Negative Thermal Expansion By ‘The Team’

Negative thermal expansion (NTE) Negative thermal expansion is the study of physical properties of solids. Thermal Expansion is affected by a change in volume of a material when heated, generally, materials increase in volume when heated. The “coefficient of thermal expansion” of a material tells you how much its volume changes with temperature over time. A select group of materials actually decrease in size when heated. This is called Negative Thermal Expansion (NTE).

Displacement of C and N atoms The diagram on the screen is a representation of local vibrational modes responsible for NTE behaviour in structures. (a) contains a single-atom and (b) diatomic linkages. The filled circles represent heavy (usually metal) atoms, and the open circles represent light bridging atoms, such as oxygen (O) or cyanide (CN) species. In both cases, population of these vibrational modes leads to a decrease in the overall metal⋯metal distance. Andrew L. Goodwin and Cameron J. Kepert Phys. Rev. B 71, 140301

How the model was created Force operates over all charged ions. Note that 1/r dependence, which causes us problems when calculating the energy of a crystal.

Morse potential for the bonds between the metal cyanide bonds- equation used above to calculate the Morse potential. Here is the distance between the atoms, is the equilibrium bond distance, is the well depth (defined relative to the dissociated atoms), and controls the 'width' of the potential (the smaller is, the larger the well). The dissociation energy of the bond can be calculated by subtracting the zero point energy from the depth of the well.

Computer modelling of the lattice To investigate the behaviour of the materials we used the super computer to run simulations of Zinc and Cadmium cyanide crystal structures at different temperatures. We later ran the same investigation keeping the temperature constant and varying the pressure. The computer simulates various interactions between particles in the lattice. We avoided the issue of a small surface area by simulating a cube where a particles leaves through one side and re-enters through the opposite side. We interfaced with the supercomputer using the DL_POLY module through Linux.

Volume

Single Cadmium Cyanide (1)

Single Cadmium Cyanide (2)

Double Cadmium Cyanide

Double Zinc

Double Zinc

Total Temperature Double Cadmium

Effects of Pressure As temperature increased , we would expect a decrease in volume (NTE) The extent of NTE also varies with pressure We observed the impact of systematic increases of pressure on volume We expect further NTE with increased pressure over the set volume range Between 5 and 20 katm

Zinc Double 5 katm 10 katm 15 katm 20 katm

Double Zinc at 15kATM 200K

Cadmium Single 5 katm 10 katm 15 katm 20 katm

Conclusions The simulation for both Cadmium and Zinc single configurations are unstable above 5 katm, resulting in implosion The double structures responded as an NTE, until a critical point whereby they began behaving as normal materials (increasing in volume)

Buckingham potential Buckingham potential between the cyanide C/N atoms and the Xe guests. This has the form

Diffusion coefficient against Rho

Diffusion coefficient against A

Uses Thermal expansion can cause many problems in engineering, specially in large architectural structures such as buildings and bridges. For example, the Sidney Harbour Bridge can expand up to 18cm over a day. Material with negative thermal expansion properties are can counter this expansion. Alternative uses of materials controlled by thermal expansion properties are in cooktops and dental fillings to expand by an amount different from the teeth, for example when drinking a hot drink, which could otherwise cause tooth ache

Further development Due to time limitations we were only able to create the simulations for single and double cadmium cyanide and double Zinc, if we had more time, we would have liked to simulate double Zinc too which would have enabled us to draw better comparisons between all of the data collected. We also would have spend more time learning and understanding the PuTTy software, which proved problematic to begin wit, this would have allowed us to send jobs out, with less chance of errors and would have provided quicker and results. When looking at the Natural guest in cadmium cyanide we would have investigated Buckingham potential, changing row as well as distance to fully see the effects on the coefficient of thermal expansion. We would also have looked at the Buckingham parameters by looking into the diffusion coefficients- where some of the guests will move freely through the framework and others will stay put. Also we could have varied pressure to see the possible changes on the coefficient of the thermal expansion, extending the simulation to show the sample at negative pressures, and seeing if the trends would continue. If given more time, we would also have look into mixed zinc and cadmium cyanides, exploring the possibility of forming a “solid solution” as both materials share the same structure, this would mean that some of the tetrahedral metal sites are occupied by zinc and other cadmiums. We would then investigate the effects of thermal expansion on this solution.