A ramble up mount improbable

Soon after he took up his appointment as chief scientific advisor to the government, Sir (as he now is) Robert May expressed a personal conviction that in all the excitement about things much larger than us and much smaller than us, there was a danger of failing to give adequate attention to the fascinating world of objects closer to us in size. The world of the life sciences is well served with popular expositions by many outstanding communicators. In the physical sciences the best-known (and best-selling) books tend to describe cosmology and particle physics. But there is a dearth of accounts at a level accessible to the enquiring non-specialist who wishes to understand the fascinating world of materials that we can see and touch. Why Things Are The Way They Are was written to fill this lacuna.

The key theme of the book is that the properties of materials of which everyday objects are made can be understood in terms of the behaviour of the atoms of which they are composed, and of the movement of electrons among those atoms. Why is it that when you use a plastic spoon to stir hot coffee, the handle does not get hot, but when you use a silver spoon it does? Why is a sheet of glass transparent, while a thinner sheet of aluminium foil is opaque? Why can you bend a piece of copper wire back and forth without breaking it, whereas a glass rod is brittle and will break? Why is a piece of copper reddish in colour, while silver is - well silvery? Why do the filament, the connecting wires, and the insulation of a light bulb behave so differently from one another? The text of the book is peppered with subsidiary questions; in each case followed by a model answer.

The physicist Richard Feynman wrote that if you ask what statement would contain the most information in the fewest words, it would be that all things are made of atoms. Atoms contain electrons, and in some solids these can move around. Though the structure of atomic nuclei is immensely important in nuclear reactions, it plays scarcely any role in understanding the behaviour of materials. Atoms are arranged in crystals in most materials, and many of the mechanical and electrical properties of materials are to be accounted for in terms of the crystalline structure. B. S. Chandrasekhar describes various crystal structures, together with some of the rules of symmetry that they obey. One of these, the fact that an infinite crystal must look the same from the point of view of every atom in it, is given the rather grand name of the cosmological principle, by analogy with the fact that the universe looks the same (on a large enough scale) from every point in it.

A chapter entitled "Particles and waves" introduces the reader to wave-particle duality, some formulas of quantum mechanics, and interpretations of the wave function. The next chapters deal in rapid succession with quantised energy levels in atoms, statistical physics, and the quantum-mechanical crystal, including accounts of the band structure of metals, semiconductors and insulators. At this point all the basics are in place to deal in turn with mechanical, thermal, optical, electrical, magnetic, and finally superconducting properties of materials. In the concluding chapter Chandrasekhar uses the metaphor of a mountain ramble to describe the book. I fear that those readers who have followed him to the end may be somewhat breathless. Others may have given up along the way.

There are some clever explanations in places in this book. For example, thermal expansion is described in terms of an increase in the phonon pressure upon heating combined with a decrease in the phonon frequency when the volume of the crystal increases. Alas, such neat (albeit somewhat obscure) explanations are outweighed by confusing or misleading ones (eg a garden tool warms up more quickly in sunshine than a bowl of water does: it is true that water has a higher specific heat capacity, but what about other effects such as size and evaporation?). Do most materials scientists or condensed matter physicists really think of quartz as made up of silicon dioxide molecules? Some of the simplifications are just plain wrong. For example we are told that normal ovens work by infrared radiation (by contrast with microwave ovens which use microwave radiation). It is asserted that the explanation of how superconductivity comes about is one of the pinnacles of physics, which is I suppose a matter of taste; it happens to be Chandrasekhar's field of research. Also that superconductivity is one of the best understood phase transformations; but even among physics graduates there are few with a good understanding of the superconducting phase transition in metals, and no one has yet come up with a satisfactory account of the superconducting phase transition in oxides.

Almost all the books which have achieved wide popular acclaim in other areas of science express a viewpoint about the limits of the material world. More than one successful author in the life and chemical sciences adopts an evangelical atheism; robustly refuted within the Oxford community by Keith Ward who shows in God, Chance, and Necessity that the same scientific evidence can be used even more convincingly to point to the activity of God. At the cutting edge of the cosmological and particle physical sciences it is more common to find an awareness of what lies beyond the material world. Steven Weinberg writes about scientific advances giving meaning to an otherwise purposeless existence. Stephen Hawking refers openly to the mind of God. Paul Davies takes up that phrase, and speaks for many when he says there is a purpose beyond the merely physical, and that it includes us. Chandrasekhar permits himself no consideration of the metaphysical. He also differs from best-selling non-specialist science writers in the amount of mathematics which he permits himself. In the preface he promises no mathematics that is more advanced than simple arithmetic. The next two pages are devoted to mathematical notation. In subsequent chapters readers are expected to be able to cope with scalar and vector equations, wave vectors and frequencies and their relation to momentum and energy, wave functions in a box, the mathematical relation between temperature and particle energy, functions of three variables (two of them vectors), Bloch waves, Fermi surfaces in reciprocal space, and much more. Rather quaintly, centimetre and gramme units are used -something of a period piece to anyone educated since the introduction of the Syst me Internationale. Apparently parts of the manuscript have been read by friends of the author in fields such as languages, law, history, classics, theatre and music. I have no doubt of the intelligence of these friends, but I have equally no doubt that the amount of mathematics that they were expected to negotiate did not enhance the accessibility of the subject.

So who is this book for? To me it reads like an elementary undergraduate textbook, but with insufficient physics to satisfy the specialist and too much mathematics for the educated layman. There is much in materials science that is both intriguing and compelling for anyone who wishes to enter the 21st century with intellectual vigour. There are many everyday observations and uses of natural and artificial materials that are fascinating to understand. Cambridge University Press is right to identify this field as one in which there should be a significant market for a good book. The topic is wide open for someone else to have a try.

Andrew Briggs is reader in materials,University of Oxford.