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Phase Diagrams of the Elements

University of California Press

Chapter One

This book is a response to the rapid development of experiment and theory in high-pressure condensed-matter physics. The diamond-anvil cell (DAC) has revolutionized the field. Experiments are now routinely performed above 100 GPa, and the first phase transitions above 100 GPa have recently been reported. There is also progress along the temperature axis, with high sample temperatures produced either by immersing a heat-resistant diamond-anvil assembly in a heat bath or by focusing laser light onto the sample and recording the temperature pyrometrically. This latter technique can be used up to the highest known melting points near 5000 K.

Theoretical methods have also been refined, and together with large supercomputers, they have been fashioned into increasingly accurate means of predicting solid structures and melting curves at high pressure. Theorists and experimentalists are now actively collaborating in the study of phase behavior at extremes of pressure and temperature, and the result has been a marked acceleration in the pace of research.

Most of the elements have now been studied in the DAC at high pressures, and numerous new crystal structures have been identified. The complex pattern of structures found in the elements is leading to a new understanding of chemical periodicity and of the old corresponding-states hypothesis. It is now clear that the structures of the solid and liquid elements reflect the full complexity of their atomic structures, and that a simple point-to-point mapping of one phase diagram onto another by a rigid application of the simple corresponding-states principle is incorrect.

The elements show a wide variety of unusual phenomena, such as insulator-metal transitions, electronic isostructural transitions, and melting-curve maxima and minima. It is therefore not necessary to consider compounds for the study of these phenomena, and the development of the theory is considerably simplified by focusing on the elements. There remains much theoretical work to be done.

Previous surveys of the phase diagrams of the elements have been compilations of experimental results[1-7], with minimal theoretical interpretation. In contrast, this book has been written with an emphasis on theory, and I have tried to show how the overall agreement between experimental data and theoretical models is now surprisingly good.

In chapters 2 and 3, I have summarized developments in experimental and theoretical methods, respectively. Chapters 4-15 are organized by the usual elemental groups of the periodic table, except that hydrogen is given a separate chapter. Each element is given a section where the experimental data and theoretical models are summarized. This is shown in Fig. 1.1. In order to cover the entire periodic table, I have summarized data for each element in telegraphic language, using abbreviations listed in Table 1.1. Where sufficient data are available for an element, one or more pressure-temperature phase diagrams are shown. The concluding section of each chapter is an attempt to develop general theoretical ideas about the group of elements in question.

In chapter 16 the low-pressure liquid-vapor transition is discussed for all of the elements. In chapter 17, there is a general discussion of the law of corresponding states and the periodic law in relation to the new high-pressure data for the elements. In the final appendixes, the important thermophysical properties of the elements are listed.

Numerous references are provided to papers where the experiments and theories are described in detail. Nearly all of the high-pressure work cited in this book was done after 1960, and I have emphasized work done since 1980. I have cited papers either published or in preprint form up to September 1990. Statements like "the structure has not been determined" should be understood by the readers as a shorthand form of "as of September 1990, to the best of my knowledge the structure has not been determined." The references emphasize the latest research and are not intended to be complete. For older references, the reader should consult the reviews in Refs. 1-7.

First-order phase transitions are emphasized in this book. Magnetism, superconductivity, and charge-density waves are mentioned only when necessary, and no systematic discussion of these phenomena is offered.

Certain conventions are here adhered to for the construction of phase diagrams: 1) The pressure axis is vertical and the temperature axis is horizontal; 2) Temperature is in Kelvins and pressure is in gigapascals; 3) The origin is always T = 0, P = 0 so that the true size of the stability fields can be seen; 4) The phase boundaries are a synthesis, sometimes subjective, of different experimental results, but with emphasis on the most recent results; 5) Dashed lines indicate extrapolated or uncertain phase boundaries; and 6) Chaotic and inconsistent phase nomenclature has prompted me to use a shorthand crystallographic notation for solid structures which is shown in Table 1.2. The notation contains the Bravais lattice type together with the number of atoms (or molecules) in the conventional unit cell. The very common lattices bcc(2), fcc(4), and hex(2) are given the usual designations bcc, fcc, and hcp for clarity. The conventional unit cells are shown in Fig. 1.2. Phase diagrams are labeled with these notations as well as with the conventional symbol.

I have used SI units where possible, but other units, such as the atomic units used in band-structure theories, are included in the text and graphics. A list of units used in the book is shown in Table 1.3. A list of the most commonly used variables and constants is shown in Table 1.4.

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Excerpted from Phase Diagrams of the Elements by David A. Young Copyright © 1991 by David A. Young. Excerpted by permission.
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