Experimentally Driven Automated Machine-Learned Interatomic Potential for a Refractory Oxide

Understanding the structure and properties of refractory oxides is critical for high temperature applications. In this work, a combined experimental and simulation approach uses an automated closed loop via an active learner, which is initialized by x-ray and neutron diffraction measurements, and sequentially improves a machine-learning model until the experimentally predetermined phase space is covered. A multiphase potential is generated for a canonical example of the archetypal refractory oxide, ${\mathrm{HfO}}_2$, by drawing a minimum number of training configurations from room temperature to the liquid state at $\sim 2900°\mathrm{C}$. The method significantly reduces model development time and human effort.

Figure 1

The experiment driven workflow. (1) Experimental high energy x-ray and neutron diffraction patterns are measured over a wide temperature range using a uniaxial laser heating system on an aerodynamically levitated ${\mathrm{HfO}}_2$ sample. (2) Cluster-based active learning enables exploration over a wide range of phase space. (3) Iterative training and fitting methods provide feedback into (2).

Figure 2

Unit cell volume of the monoclinic (pentagon), tetragonal (triangles), and cubic (squares) forms of hafnia measured in an argon atmosphere. Open symbols represent mixed phases and solid symbols are single phase. The cubic form was only observed as a mixed phase with the tetragonal polymorph. The average cell volume estimates from GAP MD simulation for $\mathrm{m}\text{−}{\mathrm{HfO}}_2$ and $\mathrm{t}\text{−}{\mathrm{HfO}}_2$ with an isothermal-isobaric ensemble are shown as green stars with error bars.

Figure 3

Diffraction versus simulation data for (a) x-ray diffraction patterns compared to the GAP MD computed x-ray intensity ($\lambda =0.123–59\AA$) for the two high temperature phases. (b) Experimental and simulated x-ray structure factors for amorphous and liquid ${\mathrm{HfO}}_2$. (c) Experimental and simulated neutron pair distribution functions for the pure phases of ${\mathrm{HfO}}_2$.