Craters formed by meteorites, projectiles, or other large objects are easily visible to the naked eye. However, even a single atom, when it hits a solid metal surface, can form a microscopic crater. These craters of different size scales are similar in shape, but their formation mechanisms are quite different.

Virtual collisions

Juha Samela and Professor Kai Nordlund, both from the University of Helsinki, have been applying molecular dynamics to investigate the formation of craters. In other words, they have created virtual collisions by letting gold atom clusters of different sizes collide into gold substrate and argon clusters into silicon oxide substrate, and then simulated the many-atom interactions during the collisions.

“This helped us to understand what level of interaction is needed between atoms before massive structural alterations are initiated, such as crater formation and material displacement from the crater,” Juha Samela explains.

The colliding argon and gold atom clusters contained from about 1000 to more than 100,000 atoms. They hit the surface orthogonally at a velocity of approximately 20 km/s, which corresponds to the speed of micrometeoroids in space.

One of the basic questions in natural sciences is the scale at which mathematical laws apply. In previous studies concerning crater formation, the sizes of colliding particles have varied from the size of an atom to asteroids with a diameter of tens of kilometers. It is clear that the formation of craters by only a few atoms does not follow macroscopic scalability. However, the question remains as to when a microscopic collision becomes macroscopic.

Different formation mechanisms

In macroscopic (involving large atom clusters) impacts the colliding atom cluster and the substrate immediately under it are first compressed into a very small volume. In the next phase, this densification expands explosively, forming a semispherical crater. Since the collision energy is retained in the densification, the crater size corresponds to the amount of collision energy, in other words, the greater the cluster colliding, the larger the crater being formed.

In microscopic collisions, atoms of even small atom clusters can move between the atoms of the target substrate, sometimes deep into the substrate. No essential densification is formed. The kinetic energy of the collision is divided between the atoms of the target substrate, and the atoms keep colliding with each other. At the collision area, the substrate becomes either liquid or gas, is displaced from the target substrate leaving a crater behind. The size of the crater is quite differently scaled in relation to the collision energy than that formed in macroscopic collisions.

“There is wide variation in microscopic collisions. There are several different mechanisms, and variation depends on the size of the colliding cluster and the pressure caused. The basic mechanism resembles radiation, as in gamma radiation penetrating a target substrate," Samela explains.

Transition by using gold, silicon oxide, or other atoms

Samela and Nordlund increased the size of the colliding atom cluster to determine the size class at which the colliding mechanism changes from microscopic to macroscopic particle collision. In the case of gold, the transition to macroscopic collision behavior occurred when the colliding cluster contained approximately 10,000 atoms.

The structure of the target substrate has a significant effect on the results of the simulated collisions. Scalability laws do not remain the same for the different atomic substrates being simulated.

In the computational experiments, gold represented a crystalline metal surface, and the experiment was continued with amorphous silicon oxide. Silicon oxide was chosen because it represents ordinary terrestrial soil and bedrock. In amorphous material the average material atom concentration is constant, but atoms are at random positions within the limits defined by their interaction.

When a sufficiently large argon cluster was collided with silicon oxide substrate, simulations showed a compressed zone in front of the cluster. However, the atom concentration in silicon oxide is lower than in gold, and argon atoms are lighter than gold atoms. Therefore, the densification was not as dense as in gold collisions and more of its energy was released dissipated away from the substrate than into the substrate. Consequently, the crater size scaled almost macroscopically, but some microscopic scaling was still observable when the colliding cluster contained more than 100,000 atoms. Hence, the transition into macroscopic collision behavior was more gradual than with gold.

Argon is a noble gas and was chosen for two reasons.
“Firstly, argon can be modeled relatively easily, because as an inert gas, it does not react with silicon or oxygen. Secondly, cluster sources can be used to generate argon clusters, and corresponding collisions can be experimentally observed and the results can be compared,” says Samela. Göteborg University is conducting experimental argon-graphite collisions, and Samela is simulating the collisions and seeing how they compare to his own studies.

The studies also clarified, whether a high-energy impact causes crack propagation in the normally fragile silicon oxide. No cracks were observed in simulations. This may have been due to the fact that the amorphous material models describing the interactions cannot produce real-world crack propagation.

Ultra-modern simulations

Basic research is research carried out to increase the understanding of fundamental principles. It is usually driven by a researcher’s fascination, without immediate ideas about applications. Samela explains his own interest:
“Molecular dynamics is a good method for studying this topic. A collision is a mechanical event. Atoms are like ping-pong balls; they collide with each other freely. This colliding is free of, for example, electronic phenomena, which would prevent the use of molecular dynamics.”

