On May 27th 1998 the youthful Arnold Beevers celebrated his
90th birthday. Over the years, his contributions to science, to the
communication of science, and simply to the good humour of scientist and
non-scientist alike have been enormous. His name has left its mark in
three places: Beevers-Lipson strips, Beevers-Ross sites and Beevers
Miniature Models. They provide a very good starting place for talking about
Arnold the man.
It is difficult for the modern crystallographer, whose Fourier syntheses are calculated so quickly that they don't even give time for a good swig of coffee, to realise the appalling task of actually carrying out even a two dimensional synthesis. A modest grid of 30 x 30 and 400 data meant that for a centrosymmetric structure, cos [2p (hx+ky)] had to be evaluated 36 000 times. This seriously limited the possibility of using Fourier methods at all, and made three dimensional summations almost unthinkable. Arnold Beevers and Henry Lipson realised that the number of sums could be greatly reduced by factoring the expression into one dimensional terms, and that for all practical purposes a simple box of paper strips could be organised for lining up and summing the necessary values. These were first published in 1936,(1) and a description of their use will appear in a future issue of Crystallography News - although it should be admitted that their efficient use depended on a standard of mental arithmetic not so common today as then! Between 1948 and 1970, 500 sets of strips were sold worldwide, and the production, trimming and packing of a new edition of strips was an unforgettable experience. The method of calculation is still used at the heart of many computer programs, even if the elegant boxes of strips have disappeared. It is, however, typical of Arnold's contribution to this work that a good fundamental idea was linked to a straightforward device for realising it.
Arnold was involved in the solution and interpretation of many key early structures, including the alums, copper sulphate and glucose. One of the most serendipitous of these was the structure of b-alumina, carried out with the late Marion Ross and published in 1937(2). This structure was of interest to ICI at that time, as this "form of alumina" was a nuisance - a gritty by-product in the production of the desired a-alumina. Beevers and Ross correctly diagnosed that it had the much more complex formula NaAl11O17, and gave their names to both possibilities for cation occupation: the Beevers-Ross sites and the anti-Beevers-Ross sites. More recently, the importance of this structure has grown immeasurably, of course, as it was recognised as a solid electrolyte.
Arnold had experimented much with models and structural representations. Not all of them were lasting - a model of the sucrose - sodium bromide complex made of glitter wax eventually had to be discarded when the amount of adsorbed dirt totally obscured the colours of the drooping balls, which were in any case falling off the dangling rods. In 1961, Arnold decided to make models of stainless steel rods and perspex balls, settling on the three basic parameters of a ball and stick model : the overall scale, the diameter of the balls and the diameter of the rods. A scale of 1 cm per Å (108) was selected, along with balls of 7mm diameter and rods of 1 mm diameter. This enables balls to be drilled to a depth of 2.5 mm, giving for a firm hold on the rod with no collision of rods in the centre, and models which are small and easy to store. In order to produce accurate models on this scale, Arnold designed several two-circle drills, to be capable of drilling any combination of angles and torsion angles. These compact, exceedingly attractive and very accurate models continue to be produced, and have invaded most of the known world.(3) They are now marketed under the name of Beevers Miniature Models.
The ability to clarify complex structures was another of Arnold's gifts. His 1946 paper in the Mineralogical Magazine (complete with colour diagram!)4 helped to explain the structure of apatite, the mineral of bone and teeth (see the cover picture) and the significance of the replacement of hydroxide by fluoride. For many years Arnold lectured to Edinburgh Dental students, and is a proud life-member of their society. He has long been an ardent advocate of preventing fluoride deficiency in humans! Another less well-known incident involved his examination of a sample of bath salts for a firm, whose customers had complained that they were "uncomfortable". Examination showed that the crystals were tetrahedral in form, and, as a bather sat on the crystals dissolving on the base of the tub, they were predictably uncomfortable! Arnold solved the problem by recommending that only salts crystallising in centrosymmetric space groups should be used in future!
His advice was usually right, although often not what was wanted! An excited poultry researcher once gave him a sample of eggshells that he claimed a test of his had shown to consist of aragonite rather than calcite. X-ray powder diffraction soon showed that they were pure calcite, like other eggs. Arnold pointed out that hens usually understand these matters better than scientists do! On a famous occasion one Christmas, he asked to see the manager of a Princes Street shop in Edinburgh to point out that decorating the windows with four and eight-pointed snowflakes was a disservice to the truth! The manager was not impressed, but there may be some meaning in the fact that while the shop has long disappeared, Arnold flourisheth yet - Happy Birthday Arnold, and many more!
R.O. Gould
University of Edinburgh
(2)Beevers C.A. and Ross M.S., Zeit. Krist., 97, 59-66 (1937)
(3)Beevers C.A., Education in Chem., 11, 198-200 (1974)
(4)Beevers C.A. and McIntyre D.B.,
Mineralog. Mag., 27, 254-7 (1946)
Twinkle, twinkle little star,
Last update: 20 Jul 98
Editor's Note:
The picture on the front cover shows the structure of apatite,
see story above. It was also provided by Bob Gould. It is a copy of that on
the 'birthday card' signed by most of those attending the BCA St,Andrews
conference, where Lindsey Sawyer recalled a ditty he wrote which was inspired
by one of Arnold's lectures:
How I wonder how you are!
For you have five points, I see,
And I know that cannot be.
You must be point group thirty-three,
A new system of symmetry.
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