symmetry

This site contains material for crystallographers, thermodynamicists and electrochemists, historians of science and technology, and mathematicians interested in group theory, potential theory, and probability. The owner of this site is Dr Michael Jewess (PHOTO), author or co-author of the work referred to below.

(For Michael Jewess’s work on intellectual property, follow the link RESEARCH IN IP.)

For forthcoming lectures, etc. by Michael Jewess, follow link LECTURES .

For lists of past publications and talks see Annex 5 at CV. Also, https://orcid.org/0000-0001-8163-6008.

Sections I to III below deal with heat capacity anomalies generally; with “orientational disorder” of ammonium, tetramethylammonium, nitrate, and carbonate ions; with “positional disorder” of copper ions; with phthalocyanine and adiponitrile copper complexes; and specifically with ammonium chloride, tetramethylammonium trichloromanganate(II) (“TMMC”), scawtite, bis(adiponitrile)copper(I) nitrate, and copper(II) phthalocyanine.

Section IV below deals with symmetry outside its relevance to heat capacity anomalies: “band groups” (the seven groups of symmetry operations for a frieze, offering an understanding by analogy of the 230 space groups); and chirality.

Section V below deals with the application of modern thermodynamic data to understand a nineteenth-century commercial chemical process, Julius Thomsen’s process for production of washing soda in which cryolite was used as the source of the sodium needed.

Section VI below deals with the thermodynamics of graphane, structurally related to the more famous graphene, and possibilities for synthesising it on a bulk scale.

Section VII below deals with optimisation problems relating to the gravity of a planet.

Section VIII below deals with two problems in probability: the “two girls” problem and the Monty Hall game show problem.

Section IX below deals with the apprenticeship of Michael Faraday in Marylebone, London from 1805 to 1812 and his subsequent recruitment to the Royal Institution by Humphry Davy, and the “blue plaque” on the place of his apprenticeship.

Section X below deals with the apprenticehip of Humphry Davy in Penzance, Cornwall from 1795 to 1798, whence he progressed to a career in scientific research, and the presentation of a blue plaque on the place of his apprenticeship on 11 September 2015.

Section XI below deals with the achievements of H G J Moseley, who would almost certainly have received a Nobel Prize for his work on atomic numbers had he not been killed in Turkey in 1915, and the blue plaque at the Clarendon Laboratory in Oxford.

Section XII below deals with the possibility of present-day electrocatalytic nitrogen fixation, including by reference to the work of Humphry Davy.

Section XIII below deals with the use of “sealed” packets in which a person deposits scientific or technical information with a trusted institution so as, without publication, to achieve priority (academic or, in France, commercial also) for that information.

Section XIV below deals with nuclear science and technology (AERE Harwell; Ernest Rutherford; artificial radionuclides).

Section XV below deals with historical technological failures.

Section XVI below deals with the development of electronic theories of valence up to the pre-war work of Pauling and a controversy that arose in 1934.

Section XVII below deals with the difficulty of locating historical sites in London because of the renaming of thousands of streets between 1857 and 1939.

SECTION I:  HEAT CAPACITY ANOMALIES OFFER A DIRECT APPROACH TO THE NUMBER OF POSITIONS OR ORIENTATIONS AMONG WHICH THERE IS DISORDER

Heat capacity anomalies offer a direct approach to the number of positions or orientations among which an entity (ion, atom, or molecule) is disordered in a crystal.*  When such a crystal is cooled, there is frequently a transition to a form in which the entities are ordered. If the specific heat is measured across the temperature range in which the transition occurs, a heat capacity anomaly is observed.  The entropy change (usually readily estimated from the measured heat capacities) includes a component R ln n  per mole of entities where n is the number of positions or orientations among which the entity is disordered in the high- temperature form.  Generally, the lower the temperature, the easier it is to estimate the R ln n component, because the vibrational entropy changes that occur over the temperature range of the transition are smaller.

The published papers referred to in Sections II and III report R ln n as closest to R ln 2 in the case of bis(adiponitrile)copper(I) nitrate (the nitrates being orientationally disordered), to R ln 3 in the case of TMMC (the tetramethylammoniums being orientationally disordered), and to R ln 4 in the case of β-modification copper(II) phthalocyanine (the copper ions being positionally disordered within the molecule).  A long-known example of an anomaly arising from positional disordering is that involving the disordering of the atoms in β-brass (CuZn) among lattice sites. 

