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What is crystallography?

Memorandum "Crystallography: current and future tasks"

The memorandum was written and published by the Wissenschaftskolleg Kristallographie of the Deutsche Gesellschaft für Kristallographie (German Crystallographic Association) in the years 1990 and 1991.

Editor: Th. Hahn, Aachen

Authors: W. Bronger (Aachen), H.J. Bunge (Clausthal-Zellerfeld), H. Burzlaff (Erlangen), G. Ertl (Berlin), K. Fischer (Saarbrücken), Th. Hahn (Aachen), S. Haussühl (Cologne), P. Paufler (Leipzig), W. Prandl (Tübingen), W. Saenger (Berlin), H. Schulz (Munich).

1. Introduction

Modern crystallography is concerned with the spatial ordering of atoms (structure) in condensed matter, with the structural changes, as well as with the physical, chemical, and technical properties of solids, as well as with relations to materials and geosciences.

In Germany, crystallography was developed from two roots: within the field of mineralogy, in the 18th century, chairs for mineralogy and crystallography were already provided, which led to a flourishing of the subject in the 19th and the early 20th century. For example, the establishment of the Zeitschrift für Mineralogie und Kristallographie by P. Groth in 1877 is mentioned, that soon developed to the internationally leading organ of the area. Since the diffraction of X-rays by crystals was discovered in 1912, important impulses were added from physics, which are connected, among others, with the names of M. von Laue and P.P. Ewald. By W.H. and W.L. Bragg, crystallography developed to a modern discipline, in which the crystal structure is the centre of interest.

Motivated by a memorandum of the DFG (German Research Foundation) an intensification and extension of the crystallographic educational and research work took place after 1960 in the former FRG. Nowadays, about 30 independent laboratories or working groups for crystallography exist, whose majority developed out of the mineralogy. At the same time, crystallographic research groups in chemistry, physics, biology and materials science were developed. Beside the universities, departments were equiped in the Max-Planck laboratories and large-scale research facilities, which substantially use crystallographic methods.

In the former GDR, crystallographically oriented research was performed in institutes in the fields of physics, chemistry and materials engineery of the universities and of the Academy of Science. At two universities, Berlin specialized in the area of physics and Leipzig in the area of chemistry, the graduation with a diploma in crystallography was created.

In Germany, the following areas of crystallography developed in particular:

  • Mathematical crystallography (symmetry)
  • Inorganic structural chemistry
  • Mineralogical crystallography
  • Biological crystallography
  • Crystal growth
  • Crystal physics
  • Diffraction physics and X-ray optics
  • Development of new experimental techniques for single crystals and polycrystalline systems

2. Crystallography in research and teaching

With the discovery of the periodic ordering of atoms in crystals by Max von Laue in Munich in 1912, modern structural crystallography developed. Its results led to serious changes in the "conception of the world" of chemistry, physics, geosciences and materials science. This established crystallography as a basic subject for the understanding of condensed matter.

The most important contributions of crystallography to the research in natural science and technology can be characterized as follows:

  • The symmetry, in particular the theory of the space groups, forms the basis for the understanding of the structure of crystals as well as of phase transtions and domain structures. Symmetries in four and more dimensions describe modulated structures and quasicrystals.
  • Basis for the investigation and the application of crystalline materials and their defects are the crystal growth and the understanding of crystal growth processes.
  • The systematic analysis of the structure of polycrystalline materials and the knowledge of their material properties resulting from it have direct meaning for materials science and technical applications.
  • The methods of the crystal analysis as well as its constantly growing automation received an unexpected boost: today more than 120,000 crystal structures are well-known, with an increase of approximately 8% per year.
  • In biology the structure solution of the DNA double helix released a rapid development of molecular biology. Crystallographic methods allow the determination of complicated three-dimensional structures of proteins consisting of thousands of atoms in such a detail, that statements about their chemical and biological functions become possible.
  • The systematic collection and interpretation of the great amount of crystallographic data, particularly in chemistry, mineralogy, biology and materials science, require the development and the application of large data bases.
  • A presently revelant point of research is the deviation from the strict lattice order: structure defects, order disorder features, pseudosymmetries, modulated structures.
  • The macroscopically anisotropic physical properties of crystals are described by tensors and find increasingly atomistic interpretations. They are substantial for the understanding of the relations between structure and (technical) properties.
  • In co-operation with scientists from other fields new physical methods and instruments with typically crystallographic topics are developed. They lead to qualitatively new or quantitatively more extensive results.

