Materials with memory H. Bargmann hold the electrolyte. However the in a sodium cyanide/sodium sulphate CERN has an obvious interest in the magnet surfaces are not flat and this bath at 60 °C to produce a satisfactory behaviour of materials and structures makes the problem of positioning the foil. For a 10 ^m iron foil, a nickel since it indulges in a great deal of anode difficult and also the probe coating of 12 is needed (other mechanical construction and since it wears away. Alternatively, it is possible thicknesses produce a cracked foil). often exposes materials to rather to use a jet of electrolyte but then The foils are still very brittle and have extreme conditions. For the most part there is a high probability of corrosion. to be stress relieved before use. the necessary knowledge can be The selected technique is to shim The vacuum furnace in which heat gathered from other fields where the magnets by sticking thin iron foils treatment is carried out is in the West applied research has had to be done onto the pole surfaces in the required workshop while the foils are made in in order to use materials under still areas. The poles are there generally the Godet workshop and the first foils more extreme conditions. For ex­ slightly concave in appearance and a broke in transit. The stress relieving ample, a great deal of the necessary male replica can be machined so operation is carried out at temper­ knowledge of how materials are going that iron foils coated with araldite atures between 700 and 900 °C and, to behave in intense fluxes of radiation can be pressed into precise positions since the foils must not be contamin­ has been gathered in the nuclear on the magnet and the resin cured by ated with either copper or nickel, reactor industry. heating with an infrared source. stress relief cannot be carried out In recent years there has been par­ This is a simple way of modifying before the supporting layers are re­ ticular interest in knowing how ma­ the magnet pole pieces and it has the moved. The diffusion of nickel and terials will stand up to loads. For advantage that, once the corrections copper into iron at low temperatures instance, the ISR vacuum chambers have been made, new field meas­ is very slow and by experiment it was at intersection regions, must withstand urements of the magnetic field can found that heat treatment at 450 °C atmospheric pressure and yet must be be carried out and further corrections gives sufficient ductility to the foils extremely thin so as to allow the par­ applied, if necessary, without delay. that, after stripping, they can be ticles emerging from the interactions The big problem is to make flat iron transported safely. A final stage of to reach the detectors outside with as foils approximately 10 microns thick, vacuum heat treatment is carried out little hindrance as possible. Also 20 cm long and 2 cm wide. to give complete stress relief while there have been material failures the flatness of the foil is maintained. To deposit this thickness of iron on, which were difficult to understand for example, a copper substrate is a Rapid heating or cooling results in because large safety factors had been relatively simple operation. However, temperature gradients in the foil used in the design. when iron is plated it is not ductile which cause local plastic deformation. This led CERN to delve into some like normal iron but very brittle. In In addition, there is an allotropic applied research to try to understand addition, there are very high internal change in iron at approximately more deeply the behaviour of ma­ stresses between the plate and the 900 °C, and this can also cause plastic terials under stress. The research in­ substrate and if the copper is che­ deformation. It is therefore necessary volved development of continuum me­ mically dissolved in 1 % nitric acid to to heat and cool the foils slowly — a chanics — the mathematics of ma­ release the foil, the strip bends and rate of 100 °C per hour was found to terial behaviour. the foil is cracked. be satisfactory. The celebrated theory of elasticity To overcome this a second layer of Having worked out how to steer for solid bodies at elevated temper­ metal can be plated on top of the iron between all these obstacles the work­ ature frequently ceases to hold — the so that when the two layers are shops finally emerged with very thin, solid becomes viscoelastic. This is removed chemically at the same time flat, stress free foils. Their cost is well known in modern aero-space the iron remains flat and unbroken. about one tenth of that asked by engineering in reactor technology, and If the second layer is copper the rate outside industry. at CERN (in connection with certain of solution of the plated layer with equipment for special heat treatment respect to the rolled copper substrate of vacuum chambers). Viscoelastic is difficult to control. It was found