“In terms of philosophy, crater formation is an example of a phenomenon in which interaction between atoms produces a macroscopic phenomenon, visible to the naked eye. At this phase, research is conducted at the borderline between quantum mechanical interaction of atoms and the visible world.”

Currently Juha Samela works as an independent researcher. Previously he worked as a post-doc researcher at the Division of Materials Physics at the University of Helsinki. Now he is no longer employed as a researcher but has a partnership in a consulting business and earns his living by developing public administration activities. For Samela, physics research is a self-financed hobby. The University of Helsinki provides resources, such as library services and trips to conferences, and Samela has access to CSC’s computing resources through the University of Helsinki.

Samela says that he has thought a lot about application possibilities for his research.
“Studies on crater formation and interaction between atoms in collisions can enhance, for example, development of applications that use particle sprays based on atom clusters.” Cluster-ion beam radiation can be used to treat surfaces and rework nanostructures. It is important to understand the collision mechanisms involved with different-sized individual atom clusters in order to understand the overall effects of cluster radiation.

“In this sense, simulations must precede development, so that they help predicting what kind of phenomena can be dealt with in 10 – 20 years time,” says Samela.

But there are also immediate application targets for the research results. Collisions with micrometeoroids are very dangerous for spacecraft, and the research of Samela and Nordlund on collisions of very fast atom clusters and crater formation can be applied to research into surface damage caused to spacecraft. The research also helps to understand the surface phenomena occurring on non-atmospheric planets and moons.

“It has been suggested that micrometeoroids have influenced protein synthesis on the Earth and thus the emergence of life itself. This is rather a far-fetched application, I admit,” says Samela.

In some recent studies published within the past few years, methods have been developed that help to reach conclusions regarding relaxation mechanisms in metals, based on the results attained via molecular dynamics. These mechanisms last so long that direct simulations would be impossible. Samela and Nordlund were able to apply molecular dynamics to simulating macroscopic collisions and were able to explain phenomena in these collisions, starting from the atomic-level structure: cracks, crater formation, bending, and surface transformations.

“By combining the results from collision simulations with these new computation techniques, at least in principle, we could now also simulate the slow phenomena occurring after the collision," Samela reflects.

Image: A continuum-like illustration of a macroscopic collision of a gold cluster colliding at 20 km/s with a gold substrate. First (Fig. 1), the gold substrate under the impact is strongly compressed by the colliding cluster. The following images show how the densification and the pressure wave spread, and the crater starts to form. Fig. 5 shows clearly how a semispherical crater has been formed, and Fig. 6 shows one more pressure wave emanating from the crater. In Fig. 7, large sputtered clusters of gold are broken off the substrate. The times for the pictures were: 1 picosecond (ps), 2 ps, 3.5 ps, 6.5 ps, 16 ps, 23 ps, and 42 ps. One picosecond equals one trillionth of a second (10⁻¹²). © Matti Gröhn and Jyrki Hokkanen, data Juha Samela and Kai Nordlund.

The Crater project

The simulations in the Crater project led by Juha Salmela and Kai Nordlund were carried out on CSC’s Louhi supercomputer, with the Parcas molecular dynamics simulation package. The MD-MC/CEM interaction model, previously found to produce relatively good results in collision simulations, was used to describe interactions between gold atoms. Silicon oxide was described with the Watanabe potential model, which is particularly suitable for describing silicon oxide behavior under high pressure.

The metal crystal structure for use as target substrate is easy to form.  Artificial formation of amorphous substrate, such as silicon oxide used in this case, requires special caution and care. The Wooten-Wiener-Weare method was used to form the silicon oxide substrate used in this study. The resultant dense structure corresponds relatively well to natural silicon oxide, which is a good basis to guarantee reliability of the simulation results.

Collision regions must be sufficiently large to prevent shock waves created due to the collision from being immediately echoed from the crater rims and hence, interfering with the simulation results. The target substrate regions comprised more than 100 million atoms over an area of 15x15 nanometers. The size requirement is the very reason why so much computing capacity was needed. The Crater project of Samela and Nordlund was classified as one of CSC’s Computational Grand Challenge projects. The Grand Challenge projects are aimed at high-impact scientific research, and the GC calls are arranged twice a year. The Crater project used approximately 700,000 processor hours (80 years) of estimated total computation time.