Peter Goodman (1928-1999).

Notoriously scientists of brilliance conform to no easily identifiable pattern in their approach to research and this was certainly true of Peter Goodman who repeatedly surprised even those of us privileged to be his close colleagues, with his oblique attack and radical experimental technique. Both of these characteristics are already impressively evident in the first of his contributions to attract international recognition.

To appreciate the significance of this work, undertaken with his friend and colleague Gunther Lehmpfuhl it is necessary to recall that theory in the fields of electron diffraction and electron microscopy was then undergoing substantial revision, with no clear experimental evidence to provide guidance on the validity of the various, and often conflicting formulations being advanced. It emerged that a crucial test would be provided, as it so often is in physics, by an appeal to symmetry; in this case an apparently straightforward question as to whether certain orders of reflection would be forbidden in the scattering of electrons from a crystal having screw axes or glide planes as elements of its space-group. The point of experimental delicacy here is that the angular resolution required to detect the effect is much greater than that achievable by means of conventional selected area diffraction. By resurrecting and greatly extending the technique of convergent beam diffraction, a method devised by Mollenstedt, used by MacGillavry and Hoerni and then substantially abandoned on the grounds of near impracticability, Peter and Gunther readily attained the requisite accuracy.

Their results, which revealed loci in reciprocal space along which specific orders of reflection remained forbidden, established a touchstone for n beam formulations. It was absolutely characteristic of Peter Goodman that he ignored the widespread folklore which held that dynamical interaction destroyed forbidden reflections, a folklore based, as it emerged, on inadequate experimental technique, and addressed only the logic of the situation.

However, much more than this result, important though it is, emerged from the investigation, for Peter, seeing convergent beam diffraction as a technique ideally suited to the exploitation of n beam effects, established a programme which is followed to this day, unfortunately not always with the precision that he himself showed to be possible. Specifically this experimental programme involved the more general study of symmetries, the analysis of defects and the precise determination of potential within the crystal as a means of elucidating bonding. Each of these activities has now developed into a field in its own right and it is in many ways a revealing exercise to examine how much Peter's insights have shaped subsequent developments.

In the first instance he had undertaken the study of one aspect of crystallographic symmetry as a test of a theory which he had shown to be correct, now he proposed to exploit predictions of that theory to devise a scheme which would, for the first time, allow the unequivocal assignment of a crystal to one of the 230 space groups. A central problem involves the determination of the presence or absence of a centre of inversion. It is a prediction of n beam theory that the direct measurement of scattered intensity should reveal this, that is, that Friedel's law is broken in the absence of a centre of symmetry. Peter and his collaborator Gunther Lehmpfuhl carried through experiments which not only showed this to be correct but constitute the foundations for a rapid and accurate procedure which is now standard in the determination of this symmetry element. Given that they had already established methods for dealing with non symmorphic groups, this opened the way for complete classification, a lengthy undertaking, not completed for many years, and involving a substantial number of workers, among whom Professor M. Tanaka must be especially mentioned for his elegant and conclusive demonstrations.

At the request of the International Union of Crystallography Peter summarised these findings and wrote what has become the definitive work on the unequivocal determination of space-groups by electron diffraction. This account can be found in section2.5.2.volumeB of the International Tables of Crystallography. It is a model of clarity and compactness, one of those exceptional works which are complete and likely to survive, substantially unchanged, into any forseeable future.

While the ramifications of dynamical symmetries formed a continuing interest they eventually came to constitute only a background to his work as Peter addressed a variety of problems associated with solid state physics and chemistry, arguably most importantly, those concerned with the accurate determination of structure amplitudes. His motivation here was, of course, the study of bonding. He was well aware of the power of X-ray technique in this field, but also of its limitations, and saw that many of these could be overcome by appropriate use of convergent beam electron diffraction. In addition he foresaw the possibility of new approaches, particularly in polyphase material. Ultimately, for some materials, he was convinced that techniques based on electron scattering would prove the more accurate. Here it would be appropriate to remark that Peter was always wryly amused by the partisan attitude that pits one radiation against another, or for that matter, one field against another, and his invariable aim was to combine techniques. However, the combination of electron and X-ray data, at least to the level of accuracy that he found acceptable, presents difficulties that can only occasionally be overcome and separate assessments of accuracy must be made.

