible effect of the sieving step, powder size separation was realized by further segmenting MS MAPI4h powder into 5 size ranges: larger than 200 µm, between 100–200 µm, between 50 and 100 µm, between 20 and 50 µm and lower than 20 µm, named MS1, MS2, MS3, MS4 and MS5 respectively. Due to its large size and poor particle dispersion in the silicone matrix, MS1 was eliminated for the measurements. No obvious dielectric resonance was observed in MS2-4 (Figure 3A). No peaks were observed in the real (μ') and imaginary (μ'') part of the complex permeability for MS2-4 size ranges of MAPI4h (Figure 3B and S5, Supporting Information). The distinct dielectric resonance at 11.4 GHz was evidenced again only with MS5 size range of MAPI4h (named MAPI4h-MS5) (Figure 3 and S5, Supporting Information). Figure 4 showed the plot of ε' versus ε'' leading to Cole–Cole semicircles for MAPI4h as a function of the different size ranges MS2-5. Compared to MAPI30 Cole-Cole plot (Figure 2A), all the samples showed one or multiple Cole–Cole semicircles, showing an enhanced Debye polarization relaxation with MAPI4h powder. The multiple semicircles for MS2-4 MAPI4h powders would indicate that multiple polarization relaxations are taken place [10,41] and the perturbated shape of the semicircles might imply the presence of several relaxation processes. [5,9] By contrast, the MAPI4h-MS5 powder displayed only one strongly enlarged and well-shaped Cole–Cole circle, suggesting that only one relaxation process would be favoured in contrast with the other size ranges MS2-4 powders of MAPI4h. Regarding the previous discussion about the different possible polarization contribution, we may suggest that the MS5-MAPI4h (<20 µm) exhibited a high dielectric loss mechanism in the range 11-13 GHz leading to an attenuation of EM waves due to an enhanced dipole polarization with this particular powder. By comparing the results obtained with MAPI30 and MAPI4h powders, on may thus notice a synergistic effect of the grinding time and powder size distribution on EMWA performance of MS MAPI powders.

<figure><img src="image_4.png" /><figcaption>Figure 2. Cole-Cole plot of A) MAPI30 and B) MAPI4h (powder size < 50 µm).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Real and imaginary parts of the A) permittivity and B) permeability of MAP14h with different powder size ranges of 100–200 µm, 50–100 µm, 20–50 µm and smaller than 20 µm (MS2-MS5 respectively).</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Cole-Cole semi-circles of MAP14h with different powder size ranges of A) 100–200 µm, B) 50–100 µm, C) 20–50 µm and D) smaller than 20 µm (MS2-MS5 respectively).</figcaption></figure>
According to the obtained dielectric properties of MS2-5 size ranges of MAPI4h, this EMWA result was thus closely related to the sieved size range. Smaller powder sizes should certainly enable a better dispersion of powders within the matrix and provide also a higher surface area to interact with the electromagnetic waves. Considering the higher defects levels in MAPI4h by comparison with MAPI30,[27] one question arises: could the optical properties and the amount of defects be different between different sieved size ranges. To try to better understand these interesting observed results, the different sieved powders have been characterized in terms of structure as well as defects.

## 2.2. Structural Characterizations of MS MAPI

### 2.2.1. Microstructure of 30 min and 4h MAPI Powder Samples

SEM images of the ground samples in Figure S6 and S7, Supporting Information, demonstrated that the particle size in powders corresponded rather well to each size range expected from the different sieving experiments. The particle size distributions of powders have also been checked by imaging analyses performed by an external specialized company (sdtech). Circular-equivalent (CE) diameter distributions of MAPI30 and MAPI4h have been so determined and are given in Figure 5 and Table 1. They confirmed that the different size ranges have been obtained after the sieving process.

SEM images at higher magnification in Figure 6 and S8, Supporting Information, showed further the morphology of powders as a function of the sieving size ranges for MAPI30 and MAPI4h. All these SEM images showed that powder particles consisted in fact of agglomerates of clusters of grains. Such observation agreed with what was generally reported for MAPI MS powders.[22–24,39,40,46,47] The grain size distribution was further deduced from these SEM images and followed a lognormal distribution (Table 2). In Table 2, the grain sizes of MAPI4h were much smaller than those of MAPI30 (417 ± 203 nm and 83 ± 43 nm for MS5 respectively). Such a decrease of the grain size with increasing grinding times was expected and has already been reported for MAPI and CsPbBr₃.[23,24,40] Thus, this decrease of the grain size could be easily related to the extended ball milling time: since 30 min of MS was necessary to finish the reaction leading to MAPI, one may expect that the prolonged grinding led to smaller grains. Leupold et al.[24] reported grain size well above 1 µm after 30 min of milling, below 1 µm after 60 min and less than 300 nm after 90 min of milling. The minimum milling time for the synthesis of MAPI was 15 min in their conditions (zirconia balls, addition of cyclohexane, balls to powder weight ratio of 10:1, etc.). Manukyan et al.[23] reported a particle size in the range 200–400 nm after 45 min of milling. However, it depends strongly on the type of ball-mill, the rotation speed, the ball to powder ratio, the presence of additives or not, etc. Considering our grain size decrease as a function of milling time and our milling conditions, our MS conditions may be considered as more “energetic”.

<figure><img src="image_7.png" /><figcaption>Figure 5. CE diameter distribution curves of sieved A) MAPI30 and B) MAPI4h powders.</figcaption></figure>

<table><caption>Table 1. Average CE diameter of all measured MAPI samples.</caption><thead><tr><th rowspan="3">Samples<sup>a)</sup></th><th colspan="6">Size range</th></tr><tr><th colspan="2">100–200 µm</th><th colspan="2">50–20 µm</th><th colspan="2">&lt;20 µm</th></tr><tr><th>Average CE diameter [µm]</th><th>Deviation [µm]</th><th>Average CE diameter [µm]</th><th>Deviation [µm]</th><th>Average CE diameter [µm]</th><th>Deviation [µm]</th></tr></thead><tbody><tr><td>MAPI30</td><td>175.1</td><td>9.1</td><td>44.91</td><td>6.94</td><td>17.13</td><td>4.61</td></tr><tr><td>MAPI4h</td><td>162.1</td><td>5.57</td><td>48.95</td><td>3.79</td><td></td><td></td></tr></tbody></table>

<footnote>a) Average CE diameter was provided and certified by stdetch by counting more than 100 000 particles for each sample.</footnote>
<figure><img src="image_8.png" /><figcaption>**Figure 6.** SEM images of A) MAPI30 powder with size larger than 200 µm B) MAPI30 powder with size smaller than 20 µm, C) MAPI4h powder with size larger than 200 µm, D) MAPI4h powder with size smaller than 20 µm.</figcaption></figure>

<table><caption>**Table 2.** Lattice parameter, crystallite size and strain from analyses of XRD patterns and SEM mean grain size in MAPI30 and MAPI4h powders with different size ranges.</caption><thead><tr><th>Sample<sup>a)</sup></th><th></th><th>Lattice parameter [±0.001 Å]</th><th>Mean crystallite size [±1 nm]</th><th>SEM mean grain size [nm]</th><th>Strain [±0.1 %]</th><th>Pb-I-Pb angle [°]</th></tr></thead><tbody><tr><td rowspan="6">MAPI30</td><td>–</td><td>a = b</td><td>c</td><td>–</td><td>–</td><td>–</td></tr><tr><td>raw</td><td>8.870</td><td>12.673</td><td>544</td><td>–</td><td>3.6</td></tr><tr><td>&gt;200 µm</td><td>8.874</td><td>12.676</td><td>295</td><td>449 ± 193</td><td>4.0</td></tr><tr><td>100–200 µm</td><td>8.871</td><td>12.673</td><td>346</td><td>465 ± 187</td><td>1.5</td></tr><tr><td>50–100 µm</td><td>8.870</td><td>12.672</td><td>434</td><td>504 ± 203</td><td>1.1</td></tr><tr><td>20–50 µm</td><td>8.872</td><td>12.674</td><td>204</td><td>470 ± 201</td><td>2.3</td></tr><tr><td rowspan="6">MAPI4h</td><td>–</td><td>a = b</td><td>c</td><td>–</td><td>–</td><td>–</td></tr><tr><td>raw</td><td>8.873</td><td>12.664</td><td>163</td><td>–</td><td>13.9</td></tr><tr><td>&gt;200 µm</td><td>8.876</td><td>12.668</td><td>140</td><td>98 ± 46</td><td>17.5</td></tr><tr><td>100–200 µm</td><td>8.873</td><td>12.665</td><td>157</td><td>94 ± 46</td><td>15.7</td></tr><tr><td>50–100 µm</td><td>8.874</td><td>12.661</td><td>131</td><td>92 ± 40</td><td>28.5</td></tr><tr><td>20–50 µm</td><td>8.875</td><td>12.667</td><td>180</td><td>81 ± 42</td><td>22.1</td></tr><tr><td rowspan="6">MAPI4h</td><td>–</td><td>a = b</td><td>c</td><td>–</td><td>–</td><td>–</td></tr><tr><td>raw</td><td>8.874</td><td>12.664</td><td>199</td><td>83 ± 43</td><td>14.0</td></tr></tbody></table>

