Mathematical methods help explain why liquid metals have wildly different breaking points

Modeling the breaking points of metallic glasses
A simulation of crack initiation in a metallic glass. The metallic glass on the left is initially more relaxed, due to a longer heat treatment, than the metallic glass on the right. The very different crack tip shapes and deformation patterns under the same external conditions result in a significantly reduced breaking resistance for the more relaxed glass. Credit: Courtesy of Christopher Rycroft, Berkeley Lab

Metallic glass alloys (or liquid metals) are three times stronger than the best industrial steel, but can be molded into complex shapes with the same ease as plastic. These materials are highly resistant to scratching, denting, shattering and corrosion. So far, they have been used in a variety of products from golf clubs to aircraft components. And, some smartphone manufacturers are even looking to cast their next-generation phone cases out of it.

But despite their potential, the of these substances are still a scientific mystery. One lingering question is why they have such wildly different toughness and breaking points, depending on how they are made. Although this may not be a huge concern for small applications like smartphone cases it will be extremely important if these materials are ever used in structural applications where they would need to support large loads.

Recently, Christopher Rycroft of the Lawrence Berkeley National Laboratory's (Berkeley Lab's) Division has developed some novel computational techniques to address this question. When Rycroft combined these techniques with a mechanical model of metallic glass developed by Eran Bouchbinder and his colleagues at Israel's Weizmann Institute, the two were able to propose a novel explanation of the physical process behind the large variations in breaking points of metallic glasses. Their results are also in qualitative agreement with laboratory experiments.

"We hope that this work will contribute to the understanding of metallic glasses, and aid in their use in practical applications. Ultimately, we would like to develop a tool capable of making quantitative predictions about the toughness of metallic glasses depending on their preparation method," says Rycroft.

Rycroft and Bouchbinder are co-authors on a paper recently published in .

What is a Metallic Glass? And, Why is it So Difficult to Model?

Scientists define "glass" as a material that cools from a liquid state to a solid state without crystallizing—which is when atoms settle into a lattice, or a highly regular spatial pattern. Because many metal lattices are riddled with defects, these materials "deform", or permanently bend out of shape, relatively easily. When crystallization does not occur, the atoms settle into a random arrangement. This atomic structure allows metallic glasses to spring back into shape instead of deforming permanently. And without the defects, some metallic glasses also have extremely efficient magnetic properties.

Rycroft notes that one of the biggest mysteries in condensed matter physics is how glass transitions from a liquid state to a solid state. To successfully create metallic glass, the metal has to cool relatively quickly before atomic lattices form.

"Depending on how you prepare or manipulate these metallic glasses, the breaking points can differ by a factor of 10," says Rycroft. "Because scientists don't completely understand how glass transitions from liquid to solid state, they have not been able to fully explain why the breaking points of these materials vary so widely."

According to Bouchbinder, computer models also have a hard time predicting the breaking points of metallic glass because the timescale of events varies dramatically—from microseconds to seconds. For instance, researchers can bend or pull the material for several seconds before it breaks, which occurs almost instantaneously. And the material's internal plastic deformation—the process where it irreversibly deforms—occurs on an intermediate timescale.

"We've actually been able to develop some numerical methods to capture these differences in timescales," says Rycroft, of the techniques used in the recent paper.

When Rycroft incorporated these methods into Bouchbinder's and calibrated it based on available data, the duo managed to simulate and better understand the breaking points of metallic glass alloys based on their preparation process. He notes that this model is rather unique as it combines novel and flexible numerical methods with recent insights about the physics of glasses. The simulations have also been able to predict the large decreases in toughness that are seen in .

"If you can vary the way is prepared in computer models and capture the differences in how it breaks, you can pose a reasonable explanation for why this occurs. This might also give you a better idea about how the glass transitions from a liquid to a solid, as well as the mechanical properties of a glass," says Rycroft. "We've essentially created something that might evolve into a tool for predicting the toughness of metallic glasses."

"For quite some time I've wanted to calculate the fracture toughness of metallic glasses, but knew that this was a very tough mathematical and computational challenge, certainly well above my abilities, and probably above the capabilities of conventional computational solid mechanics," says Bouchbinder. "I think that Rycroft's methods have opened the way to new possibilities and I am enthusiastic to see where this can lead us."

Explore further

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Journal information: Physical Review Letters

Citation: Mathematical methods help explain why liquid metals have wildly different breaking points (2012, November 26) retrieved 23 October 2019 from
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Nov 26, 2012
Could it be that metallic glass has very short strands of crystals arranged randomly? Then when a crack starts it is stopped almost immediately by short crystals arranged in different directions. This could also explain why they can take extreme bending and return to their original shape.

Nov 26, 2012
There is a "universal law" governing all condensed matter. One can quite easily write down a quantum mechanical equation that describe a collection of electrons and ions at a given thermodynamic state. It's just that the exact (or accurate) solutions are beyond our current capabilities except for some rather simple model cases.

AFAIK metallic glasses (and other glasses) do have short range order that resembles crystalline materials. But picturing them as a collection small randomly oriented crystals is not sufficient to explain the mechanical properties of metallic glasses, since in that case powdered metals would have similar properties. Unfortunately experimental methods that have access to medium range atomic structure are scarce. We know that there is no long range order, but no short range order and there's only one place we haven't looked at yet..

Nov 27, 2012
slight correction: but no short range order = but there is short range order

Nov 27, 2012
You don't need quantum mechanics to explain metallic glass. Explaining this is the same thing as the age old quenching of steel. As for comparing this to powdered metals, that just doesn't fit because in powdered metals the chemical bonds are broken. Do two or more steel bars bond? No. It would take a catalyst to reform the bonds in the powder metal or in the steel bars and heat is that catalyst.

Nov 27, 2012
Maybe I misunderstood what you mean by "very short strands of crystals arranged randomly"? That sounds like a powder to me. English isn't my first language and I'm not sure what a strand means in this context. If it means elongated crystallites, I'm rather certain that it would show up in diffraction experiments.

You do need quantum mechanics to properly explain why a given material has a given set of properties. But naturally this level of explanation is not necessary in many cases.

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