The Earth’s core is composed mostly of iron, which exists there at conditions well exceeding what can be reliably measured in the laboratory: the temperature is thousands of degrees Kelvin and the pressure is more then three million times the pressure at the Earth’s surface. As a consequence, the crystalline structure of the core material can only be estimated through inferences from seismic measurements. But knowledge of this structure is needed to inform theories of the Earth's evolution, aid understanding of its physical features (e.g., magnetic, gravitational fields), and guide interpretation of seismological measurements.
Researchers worldwide have turned to the computer to try to address this gap in our understanding, with the goal of computing from first-principles physics that which cannot be measured in the laboratory.
Efforts of computational chemists over the past decade have eliminated a key obstacle to realizing this vision, through the development of “density functional theory” (DFT), which provides a very accurate model of the atom-atom interactions. But that’s not enough. We need to understand how many atoms behave collectively in order to compute physical properties, and the crystal structures in particular. This is extremely difficult to do with with the necessary accuracy and precision using these DFT methods.
The group of David Kofke has broken through this problem and brought within reach the capability of first-principles calculation of the crystal structure of metallic systems, and iron in particular. Several advances come together to make this possible. Most significant is an innovative “harmonically mapped averaging” method that computes anharmonic behavior directly, eliminating noise from harmonic motion that is already well understood. They also introduce methods leveraging fast low-quality DFT methods to provide accurate data for high-quality counterparts. Additionally they make the key observation that small-system effects are largely restricted to easily computed harmonic behavior, allowing more expensive anharmonic features to be treated with relatively few atoms. All of this has allowed them to compute — purely from quantum physics — the free energy of hcp iron to within 2 meV/atom at Earth’s inner-core conditions. This is considered the threshold accuracy needed to distinguish the phases of crystalline iron.
The methods demonstrated by this application can be used to a much broader variety of problems. As materials of all types come to be studied on the computer as much or more than in the laboratory, new frontiers will open up both for the design of new materials and for study of behavior inaccessible to experiment (such as demonstrated for iron at the Earth’s inner core).
The work described here was completed by the joint efforts of Kofke with Research Scientist Andrew Schultz, postdoctoral fellow Sabry Moustafa, and Professor Eva Zurek of UB’s Department of Chemistry.