william cochran. 30 july 1922 − 28 august 2003: elected...

FRS 1962 28 August 2003: Elected−William Cochran. 30 July 1922

Michael Woolfson

, 67-85, published 1 December 2005512005 Biogr. Mems Fell. R. Soc.

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WILLIAM COCHRAN30 July 1922 — 28 August 2003

Biogr. Mems Fell. R. Soc. 51, 67–85 (2005)

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WILLIAM COCHRAN

30 July 1922 — 28 August 2003

Elected FRS 1962

BY MICHAEL WOOLFSON FRS

24 Sandmoor Green, Leeds LS17 7SB, UK

FAMILY BACKGROUND

William Cochran was born at Driffenbeg, a moorland sheep farm, on 30 July 1922, to JamesCochrane and Margaret Watson Baird; the final ‘e’ in the family name drifted in and out in ran-dom fashion through the generations. He traced his ancestry back more than 350 years to hisgreat-great-great-great-great-great-grandfather, another William Cochran. In 1649 this fore-bear obtained title to Maynes of Craig ‘the four merks five shilling land of the five pound landsof Craig’ near Strathaven from Robert Hamilton of Sillertounhill. At around this time he mar-ried a widow, Alison Lawson, a marriage that provided a sound, if not abundant, foundationto the family fortunes from that time forth. The farm was passed from son to son—fromWilliam to John in 1669, to Alexander in 1717, to William in 1745 and to yet another Williamin about 1795. The most interesting of these early kin was John, who was a Covenanter, aPresbyterian rebel who opposed Anglicanism. He took part in the Covenanter Rebellion of1679 in which, at Drumclog, the Covenanters defeated the forces of John Graham, Vicount ofDundee, who, in 1678, had been charged with task of suppressing the Covenanters. However,later the tide turned against the rebels and John was for some time imprisoned in Edinburghwith his farm ‘forfault’.

Cochran’s great-grandfather, John Cochrane, was born in 1803; as a younger son he did notinherit the family farm but became a tenant farmer, as did Cochran’s grandfather (1837–1914)and father (1885–1955). Cochran recalls that he visited his grandfather’s farm, Townhead ofGrange, near Dunlop, and it looked much as it must have done when his grandfather was there.

The farming background came from both sides of the family. Driffenbeg was close to SouthWalton farm, where Cochran’s mother lived before her marriage. However, in 1928 the familymoved to Hillwood farm, some eight miles west of Edinburgh. This farm is still in the family,

doi:10.1098/rsbm.2005.XXXX 69 © 2005 The Royal Society



being farmed by Robert Fleming, who is married to Cochran’s eldest sister, Margaret. His sec-ond sister, Agnes, a General Practitioner, is married to John Doney, a research worker with theHill Farming Research Organization, and his youngest sister is married to James Hamilton,who farms near Kelso.

From about the age of 10 years Cochran spent much time in farming activities, especiallyduring the war years. However, his father, a reserved and somewhat withdrawn man, did notencourage him towards farming—in the economic conditions of the 1930s farming was not anattractive proposition. Clearly, young William had to look elsewhere for his future career.

EARLY EDUCATION

Driffenbeg was very remote, so Cochran did not begin his formal education until the move toHillwood farm when he was six years old. He had already been taught to read by Alex King,a farm servant who lived with the family. The schoolmistress at the ‘wee school’ was aredoubtable Miss Elliott who, in series with her aunt, had run the school for 60 years. Afterone year Cochran moved to the ‘big school’ at the other end of the village, overseen by theheadmaster, John Poustie, whose simple, but effective, teaching methods would have beenanathema to any modern educationalist. It was Poustie who suggested to Cochran’s parents, in1934, that he should be sent to a secondary school in town, which was how he became a pupilat Boroughmuir, a corporation school within the boundary of Edinburgh. Because Hillwoodfarm was outside the boundary, Cochran’s father had to pay an annual fee of £5.

Boroughmuir was a school founded for the education of the children of artisans and thelower middle classes, and its pupils had their sights more on a career in the civil service thanon going to university. The general ethos of the school, with no pressure to conform, no uni-form and not even the requirement of wearing a tie, suited Cochran well. He had no aptitudefor sport and the school cared little if he took the train home rather than spent time on thesports field. However, Cochran sometimes wondered in later life whether a school with moretraditional values would have instilled in him some of the qualities he lacked—self confidenceand sociability. On the whole his period at Boroughmuir was happy and uncomplicated, dis-turbed only by his mother’s death when he was 15 years old. His sister Margaret, two yearshis junior, promptly left school and took over the running of the household.

Academically, Cochran was always in the top two or three of the class, with his best per-formances in English and French. However, at the age of 15 years the gift of a Meccano setgave him an interest in engineering and in his fifth year a good teacher by the name ofMcLean, known as Cherry Blossom because of his well-polished shoes, pointed him towardsphysics—a subject he was good at but perhaps not particularly enthused about at this stage. InSeptember 1939 the war began and Cochran decided not to stay on at school for a sixth yearbut rather to get some time in a university before the inevitable call-up.

A WARTIME UNDERGRADUATE

The admission procedure to the Physics Department of Edinburgh University at that time wasperfunctory, consisting of a five-minute interview with the Director of Studies. Cochran foundthe physics straightforward but, at first, struggled somewhat with mathematics. He could only

70 Biographical Memoirs



manage a midway position in the first mathematics class examination but eventually ended upnear the top. At the end of his first year he was awarded the Newton Scholarship in Physicsand a year later the Donald Fraser Bursary, but these were given up when he took up one ofthe new state scholarships in September 1941. A condition of acceptance of this award was totake a course in radio, and thereafter Cochran’s course was heavily biased in that direction. Bythe end of his third year many of his classmates had left to take up Royal Air Force commis-sions, manning radar stations as he later discovered. Cochran had given the RAF as his ownchoice of service and had an interview and medical. However, in May 1942 he received acryptic letter, which ran as follows: ‘With reference to your application for a Commission inthe Technical Branch of the Royal Air Force Volunteer Reserve under the Hankey RadioTraining Scheme, I am directed to confirm, in view of information received from the Ministryof Labour and National Service, that your candidature has been withdrawn.’ He did not, andnever did, understand the basis of that letter, so his war service was confined to the HomeGuard, of which he was a member for the whole of its existence.

