# Reminiscences About a Chemistry Nobel Prize Won with Metallurgy: Comments on D. Shechtman and I. A. Blech; *Metall. Trans. A*, 1985, vol. 16A, pp. 1005–12

- First Online:

A paper, “The Microstructure of Rapidly Solidified Al_{6}Mn,”[1] was submitted for publication in October 1984 by D. Shechtman and I. Blech to the *Metallurgical Transactions A* (now *Metallurgical and Materials Transactions*) after having been rejected by *The Journal of Applied Physics* (JAP) in the summer of 1984. A second paper, “Metallic Phase with Long-Range Orientational Order and No Translational Symmetry,”[2] was submitted within a week by Dan Shechtman and coworkers to the *Physical Review Letters* (PRL). Both papers announced the creation by rapid solidification, at the National Bureau of Standards (NBS)—now the National Institute of Standards and Technology (NIST)—of a sharply diffracting metallic Al-Mn solid phase that, because of its icosahedral symmetry, could not be periodic. In 2011, Dan Shechtman was awarded the Nobel Prize in Chemistry for this discovery. The Award cites him for “changing the way chemists looked at the solid state.”[3] We, the three co-authors of these papers, are pleased to have been invited by the editor of *Metallurgical and Materials Transactions* to recount our participation in this work and to summarize its significance.

The two papers differ in several ways. The *Physical Review Letters* paper was confined to the compelling case made by the NBS experiments alone that challenged several prevailing paradigms of crystallography. The *Metallurgical Transactions A* paper had, in addition, a model created by Ilan Blech, then at the Technion, demonstrating that an icosahedral electron diffraction pattern could result from a special sort of an icosahedral glass in which the translational symmetry is broken while retaining icosahedral orientational symmetry. This model was referred to, but left out of the *Physical Review Letters,* for three main reasons: (1) The experimental case by itself was strong and sufficient to force a change in thinking, (2) the model was open to criticism and might distract attention from the experiments, and (3) *Physical Review Letters* has a page limitation.

According to the then-prevailing crystallographic theories, crystals with icosahedral symmetry could not exist. Within a short time of publication, the existence of many others with forbidden symmetries were reported. Their undeniable existence and properties formed a classic example of the truism that experiments are unsurpassed at disproving theories. Nothing else was needed to force a change in the prevailing theories.

The discovery challenged two basic principles of crystallography. In the late 1700s, René Just Haüy[4] postulated that all crystals were made up of clusters of atoms repeated periodically in three dimensions. The severe restrictions that periodicity places on crystals became a cornerstone of crystallography. In the 19th century, it was established that only 1-, 2-, 3-, 4-, and 6-fold rotation axes, only 14 Bravais lattices, 32 point groups, 51 crystal forms, and 230 space groups can be consistent with periodicity.[5] Throughout the 19th century, all measured properties and external forms had been consistent with these restrictions. In 1912, the diffraction of X-rays by crystals brilliantly confirmed both that X-rays were short wavelength light and that crystals were periodic. The point group symmetries of the diffraction patterns, which are the same as those of the objects, also conformed to what was allowed by Haüy’s postulate. With no exceptions reported in almost 200 years, periodicity became the definition of a crystal and an axiom or a law of crystallography.

Diffraction from periodic objects results in sharp spots arrayed on a reciprocal lattice. The converse, that sharp diffraction spots could only come from a periodic object, was a widely accepted fallacy. By the definition of quasiperiodicity, the diffraction from quasiperiodic objects is sharp.[6] Quasiperiodic objects have no lattice, and their diffraction spots will not form a reciprocal lattice. Because of the 5-fold axis, a frequent ratio of spacing of spots in Figures 2 and 6^{1} is the golden mean, *τ* = 2 cos (*π*/5) = (1 + √5)/2. There is no reciprocal lattice in those diffraction patterns.

