The simultaneous measurement of structural and chemical information at the atomic scale provides fundamental insights into the connection between form and function in materials science and nanotechnology. We demonstrate structural and chemical mapping in ${\mathrm{Bi}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_3$ using an aberration-corrected scanning transmission electron microscope. Two-dimensional mapping is made possible by an adapted method for fast acquisition of electron energy-loss spectra. The experimental data are supported by simulations, which help to explain the less intuitive features.

One of the unusual features of the $M_{n+1}A{X}_n$ phases (where $M$ is a transition metal, $A$ is a group A element, $X$ is carbon or nitrogen, and $n=1,2,3\dots$) is that for a given $M\text{−}A\text{−}X$ system, only certain values of $n$ are found to occur and there is no systematic behavior between the different systems. Density-functional theory was used to verify the stability of the different phases by comparing their total energy to that of the appropriate competing phases. Five systems (Ti-Al-C, Ti-Si-C, Ti-Al-N, Ti-Si-N, and Cr-Al-C) were studied for $n=1–4$. Complete agreement with observed occurrences of these phases was found. Very small energy differences suggest that it may be possible to fabricate ${\text{Ti}}_2\text{SiC}$, ${\text{Ti}}_2\text{SiN}$, and ${\text{Ti}}_3{\text{AlN}}_2$ as metastable phases. None of the $M_{5}A{X}_4$ phases were predicted to occur and in all cases the $\alpha$ phases were found to be more energetically favorable than the $\beta$ phases.