Test of the Dynamic-Domain and Critical Scattering Hypotheses in Cubic Methylammonium Lead Triiodide

We investigate the hypothesis of dynamic tetragonal domains occurring in cubic ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ using high-resolution neutron spectroscopy to study a fully deuterated single crystal. The $R$-point scattering above the 327.5 K cubic-tetragonal phase transition is always resolution limited in energy and therefore inconsistent with dynamic-domain predictions. This behavior is instead consistent with the central peak phenomenon observed in other perovskites. The scattering may originate from small, static, tetragonal-phase domains nucleating about crystal defects, and the temperature dependence demonstrates the transition is first order.

Figure 1

Scattering at the cubic $R$-point $\mathbf{Q}=\frac{1}{2}(133)$ in $d_6$-MAPI measured with thermal and cold neutrons. In (a), the width of the scattering matches the energy resolution. Data were taken at 340 K on BT4 (dotted line) and SPINS (three other spectra). $R$-point scattering (b) energy and (c) wave-vector (at $\hslash \omega =0$) dependence as a function of temperature measured with an energy resolution HWHM of 0.095 meV ($E_f=4\mathrm{meV}$).

Figure 2

Fits to the QES-subtracted $R$-point E scan (resolution $\mathrm{HWHM}=0.095\mathrm{meV}$) at 330 K using the (a) dynamic-domain (reduced-${\chi }^2=3.41$) and (b) CP models (reduced-${\chi }^2=1.42$). The resolution-broadened total fits are plotted as a red dash-dot line, the Lorentzian components $\mathcal{L}$ as black dashed lines, and the resolution-broadened delta function $\delta$ as a solid black line. The dynamic-domain model does not fit the tails or peak as well as the $CP$ model. (c) Fit (dash-dot red line) of the QES offset from the R point to a model consisting of two $\mathcal{L}$ (dashed and solid black lines) and a $\delta$ function (dotted black line) convolved with the instrument resolution function plus a flat background (not shown).

Figure 3

(a) Minimum $\tau$ (and 95% confidence interval $\alpha$) of tetragonal domains determined from maximum likelihood estimation. Temperature-dependent $\tau$ are determined from $R$-point E scans with resolution $\mathrm{HWHM}=0.095\mathrm{meV}$. The single point at $T-T_C=12.5\mathrm{K}$ corresponds to the $R$-point E scan with resolution $\mathrm{HWHM}=0.065\mathrm{meV}$. (b) Peak area obtained from $R$-point E scans, the $CP$ model corresponds to the resolution-broadened $\delta$ component only. Error bars may be smaller than the corresponding marker.

Figure 4

(a) Representative elastic $\mathbf{Q}$ scan from SPINS at 330 K along [100] at the $R$ point. The data (gray markers) are fit to both $\mathcal{L}$ (dashed) and ${\mathcal{L}}^2$ (dash-dot) line shapes, with corresponding reduced-${\chi }^2$ values indicated in the legend. Resolution FWHM is indicated with a black line. (b) Correlation lengths $\xi$ extracted from ${\mathcal{L}}^2$ linewidths for $R$-point scans along [100] (SPINS, BT4) and [011].