Definitions

The materials encountered in metallurgy are usually crystalline. Melts and vapour and, very recently, glassy materials (supercooled, frozen melts) are considered only as limiting cases. We start by assuming that we know the crystal structure of every substance. It can be determined by the well-known X-ray methods and described crystallographically in terms of atomic positions, symmetry, unit cell, etc. (A structural description can be given for non-crystalline substances also, but the atoms do not adhere to it as strictly as in a crystal.) As stated in the introduction, bulk metal does not normally consist of a single crystal but of many crystal ‘grains’, in other words it possesses a microstructure. The grains differ from one another in orientation and sometimes also in crystal structure or composition. In the former case the system is described as homogeneous, in the latter heterogeneous. The constituents of the latter, which are in themselves homogeneous, are called phases. The crystal structure, composition and volume fraction of each vary in such a way that the free enthalpy of the system in equilibrium is a minimum. Phases as defined here transform into one another by first-order transformations (defined thermodynamically by discontinuities in the first derivative of the enthalpy with respect to temperature) such as melting (see chapter 5).

Since metals constitute a class of solids it might well be asked what aspects of Physical Metallurgy do not already fall within the scope of solid state physics. If Kittel's book [1.1] is taken as a guide there is at least one basic metallurgical concept which is unfamiliar to solid state physicists. Metallurgy relates the properties of metals and metallic ‘mixtures’ or alloys to their microstructure. Whereas solid state physics is based on the crystal structure of a single crystal in which all the atoms occupy sites in a three-dimensional lattice, metallurgy takes into account that the perfect regularity of the arrangement is often restricted to microscopic regions and differs from that in neighbouring regions. In other words, superimposed on a macroscopic piece of metal there is another pattern known as the microstructure, much coarser than the crystal structure which forms the foundation of solid state physics.

It happens that many of the properties of metals, especially those that are technologically important, are determined by the microstructure. The most important property from the point of view of mechanical engineering is the strength. This is strongly influenced by the microstructure and is thus one, but by no means the only, microstructure sensitive property. In order to define ‘strength’ and give it some physical meaning (chapters 12 and 14) we must first (chapters 3, 4, 11, 13, 15, etc.) examine the microstructure of metals and describe it quantitatively. The experimental techniques used to characterize the metallic microstructure are described in chapter 2.

Preface to the First English Edition

A number of English and American colleagues have expressed a desire for an English translation of this book, which they feel would be useful in final year B.Sc. Honours Metallurgy or master's degree courses. I am very pleased that two of my friends and former co-workers, Janet and Barry Mordike, have undertaken this work since they are familiar with the Göttingen as well as the British lecture courses. I would like to thank them for their careful and sensitive translation.

The English edition has provided the opportunity to correct a number of errors in the German version which have been pointed out to me by students and colleagues, especially Professor A. W. Sleeswyk, Drs H. H. Homann and V. Schlett. SI units are now used wherever it seemed advisable. Drs L. Schultz and R. Wagner have helped in proof-reading.

Peter Haasen

Caen, July 1976

Preface to the Third English Edition

The third edition of this book follows that of the German original as it was revised and enlarged in 1993. I am pleased that many English and American colleagues use the text in their courses and give me the benefit of their comments.

Peter Haasen

Göttingen, Summer 1993

For more than 20 years P. Haasen's book Physical Metallurgy has been not only an introductory textbook for students of both physics and materials science, but has also been used by scientists as a concise review of the whole field of metal physics.

Based on classical methods of solid state physics and physical chemistry, it covers many methods and nearly all problems of physical metallurgy except magnetism and superconductivity. The latter were intentionally left out for a second volume, which P. Haasen was not able to finish.

Each chapter of the book is designed to guide the reader from the simpler to the more complex metallurgical phenomena, to give them some physical meaning and to lead the reader to the current state of knowledge.

The third edition was completely revised. Major additions deal with ‘Hydrogen in Metals’, with ‘Shape-Memory Alloys’ and with ‘Plasticity of Intermetallics’. These are rapidly developing areas of research in metal physics. At the time of my retirement I hope that this book will continue to be useful and to set standards. (P. Haasen)

P. Haasen finished the manuscript of the third English edition only weeks before his death on 18th October, 1993.

Final revisions and corrections were accomplished with the help of Brian M. Watts, Haverhill, UK. Drs G. Brion, D. Isheim, and A. Pundt have helped in proof-reading.

