Alan Lindsay Mackay FRS (born 6 September 1926) is a British crystallographer, born in

Wolverhampton Wolverhampton () is a city, metropolitan borough and administrative centre in the West Midlands, England. The population size has increased by 5.7%, from around 249,500 in 2011 to 263,700 in 2021. People from the city are called "Wulfrunian ...

. He spent his scientific career at

Birkbeck College Birkbeck, University of London (formally Birkbeck College, University of London), is a public university, public research university, located in Bloomsbury, London, England, and a constituent college, member institution of the federal Universit ...

, founded by

George Birkbeck George Birkbeck Royal Society of London, FRS (; 10 January 1776 – 1 December 1841) was a British physician, academic, philanthropist, pioneer in adult education and a professor of natural philosophy at the University of Strathclyde, Andersonia ...

, one of the Colleges of the

University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom. The university was established by royal charter in 1836 as a degree ...

, where he was immersed in a liberal scientific atmosphere under the leadership of

John Desmond Bernal John Desmond Bernal (; 10 May 1901 – 15 September 1971) was an Irish scientist who pioneered the use of X-ray crystallography in molecular biology. He published extensively on the history of science. In addition, Bernal wrote popular book ...

. Mackay has made important scientific contributions related to the structure of materials: In 1962 he published a manuscript that showed how to pack atoms in an

icosahedral In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...

fashion; a first step towards five-fold symmetry in materials science. These arrangements are now called Mackay icosahedra. He is a pioneer in the introduction of five-fold symmetry in materials and in 1981 predicted

quasicrystals A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical ...

in a paper (in Russian) entitled "De Nive Quinquangula" in which he used a

Penrose tiling A Penrose tiling is an example of an aperiodic tiling. Here, a ''tiling'' is a covering of the plane by non-overlapping polygons or other shapes, and ''aperiodic'' means that shifting any tiling with these shapes by any finite distance, without ...

in two and three dimensions to predict a new kind of ordered structures not allowed by traditional crystallography. In a later manuscript, in 1982, he took the optical

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

of a 2-D Penrose tiling decorated with atoms, obtaining a pattern with sharp spots and five-fold symmetry. This brought the possibility of identifying quasiperiodic order in a material through diffraction.

Quasicrystals A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical ...

with icosahedral symmetry were found by

Dan Shechtman Dan Shechtman ( he, דן שכטמן; born January 24, 1941)Dan Shechtman
. (PDF). Retri ...

and co-workers in 1984. For his contributions to

in 2010 Mackay was awarded the

Buckley Prize The Oliver E. Buckley Condensed Matter Prize is an annual award given by the American Physical Society "to recognize and encourage outstanding theoretical or experimental contributions to condensed matter physics." It was endowed by AT&T Bell Lab ...

, of the

American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of k ...

, with Dov Levine and

Paul Steinhardt Paul Joseph Steinhardt (born December 25, 1952) is an American theoretical physicist whose principal research is in cosmology and condensed matter physics. He is currently the Albert Einstein Professor in Science at Princeton University, where he ...

. The

Nobel Prize in Chemistry ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "M ...

was awarded in 2011 to

Dan Shechtman Dan Shechtman ( he, דן שכטמן; born January 24, 1941)Dan Shechtman
. (PDF). Retri ...

for the discovery of

. Mackay has been interested in a generalised crystallography, which can describe not only crystals, but more complex structures and nanomaterials. He has applied his ideas of

minimal surfaces In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...

to graphitic materials, proposing, with Humberto Terrones, periodic arrangements of carbon atoms with negative Gaussian

curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonic ...

known as Schwarzites, which are the periodic cousins of

Buckminsterfullerenes Buckminsterfullerene is a type of fullerene with the formula C60. It has a cage-like fused-ring structure (truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a soccer ball. Each of its 60 carbon atoms is bonded t ...

Mackay has compiled a book of scientific quotations and has co-authored a book on geometry with Eric Lord and S. Ranganathan. He has also written a book of poetry and has translated from the German, with commentaries,

Ernst Haeckel Ernst Heinrich Philipp August Haeckel (; 16 February 1834 – 9 August 1919) was a German zoologist, naturalist, eugenicist, philosopher, physician, professor, marine biologist and artist. He discovered, described and named thousands of new sp ...

's last book "Kristallseelen", (1917). He produces scientifically inspired visual art under his artistic pseudonym Sho Takahashi. Some of his 3D printed minimal surface designs can be found at his shapeways store. He became a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

(FRS) on 17 March 1988 and a Fellow of Birkbeck College on 2 March 2002. He is also a Fellow of the

Mexican Academy of Sciences The Mexican Academy of Sciences ''(Academia Mexicana de Ciencias)'' is a non-profit organization comprising over 1800 distinguished Mexican scientists, attached to various institutions in the country, as well as a number of eminent foreign colle ...

References

External links

Alan Mackay's publications
*
The text of the oration to welcome him as Fellow of Birkbeck College, 9 March 2002

Alan Mackay's 3D minimal surface designs

* [https://www.theguardian.com/science/1999/sep/09/technology "The big picture: Michael Brooks explains why a fake Japanese artist is the perfect symbol for nanotechnology", a report in The Guardian on a 1999 Sho Takahashi exhibition at Sussex University ]
Pentagonal Snowflake, 1975. Published in "De Nive Quinquangula", 1981. Original signed by Roger Penrose, 2005.
{{DEFAULTSORT:Mackay, Alan Lindsay 1926 births Living people People from Wolverhampton People educated at Oundle School British crystallographers Academics of Birkbeck, University of London Fellows of the Royal Society Oliver E. Buckley Condensed Matter Prize winners