Abstract
Strain engineering is used to obtain desirable materials properties in a range of modern technologies. Direct nanoscale measurement of the three-dimensional strain tensor field within these materials has however been limited by a lack of suitable experimental techniques and data analysis tools. Scanning electron diffraction has emerged as a powerful tool for obtaining two-dimensional maps of strain components perpendicular to the incident electron beam direction. Extension of this method to recover the full three-dimensional strain tensor field has been restricted though by the absence of a formal framework for tensor tomography using such data. Here, we show that it is possible to reconstruct the full non-symmetric strain tensor field as the solution to an ill-posed tensor tomography inverse problem. We then demonstrate the properties of this tomography problem both analytically and computationally, highlighting why incorporating precession to perform scanning precession electron diffraction (SPED) may be important. We establish a general framework for non-symmetric tensor tomography and demonstrate computationally its applicability for achieving strain tomography with SPED data.
Highlights
In this paper, we examine whether it is theoretically possible to recover the three-dimensional strain tensor field within a material using scanning electron diffraction (SED) data and tensor tomography methods.Nanoscale strain is widely used to engineer desirable materials properties, for example, improving field effect transistor performance [1], opening a bulk bandgap in topological insulator systems [2] and enhancing ferroelectric properties [3]
We demonstrate the properties of this tomography problem both analytically and computationally, highlighting why incorporating precession to perform scanning precession electron diffraction (SPED)
The fact that strain maps are rank 2 tensor fields immediately puts us in the domain of tensor tomography, and the physical characteristics of diffraction imaging seen in approximation 1 highlights the transverse ray transform (TRT) as the natural parallel
Summary
We examine whether it is theoretically possible to recover the three-dimensional strain tensor field within a material using scanning electron diffraction (SED) data and tensor tomography methods. 3D strain has been assessed by atomic resolution tomography [16] and in a proof-of-principle reconstruction of a single strain component using SED [17]. We establish such a framework for three-dimensional reconstruction of the full strain tensor field from S(P)ED data via consideration of an analytical forward model (see sections 2–4). Our analytical and numerical results establish a robust framework for three-dimensional strain tensor field reconstruction using S(P)ED data
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