Ferdinand Haider, Fritz D. Wöhler

Göttingen, Summer 1995

Most crystalline metals and alloys are produced by the process of solidification from the liquid phase. Mixing of components and purification of metals are both best undertaken in the molten state and casting can often be used to produce a desired shape. The microstructure is determined largely by the process of solidification. If solidification is sufficiently rapid the material remains in the state of an undercooled and frozen melt, called a glass. Crystallization begins with the formation of solid nuclei which then grow by consuming the melt. These two processes generally govern the formation of new phases. When a homogeneous alloy melt solidifies, inhomogeneous distributions of the components are set up in the resulting solid often leading to the formation of several crystalline phases. The phase or equilibrium diagram which will be introduced empirically in this chapter shows which phases exist under given conditions. The thermodynamic basis for the phase diagram follows in chapter 5. Pure metals will be considered first of all.

Homogeneous nucleation

As soon as the temperature T falls below the melting point Tm a crystal has a smaller free energy f s per unit volume than the melt f L. (In reality we should compare free enthalpies, but it makes no difference at atmospheric pressure.) To a first approximation, the difference Δf v = f L − f s can be considered proportional to the undercooling ΔT = T m − T, (Δf v = αΔT).

In previous chapters we have occasionally made reference to thermodynamics and in particular postulated a state of thermodynamic equilibrium. We must now specify quantitative conditions if we are to derive phase diagrams and interpret them in physical terms. We assume an understanding of the basic principles of classical thermodynamics, in particular of state functions such as internal energy, entropy, etc., of a system under different imposed conditions. To interpret these macroscopic state functions on a microscopic scale we use statistical thermodynamics, which averages over the energies and distributions of all the participating atoms. In the case of alloys, which are of the greatest interest in metallurgy, the atomic arrangements are known only for highly simplified model systems, from which model state functions and phase diagrams can be derived. The matching of these to a real system must be largely empirical and involves thermochemical measurement of the state functions. The discussion of binary and ternary systems which follows is of a more physico-chemical nature. Complementary physical arguments, which have been developed for a few structures, follow in chapter 6.

Equilibrium conditions

It is well known that in a (thermally and materially) isolated system the entropy S has a maximum value at equilibrium. In alloys, equilibrium is more frequently established at constant temperature, that is in contact with a thermostat (furnace). If in a reaction the volume (as well as the number of particles) remains constant, a good approximation in condensed systems, the (Helmholtz) free energy, F = E − TS, becomes a minimum. E is the internal energy of the system.

JUVENAL AND SATIRE

Juvenal, perhaps more than anyone else, is responsible for the modern concept of satire. Satire was a genre of poetry invented and developed by the Romans. When it came into Juvenal's hands, he stamped his mark upon it: indignation. Not all of Juvenal's Satires are indignant; but that is what he is remembered for. His angry voice had an overwhelming influence upon later satirists and persists into modern manifestations of satire, although what we mean by ‘satire’ is different: for the Romans and for English satirists of Elizabethan and Jacobean times, ‘satire’ denoted a particular form of discourse, a genre of poetry with ‘rules’, whereas for us ‘satire’ tends to imply an attitude and a tone of voice. In this Introduction we shall briefly examine the origins of the genre of Roman satire and discuss Juvenal's predecessors in the genre, Lucilius, Horace and Persius. The evidence for Juvenal's life will be considered, then the characteristics of his satire, including his style and metre, will be discussed. There follows an integrated reading of Book I; discussions of the five individual poems of Book I will be found after the commentary on each poem. The Introduction is concluded by an overview of Juvenal's influence from antiquity to the present and a discussion of the text and its transmission.

THE GENRE OF ROMAN VERSE SATIRE

For a full understanding of Roman verse satire, two possibly unfamiliar concepts must be grasped. The first is that the Roman writers of satire, like all authors of Greco-Roman literature, were working within a particular literary genre which had its unwritten ‘laws’. In the case of Roman verse satire, these ‘laws’ prescribed the choice of metre and form, material, presentation and language. The metre was the dactylic hexameter (the metre of epic poetry such as Virgil's Aeneid) and the form required compositions of short to middle length, usually in the range of 50-250 lines. The material included matters of morality, education and literature. The type of presentation was the autobiographical monologue with occasional extensions into dialogue, epistle or narrative. The language was permitted to range from the extravagances of mock-epic grandeur, through the everyday discourse of polite gentlemen, to explicit crudity. This set of ‘laws’ was established by Lucilius, the founder of the genre, writing in the second century BC, who is discussed below.

