and by Albert Hull at the General Electric Laboratories, Schenectady, USA [71–
73]. In 1913 Debye had published papers which calculated the influence of lattice
vibrations on the diffracted intensity (the Debye factor), and, in February 1915, he
calculated the intensity of a diffracted beam for a random distribution of molecules.
This encouraged him to propose to his student Paul Scherrer that he try and observe
the diffraction of X-rays by a crystalline powder. They obtained very sharp lines
when they studied the diffraction pattern from powdered LiF, and related studies on
other halide salts confirmed the usefulness of the technique and also demonstrated its
ability to show the presence of impurities. They also studied graphite and proposed
that it belonged to a trigonal space group. In 1918 they published a very important
analysis which calculated the effect of grain size on the line broadening of the
powder diffraction patterns. The same year, Debye and Scherrer deduced from the
analysis of the intensity of the diffraction lines that, in LiF, one valence electron is
shifted from the lithium ion to the fluorine ion, a first step towards the study of
electron density with X-ray diffraction. This area has attracted much interest in
recent years because of the increased accuracy of the structural data and the ability
to calculate the electron density distribution in molecules with great accuracy [74].
Hull [71, 72] did not have access to a single crystal of iron but discovered that he
could obtain a good diffraction pattern from iron filings and interpreted the data on
the basis of a body-centred cubic lattice. Observing the decrease in intensity with
increasing Bragg angle, Hull concluded that the X-rays were diffracted by the
electron cloud around the nucleus, and not by point diffraction centres. Diffraction
by powders thus led both Debye and Scherrer and Hull to make observations of a
fundamental nature. Hull then undertook an impressive series of 26 structure determinations of elements including Al, Ni, Li, Na and graphite. Debye and Scherrer had
concluded that graphite was trigonal, but Hull’s reinvestigation showed that it is
hexagonal and based on layers of carbon atoms.
If a flat detector is placed perpendicular to the incident beam, on the opposite side
of the sample, the set of reflections from the multiple crystals appear as continuous
circles. The overall result is a set of concentric circles with radii governed by the
Bragg equation. Therefore, the information obtained is identical to that gained from
the conventional Bragg experiment, i.e. the unit cell dimensions and unit cell
symmetry are in principle identical. The net effect of using powder sample rather
than a single crystal is to effectively compress the information into a
one-dimensional output where the only variable is θ. This technique proved to be
particularly useful for studying minerals and solid-state inorganic compounds which
crystallised in high-symmetry space groups. For high-symmetry crystals, it is possible to assign each circle a unique Miller index and measure its intensity. The unit
cell structure can then be solved from these data [75–77]. The compression of the
data in this way can be problematic when the diffraction circles for different (h,k,l)
reflections have similar values of θ. This is particularly problematic for monoclinic
and triclinic crystals. The technique proved to be very useful for studying interrelated isomorphous compounds with the same stoichiometry and was very effectively
developed by Goldschmidt to study minerals and solid-state compounds [44]. Within
a few years, this group had solved the structures of more than 200 structures
Early History of X-Ray Crystallography
29
73]. In 1913 Debye had published papers which calculated the influence of lattice
vibrations on the diffracted intensity (the Debye factor), and, in February 1915, he
calculated the intensity of a diffracted beam for a random distribution of molecules.
This encouraged him to propose to his student Paul Scherrer that he try and observe
the diffraction of X-rays by a crystalline powder. They obtained very sharp lines
when they studied the diffraction pattern from powdered LiF, and related studies on
other halide salts confirmed the usefulness of the technique and also demonstrated its
ability to show the presence of impurities. They also studied graphite and proposed
that it belonged to a trigonal space group. In 1918 they published a very important
analysis which calculated the effect of grain size on the line broadening of the
powder diffraction patterns. The same year, Debye and Scherrer deduced from the
analysis of the intensity of the diffraction lines that, in LiF, one valence electron is
shifted from the lithium ion to the fluorine ion, a first step towards the study of
electron density with X-ray diffraction. This area has attracted much interest in
recent years because of the increased accuracy of the structural data and the ability
to calculate the electron density distribution in molecules with great accuracy [74].
Hull [71, 72] did not have access to a single crystal of iron but discovered that he
could obtain a good diffraction pattern from iron filings and interpreted the data on
the basis of a body-centred cubic lattice. Observing the decrease in intensity with
increasing Bragg angle, Hull concluded that the X-rays were diffracted by the
electron cloud around the nucleus, and not by point diffraction centres. Diffraction
by powders thus led both Debye and Scherrer and Hull to make observations of a
fundamental nature. Hull then undertook an impressive series of 26 structure determinations of elements including Al, Ni, Li, Na and graphite. Debye and Scherrer had
concluded that graphite was trigonal, but Hull’s reinvestigation showed that it is
hexagonal and based on layers of carbon atoms.
If a flat detector is placed perpendicular to the incident beam, on the opposite side
of the sample, the set of reflections from the multiple crystals appear as continuous
circles. The overall result is a set of concentric circles with radii governed by the
Bragg equation. Therefore, the information obtained is identical to that gained from
the conventional Bragg experiment, i.e. the unit cell dimensions and unit cell
symmetry are in principle identical. The net effect of using powder sample rather
than a single crystal is to effectively compress the information into a
one-dimensional output where the only variable is θ. This technique proved to be
particularly useful for studying minerals and solid-state inorganic compounds which
crystallised in high-symmetry space groups. For high-symmetry crystals, it is possible to assign each circle a unique Miller index and measure its intensity. The unit
cell structure can then be solved from these data [75–77]. The compression of the
data in this way can be problematic when the diffraction circles for different (h,k,l)
reflections have similar values of θ. This is particularly problematic for monoclinic
and triclinic crystals. The technique proved to be very useful for studying interrelated isomorphous compounds with the same stoichiometry and was very effectively
developed by Goldschmidt to study minerals and solid-state compounds [44]. Within
a few years, this group had solved the structures of more than 200 structures
Early History of X-Ray Crystallography
29