Quasicrystals A Primer

by Janot, C.

• ISBN13: 9780198517788
• ISBN10: 0198517785
• Edition: 2nd
• Format: Hardcover
• Copyright: 1995-06-15
• Publisher: Oxford University Press

Summary

In 1984, physicists discovered a totally unexpected form of matter--a structure that appeared to contain five-fold symmetry axes, which cannot exist in strictly periodic structures--that became known as quasicrystals. In an effort to understand these structures, a theory that employed higher dimensional space groups was conceived, enabling the creation of new alloy phases that exhibited the properties expected from this model. Now in its second edition, Quasicrystals: A Primer offers an up-to-date and accessible introduction to the subject for students approaching it for the first time. Providing lively treatments of a range of practical, experimental, and theoretical topics, the book has been completely updated to reflect the latest advances in quasicrystal research and application. Helpful problem sets and a computer program that generates a Penrose lattice are included as well. Students and researchers in materials science, crystallography, and condensed matter physics will welcome this new edition of a trustworthy, user-friendly survey of an important topic in crystallography.

Table of Contents

How to fill space with atoms in condensed matter states	1	(55)
Introduction	1	(1)
Periodic structures	2	(12)
Lattices, cells, bases, and space groups	2	(3)
Atomic planes, rows, and indices	5	(1)
The reciprocal lattice	6	(1)
Experimental determination of crystal structures	7	(5)
The notion of forbidden symmetries	12	(2)
Liquids, glasses, and amorphous alloys	14	(8)
Description of `disordered' systems	14	(5)
Diffraction with disordered systems	19	(3)
Quasiperiodicity: another type of long-range order	22	(31)
A one-dimensional example of non-periodic long-range order	22	(2)
The sharp diffraction peaks of a Fibonacci chain	24	(2)
Orientational order in quasicrystals	26	(6)
Direct quasiperiodic space tiling procedures	32	(3)
Quasiperiodicity as generated by projection or cut from higher dimensional space	35	(12)
Modulated crystals and quasicrystals	47	(6)
Problems	53	(3)
References	54	(2)
Real quasicrystals: preparation and characterization	56	(56)
Introduction	56	(1)
Preparation methods	56	(7)
The melt spinning technique	56	(1)
Other production techniques for metastable quasicrystals	57	(3)
Conventional casting	60	(3)
Characterization of quasicrystalline samples	63	(15)
Electron, X-ray, and neutron interactions with matter	63	(2)
Electron diffraction	65	(7)
High-resolution electron microscopy	72	(6)
Neutron and X-ray diffraction	78	(1)
The various families of quasicrystals and their order perfection	78	(7)
Quasicrystals versus twinned crystals	85	(6)
The AlCuFe microcrystalline state	88	(2)
The AlCuFe perfect icosahedral state	90	(1)
Phason-induced phase transition and phase diagram in the AlFeCu system	91	(5)
A Phase diagram for the AlPdMn system	96	(5)
Conclusion	101	(2)
Problems	103	(9)
References	106	(6)
High-dimensional crystallography	112	(63)
Introduction	112	(1)
The basic principles of quasicrystallography	113	(25)
The general scheme of experimental crystallography	113	(1)
Particular aspects of quasiperiodic structures	114	(3)
Further problems...and further solutions	117	(13)
`Tailoring' the n-dim atomic objects: final modelling of quasicrystal structure	130	(1)
The high-dim representation of some imperfection: phason shift and strain	131	(7)
Six-dimensional crystallography for 3-dim icosahedral quasicrystals	138	(20)
Why six dimensions?	138	(2)
Possible space group for icosahedral quasicrystals	140	(5)
Body-centred and face-centred icosahedral quasicrystals	145	(1)
The choice of a coordinate system in 3-dim for the PI space group	146	(3)
Some useful properties	149	(4)
Indexing other structure patterns	153	(1)
Direct space description and basic principles for a cut algorithm	153	(5)
