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Predicting Metallic Glass Formation

May 28, 2018

The recent passing of theoretical physicist, Stephen Hawking, on March 14, 2018, reminds us that many people with physical disabilities have contributed to human culture. Possibly the earliest example is the blind poet, Homer, who composed the Iliad and the Odyssey. Mathematician, Leonhard Euler (1707-1783), had impaired vision from age 30, and he was nearly blind at age sixty. His response to such disability was merely, "Now I will have fewer distractions," and his mathematical output was essentially undiminished.

German physicist, Gustav Kirchhoff (1824-1887), had limited mobility that required his use of crutches and a wheelchair for most of his life, but that didn't stop him from developing five significant discoveries; namely, Kirchhoff's circuit laws, Kirchhoff's law of thermal radiation, Kirchhoff equations of fluid dynamics, Kirchhoff's three laws of spectroscopy, and Kirchhoff's law of thermochemistry. I wrote about Kirchhoff in an earlier article (Kirchhoff–Plateau Problem, June 15, 2017).

Gustav Kirchhoff at a spectroscope

An experimental physicist in his natural abode, the laboratory.

Here, Kirchhoff is using a spectrometer of his own design.

(An illustration from the History of Physics by Poul la Cour and Jacob Appel, 1896, via Wikimedia Commons.)

Preminent electrical engineer, Charles Proteus Steinmetz (1865-1923), had the multiple birth defects of dwarfism, hunchback, and hip dysplasia. Despite these physical disabilities, Steinmetz was a prodigy in physics and mathematics. After his 1889 emigration to the United States, he discovered how magnetic hysteresis of transformer cores contributes to electrical power losses. While working at General Electric, Steinmetz designed the generators for the Niagara Falls power-generation station. I wrote about Steinmetz in an earlier article (Charles Proteus Steinmetz, May 3, 2012).

Charles Proteus Steinmetz

Charles Proteus Steinmetz (1865-1923).

Charles Proteus Steinmetz was born as Carl August Rudolph Steinmetz on April 9, 1865, in Breslau (now, Wrocław, Poland).

Upon emigration, Steinmetz changed his name, deciding that "Charles" sounded more American that "Carl." The added "Proteus" was a reference to the god of Greek mythology, Proteus (Πρωτευς), who would foretell the future to anyone who captured him, but he would change shape to avoid being captured. As a theorist, Steinmetz could be said to have foretold the future.

Since Steinmetz's father and grandfather had birth defects similar to his own, he decided he would never marry.

(Wikimedia Commons image)

Deafness afflicted American inventor, Thomas Alva Edison (1847-1931), some of whose many accomplishments I reviewed in several previous articles (Edison's Iron Mine, September 20, 2010, People Who Live in Concrete Houses..., June 30, 2011, His Master's Voice, August 15, 2011, and Edison's Nickel-Iron Battery Modernized, July 9, 2012). Deafness also afflicted biochemist and Nobel Laureate, Edwin Krebs (1918-2009), who collaborated on the identification of phosphorylation as the way that a small quantity of hormone can produce a large bodily effect.[1]

English materials scientist and metallurgist, William Hume-Rothery (1899-1968), was deaf, his total hearing lose caused by a viral infection just before his entering college in 1917. This didn't prevent him from achieving a First-Class Honours degree in chemistry as an undergraduate and his subsequent studies for his Ph.D. at the Royal School of Mines. In 1926, he devised his Hume-Rothery rules as an aid to determining how metals will mix to form alloys.[2] This was one of the first attempts at alloy system modeling.

Hume-Rotherey realized the importance of atomic size in the crystallization of materials. Chemically similar metals (chemically-similar defined as having the same crystal structure with atoms having the same valency and nearly equal electronegativity) will enter into substitutional solid solution if the size of their atoms differ by no more than 15%. If their size differs by more than this, there's a likelihood that secondary phases will form, some of which are detrimental to alloy strength. This is more likely when the electronegativity difference is large.

As we know from steelmaking, carbon easily dissolves in iron, but carbon atoms are very much smaller than iron atoms. The reason for this is that carbon is not substitutional, but interstitial; that is, the carbon atoms position themselves between iron atoms rather than replacing the iron atoms. Hume-Rothery's rule for interstitial substitution is that the atomic radius of the interstitial solute atoms should be less than about 60% the atomic radius of the solvent atoms. These Hume-Rothery rules, if proposed today, this would be an excellent data mining exercise.

This leads us to the problem of how to define atomic size. Xray diffraction allows us to examine the spacing between atoms in crystals to assess the atomic radii; but, as we find, the spacing does not give an identical atomic radius for the same chemical element in different crystals. It depends on such factors as the valence state, whether the chemical bonding in the crystal is covalent or ionic, and the number of neighboring atoms, which is called the coordination number. In order to "compare apples with apples," we need to use the proper atomic radii for the elements in our alloys.

Fortunately, some scientists have created tables that list the atomic radii for all these variations, the most popular of which is the listing of Shannon and Prewitt, which I've used in my own work.[3-4] As noted on Google Scholar, the principal Shannon paper has 43,526 citations. Today, these data are available online in an easily accessible format.[5] Example data for hafnium, with radii in Angstrom units, appear below.

