Interview of Professor David G. Pettifor by Bernadette Bensaude-Vincent

Director of Materials Modeling Laboratory, Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK

December 13, 2002

David Pettifor - Professor Hirsch told me that you might be interested in the fact that I wrote a short biographical sketch about the founder of our department, William Hume-Rothery (H-R).  When he died in 1968 the TMS (The Minerals, Metals and Materials Society) in America set up an award, the William Hume Rothery Award for distinction in the science of alloys.  This award has been given out every year.  At the time of the millennium they decided it would be nice to have a special symposium to evoke H-R’s science.  Since I am based in Oxford, I was asked by the Committee to give a presentation, a biographical sketch.  That was very interesting for me.

Bernadette Bensaude-Vincent - What is your background, in physics or chemistry?

David Pettifor - I had registered at University to read Chemical Engineering, because I loved the chemistry laboratory at school.  Fortuitously, I bumped into my old physics teacher just before the start of the university year, who persuaded me that physics was the most fundamental of the sciences.  So I changed my mind and went into physics.  I did my first degree in South Africa at the University of the Witwatersrand in Johannesburg, where Professor Frank Nabarro had built up a strong department of physics.  I found my first three undergraduate years of classical physics pretty boring, being challenged mainly by some inspiring young lecturers in the Mathematics department.  Fortunately, in my honours year we had excellent lectures in quantum mechanics and solid state physics.  I was awarded a National Postgraduate Scholarship and came over to Cambridge at the Cavendish Laboratory in October 1967 to do my Ph.D. with Volker Heine in theoretical condensed matter physics.  By the time I visited Oxford as a graduate student, H-R had already died, so that I never met him.  So I found it intriguing to research a bit into his life and science, using manuscripts and correspondence in the Bodleian Library and interviewing his daughter Jennifer Moss.  Here is the paper (D.G. Pettifor, <<William Hume-Rothery: His life and science>>, in E.A. Turchi, R.D. Shull, A. Gonis eds. The Science of Alloys for the 21^st Century: A Hume-Rothery Celebration, TMS, 2000, p. 10-32).  H-R was the holder of a professorial chair in metallurgy endowed by the Wolfson Foundation.

Bernadette Bensaude-Vincent - What is the Wolfson Foundation?

David Pettifor - Isaac Wolfson was a merchant trader in Manchester who set up Great Universal Stores (GUS), a mail order company, in the interwar period.  He became very wealthy and was interested in supporting science and education.  For instance, there is a Wolfson College in Cambridge and one also in Oxford.  H-R got the first Isaac Wolfson Chair in 1966.  Now there are Wolfson Chairs in various other universities around the UK.

H-R basically was a chemist.  He did his undergraduate degree in Oxford.  You know the story: he was totally deaf.  His family wanted him to enter a military career but meningitis contracted in 1917 left him totally deaf.  He wanted to go to Trinity College in Cambridge where his father had been.  But Trinity wouldn’t accept him because he was deaf.  He then came to Oxford’s Magdalen College in 1918 to read Chemistry.  On the advice of Frederick Soddy, he went to do his Ph.D. at the Royal School of Mines at Imperial College, London.  He worked in Metallurgy with Professor Harold Carpenter.  He specialized in the stability of intermetallic phases.  They do not follow normal valence rules.  In seeking for a solution to the stability of intermetallic compounds, H-R developed the concept of electron concentration as a controlling factor in structural stability.  He got his Ph.D. from the University of London in 1925.  In that thesis he came up with his famous electron per atom rule for the structure of noble metal alloys with sp-valent elements.  At that time chemists had simple chemical valence bond rules.  For instance, sodium chloride forms a stable octet system NaCl.  So how to explain that intermetallics had crazy stoichiometries, like the sodium tin phases Na₄Sn, and Na₃Sn₂?  That was the start of the so-called Hume-Rothery rules.  That was seminal work.  [The <<Hume-Rothery rules>> on alloy phase behaviour were published in the early 1930s.  The first two rules emphasize the importance of the atomic size factor and the electrochemical fact respectively, whereas the third rule concerns the role of the electron concentration (or electron per atom ratio)].  In Oxford the chairs have to be attached to colleges.  Because metallurgy was considered as a ‘dirty’ subject it was not attached to a proper, well-established college.  St. Edmund Hall, on the other hand, was a very poor college, a not well endowed college.  In the 1950s, they were trying to build up their reputation academically rather than just being famous for their rugby players and oarsmen.  So when the metallurgy professorship was passed round the colleges, St. Edmund Hall picked it up so that the Isaac Wolfson chair is held at St. Edmund Hall.  H-R was there, then Sir Peter Hirsch was there and I am there now.  In retrospect, it has brought great prestige to the College because all the metallurgists at St. Edmund Hall have been elected fellows of the Royal Society.