The main competitor for Cochran’s time as a student was helping on the farm, especiallyin his third year when his father was ill and he had to do the milking at 5.30 a.m. Then at4.00 p.m., when he arrived home, he operated the milking machine for another hour and a half.In the summer of 1942 he took a vacation job with the Telegraph Condenser Company inNorth London, an experience that did nothing to attract him towards a career in industry. Inthe following summer he was a temporary civil servant at the Air Defence and ResearchEstablishment in Malvern, an experience he much enjoyed.

The physics course taken by Cochran was inadequate in many respects. The head of depart-ment, Professor C. G. Barkla FRS, a Nobel laureate for his work on X-rays, was involved ina search for some mythical J-rays and had frozen the course to about the state of knowledgein 1925. Consequently Cochran knew virtually nothing about atomic and nuclear physics, andlittle about relativity and quantum mechanics, when he graduated in 1943. The department hadother distinguished professors, such as Max Born FRS in mathematical physics, but Cochranwas only vaguely aware of their presence. What modern physics he did know was due to somevoluntary lectures given by Professor R. Fürth, a refugee from Prague who was in Born’sdepartment. Cochran did not compensate for these deficiencies by general reading outside thesyllabus. When he graduated he owned just half a dozen textbooks, having relied on the uni-versity library. This was not due to family poverty because, compared with the 1930s, theywere comparatively comfortably off. However, Cochran’s father encouraged thrift—familymembers took what money they required, signing for it in a book kept on his father’s desk withno questions asked.

Cochran’s undergraduate days in Edinburgh, for all their shortcomings, were on the wholefree of worry or depression, despite the pressures of the war. He had virtually no spare timeand little social life, and his shyness reduced even further his ability to interact with others. Bythe time he graduated in 1943, in the company of one other physics student and five in math-ematics, he was aware of the department’s shortcomings and was anxious to leave. But thatwas not to be.

William Cochran 71



A POSTGRADUATE IN EDINBURGH

Cochran thought that he had arranged to join Admiralty Research but a letter he received fromProfessor Barkla stated that a message from some Whitehall source indicated that he wasrequired to teach at Edinburgh. For the next three years Cochran taught electronics as anAssistant, a lowly post that dated from the times that Scottish professors paid for Assistantsout of their own pockets. The salary was low, £200 per annum, but the work was not time con-suming, consisting of taking tutorials and practical classes and giving some lectures on theproperties of matter in the second year. Consequently there was plenty of time for research thatinitially consisted of checking the results of Stevens, one of Barkla’s research assistants. Threeother research students were engaged in a similar activity to that of Stevens, using gas tubesexcited by induction coils and measuring the intensity of X-rays using gold-leaf electroscopes.Stevens had been doing similar experiments for about 20 years and resented a beginner beingasked to check his results that, in any case, were highly irreproducible. The morale of thegroup was low and much time was spent in playing bridge.

After a year of this rather dispiriting activity Cochran met C. A. Beevers from the Chem-istry Department, who told him about his research in X-ray crystallography. This seemed toCochran much more interesting than what was doing and he wrote to Professor Barkla to tellhim that he would like to change his field of research. Barkla’s response was negative. In areply, written on holiday, he stated ‘Your full time as Assistant is of course under my directionas Head of Department…. The question of what you would like to do has not arisen…. Toapply your qualities to the routine of crystallography would be a sheer waste of power.’ WhenCochran countered by pointing out that the Cavendish Professor was a crystallographer theresponse was that ‘Some of us believe the appointment was a great mistake.’ The impasse wasbroken in 1944 with Barkla’s death, and Cochran was able to begin a fruitful collaborationwith Arnold Beevers.

Cochran was first introduced to Beevers by John Robertson, a fellow student who hadbegun work with him but was about to leave for war work. Beevers instructed Cochran in theart of preparing crystal specimens and taking X-ray photographs. He also suggested a prob-lem and then left Cochran to get on with it, with Bragg’s The crystalline state, the only worth-while textbook on crystallography at that time, as his source for learning about the details ofthe subject.

The problem that Cochran was tackling was that of the crystal structure of sucrose. Themeasurements of X-ray intensities had been made by Beevers and Robertson, and Cochranused these to calculate a Patterson function, a map that, in principle, shows all the interatomicvectors although in practice these maps are difficult, sometimes even impossible, to interpret.The Fourier-series maps were calculated using Beevers–Lipson strips, a computing aid thatenabled maps to be calculated on a timescale of days (the same maps in the computer age arecalculated in less than a millisecond). After a year Cochran had a drawer full of calculationsbut no solution to the problem, which was probably impossible to solve in that way at thattime. A few years later Beevers and Robertson found the structure of sucrose by a more sophis-ticated approach.

All this time Cochran had not been registered as a research student but Dr Carse, who wasacting Head of Department, gave permission for Cochran to register. The problem was thatwith only about one half of his three-year Assistantship available he had nothing that could gointo a thesis. Fortunately Robertson, before he left, had made up solutions of sucrose with




sodium chloride and with sodium bromide, each of which produced crops of crystals. Thesewere respectively sucrose.NaCl.2H2O and sucrose.NaBr.2H2O, which were isomorphous; thatis, identical crystal structures except that chlorine in one is replaced by bromine in the other.This enabled the objective and infallible method—isomorphous replacement—to be used tosolve the structures and this provided the material for Cochran’s thesis, presented in time forhim to graduate in July 1946, and also his first published papers (1, 2)*. That summer he wentwith three other research students to Holland for a three-week glassblowing course. The glass-ware all cracked on cooling but he much enjoyed his first trip abroad.

During the war period Cochran, like so many young men of his time, became something ofa socialist idealist and was influenced by the writings of Bernard Shaw, G. D. H. Cole andGeorge Orwell, among others. During his last four years in Edinburgh he broadened his socialskills, especially as a member of a Physical Society group that rented a cottage near Aviemorein the summer. Cochran spent many occasions there, sometimes in party mode as when thefinals results were announced, but otherwise mainly hill-walking by day and playing cards atnight.

By the end of his Assistantship Cochran was inclining towards a life in academia—but notin Edinburgh.

