Shechtman and Pauling Debate Quasicrystal Theory

Linus Pauling, 1986.

[Part 3 of 4]

David and Clara Shoemaker were not the only scientists who felt that Linus Pauling’s quasicrystals hypothesis, while admirable, was unsubstantiated by experimental data.

In fact, in “Metallic Phase with Long-Range Orientational Order and No Translational Symmetry,” the article that introduced quasicrystals to the scientific community, Dan Shechtman and co-author Ilan Blech noted that twins were initially suspected as being the reason for the unusual structure, but that after subjecting the crystals to a broad range of experiments and even using data from the x-ray diffraction patterns themselves, they determined that their sample was not composed of twins.

Their argument centered on the fact that twins should have been visible when they employed a method called “dark-field microscopy,” which illuminates whole grains, and that the twins should have changed, in some fashion, the patterns resulting from their electron diffraction experiments at various resolutions. Furthermore, they argued, twinning would not interfere with matching a Bravais lattice to a crystal in an x-ray diffraction pattern. Therefore, the fact that scientists were having difficulty assigning lattices – and, by extension, unit cells – to quasicrystals would not, in itself, be an indication that their structure was based on twins. Because of the overwhelming evidence against twins, the research team concluded that the sample “[did] not consist of multiply twinned regular crystal structures.”1

Pauling, however, cautioned Shechtman and Blech against discounting the influence of twins. In a letter dated April 24, 1985, he mentioned that certain previously analyzed crystalline structures shared some of the characteristics of the newly-discovered quasicrystals, and that there had been structures in the past that initially surprised researchers, but were found to accord with existing crystallography paradigms. To develop his theory, Pauling requested copies of Shechtman and Blech’s MnAl6 x-ray diffraction data.2

Shechtman, who was working at Technion, the Israel Institute of Technology in Haifa, responded promptly. In a letter received by the Linus Pauling Institute on May 15th, he emphasized that a number of different experiments had yielded no evidence of twins, and that other research teams had backed his findings. Nonetheless, Shechtman included prints of the x-ray diffraction patterns and copies of data on the sample’s Bragg peaks.3

Pauling’s handwritten notes on a copy of MnAl6 diffraction patterns in Shechtman and Blech, et. al. “Observation par microscopie électronique de la quasi-periodicite dans un solide a symetrie icosaedrique” (roughly, “An Observation by Electron Microscopy of the Quasiperiodicity in a Solid Having Icosahedral Symmetry”) from the French journal, Comptes Rendus de l’Académie des Sciences, 1985. The notes are concerned with calculating interplanar distances between the diffraction peaks shown, as well as extrapolating this to a 23.36Å unit cell.

In a response dated June 6, 1985, Pauling thanked Shechtman for the diffraction images, and requested permission to use them in an article introducing his multiple-twinning theory. He explained, very briefly, his hypothetical twinned, twenty-icosahedral structure as the basis for the icosahedral symmetry seen in quasicrystals, and mentioned certain pieces of evidence that he felt Shechtman and his team had overlooked. In particular, Pauling noticed three to five weak lines in the x-ray diffraction patterns that, to Pauling, supported a twinned structure.4

Then Pauling made a strange offer: he asked Shechtman if he would like to co-author an article on twinning with him. The difficulty, Pauling pointed out, would be that Shechtman would have to contradict himself and, to some extent, negate his own findings. In essence, Pauling offered Shechtman an opportunity to admit that he was wrong.4

It is unclear what, exactly, Shechtman’s response was; no letter from him about the offer is preserved in the Pauling Papers, and the tone of Pauling’s next letter implies that the two did not discuss it.