Some further consideration of the atomic objects of the n-dim image	158	(8)
A summary of the general properties	158	(1)
From the sphere approximation to faceted objects	159	(2)
Formal faceting conditions of the Aperp atomic surfaces	161	(1)
Is it compulsory to have polyhedral Aperp?	162	(4)
Problems	166	(9)
References	172	(3)
Where are the atoms?	175	(65)
Introduction	175	(1)
Experimental determination of quasicrystal structures	175	(43)
Data collection and scaling procedures	175	(3)
Experimentally determined structure of the AlLiCu quasicrystal	178	(21)
An insight into the experimental determination of AlMn-like quasicrystal structures: an example of parallel components in the atomic surfaces	199	(3)
Structures of the perfect quasicrystals of the AlFeCu and AlPdMn families	202	(10)
Structures of decagonal quasicrystals	212	(4)
Another way of solving the phase problem	216	(2)
Three-dimensional atomic models	218	(14)
General statements about the 3-dim approach	218	(1)
Classes of `quasilattice' and decorations of tiles	219	(4)
The periodic approximants of a quasicrystal structure: basic definitions	223	(6)
Examples of the 3-dim tiling model for icosahedral quasicrystals	229	(3)
Conclusion	232	(2)
Problems	234	(6)
References	235	(5)
Phonons, phasons, and dislocations in quasicrystals	240	(84)
Introduction	240	(1)
Basic knowledge about lattice dynamics and defects in periodic structures	241	(17)
Elastic waves in solids	241	(3)
Lattice waves and Brillouin zones	244	(4)
Superstructure effects and energy gaps	248	(2)
Lattice waves in three-dimensional lattices	250	(3)
Strain/stress distribution in periodic lattices due to structure defects	253	(3)
Generalized continuum elasticity and influence of fluctuating strain fields on diffraction patterns	256	(2)
Phonons in disordered materials	258	(6)
Vibration modes in an atomic chain with mass defects	258	(3)
Vibration modes in `amorphous solids'	261	(1)
Fractal structures and fractons	262	(2)
Modulation and quasiperiodicity effects on lattice dynamics	264	(34)
A qualitative approach to modulation effects	264	(4)
The notions of phason and amplitudon modes	268	(3)
The modulated spring model	271	(4)
Excitation in incommensurate phases	275	(3)
Numerical results for a Fibonacci chain	278	(11)
Lattice dynamics of three-dimensional quasicrystals: calculations and experiments	289	(9)
Concepts of elasticity and defects in quasiperiodic structures	298	(22)
The density wave picture and the high-dim representation of quasiperiodic structures	298	(8)
Examples of phonon-like strain fields	306	(4)
Examples of phason-like strain fields	310	(6)
Examples of dislocation configurations in quasicrystals	316	(4)
Conclusion	320	(1)
Problems	321	(3)
References	322	(2)
A little more about the physics of quasicrystals	324	(83)
Introduction	324	(1)
Is perfect quasicrystal growth an acceptable physical concept?	325	(22)
The one-dimensional case as an illustration	325	(4)
Criteria for the physical growability of a 2-dim Penrose tiling	329	(4)
The vertex matching rules as local growth requirements for a quasicrystal	333	(7)
Decapods acting as very efficient screw dislocations	340	(7)
Can icosahedral order be grown out of disorder?	347	(4)
The Landau theory	347	(1)
Liquid-solid transitions	348	(1)
Liquid to isosahedral solid transitions	349	(2)
The alternative ways for a quasicrystal to grow	351	(8)
Random accretion models or relaxation processes	351	(1)
What about random tiling growth?	352	(4)
Quasicrystal growth via `relaxation processes'	356	(3)
Where are the electrons and how do they move?	359	(39)
The basic concepts as introduced for regular crystalline structures	359	(8)
Effect of disorder on electron behaviour	367	(5)
Experimental electronic properties of quasicrystals	372	(10)
The theoretical aspects of electrons in quasicrystals: the critical states	382	(10)
Quasicrystals as a hierarchy of clusters	392	(6)
Conclusion	398	(1)
Problems	399	(8)
References	401	(6)
Index	407