UNTENURED YEARS IN CAMBRIDGE

Beevers suggested to Cochran that he should go to Cambridge, where Sir Lawrence BraggFRS was Cavendish Professor and W. H. Taylor was in charge of the organic crystallographygroup in the Cavendish Laboratory. In September 1946 Cochran began work at the Cavendishas a research assistant to Taylor at a salary of £300 per annum, the other members of the groupbeing C. J. B. Clews and June Broomhead. The problem the group was tackling, suggested byProfessor A. R. (later Lord) Todd FRS, was to determine the crystal structures of purines,pyrimidines, nucleosides and nucleotides, the basic components of DNA. In the next threeyears some pyrimidines and purines were solved (3, 4, 9) but Cochran’s experience withsucrose made him pessimistic about the chances of solving nucleosides or nucleotides unlesssome heavy-atom derivatives could be produced. An interesting outcome of this work was thatthey found that electron density could be determined with sufficient accuracy to establish thepositions of hydrogen atoms and so to study the nature of hydrogen bonding. During thisperiod Cochran’s interest shifted away from the solution of structures towards the theoreticaland practical aspects of accurate structure analysis, something he had previously consideredin Edinburgh (5). Very quickly there followed papers on the steepest-descents method forrefining structures (6) and an analysis of the Fourier method of refinement and its relationshipwith the least-squares method (7, 8). He also developed a Geiger-counter diffractometer forthe precise measurement of X-ray intensities (10) and with its aid he showed that an (Fo�Fc)synthesis (13) could accurately detect hydrogen atoms and even excess electron density withincovalent bonds (11, 12).

Life in Cambridge was having a powerful effect on Cochran. June Broomhead was anattractive girl and they had an off-again, on-again relationship—but one conducted on a ratherintellectual plane. However, June had a beneficial effect, sending him to get a new suit,

William Cochran 73

* Numbers in this form refer to the bibliography at the end of the text.



recommending a dentist to deal with his neglected teeth, persuading him to change to betterdigs and encouraging him to drop those Scotticisms that made him difficult to understand.Through her he made his first contact with the college system and supervised DowningCollege undergraduates. After a while June moved to Oxford to work with Dorothy Hodgkin(FRS 1947) and eventually married George Lindsay, but she had an important influence onCochran’s future in Cambridge.

In 1947 Cochran suffered the first and most severe spell of depression, from which heemerged after a few months. He was looking round for some more permanent post, makingunsuccessful applications for a lectureship in physics at Bristol and a demonstratorship in min-eralogy at Cambridge. When Taylor told him that Bragg had arranged a demonstratorship forhim at the Cavendish his first reaction was to refuse it, but after two days he was persuaded tochange his mind. His new status required him to become a member of the university, whichinvolved being awarded a Cambridge MA, and he acquired high-table dining rights atDowning College for one night each week. Although he had initially regarded the universityas aloof he eventually developed warm feelings for the university and felt fully a part of it.With his new status Cochran was able to take on research students and establish his owngroup. In 1948 a South African, Henry Dyer, became his first research student; a year or solater he was joined by Jack Zussman, a Cambridge physics graduate, and Bruce Penfold, aNew Zealand chemist.

Cochran began his time in the Cavendish when it already contained many talented peopleand was beginning to receive a flood of others. Bragg regularly visited the crystallographers,and the suggestions he made from time to time stimulated a great deal of useful and importantwork, not least by Cochran. Taylor managed the crystallography group, which contained sev-eral ‘prima donnas’, with great diplomacy. Helen Megaw gave lectures on ferromagneticmaterials, from which Cochran learned about the subject. John Kendrew (FRS 1954) and MaxPerutz (FRS 1954) were busy on the protein structures that would earn them their Nobelprizes, and Hugh Huxley (FRS 1960) and Francis Crick (FRS 1959) joined them in 1949.From his experience with sucrose Cochran concluded that the solution of protein structuresmight be impossible. Fortunately, the protein crystallographers had never tried to solve smallstructures and so were not deterred!

Social life centred on coffee parties, sherry parties and the occasional dinner. The Braggssometimes gave Christmas parties to which all crystallographers were invited. Cochran regularlyattended the Kapitza Club, run by David Shoenberg (FRS 1953), and once gave a talk on the useof Hollerith punched-card machines for calculating Fourier syntheses. For some time Cochranwas in charge of teaching physics to medical and veterinary students, mainly carried out throughthe medium of tutorials. He discovered that as a university Demonstrator he could claim extrapayment if he did less than six hours of tutorials per week. The concept of being paid for notworking was so alien to him that he never made any claim for payment; others did it routinely.

Cochran felt that the nuclear physicists at the Cavendish rather looked down on the crys-tallographers and he thought that they might have some justification for doing so. The goldenage of crystallography was yet to come.

In 1949 Cochran developed an interest in the symmetry of real periodic two-dimensionalfunctions (17) that occurred in structure analysis as ‘generalized projections’ of electron den-sity. He was hampered by a lack of knowledge of group theory but derived interesting and use-ful results by working from first principles. Another new interest arose in 1949 as a result ofmeeting David Sayre, a postdoctoral worker with Dorothy Hodgkin in Oxford. Sayre’s PhD




thesis was on what became known as ‘Sayre’s equation’, a relationship between structure fac-tors based on the similarity of the electron density and squared electron density for a structureconsisting of equal resolved atoms. This began Cochran’s interest in direct methods of solv-ing crystal structures, mathematical methods depending for the most part on probabilistic rela-tionships between the phases of structure factors. A structure factor Fh is a complex quantitywith amplitude |Fh| and phase �h. To calculate the electron density in a crystal requires knowl-edge of both amplitudes and phases, but experiment yields only the amplitudes. This consti-tutes the ‘phase problem’ in crystallography that direct methods seek to solve.

At about this time there was a great deal of interest in XRAC, an electronic analogue com-puter for calculating two-dimensional Fourier series that had been developed by Professor RayPepinsky at Pennsylvania State University. Bragg suggested that Cochran should spend sixmonths with Pepinsky so, with the help of the Rockefeller Foundation, Cochran sailed toAmerica on the Queen Elizabeth in December 1950.

Cochran recorded that when he arrived in New York, a few days before Christmas 1950, hewas more impressed by the traffic than the famous skyline. When he arrived at White RiverJunction, the station for Pennsylvania State University, he was met by Ray Pepinsky and theytalked well into the night. Pepinsky was rarely seen during the day because it was his practiceto go to the laboratory when others had left and stay for half the night. He was very depend-ent on Paul Jarmotz, the electronics man who kept XRAC running. Pepinsky always claimedthat Jarmotz was more temperamental and subject to breakdown than XRAC itself, and Paulwas either sacked, or resigned, or both, about once per week. There were very few permanentpeople in Pepinsky’s group but at the time of Cochran’s visit there were about a dozen visi-tors, including John Robertson and June Broomhead. The sponsors of the visitors usuallyrequired reports on their activities and Ray frequently demanded material to include in these.He had a practice of adding his own name to material being prepared for publication, some-thing that led to frequent disputes.