### 2.2.2. TEM of MAPI30 and MAPI4h Powder Samples

TEM has also been used to characterize the grains constituting the clusters of MAPI30 and MAPI4h powders with size smaller than 20 µm. The low magnification TEM images in Figure S9,

Supporting Information, showed one characteristic cluster obtained after MS. However, high-resolution TEM (HRTEM) images and the corresponding filtered images in **Figure 7** showed that these grains were in fact constituted of nanograins or consist of clusters of nanograins (<5–10 nm). We already

<footnote>a) SEM mean grain size was obtained from lognormal distribution with the mode value as the average grain size by more than 300 countings for each sample.</footnote>
<figure><img src="image_9.png" /><figcaption>**Figure 7.** HRTEM images of grains in powders with size smaller than 20 µm of A) MAPI30 with B) the corresponding filtered higher solution image obtained from reverse FFT analysis and C) MAPI4h with D) the corresponding filtered higher solution image obtained from reverse FFT analysis (inserts: the corresponding FFT images).</figcaption></figure>

noticed this in our previous study[27] and to the best of our knowl-
edge, such nanostructuration of grains was never reported
before. A hierarchical/fractal structure of MS MAPI powders
was thus evidenced. The powder was in form of micrometric
agglomerates of clusters, which consisted of closely attached
grains with average sizes varied from around 100 nm to several
hundred nm according to the ball milling time, and these grains
were themselves composed of smaller-sized nanograins.

In addition, common crystallographic orientations between
the nanograins inside grains were again remarked in both sam-
ples (Figure 7B,D). Such oriented aggregation of nanograins in
grains already discussed in our previous study[27] for MAPI30,
was confirmed again and was also observed here in powders
ground for 4 h. This feature appeared to be a specific character-
istic of MS MAPI. Furthermore, the surface of the MAPI4h
grains in Figure 7C seems to exhibit a thin brighter layer with
a thickness around 10–20 nm. This brighter layer was much thin-
ner in MAPI30 grains and the contrast difference in Figure 7C
may be due to a thickness contrast or to a certain surface modifi-
cation at the surface of MAPI4h grain resulting from the pro-
longed ball milling process. Indeed, long grinding times have
already been reported to induce surface modifications in ground
oxides[48–54] and thus this surface modification was possibly due
to the grinding process. Both HRTEM and filtered images

(Figure 7C,D) demonstrated the crystalline nature of this thin
layer in MAPI4h, revealing that the surface change was not a sim-
ple amorphization induced by collision or friction during the MS.

2.2.3. *Crystallographic Structure of 30 min and 4 h MAPI Powder Samples*

The formation of the tetragonal I4/mcm MAPI phase was confirmed by X-Ray diffraction as shown in Figure S10A,B, Supporting Information. The lattice parameters, crystallite size and strain were determined and given in Table 2 (Figure S1C and S10D, Supporting Information). The lattice parameters of the powder samples remain quite similar whatever the powder size ranges and MS time. Even if the so determined crystallite sizes from XRD pattern were at the calculation limit of nano-size by the used XRD equipment, the crystallite size of the different sieved MAPI30 samples was lower than the grain size observed by SEM and was higher than that of the nanograins constituting the grains (Table 2 and Figure 7). Witt et al.[55] reported also grain and crystallite sizes of 400 and 340 nm respectively for one of their MS MAPI. Such observations confirmed here the oriented aggregation of nanograins within MAPI30 grain. Indeed, the nanograins within grains shared common crystallographic plans
and diffract thus all together leading to larger crystallite sizes. These results suggested that the nanograins inside one MAPI30 grain might not all be oriented in the same direction, and we suppose a less organized surface layer.

By comparison with MAPI30 powders, a lower crystallite size was noticed in all MAPI4h powders: they were in average around 150 ± 50 nm and 300 ± 50 nm for MAPI4h and MAPI30 respectively. However, the crystallite sizes of MAPI4h were higher than the mean grain sizes obtained from SEM. These results confirmed again an oriented aggregation also in MAPI4h grains and would suggest that the oriented aggregation was extended on a longer scale in MAPI4h than in MAPI30min and to closely packed adjacent grains in clusters. Indeed, the nanograins were highly oriented within grains, thus grains behaved like monocrystals and may share common crystallographic planes with adjacent grains. This oriented aggregation between grains in clusters may be related to the extended milling time promoting the welding of grains, which is supported by the high pressure and high temperature reported during MS. Indeed, Witt et al.[55] reported on a sintering effect during ball-milling supported by the fact that MAPI sintering would occur below 34 °C at 10 MPa and that temperatures around 40 °C could be reached during the MS process.[56] In our case, MS was conducted in dry conditions and with a higher ball to powder ratio and thus local temperatures were certainly higher.

A high increase in strain was shown in MAPI4h by comparison with MAPI30 whatever the size ranges. Such strain was defined as the root mean square of variations in the lattice parameters across the sample and may be due to distortions present in the crystalline lattice or to the presence of defects (faulting, dislocations, antiphase domain boundaries, and grain surface relaxation). Based on the synchrotron X-Ray diffraction data, the distorted Pb-I-Pb angles were collected, and all the samples were shown to present similar angles, giving an average value of 163.5° in good agreement with the reported values.[57,58] Therefore, such strain may not be attributed to lattice distortions but rather to the presence of defects.

Therefore, these XRD and synchrotron structural characterizations would support that the crystallographic structure of bulk MAPI was not affected neither by the grinding time nor by the sieving step/powder sizes. Both SEM, TEM and XRD analyses showed that the MS MAPI powders displayed a fractal/

hierarchical microstructure as described in **Figure 8** with agglomerates of clusters of grains, which consisted further of oriented clusters of nanograins. In addition, an oriented aggregation between grains in clusters would exist in MAPI4h powder.

## 2.3. Defect Characterization Through Optical Properties
### Characterization

Long grinding times have already been reported to introduce more defects in powders, in particular in oxide grains, as well as to affect their surface.[48–54] In our previous study,[27] we have shown that MAPI powders obtained after 4 h of grinding displayed a lower PL intensity by comparison with MAPI30 powders and we attributed this to the presence of more defects in MAPI4h. At first, PL measurements and UV-Vis spectroscopy were performed here for MAPI30 and MAPI4h raw (without sieving) powders used for the first EMWA measurements. Even if the PL spectrum of MAPI4h was too noisy to obtain a reliable PL spectrum, a distinct blue shift is noticed when the grinding time was extended from 30 min to 4 h (Figure S11A, Supporting Information): MAPI30 PL spectrum displayed a maximum peak at 1.56 eV while the maximum PL emission peak of MAPI4h was shifted at around 1.65 eV with a broad side peak at 1.54 eV (Figure S12A, Supporting Information). The absorption UV-Vis spectrum of MAPI4h was also slightly blue shifted (shifted to higher energy) by comparison with that of MAPI30 (Figure S11B, Supporting Information). PL quantum yield measurements were also tested with these samples, but no distinct quantum yield could be detected, implying that the MS MAPI was not suitable for producing high luminescence yield.

Therefore, a complete study with MAPI30 and MAPI4h sieved powders has been conducted to study more in depth the influence of powder sizes (Figure 9). The MAPI4h PL spectra in Figure 9B were observed to display too low intensities to be finely studied (confirming again the generation of defects after a long ball-milling time). However, one noticed a shift of the PL peaks towards lower energy when the powder size decreases. The PL spectra of MAPI30 powders in Figure 9A displayed clearly a similar red shift trend and have been thus considered more in depth.

Figure S13, Supporting Information, reporting the maximum PL peak position of MAPI30 powders as a function of the powder size range confirmed a PL peak red shift when the powder size

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Fractal structure of MAPI powders.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 9.** PL spectra of A) MAP130 and B) MAP14h with different size ranges.</figcaption></figure>

decreases. Yamada et al.[59] have related such PL peak position shift to a thickness-dependent reabsorption. We have varied the amount of powder for PL measurement as shown in Figure S14, Supporting Information, and observed that the PL peak broadens when the amount of powder increased, and the broadening occurred more towards lower energies. In fact, reabsorption was more often reported to lead to red-shifted PL peak and reabsorption should thus occur when the powder amount increased. A reabsorption phenomenon in HPs has also been evidenced by Diab et al.[60] in MAPbBr₃ single crystal. Reabsorption phenomena in MAPI films have been reported as well.[61–63] Thus, the “red-shift” that we observed when the powder size decreased could be attributed to a reabsorption phenomenon. Indeed, the PL peak position of MAPI without reabsorption would be located at around 1.62–1.63 eV from theoretical calculations.[64,65] This suggested that reabsorption phenomena occurred in all the MAP130 powder size ranges. However, all PL peaks were very broad and PL peak deconvolutions were thus carried out. As shown in Figure S15, Supporting Information, the emission peaks of MAP130 actually integrate the contribution of both the MAPI PL peak and a PL peak at lower energy due to reabsorption. The comparison of the intensity ratio of the reabsorption and MAPI PL peaks in Figure S13, Supporting Information, evidenced an increase in the relative intensity of reabsorption peak when the MAP130 powder size decreased (Figure S13 and Table S1, Supporting Information). With large particle powder sizes, one may expect more volume contribution, more grain boundaries and low “exposed” surface whereas in small sized powders, we have more exposed surface and a lower amount of grains boundaries. This led us to propose that this PL red shift and thus enhanced reabsorption would be rather due to surface effects.