Many Nobel prizes for physics, chemistry and medicine were assigned to crystallographically oriented research, beginning with von Laue in 1914 and the two Braggs in 1915, until Deisenhofer, Huber and Michel in 1988 for their contributions to photosynthesis.

The interdisciplinary nature of crystallography is also apparent in the teaching of the field:

  • The students receive deepened knowledge in neighbouring fields: chemists with a predominance for materials, mineralogists and biologists are made familiar with physical techniques and measuring methods; physically oriented students learn "substance thinking" and are confronted with a variety of complicated structures and symmetries.
  • Intensive handling of practical mathematics, processing of large quantities of data, with computers and program systems.
  • Overview of all the aspects of a solid, from the synthesis and crystal growth over the structure and crystal defects to subtle, also technically interesting properties of crystals and polycrystalline systems.
  • For students who elect crystallography as a major or minor field of their studies, interesting topics for graduate research as well as attractive and diverse employment possibilities, both in the industry and in research institutions exist.

For a long time, crystallography is firmly established as a core subject in the diploma course of studies in mineralogy. At numerous universities, crystallography is a choice subject in different other diploma courses of studies; at some universities it is already mandatory for materials science.

3. Crystallography in mineralogy, chemistry and physics


One of the first important results of the X-ray structure analysis after 1912 was a based on structural crystal chemistry mineral systematics for oxides, sulfides and silicates, which is nowadays still valid. In particular, the discovery of the various and complex connectivity of tetrahedra in the mineralogical fundamental group of silicates led to important results about rock forming and technical processes. In minerals on one hand phase transitions as function of temperature and pressure (polymorphic phases) are common, on the other hand a large variety of atomic substitutions (solid solutions) occur quite often; special petrologic meaning refers to the Si/Al order-disorder procedures in feldspar.

In geoscience, these crystallographic research fields contribute to the understanding of the structure of the earth's crust and the upper earth's mantle, the moon and the meteorites, as well as time-dependant reactions, frequently running in geological times. Geochemistry uses crystallographic results for the geo thermal barometrics, for the development of models about the moon and the planets, as well as most recently also to a reasearch on the environment. Technical mineralogy uses crystallographic methods and conceptions for the improvement of technical materials and procedures.


Within the field of molecular chemistry, the rapid development of modern X-ray crystal analysis led to the fact that it became the main method for the analysis of the constitutions of small molecules up to polymers and proteins. It is used by routine in research and industrial laboratories for the characterisation of the products as well as for the evaluation of synthesis strategies. So far about 70,000 structures were solved for molecular crystals.

Solid-state chemistry received a fundamentally new concept by the results of the structural analysis: the replacement of the pure molecule conception in the 19th century by the "collective structure" of the solid, in which the atoms are three-dimensionally linked. Furthermore non-stoichiometry was understood, in particular the "phase width" of intermetallic compounds, which was up to then inexplicable. Only crystal structure analysis made a deeper understanding of the "nature of the chemical bonding" in solids possible, e.g. by the direct illustration of bonding electrons.

These developments led to a better understanding of important physical properties of solids and decreased the gaps between chemistry and physics in solid-state research.


The relations between physics and crystallography are traditionally particularly close. This fact is based on one hand on the physical techniques, which are predominantly used by crystallographers, such as diffraction, topography and spectroscopy. On the other hand, it results from the great importance of crystallographic research results for different areas of physics.

In the field of solid-state physics, these relations are shown by two examples: crystallography supplies crystals with structures of increasing complexity for physical experiments and their atomistic interpretation: from diamond and graphite to ferroelectrics and low-dimensional electrical conductors. Typical crystallographic concepts, e.g. distortion of coordination polyhedra under a crystal field, structure domains (twins) and structural defects, find direct applications in the physical research.

The theory of the space groups and their representations developed to an essential tool for the theoretical treatment of phase transitions, chemical bonds (band structure), Brillouin zones as well as thermal vibrations in crystals (phonon dispersion, lattice dynamics).