The work done by Cochran at Penn State arose from his conversations with David Sayre.For a centrosymmetric structure the structure factor phases are either 0 or � and may be rep-resented as a sign, s(h), of the structure factor Fh(ei0�1, ei��1). He noticed that Sayre’sequation and some inequality relationships discovered by Harker and Kasper both pointed tothe conclusion that the product s(h)s(h�)s(h�h�) was probably positive, especially if the threeassociated structure amplitudes were large. Using these sign relationships Cochran solved thestructure of glutamine that his student Bruce Penfold had been working on for some time.Another visitor to the department, W. H. Zachariasen, applied his own variant of these ideasto the solution of the structure of metaboric acid. Three papers, produced by Sayre, Cochran(14) and Zachariasen respectively, that appeared in Acta Crystallographica in 1952 providedthe foundation of modern direct methods that were to have a profound effect on structuralcrystallography.

Cochran described Pepinsky’s laboratory as something of a madhouse. There was a greatdeal of red tape, with all XRAC output results being required in six copies. The laboratory hada public address system by which individuals could be called to the telephone but which alsoenabled Pepinsky to listen in to all conversations and discussions. Cochran was rather sur-prised when, a few minutes after a short conversation on sign relationships, Pepinsky appearedwith a typed abstract of a joint paper to be presented at a forthcoming American PhysicalSociety meeting. Cochran stayed in the ultra-modern Pepinsky home for a short time butmoved out into lodgings when the plumbing completely collapsed.

William Cochran 75



In May 1951 Cochran left Penn State to spend a month in California with the group of LinusPauling ForMemRS at California Institute of Technology. This group had the greatest concen-tration of talent in chemical crystallography in the world at that time, including R. B. Corey, E.Hughes, Verner Schomaker, Jerry Donohue, David Shoemaker and Jack Dunitz (FRS 1974).Cochran did not have the time to embark on anything new but he benefited greatly from his inter-actions with members of the group. In particular he was impressed by Pauling and attended afew of his postgraduate lectures. Pauling would come in without notes, look round and say ‘Wellfellows, what would you like me to talk about this morning?’ When someone suggested a topiche would then launch into a 50-minute discourse. Cochran’s time at CalTech, which includedoutings and picnics, was a welcome change from the frenetic atmosphere at Penn State.

Cochran’s return to Europe led to a very significant event in his life. He travelled on theliner Stockholm because he was going directly to an International Congress on Crystallog-raphy in the Swedish capital. Cochran’s natural shyness seemed to disappear once he wasaway from dry land and he describes the transatlantic voyage as all too short. On the trip fromStockholm back to England he met a young Swedish girl, Ingegerd Wall, who was making herfirst attempts to converse in English. Cochran and Ingegerd met again several times in Londonand in Cambridge. They became engaged in Stockholm in August 1952 and married inUddevalla in April 1953.

TENURE IN CAMBRIDGE

When Cochran returned from the Stockholm conference he found that he had been promotedto lecturer, his first tenured position, at the age of 29 years. Later that summer he was invitedto dinner at Trinity Hall by George Kenner (FRS 1964), one of Professor Todd’s team who hadgiven him help and advice. A few days later he was surprised to receive the offer of a collegeFellowship from the Master, Professor Dean. As a bachelor he was expected to live in collegeand he moved into rather bare college rooms in September 1951.

Cochran took some time to settle into college life. He rather begrudged the hours spent overdinner and afterwards in the Senior Common Room. He had never been much of a conversa-tionalist. However, the older Fellows, and especially the Master, went out of their way to puthim at ease. Eventually, with the help of the other Fellows and his gyp (college runner),Donald Tarrant, he settled in to college well and was indeed sorry to leave after 18 months toset up house with his new bride in a flat in Grantchester Street.

While living in college Cochran had his first phase of writing poetry. He claimed that, likeRobert Burns, he only started writing poetry after he had fallen in love. His verses addressedto Ingegard were successful to the extent that she did not change her mind about marrying him.His verses at this time were mostly of a bantering kind, an example being:

My reprobate muse is a bitch who inspiresThe kind of blank verse no young lady admires,But on this occasion, appraised of your charm,She’s promised to give you no cause for alarm.Alas, as you see from this premature endShe finds that the way is to keep words un-penned.

As a lecturer Cochran had more formal teaching to do and, in addition to Part II supervision,he gave a lecture course on classical mechanics and relativity. Cochran suspected that it was a




course that nobody else wanted to give, but he particularly enjoyed teaching relativity and gavethe course until he left Cambridge. His research at this time was in three distinct areas, althoughall within crystallography. The first was to make accurate electron-density measurements tostudy hydrogen bonding and covalent bonds. This work was carried out by a succession ofresearch students—Tom McDonald, Roger Calder, Stuart Darlow and Chatar Singh. The sec-ond was on structural studies of molecules of biochemical interest, worked on by June Sutor,Patrick Tollin and George Sim. The third area, and the one of greatest interest after his visit toPenn State, was that of the phase problem. EDSAC, an early and rather primitive digital com-puter, was available in Cambridge, and Cochran struck up a fruitful collaboration with SandyDouglas, who knew how best to use EDSAC. Together they produced a program for using signrelationships to give automatic solutions of the phase problem in two dimensions (19, 23, 24).This was the first program of its kind and the forerunner of more powerful programs that even-tually were to revolutionize structural crystallography. In 1952 Michael Woolfson (FRS 1984)joined the group as a postdoctoral research assistant and worked with Cochran in developingthe theory of direct methods (21). They also showed that the claims made by the AmericansJerry Karle and Herbert Hauptman in their monograph The solution of the phase problemwere exaggerated (20). In 1955 Cochran made a critical advance in direct methods by extend-ing their application to non-centrosymmetric structures through general phase relationships(22). Despite his important contributions to direct methods, Cochran became rather discouragedby their slow progress and by 1960 he stopped work in that area.