We have studied further the effect of MAP130 powder range sizes on charge carrier recombination by considering the time-resolved PL (trPL), which is sensitive to the defect states and recombination process. The trPL measurements and fitting are detailed in the SI part. The trPL curves in Figure S16, Supporting Information, were fitted with a double exponential

model, which is widely used for the decay curve fitting of HPs to extract the charge carrier lifetime.[22,66,67] The τ₁ and τ₂ lifetimes, as well as the τ mean in Table S2, Supporting Information, decreased when the particle size decreased and could probably be related to the decreased carrier diffusion probability in smaller powder particles. We thus also noticed a slight dependency of carrier lifetime on particle size: long lifetimes would be correlated to bigger particle sizes. Considering the fact that the amount of grain boundaries in particles increased with the cluster size, the grain boundaries would not explain the decrease in mean lifetime when the powder size decreases. This would be in agreement with Yang et al.[68] who reported that the grain boundaries would not be dominant in the non-radiative recombination in MAPI thin film. The observed slight decrease of lifetimes when the particle powder size decreases could be thus also attributed to surface defects. Thus, the static and time-resolved PL results suggested the contribution of rather surface defects than grain boundaries defects.

The bandgap (Eg) values were also determined through Tauc plot from UV-Vis diffuse reflectance spectra. The PL peak position of all the samples was slightly higher than the bandgap and the overlay of both PL and UV-Vis absorption spectra (Figure S17, Supporting Information) was similar to that reported for polycrystalline MAPI films.[69] The deduced bandgap values, given in Figure S18, Supporting Information, were around 1.53–1.54 eV. These values were in agreement with reported bandgap values for MAPI in the range of 1.5–1.65 eV.[22,70] The bandgap values stayed quite similar whatever the grinding time and the sieved size ranges, which would suggest that no obvious lattice distortions were induced during the milling step as also suggested by synchrotron measurements.

Therefore, static PL measurements with MAP130 samples evidenced an enhancement of the reabsorption phenomenon when the particle size decreases and trPL measurements evidenced a decrease of the mean lifetime when the particle size decreased. All these results led us thus to conclude on the presence of surface defects in MAP130 grains. Taking look at MAP14h, the low PL intensity put in evidence higher defect level generated by a
ball-milling for 4 h in comparison with MAPI30. In the PL spec-
tra of MAPI4h, there were also two PL peaks: the main peak posi-
tion was close to the theoretical PL peak position of MAPI at
≈1.62 eV[⁶⁴,⁶⁵] and the side peak at 1.54 eV may be attributed
to the reabsorption. The two PL peaks related to MAPI PL
and reabsorption peaks were observed more clearly in
MAPI4h by contrast with MAPI30 displaying one broad PL peak
including these two contributions. The observation in MAPI30 of
a red-shift or rather of an increased reabsorption when the pow-
der size decreases was also noticed in MAPI4h. Therefore, as
what was previously discussed with MAPI30, as the surface
becomes more important when the powder size decreases,
one could attribute the increased reabsorption to surface effects.
All these results led to a reabsorption enhancement due to sur-
face effects. Surface modifications through long high-energy ball
milling was already reported in oxide particles[⁴⁹,⁵³,⁵⁴,⁷¹] with the
formation of a defective surface layer.[⁵¹,⁵⁴,⁷²] Thus, we propose
that the extended ball-milling time induced change of the surface
state of the grains by creating a defective layer. This defective
surface would be thicker in MAPI4h than in MAPI30 and would
be responsible for the reabsorption phenomenon.

**2.4. Characterization of Surface Defects**

2.4.1. X-Ray Photoelectron Spectroscopy of MAPI30 and MAPI4h

XPS was used to characterize the surface states of MS5 (<20 µm)
MAPI30 and MAPI4h powders. Small oxygen peaks were present
in all samples at around 534 (O=C—O) and 532 (C=O) eV, indi-
cating a slight amount of oxygen on the surface (Figure S19,
Supporting Information) (Ratio O/Pb:0.79 for MAPI30,
<20 µm and 0.63 for MAPI4h, <20 µm). These peaks are typical
for most air exposed samples and are known as adventitious car-
bon, corresponding to a variety of hydrocarbon species with both
singly and doubly bound oxygen functionality. As shown in
Figure S20A, Supporting Information, the Pb 4f<sub>7/2</sub> and Pb
4f<sub>5/2</sub> core level peaks of MAPI30-MS5 were located at 138.3
and 143.2 eV respectively, which was in good agreement with
the reported peak position of Pb<sup>2+</sup> in MAPI.<sup>[10,73]</sup> The peak posi-
tions in MAPI4h-MS5 of Pb 4f<sub>7/2</sub> and Pb 4f<sub>5/2</sub> were at similar
positions. Taking look at the core-level spectrum of 13 d
(Figure S20B, Supporting Information), two peaks positioned
at 619.1 and 630.6 eV were attributed to I 3d<sub>3/2</sub> and I 3d<sub>5/2</sub> for
both MAPI30-MS5 and MAPI4h-MS5. Figure S2C, Supporting
Information, represented the N 1s XPS spectra related to the
methylammonium cation (MA<sup>+</sup>) group. A XPS peak cantered
at 402.0 eV was observed for both MAPI samples. The attribution
of this peak to the C—N bonding in MA<sup>+</sup> was confirmed by the
presence of the C 1s binding energy at about 286.2 eV for
MAPI30-MS5 and MAPI4h-MS5 (Figure S20D, Supporting
Information). Indeed, this peak is usually attributed to methyl
carbons in the MAPI film and may include some additionally
adsorbed surface carbon bonded to a hydroxyl group.[74] Also,
an additional peak at round 289 eV was observed in both samples
(Figure S20D, Supporting Information) and attributed to carbon-
oxygen bonding as the presence of oxygen was detected (Figure
S19, Supporting Information). Rocks et al.[75] reported that the
vanishing of the MAI component may lead to iodine vacancies
that can be easily terminated by intercalated oxygen species to

create other bonding arrangements such as PbO/Pb(OH)₂,
IO₂ and PbCO₃/PbC₂O₄.

Stoichiometry analysis was then realized based on the survey
spectra to analyze further the atomic ratios between different ele-
ments. The ratio of I and Pb (I/Pb) decreased from 3.3 to 2.7 for
MAPI30-MS5 and MAPI4h-MS5 respectively. Considering the
incertitude/standard deviation in the elemental analysis (around
5–10%), the I/Pb ratio in MAPI30-MS5 could be considered as
being at the good stoichiometry. Thus, the observed strong ratio
decrease in MAPI4h-MS5 would indicate the presence of iodine
vacancies at the surface of MAPI4h powder. Even though, this
value is still in the tolerance region of MAPI,[⁷³] it demonstrated
the presence of defects resulting from the prolonged ball-milling.
Despite the difficulty in correctly determining the peak position
in high-resolution XPS spectra due to different-surface charge-
induced broadening when the particle size is quite high, the sur-
vey spectrum was still carried out on MAPI4h with powder size
of 100-200 µm, which was the largest powder size tested for
EMWA experiments and a I/Pb ratio of 3.1 was obtained. The
slight decrease of I/Pb ratio would agree with the effect of
extended grinding time through defect concentration alteration.
The difference in stoichiometric values in large and small pow-
der particles of MAPI4h would suggest that the defect level varied
according to the particle size: surface modification and defects
were more present/visible in smaller particles. The N/Pb ratio
was also remarked to decrease from 1 for MAPI30-MS5 to 0.8
for MAPI4h-MS2 and to 0.6 for MAPI4h-MS5, implying the loss of
MA⁺ through prolonged ball milling time and strong loss of
volatile MA⁺ in smaller cluster for the same mechanosynthesis
duration (4 h).

The reduced stoichiometry here was attributed to iodine and methylammonium vacancies, implying a surface modification due to extended ball milling time, which was already reported previously on ground oxides.[⁴⁹,⁵¹,⁵³,⁵⁴,⁷²] From the obtained elemental ratios in **Table 3**, we suggest the formation of a thin layer of defective non-stoichiometric MAPI layer with a chemical formula of MA<sub>0.6</sub>PbI<sub>2.7</sub> (calculated from survey scan) at the surface of particle when the ball milling time was extended. In the smaller particles, more specific surfaces were accessible, therefore, the highest defect and vacancy concentrations were observed. We can thus conclude that the extended balling time from 30 min to 4 h modified the surface state of the particle, notably by increasing the defect density and hetero-interfaces. This surface modification was most pronounced in the smallest size range (<20 µm) due to their higher specific surface area.