In mid-July 1985, Pauling again wrote to Shechtman, revealing a proposed structure composed of “icosatwins” and 1000-atom unit cells. He acknowledged that the unit cell size was unusually large, but stood by his hypothesis, noting that he himself had discovered a few complex crystal structures during the 1920s, when 1200-atom cells were inconceivable. He also mentioned that, since he had not received any correspondence from Shechtman indicating interest in co-authorship, he had sent the article he offered Shechtman off to the journal Nature for review.5 (This article would be accepted and published later that year, and was the first article in which Pauling discussed his twinning hypothesis.6)

Shortly after this exchange, correspondence indicates that Shechtman and Pauling met in person at the Linus Pauling Institute of Science and Medicine in Palo Alto. Mentioning that he would be in America on business, and available during the week of August 19, 1985, Shechtman wrote that he hoped they could meet and discuss quasicrystals in detail.7 Pauling obliged and extended an invitation. Though the details of the meeting are unclear, it does not seem to have gone especially well.

Dan Shechtman, 1983. (Credit: Technion – Israel Institute of Technology)

In a letter dated September 3, 1985, Shechtman wrote to Dr. Sten Samson of the California Institute of Technology (and a former graduate student under Pauling), carbon-copying Pauling, and enclosing a sample of a mostly – but not entirely – icosahedral, rapidly cooled, powdered ribbon of material. He wrote that he was fulfilling a request made by Pauling, and that Samson had, apparently, been forewarned that he would be receiving the sample and was aware of the analyses that Pauling wanted performed. The tone of Shechtman’s letter seems somewhat begrudging and reticent.8

The results of Samson’s analysis are not preserved among the Pauling Papers, but correspondence between Pauling and Shechtman appears to have dissipated for nearly a year. In mid-April 1986, Shechtman sent a brief letter requesting that Pauling keep him apprised of his activity with regard to quasicrystals.9 No reply on Pauling’s part is preserved amongst his papers.

It seems it was not until August 12, 1986 that Pauling again wrote to Shechtman. Addressing both Shechtman and his original quasicrystal article co-author Ilan Blech, Pauling claimed that he had found an error of 14.4% in their scale for the electron diffraction patterns of MnAl6 – the sample used in their first article – and that, adjusted against this error, the data strongly supported Pauling’s twinning hypothesis. He went on to call the error “easily avoidable” and (in a somewhat patronizing tone) detailed a fairly basic process by which the team could have – but, Pauling presumed, did not – verify their scale’s accuracy. Pauling’s tone was curt. “This error caused me several months of unnecessary effort,” he wrote. He went on to say that, after correcting this alleged error, “there no longer remains any doubt about the nature of the ‘icosahedral quasicrystals.’ They are twins of a cubic crystal with edge 26.73Ǻ.” Pauling closed his letter by noting: “Verification of my statement that your scale is in error by 14.4% would, of course, provide additional evidence for the foregoing conclusion.”10

Though Shechtman’s response is not among Pauling’s correspondence, it seems to have humbled Pauling. A letter dated September 8, 1986 – written less than a month after Pauling’s terse note – reveals Pauling to be in a more deferential mood. He thanked Shechtman for his letter and photographs, and acknowledged that they clearly showed that Shechtman and Blech’s original quasicrystals scale was correct. The error, Pauling wrote, occurred from misinterpreting what he called a “statement about scale made to me by another investigator.” Despite acknowledging his error, Pauling did not directly apologize, but instead went on to state concerns about a different set of photographs showing decagonal relationships, estimating calculations based on them to be off by 8%.11 The gap in correspondence in the Pauling Papers implies that Pauling and Shechtman did not correspond again for an entire year.