His assessment was based on the circumstances that the theory of forward elastic scattering is known to very high accuracy for fast electrons, that efficient numerical methods can be devised to exploit this, he himself being largely responsible for the initial programming, and that the technique of convergent beam diffraction can be made to conform closely to the constraints demanded by the theory. He was at particular pains to test this latter point and in his subsequent work he repeatedly emphasised its importance. A remark that he was fond of making was that while the most cursory examination of a lattice image will reveal faulty technique and at least discourage facile interpretation a convergent beam pattern, which requires equally stringent setting, can, with the same technique, appear dangerously plausible.

Eventually he developed the method of measuring structure amplitudes to the point where the only sources of appreciable error derived from absorption and temperature. Again he brought his own experimental approach to the assessment of the importance of those factors, thereby initiating lines of enquiry which are still current. Any adequate account of these meticulous experiments would result in a lengthy tale, but, although a small part of the investigation, Peter's experimental demonstration of the significant dynamical elastic component in the electron Borrmann effect, heretical at the time, now conventional, is worth mentioning if for no other reason than to illustrate his capacity to set aside received wisdom, in this case reinforced by a wealth of misinterpreted experiment. Having established the principles on which refinement by means of convergent beam diffraction stand and the experimental approach which remains the preferred model Peter turned his attention to structure analysis, defect and surface structure, and where appropriate, some combination of those.

In order to implement such studies a variety of methods will, in general, be required and Peter was among the first to demonstrate the feasibility of moving smoothly from convergent beam to lattice imaging modes, a powerful technique in solid state investigations. A small example will illustrate the point as well as exemplifying the elegance of Peter's attack. The approach to an alleged kinematical, or single scattering limit as the thickness of a crystal approaches zero is, even now, a hallowed concept in electron diffraction and microscopy. Peter undertook a quantitative investigation of this matter, successively cleaving crystals, in some cases down to a few unit cells in thickness. His results not only revealed a complex structure dependent approach to the limit which he described in detail by n beam theory, but, in some materials demanded the assignment of different space-groups to neighbouring regions of the same crystal. The reason for this turned out to be the presence of growth or cleavage steps a fraction of a unit cell in height and of different symmetry to the bulk crystal. Whether they were on the top or bottom surface Peter determined by means of his "top-bottom contrast" technique which exploits the sign of the excitation error in order to establish phase. The methods themselves are of considerable utility, but the real importance of the experiments arguably lies, again, in the ways in which they extended perceptions in the field.

Peter's contributions to structure analysis, undertaken with a variety of collaborators, notably Whitfield, Olssen, MacLean and Dowell, in a sense can be seen as applications of the methods that he had developed in the course of investigating dynamical scattering. Nevertheless he had an abiding interest in solid state physics and chemistry in many of its forms, from optical activity to superconductivity and contributed, for instance, to both of the latter.

It is likely that Peter Goodman's most lasting achievements will be seen as his development of the convergent beam method into the pre-eminent technique of electron diffraction, and in his decisive experimental determinations of crystallographic symmetries. Yet many of those who collaborated with him, and certainly myself, will carry away the strong impression of a man whose significance in science extended beyond those achievements, important though they may be, for Peter brought to research a vividness and originality, a freshness and directness that transformed the everyday routine that forms the background to all substantial investigations into an opportunity to pursue the centre of current interests even more strongly. While dismissive of facile approaches to measurement he had little sympathy with what he described as professional pessimists, being committed to the view that a primary duty of an experimentalist is to make things work, and not to explain why they cannot. This sometimes led to remarkable, even alarming developments, but things moved forward and, of central importance to Peter, definite conclusions were reached.

All of this may suggest a rather aggressive attitude to living but to those forceful tenets must be adjoined an insight into and passion for the graphic arts that permeated his life, and a deep sympathy for classical music. Those influences, an abiding sense of humour and a deep sympathy with human frailty made of Peter an unforgettable friend, a man round whom legends grow and to whom sayings are attributed - though I can personally attest to his advice to those who would understand scattering to put yourself in the position of the electron - and of whom it could only be said that to know him enhanced the zest which he, above all, contributed to living.

Peter is survived by his wife Patricia, his daughter Robin and his two sons David and Richard.