Dr Raquel Lizárraga from the Royal Institute of Technology (KTH) together with two experts from academia and industry, Professor Levente Vitos from KTH and Dr Erik Holmström from Sandvik Coromant, discuss the success of density functional theory in aiding the design of innovative materials.
A piece of matter contains billions and billions of atoms. It is only natural, then, that it is a rather big problem to describe their behaviour. The work of Walter Kohn and others opened up a path to help us in the quest to master the size of this problem. His work led him to lay the basis of density functional theory and culminated with him receiving the Nobel prize in Chemistry in 1998. However, the legacy of that work is still revealing itself to us.In the middle of 1960s, when the celebrated work of the physicists Walter Kohn, Pierre Hohenberg, Lu Jeu Sham1 and others introduced a way to calculate the energy of complex quantum mechanical systems, like a chunk of iron or precious diamonds, computers were not the household goods they are today. The possibility to use a computer to simulate the behaviour of materials was not on the map just yet. Today, however, the advent of large and fast supercomputers has enabled us to investigate the physical properties of materials using their Nobel prize theory: density functional theory (DFT).
The fact that one can study any material, existing or not existing, using DFT is one of its major strengths. Because DFT does not need experimental inputs, it can be used as an exploratory tool for searching for new materials. If, say, someone is interested in searching for a material to manufacture a strong magnet, then a suitable criterion for such a material is to have high atomic magnetic moments and high magnetic anisotropy so that its magnetic response is strong. One can scan a large span of materials and calculate these properties using DFT. Candidates fulfilling the initial criteria can be then handed over to materials developers to be tested thoroughly.
The gain is tremendous. Firstly, it avoids expensive and time-consuming laboratory tests over a large range of materials. Experimental efforts can focus on those previously DFT-scanned materials that are really interesting and promising for the products that they are intended for.
Secondly, DFT can be used to analyse physical trends in large set of materials to learn how to tune their properties so one can better use them. Most importantly, materials that have not yet been synthesised can be equally investigated by DFT, which is a fantastic avenue to innovation.
The quantum mechanical interactions between atoms
The understanding that comes from fundamental research about what goes on inside materials, the quantum mechanical interactions between atoms, is of great importance in predicting the properties of materials and, eventually, tuning them to achieve the desired effect on the application being designed.
Researchers at five prestigious research institutions in Europe – the Royal Institute of Technology (KTH), Uppsala university, Darmstadt university, Milano-Bicocca university and Radboud university – are experts in DFT and have formed a network of infrastructure funded by the European Institute of Innovation and Technology (EIT) Raw Materials. The project is called ‘Designing materials with quantum mechanics’ (QM-FORMa), and is being led by Dr Lizárraga.
QM-FORMa aims to raise awareness of the capabilities of DFT and how they can be used when designing materials with special properties that fit the needs of modern industry.
Substituting toxic materials
A long term goal of QM-FORMa is to assist companies to better understand their products to design the materials that those products require. One of the biggest problems of our society is to deal with the contamination of our environment, and this comes together with a significant need to replace materials that no longer comply with today’s anti-pollution regulations – as was the case of lead in gasoline, which was finally banned in USA in 1990s. In many cases which require the substitution of hazardous materials, there is no easy solution, and it is in the list of priorities in Europe and many countries elsewhere to deal with the substitution of toxic materials.
QM-FORMa has been involved in the investigation of one of such problem – the replacement of cobalt in cemented carbides. Researchers at KTH have proposed a multi-component alloy to substitute cobalt.2 These so-called ‘high entropy alloys’ are made of five or more elements in nearly equal concentrations and have only recently started to attract the attention of the scientific community thanks to the work of Yeh and Cantor.3
However, they have not yet been used in practical applications. DFT has contributed enormously to the study of these materials in order to reach the sufficiently developed stage needed for them to be utilised in the manufacturing of a product. In their investigation, researchers at KTH identified the structural phase transition of Co as a critical property to emulate in the alternative material. Using this as a criteria, they performed a set of DFT calculations to search for a good candidate. The selected alloy was then used to make a cutting tool that was tested in a real machining operation. The new cutting tool showed exceptionally high resistance against plastic deformation at all tested cutting speeds in the machining test, outperforming the reference Co-based tool.
In another related example of applications of DFT to real industrial problems, KTH researchers worked on the development of a quality control based on DFT calculations.
In the metal cutting tools industry that uses cemented carbides as a main material, the measurement of the magnetic saturation is employed as a measurement of a product’s quality. The magnetic saturation can reveal the amount of dissolved tungsten in the binder of the composite without destroying the sample. However, when the binder is replaced, which in cemented carbides is typically cobalt, the quality control needs to be changed as well. DFT calculations have been used by researchers at KTH to provide a quantum mechanical relation between the magnetic saturation and the components of the binder. Thus, a binder made of any complex alloy can then be tested quickly and inexpensively by using this expression.
A key aspect of these success stories is to identify a relevant property that can be used to mimic in an alternative material, and that can be used as a criterion to scan a large span of materials by means of DFT calculations. Often, this is not as simple as one may imagine due to the complexities of products and hence it is only possible if one has a deep understanding of both products and materials.
Closer collaboration between researchers and industry developers is needed. QM-FORMa is working towards a closer relationship with the industrial units, for example, our partner Sandvik Coromant. The strengthening of the collaboration is also fostered by the mobility action of the Swedish Foundation for Strategic Research (SSF), awarded to professor Levente Vitos. The results of this fruitful relationship is demonstrated in several ways: by new patents applications, the generation of new knowledge of products, and the opening up of new areas of interest.
During the three decades that followed the birth of DFT up until Kohn’s Nobel Prize, computer possibilities grew tremendously. Today, we face the challenge of materials being better equipped than ever before and computational capabilities continue to develop very quickly. That is why it is a smart approach to use the predictive power of DFT to design innovative materials to solve industrial problems.
1 P. Hohenberg and W. Kohn, Phys. Rev. 136:B864, (1964). W. Kohn and L. Sham, Phys. Rev. 140:A1133, (1965)
2 E. Holmström et al. Appl. Mat. Today 12:322-329, (2018); R. Lizárraga et al. Phys. Rev. Mat. 2:094407 (2018)
3 J. W. Yeh et al. Adv. Eng. Mater., 6:299-303, (2004). Cantor et al. Mater. Sci. Eng. A, 375-377:213-218, (2004)
Dr Raquel Lizárraga and Professor Levente Vitos
Department of Materials Science and Engineering
Royal Institute of Technology (KTH)
Dr Erik Holmström
Sandvik Coromant AB
+46 8 790 90 42