Bragg was always keen to involve Cochran in the work of the protein-crystallographygroup in the Cavendish. Cochran was rather pessimistic about the prospects for solving macro-molecular structures but he frequently acted as a consultant for the group. An important con-tribution came as a result of being shown a paper by Vladimir Vand, which Bragg had beenasked to referee, on the X-ray diffraction pattern of atoms arranged on a helix. Cochran couldsee that Vand’s result was correct for a continuous helix but was incorrect for atoms on a helix.Francis Crick had also seen Vand’s paper and the following day Cochran and Crick found thatthey had both come to the same correct answer by completely different routes (15, 16). Sometime previously, Bragg had given Cochran a semicrystalline specimen of polymethyl gluta-mate, a synthetic polypeptide obtained from a Courtaulds research group. Cochran had takensome X-ray photographs of the material but had concluded that not much could be learnt fromthem. However, after the helix-theory work he suddenly realized that the photographs revealedthe presence of helices of different radii within the structure. It was about this time that itbecame clear that the method of isomorphous replacement was going to make possible thesolution of proteins and Cochran realized that his previous pessimism had been mistaken.However, he declined to become involved in protein crystallography even then, because ‘itwould have looked as if I was clambering onto the bandwagon.’

In this period James Watson (ForMemRS 1981) had arrived at the Cavendish; in Thedouble helix he referred to Cochran as ‘a small quiet Scot’. When Crick and Watson invitedhim to look at their first, and incorrect, structure for DNA Cochran was not impressed. He latersaid that he would have been equally unimpressed if it had been the correct structure! Cochranknew of Rosalind Franklin’s work on the A-form of DNA because he had discussed this withher at the Stockholm Congress and later in Cambridge. Cochran remembers a sherry party inthe spring of 1953 in which Watson explained to him the importance of hydrogen bonding andbase pairing in the DNA structure. He did not know that they had seen Rosalind Franklin’sstriking photograph of B-type DNA on which to base their ‘speculations’.

William Cochran 77



In early 1953 Bragg became impatient with the progress of volume 3 of the series of booksof which he had written volume 1 and asked Cochran to become involved. This led to the firstcomprehensive textbook on the solution of crystal structures (18). In 1954 Bragg departedfrom the Cavendish to take up Directorship of the Royal Institution, and the removal of hisstimulating presence may have been a contributory factor in Cochran’s declining interest incrystallography. Professor N. F. (later Sir Nevill) Mott FRS had become the CavendishProfessor and one of his first moves was to banish the protein crystallographers from hisphysics laboratory into wooden huts in the Cavendish courtyard.

As a distraction from crystallography, in the mid-1950s Cochran became involved in a pub-lic controversy with Professor Dingle involving the ‘twin paradox’ of relativity (25, 26).Dingle had asserted that time intervals were absolute and hence that the interval betweenevents was independent of the motion of an observer. Cochran argued for the result that camefrom special relativity theory, one that is now confirmed by experiment. Cochran gave a talkon this to a huge and largely hostile undergraduate audience in the Maxwell Lecture Theatre.He had a more receptive audience when he spoke to the Kapitza Club, and the talk was sub-sequently published (27).

In 1957, en route to the Third Crystallography Congress, Cochran attended a short meetingat Massachusetts Institute of Technology, the purpose of which was to bring together physi-cists and crystallographers. A talk that greatly interested him was by B. N. Brockhouse (FRS1965), who described the use of neutron spectroscopy to investigate the dynamics of crystals.Cochran knew something of lattice dynamics as a theoretical subject; it had been one of Born’sinterests when he was in Edinburgh. After the Congress, Cochran wrote to Brockhouse, whoarranged for Atomic Energy of Canada to finance a one-year visit at Chalk River. This was thebeginning of a new and important phase of Cochran’s research career. In September 1958 hesailed from Liverpool with Ingegerd and his daughter, Margaret, aged four years. While inCanada they added a son, Robert, to the family. Brockhouse had just determined the firstphonon dispersion curves for germanium with the use of neutron spectroscopy, and Cochranjoined in the work on sodium iodide that was just beginning. Quite by accident he came acrossa recently published paper by Dick and Overhauser on the theory of the dielectric constant ofan alkali halide. Cochran found that their shell model to explain the polarizability of ions in acrystal was just what was needed to explain the lattice dynamics of sodium iodide. It was atheory that suited him well, involving good classical concepts without much need of quantumphysics. The shell model explained the measured phonon dispersion curves of NaI and KBrand reconciled their dielectric and dynamical properties (30). Cochran extended the theory togermanium, where again it was successful (28, 29).

A textbook by Born and Huang introduced Cochran to the Lyddane–Sachs–Teller equation,which relates the static and high-frequency dielectric constants to two lattice-dynamicalfrequencies:

Cochran extended this equation to apply to cubic crystals (31) and this led him to speculatethat the relationship

� (0) � (T�Tc)�1

e (0)e (∞)

=w2

L (q → 0)w2

T (q → 0).




that applies near the phase transition in a ferroelectric such as BaTiO3 implied that

2T (0) � (T�Tc).

Cochran interpreted this result as an instability of the crystal at T�Tc against a particularmode of vibration. He developed some of the consequences of this idea in a short paper (32).Later he discovered that others had had much the same idea, in particular P. W. Anderson, whohad a paper in press based on a contribution given at a meeting in Moscow in 1958. In a con-ference paper in 1971 (39) Cochran traced the origin of the idea back to a paper by Raman andNegundagi in 1940. It is typical of the man that Cochran gave full credit to those others whohad similar ideas to his own, but Cochran certainly took the subject forward to a much greaterextent than did the others and two papers he wrote (33, 34) were very influential and widelycited.

The period in Canada was both fruitful and demanding, with Cochran working 80-hourweeks—although he still found time to potter around the local park on skis. In the summer thefamily visited the Woolfsons, who were spending the year in New York, and then went on toa Gordon Conference at Meriden, where Cochran gave an unscheduled paper on ferroelec-tricity. Later the family toured the New England states and then returned from New York toSouthampton on a Dutch ship.

On returning to Cambridge, Cochran briefly readdressed the phase problem and also tookan interest in the work of George Sim and Pat Tollin, who had just solved the structure ofadenosine. However, before long he turned his attention almost completely to lattice dynam-ics and thereafter he took little part in conventional crystallographic research.

Cochran took on Stuart Pawley (FRS 1992) as a research student in 1959 and RogerCowley (FRS 1978) a year later, both of whom later became his professorial colleagues.Cochran first wrote a long paper on the theory of ferroelectricity (33). Then he turned hisattention to the lattice dynamics of molecular crystals, which he suggested as a thesis problemto Stuart Pawley, and did some work on the theory of the lattice dynamics of sodium. AlistairJohnson, who had given a colloquium in the Cavendish, invited him to spend some time atRoyal Radar Establishment Malvern in the summer of 1960. Cochran extended the shellmodel to GaAs, and the calculated two-phonon infrared spectrum of this material agreed wellwith Johnson’s measurements (35). In the course of this work on GaAs Cochran realized thathis early work on ferroelectricity and crystal stability could be extended to piezoelectric crys-tals in a way that linked the dielectric, elastic and piezoelectric anomalies in a ferroelectricmaterial with the lattice dynamics (34). During this time Cochran was looking for a suitablematerial to test this theory. He managed to borrow a crystal of SrTiO3 and Roger Cowley didthe experiment in Chalk River, under Brockhouse’s guidance, which found the transversemode for which 2

T � (T�Tc). By then Cochran was established as the leading figure in thetheory of lattice dynamics and this was recognized when he was elected a Fellow of the RoyalSociety in 1962.