2.4.2. HRTEM-EDXS of 30 min and 4 h MAPI Powder Samples

HRTEM-EDXS was performed by probing different points at the
near-surface part of grains constituted of nanograins of both
MAPI30 and MAPI4h powders with size lower than 20 µm
(MS5). The HAADF-STEM dark field images with the corre-
sponding analysis point locations were provided in Figure
S21, Supporting Information. The I/Pb atomic ratios of all points
are given in Figure S22, Supporting Information, and the mean
values in Table 3. The I/Pb ratio at the surface of MAPI30-MS5
was found around 2.7 which was lower than the stoichiometric
ratio and also lower than the ratio found by XPS. This might
<table><caption>**Table 3.** I/Pb and N/Pb ratio of MAPI30 and MAPI4h powders obtained from HRTEM-EDXS and XPS.</caption><thead><tr><th rowspan="2">Sample</th><th colspan="2">I/Pb ratio</th><th colspan="2">N/Pb ratio</th></tr><tr><th>HRTEM-EDXS<sup>a)</sup></th><th>XPS<br/>[≈10 nm depth]</th><th>XPS<br/>[≈10 nm depth]</th></tr></thead><tbody><tr><td>Stoichiometric MAPI</td><td>3</td><td></td><td>1</td><td></td></tr><tr><td>MAPI30 &lt; 20 µm</td><td>2.7</td><td>3.3</td><td>1</td><td></td></tr><tr><td>MAPI4h 100–20 µm</td><td></td><td>3.1</td><td>0.8</td><td></td></tr><tr><td>MAPI4h &lt; 20 µm</td><td>2.4</td><td>2.7</td><td>0.6</td><td></td></tr></tbody></table>

probably be due to an electron beam effect as MAPI is a sensitive material to the electron beam. Indeed, it is well known that the electron beams induced degradation of the MAPI perovskite into PbI₂, even at low electron dose.[76] This can explain the slight decrease of the I/Pb atomic ratio compared to the MAPI stoichiometry. Nevertheless, under the same electron beam conditions, a decrease of I/Pb ratio was found at the surface of MAPI4h-MS5 grains, with a value around 2.4 (I/Pb). By comparing, in similar electron beam exposure conditions, the so obtained I/Pb atomic ratio by EDXS, a lower amount of I⁻ was remarked again at the grain surface of MAPI4h (<20 µm), which was in good agreement with the XPS results, implying a surface modification with iodine vacancy resulting from the extended ball milling.

### 2.4.3. Positron Annihilation Lifetime Spectroscopy of MAPI30 and MAPI4h Samples

PALS measurements were conducted on MAPI30 and MAPI4h powders compacted in wafer under a pressure of 100 MPa and are detailed in the SI part. The positron annihilation lifetime as a function of the positron beam energy in MAPI30 and MAPI4h wafers is shown in **Figure 10**. Thus, the single lifetime resolved from PALS pointed out the existence of a gradient of defects as the depth increases in MAPI30 and MAPI4h wafers with increasing e⁺ beam energy. As revealed by the maximum of the e⁺ lifetime at about 3 KeV in both wafers, there is a near surface region and a deeper one where the defect populations displayed different type of variations. For the low e⁺ beam energy range, $1.5 \le E(\text{keV}) \le 3$, more or bigger open volume defects tended to trap positrons as the e⁺ mean implantation depth increased in the range from 18.4 to 55.9 nm. This was reversed above 3 keV where e⁺ capture at less or smaller open defects slowly tended to prevail as positrons were implanted deeper.

The e⁺ lifetimes were found to be characteristic of annihilations in the first layers of monocrystalline grains (≈80 nm for MAPI4h and ≈400 nm for MAPI30) from the surface as the obtained positron stopping probability maximal values in the first monocrystalline layers were close to 100% (detailed in Supporting Information). It also confirmed the existence of the gradient of e⁺ capture inside the monocrystalline grains forming those first layers in both MAPI30 and MAPI4h wafers.

The weak variations of the e⁺ lifetimes with depth in both wafers suggested that e⁺ capture took place in defect populations

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Positron annihilation lifetime versus MePs (HZDR) positron beam energy in MAPI30 and MAPI4h wafers. The e⁺ lifetimes are those of the single exponential decay components resolved in the e⁺ lifetime spectra.</figcaption></figure>

where one type of open-volume defects was dominant. For any e⁺ beam energy in the range from 1.5 to 10 keV, the e⁺ lifetimes in MAPI4h tended to be about 1.5 ps longer than those in MAPI30. This systematic trend corresponded to small variations of about, 0≈1%, depending on the e⁺ beam energy. It was consistent with a systematic higher positron capture in the dominant open-volume defects in MAPI4h than in MAPI30. It suggests that the grinding time modulated the defect density in the monocrystalline grains as it did for the grain mean size. As the grinding duration increased from 30 min to 4 h by a factor of eight, nearly one order of magnitude, the grinding promoted a higher density of open volume defects both near the surface and deeper inside the MAPI monocrystalline grains, independently of their mean grain size, ≈400 nm in MAPI30 and ≈80 nm in MAPI4h. It was earlier reported by Dhar et al.[46] that by increasing of 15 min the grinding duration of MAPI, a huge increase on the e⁺ lifetime of about 20 ps from 335 ± 5 to 351 ± 5 ps was noticed. The authors attributed this large increase to the production of defects with different nature and bigger volume than those produced at the shorter grinding time.

The lifetimes in MAPI30 and MAPI4h as a function of e⁺ beam energy varied by 5 ps in the range of ≈382 ± 0 to 387.0 ± 0.2 ps. The e⁺ annihilation lifetime in the dominant open-volume defects, τ<sub>ov</sub>, was reached when all positrons annihilated after localisation in the defects. The defect e⁺ annihilation lifetime was consequently equal or higher than the maximal value measured in the wafers (τ<sub>ov</sub> ≥ 387.0 ± 0.2 ps). This value was about 16% longer than those reported in the bulk for thick 400–500 µm MAPI pellets and single crystal (≈334 ± 1 ps)[77] or about 18% and 29% longer than the ones in MAPI bulk pellet before and after 350 K annealing[78] (326 ± 5 and 309 ± 5 ps respectively). The maximal value was also about 6% longer than those recorded in thin MAPI layers prepared by spin coating.[79] This comparison led to conclude that the grinding conditions used here for the powder preparation favored the presence of specific defects not earlier observed via positron annihilation

<footnote><sup>a)</sup>I/Pb ratio from HRTEM-EDXS was obtained from the average of 19 and 22 points for MAPI30 < 20 µm and MAPI4h < 20 µm respectively.</footnote>
lifetime spectroscopy in MAPI layers or single crystals obtained by other processes.

The calculations of positron lifetimes were still in early stages for positron lifetimes in compounds such as hybrid perovskites. With this remark in mind, it is however interesting to compare the defect $e^+$ lifetime in the wafers, MAPI30 and MAPI4, $\tau_{ov} \ge 387.0 \pm 0.2$ ps, with recent computational calculations of positron lifetimes.[79] The measured lifetime was much longer than those calculated for perfect lattice, $348 \pm 6$ ps and was only 5–13 ps longer than the $e^+$ lifetime calculated for the Pb-I divacancies ($V_{PbI_1}^{-}$), 377 ps. It was shorter than those calculated for the methylammonium-iodine interstitial complex ($V_{MAI_1}^{2-}$), 403 ps, or the methylammonium vacancy ($V_{MA}^{-}$), 419 (–18, +23) ps. Based on this comparison, the defects in the wafers of MAPI30 and MAPI4h, might be composed of vacancy complexes associating different types of vacancies. Their nature was specific to defects produced under the grinding conditions used in this work.

The $e^+$ capture at open volumes went through a maximum for $e^+$ mean depth of ≈55.9 nm. The decrease of $e^+$ capture was steeper towards the surface than into the inner region of the MAPI grains. Such variations suggested that the formation of the defect population involved different competing processes. Surface appeared to be a sink for some vacancy-type defects produced inside the MAPI grain during grinding. This suggested that some vacancy-type defects could migrate towards the surface during grinding. According to calculations, $I^-$ and $MA^+$ vacancy displayed lower migrations activation energy (0.1–0.6 eV and 0.5–0.8 eV respectively) than $Pb^{2+}$ vacancy (0.8–2.3 eV).[80–82] Thus, migration of iodine or methylammonium vacancies to the surface were more likely than that of lead vacancies. The $e^+$ lifetime spectra in the first layer of monocrystalline wafer grains were consistent with the existence of different types of vacancies and vacancy complexes involving methylammonium and/or iodine vacancies in the near-surface of the grains. It was also in good agreement with the conclusions drawn from the XPS and HRTEM-EDXS analyses. Moreover, despite the possibility of vacancy-type defect elimination at surface/grain boundaries, the defect density remained systematically higher in MAPI4h monocrystalline grains. This suggested that the production of open-volume defects largely compensated their elimination at surface/grain boundaries in the smaller MAPI4h grains.

Therefore, the profiling positron annihilation lifetime spectroscopy in MAPI30 and MAPI4h wafers revealed the presence of specific open defects in MAPI that differ from those earlier observed in MAPI layers or single crystals prepared by solution or dry processes. A density peak in the defect distribution was located at a mean depth of about 55.9 nm from the surface of the first layer of monocrystalline grains in the wafers. Its existence suggested that the defect population resulted from competitive reaction of generation and recombination where the grain surface played a role of sink. The density peak tended to increase with longer grinding time.