Bernadette Bensaude-Vincent - Is metallurgy still prestigious now?

David Pettifor - As you know, during the past forty years metallurgy departments around the world have transformed to embrace materials in general.  This is reflected in the history of our own department where the undergraduate course was re-titled ‘Metallurgy and Science of Materials’ shortly after the arrival of Sir Peter Hirsch as the new Isaac Wolfson Professor in 1966.  Then shortly before his retirement in 1992 the name of the department was changed to simply ‘Department of Materials’.  Nevertheless, metallurgy still plays a key role in the department with outstanding, internationally-funded research being performed on developing new process routes for metals and alloys.  When this department was created industrial sponsors wanted undergraduate programs to train people for industry rather than the setting up of a purely research institute.  In practice, our undergraduate numbers have always remained small (around 30) in comparison to the physicists, chemists and engineers with their annual intake of two hundred students each.  Our sizable faculty is heavily supported by our successful graduate programs and postdoctoral research.  Expansion to the green-field site at Begbroke was successfully carried through by our previous Head of Department, Brian Cantor, who persuaded the university several years ago to buy a recently constructed but then vacated laboratory 5 miles outside of Oxford.  It is where we have spin-off companies with young researchers.  The Oxford department is by far the top materials department in the country according to the latest research assessment exercise that the UK universities had.  That is also true for teaching.  It is not however, the biggest one.

Bernadette Bensaude-Vincent - Which is the biggest one?

David Pettifor - This depends on how the counting is done, as many courses are joint with engineering departments.  But, on undergraduate numbers, Birmingham, Imperial College and Manchester would be amongst the front runners.

Bernadette Bensaude-Vincent - Could you go back to the beginning of your own career?

David Pettifor - At the time I joined Heine’s group, the measurement and calculation of the band structure of how electrons move in materials was a major topic. I was given the project to develop an electron theory to explain the structure of transition metals.  It was a theoretical project but it was a well known experimental fact that if you go across the transition metals series from yttrium to zirconium, niobium, molybdenum, technetium, ruthenium, rhodium and palladium the structure changes from hexagonal close-packing to a body centric cubic packing, back to hexagonal and then cubic close-packing.  There was a theory, the so-called Engel-Brewer theory, that correlated the crystal structure of metals with the number of valence s and p electrons in the system.  H-R did not believe in it.

At that time the Cavendish Laboratory in Free School Lane was a very exciting place to work.  Phil Anderson, who later got the Nobel prize with Mott, spent 6 months in Cambridge each year.  Brian Josephson, who got the Nobel Prize for superconductivity, was the young star in our group. And Sir Nevill Mott was the fantastically charismatic leader of the Cavendish. They used to come to the seminars and inspired us younger researchers.  Well I  was very fortunate to be able to crack the problem I had been set, showing unambiguously that the structural trends across the transition metal series were driven by the changing number of valence d electrons, not the s and p electrons as claimed by Engel and Brewer.  This work brought me for the first time directly into contact with the metallurgical community, in particular Larry Kaufman and his CALPHAD group who were developing a semi-empirical thermodynamic technique for predicting the phase diagram behaviour of multicomponent alloys.  After completing my thesis, I then went down to London as a post-doc in the Physics Department at Imperial College.  I had still not resolved my future career path, so shortly afterwards I went off to Tanzania to teach on a two-year contract at the University of Dar es Salaam.  I did not want to go back to South Africa.  In South Africa I was involved in student politics.  I didn’t want to go back as a white liberal.  After two years in Dar es Salaam, I realized that emotionally and scientifically I wanted to work in Europe or in America.  I returned to Imperial College for a year, then back to Cambridge as a post-doc for 4 years.  During that time I did my work on the binding energies of the transition metals, performing some of the first-ever Density Functional Theory (DFT) calculations of total energies.  In 1978 Bell Labs invited me for 6 months as a visiting scientist.  I went to Bell Labs clearly with the idea of sorting out the underlying theory for the heats of formation of metallic alloys.

