Mechanochemically-induced glass formation from two-dimensional hybrid organic–inorganic perovskites

Hybrid organic–inorganic perovskites (HOIPs) occupy a prominent position in the field of materials chemistry due to their attractive optoelectronic properties. While extensive work has been done on the crystalline materials over the past decades, the newly reported glasses formed from HOIPs open up a new avenue for perovskite research with their unique structures and functionalities. Melt-quenching is the predominant route to glass formation; however, the absence of a stable liquid state prior to thermal decomposition precludes this method for most HOIPs. In this work, we describe the first mechanochemically-induced crystal-glass transformation of HOIPs as a rapid, green and efficient approach for producing glasses. The amorphous phase was formed from the crystalline phase within 10 minutes of ball-milling, and exhibited glass transition behaviour as evidenced by thermal analysis techniques. Time-resolved in situ ball-milling with synchrotron powder diffraction was employed to study the microstructural evolution of amorphisation, which showed that the crystallite size reaches a comminution limit before the amorphisation process is complete, indicating that energy may be further accumulated as crystal defects. Total scattering experiments revealed the limited short-range order of amorphous HOIPs, and their optical properties were studied by ultraviolet-visible (UV-vis) spectroscopy and photoluminescence (PL) spectroscopy.


Quantitative Phase Analyses (QPA) and microstructural evolution analysis details
Rietveld QPA of experimental diffraction patterns was performed using the TOPAS-Academic V7 software. 3The structural model of (S-NEA) 2 PbBr 4 was refined on PXRD data obtained from a laboratory X-ray diffraction instrument (see following section).
The scattering signal out of a m (S-NEA) 2 PbBr 4 was modelled with a single Gaussian peak.The structural models of tetragonal and orthorhombic lead oxide minimum, which were found as minor impurities in the powder mix, were retrieved from the Inorganic Crystal Structure Database. 4The in-situ PXRD dataset under milling conditions was fit sequentially, with a convergence criterion of 0.001 and a maximum number of iterations of 10000.An experimental, fixed background profile measured on an empty section of the jar before milling, was subtracted by fitting a background scale parameter together with a 2 terms polynomial function.As described elsewhere, 5,6 the sample powders inside the milling jar are distributed across different locations, e.g.some powders float randomly inside the jar, while some are more attached to the walls of the jar, which accordingly leads to a range of distances from the sample to the detector.As such, diffraction with the ball-milling setup results in splitting of each Bragg reflection into a convolution of 2θ positions.The difference in 2θ angle can be minimised when the jar is accurately aligned, with negligible scattering contribution from the sample distributed within the jar.Therefore, in our work, the crystal structure model of each compound was introduced twice ("top phase" and "bottom phase" from here on) with two modified Thompson-Cox-Hastings pseudo-Voigt functions (TCHZ) peak shape functions (with fixed parameters as refined on the Si standard) and independent scale parameters.
As described by Lampronti et al., 5,6 the dependence of the profile full-width-at-halfmax (FWHM) on 2θ was described with a modified TCHZ function where U, V, W (Gaussian) and X (Lorenzian) are the parameters that have been refined in the current case.

Equation S1
Microstructural investigations were performed assuming that the sample contribution to peak broadening was related to size only.A Lorentzian function was convoluted for each phase, with a single isotropic Crystal Size (CS) parameter related to as in the Γ  Scherrer equation (equations S8 and S9), 7 Equation S8 in which, L is the mean size of the ordered (crystalline) domains, K s is a shape factor constant in the range (typically 0.9), λ is the X-ray wavelength, τ is the peak width in radians at FWHM.The top and bottom phases of the same compound were constrained to have the same CS parameter.We here remind that the estimated standard deviation (ESD) from the Rietveld calculation has no bearing on the precision or accuracy, but is merely related to the mathematical fit of the model. 8In other words, absolute numbers have a degree of uncertainty that cannot really be measured.On the other hand, so long as the same approach is used for all scans within a dataset, trends are reliable.For what concerns the accuracy of the size determination, it is known that for a typical laboratory X-ray diffraction instrument the Scherrer analysis provides sensitivity to crystallite size in the 1-100 nm range, the upper limit being set by the instrumental broadening. 9This also means that the smaller the crystal size, the less the Scherrer size value is affected by how the instrumental broadening is defined.For example, modeling the instrumental contribution for the analyzed datasets with a single conventional TCHZ function, instead of two split TCHZ functions, has a more significant effect on the estimated CS for larger CSs.To summarize, the smaller the crystal size, the more reliable the number.It is also important to note that the peak shape tends to be dominated by the larger crystallites rather than the smaller ones, so the calculated size tends to be overestimated. 9The scale factors of the crystalline and amorphous phases were normalized using their respective maximum scale factor, i.e. the scale factor from the refinement of the first pattern for the crystalline phase, and the scale factor from the refinement of the last pattern for the amorphous phase.For each refinement the weight percentage of each of the two phases was calculated as the ratio between its normalized scale factor and the sum of the two normalized scale factors times 100.
Error propagation rules were applied accordingly to calculate the estimated standard deviation.
While the visual inspection of a Rietveld plot is the most reliable way to determine the quality of a fit, this is not practical for large datasets, such as those presented here.A global check of a sequential refinement can be efficiently performed by comparing a number of "goodness of fit" indices.One is the weighted profile R-factor (R wp ), Equation S10 Where y c and y o represent the calculated and observed intensity respectively for each point i. and the weight w i is equal to .The second index is "chi squared": where (R exp ), the "expected R factor", is: with N as the number of data points.