**2.5. Discussion on Surface Defect in MS MAPI Powders and Correlation to EMWA Performances**

Optical characterizations have previously suggested a surface modification of MAPI30 and MAPI4h powder and especially

of MAPI4h powder displaying higher vacancy-type defect levels (evidenced with smaller sized particles enhancing the surface contribution). Indeed, the presence of surface vacancy-type defects was confirmed by combining different surface characterization techniques (XPS, HRTEM-EDXS and PALS) for both MAPI30 and MAPI4h particles but particularly for MAPI4h. HRTEM-EDXS and XPS supported the presence of a vacancies defective surface layer and a composition close to $MA_{0.6}PbI_{2.7}$ in MAPI4h with particle size <20 µm was deduced from XPS. PALS confirmed the presence of open volume defects with a concentration gradient from the grain surface. A defect density peak was shown to be located at a mean depth of about 56 nm from the grain surface in MAPI30 and MAPI4h wafers. This peak tended to increase for MAPI4h accompanied by a defects gradient over a great depth in the grain. The observed vacancy-type defects were found to differ from those earlier observed in MAPI layers or single crystals prepared by solution or dry processes. Indeed, the extended ball-milling time enhanced the surface defect concentration by the continuous welding and fracturing processes induced during mechanical synthesis. Such strong surface modification with grinding time and the resulting formation of core-shell particles were already reported during the ball-milling of oxides.[54]

The observed enhancement of reabsorption with the decrease of the particle size could thus be related to the increase of defective surface contribution. The reabsorption would occur mainly within this defective surface layer.

Concerning the EMWA performance of MAPI4h powders with a mean size of 20 µm, the Cole-Cole plot obtained from EM wave absorbing measurement implied multiple dipole polarization relaxation processes taking place in MAPI4h with cluster size higher than 20 µm while only one strong Debye polarization relaxation occurred in MAPI4h <20 µm. Considering grain boundary and surface defects, we can suggest that in MAPI4h powders >20 µm, all the defects induced by extended ball milling at grain boundary, interfaces and surface contribute to the multiple polarization relaxation processes. Meanwhile, in MAPI4h powders with a particle size <20 µm, the defective surface layer contribution is strongly enhanced and is extended in depth in grains leading thus to one strong dipole polarization relaxation. Indeed, the defects in MAPI contribute critically to the sample polarization, piezoelectricity and ferromagnetism. The defects would behave as dielectric polarization centers and thus resulted in polarization relaxations, which is an essential step in the EM wave absorption mechanism.[41]

The polarization of MAPI could be due to either the ionic polarization by the off-center shift of Pb in the $PbI_6$ octahedral or by the displacement of the positive charge centre ($MA^+$) from the negative charge centre ($PbI_3^-$) or the orientation polarization of the $MA^+$ dipole. Regarding the absence of contribution of ionic polarization under the studied EM wave range, our results and defect study would suggest a dipole polarization favoured by the surface ionic vacancies and ionic mobility. This was also supported by computational simulation results showing that both $I^-$ and $MA^+$, especially $I^-$ vacancy, could stabilize the structure with $MA^+$ opposite dipoles.[83] One may expect that the defect gradient in quite the whole volume of the grains could induce a migration of $MA^+$ to compensate these defects leading thus to a strong dipole polarization relaxation improving dielectric
<figure><img src="image_13.png" /><figcaption>**Figure 11.** Schema of EM absorption efficiency difference MAPI30 (powder size > 200 µm) and MAPI4h (powder size < 20 µm).</figcaption></figure>

loss.[28] Other measurements such as impedance and polarization measurements will be necessary to confirm this conclusion as well as full studies at different milling times.

The effect of the powder range size on the EM absorption efficiency is illustrated in **Figure 11** using two extreme cases: MAPI4h > 200 µm and MAPI4h < 20 µm. The lower particle size would provide better surface interactions with EMW as well.

**3. Conclusion**

In this study, we have investigated the electromagnetic wave absorption (EMWA) behaviour of MAPI powders processed through a green approach, high-energy ball-milling, for 30 min and 4 h. Notably, we reported, for the first time, a distinct and strong resonance at 11.4 GHz in both the real and imaginary parts of the permittivity for the mechanosynthesized MAPI4h powders, and only with particle sizes below 20 µm.

The structural characterisations evidenced a fractal microstructure of powders with agglomerates of clusters of (nano) grains them-self constituted of oriented smaller-nanograins. No lattice distortions were observed from synchrotron and UV measurements. Static and transient PL measurements showed an enhanced reabsorption phenomenon in smaller particles displaying higher surface area. Such enhanced reabsorption was correlated to strong surface effects and would occur within this surface defective layer.

Surface characterization techniques such as PALS, HRTEM, HRTEM-EDXS, and XPS confirmed significant surface alterations in both MAPI30 and MAPI4h powders, with defected layers extending up to 56 nm. As expected, MAPI4h powders displayed a higher vacancy-type defect density and a deeper gradient of defects extending from the surface to the core of grains. These vacancy-type defects, induced by the dry, high-energy milling process, are unlike those typically seen in MAPI thin films or single crystals. The observed defects likely enhanced dipole polarization, leading to an increase in permittivity and providing a mechanism for improving the material's EMWA performance.

This study demonstrated that mechanosynthesis is a very promising green synthesis method to explore the EMWA properties of hybrid perovskites and also to study more in depth the nature of defects in hybrid perovskites. Further investigations, including study of FWHM of PL peak, PALS, XPS and

impedance and polarization measurements are undergoing with the aim of studying the evolution of defects with the milling time and especially the nature of vacancy-type defects in mechanosynthesized MAPI. Indeed, our results highlight the critical role of defect engineering in designing hybrid perovskites for high-efficiency electromagnetic wave absorption, opening avenues for further research into defect-driven improvements in perovskite-based materials through a sustainable synthetic strategy.

**4. Experimental Section**

**Mechanosynthesis of MAPI:** The mechanosynthesis conditions of MAPI are reported in the previous study.[27] In brief, the precursor powders MAI and PbI₂ were weighted according to the stoichiometry and a ball to powder weight ratio R = 40 under an argon atmosphere. Then, they were transferred into a stainless-steel milling jar with filling seven stainless steel balls in a glove box under an argon atmosphere. The ball milling was also carried out at a 350-rpm rotation speed under argon condition by using a laboratory planetary micro mill (Fritsch PULVERISETTE 7). The grinding times were 30 min and 4 h according to our previous study[27] to have a quite free defects MAPI and one containing large amount of defects.

**Particle/Cluster Size Separation:** Sieves of different granulometries (200, 100, 50 and 20 µm) were used to manually separate the as-ground MAPI powder into five size ranges: larger than 200 µm; between 100 and 200 µm; between 50 and 100 µm; between 20 and 50 µm and smaller than 20 µm.

**Granulometry Measurement:** Granulometry of the sieved powders were carried out by an external company, sdtech, by using Morphologi G3S through dry dispersion. The measured sizes were converted to circular-equivalent (CE) diameters: the diameter of the circle having the same area as the aggregated particle. These measurements allowed checking the efficiency of the sieving process.

**X-Ray Diffraction (XRD):** XRD patterns were collected using BRUKER D8 DISCOVER equipped with a copper X-Ray anode ($K_{α1}$ = 0.154 056 nm), a motorized anti-scatter screen and a front monochromator. The measurements employed a 0-θ Bragg-Brentano geometry, and a Lynxeye XE-T energy-resolved linear detector to filter the fluorescence. Diffraction patterns were measured in the 5° to 90° in 2θ with a step of 0.02°. The nature of crystalline phases can be identified by XRD. Lattice parameters, mean crystallite size and strain were obtained from experimental data using the Fullprof software. Le Bail analysis has been performed and a Thomson-Cox-Hasting (TCH) function has been chosen for the profile. An internal standard instrumental contribution was measured by corundum.

**UV-visible Diffuse Reflectance Spectroscopy and Band Gap Determination:** Ultraviolet-visible diffuse reflectance spectroscopy was performed using a Perkin Elmer Lambda 950 UV/Vis Spectrometer using the STD Detector Assy. The spectral range was from 300 to 1000 nm. The measured
reflectance spectra were transformed into corresponding absorption spectra by applying the Kubelka-Munk function: $F(R_∞) = \frac{K}{S} = \frac{(1-R_∞)^2}{2R_∞}$ where K stands for the absorption coefficient and S is a semi-empirical scattering coefficient. $R_∞$ is the reflectance of an infinitely thick specimen: $R_∞ = \frac{R_{sample}}{R_{standard}}$. The band gap energy determination is based on the Tauc method where energy-dependent absorption coefficient α can be expressed by: $(α × hν)^{1/γ} = B(hν - E_g)$, where h is the Planck constant, ν is the photon's frequency, $E_g$ is the band gap energy, and B is a constant. The γ factor equals to ½ considering MAPI is a direct-band semiconductor. By replacing α with $F(R_∞)$ and plotting $(F(R_∞)·hν)^{1/γ}$ as a function of $hν$ the x-axis intersection point of the linear fit of the Tauc plot gives an estimated band gap energy.

