Using our strict definition of Atomic Scale Analytical Tomography (ASAT), we explore the current landscape of materials characterization tools and discuss how electron microscopy, field ion microscopy, and atom probe tomography are each approaching ASAT. State-of-the-art electron microscopy can achieve sub-angstrom spatial resolution imaging in 2-D and small volumes in 3-D but lacks single-atom chemical sensitivity, especially in 3-D. Field Ion Microscopy can achieve 3-D imaging on small volumes but not for all materials. Atom probe tomography can achieve single-atom elemental quantification in 3-D but lacks the spatial resolution necessary for ASAT. The chapter concludes with a comparison of the different techniques and discusses how different techniques may be complementary.

The historical backdrop for the role of microscopy in the development of human knowledge is reviewed. Atomic-scale investigations are a logical step in a natural progression of increasingly more powerful microscopies. A brief outline of the concept of atomic-scale analytical tomography (ASAT) is given, and its implications for science and technology are anticipated. The intersection of ASAT with advanced computational materials engineering is explored. The chapter concludes with a look toward a future where ASAT will become common.

We discuss how ASAT has the potential to make important advances on critical frontiers in crystallography. These key frontiers include unequivocal quantification of the nearest-neighbour relationships in materials, compositional information, and details of the degree of both short-range order and long-range order. Interfaces represent a particular opportunity. We discuss the present challenges in experimental microscopy-based methods to incorporate both the structural crystallographic information at crystal interfaces with the local chemical compositional information. We anticipate that ASAT will drive forward the field of interface science and interface engineering.

We conclude our contribution with a prospective and optimistic look to the art of what might be possible with the advent of ASAT. We see a convergence between the digital or computational world and the experimental, and envisage ASAT as an enabler for the design and development of new materials. This potential arises because real-world 3D atomic-scale information will bring direct insights into thermodynamic, kinetic, and engineering properties. Moreover, when coupled with machine learning and other computational techniques, it may be envisaged that discovery-based procedures could follow that adjust the observed real-world atomistic configurations toward configurations that exhibit the desired engineering properties. This will fundamentally change the role of microscopy from a tool that provides inference to a materials behaviour to one that provides a quantitative assessment. This opens the pathway to atomic-scale materials informatics.

A complete, albeit brief review of the history of atoms and atomic-scale microscopy is offered. From the concept of the atom developed by Greek philosophers to the ultimate microscopy, the path of development is examined. Atomic-Scale Analytical Tomography (ASAT) is cited as the ultimate microscopy in the sense that the objects, atoms, are the smallest building blocks of nature. The concept of atoms developed as the scientific method grew in application and sophistication beginning in the Middle Ages. The first images of atoms were finally obtained in the mid-twentieth century. Early field ion microscopy evolved eventually into three-dimensional atom probe tomography. The crucial role of the electron microscope in atomic-scale microscopy is examined. Recently, combining atom probe tomography and electron microscopy has emerged as a path toward ASAT. The chapter concludes with the point that ASAT can be expected in the next decade.

Based on the discussion in Chapters 4 and 5, combining information from both electron microscopy, presumably (Scanning) Transmission Electron Microscopy ((S)TEM), and Atom Probe Tomography (APT) is a likely path toward ASAT. Experimentally, concurrent (S)TEM and APT may appear to be a straightforward experiment, but the instrumentation required can be complex and require significant capital investment. In this chapter, we consider what instrumentation is necessary for each technique and what could be done to both simplify and improve the ASAT technique in a combined instrument that solves many of the complexities in experimentation. Experimental conditions such as vacuum pressure, cryogenic temperatures, electron imaging and diffraction, laser wavelength and positioning, and specimen holder designs must all be taken into account.

A burgeoning number of research studies are emerging where scientific questions are being successfully addressed because of the combination of information revealed from atom probe microscopy and density functional theory (DFT). Situations where high-quality experimental data alone would not wholly answer the question at hand and, equally, situations where atomistic simulations would have no obvious starting place were it not for the atom probe. Atomic-scale analytical tomography holds great potential to expand the realm of mediation between experimentation and computer simulation of materials properties. Any model framework is applicable, but we have delved into detail for the case of DFT because it is a self-consistent theory that has arguably the most immediate and exciting intersection with ASAT data.