In 1954 the Cochrans had bought a house in Arbury Road, Cambridge, of rather uncon-ventional design in which all rooms opened on to a central courtyard. It was cold in winter andin 1959, on returning from Canada, they sold the house and moved into a college flat on KingsParade. When their second daughter, Jennifer, was born in 1961 conditions became somewhatcramped and they moved to a conventional house on Huntingdon Road. Cochran occasionallyconsidered moving away from Cambridge and in the period 1961–62 he had opportunities toaccept chairs at Southampton and Sheffield, which he declined. Cochran often remarked that

William Cochran 79



the only place to which he would consider moving was Edinburgh and when a second chairwas advertised there in 1963 he called on Norman Feather FRS during a visit to Hillwood. Hewas deterred by the conditions for the post that required the new professor ‘to pull togetherthe different lines of research being pursued in the department’. As these included nuclearphysics, atomic physics, metal physics and fluid dynamics, all headed by independentlyminded people, Cochran thought that this task would be beyond his, or indeed anybody’s,capability. Later in the year Michael (later Lord) Swann FRS, the Dean of the Faculty inEdinburgh, called on Cochran during a visit to Cambridge and said that the conditions for thepost had been dropped and that Cochran would be able to join in the work of the departmentand continue his own research. After a week of consideration Cochran decided to make themove.

RETURN TO EDINBURGH

The move to Edinburgh was made in September 1964 and was not a happy one in the earlystages. An attempt at Easter to find a house that they both liked had been unsuccessful;Ingegerd disliked the house they eventually occupied in the suburbs and was homesick forCambridge. Cochran himself had an office in a temporary prefabricated building but theremainder of the department was much as he had known it in the 1940s. Cochran thought thatthe standard of research in the department as a whole was low and there was very littleResearch Council support of the activity. The theme of Cochran’s inaugural lecture was thatthe resources required by physics had outgrown what individual departments could provide sothat these must be provided nationally and internationally.

At first his research activity also went very badly in Edinburgh. Cochran concentrated onbuilding up a research group, which was uphill work although he did persuade Stuart Pawleyto join him as a lecturer. Philip Bradford, who had begun research with Helen Megaw inCambridge, transferred to his supervision but never submitted a thesis. A second student, fromoverseas, also did not submit as he was found to have manufactured some of his results. TheHilger & Watts diffractometer, purchased with £30000 of Science Research Council money,was a disaster; the one he built in Cambridge for £300 would have given better service! To topit all, the new building, which was planned to house several departments, seemed to recedeinto the distance as funds for the Robbins expansion of higher education began to dry up.When he returned from a conference in India in 1966 Cochran compared unfavourably theaccommodation in the department, and by implication the department itself, with what he hadseen in India. This offended Swann, and Cochran thought that Swann wrote him off as a badappointment.

Gradually things began to improve. Richard Nelmes (FRS 2003), from Cambridge, joinedhim as a research student, and E. R. Cowley and Margaret Elcombe, who had been his stu-dents during his last two years in Cambridge, joined him as a postdoctoral fellow and demon-strator respectively. John Derby and Susan Kay also obtained postdoctoral appointments.Construction of the James Clerk Maxwell building began, the first phase being the RegionalComputing Centre.

In Cambridge W. H.Taylor was due to retire and he was keen that Cochran should succeedhim. Lord Todd, who was chairing a party on the future of crystallography at the Cavendish,asked Cochran to give evidence and Cochran expressed the view that there was place for a




solid-state physics group but that crystallography per se was no longer appropriate in a physicsdepartment. That probably put paid to any chance he had of being invited back, although, hadthe invitation been made, it would have posed a dilemma for him. At about this time Bristolalso made tentative approaches to him but Cochran decided that his future was in Edinburgh.

Cochran continued to follow up his ideas on ferroelectricity, mainly using the Chalk Riverfacility for neutron spectroscopy. The crystal stability theory predicted that a diatomic crystalcould be a ferroelectric, but TlBr, which was investigated by Roger Cowley and a Japanesevisitor, A. Okazaki, did not have a phase transition. Before Cochran left Cambridge a visitor,R. S. Allgaier, had told him that PbS, and related crystals, had anomalous dielectric properties.Margaret Elcombe studied this material and later PbTe and SnTe and they were found to haveproperties similar to those of SrTiO3—that is, they were near ferroelectric—and it has sincebeen shown that for specimens of slightly different composition a phase transition occurs.These were his first successful Edinburgh-based experiments.

Roger Cowley became a member of staff at Chalk River and provided a strong link betweenthat research establishment and Edinburgh. Cochran had pointed out in his first paper on fer-roelectricity that an anti-ferroelectric phase transition would be associated with a mode of lowfrequency whose wavevector was at the Brillouin zone boundary, and a search was made fora confirmatory example. The change in crystal structure of LaAlO3 at the phase transition sug-gested that it could be one; a Russian visitor, Vladimir Plakhty, made an X-ray study of thematerial, which was not conclusive (36). Before an experiment could be done at Chalk River,Gen Shirane and John Axe used the new high-flux reactor at Brookhaven to perform a num-ber of experiments that showed the validity of Cochran’s prediction. Ironically it turned outthat SrTiO3, which they had worked on previously, had a low-frequency zone-boundary modeassociated with a phase transition at 105 K, demonstrated by nearly simultaneous experimentsat Brookhaven and Chalk River.

Another idea put forward by Cochran in early papers was that even a hydrogen-bonded fer-roelectric such as KH2PO4, in which the phase transition is known to involve the ordering ofhydrogen atoms onto widely separated sites, would have a ‘soft mode’. This was confirmed in1967 by an Australian research student, George Paul, although Cochran also took part in thisexperiment when he visited Chalk River that year (37).