by solids do not respond only to the pre­ experiment that if a layer of nickel of vailing external influences but have a controlled thickness is plated on the memory of what has happened to iron both the nickel and the copper them during their entire past. can be dissolved at equivalent rates To some extent all structural ma- 372 An example of creep in crystalline material. The distortion of the snow cap on a garden fence in Sweden developed over a couple of days while the external influences on the snow remained virtually unchanged. (Photo from F.K.G. Odquist's book 'Mathematical theory of creep and creep rupture' by courtesy of the Clarendon Press.) A cylindrical shell 50 cm in diameter (made of niomic 75) which has creep buckled under atmospheric pressure after some time, despite no change in the stresses to which it was subjected and despite having a generous safety factor above the strength needed to resist ordinary elastic buckling. terials possess the property of elastici­ yarn. At still higher temperatures it ty — the deformation of a body disap­ becomes like a dish of spaghetti pears when the load to which it has — additional viscous flow appears as been subjected is removed. This was the temperature increases, mainly due first announced for the special linear to shorter segments of chains of case in 1676 by Robert Hooke in the molecules sliding more easily over form of the anagram 'ceiiinosssttuv' one another (viscoelasticity). Finally, which he spelled out two years later the polymer turns into a viscous fluid. as 'Ut tensio sic vis' or The power of In all these cases, creep has a linear every springy body is proportional to viscoelastic nature and hence can be its extension'. Practically all the great treated by good clean mathematics. mathematical physicists of the follow­ Metal creep at elevated temper­ ing 300 years spent some time ela­ atures is mainly due to time- borating on the terms ' power dependent plastic deformation of ' springy ', and ' extension ' and the grains, grain-boundary sliding, or di­ theory of elasticity has found wide rect diffusion. Here, non-linear be­ application in the solution of engi­ haviour is predominant and it is also neering problems during the past cen­ in the corresponding mathematics. tury. Many good engineers still believe Modern continuum mechanics is in Hooke's law as the only law de­ now based on non-linear thermody­ scribing the behaviour of solid ma­ namics : from the first and second terial. And if there are obvious de­ law (together with certain invariance viations such as when, under constant requirements that the material pro­ load, plastic deformations increase perties should not depend on the with time (so-called 'creep') and so observer) all the thermo-mechanical on... these faithful engineers take equations emerge and they severely care of them by adding generous restrict the possible laws describing safety factors into their design. material behaviour. What remains is Hooke's simple law is very often still a wide class of functional rela­ violated since creep effects under tions — relating, for example, the pre­ mechanical stress are observed in sent state of stress of a body with its most solids. They are known in glass previous history of deformation. From and bitumen (liquids, more or less, these relations it emerges that a solid with very high viscosity) in concrete at low temperatures obeying Hooke's and in organic polymer. Organic poly­ law has a memory of one state only mer at low temperatures is a brittle, (the unstressed initial configuration) glassy solid. At elevated temperatures while at high temperatures, visco­ it is a rubbery material, like tangled elastic solids have memory of their 373 Handling high voltages a) Voltage holding in vacuum F. Rohrbach entire past (frequently a fading me­ In addition to the specialized systems search has shown that, depending on mory as with human beings). which are to be found around the the gap between the electrodes, one These problems and their mathema­ large particle accelerators, there are or other of the phenomena pre­ tical treatment have been tackled at many other devices which have to dominates. CERN since the solutions were not operate in vacuum and at high voltage. In the case of short gaps (less than available from elsewhere. The follow­ Apart from electrostatic separators, about 10 mm), the electrical discharge ing case will indicate that the solu­ accelerating columns, deflectors and is initiated by the explosion of a tions are certainly needed. electrostatic septums, there are other cathode micropoint (0.1 to 0.5 The cylindrical shell of a vacuum applications such as cathode-ray high), caused by too intense a field furnace at CERN buckled under ex­ tubes, electron microscopes, high- emission leading to thermal instability ternal atmospheric pressure, at high power cryolinks, generators for use in of the emitting point.