William Barlow
Crystallography
1845 - 1934
Contributed by Kent Barlow
Barlow William --born Islington, London, England, 8 August 1845; died Great Stanmore, Middlesex, England, 28 February 1934--
Crystallography
Barlow, a privately educated genius, was perhaps one of the last great amateurs in science. It was only when he was in his early thirties, however, after he attained the leisure afforded by an inheritance from his father, that he began to study and work in crystallography. His original view of the nature of crystalline matter united the mathematical system of symmetry, for which he wrote his own final chapter in the 1890's,
with an anticipation of the new determinations of atomic structure that were to follow after 1910 and also with certain speculations on the relation of symmetry to structure that have not yet been fully elucidated.
The nineteenth century saw a succession of researches into the reason for the order exhibited by crystals.
It was a search joined not only by mineralogists from C.S. Weiss to E.S. Fedorov, but also by mathematicians, notably Auguste Bravais, Louis Jordan, and Artur Schonflies.
Barlow's theories of the properties of crystals were based on the close packing of atoms. His first paper --1883-- in some respects marked no great departure from earlier theories - some dating from the time of Kepler - in which a crystal was regarded as resembling an orderly stack of cannonballs. Barlow was probably unaware of these earlier theories, for by this time a considerable body of chemical theory emphasized the association of atoms into the molecular groupings of compounds. Nearly all of the two-element crystals that Barlow knew, principally the alkali halides, formed cubic crystals, whatever their chemical composition. As he stated in his introductory sentence of "Probable Nature of the Internal Symmetry of Crystals" --page 186--
this ".... led him to believe that in the
atom-groupings which modern chemistry reveals to us the several atoms occupy
distinct portions of space and do not lose their individuality."
Thus, by treating the atoms as individual spheres, Barlow was able to stack
them in five arrangements
that he considered to be the only "very
symmetrical" ones; these correspond to structures known today as body-centered
cubic, simple cubic, face-centered cubic --cubic closest-packed--, body-centered
hexagonal --hexagonal closest-packed--, and one kind of double hexagonal
--but not closest-packed--. Leonard Sohncke criticized Barlow for
including the last structure, claiming that it did not fulfill a strict
definition of homogeneous symmetry around each sphere --the spheres in
alternate layers are surrounded by different configurations--. In
this Sohncke was correct, but Barlow here shown for the first time that
not all the atoms in a symmetrical structure need correspond to a single
set of symmetrically equivalent points.
In his first paper, Barlow also recognized
that body-centered cubic and simple cubic structures admit packing of spheres
of two kinds -- but of equal size, and are therefore suited to be structures
of the alkali halides. Not until his definitive paper on structure,
read before the Royal Society of Dublin in 1897, did Barlow explicitly
display the variations possible in making the two kinds of spheres of two
corresponding sizes. This was a correct guess for the structure of
alkali halides, and through Barlow's collaboration with W. J. Pope, later
professor of chemistry at Manchester, this structure was suggested by Pope
to W. L. Bragg, who in 1913 confirmed it with the first structure determination
by X-ray diffraction.
Barlow also suggested that face-centered
cubic and body-centered hexagonal structures admitted of two kinds of spheres
in the ratio 2:1, and ascribed the latter structure first to ice --wrong!!--
and then to calcite and aragonite only by writing the composition CaC2CO3
--worse!!--
In this paper he also entatively introduced the idea that while a structure might be nearly close-packed, slight changes of the groupings might be important for symmetry. His proposed structure
for quartz was not borne out by X-ray diffraction, because quartz is not
in the class of crystals that approximate close-packing. But he was
on the right track when he used his hypothesis to explain the circular
polarization in quartz, recognizing that a spiral of atoms could be left-handed
or right-handed in similar structures. This was characteristic of
Barlow's approach; he attempted to explain the widest range of crystal
phenomena with his structures: cleavage, such polar properties as pyroelectricity,
varieties of crystal growth, solid solution, and chemical reactivity.
Most of those explanations were in principle correct, if not entirely original,
and contributed to the unraveling of crystal physics in the ensuing
thirty years.
Today it is clear that only a small fraction
of crystalline species can be regarded as close-packed; most, but not all,
are elements or simple compounds of dominantly ionic bonding. But
many more crystals are nearly close-packed with interatomic distances and
angles slightly deformed by covalent bonding. Barlow saw clearly
that deformation of his "root forms" was necessary, and ascribed it to
an unequal contraction of interatomic distances during crystallization
from a more symmetrical but more loosely packed liquid. This led
to the important concept of what is today known as pseudosymmetry, which
Barlow used as a structural explanation of twinning, polymorphism, oriented
overgrowth, and anomalous birefingence in crystals. Similar ideas
were developed by E.S. Fedorov and T.V. Barker, between 1900 and 1930,
into an elaborate system of "syngony" relating the morphlogy of crystals
to similar but not equivalent angles. Although this system has had
little direct use, the general basis set out by Barlow is still fundamental
to the understanding of these crystal properties.