It should be noted that heat capacity anomalies are associated also with other types of order-disorder transitions in crystals, for instance, magnetic transitions, transitions from libration to rotation of ions or molecules, and electronic transitions (the anomalies in the last case being known as “Schottky anomalies”).

* For a compendious discussion, see Neville G Parsonage and Lionel A K Staveley, Disorder in crystals (Oxford University Press, 1978).

SECTION II: DISORDER OF POLYATOMIC IONS IN CRYSTALS 

There follows a link to the full text of an Acta Cryst. paper on the treatment of “orientational disorder” for crystallographers: ORIENTATIONAL DISORDER   (The corresponding doi link is http://dx.doi.org/10.1107/S0567740882006062.) The key conclusion of this paper is that it is often wrong to locate the central atom of a disordered ion at the centre of symmetry of the site in which the ion is located.  While, with suitably chosen positions among which the ion is disordered, this allows the average symmetry of the ion to be made to match that of the site, it may be that the precise positions (differing only in the orientation of the ions) are energetically impossible because they cannot correspond to potential energy wells.  X-ray crystal determinations in which this mistake has been made are shown to have resulted in structures that are materially questionable.   

There follows a link to a J. Chem.Thermodynamics  paper on the heat capacity of tetramethylammonium trichloromanganate(II) (often known as tetramethylammonium manganese chloride, “TMMC”) :  TMMC.  (The corresponding doi link is http://dx.doi.org/10.1016/0021-9614(83)90064-2.) This is one of the crystals referred to in the paper disorder.pdf linked above;  tmmc.pdf reports a heat capacity anomaly associated with disordering of the tetramethylammonium ions.  

There follows a link to a J. Chem. Soc. paper on the heat capacity of bis(adiponitrile)copper(I) nitrate: CU(ADIP)2NO3;this reports a heat capacity anomaly associated with disordering of the nitrate ions in this crystal, more fully discussed in the Acta Cryst. paper linked above. (The corresponding doi link is http://dx.doi.org/10.1039/F29807600803.)

The Acta Cryst. paper discusses also the structures of ammonium chloride and scawtite, which at room temperature have disordered ammonium and carbonate ions respectively.

SECTION III: POSITIONAL DISORDER OF THE COPPER ION IN β -MODIFICATION COPPER(II) PHTHALOCYANINE

There follows a link to a J. Chem. Soc. paper which reports the heat capacity of β-modification copper(II), nickel(II), and hydrogen phthalocyanines:   PHTHALOCYANINE.  (The corresponding doi link is http://dx.doi.org/10.1039/F29817701757.) This suggests that, on account of the rigidity of the essentially square-planar phthalocyanine divalent anion, the copper (II) ion does not have a minimum energy when located at its centre.  Instead, there may be a local maximum, with four equivalent positions of minimum energy in a square around the centre.  The height of the maximum is small and the effect is observed only at very low temperatures, in a particularly large heat capacity anomaly.  Above the temperature of the anomaly, the ions are apparently disordered among the four positions with equal probability.

SECTION IV:  SYMMETRYTHE “BAND GROUPS” (“FRIEZE GROUPS”)

(a) “Band groups” (“frieze groups”)

The student of crystallography finds it reasonably possible to satisfy himself of the existence of 32 point groups in three dimensions.  The existence of 230 space groups is usually taken on trust rather than checked personally.  A student can be given confidence in this if he considers the seven “band groups” (or “frieze groups”) that can occur in a repetitive two-dimensional pattern repeating only in one dimension, ie a frieze.  Once he is satisfied that these are correct, then his confidence in the space groups is based on analogy rather than trust. 

Adolf Pabst of UC Berkeley (1890-1990) is said to have recommended construction of the seven band groups as an exercise for the student.  However, this is not a trivial task, and the following links to such an exercise:  BANDGROUPS.

(b) Chirality

To be chiral so that it displays optical activity, a molecule must not be superimposable on itself. For this, it must lack any improper rotation axis (centre of inversion, mirror plane, or a higher improper rotation axis). Chirality is of great biological significance, a discovery which was anticipated by Lewis Carroll, see ALICE. For an abbreviated account of all talks given on Wednesday 13 October 2021, at “The handed world – 150 years of chiral molecules”, meeting at the Royal Society of Chemistry, London (of which Michael Jewess was the principal organiser), follow link CHIRALITY. This includes Michael Jewess’s introductory talk together with illustrations provided by by him.