Although Cochran was no longer interested in the kind of crystallography he had done inCambridge, he did set up an X-ray laboratory to investigate ferroelectric and other structuralphase transitions. This side of the work was successfully pursued by Richard Nelmes and hisstudents. Cochran also thought that Edinburgh, with its strong interests in structural biology,should be a centre for protein crystallography. Swann was enthusiastic but attempts to attractfirst David (later Lord) Phillips FRS and then David Blow (FRS 1972) to Edinburgh wereunsuccessful. David Green, who had worked with Max Perutz, came as a senior lecturer butGreen fell ill, the work languished, and Green eventually died in 1976. It also seemed toCochran that Raman spectroscopy, which had been revolutionized by the advent of the laser,was another technique for studying phase transitions. After a slow start this work flourishedand was the group’s most productive home-based technique. Cochran also thought thatMössbauer spectroscopy could be applicable, and Hugh Montgomery, with the help of FrankPlacido, performed some experiments. However, the technique was of limited application andwork in this area was eventually discontinued.

In 1969 the department, having expanded in numbers and with a new building imminent,decided it could appoint a second Professor of Physics (Feather was Professor of Natural

William Cochran 81



Philosophy). Cochran strongly urged the appointment of Roger Cowley, against some opposi-tion based on the closeness of his interests with those of Cochran, but he was appointed at theearly age of 29 years—although he did not arrive in Edinburgh until 1970. Taking stock at thattime, Cochran concluded that research in the department had improved since he had arrived,particularly in nuclear physics, where they had taken his advice and increased cooperationwith Harwell and the Kelvin Laboratory. However, Cochran did not feel he could take muchcredit for these improvements. He was suffering from periods of depression in 1969, perhapsaccentuated by several bouts of a flu-like illness. He became rather tired of travelling toLondon for meetings of the SRC Physics Committee, The Neutron Beam Research Committeeand a Working Party considering the provision of a new British neutron source. Cochran hadno enthusiasm for the ‘super-booster source’, which he thought would be inferior to the cur-rently available reactor sources.

Cochran applied for a six-month sabbatical in 1970, which he intended to spend partly atthe Bell Telephone Laboratory and partly at Brookhaven. However, just before they were dueto leave, Ingegerd had to enter hospital for an operation so Cochran stayed at home to write areview article (38). They were able to go to Brookhaven as planned, leaving daughterMargaret behind with her aunt as she had examinations to sit. It was a very pleasant break,especially for Ingegerd, who much enjoyed the campus-type environment and mixing with theinternational community. Cochran gave some lectures at Stony Brook University, some ofwhich provided material later for his monograph Dynamics of atoms in crystals (41). He tookwith him some crystals of KTaxNb1�xO3 which his research student, Joe Zaccie, had beenworking on for some time. This material, and some other perovskites, gave curious streaks onmonochromatic X-ray photographs that had led to an alternative theory of ferroelectricity tothat proposed by Cochran. The correct explanation of the streaks was not found from theexperiment in which he participated (40). When Gen Shirane and R. Comès (who proposedthe alternative theory) found the correct explanation some months later it was, in fact, quiteconsistent with the lattice-dynamical approach.

The Cochrans enjoyed their stay on Long Island and took the opportunity to visit severalfriends. He remembered, in particular, a vigorous debate he had with David Sayre’s wife,Anne, who was writing a book about Rosalind Franklin from a very feminist viewpoint.

In 1972 Cochran was invited to spend the summer at the IBM laboratory at YorktownHeights. This time he was accompanied only by Ingegerd, the children being looked after bytheir Swedish grandmother. They stayed in a very pleasant house, set back in the woods with apond and a large garden but, with a month of the stay still to run, the owners returned. Ingegerdthen went to Sweden and Cochran was given a room by Alan Grant, a compatriot in the labora-tory. This visit stimulated a new line of research for Cochran that lasted for two years or so. AnIBM group, led by Mark Brodsky, was interested in the dynamics of amorphous materials, par-ticularly germanium and silicon. A colloquium attended by Cochran soon after his arrival madeit clear that the random-network structure for these materials was by no means certain and thatrecent electron microscopy work seemed to favour a microcrystallite structure. Cochran showedhow to calculate typical electron micrographs for these alternative structures, taking into accountknown aberrations of the electron microscope, and he showed that the random structure couldnot produce the ‘lattice’ fringes that had been seen experimentally. He continued this work inEdinburgh with Craig MacFarlane, an SRC-supported assistant. They, and others, showed thatadditional, and previously unconsidered, aberrations in the electron microscope made the evi-dence from it inconclusive so that the random-network structure remained the favoured one.




In 1975 Norman Feather retired and, because the university was having a saving campaign,they did not want to replace him and persuaded Cochran to transfer to his chair. The depart-ment was in the mood to introduce more democracy at the end of Feather’s headship, and anew Teaching Committee and Head of Department’s Committee were set up, with the Head ofDepartment being elected for three years. Cochran was elected in 1975 and did not find theheadship particularly onerous although he did too much himself rather than devolving tasks toothers. There was no discontinuity with the previous order although decisions took longer withthe committee structure. The need to make continual savings put a strain on the Head ofDepartment and it was not a particularly happy time for Cochran. When Roger Cowleyreturned from a year’s leave in Brookhaven in 1976 Cochran asked him to take over theadministration of the departmental research and also leadership of the solid-state group forwhich, by this time, he was the main source of ideas. Cochran was well supported by the staffduring this period and his able running of the department led to his being invited to becomeDean of Science in 1978, to which post he was duly elected. In his period as Dean there wasa general slow contraction of science activity except in electrical engineering and computerscience, which had benefited from the microprocessor revolution.

By 1980 Cochran had accepted that his days as a research scientist were over and he con-tinued to serve the university in an administrative capacity. He was widely admired in the uni-versity and known as someone who set high standards, both for himself and for others. He wasVice-Principal from 1984 to 1987 and at the same time he was a Curator of Patronage, theCurators being a formal body that appoints the Principal and to the older chairs when theybecome vacant. Only those individuals held in the highest esteem by their colleagues are everappointed as Curators of Patronage.

Cochran’s early poetry phase, stimulated by meeting his future wife, flowered again in1973, much influenced by the work of Robert Fergusson, Edinburgh’s leading poet. He spentmany happy hours in trying to compose poetry in the style of Fergusson, which is light andgently satirical. His active retirement years were spent on his abiding interest in tracing hisfamily genealogy, which broadened into an interest in Scottish history and culture. He alsotook great pleasure in going with his wife to a caravan, later replaced by a log cabin, close toa river near Callander in the Trossachs.