4. Crystallography in molecular biology

All biological processes are regulated and carried out by nucleic acids (DNA) and proteins. These processes can only be understood if the spatial structures of such complicated macromolecules and in particular the geometry of their active centers are known in atomic detail. Since it is possible to crystallize nucleic acids, proteins and even intact viruses, they are accessible to X-ray structure analysis; therefore crystallography received a key function in molecular biology.

The gene technology allows to change the structure and thus function of a protein to a large extent. This "protein design" is only possible if the structure of the protein is well-known, which stressed the importance of structural analyses even more. Methodical innovations, such as the development of area detectors and the availability of intensive synchrotron radiation, permit the rapid measurement of extensive data sets. More efficient computers and graphic screens allow "on-line" interpretation of the data and representation of the complicated structures. Computer simulations extend structural analysis and "protein design", since they represent time-dependent dynamic operational sequences, in particular the formation of complexes with smaller molecules, which affect proteins.

Substantial for "protein design" is the availability of increasing data bases, which contain above all crystallographically obtained structural data. Thus, crystallography gave important insights into biology to the basic research and opened new possibilities in the medical and pharmaceutical research.

5. Crystallography in materials science

Growth and application of single crystals

A systematic and comprehensive investigation of the physical and physicochemical properties of crystallized matter requires the availability of large crystals of high quality. Their growth and characterization belong to the most important tasks of crystallography, together with the development of new materials, which are closely related to technological applications, like for example electronics of semi-conductors, integrated optics, optoelectronics, ultrasonics, high-frequency engineering, solid lasers, radiation detectors, optical memories, piezoelectric position indicators, elements for energy conversion as well as synthetic jewels and hard materials. Improvement of the technologically relevant properties of crystalline materials nearly always presupposes a thorough knowledge of the appropriate properties of the single-crystal bodies, including their defects (real structure).

Polycrystalline systems

Most materials such as metals, ceramic materials and partly crystalline polymers have polycrystalline structures. The same applies also to nearly all the materials of the earth's crust studied in geosciences. A quantitative understanding of the properties of such materials must proceed from the crystal structure and the properties of the individual crystallites. In addition to this, numerous further structural parameters are to be taken into account, which characterize the polycrystalline aggregate. These are statistic distribution functions of size, form and arrangement as well as the crystallographic orientation (texture parameters) of the crystallites in the aggregate. These parameters determine typical aggregate properties such as macroanistropy, micro heterogeneity, grain boundary heterogeneity and porosity. For the investigation of the polycrystal parameters, primarily microscopic imaging as well as X-rays, electrons or neutrons diffraction methods are used (crystallography of the polycrystal).

Polycrystalline aggregates result from or are modified by solid-state processes of all kinds, like primary crystallization, plastic deformation, recrystallization, phase transitions as well as rigid rotation of crystallites. The study, particularly of the orientation parameters of the polycrystal is therefore a very powerful method for the study of these processes themselves. In geology these parameters give information about processes, which were finished millions of years ago. Processes of the solid state in the polycrystal are the basis for the production of very different polycrystalline materials with desired macroscopic properties. This applies particularly to many new "High Tech" materials, like intermetallic phases, structural and advanced ceramics, high temperature superconductors, hard coating materials, liquid crystal polymers, etc. These materials often consist of crystals with complicated crystal structures and strong anisotropies. Their development takes place on the basis of crystallography. The crystallography of polycrystalline aggregates is therefore connected particularly closely with modern materials science.

A special working field (powder diffraction) is concerned with the analysis of diffraction diagrams from polycrystals with the goal of the crystal analysis, phase analysis, stress measurement, texture analysis, as well as the determination of stacking faults. A central problem of this field is the mathematical "deconvolution" from diffraction diagrams with an arbitrary orientation distribution of the crystallites of the polycrystalline system.

