The human brain is highly capable of interpreting the 3-D world in which we live. Not only do we continuously navigate 3-D spaces, but we can visualize in our mind what an object would look like as we spin it around. This advanced 3-D perception ability has evolved over eons out of the need to be able to function in the complex world around us.

It has only recently become possible to look at the internal structure of engineering materials in a way that is “natural” to our brain (i.e., in 3-D).

Looking inside a material to determine its microstructure – or the arrangement and shapes of phases and grains and the underlying structure of defects – requires some rather advanced characterization tools, but the basic principles are straightforward.

There are two main approaches: one nondestructive and the other destructive. Imagine having a complex but transparent object. Its transparency allows us to look inside to see how things are organized so that we can figure out how the object functions (think of plastic models of combustion engines or the human body). Metals are not transparent to visible light, but we can use high-power X-ray beams to penetrate through the material and thus reveal its interior structure. This is commonly known as X-ray computed tomography, or XCT.

The word tomography has a Greek origin and loosely means “to image by cutting or slicing.” By recording images of a material sample as we rotate the sample around an axis, we obtain a series of projections known as a sonogram. Using advanced mathematical techniques, one can convert those projections into a 3-D object representing the material’s internal microstructure.

The process is very similar to a medical XCT scan. In our labs at Carnegie Mellon, we have the ability to perform XCT experiments with a spatial resolution of a few tens of nanometers on samples with a volume of only a few thousand cubic micrometers. For larger samples, we often make use of the beam line facilities at national laboratories. The sample is not damaged during a scan, so we can repeat the measurements while changing the external conditions (e.g., heating, cooling, deforming).

Another way to look at the internal structure of an object is to cut into it and see what’s there. If we want to know the shapes and sizes of the holes in a block of Swiss cheese, we could take a sharp knife and cut parallel slices from the block; if we take a picture of each slice and put those pictures together using an image-editing program, we can then reconstruct what the internal structure of the block of cheese looks like. It is then only a small additional step to determine statistical distributions of hole sizes and densities, or the spatial correlations of the holes.

This type of serial sectioning is obviously destructive, but it allows us to obtain very high-quality 3-D reconstructions of complex microstructures. Typically, we use a focused ion-beam instrument, like a scanning electron microscope equipped with a high-energy ion gun that provides the “knife” to cut through the material.

In our facility at Carnegie Mellon, we have two such instruments: one with a Gallium ion beam and the other using Xenon ions. They are in almost continuous use for the study of 3-D microstructures in both metallic (magnesium alloys, superalloys) and ceramic (strontium titanate, solid-oxide fuel-cell components) systems.


A Deeper Dive into Professor De Graef’s Research

Over the past two decades, Prof. De Graef’s research group has been at the forefront of developing the numerical tools that allow us to convert raw experimental data from serial sectioning experiments into accurate 3-D reconstructions. This requires algorithms to align individual slices and to extract from each slice the different microstructural components, a process known as segmentation.

'The figure shows a typical two-phase microstructure in a Ni-Cr-Al superalloy, in which ordered intermetallic precipitates are densely packed inside a disordered matrix. It is this dense packing that gives rise to the outstanding creep resistance at elevated temperature, enabling the use of these materials in the extreme conditions encountered in modern jet engines.