All of the experimental work was done at NBS/NIST. Robert J. Schaefer initiated the study of rapid solidification of dilute Al-Mn alloys because of his interest in achieving plane front solidification that would produce alloys free of microsegregation.[7] It was Dan Shechtman’s decision to explore higher manganese content. The alloys containing the quasicrystals were prepared by Schaefer and Frank Biancaniello. C.R. Hubbard did the X-ray experiments. Denis Gratias travelled to NIST from the Institute of Theoretical Physics at Santa Barbara to work with us. Special thanks are due to the NIST’s internal review committee, which took unusual care to review the PRL manuscript quickly and thoroughly. The PRL paper was reviewed and in print 5 weeks after submission.

## 1 Acceptance

Shechtman observed the electron diffraction patterns with its icosahedral symmetry in the spring of 1982 at NIST, but he only showed the 10-fold diffraction data to his NIST colleagues. Without seeing his dark-field images in Figure 4 (in the original *Metallurgical Transactions A* paper), the common reaction was that he was seeing multiple twinning. Most of us did not realize that twinning of periodic crystals would have resulted in overlapping reciprocal lattices and distortions; neither are found in the patterns. Quasiperiodicity was unknown to us; so was Mackay’s demonstration that Penrose’s aperiodic two-dimensional tiling would diffract sharply.[7] Discussions at NIST ceased and no further work was done on quasicrystals. Before Shechtman returned to Israel in the fall of 1983, he completed another important rapid solidification work.[8]

Although no explanation was necessary to refute both the universal periodicity of crystals and that only periodic objects can give sharp diffraction patterns, Shechtman apparently felt a need for an explanation of his finding. The observation lay dormant for 2 years. In 1984, as a result of Blech’s model, Shechtman gained enough confidence to return to his findings and pursue publication.

### 1.1 The Blech Model

*Metallurgical Transactions A*paper is devoted to the understanding of the electron diffraction pattern by considering the icosahedral phase to be a special sort of an icosahedral glass. Blech achieved this by aggregating parallel oriented icosahedra connected pairwise along common edges. The model succeeds because of two key facts:

- (a)
The icosahedra are all oriented the same way,

- (b)
Their pairwise connections form a unique set of vectors (along the 2-fold directions) that are a complete orbit of the icosahedron.

Icosahedral symmetry can be periodic in six dimensions, where each axis is perpendicular to the other five. Perfect icosahedral quasicrystals are given by three-dimensional straight cuts on irrational planes, oriented to retain the icosahedral symmetry and, thus, be quasiperiodic. They are the higher dimensional version of the black line in Figure 3(d). The structures in those cuts are icosahedral in three dimensions and diffract with Bragg peaks; they are to quasicrystals what ideal crystals are for standard crystallography. Large unit cell, approximant, periodic structures, including those proposed by L. Pauling, can be generated by performing a high-index rational cut with respect to the six-dimensional lattice, as already suggested by the green line in Figure 3(d). These can only approximate icosahedral symmetry. Finally, the Blech model can be viewed as a wavy three-dimensional cut meandering about the planar cut, represented by the blue line. Icosahedral symmetry is retained as long as it fluctuates around the planar cut.

The fluctuations’ contributions to background diffuse intensity were not determined in the original Blech’s computations, which focused on the expected Bragg peaks. In the original *Metallurgical Transactions A* paper, the main understanding of this localized diffraction is based on the remark that the set of interplanar distances of the model form a discrete uniform ensemble of vectors. Amusingly enough, this property was shown in 2005 to be one of the main ingredients in the Strungaru theorem that states that a Delaunay distribution of atoms has a sharp diffractive component in its Fourier spectrum if the pair interatomic vectors form a uniformly discrete set.[9] The Blech model has been the starting point of an enormous body of work on random tilings, especially in the United States, mainly by theoretical physicists.

Shechtman and Blech submitted a paper to the *Journal of Applied Physics* in the spring of 1984 reporting both Shechtman’s experimental finding of the icosahedral electron diffraction pattern and Blech’s computer simulation. The paper suggested the existence of a new class of solids, which they termed “multipolyhedral.” When Cahn saw the manuscript in the July of 1984, it was the first time he had seen all the data. He told Shechtman and his NIST colleagues that this work was of enormous importance, but he also told Shechtman that the paper was poorly written and that JAP was the wrong journal. In August, the paper was rejected by JAP with the suggestion that it be submitted to another journal. Shechtman told Cahn that he immediately submitted the unchanged manuscript to *Metallurgical Transactions A*, but there is no record of this. The published version was received by *Metallurgical Transactions A* early in October.