6. Crystallography of surfaces and boundary surfaces

Each solid is limited by surfaces. Because of its boundary surface environment, an atom or molecule situated close to the surface has a different atomic environment than a particle situated in the bulk. Molecules close to a boundary between the bulk and a gas or liquid phase can interact chemically and cause further changes of the surface texture. These processes form the basis of the heterogeneous catalysis or of the corrosion processes; also in microelectronics, the reducing the dimensions of the components, give more importance to surfaces and boundaries. The key to understand the properties of surfaces and boundary surfaces lies, beside the direct observation with electron microscopy or raster tunnel microscopy, in the analysis of their structure by means of crystallographic methods.

Technically used solid materials are usually polycrystalline, like for example the ones used as catalysts. For the investigation of the elementary processes taking place in those materials, single crystals are appropriately used as model systems. The solution of the atomic structure is preferably done via application of the diffraction of low-energy electrons (LEED). In addition, the methods of the X-ray structure analysis, together with the use of synchrotron radiation, are increasingly applied.

7. Instrumental and methodical developments at large-scale research institutions

For the structural research with atomic resolution, neutron and synchrotron radiation sources caused an evolution thrust. The diffractometers, first designed similarly to conventional X-ray instruments, were soon adapted to the special characteristics of the radiation.

An important step for neutron scattering was the establishment of the high-flux reactor at Institut Laue Langevin in Grenoble. While initially, the structure analysis concerning light atoms, in particular hydrogen isotopes, dominated, more advanced methods of neutron scattering gained growing importance later: use of the continuous neutron spectrum, including shift of its intensity maximum by "hot" and "cold sources", time structure of pulsed sources, the magnetic moment (magnetic structures, polarized neutrons) and the well measurable energy transfer by means of inelastic neutron scattering (dynamics, see section 8). The deficit in neutron sources, which exists in Germany since years, delayed new developments and generated great demand. The conception of new methods and instruments for spallation neutron sources is a further challenge for the next years.

Crystallography with synchrotron radiation is operated almost exclusively with X-rays in the range of medium to short-wave lengths, with a particle energy of E>2keV, in Germany mainly in the HASYLAB at DESY. It requires a compatibility of the devices with the special properties of the radiation, and hence numerous deviations from traditional instrument types. Synchrotron radiation makes possible qualitatively new experiments: use of the tunability of the incident radiation (e.g. for energy dispersive powder diffractometry, anormalous dispersion, EXAFS), its collimation (e.g. high resolution, interferometry, stationnary waves), its polarization (non Bragg scattering, atomic anisotropy, X-ray crystal optics) and time structure (kinetics). These research field are developing rapidly.

For both kinds of radiation, strong interactions exist between the construction of new radiation sources, in particular so-called "dedicated sources" (in Europe e.g. the European Synchrotron Radiation Facility, Grenoble), the design of instruments and the developement of new methods by physicists and crystallographers.

8. Dynamic processes in condensed matter

A large number of physical properties of crystals and amorphous or badly crystallized materials (such as glasses, polymers and bio polymers) are of a dynamic and/or kinetic nature. Both effects, "dynamics" and "kinetics", can be very roughly distinguished by their time scales: in the first case atomic or molecular times, from approximately 10-14 up to 10-7 seconds are involved, in the second case macroscopic times, from 10-6 seconds up to hours. This large time scale spans a large variety of phenomena: the shortest of the periods mentionned above correspond to the thermal vibrations of the atoms (phonons) in crystlas (e.g. in the structures of diamond or silicon); times around 10-9 seconds are characteristic for the diffusion of atoms in crystals and for atomic movements in polymers and bio polymers.

Since the full range of the time scale spans to about 18 orders of magnitude, a simple experimental method is not sufficient for the elucidation of the phenomena. The shortest times (within the range of 10-14 to 10-11 seconds), with simultaneous spatial resolution, are measured by means of energy shifts of neutrons in triple-axis spectrometers (inelastic neutron scattering). Slower structural changes are accessible to direct measurements by stroboscopic methods. Changes of the crystal structure within the range of one second can today already be recorded continuously.

The movement of atoms in solids as well as the chemical bonds between the atoms depend on pressure and temperature. By changes of these variables of state, structural phase transformations can be initiated, the mechanisms of which can be elucidated by means of diffraction experiments with neutrons and X-rays as well as of the anomalous behavior of macroscopic properties. From this a deeper understanding of the characteristic dynamic interaction processes on the atomic level can be gained.