However sparse the exchange between Shechtman and Pauling during that time, it did not mirror a reduction in Pauling’s work on his twinning hypothesis. The news that Shechtman and Blech’s scale was indeed accurate caused a small crisis for Pauling, who was certain that the “correction” he proposed would justify his structure. For most of the month of October 1986, Pauling contemplated the multiple-twinning structure at either his ranch in Big Sur or on airplanes and in hotel rooms between peace talks and chemistry lectures. Dozens of pages of calculations, diagrams, and hypotheses on legal pads reveal a constant refinement of the twinning theory. Pauling’s meticulousness in noting the date and time reveals that the “quasicrystal problem,” as he called it, occupied his mind even into the early morning hours.12

On October 16, 1986, Pauling arrived at a 920-atom unit cell composed of eight 117-atom clusters arranged snugly at 90-degree angles of rotation, repeating along all three axes. Triumphantly, Pauling wrote “Hurray! The Quasi Problem is Solved.13

After weeks of calculations and creative spatial configurations, Pauling believed he finally explained quasicrystals in terms of Bravais lattices, announcing, “Hurray! The Quasi Problem is Solved.”. However, further thought led him to reconsider, and he later added the phrase, “But see page 11!!!” on which he recalculated and abandoned his findings.

Yet, a small note in the margin underneath redirects to work done two days later, in which Pauling recalculated his cell size based on Shechtman and Blech’s electron diffraction photos. The new cell was still composed of eight 117-atom clusters, but as many as 72 of those atoms were shared, making the unit cell 840 atoms instead of 920. Pauling also concluded that the cell would be essentially body-centered cubic.14 Eventually that cell also succumbed to scrutiny, and on October 24, Pauling considered an 804-atom unit cell.15

Finally, Pauling concluded that the unit cell likely contained 820 atoms, formed from 104-atom clusters sharing outer electron shells. It was this structure that formed the core of Pauling’s article, “Evidence from x-ray and neutron powder diffraction patterns that the so-called icosahedral and decagonal quasicrystals of MnAl6 and other alloys are twinned cubic crystals,” published in June 1987 in the Proceedings of the National Academy of Science (PNAS).

Pauling’s clusters were arranged such that each was at the corner of a unit cube and surrounded by twelve more clusters in the shape of a nearly regular icosahedron. He noted, “All of the clusters have the same orientation, and any one cluster could serve as a seed for twinning.” To defend this structure, Pauling pointed to its considerable correlation with diffraction patterns, and argued that any mismatching that occurred around cube edges was due to slight variations in alloy compositions. He also noted that another alloy, Mg32(Al9Zn)49, is known to have a tightly-packed cluster-based structure, making such a structure in MnAl6 not unprecedented. In fact, Pauling argued, the intense heating and the rapid cooling process used to form MnAl6 crystals (which are typically referred to as “rapidly quenched”) likely led to closely packed alloy clusters.16

Papers arranged on Pauling’s desk, 1987.

By the time of the article’s publication, over a one-hundred other alloys with icosahedral quasicrystalline structures had been found.17 Pauling, like many scientists, began to expand his theory to account for even more alloy structures, beyond the first anomalous discovery, MnAl6.

Breaking the apparent year of silence, Pauling wrote once more to Shechtman on October 6, 1987. By now his tone had shifted from cordially tense scientific competition to that of camaraderie. In addition to thanking Shechtman for the many glossy x-ray photographs and diffraction data calculations he had provided him over the years, Pauling also thanked Shechtman for his very discovery of quasicrystals. He wrote,

This discovery has resulted in a great contribution to crystallography and metallurgy, in that it has stimulated hundreds of investigators to study alloys and has led to much additional knowledge about intermetallic compounds….Your discovery has also made me happier…. For over two years I have worked on this problem, and have enjoyed myself while doing it. I estimate that I have spent nearly 1,000 hours just thinking about this whole question, and more than 1,000 hours making calculations, and writing papers.