Initial structural Rietveld refinement of PXRD
The structural model of (S-NEA) 2 PbBr 4 was refined on PXRD data obtained from a laboratory X-ray diffraction instrument using TOPAS-Academic V7. 3 A Chebyshev polynomial function with ten parameter was used to fit the background.The position and orientation of the organic molecules were optimized as rigid bodies.The position of the inorganic ions was refined with no constraints.One thermal parameter was applied for each atomic species.The Pseudo-Voigt function used to model the peak shape and the parameters describing the diffractometer geometry were first optimized using an LaB 6 standard with a fundamental parameter approach. 10These were fixed for the structural refinements, while one further isotropic parameter was used to take into account the sample Lorentzian contribution to peak broadening (see previous section).The March-Dollase model for preferred orientation was applied on the (0 0 1) crystallographic direction.The refinement converged with χ 2 and R wp values of 16.72% and 3.56 respectively.The Rietveld refinement plot is shown in Figure S21.and a m (S-NEA) 2 PbBr 4 (blue) obtained at ambient temperature using a 300 nm light source.

Fig. S12 .
Fig. S12.TGA and DSC profiles of the recrystallised a m (S-NEA) 2 PbBr 4 after two days stored in an ambient environment.

Fig. S5 .
Fig. S5.Full DSC scan of a m (S-NEA) 2 PbBr 4 , where the sample was heated to 190 o C at 10 o C min -1 , cooled to 30 o C at 10 o C min -1 , then heated again to 190 o C at 10 o C min -1 .In the first heating upscan, the glass transition temperature of a m (S-NEA) 2 PbBr 4 was recorded as 51 o C and the crystallisation temperature was recorded as 94 o C. In the second heating upscan, the glass transition temperature of a g (S-NEA) 2 PbBr 4 (a g : meltquenched glass) was recorded as 70 o C, coincident with the literature value. 2

Fig. S11 .
Fig. S11.PXRD pattern of the as-synthesised crystalline (S-NEA) 2 PbBr 4 , the freshly prepared a m (S-NEA) 2 PbBr 4 and a m (S-NEA) 2 PbBr 4 products when stored (a) in a freezer at ca. 0°C or (b) under vacuum over a period of time.The dashed lines show the position of the strongest Bragg peak in the as-synthesised crystalline (S-NEA) 2 PbBr 4 .X-ray wavelength = 1.5418Å.

Fig. S12 .
Fig. S12.(a) TGA and (b) DSC profiles of the recrystallised a m (S-NEA) 2 PbBr 4 sample after two days stored in an ambient environment and the same batch of sample that was then vacuum dried at 90°C for 2 hours.The recrystallised sample without further vacuum drying showed a minor mass loss of 0.53% at around 70°C in TGA and its DSC profile had an endothermic peak at around the same temperature region.After being vacuum dried at 90°C for 2 hours, these features almost disappear, indicating that the sample recrystallised in an ambient environment might have absorbed moisture from air.

Fig. S16 .
Fig. S16.FT-IR of the as-synthesised crystalline (S-NEA) 2 PbBr 4 and a m (S-NEA) 2 PbBr 4 with different milling times.The regions exhibiting peaks of interest are shaded grey.
.69269;  = 2.42843; = 4.47163; = 0.07842Where is the Pseudo-Voigt mixing parameter, and and are the Gaussian and  Γ  Γ  Lorentzian full width half maxima, respectively.Additionally, to model the evident peak asymmetry, the TCHZ was further split to differentiate the contribution at the left-hand side and at the right-hand site to the overall peak profile for the inner and outer scattering vectors and .The final TCHZ split function is applied to describe the ⃗  1 ⃗  3 overall dependence of the FWHM according to Equation S7, Equation S7

Fig. S19 .
Fig. S19.An example Rietveld fit using the X-ray diffractograms collected at PETRA-III, showing experimental (blue line), calculated (red line), and difference (grey line) patterns of (S-NEA) 2 PbBr 4 under milling conditions at time 0. Peak marks are indicated for (S-NEA) 2 PbBr 4 (top), tetragonal minimum, Pb 3 O 4 , (middle) and orthorhombic minimum (bottom).Each symmetry-allowed reflections are marked twice, as diffraction with this setup results in splitting of each Bragg reflection into a convolution of 2θ positions.Synchrotron radiation wavelength λ = 0.207351 Å.As shown in Fig. S18, the broad peaks at approximately 1.8° and 4.1° originate from the PMMA milling jar.

Fig. S20 .
Fig. S20.An example Rietveld fit using the X-ray diffractograms collected at PETRA-III, showing experimental (purple line), calculated (red line), and difference (grey line) patterns of (S-NEA) 2 PbBr 4 under milling conditions after 8 minutes.Peak marks are indicated for (S-NEA) 2 PbBr 4 (top), tetragonal minimum, Pb 3 O 4 , (middle) and orthorhombic minimum (bottom).Each symmetry-allowed reflections are marked twice, as diffraction with this setup results in splitting of each Bragg reflection into a convolution of 2θ positions.Synchrotron radiation wavelength λ = 0.207351 Å.As shown in Fig. S18, the broad peaks at approximately 1.8° and 4.1° originate from the PMMA milling jar.The small broad peak at approximately 0.8° is attributed to diffuse scattering of the amorphous product.

Table S5
Crystallographic data from Pawley refinement of the PXRD for recrystallised (S-NEA) 2 PbBr 4 after 27 hours stored in an ambient environment.