**Photoluminescence (PL) Measurement:** The measurements were performed with a 320 nm wavelength excitation source using a HORIBA FLUOROLOG spectrofluorometer. The powders were fixed between two glasses of quartz.

**Time Resolved PL (trPL) Measurement:** The time-resolved photoluminescence measurements were performed using a PicoQuant FluoTime 300 spectrophotometer by exciting samples with at 445 nm. For MAPI30 raw powder and MAPI30 with size larger than 200 µm, the trPL measurement was probed at 770 nm. For the MAPI30, with size ranges between 100 and 200 µm, between 50 and 100 µm, between 20 and 50 µm and lower than 20 µm, the trPL measurement was probed at 800 nm. The powders were put in quartz tubes.

**Scanning Electron Microscopy (SEM):** Scanning Electronic Microscopy (SEM) was used to observe as-mechanosynthesized powders and MAPI-loaded silicone band using a Zeiss Gemini SEM 500 scanning electronic microscope operating at 3.00 kV. The silicone band was broken manually after dipping in liquid nitrogen for few seconds to access to the cross-section. Lognormal distribution was applied and the mode value (the point of global maximum) obtained from the distribution curve was used as the average grain size.

**Transmission Electron Microscopy (TEM):** The MAPI powders were characterized by transmission electron microscopy (TEM) using a LaB6 microscope operated at 200 kV. The samples were deposited on a holey carbon-coated TEM grid. The elemental analysis Chemical analysis using Energy-Dispersive X-Ray Spectroscopy (EDXS) were performed on a JEOL 2100 F/Cs (S)-TEM operating at 200 kV using a SDD detector. Imaging during EDXS characterization was performed in high-angle annular scanning TEM mode (HAADF-STEM). Spectra with atomic composition (%) and the corresponding atomic ratio were obtained using point or line scan modes, with a live acquisition time of 30 s for each spectrum. The filtered images were obtained by selecting two symmetrical diffraction dots on the corresponding FFT images (see RED circled points in the corresponding FFT), deleting the background and performing a reverse FFT using image) software.

**Synchrotron X-Ray Diffraction:** The MAPI powders were sieved into size ranges of 50–100 µm, 20–50 µm and lower than 20 µm to be able to be loaded into glass capillary for high energy synchrotron X-Ray diffraction using transmission geometry at Synchrotron SOLEIL. The used beam line was CRISTAL with a beam energy of 0.4366 Å.

**X-Ray Photoelectron Spectroscopy (XPS):** XPS was used to analyse the surface chemical state of ground MAPI samples. Experiments were conducted in an ultrahigh vacuum spectrometer equipped with a RESOLVE 120 MCD5 hemispherical electron analyzer. The XPS spectra presented here were obtained using Al Kα radiation of a twin anode source and pass energies of 100 and 20 eV for survey and high-resolution spectra, respectively. All XPS spectra were calibrated to 284.8 eV according to the C 1s binding energy for adventitious carbon or adsorbed surface hydrocarbon species from the atmosphere. Analysis of the spectra was done by CASA-XPS software, with the application of Shirley background subtraction and a combination of Gaussian-Lorentzian symmetric and asymmetric line shapes for the peak fitting.

**Depth-Profiling Positron-Annihilation Lifetime Spectroscopy (PALS):** The PALS spectra were recorded with high resolution as a function of energy in the range of 1–11 keV at the Mono-energetic Positron Source (MePS) at

the Helmholtz Center Dresden-Rossendorf.[84] At least $1 × 10^7$ counts were accumulated per spectra and the peak-to-background ratio of the recorded spectra was higher than $1 × 10^7:1$. The resolution function of the MePS lifetime spectrometer was stable during the experiment and for all positron implantation energies. It has a short 230 ps FWHM resulting from the high quality of the low energy $e^+$ beam pulse production and gamma detection. This high resolution gives the possibility to resolve lifetime annihilation components arising from $e^+–e^−$ unbound pairs and $e^+–e^−$ bound pairs forming positronium.

**Magnetic Measurement:** The magnetic response of mechanosynthesized MAPI was carried out at ambient temperature by using the SQUID (Superconducting Quantum Interference Device).

**Electromagnetic Wave Adsorption (EMWA) Measurements:** To obtain good dispersion of powder, mechanosynthesized MAPI powders were sieved flowing the steps mentioned at size separation part and then mixed with silicone gel (from RESIN PRO) with a ratio of 2:3 (MAPI : silicone). The mixture was transferred to the mold with the shape of the measure cavity of the set-up to from thin bands and was left overnight for curing. Microwave transmission measurements were performed on the fabricated composite using an X-band waveguide. The dielectric permittivity and magnetic permeability of the composite were determined owing to the four-component S-parameter matrix signal obtained from a Vector Network Analyzer (VNA) by using the Nicolson-Ross-Weir method.[85]

**Statistical Analysis:** Permittivity measurements and Cole-Cole plots were conducted on one batch of MAPI30 and MAPI4h (powder size < 50 µm) and on two replicates of MAPI30 and MAPI4h (powder size < 20 µm). Magnetic measurements were conducted on one batch of MAPI4h with different size ranges. CE diameter measurement and the average CE diameter values were provided and certified by sdetch on two two replicates of MAPI30 and one batch of MAPI4h with different size ranges and more than 100 000 particles were counted for each sample. SEM was conducted on one batch of MAPI30 and MAPI4h with different size ranges and the mean grain size was obtained from lognormal distribution with the mode value as the average grain size by more than 300 countings for each sample. Several MAPI30 and MAPI4h samples are regularly observed by SEM and HRTEM with grain and nanograin size in the range reported here. HRTEM was conducted on three replicates of MAPI30 and three replicates MAPI4h (powder size < 20 µm). 1/Pb ratio and N/Pb ratio form HRTEM-EDXS was performed on one batch of MAPI30 and MAPI4h (powder size < 20 µm) respectively and was averaged from 19 and 22 points for MAPI30 < 20 µm and MAPI4h < 20 µm respectively. XRD was conducted on two replicates of MAPI30 and one batch of MAPI4h with different size ranges and Le Bail refinements were conducted on one batch of MAPI30 and one batch of MAPI4h with different size ranges. XRD patterns were normalized by the highest diffraction intensity. However, XRD measurements are also regularly performed on such MAPI30 and MAPI4h samples and the lattice parameters match always with those reported here. PL and UV-visible diffuse reflectance spectroscopy were performed on three replicates of MAPI30 and one batch of MAPI4h with different size ranges. PL and UV-Vis spectra were normalized by the highest intensity and the PL spectra were deconvoluted by using Gaussian function. trPL was performed on one batch of MAPI30 with different size ranges and the trPL spectra were normalized by the highest intensity and fitted with a double exponential model. We regularly performed PL and UV-Vis measurements on our samples and they are reproducible with here reported results. XPS and PALS was performed on one batch of MAPI30 and MAPI4h but at least three analyses have been performed per sample.

Abbreviations

<table><tr><td>HP</td><td>Hybrid perovskites</td></tr><tr><td>MAPI</td><td>Methylammonium lead iodide</td></tr><tr><td>MS</td><td>Mechanosynthesis methylammonium lead</td></tr><tr><td>EMW</td><td>Electromagnetic wave</td></tr><tr><td>PL</td><td>Photoluminescence</td></tr></table>
<table><tr><td>trPL</td><td>Time resolved photoluminescence</td></tr><tr><td>XRD</td><td>X-Ray diffraction</td></tr><tr><td>UV</td><td>Ultraviolet</td></tr><tr><td>Vis</td><td>Visible</td></tr><tr><td>SEM</td><td>Scanning electronic microscopy</td></tr><tr><td>HRTEM</td><td>High-resolution transmission electron microscopy</td></tr><tr><td>TEM</td><td>Transmission electron microscopy</td></tr><tr><td>XPS</td><td>X-ray photoelectron spectroscopy</td></tr><tr><td>MA</td><td>Methylammonium</td></tr><tr><td>PALS</td><td>Positron annihilation lifetime spectroscopy</td></tr><tr><td>HAADF-STEM</td><td>High-angle annular scanning TEM mode.</td></tr></table>

**Andreas Wagner:** investigation (supporting); methodology (supporting); validation (supporting). **Vasiliki Papaefthimiou:** investigation (equal); methodology (equal); validation (equal); writing—review & editing (supporting). **Spiros Zafeiratos:** investigation (supporting); methodology (equal); validation (supporting). **Damien Cianferani:** methodology (supporting); validation (supporting). **Loic Mager:** investigation (supporting); methodology (supporting); validation (supporting); writing—review & editing (supporting). **Ovidiu Ersen:** investigation (supporting); methodology (equal); validation (supporting). **Catherine Corbel:** investigation (equal); methodology (equal); validation (equal); writing—review & editing (supporting). **Clément Sanchez:** conceptualization (equal); formal analysis (equal); methodology (equal); project administration (supporting); supervision (equal); validation (equal). The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

The authors thank the XRD, SEM and PL platforms of the IPCMS and ICPEES. Cédric Leuvrey and Marc Lenertz are thanked for SEM and XRD analyses respectively. The authors thank GDR HPERO for its scientific activities on hybrid pervoskites. The authors acknowledge the COST action COSY-STAR-CA21101 for its scientific strucuration on CONFINED MOLECULAR SYSTEMS: FROM A NEW GENERATION OF MATERIALS TO THE STARS. We thank the CNRS, University of Strasbourg, and the French Ministry of Research (fellowship to Yihui Cai) for financial support. This project received funding from National Institute of Physics of CNRS (AAP Tremplin@INP) and from Jean-Marie Lehn Fondation-ICFRC.