Bernadette Bensaude-Vincent - Well this was more or less like physics. When did you shift from theoretical physics to materials science?

David Pettifor - I think I’ve never shifted in the true sense.  I come from physics, but I have always had a very broad vision that encompasses the ‘dirtier’, more complex world of the metallurgist or materials scientist.  I deal with atoms and electrons.  My colleague Adrian Sutton has been educated in this department.  He is a materials scientist.  He is more in tune with the microstructure, the mechanical properties of materials, which for myself have never been really close to my heart.  I am much more into the chemistry, the growth of films, into the nanotechnology.  My research starts from the fundamental quantum mechanical Schroedinger equation, but I have always enjoyed the challenge of extracting the essential physics, making simple models for explaining, for instance, the heats of formation. If you mix atom A with atom B, Pauling would say that a charge flows from the more electropositive atom to the more electronegative atom, thereby setting up an ionic bond.  Therefore, if you have just this attractive ionic term, elements A and B should always mix.  In practice, nearly half of all binary systems do not mix.  In the mid seventies a Dutch physicist who worked at Philips, Andreas Miedema, came out with a simple generalization of the Pauling predictions for the heats of formation.  You don’t have just an attractive term but also a repulsive term and by a very clever adjusting of the parameters he could separate the sheeps from the goats, he could separate the alloys with positive heats of formation from those with negative heats of formation.  Still the concepts he was pushing were ionic.  My early expertise was in metals where concepts of ionicity and the ionic bond do not really make any sense due to the perfect screening by the conduction electrons in a metal.  Whilst I was in Cambridge I had performed these first-principles density functional calculations - what everybody does now - what Walter Kohn got a Nobel Prize for.  These density functional calculations allowed me to derive a rigorous understanding of the different roles played by the s, p and d electrons in transition metal bonding.

Bernadette Bensaude-Vincent - Did you start with transition metals?

David Pettifor - My thesis took the fundamental scattering theory of electrons in metals and transformed it into a computational tool that allowed me to predict the structural changes across the transition metal series.  You are looking at extremely small energy differences between one structure and another.  The mathematical transformation that I did from scattering theory to the tight-binding model of Jacques Friedel, allowed the correct prediction of these very small energy differences.

Bernadette Bensaude-Vincent - What do you call a model?

David Pettifor - Well, this is what physicists spend their whole time constructing and solving. We make approximations. When I came to Oxford ten years ago I set up the Materials Modeling Laboratory. People wanted me to call it the Laboratory for Computational Materials Science.  I said no. Computing, solving numerically quantum mechanical or classical equations, is not the key step in providing insight into the complex world of materials and their properties. The critical step, the creative step, is finding a model that encompasses the dominant mechanisms of the complex process one is wishing to describe. Only then can we write our computer program to provide quantitative answers.  Hence, I kept the name Materials Modeling Laboratory. But they laughed at me and said: Here you go with your plasticine.

Bernadette Bensaude-Vincent - So what is a model?  I guess it is not a small plasticine shape that you were trying to do.