Because Cahn continued to feel that a short paper needed to be written to reach a broader audience, Shechtman invited him to write the PRL paper in August with the input from Gratias. It was finished mid-September, days before Shechtman returned to Israel.

As was his custom, Cahn sent the PRL manuscript out widely for comment. A copy of a copy reached Paul Steinhardt who, with Dov Levine, had been working on a model that was quickly submitted to PRL.[10] They coined the name quasicrystal, and their work had enormous influence in stimulating theory.

There was immediate worldwide acceptance, excitement, and confirmation about quasicrystals. Although the deadline for submission of abstracts for the March 1985 APS meeting was early December of 1984, 13 abstracts were received and there was an entire quasicrystal session. Lou Testardi, Division Chief of Metallurgy at NIST recommended that Shechtman be an invited speaker at that meeting. The fall 1985 meeting of the Metallurgical Society devoted a session to them. About 300 papers were submitted worldwide in 1985; by now, there are tens of thousands. Powder pattern of quasicrystals had been seen often and ignored as uninteresting intermetallic crystals with unknown symmetry and large unit cells. Stable quasicrystals, not produced by rapid solidification, were present in commercial alloys,[11] especially in the (Al-Cu-Li) alloy where quasicrystalline intergranular grains had been observed.[12] Quasicrystals have found all kinds of useful applications.[13] Quasicrystals spawned a renewed interest in aperiodic tilings, higher dimensional crystallography, and mathematics.[14]

By 1992, this realization that in a quasicrystal, the atoms are patterned in an orderly but nonperiodic manner, led the International Union of Crystallography (IUC) to alter its definition of a crystal. Previously, IUC had defined a crystal as “a substance in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating three-dimensional pattern.” The new definition became “A material is a crystal if it has *essentially* a sharp diffraction pattern…” (emphasis added). The word *essentially* means that “most of the intensity of the diffraction is concentrated in relatively sharp *Bragg peaks*, besides the always present diffuse scattering*. …*”[15] This definition is broader and allows for possible future discoveries of other kinds of crystals.

As with any major paradigm change, there was strong opposition, most notably by Linus Pauling, who had considerable influence and access to media. By the time he began, there was much literature confirming Shechtman’s finding. Pauling initially chose to ignore electron diffraction and tried to describe the powder patterns of quasicrystals both by twinning and by very large unit cells; either would have sufficed, but his models did not fit the electron diffraction pattern from a single quasicrystal. No one ever provided experimental evidence confirming Pauling’s proposed structures, and most of the workers in quasicrystals did not take him seriously.

Within a short time Shechtman was awarded many honors, culminating thirty years later in the 2011 Nobel Prize in Chemistry.Open image in new windowOpen image in new windowOpen image in new windowOpen image in new windowOpen image in new windowOpen image in new windowOpen image in new windowOpen image in new window

## Footnotes

- 1.
Figure numbers refer to figures in the

*Metallurgical Transactions A*paper.

## Notes

### Acknowledgments

We have benefitted greatly from reminiscences and files from many involved in these events, among them, Frank Gayle, Leo Bendersky, William Boettinger, and Robert Schaefer at NIST, as well as David Brandon from the Technion. The following acknowledgement was omitted from the revised manuscript and is not in the publication. “The authors wish to thank F.S. Biancaniello for alloy preparation and R.C. Hubbard for performing (the) X-ray experiment. The work was partially supported by DARPA.” Although there is no mention of NBS at all, the original submitted manuscript contained the following affiliations: “D. Shechtman* and I. Blech, Dept. of Materials Eng., Technion, Haifa, Israel, *Center for Materials Research, The Johns Hopkins University, Baltimore, Maryland and Guest Worker at NBS, Gaithersburg, Maryland.”

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