2D Geometry solves heat effect problems

A simple idea copes with heat effects in fibre optic components, electronic packaging and advanced sandwich composite constructions. Tom Shelley reports The definitive answer to problems caused by thermal expansion seems to have at last been discovered. It is not to use novel and expensive materials whose internal structures provide an effectively negative or near zero thermal coefficient of expansion, although this can be done, but to turn to a simple 2D geometry. Archimedes and Stephenson could have invented it but it has had to wait for UK university professor to come up with the idea, with the original intention of improving the performance of fibre optic communication devices designed to sort signals modulated on light of slightly different wavelengths. Early attempts to invent zero thermal expansion structures were mainly aimed at improving the time keeping of pendulum clocks in order to assist ship navigation. Early solutions include George Graham's addition of a mercury column to the lower end of a pendulum rod in 1715. When the temperature went up, the length of the mercury column increased, keeping the centre of mass of the system the same distance from the pivot point. In 1725 John Harrison invented the gridiron pendulum in which brass and iron rods, with different temperature coefficients of expansion, were fastened alternately top and bottom in a gridiron pattern to keep the centre of mass at the same point. Professor Bill Clegg, in the Department of Materials Science and Metallurgy at Cambridge came up with his idea rather more recently. His intention was to find a better way to stop fibre optic Bragg gratings used in wavelength division multiplexed systems from changing their performances with temperature. The effect comes partly from thermal expansion but more from a change in refractive index. Typically, if a grating goes through a temperature change of 120 deg K, the reflected wavelength can shift by 1.6nm. This is too much for many applications and so there is a demand to reduce it. If the rod of grating material is subjected to a compressive stress as temperature rises, the change can be almost entirely suppressed. This may presently be achieved by mounting the device in a component in which one end is mounted in the bottom of a cup and the other is mounted in a protruding member whose thermal expansion pushes it towards the base of the cup. It is however, very difficult to mount the fibre sufficiently accurately, so Professor Clegg and his colleagues have come up with a geometrical frame with much more relaxed mounting tolerance requirements. The frame is formed from four stiff beams of material of low coefficient of thermal expansion connected by pin joints, while a rod connecting the diagonal points is made of material with a high coefficient of thermal expansion and is much stiffer than the frame. The fibre grating is attached to the frame at the opposing diagonal points and runs perpendicular to the rod. When the temperature rises, the rod expands, and geometry applies a compression force to the fibre grating. In a test construction, frames were cut out of Invar by electric discharge machining a 0.5mm thick sheet. A 40mm thick aluminium block acted as the rod. Germania doped silica fibres were attached to the device with epoxy and the whole arrangement temperature cycled between 233 deg C and 353 deg K. By choosing optimum geometric angles for the frame, it was found possible to reduce the change in reflected wavelength from 1.575nm to 0.078nm over a 120 deg K temperature range. But making the rod element in the form of a plate, and surrounding it with a series of isosceles triangle frames of the low coefficient material, it is possible to devise a structure that maintains its linear dimensions in two dimensions. Conversely, it is also possible to devise structures that have an increased effective coefficient of thermal expansion relative to the central plates either in one direction or both directions. While the fibre Bragg gratings are objects on a macroscopic scale, it is possible to engineer structures on a microscopic scale using photolithography techniques. It is then not necessary to make mechanical pin or bolt joints at the joining points, but merely to make overall etched frame structures that lock into the corners of the plates, with geometrical changes being accommodated by frame strut bending. Some experiments have been undertaken with such structures, mainly in order to verify mathematical models of their mechanical behaviour under the effects of heat and load for different design parameters. This is essential if such structures are to be designed for any specific practical purpose, since mathematical models inevitably have to be simplified relative to real life, even when run on powerful computers. In one series of experiments, frame patterns were etched out of 0.5mm copper plate, and plates cut out of 0.5mm Invar sheets, and attached using lead tin solder. This is the opposite way round to a structure designed to minimise the overall effects of thermal expansion, but was done in order to provide a understanding of the mechanics in order to verify and improve modelling. Not surprisingly, it was found that the beams behave more like jointed struts if they are thin than if they are thick. This has led onto schemes for having layers of material of widely different thermal expansion coefficients mounted above each other, each attached to an intervening frame to accommodate their different expansions. The main potential applications are seen in electronic systems. The 2D arrangement already looks like a mounting system for multiple integrated circuits, held by the frame in such a way that they would undergo no movement relative to each other. This neither requires mechanical support forces to be born entirely by solder joints on a printed circuit board or by potting compounds, with their associated thermal mismatch problems. While the electronics industry has shown interest, it has yet to make use of the ideas, although with ever increasing heat outputs on chip coupled with a desire for maximum system reliabilities, this situation could change quite abruptly. The other main potential area of potential applications is in composite sandwich constructions. Professor William J Clegg Eureka says: This is the first major advance to be made in coping with thermal expansion of materials since the development of temperature compensation pendulums for chronometers in the early eighteenth century Pointers * By mounting a Bragg Fibre Grating in a frame of low thermal expansion coefficient materials, with a rod of high thermal expansion coefficent material, it is possible to counteract thermal effects in the fibre * The same idea can be extended to 2D structures which can be made to maintain their overall dimensions, or, if desired, change them appreciably in response to thermal changes * The ideas have relevance to electronic packaging required to cope with even greater heat generation than today's chips and to novel composite sandwich materials involving widely differing materials