Charge Coordination Covalent
4 IV 0.72 0.58
4 VI 0.85 0.71
4 VII 0.90 0.76
4 VIII 0.97 0.83

Atomic radius and electronegativity are simplistic concepts that give guidance, but there are more effective modeling techniques for prediction of alloy phases. In the 1970s, I designed computer models in which thermodynamic free energy was used to predict alloy phases. Since such thermodynamic data were limited, many approximations and rules of thumb were required. One such rule is Trouton's rule, which states that the entropy of vaporization, which is the enthalpy of vaporization divided by the normal boiling point, is about 75 J/mol-K.

As everyone has noticed, artificial intelligence is taking over the world, and it's been applied to the problem of predicting what compositions of elements will yield metallic glasses. In a similar fashion to the alloy-forming rules that I mentioned above, metallic glass compositions have been discovered using empirical rules, such as Turnbull's rule that metallic glasses form near deep eutectics in the alloy phase diagrams. Metallic glasses are amorphous, non-crystalline solids. Since some compositions exhibit low magnetic hysteresis, they're used to make energy-efficient transformers with an amorphous metal core. Some metallic glasses have a high magnetic permeability, so they are very effective electromagnetic shielding materials.

Scientists from the SLAC National Accelerator Laboratory (Menlo Park, California), Northwestern University (Evanston, Illinois), the University of Chicago (Chicago, Illinois), the University of South Carolina (Columbia, South Carolina), the University of New South Wales (Sydney, Australia), and the National Institute of Standards and Technology (Gaithersburg, Maryland) have applied machine learning techniques to the task of discovering metallic glasses. They report their progress in a free, open access paper in Science Advances.[6-8]

The motivation for this approach is the slow rate of progress to discovery of new metallic glass compositions by the traditional empirical techniques. The periodic table is teaming with elements, leading to numerous combinations that should yield millions of metallic glasses. However, only about 6,000 have been discovered.[7-8] They are hard to find, since they often contain three or more elements, and they are sensitive to processing technique.[6]

Such machine-learning requires an initial dataset. The research team used data from 6780 melt spinning experiments at 5313 unique compositions in the Landolt-Börnstein handbook, a compendium of fifty years of such data. This handbook contains 315 binary systems (25% of the possible binaries of the 51 examined elements) and spot data from 293 different ternary systems, with a bias towards data for the Al-La-Ni ternary.[6] As can be expected, this dataset is biased towards positive results, with 71% of listed experiments leading to amorphous metals.[6]

The research team combined taught a machine learning algorithm about conditions favorable to metallic glass formation with this initial dataset, and then proceeded with iterative high-throughput experiments to refine the algorithm.[6] The improved model was able to refine predictions for the Co-V-Zr alloy system, and it eventually discovered of metallic glasses in two previously unreported ternaries.[6] Says paper co-author, Apurva Mehta of SLAC, "We were able to make and screen 20,000 (compositions) in a single year."[7-8]

Metallic glass, machine learning predictions vs experiment

Metallic glass, machine learning predictions vs experiment. (SLAC National Accelerator Laboratory image by Yvonne Tang.)

Says Jason Hattrick-Simpers, a materials research engineer at NIST and an author of the paper,
"One of the more exciting aspects of this is that we can make predictions so quickly and turn experiments around so rapidly that we can afford to investigate materials that don’t follow our normal rules of thumb about whether a material will form a glass or not... AI is going to shift the landscape of how materials science is done, and this is the first step."[7-8]

This artificial intelligence approach has paid off, since the discovery rate for metallic glass increased from about 0.25% of samples tested to nearly 50%.[7-8] This study was funded by the US Department of Energy, the Center for Hierarchical Materials Design at Northwestern University, and the National Institute of Standards and Technology.[7-8]


  1. Neeraja Sankaran, "Scientists With Disabilities Must Confront Societal As Well As Physical Challenges," The Scientist, January 23, 1995.
  2. W. Hume-Rothery, "Research on the nature, properties and conditions of formation of intermetallic compounds, with special reference to certain compounds of tin," J. Inst. Metals., vol 35 (1926), pp. 295-307.
  3. R. D. Shannon, "Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides," Acta Crystallographica Section A, vol. 35, no. 5 (September, 1976), pp. 751-767.
  4. R. D. Shannon and C. T. Prewitt, "Revised values of effective ionic radii," Acta Cryst., vol. B26, no, 7 (July 15, 1970), pp. 1046-1048, https://doi.org/10.1107/S0567740870003576.
  5. Database of Ionic Radii, Atomistic Simulation Group, Materials Department, Imperial College.
  6. Fang Ren, Logan Ward, Travis Williams, Kevin J. Laws, Christopher Wolverton, Jason Hattrick-Simpers and Apurva Mehta, "Accelerated discovery of metallic glasses through iteration of machine learning and high-throughput experiments," Science Advances, vol. 4, no. 4 (April 13, 2018), Article no. eaaq1566, DOI: 10.1126/sciadv.aaq1566. This is an open access article with a PDF file here.
  7. Artificial intelligence accelerates discovery of metallic glass, Northwestern University Press Release, April 13, 2018.
  8. Glennda Chui, "Scientists Use Machine Learning to Speed Discovery of Metallic Glass," SLAC Press Release, April 13, 2018.

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