The fruit of this labor, for Pauling, was the discovery of “five new complicated structures,” the details of which Pauling shared with Shechtman. He even – in what looks like a conciliatory acknowledgement of Shechtman’s expertise – asked Shechtman to check on the diffraction patterns of a slowly cooling structure to see if the intensity spots shifted in position or intensity.18

Furthermore, Pauling reiterated his previous desire to write a paper with Shechtman about two- and six-fold symmetry, saying, “I should be very pleased if a paper could be published with the authors Shechtman and Pauling.” He even acknowledged, to some extent, the tension that had existed between them, writing, “I hope that we can cooperate in the attack on this problem. I have the impression from referees’ reports on papers that I have submitted to Physical Review Letters that at least one of the referees considers me to be an antagonist.” Though Pauling did not agree with this assessment, or apologize for any of his behavior, he did write, “It is something like the situation between the United States and the Soviet Union. It would be much better if they were to cooperate in attacking world problems, rather than to function as antagonists.”18

Responding quickly to this letter, Shechtman cabled Pauling, thanking him and saying that his communication “made me very happy.”19 In a follow-up letter sent November 10th, Shechtman expressed interest in collaborating with Pauling on a joint quasiperiodic structures article, and offered to host Pauling at Technion in Haifa, covering all of his expenses.20 In response, Pauling wrote that he was cutting down on his amount of travel, and so would not likely travel to Israel. Rather, Pauling wrote, the nature of their collaboration could be such that Pauling would send Shechtman manuscripts for his consideration and input, implying that, while Shechtman was welcome to visit the Institute in Palo Alto, their collaboration would be a long-distance one.21

That letter, dated December 8, 1987, is the last archived bit of correspondence between Pauling and Shechtman. The two never co-authored an article.


1  Shechtman, D., I. Blech, D. Gratias, and J.W. Cahn. “Metallic Phase with Long-Range Orientational Order and No Translational Symmetry.” Physical Review Letters 53.20: 1951-3 (1984).

2  Pauling, Linus. Letter to Dan Shechtman and Ilan Blech. 24 April 1985. Ava Helen and Linus Pauling Papers, Sci 4.005.2.

3  Shechtman, Dan. Letter to Linus Pauling. 15 May 1985.

4  Pauling, Linus. Letter to Dan Shechtman. 6 June 1985.

5  Pauling, Linus. Letter to Dan Shechtman. 10 July 1985.

6  Pauling, Linus. “Apparent icosahedral symmetry is due to directed multiple twinning of cubic crystals.” Nature 317 (October 1985): 512-14.

7  Shechtman, Dan. Letter to Linus Pauling. 3 July 1985.

8  Shechtman, Dan. Letter to Sten Samson, cc Linus Pauling. 3 September 1985.

9  Shechtman, Dan. Letter to Linus Pauling. 20 April 1986.

10  Pauling, Linus. Letter to Dan Shechtman and Ilan Blech. 12 August 1986.

11  Pauling, Linus. Letter to Dan Shechtman. 8 September 1986.

12  Pauling, Linus. Hand-numbered series of LP Quasicrystal Notes and Calculations, October 7-10, 1986; October 12-27, 1986.

13  Pauling, Linus. Hand-numbered series of LP Quasicrystal Notes and Calculations, October 16, 1986.

14  Pauling, Linus. Hand-numbered series of LP Quasicrystal Notes and Calculations, October 18, 1986.

15  Pauling, Linus. Hand-numbered series of LP Quasicrystal Notes and Calculations. October 24, 1986.

16  Pauling, Linus. “Evidence from x-ray and neutron powder diffraction patterns that the so-called icosahedral and decagonal quasicrystals of MnAl6 and other alloys are twinned cubic crystals.” Proceedings of the National Academy of Sciences 84:12 (1987) 3951-3.

17  The Scientist, “Quasicrystal Research: Where The Action Was In 1988”. May 29, 1987.

18  Pauling, Linus. Letter to Dan Shechtman. 6 October 1987.

19  Shechtman, Dan. Telegram to Linus Pauling. 26 October 1987.

20  Shechtman, Dan. Letter to Linus Pauling. 10 November 1987.

21  Pauling, Linus. Letter to Dan Shechtman. 8 December 1987.

One Response

  1. […] lines being reviewed, the invention of amorphous metals like Vitreloy, and Linus Pauling (wrongly) fighting Shechtman about […]

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