SECTION V:  JULIUS THOMSEN’S COMMERCIAL PROCESS FOR MANUFACTURING WASHING SODA

There follows a link to an essay in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: THOMSEN. This paper relates to the commercial activities of the Danish chemist, Julius Thomsen (1826-1909), best known for his work on the periodic table and on thermochemistry. He made his fortune by a process which manufactured washing soda from cryolite (Na₃AlF₆) mined in Greenland, a Danish possession. The paper applies modern thermodynamic knowledge to understand how his process works. It raises the intriguing possibility that one or more compounds believed to have been first discovered in the 1980s were in fact produced a century before, on an industrial scale, as an intermediate in Thomsen’s process.        

SECTION VI:  THERMODYNAMICS OF GRAPHANE

There follows a link to a report on graphane: GRAPHANE. Graphene is a celebrated material consisting of a single layer of carbon. Graphane consists of such a layer hydrogenated on both sides (empirical formula CH), and has been formed in small quantities from graphene and atomic hydrogen. The report estimates its thermodynamic properties and considers which chemical reactions not involving such exotic reactants might be used to synthesise it in bulk.

SECTION VII: OPTIMISING THE ACCELERATION DUE TO GRAVITY ON A PLANET’S SURFACE

There follows a link to a Mathematical Gazette paper with the above title: GRAVITY. (The corresponding doi link is https://doi.org/10.1017/S002555720000646X.)Two problems are addressed, each concerning how a hypothetical planet-builder can make best use of a given amount of incompressible uniform material if he wishes to obtain, if only at one or two points on the surface, the maximum acceleration due to gravity. The planet-builder is also granted planet rigidity; he can form the planet into the shape he chooses, without worrying that the planet will under its own gravity revert to being a sphere. The first optimisation problem constrains the planet-builder to form the material into a spheroid (of any degree of oblateness); the second imposes no constraint on the form, and therefore is a “calculus of variations” problem. The solution to the first problem is a surprisingly oblate spheroid, with the acceleration due to gravity maximised at the two poles. The solution to the second problem is a particular ovoid of revolution, also surprisingly flattened, with the acceleration due to gravity highest at the pole at the blunt end.        

SECTION VIII:  THE “TWO GIRLS” PROBLEM AND THE MONTY HALL PROBLEM COMPARED

There follows a link to a Mathematical Gazette contribution on the “two girls” problem: TWO GIRLS. In a randomly chosen family with two children, if boys and girls are equally likely, there is a ¼ chance that there are two girls. This problem is concerned with what more accurate statistical inference can be made from the additional, true statement that, in the family, “at least one of the two children is a girl who was born on a Tuesday”. It is shown that what one infers depends on the process that generated the additional, true statement. This is analogous to the famous Monty Hall game show, where what one infers from the facts that one of three doors is open showing there is no prize behind it and that one of the other two conceals a prize depends on the process by which the first door came to be opened.

SECTION IX:  APPRENTICESHIP OF MICHAEL FARADAY

There follows a link to an essay in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: FARADAY. This paper relates to Faraday’s apprenticeship with George Riebau, bookbinder and bookseller, from 1805 to 1812. The shop (now 48 Blandford St in the Marylebone area of London) bears a splendid plaque erected in 1875-1876 under the scheme which was the predecessor of the blue plaque scheme. The paper describes how Riebau’s help and encouragement allowed Faraday to make the leap to scientific work at the Royal Institution in 1813, and contains modern and contemporary illustrations.

SECTION X: APPRENTICESHIP OF HUMPHRY DAVY

There follow links to articles describing the installation of a Royal Society of Chemistry Chemical Landmark plaque in the newsletter of the Society for the History of Alchemy and Chemistry, Chemical Intelligence, http://www.ambix.org/wp-content/uploads/2016/01/ChemIntelJan2016.pdf (see pages 30-31), and in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: DAVY). The author acted as master of ceremonies at the event to present the plaque on 11 September 2015. Davy was apprenticed to an apothecary, John Bingham Borlase from 1795 to 1798 at No 1 Market Place, Penzance, Cornwall. Like Faraday, a decade and more later, Davy benefited from a generous master, who in his case released him early from his indentures so that he could pursue a career in scientific research.