## Conflict of Interest

The authors declare no conflict of interest.

## Author Contributions

**Sylvie Begin-Colin:** conceptualization (lead); formal analysis (equal); funding acquisition (lead); investigation (lead); methodology (equal); project administration (lead); resources (lead); supervision (equal); validation (equal); writing—review & editing (equal). **Yihui Cai:** formal analysis (supporting); investigation (lead); methodology (equal); visualization (lead); writing—original draft (lead). **Dominique Begin:** conceptualization (supporting); formal analysis (supporting); investigation (equal); methodology (supporting); project administration (equal); supervision (lead); visualization (supporting); writing—review & editing (supporting). **Christophe Lefevre:** formal analysis (supporting); investigation (equal); methodology (equal); validation (supporting); visualization (supporting). **Charles Sidhoum:** investigation (supporting); methodology (supporting); validation (supporting); visualization (supporting); writing—review & editing (supporting). **Erik Elkaim:** investigation (supporting); methodology (supporting); validation (supporting). **Pascal Boulet:** investigation (supporting); methodology (supporting); validation (supporting). **Pierre Desgardin:** investigation (supporting); methodology (supporting); validation (supporting). **Marie-France Barthe:** investigation (supporting); methodology (equal); validation (supporting); visualization (supporting). **Ricardo Helm:** investigation (supporting); methodology (supporting); validation (supporting). **Werner Egger:** investigation (supporting); methodology (supporting); validation (supporting). **Maik Butterling:** investigation (supporting); methodology (supporting); validation (supporting).

## Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.

## Keywords

electromagnetic wave absorbing materials, MAPbI₃, positron annihilation lifetime spectroscopy, reabsorption, solvent-free mechanosynthesis, vacancy-type defects

Received: January 30, 2025

Revised: April 22, 2025

Published online:

[1] H. Kim, J. S. Han, J. Choi, S. Y. Kim, H. W. Jang, *Small Methods* **2018**, *2*, 1700310.

[2] Y.-Y. Tang, Y. Shen, J.-K. Wang, X.-Y. Qian, M.-L. Guo, Y.-Q. Li, J.-X. Tang, *Small Struct.* **2021**, *2*, 2100084.

[3] C. Zhang, C. Mu, J. Xiang, B. Wang, F. Wen, J. Song, C. Wang, Z. Liu, *J. Mater. Sci.* **2017**, *52*, 13023.

[4] Z. Zhang, Y. Yao, J. Zhang, Y. Ma, P. Xu, P. Zhang, Z. Yang, W. Zhou, *Mater. Lett.* **2022**, *326*, 132926.

[5] H. Guo, J. Yang, B. Pu, H. Chen, Y. Li, Z. Wang, X. Niu, *J. Mater. Chem. C* **2018**, *6*, 4201.

[6] Z. Zhang, Z. Xiong, Y. Yao, D. Wang, Z. Yang, P. Zhang, Q. Zhao, W. Zhou, *Adv. Funct. Mater.* **2022**, *32*, 2206053.

[7] H. Lin, M. Green, L. Xu, X. Chen, B. Ma, *Adv. Mater. Interfaces* **2020**, *7*, 1901270.

[8] Z. Zhang, Z. Xiong, Y. Yao, X. Shi, P. Zhang, Z. Yang, Q. Zhao, W. Zhou, *Adv. Electron. Mater.* **2023**, *9*, 2201179.

[9] M. Li, X. Zhao, P. Tang, X. Zhang, Y. Wu, T. Jin, R. Liu, G. Wu, X. Wang, *Ceram. Int.* **2023**, *49*, 40970.

[10] H. Yu, H. Liu, Y. Yao, Z. Xiong, L. Gao, Z. Yang, W. Zhou, Z. Zhang, *Micromachines* **2023**, *14*, 1611.

[11] H. Lv, J. Cui, B. Li, M. Yuan, J. Liu, R. Che, *Adv. Funct. Mater.* **2024**, *35*, 2315722.

[12] M. F. Elmahaishi, R. S. Azis, I. Ismail, F. D. Muhammad, *J. Mater. Res. Technol.* **2022**, *20*, 2188.

[13] Y. Akinay, U. Gunes, B. Çolak, T. Cetin, *ChemPhysMater* **2023**, *2*, 197.

[14] Z. Wei, Z. Li, D. Chen, J. Liang, J. Kong, *Small Struct.* **2024**, *2400615*.

[15] J. Du, T. Li, Z. Xu, J. Tang, Q. Qi, F. Meng, *Small Struct.* **2023**, *4*, 2300152.

[16] X. Xu, D. Li, L. Li, Z. Yang, Z. Lei, Y. Xu, *Small Struct.* **2023**, *4*, 2200219.
[17] J. N. Wilson, J. M. Frost, S. K. Wallace, A. Walsh, *APL Mater.* **2019**, *7*, 010901.

[18] D. Prochowicz, M. Saski, P. Yadav, M. Grätzel, J. Lewiński, *Acc. Chem. Res.* **2019**, *52*, 3233.

[19] C. C. Stoumpos, C. D. Malliakas, M. G. Kanatzidis, *Inorg. Chem.* **2013**, *52*, 9019.

[20] F. Palazon, Y. El Ajouri, H. J. Bolink, *Adv. Energy Mater.* **2020**, *10*, 1902499.

[21] Z. Hong, D. Tan, R. A. John, Y. K. E. Tay, Y. K. T. Ho, X. Zhao, T. C. Sum, N. Mathews, F. García, H. S. Soo, *iScience* **2019**, *16*, 312.

[22] D. Prochowicz, M. Franckevičius, A. M. Ciešlak, S. M. Zakeeruddin, M. Grätzel, J. Lewiński, *J. Mater. Chem.* **A** 2015, 3, 20772.

[23] K. V. Manukyan, A. V. Yeghishyan, D. O. Moskovskikh, J. Kapaldo, A. Mintairov, A. S. Mukasyan, *J. Mater. Sci.* **2016**, *51*, 9123.

[24] N. Leupold, K. Schötz, S. Cacovich, I. Bauer, M. Schultz, M. Daubinger, L. Kaiser, A. Rebai, J. Rousset, A. Köhler, P. Schulz, R. Moos, F. Panzer, *ACS Appl. Mater. Interfaces* **2019**, *11*, 30259.

[25] B. A. Rosales, L. Wei, J. Vela, *J. Solid State Chem.* **2019**, *271*, 206.

[26] N. Leupold, F. Panzer, *Adv. Funct. Mater.* **2021**, *31*, 2007350.

[27] Y. Cai, D. Begin, C. Sidhoum, A. Girault, T. Fix, C. Lefevre, W. Belayachi, A. Dinia, D. Preziosi, M. Gallart, P. Gilliot, E. Gros-Daillon, F. Ledee, O. Ersen, C. Sanchez, S. Begin-Colin, *Chem. Mater.* **2023**, *35*, 10188.

[28] B. Zhao, Y. Du, Z. Yan, L. Rao, G. Chen, M. Yuan, L. Yang, J. Zhang, R. Che, *Adv. Funct. Mater.* **2023**, *33*, 2209924.

[29] H. Jin, E. Debroye, M. Keshavarz, I. G. Scheblykin, M. B. J. Roeffaas, J. Hofkens, J. A. Steele, *Mater. Horiz.* **2020**, *7*, 397.

[30] A. Musiienko, J. Čížek, H. Elhadidy, P. Praus, K. Higgins, B. Dryzhakov, A. Kanak, F. Sureau, J. Pipek, E. Belas, M. Betušiak, M. Brynza, E. Lukosi, B. Hu, M. Ahmadi, *Chem. Mater.* **2022**, *34*, 297.

[31] A. Musiienko, D. R. Ceratti, J. Pipek, M. Brynza, H. Elhadidy, E. Belas, M. Betušiak, G. Delport, P. Praus, *Adv. Funct. Mater.* **2021**, *31*, 2104467.

[32] S. Kosar, A. J. Winchester, T. A. S. Doherty, S. Macpherson, C. E. Petoukhoff, K. Frohna, M. Anaya, N. S. Chan, J. Madéo, M. K. L. Man, S. D. Stranks, K. M. Dani, *Energy Environ. Sci.* **2021**, *14*, 6320.

[33] M. Pratheek, T. Abhinav, S. Bhattacharya, G. K. Chandra, P. Predeep, *Mater. Sci. Energy Technol.* **2021**, *4*, 282.

[34] F. Wang, S. Bai, W. Tress, A. Hagfeldt, F. Gao, *Npj Flex. Electron.* **2018**, *2*, 22.

[35] F. Panzer, C. Li, T. Meier, A. Köhler, S. Huettner, *Adv. Energy Mater.* **2017**, *7*, 1700286.

