Through the looking glass

For the past month, I’ve been living in Berkeley, California to run experiments at Lawrence Berkeley National Laboratory (LBNL). I miss my friends at Penn State, my bed, and my daily routine back home, but working at Berkeley certainly has its perks: good weather, good food, and the opportunity to be part of a community that lives and breathes science.

Although the primary reason I take trips to Berkeley is to use their world class facilities, I find that my West coast productivity is not necessarily due to the equipment I get access to, but rather the people I meet, the conversations I have with co-workers over lunch, and the opportunities around campus such as User Meetings and seminars that expose me to new areas of research and creative ideas that I would otherwise never be challenged to think about.

Today, I attended a talk by Mary Scott, assistant professor of materials science and engineering at UC Berkeley and faculty scientist at LBNL, entitled Advancing Electron Microscopy to Atomic Resolution 3D. I enjoyed this talk not only because of the science behind it (imaging individual atoms in three dimensions is kiiiiind of amazing), but because I thought Dr. Scott’s presentation of the work was particularly clear, starting with an overview of the technique followed by an emphasis on the technology at LBNL that made the work feasible and ending with a few examples of materials that the technique has helped us better understand. Because I took a ton of notes, and because I’m procrastinating doing my real work, here’s the low-down:

Before I begin, let me just give a super quick explanation of transmission electron microscopy (TEM). Imagine a light microscope — except instead of light, you have electrons, and instead of glass lenses, you have electromagnetic lenses. It’s also a lot bigger and way more expensive (if you don’t believe me, see below). The electromagnetic lenses guide a high voltage electron beam down the microscope column and through your sample, creating a two-dimensional black and white image. Due to the tiny wavelength of an electron, TEM is capable of imaging to much greater detail than light microscopy, with the most advanced instruments reaching sub-angstrom resolution. That’s less than 1/1,000,000 of the diameter of your hair!

Left: Me at a science museum playing around with a microscope that was definitely meant for kids…Right: Me climbing a ladder in order to load a sample in one of the TEMs at Berkeley Lab’s National Center for Electron Microscopy.

Dr. Scott and her group take this to the next level — instead of just electron microscopy, they do electron tomography. In this extension of TEM, rather than just taking one image and being done with it, the user will tilt the sample ever so slightly and take another image. Tilt again, take another image. Tilt again, take another image, so on and so forth (for 8 hours, apparently!) until a full tilt series, typically positive to negative 60 or 70 degrees at an increment of 1 to 2 degrees, is collected.

But now comes the hard part. How do we convert all these 2D images into a 3D structure? While there are different algorithms for doing this, Dr. Scott uses GENFIRE — whoever came up with that name is pretty rad, and it stands for GENeralized Fourier Iterative Reconstruction. The first step in this process is the creation of what’s called a Fourier grid. Basically, we take the Fourier transform of each 2D image, where each 2D Fourier transform is a plane slicing through the origin of the Fourier transform of the 3D object. Then, the algorithm will iterate back and forth between real space and reciprocal space until a solution that is both consistent with the collected images and general physical constraints is reached. If you’re a math whiz and want to understand this algorithm in more detail, I’d recommend checking out this paper. Luckily, it is also licensed under Creative Commons (yay for open access), so I’ve included a lovely summary figure of the algorithm from the paper below!

Workflow for GENFIRE! (I feel like the name warrants an exclamation point at the end of it.) The algorithm creates a Fourier grid, which it then iterates in real space and Fourier space until a global solution is reached.

In the last part of her talk, Dr. Scott summarized two examples in which this technique has been employed. The first example culminated in the 3D coordinates of 3,769 individual atoms in a tungsten tip. With this 3D map in hand, the authors were able to measure strain in the material by calculating an average structure and then looking at each atom’s deviation from this average. I think this example highlights one of the most important benefits of this technique: while many 3D characterization techniques such as X-ray crystallography are capable of seeing average 3D structures, only atomic resolution tomography can see local deviations from the crystal lattice without any assumption of the internal structure.

In her final example, Dr. Scott discussed the 3D atomic imaging of iron-platinum, an intermetallic compound with a promising future in next-generation magnetic data storage. In order to better understand the chemical order/disorder that is so crucial to the properties and functionality of this material, the authors determined the 3D coordinates of 6,569 iron and 16,627 platinum atoms in an iron-platinum nanoparticle.

Good science always comes from collaboration, though. Besides the researchers collecting the tilt series and running reconstruction algorithms, Dr. Scott emphasized that the piezo-driven stage developed at LBNL at the National Center for Electron Microscopy is essential for this type of experiment, as the needle geometry allows angles of tilting and precise control that are not feasible with a conventional holder.

I can’t find my keys half the time, yet scientists at Berkeley are pinpointing the locations of thousands of atoms within tens of picometers. All I can say is, I hope their brilliance rubs off on me while I’m here! 😊