David Pettifor - A model is an attempt to extract the essential ingredients, the dominant mechanisms that you feel responsible for what you want to explain.  For example, you can take Walter Kohn’s equations.  They had transformed a many-body problem into a simpler one-body problem.  I would not call that a model.  That is a theory, the so-called Density Functional Theory (DFT).  These equations are however, still very complicated.  In order to be able to simplify these equations, we use a chemistry description.  We imagine bonds between the atoms.  We reduce very complicated equations by using a chemical bonding picture that is familiar to all undergraduates.

Bernadette Bensaude-Vincent - Do you mean that you transformed a matter of calculus into something visual?

David Pettifor - No, although the underlying physics can be visualized in terms of chemical bonds, the model remains analytic.  Take the heats of formation, for example.  People at IBM and all around the world started DFT calculations with the help of computers: In order to calculate the heat of formation of a mixture of rhodium with palladium, for instance, they compared the total energy of the separate metals, namely 1,000,000 units of energy say, with that for the alloy namely 1,000,000.1 units of energy.  The question was what is responsible for that very small energy difference of 0.1?  I developed an analytic model.  It was not based on the Pauling-Miedema model of ionicity but was based on the idea of the importance of the strong, covalent bonding between the valence d orbitals in transition metals.  I can do that on the back of an envelope.  Solve that model analytically and make the prediction that the heat of formation should change sign while you go through the transition metal series, depending on the average number of valence d electrons in the band.  That model was published in Physical Review Letters 42 (1979) 846 and there was a lot of controversy.  The established community did not like it.

Bernadette Bensaude-Vincent - Why did they refuse it?

David Pettifor - I tried to work in the spirit of what Wigner and Seitz did in 1933 when they applied quantum mechanics to the problem of bonding in metals.  They solved for the binding energy curve of metallic sodium.  They replaced the atomic polyhedron in the metal by a sphere which is a good approximation that you can solve.  What they did in the early days of quantum mechanics for the sp-valent alkali metals, I generalized when I was in Cambridge to the case of the elemental transition metals.  For the binary alloy the picture I had in mind was originally that of Miedema’s model.  It suggested that if you mix a metal A with a metal B, then you start by cutting out the Wigner-Seitz sphere for metal A and the Wigner-Seitz sphere for metal B and bring them together to form the alloy.  I started with that model and tried to show that within DFT you could get an ionic term and a repulsive term like in Miedema’s picture.  But that was not possible.  I realized that I could not justify Miedema’s model and I went back to the more chemically intuitive tight-binding model, championed by Jacques Friedel at the time.

Bernadette Bensaude-Vincent - Could you clarify what you mean by analytic model?

David Pettifor - Consider making a model able to predict the heat of formation of transition metal alloys.  You start with a real transition metal.  It has two types of valence electrons: free electrons and electrons more tightly bound to their parent atoms.  The latter are more like the electrons in diamond, in the carbon atom.  They overlap and give strong, covalent bonds.  If you look at which element has the highest cohesive energy, it is not carbon, diamond or graphite, but actually tungsten which is a transition metal.  It comes not from the free electrons but from the tightly-bound d electrons.  The model relies on three simplifications that help understand the changing energy when A and B mix.  The first simplification is the assumption that the d electrons are the critical electrons whereas the s and p can be neglected. The second simplification is that we assume a constant density of states throughout the d band. We don’t want to calculate the exact electronic structure.  The third simplification is that we assume that the atoms remain neutral, i.e. there is no net flow of charge from A to B on the formation of the alloy.  I call it a model because it is a simple representation of reality, but it is a mathematical model.  It is not a qualitative representation.  It is a rigorous model because we try to make it internally consistent.

Bernadette Bensaude-Vincent - Which of these assumptions were controversial in your model?

David Pettifor - The third one was critical.  Miedema was unhappy about it.  There was a big fight at Bell Labs with the person I worked with, who was also unhappy about this lack of explicit ionicity within my model.  Nonetheless, I got permission from my bosses at Bell Labs for my paper to go out with myself as the sole author.  But to show you the power of scientists at Bell Labs at that time: I went to Imperial College as a new lecturer with my paper already accepted by the Physical Review Letters.  Soon afterwards the editor wrote to me saying there was someone at Bell Labs who was submitting similar results.  We would like you to withdraw your earlier paper and write instead a joint paper.  I wrote back and said I am sorry but this question had already been officially resolved whilst I was at Bell Labs.  So it came out just with my name on it.  Finally, scientists at IBM Laboratories in Yorktown Heights did DFT calculations and confirmed the basic assumptions of my model. 

