Crystals and Crystallinity
- the substance of a talk to ERMS in February 2011 by Ian Mercer
A colourless crystal of topaz just as it grew in the rock
Many ERMS Members enjoy the delights of crystals and the variety and beauty of crystal form as part of their hobby. Yet materials may be crystalline inside and have no visible external crystal form. A deeper delight and appreciation of materials starts with having some idea of what is meant by the word crystalline.
Inside information is neat and tidy
For any material to be considered as crystalline, it has to be made up of atoms arranged with some degree of order. It need not display any external crystal form - it may even be a pebble or a fashioned gem with all external crystal evidence removed: cut, ground or worn away. It is still crystalline inside - nothing has changed there. The internal orderly arrangement of atoms in each crystalline material is referred to as its crystal structure. Crystal structures are classified in crystal systems, based on three-dimensional patterns and their symmetry. The significance of non-crystallinity also is important in the study of materials.
The crystal structure of diamond
Inner 'Design'
A crystalline material is a 3-D arrangement of electronically-linked atoms in a regularly-repeating pattern, a sort of natural 'atomic design'. The fundamental property of the crystal is its atomic pattern, and the external form is only one result of this pattern. X-ray methods probe deeply into the crystal structure, telling us how the atoms are arranged and throwing light on the relation between structure and physical properties.
Artificial crystals of quartz made in a factory
Natural and Artificial Crystals
Conditions for the crystalline assembly of atoms and molecular units are found within, upon and far out from this planet – and even inside you. Different conditions allow different assemblies of atoms, so long as the atoms are available. Natural crystalline materials in and upon this planet are both inorganic and organic in origin. Crystalline solids of natural, inorganic, geological origin are referred to as minerals. However, artificial crystalline materials are of ever greater importance to us. There is a constant drive for new techniques of growing and using crystalline materials for optics, electronics and other industrial processes and research, including semiconductors, magnetic and optical crystals, organic and biological crystals, metals and thin film crystals. This involves physicists, chemists, materials scientists, electronics engineers and metallurgists.
Submicroscopic mystery
Despite all this interest and consequent rapid developments, the mechanics of crystallization still remain largely mysterious, which is an important and fundamental problem. The essential difficulty is that the processes taking place at the atomic scale are still barely or not at all accessible to current experimental methods. Crystallinity and the word crystal are concepts that are based on a submicroscopic scale of pattern. The crystalline world of atoms, with its natural, three-dimensional designs, is not particularly familiar to us. However, certain relevant and fascinating aspects of design and pattern are well within our everyday experience. It is ‘easy’ - that is, energetically favourable - for salt or sugar to crystallize in our kitchens; it is energetically ‘easy’ for the crystallinity of bone and fingernails to develop in the womb; technologists make furnace conditions energetically favourable for the natural coming together of a crystalline pattern of atoms in a synthesis of a beautiful ruby, to copy what the Earth has long produced.
There are just five lattice patterns in two dimensions
A 2-D design with a rectangular lattice pattern
Design, Structure, Pattern, Lattice
Crystalline materials, whether they are natural, artificial, inorganic or have an organic origin, can be imagined as naturally-formed 3-D designs of atoms and atomic links in regular, repeating arrangements. There are many thousands of different regular atomic arrangements, or crystal structures, yet they all conform to only fourteen different types of 3-D pattern. Such patterns are mathematical lattices and they are used as an aid to the classification of the huge variety of crystal structures.
AND
Pattern of atoms related to crystal face angles
Shapes of Crystals
The internal structure of a particular crystalline substance is constant and any outward shape of a crystal must have a definite relationship to this structure. The regularly repeating arrangement of the atoms and bonds which make up any crystal is the inward reason for the arrangement of exterior natural crystal faces. Many crystals show a symmetrical arrangement of crystal faces and such external evidence can be of use in its identification. Crystal faces are natural surfaces which reveal where layers of atoms and bonds in crystal structures have stopped growing or reforming. Crystal faces are relatively rare in crystalline materials because most crystals have grown together, leaving no chance for faces to develop. Well-formed crystals may be made up of similar, symmetrically-related faces to give a single form. A cube and an octahedron are examples of single forms, while a crystal which consists of two or more forms is termed a combination of forms.
Directional face striations and cleavage fissure in calcite
Directional properties
The term directional normally refers to all variations in material properties where the variation is controlled by the structure of the material. This internal structure influences a material’s physical, including optical, properties in particular ways by producing certain directional effects both on the surface and within the material. Directional physical properties are characteristic of all crystalline materials. These properties may be evident on the surface of the material, e.g. crystal form, face-markings (e.g. etch and growth pits, growth marks and face striations) and differential hardness, as well as within the material, e.g. oriented colour zones, internal crystal growth zones or ‘grain’, oriented inclusions and cleavage. Note that fracture is not a directional property, as it is not crystal-structure controlled: it is a property of solid materials in general and is not specific to those that are crystalline. Directional properties influence how crystalline materials may be used and they can assist greatly in the observation, recognition and identification of many crystalline materials.
