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. The
following links to a Note in the Royal Society of Chemistry’s Historical Group Newsletter and summary of papers: ALICE.
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
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 18 February 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.