Such models are important.  You asked me why as a physicist I work in Materials Science.  People in Materials Science found they could understand the concepts and use them to help design less brittle, more ductile alloys, for example.  15 years ago scientists and engineers at Oak Ridge National Laboratory were attempting to stabilize cubic close-packed phases of the titanium alumini rather than the naturally occurring tetragonal or hexagonal binary phases which were very brittle at room temperature.  I had recently ordered the structural database of binary compounds within a simple two-dimensional structure map.  Conventionally, structure maps had been constructed by taking coordinate axes to reflect those physical properties which were deemed important for controlling structural stability: for example, the difference in electronegativity of the two elemental constituents ∆X, the difference in atomic size ∆R, or the average number of valence electrons per atom e/a.  During the early 1980s Pierre Villars had constructed such three-dimensional maps (∆X, ∆R, e/a) in an effort to separate the binary compounds into distinct structural domains within the map.  Unfortunately, the structural separation was not good because these maps relied solely on the classical coordinates of electronegativity, size and number, neglecting completely the quantum mechanical character of the valence orbitals (which describe the bonding hybrids or ‘hooks’ that stick out from the atoms to form directed bonds).  I realized that if we were to present the structural data in a user friendly fashion for the alloy developers, then we could not use physical coordinates (that required at least four dimensions!) but instead must use a single phenomenological coordinate.  This I obtained by running a string through the periodic table, as shown in Picture 1.  Pulling this string apart orders all the elements with respect to each other, so that two dimensional maps can be plotted for any given stiochiometry (see Picture 2).  These maps suggested to the alloy developers how best to alloy their binary titanium aluminides to drive the pseudobinary into cubic domains of stability.  They found that these cubic phases were indeed less brittle than the original tetragonal or hexagonal phases, but alas they were still not ductile enough to fly in a jet engine!  This required the expertise of traditional metallurgists who subsequently found clever processing routes to control the microstructure of the alloy.  Nevertheless, these two-dimensional structure maps are very powerful pedagogically.  The string is the simplest representation that keeps the chemistry by grouping like elements in sequential order.  I would call this a model.

Bernadette Bensaude-Vincent - So would you call the Mendeleev periodic table a model as well?

David Pettifor - I don’t have such deep philosophical thoughts.  I would call it a table and I call that a string.  So maybe it is not a model.  But the periodic table is a representation of reality that topologically orders all hundred elements within a matrix that rationalizes their chemical properties.  Similarly, this string helps order empirical data on compounds, thereby allowing the search for new alloy phases with improved mechanical properties.

Bernadette Bensaude-Vincent - Is it the kind of models that you are doing at the Materials Modeling Laboratory ? What is the role of modeling now in Materials Science ?

David Pettifor - When I came here ten years ago the idea was to set up a Materials Modeling Laboratory that was unique at that time.  We wanted to go the whole way from quantum mechanics up to the engineering level within one laboratory. (Picture 3 : hierarchy of models).  I have colleagues who do the modeling of processes, for instance, the solidification of metals, or the spray forming of metals. Obviously they use continuum modeling rather then quantum mechanics.  The goal was to get this community to talk together.  The chemists doing drug design had always had good contacts with fundamental ab initio theorists.  But the drug design did not really get beyond the atoms, they did not have to worry about the microstructure.  My community had a quantitative basis from which to start.  So we could solve the density functional equations on huge computers and get binding energies, heats of formations, and even phase diagrams from first principles.  Going from the electronic world through to the world of atoms, then up through the microstructural domain to the continuum world, the idea was to bridge the gaps between these different modeling hierarchies.  Ten years ago people started talking to each other but there was not much interaction, except in the polymer world where the chemists had made the most advance in so-called multi-scale materials modeling.  But it was also political because at each length-scale there was a different community, loosely corresponding to a different discipline.  During my inaugural lecture in Oxford ten years ago, I plotted the vertical scale as drawn in Picture 3 to show that our lab had to be interdisciplinary.