SECTION XI: H J G MOSELEY

H J G (“Harry”) Moseley was killed at the battle of Chanuk Bair in Turkey in August 1915. Had he not been killed, he almost certainly would have won a Nobel Prize for his work in determining atomic numbers, ie the charge on the nucleus of atoms. These in turn determine the number of elecrons in the electrically neutral atom, and thereby the chemical properties of elements. The modern periodic table is in order of atomic number. The following link is to a radio interview with given by Michael Jewess: http://www.bbc.co.uk/programmes/p03hxbx0. The following link is to a review by Michael Jewess recommending a recent book of essays on Moseley: https://www.tandfonline.com/doi/full/10.1080/00026980.2018.1548411. The following link is to a report by Michael Jewess in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers which relates to the plaque commemorating Moseley at the Clarendon Laboratory in Oxford: MOSELEY. The same report contains a short biography of Moseley and a review the RSC Chemical Landmark scheme from its inception in 2001.

SECTION XII: ELECTROCATALYTIC FIXATION OF NITROGEN

Fixation of nitrogen from the air by electrolytic means is thermodynamically allowed with low applied potentials. Reports of such fixation go back to Sir Humphry Davy. With molecular catalysis, such fixation might be practical today. There follows a link to an American Chemical Society paper on the possibility of nitrogen fixation by electrolysis in the presence of suitable catalysts: N2FIXATION. (The corresponding doi link is http://dx.doi.org/10.1021/acssuschemeng.6b01473.) The reception of this paper was considerably affected by the historical background presented: see the essay “Davy hits the headlines (again)” in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: DAVYHEADLINE.

SECTION XIII: “SEALED PACKETS”

There follows a link to an essay in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: SEALEDPACKETS. This deals with the use of sealed packets by Michael Faraday, William Ramsay, and (in France) by commercial enterprises to secure priority for unpublished ideas.

SECTION XIV: NUCLEAR SCIENCE AND TECHNOLOGY

There follows a link to an essay in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: AEREANDAEAT. This deals with the history of AERE Harwell from 1946 and AEA Technology until the latter went into administration in 2012, and with the renaissance of the site as the “Harwell Campus”.

There follows a link to an essay in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: RUTHERFORD. This deals with the chemical (including medical) uses of radionuclides produced by induced (or artificial) transmutation in the 100 years following Ernest Rutherford’s report that protons were produced when ¹⁴N atoms were bombarded with alpha particles.

SECTION XV: TECHNOLOGICAL FAILURES

There follows a link to an essay in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: CATALYTIC. This deals with a commerical catastrophe caused by Unilever’s launch of PERSIL POWER, containing a manganese catalyst, in 1994, and compares it with previous chemistry and materials failures.

SECTION XVI: DEVELOPMENT OF ELECTRONIC CONCEPTS OF VALENCE

There follows a link to an article in Ambix, the journal of the Society for the History of Alchemy and Chemistry: VALENCE. (The corresponding doi link is
https://doi.org/10.1080/00026980.2021.1984623.  The author – contact details below – still has outstanding electronic “offprints”.) This reviews with careful science the development of electronic concepts of valence up to the pre-war work of Linus Pauling and specifically discusses a controversy that arose in 1934.

SECTION XVII: SCIENTIFIC SITES IN LONDON

There follows a link to an article in Viewpoint, the magazine of the British Society for the History of Science concerning the difficulty of locating historical sites in London because of the renaming of thousands of streets between 1857 and 1939: RENAMING.

SECTION XVIII: SCIENTIFIC CALCULATION

There follows a link to an essay in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: CALCULATION. This deals with the means of scientific calculation available before the 1970s and the transfomational change thereafter.

CONTACT

E-mail michaeljewess[AT]researchinip.com. 

This sub-site was last updated on 23 April 2023.

ADDITIONAL KEYWORDS: specific heat, history of technology, Isaac Newton, London street names, Marylebone street names, RSA, Royal Society of Arts, memorial tablets, Outhgill, Humphry Davy, Henry Moseley, Harry Moseley, French patent law, spy, Fuchs, Pontecorvo, Magnox, fast breeder, Brunel, atmospheric railway, Challenger disaster, Pilkington float glass, Snow, Broad Street, coordinate bond, dative bond, Hunter, Samuel, computers, pocket calculators, mechanical calculators, logarithm tables, slide rules.