[36] K. Miyata, T. L. Atallah, X.-Y. Zhu, *Sci. Adv.* **2017**, *3*, e1701469.

[37] Y. Shi, Y. Zheng, X. Xiao, Y. Li, D. Feng, G. Zhang, Y. Zhang, T. Li, Y. Shao, *Small Struct.* **2024**, *5*, 2400132.

[38] S. Sil, H. Luitel, J. Dhar, M. Chakrabarti, P. P. Ray, B. Bandyopadhyay, D. Sanyal, *Phys. Lett. A* **2020**, *384*, 126278.

[39] N. Leupold, P. Ramming, I. Bauer, C. Witt, J. Jungklaus, R. Moos, H. Grüninger, F. Panzer, *Eur. J. Inorg. Chem.* **2023**, *26*, e202200736.

[40] F. Palazon, Y. El Ajouri, P. Sebastia-Luna, S. Lauciello, L. Manna, H. J. Bolink, *J. Mater. Chem. C* **2019**, *7*, 11406.

[41] B. Quan, X. Liang, G. Ji, Y. Cheng, W. Liu, J. Ma, Y. Zhang, D. Li, G. Xu, *J Alloys Compd.* **2017**, *728*, 1065.

[42] T. Liu, Y. Pang, M. Zhu, S. Kobayashi, *Nanoscale* **2014**, *6*, 2447.

[43] D. Ding, Y. Wang, X. Li, R. Qiang, P. Xu, W. Chu, X. Han, Y. Du, *Carbon* **2017**, *111*, 722.

[44] W. Gu, J. Chen, Y. Zhao, G. Wang, F. Wang, T. Zhang, B. Zhang, *Sci. Rep.* **2020**, *10*, 16044.

[45] M. Qin, L. Zhang, H. Wu, *Adv. Sci.* **2022**, *9*, 2105553.

[46] J. Dhar, S. Sil, N. A. Hoque, A. Dey, S. Das, P. P. Ray, D. Sanyal, *ChemistrySelect* **2018**, *3*, 5304.

[47] S. Bonomi, V. Armenise, G. Accorsi, S. Colella, A. Rizzo, F. Fracassi, L. Malavasi, A. Listorti, *Appl. Sci.* **2020**, *10*, 4775.

[48] N. Guigue-Millot, S. Bégin-Colin, Y. Champion, M. J. Hštch, G. Le Caër, P. Perriat, *J. Solid State Chem.* **2003**, *170*, 30.

[49] S. Bégin-Colin, G. Le Caër, F. Villieras, X. Devaux, M. O. Simonnot, T. Girot, P. Weisbecker, *J. Metastable Nanocryst. Mater.* **2002**, *12*, 27.

[50] S. Begin-Colin, G. Le Caër, M. Zandona, E. Bouzy, B. Malaman, J. *Alloys Compd.* **1995**, *227*, 157.

[51] S. Begin-Colin, T. Girot, A. Mocellin, G. Le Caër, *Nanostruct. Mater.* **1999**, *12*, 195.

[52] G. Caër, S. Begin-Colin, P. Delcroix in *Material Research in Atomic Scale By Mössbauer Spectroscopy* (Eds: M. Mashlan, M. Miglierini, P. Schaaf), Springer Netherlands, Dordrecht, **2003**, pp. 11–20.

[53] S. Begin-colin, G. L. Caër, A. Mocellin, M. Zandona, *Philos. Mag. Lett.* **1994**, *69*, 1.

[54] V. Šepelák, S. Bégin-Colin, G. Le Caër, *Dalton Trans.* **2012**, *41*, 11927.

[55] C. Witt, N. Leupold, P. Ramming, K. Schötz, R. Moos, F. Panzer, *J. Phys. Chem. C* **2022**, *126*, 15424.

[56] P. Sadhukhan, D. Ghosh, P. Sengupta, S. Bhattacharyya, S. Das, *Langmuir* **2021**, *37*, 5513.

[57] L. Guo, G. Xu, G. Tang, D. Fang, J. Hong, *Nanotechnology* **2020**, *31*, 225204.

[58] Y. Ren, I. W. H. Oswald, X. Wang, G. T. McCandless, J. Y. Chan, *Cryst. Growth Des.* **2016**, *16*, 2945.

[59] T. Yamada, Y. Yamada, Y. Kanemitsu, *J. Lumin.* **2020**, *220*, 116987.

[60] H. Diab, C. Arnold, F. Lédée, G. Trippé-Allard, G. Delport, C. Vilar, F. Bretenaker, J. Barjon, J.-S. Lauret, E. Deleporte, D. Garrot, *J. Phys. Chem. Lett.* **2017**, *8*, 2977.

[61] C. Witt, K. Schötz, M. Kuhn, N. Leupold, S. Biberger, P. Ramming, F.-J. Kahle, A. Köhler, R. Moos, E. M. Herzig, F. Panzer, *J. Phys. Chem. C* **2023**, *127*, 10563.

[62] L. M. Pazos-Outón, M. Szumilo, R. Lamboll, J. M. Richter, M. Crespo-Quesada, M. Abdi-Jalebi, H. J. Beeson, M. Vručinić, M. Alsari, H. J. Snaith, B. Ehrler, R. H. Friend, F. Deschler, *Science* **2016**, *351*, 1430.

[63] D. Hong, J. Li, S. Wan, I. G. Scheblykin, Y. Tian, *J. Phys. Chem. C* **2019**, *123*, 12521.

[64] J. Even, L. Pedesseau, C. Katan, *J. Phys. Chem. C* **2014**, *118*, 11566.

[65] M. Baranowski, P. Plochocka, *Adv. Energy Mater.* **2020**, *10*, 1903659.

[66] H. Kim, J. Lee, B. Kim, H. R. Byun, S. H. Kim, H. M. Oh, S. Baik, M. S. Jeong, *Sci. Rep.* **2019**, *9*, 15461.

[67] M. J. Ashley, E. J. Kluender, C. A. Mirkin, *ACS Nano* **2018**, *12*, 7206.

[68] M. Yang, Y. Zeng, Z. Li, D. H. Kim, C.-S. Jiang, J. van de Lagemaat, K. Zhu, *Phys. Chem. Chem. Phys.* **2017**, *19*, 5043.

[69] A. M. A. Leguy, P. Azarhoosh, M. I. Alonso, M. Campoy-Quiles, O. J. Weber, J. Yao, D. Bryant, M. T. Weller, J. Nelson, A. Walsh, M. van Schilfgaarde, P. R. F. Barnes, *Nanoscale* **2016**, *8*, 6317.

[70] B. Saparov, D. B. Mitzi, *Chem. Rev.* **2016**, *116*, 4558.

[71] S. Bégin-Colin, T. Girot, G. Le Caër, A. Mocellin, *J. Solid State Chem.* **2000**, *149*, 41.

[72] T. Girot, X. Devaux, S. Bégin-Colin, G. L. Caër, A. Mocellin, *Philos. Mag.* **A** **2001**, *81*, 489.

[73] K. X. Steirer, P. Schulz, G. Teeter, V. Stevanovic, M. Yang, K. Zhu, J. J. Berry, *ACS Energy Lett.* **2016**, *1*, 360.

[74] S. Béchu, M. Ralaiarisoa, A. Etcheberry, P. Schulz, *Adv. Energy Mater.* **2020**, *10*, 1904007.

[75] C. Rocks, V. Svrcek, P. Maguire, D. Mariotti, *J. Mater. Chem. C* **2017**, *5*, 902.

[76] S. Chen, P. Gao, *J. Appl. Phys.* **2020**, *128*, 010901.

[77] J. Dhar, S. Sil, A. Dey, D. Sanyal, P. P. Ray, *J. Phys. Chem. C* **2017**, *121*, 5515.

[78] J. Dhar, S. Sil, A. Dey, P. P. Ray, D. Sanyal, *J. Phys. Chem. Lett.* **2017**, *8*, 1745.
[79] D. J. Keeble, J. Wiktor, S. K. Pathak, L. J. Phillips, M. Dickmann, K. Durose, H. J. Snaith, W. Egger, *Nat. Commun.* **2021**, *12*, 5566.

[80] C. Eames, J. M. Frost, P. R. F. Barnes, B. C. O'Regan, A. Walsh, M. S. Islam, *Nat. Commun.* **2015**, *6*, 7497.

[81] D. Yang, W. Ming, H. Shi, L. Zhang, M.-H. Du, *Chem. Mater.* **2016**, *28*, 4349.

[82] E. Mosconi, F. De Angelis, *ACS Energy Lett.* **2016**, *1*, 182.

[83] W. Geng, Q. Hu, C. Tong, Z. Tang, L. Liu, *Adv. Theory Simul.* **2019**, *2*, 1900041.

[84] A. Wagner, M. Butterling, M. O. Liedke, K. Potzger, R. Krause-Rehberg, in *AIP Conf. Proc. Positron Annihilation Lifetime and Doppler Broadening Spectroscopy at the ELBE Facility*, Newport News, VA, USA **2018**; p 040003. https://doi.org/10.1063/1.5040215.

[85] A. M. Nicolson, G. F. Ross, *IEEE Trans. Instrum. Meas.* **1970**, *19*, 377.