A clear calcite crystal optically doubles a laser beam
Crystal Optics
Directional effects upon light, i.e. directional optical properties, are possessed only by optically anisotropic materials due largely to their ability to polarize the transmitted light. Not all crystals are optically anisotropic; even though all crystals are physically anisotropic. Again, it is the inner structure of a crystalline material that exerts its control of the optical behaviour of the material. Structurally-controlled optical behaviour may be detected in, and used in the testing of, uncut as well as cut and polished crystalline materials, including those which possess no crystal form as external evidence. Interesting and useful interactions of crystal structure and light waves are observed as, for instance, double refraction, pleochroism, optical extinction and in interference colours and interference figures.
Crystal Observation
Simple, first-line observation of crystal form, face markings e.g. striations and trigons, of colour, growth zones, ‘grain’ and oriented inclusions, of double refraction, is a process that is rapid and constantly available to anyone interested to look; with a 10x lens and simple flashlight, useful observation is possible in virtually any circumstance. Of similar importance is the observation of cleavage cracks and surfaces in single crystals, as in a cut diamond or in a rough pebble of topaz; of crystal growth- and colour-zones as in many amethysts; of oriented inclusions, as in ruby and sapphire. Observation of cleavage ‘twinkles’ in the grains within marble and jadeite can greatly aid identification and distinction from other, similar materials. With simple and portable instruments, observation can be extended, for instance to the detection of optical extinction effects in a polariscope, including interference figures; and of pleochroism, e.g. in tourmaline or ruby using a dichroscope. The use of many such observations is possible with both cut and uncut materials. Well-shaped crystal specimens are a rather rare manifestation of the neat order of electronic bonds within – they can provide an extra clue to the 'natural design' of inner crystal structure.
Feldspar crystals in Shap granite outside St.Paul's Cathedral
You can see the crystals in jade by reflected light
A collector's crystal of calcite at the ERMS Show
A beautiful sapphire crystal in calcite
For the enjoyment of crystal form and beauty, the collecting of beautiful and unusual or particular crystals or groups of crystals has for long been a very important hobby, even contributing to the advent of the world’s most acclaimed natural history museums; crystal collecting has a dedicated, sometimes fanatical, following, with an important specialist literature and full mineral and gem show calendar. The enjoyment of crystalline materials, of building and facing stones, gems and antiques, rocks and minerals, artificial and special crystals, design and architecture, is open to all who open their eyes to the fascination of crystallinity.
An extended version of this article is available to ERMS Members from Ian Mercer.
Book and websites
Cochranes sell kits of structural crystal models for you to make and investigate structure and symmetry; diamond gives an enjoyable and instructive start; ice is beautiful to put up on the wall: see http://www.cochranes.co.uk/main.asp
http://books.google.com/books allows you to find many older books to read on your screen. Just enter the title or keywords such as 'crystal' and 'growing' or 'light' and you will find two of the most enlightening crystal books ever written. These are:
Crystals and Crystal Growing, a paperback by Alan Holden and Phylis Morrison MIT 1982;
ISBN-13: 978-0262580502 (originally Holden and Singer, Heinemann 1960, but it hasn't changed).
Crystals and Light, a paperback by Elizabeth Wood; Dover Publications Inc.; 2nd edition 1977; ISBN-13: 978-0486234311 (originally Van Nostrand 1964, it remains unchanged); another truly excellent book.
Don't be put off by the early original publication dates of these two books – they are ideal guides which take you well into the world of the crystalline state. They are written in simple and straightforward language but be prepared to concentrate.
The Material World – Hardback ISBN-13: 9780521451475 This book was also available as a paperback 'The Cambridge Guide to the Material World'. A great insight into atoms, bonding, crystalline and non-crystalline materials.
http://www.clarku.edu/%7Edjoyce/wallpaper/ - a beautiful education into wallpaper designs, their symmetry groups and lattice patterns.
http://www.mcescher.com/Gallery/gallery-symmetry.htm - enjoy M C Escher!
http://www.quartzpage.de/intro.html - absolutely everything about quartz...
http://www.students.bucknell.edu/projects/xray/betatest/PlaneGroupSymmetry/PlaneGroupSymmetryElements.html
- deeper 2-D symmetry explained in moving images.
http://www.ibiblio.org/e-notes/Mview/Packed.htm - move these structures in 3-D.
There is a complete, well-illustrated crystallography course for you at -
http://www.xtal.iqfr.csic.es/Cristalografia/index-en.html
For designers, mathematicians and those with a curious mind: the trouble with five - http://plus.maths.org/issue45/features/kaplan/index.html