Isotope analysis in the transmission electron microscope

Abstract

The Ångström-sized probe of the scanning transmission electron microscope can visualize and collect spectra from single atoms. This can unambiguously resolve the chemical structure of materials, but not their isotopic composition. Here we differentiate between two isotopes of the same element by quantifying how likely the energetic imaging electrons are to eject atoms. First, we measure the displacement probability in graphene grown from either 12C or 13C and describe the process using a quantum mechanical model of lattice vibrations coupled with density functional theory simulations. We then test our spatial resolution in a mixed sample by ejecting individual atoms from nanoscale areas spanning an interface region that is far from atomically sharp, mapping the isotope concentration with a precision better than 20%. Although we use a scanning instrument, our method may be applicable to any atomic resolution transmission electron microscope and to other low-dimensional materials.

Coherent diffraction of hydrogen through the 246 pm lattice of graphene

“…In this proposal we consider that each atom is diffracted at a membrane in thermal equilibrium. This is reasonable as phonons excited by the H atoms are damped on the ps time scale [45], much shorter than the expected arrival rate of individual atoms at the grating, which is on the order of one hydrogen atom per hexagon and second. In a realistic diffraction pattern, the observed contrast is reduced due to a number of effects.…”

“…If Δp coll <p uncert , it is fundamentally impossible for the membrane to resolve the position of the diffracted particles and atomic coherence should be maintained. We estimate p uncert using the in-plane and outof-plane mean square velocities á ñ v 2 [45] and the mass m C of the carbon atoms…”

“…At the zero-point vibrational level this yields an average out-of-plane momentum of @´p 1.0 10 23 kg m s −1 and an in-plane momentum of @´- p 2.1 10 23 kg m s −1 . The mean square velocities á ñ v 2 have been calculated ab initio within the harmonic approximation and the equipartition of thermal energy based on the phonon density of states [45].…”

A time-dependent atomistic reconstruction of severe irradiation damage and associated property changes in nuclear graphite

“…using TEM and DFT [55]) and graphite (25 eV using MD simulations [16,50]). A last point to mention here is that, for simplicity and because of lack of available data, we have considered here that the dose is a linear function of irradiation time (or electron fluence).…”

Direct visualization of the 3D structure of silicon impurities in graphene

“…A Poisson fit yields the mean values λ u = 2.87 × 10 6 e −Å −2 for the flip from up to down and λ d = 4.96 × 10 5 e −Å −2 for the flip from down to up.Based on a DFT molecular dynamics simulation[8], the kinetic energy perpendicular to the graphene lattice that a probe electron would need to transfer to a Si substitution in order to shift it from one side of the graphene lattice to the other is between [1.375,1.50] eV. For our 60 keV electron beam, this corresponds to a cross section of about 1100 barn[25]. The experimentally observed areal event dose of 0.5 × 10 6 e −Å −2 corresponds to a cross section value of 200 barn.…”