Cochran’s scientific achievements were considerable. He made important contributions inthree areas that eventually earned Nobel prizes for others—in understanding the helical struc-ture of DNA (Crick and Watson), in direct methods in crystallography (Karle and Hauptman)and in lattice dynamics (Brockhouse). His work was well recognized. Apart from hisFellowship of The Royal Society he was also a fellow of the Royal Society of Edinburgh andan Honorary Fellow of Trinity Hall, Cambridge. He was awarded the Hughes Medal by theRoyal Society, the Guthrie Medal of the Institute of Physics and the Potts Medal of theFranklin Institute.

His last few years were blighted with motor-neuron disease, which he bore with character-istic quietness and courage.

ACKNOWLEDGEMENTS

I am grateful to the many individuals who provided the many snippets of information that enabled a rounded biogra-phy to be written. These include William Cochran’s widow, Ingegerd Cochran, his son, Robert, and his colleague

William Cochran 83



Stuart Pawley. However, my greatest thanks must go to Roger Cowley, who revised some sections on the latticedynamics work that had previously been understated—because they were based on William Cochran’s modestaccount of his own work.

The frontispiece photograph was taken by Walter Stoneman and is reproduced with permission from GodfreyArgent.

BIBLIOGRAPHY

The following publications are those referred to directly in the text. A full bibliography, num-bered as in the second column, is available from the Royal Society’s Library and online atwww.pubs.royalsoc.ac.uk.

(1) (1) 1946 Addition compounds between sucrose and sodium halides. Nature 157, 321.(2) (3) (With C. A. Beevers) The crystal structure of sucrose sodium bromide dihydrate. Proc. R. Soc.

Lond. A 190, 257–272.(3) (4) 1947 (With C. J. B. Clews) The crystal structure of certain chloropyrimidines. Nature 159, 264–265.(4) (5) (With C. J. B. Clews) The structures of pyrimidines and purines. I. Acta Crystallogr. 1, 4–11.(5) (6) 1948 A critical examination of the Beevers–Lipson method of Fourier series summation. Acta

Crystallogr. 1, 54–56.(6) (7) X-ray analysis and the method of steepest descents. Acta Crystallogr. 1, 273.(7) (10) The Fourier method of crystal structure analysis. Nature 161, 765.(8) (11) The Fourier method of crystal structure analysis. Acta Crystallogr. 1, 138–142.(9) (12) 1949 (With C. J. B. Clews) The structures of pyrimidines and purines. III. Acta Crystallogr. 2, 46–57.(10) (14) 1950 A Geiger-counter technique for the measurement of integrated reflexion intensity. Acta

Crystallogr. 3, 268–278.(11) (15) 1951 The electron distribution in adenine hydrochloride. Acta Crystallogr. 4, 81–92.(12) (16) The crystal structure of salicylic acid. Acta Crystallogr. 4, 376–377.(13) (17) Some properties of the (Fo�Fc) synthesis. Acta Crystallogr. 4, 408–411.(14) (18) 1952 A relation between the signs of structure factors. Acta Crystallogr. 5, 65–67.(15) (19) (With F. H. C. Crick) Evidence for the Pauling–Corey -helix in synthetic polypeptides. Nature

169, 234–235.(16) (20) (With F. H. C. Crick & V. Vand) The transform of atoms on a helix. Acta Crystallogr. 5,

581–586.(17) (21) The symmetry of periodic two-dimensional functions. Acta Crystallogr. 5, 630–633.(18) (25) 1953 (With H. S. Lipson) The determination of crystal structures. London: Bell.(19) (28) (With A. D. Douglas) A new application of EDSAC to structure analysis. Nature 171,

1112–1113.(20) (31) 1954 (With M. M. Woolfson) Have Hauptman and Karle solved the phase problem? Acta

Crystallogr. 7, 450–451.(21) (34) 1955 (With M. M. Woolfson) Theory of sign relationships between structure factors. Acta

Crystallogr. 8, 1–12.(22) (35) Relations between the phases of structure factors. Acta Crystallogr. 8, 473–478.(23) (36) (With A. S. Douglas) The use of a computer for the direct determination of crystal structures.

I. Proc. R. Soc. Lond. A 227, 486–500.(24) (42) 1957 (With A. S. Douglas) The use of a computer for the direct determination of crystal structures.

II. Proc. R. Soc. Lond. A 243, 281–288.(25) (43) A suggested experiment on the clock paradox. Nature 179, 977–978.(26) (44) A suggested experiment on the clock paradox. Proc. Camb. Phil. Soc. 53, 646–650.(27) (47) 1958 The clock paradox. In Vistas in astronomy (ed. A Beer), vol. 3, pp. 78–87. London: Pergamon

Press.(28) (49) 1959 Theory of the lattice vibrations of germanium. Phys. Rev. Lett. 2, 495–497.




(29) (50) Theory of the lattice vibrations of germanium. Proc. R. Soc. Lond. A 253, 260–276.(30) (51) Lattice dynamics of alkali halides. Phil. Mag. 4, 1082–1086.(31) (52) Dielectric constants and lattice vibrations of cubic ionic crystals. Z. Kristallogr. 112, 465–471.(32) (53) Crystal stability and the theory of ferroelasticity. Phys. Rev. Lett. 3, 412–414.(33) (55) 1960 Crystal stability and the theory of ferroelectricity. Adv. Phys. 9, 387–423.(34) (57) 1961 Crystal stability and the theory of ferroelectricity. II. Adv. Phys. 10, 401–420.(35) (58) Lattice absorption in gallium arsenide. J. Appl. Phys. 32, 2102–2106.(36) (86) 1968 (With A. Zia) Structure and dynamics of perovskite-type crystals. Phys. Stat. Sol. 25, 273–283.(37) (95) 1970 (With G. L. Paul, W. J. L. Buyers & R. A. Cowley) Ferroelectric transition in KD2PO4. Phys.

Rev. B2, 4603–4612.(38) (97) 1971 Lattice dynamics of ionic and covalent crystals. CRC Crit. Rev. Solid State Sci. 1, 2–44.(39) (98) Landau’s theory and structural phase transitions. In Structural phase transitions and soft modes

(ed. J. Feder), pp. 1–13. Oslo: Universitets-Forlaget.(40) (100) (With B. Yelon & G. Shirana) Neutron scattering study of the soft modes in cubic potassium

tantalite-niobate. Ferroelectrics 2, 261–269.(41) (103) 1973 The dynamics of atoms in crystals. London: Arnold.

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william cochran. 30 july 1922 − 28 august 2003: elected...

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