Abstract

In this paper we introduce an electron ptychography reconstruction framework, CAVIAR – Correlated Atomic Vibration Imaging with sub-Ångstrom Resolution – that reveals an entirely new channel of information: spatial correlations in atomic displacements at the atomic scale. We show reconstructions of a symmetric Σ9 grain boundary in silicon from realistically simulated data and experimental data for hexagonal boron nitride. By reconstructing the object as an ensemble of multiple states we are able to observe correlations between movements of atoms in the range of 10-20 pm at room temperature in agreement with the expectation. Moreover, using only the masses of the atomic species and the temperature as input, we obtain average frequencies of 10.8±0.1, 13.6±0.6, 18.0±0.2, 25.5±1.5 THz for the longitudinal and transversal acoustic and optic phonons, respectively, in agreement with inelastic neutron scattering, albeit from just a few nm3 volume.

Abstract

In this paper we introduce an electron ptychography reconstruction framework, CAVIAR – Correlated Atomic Vibration Imaging with sub-Ångstrom Resolution – that reveals an entirely new channel of information: spatial correlations in atomic displacements at the atomic scale. We show reconstructions of a symmetric Σ9 grain boundary in silicon from realistically simulated data and experimental data for hexagonal boron nitride. By reconstructing the object as an ensemble of multiple states we are able to observe correlations between movements of atoms in the range of 10-20 pm at room temperature in agreement with the expectation. Moreover, using only the masses of the atomic species and the temperature as input, we obtain average frequencies of 10.8±0.1, 13.6±0.6, 18.0±0.2, 25.5±1.5 THz for the longitudinal and transversal acoustic and optic phonons, respectively, in agreement with inelastic neutron scattering, albeit from just a few nm3 volume.

Abstract

In this paper we introduce an electron ptychography reconstruction framework, CAVIAR – Correlated Atomic Vibration Imaging with sub-Ångstrom Resolution – that reveals an entirely new channel of information: spatial correlations in atomic displacements at the atomic scale. We show reconstructions of a symmetric Σ9 grain boundary in silicon from realistically simulated data and experimental data for hexagonal boron nitride. By reconstructing the object as an ensemble of multiple states we are able to observe correlations between movements of atoms in the range of 10-20 pm at room temperature in agreement with the expectation. Moreover, using only the masses of the atomic species and the temperature as input, we obtain average frequencies of 10.8±0.1, 13.6±0.6, 18.0±0.2, 25.5±1.5 THz for the longitudinal and transversal acoustic and optic phonons, respectively, in agreement with inelastic neutron scattering, albeit from just a few nm3 volume.

Abstract

In this paper we introduce an electron ptychography reconstruction framework, CAVIAR – Correlated Atomic Vibration Imaging with sub-Ångstrom Resolution – that reveals an entirely new channel of information: spatial correlations in atomic displacements at the atomic scale. We show reconstructions of a symmetric Σ9 grain boundary in silicon from realistically simulated data and experimental data for hexagonal boron nitride. By reconstructing the object as an ensemble of multiple states we are able to observe correlations between movements of atoms in the range of 10-20 pm at room temperature in agreement with the expectation. Moreover, using only the masses of the atomic species and the temperature as input, we obtain average frequencies of 10.8±0.1, 13.6±0.6, 18.0±0.2, 25.5±1.5 THz for the longitudinal and transversal acoustic and optic phonons, respectively, in agreement with inelastic neutron scattering, albeit from just a few nm3 volume.