Bernadette Bensaude-Vincent - Practically how did you interact?

David Pettifor - I introduced the Friday lunchtime seminars. The MML (Materials Modeling Laboratory) seminars are different from the department colloquia. These weekly seminars were a learning experience for all of us. My colleagues in the department saw them as highly successful in integrating the modeling and experimental work within the department. 

Bernadette Bensaude-Vincent - So is it by this way that your own research belongs to materials science?

David Pettifor - Yes, I believe very strongly in the goal of multiscale materials modeling where the ultimate driver is to understand and control the processing and properties of materials.

Bernadette Bensaude-Vincent - What kind of models did you work out in this department?

David Pettifor - With multiscale modeling we got funding several years ago from DARPA on the chemical vapor deposition of diamond films.  That brought together a team involving a chemical engineer for modeling the flow of gases through the reactor, a materials scientist for modeling the growth of the film, and us in Oxford doing the quantum mechanical atomistic studies on the dominant growth mechanisms at the diamond surface.  In America that particular program was called virtual integrated prototyping, VIP.  That was a very exciting dynamic program.  It was unusual for non US scientists to get funding from DARPA.  The same project to model the CVD growth of films was considered as too ambitious in this country by the Engineering and Physical Sciences Research Council (EPSRC).  We have just put a new application into the DARPA spintronics program that is centered on deriving interatomic bond-order potentials to bridge the gap between the electronic and atomistic modeling hierarchies.

Bernadette Bensaude-Vincent It seems that the Americans have been extremely important to you

David Pettifor - Yes, DARPA has been important in supporting this work on bridging these gaps.  Also it was the Americans who funded the work on the structure maps.  The US Department of Energy gave me money that allowed me to take a sabbatical.  When this lab was set up ten years ago we got funding from Hewlett Packard Laboratories in Palo Alto for two modeling postdocs and one experimental postdoc.  They are currently funding a postdoc to model the writing with an electron beam in phase change materials for atomic resolution storage.

Bernadette Bensaude-Vincent - How do you see nanotechnology?

David Pettifor - I am obviously in favor of it. I am involved with a colleague in this department, Andrew Briggs, on quantum computing in collaboration with people in Cambridge and from the Clarendon Laboratory on the other side of this road.  He got a big grant last year.  He is looking at different ways of building solid state quantum computers.  One of the ways is based on putting nitrogen inside a fullerene inside a nanotube of carbon.  Nitrogen has a spin which is a good quantum bit.  There was an excellent discussion meeting about quantum information processing a month ago at the Royal Society.  The science coming out is absolutely amazing.  Even if we don’t have a quantum computer in twenty years time, it is pioneering science.  The concepts are totally different from classical computing.  That is only one part of nanotechnology but it is a very exciting area.

Bernadette Bensaude-Vincent - Do you think that nanotechnology can bring more coherence into the cluster of research fields covered by materials science?

David Pettifor - Tony Evans, probably the most cited materials scientist in the world, currently at Santa Barbara, was the chair of the Panel of Assessment of materials science departments in this country.  He started his presentation stating that "Materials science is an enabling science".  If it is a science that enables engineers to make things, it is not about to gain coherence as it spreads and dilutes itself into more and more fields such as biomaterials and nanotechnology.  May be it will disappear from most universities as a unique undergraduate discipline in the future, as the core disciplines of physics, chemistry, biology and engineering set up interdisciplinary courses and modules.  For the present, however, here in Oxford our multidisciplinary materials science course is becoming increasingly popular with school applicants, who enjoy the mix of physics, chemistry and engineering that we offer.

This page was last updated on 28 April 2003 by Arne Hessenbruch