‘Satire is a sort of glass, wherein beholders do generally discover everybody's face but their own.’ Thus Swift, in his Preface to The Battle of the Books. The Preface to a commentary such as this is conventionally the place for self-justification and explanation of the approach adopted. In true satiric spirit, then, I subvert the generic conventions and start with speculation. It is indeed hard to discover oneself in satire; yet, I suppose that anyone who has worked on Juvenal for a decade or more must be rather odd. Whether this is cause or effect, I cannot say. But it seems to me that immersion in indignatio is not necessarily good for the soul, even if it sharpens the tongue… Of course, I was delighted to be offered the opportunity of writing a new commentary on the Satires of Juvenal, especially when the Press agreed to the inclusion of Satire 2, since this meant I could present an integrated reading of Book 1 as an organic structure. But during the ten years or so it has taken to bring this project to fruition, there were times when I despaired of completing it, not least because of the government's obsession with accountability, which has surely doubled the administrative workload on university lecturers during this period. I therefore wish to express profound gratitude to the numerous friends and colleagues who offered multifarious encouragement: to David Braund, Duncan Cloud, Charles Martindale, Adam Morton, Patricia Mover, Jonathan Walters, John Wilkins, Peter Wiseman. Thanks to Barbara Gordon for her scrupulous proof-reading. To Ted Kenney is due the highest accolade for scrutinising the entire typescript more than once; as always, I have benefited enormously from his advice (even if I have not always taken it).

My thanks also go to the classes of students at the University of Exeter in the 1980s who responded so helpfully to my Juvenal lectures, especially Julia Mobsby and Jack Marriott; the desire to introduce new generations of undergraduates to Juvenal has provided inspiration for the undertaking and parameters for the book.

SATIRE 1

1-6 The speaker plunges straight into his self-justification, declaring that he will take revenge for all the recitations he has sat through in the past. Implicit in this apologia is a recusatio, a ‘refusal’ to tackle epic, in favour of satire. He begins with a series of four rhetorical questions, the first two introduced by the antithetical extremes semper and numquam; the second two by anaphora of inpune which reiterates numquam … reponam. The increasing length of the questions conveys his vehemence.

I ego auditor: supply ero or sim; the omission of the verb conveys indignation, egoindicates the speaker's self-centredness. He portrays himself as an auditor at a recitation (hence 3 recitauerit and 13 lectore), a regular social event in Rome ranging from the private dinner-party (Mart. 3.45, 11.52.16-18; J. 11.179-81) to grander affairs to which the educated public was invited (Plin. Ep. 1.13). The Romans tended to listen to ‘literature’ rather than simply read it as we do. tantum ‘only’. This prepares us for his desire for revenge. reponam ‘retaliate’, literally ‘repay (a debt)’, with no object expressed here. For the idea of taking revenge for recitations, cf. Hor. Ep. 1.19.39 ego nobilium scriptorum auditor et ultor.

2, uexatus: the past participle has a concessive or causal force, ‘though harassed’ or ‘for having been harassed’ (Woodcock §92). Theseide Cordi: the poet Cordus is unknown to us and the name possibly fictitious. His poem is an epic about the Athenian hero Theseus (cf. Aeneas - Aeneid), a hackneyed subject; totiens and rauciy ‘hoarse’, imply that it is very long.

3-4 inpune … recitauerit … consumpserit … : fut.perf.: ‘shall he have got away scot-free with reciting … with taking up … ’. ergo: on J.'s prosody see Introduction §8. togatas: i.e. fabulae togatae, comedies with a Roman setting, as opposed to fabulae palliatae, Latin comedies with a Greek setting, such as those of Plautus and Terence. elegos: the genre of Roman love elegy bloomed in the first century BC (Gallus, Tibullus, Propertius, Ovid), but elegies were still recited and written in J.'s time (Mart. 8.70.7; Plin. Ep. 6.15).