In his first paper, it seems that Barlow
was not aware of symmetry theory beyond the most elementary description
of crystal systems. He was brought up short, apparently, by Sohncke's
comments --1884--, and a couple of years later took a course in crystallography
from H. E. Armstrong and also began associations with H. A. Miers and W.
J. Pope. In 1879 Sohncke published his "Entwickelung einer Theorie
der Krystallstrucktur," in which he expanded the work of Bravais to
sixty-five infinite groups of equivalent points that might be possible
in crystals. Since Sohncke confined himself to congruent equivalence,
however, he could not explain the many known crystals with polar symmetry. Barlow realized the importance of this general mathematical approach, and
in his usual independent and original fashion he set about fitting it into
his models of structure. At the British Association for the Advancement
of Science, on 26 August 1891, he "....concludes his paper by referring
to some geometrical properties of the symmetrical systems of the crystallographer
which he has discovered by an extension of the methods adopted by Bravais
and by Sohncke, and which have greatly facilitated his work in finding
symmetrical groupings to fit the forms and composition of a variety of
different substances. -- page 582-- For ten years, apparently unknown
to Barlow, Fedorov had also been working --and publishing-- on the problem
of explaining crystal symmetry by systems of points, taking his departure
from A.V. Gadolin and including both congruent and mirror-image --enantiomorphous--
equivalence. In January 1891, Fedorov had published in Russian his
complete derivation of the 230 space groups. Artur Schonflies, professor
of applied mathematics at Gottingen, was also pursuing this problem independently,
and following an exchange of letters with Fedorov, he published his version
of the 230 space groups later in 1891 in the Zeitschrift fur Krystallographie.
Barlow did not get into print his own derivation of the 230 space
groups until 1894. In answering a criticism of his work that was
published in the same journal in 1895, he complained that he did nt have
access to the original works of Schonflies and Fedorov.
The differences in method by which the three
authors derived the 230 space groups are no longer of much interest--both
more elegant and simpler systems have since been published. Barlow
was the last of the three to publish, and consequently has had little credit.
In contrast with Feorov and Schonflies, however, Barlow had as his goal
nothing less than a total explanation of crystals interms of structure.
His long paper on crystal structure appeared
next, in 1897, and incorporated his work with space groups. He could
not go further in solving the puzzle without one very important piece of
information, however: the size, or at least the relative size, of
the atoms. He had at one point assumed, on the model of Rudjer Boskovic,
that atoms were points with surrounding fields of attraction and repulsion;
but the forms of these fields, or the corresponding sizes of the corresponding
atoms, were illusory. For the next fifteen years, then, he worked
with W.H. Pope in assembling data on solid-solution substitutions and the
variation of the morphological axial ratios that should reflect variations
in atomic size. While this approach was a valid one, it still contained
a minimum ambiguity, which led Pope and Barlow to postulate that ionic
volumes were proportional to valency. These papers were published
in the Journal of the Chemical Society between 1906 and 1910; after only
a few years, results from X-ray diffraction were sufficient to show that
volumes of ions were, if anything, related to negative charge. But
even in late --December 7 -- 1916, Barlow was still inclined to say, in
a letter to G.F. Herbert Smith of the British Museum --Natural History--
"....I regard the Paper in the Philosphical Magazine, so far as it relates
to the Law of Valency Volumes, as a 'mare's nest' indeed feel confident
that the x-ray results instead of weakening will greatly strengthen the
case for the Law of Valency Volumes."
--letter in files of the Mineralogical
Laboratory--
Barlow was elected to the Royal Society
in 1908 and was president of the Mineralogical Society in 1915-1918.
His career spanned a critical stage in the development of crystallography. His self-educated guesses were sometimes off the mark, but often clear and to the point, and always provocative. In his obituary of Barlow, Pope says:
Although X-ray analysis has increased our knowledge of crystal sturcture in an astounding way and has proved a most useful tool, it has not led to a mechanical theory of crystal structure; it reveals the atomic arrangement but offers no reason why the component atoms seem to be closely packed in some crystalline structures and often loosely in others. The required mechanical theory of crystal structure may be found in some kind of generalisation of Barlow's conception of equilibrium conditions& ---Journal of the Chemical Society--- page 1330
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