Dynamic delivery - teaching thermodynamics
The teaching of thermodynamics in materials needs to be made more tangible to engage students' interest argues John Gisby from the National Physical Laboratory, Teddington, UK. He suggests a new framework.
The National Physical Laboratory, Teddington, UK, in collaboration with Dr Fred Hayes from The University of Manchester, UK, has developed a portfolio of educational materials, including lecturers’ notes, presentations, instructions for illustrative calculations and underpinning thermodynamic databases for use with the software MTDATA.
Some students following materials science, chemistry, geology and engineering degree courses become disillusioned by the large numbers of proofs, without obvious practical applications, that feature in traditional thermodynamics teaching.This is despite the key role played by thermodynamics in understanding and improving materials’ properties and processes in industry and the environment.
Hayes has suggested that software for calculating phase equilibria, which is used in industry to solve real problems in multicomponent chemical systems, be introduced to students earlier to stimulate their interest in thermodynamics. The software searches for the particular combination of phase amounts and compositions, which gives the lowest possible Gibbs energy for each system under consideration, which is the equilibrium configuration.
The aim is to ensure that all examples relate to real systems with clear industrial or environmental relevance, that all diagrams are easily calculable and, mostimportantly, offer the opportunity for students to explore further by changing input parameters, such as temperature, pressure or composition, to view the impact upon calculated results.
The materials produced broadly correspond to a three-year undergraduate course. The aim is to provide source materials for lecturers from different disciplines to supplement their own ideas. Examples cover a range of materials types, including metals, oxides, gases, aqueous solutions and polymers, and applications such as tailoring the properties of steels, finding replacements for lead in solders, metal extraction from ores, molten salt processing, concrete carbonation, pollutants reduction during combustion and even rocket science.
The course covers the first, second and third laws of thermodynamics, definition sof state functions and the relationships between them, isolated and closed systems. It introduces phase equilibria between ideal phases, such as ideal gases, and immiscible solids. An example of a calculated single-component phase diagram, a pressure-temperature diagram for H2O, showing the triple point at which solid, liquidand gaseous phases exist in equilibrium, is shown.The triple point of water is the basis for defining the unit of temperature and occurs at 0.01°C.
Thermodynamics and phase equilibria
The course moves from single-component systems to consider binary, ternary and multicomponent phase equilibria, showing the relationship between Gibbs energy and phase diagrams. It introduces concepts such as polymorphism, intermediate phases, metastability and immiscibility. It illustrates different types of binary phase diagrams, and how they arise fromthe interplay of Gibbs energies of mixing in solid and liquid phases. Also covered in graphical representation are ternary phase equilibria, includingisothermal sections, monovariant curves and fields of primary crystallisation. Multicomponent equilibria are introduced with temperature-composition sectionsand phase fraction diagrams.
The diagram shows calculated Gibbs energies for the face centred cubic (fcc) and liquid phases inthe silver-copper (Ag-Cu) system at, 1,053K, the eutectic temperature, plotted as a function of the Cu mole fraction. A common tangent can be drawn between the silver-rich end of the fcc curve, the centre of theliquid curve and the Cu-rich end of the fcc curve (in red), indicating that twofcc phases coexist with a liquid phase at the chosen temperature. The composition of each equilibrium phase can be read from the abscissa by droppinga vertical line (in green) from the point that the Gibbs energy curve meets the common tangent.
Following the procedure demonstrated in the diagram, students can build up a simple phase diagram, with a calculator, a pencil and paper, in around half a day. The same construction can be completed automatically and instantaneously using MTDATA,demonstrating the relationship between Gibbs energy and phase equilibria, but also the usefulness of phase equilibrium calculations. Computer-based calculations allow more complex phase diagrams to be considered than is possible by hand, which broadens students’ knowledge.
The diagrams illustrate the effects of changing Gibbs energies of interaction in solid and liquid phases on calculated binary phase equilibria and, again, represent calculations that students can perform for themselves. The reddiagram is that calculated for the germanium-silicon (Ge-Si) system. It takes the form of a simple lens-shaped combination of liquidus and solidus boundaries, typical of two elements, which interact almost ideally in solid (diamond structure here) and liquid phases. Germanium-silicon solid solutions, which form in a continuous series below the solidus, are widely used as semiconductors in the manufacture of electronic devices. It is possible to create faster devices based on Ge-Si than on Si alone.
If the Gibbs energies of interaction in the liquid and solid phases are made more positive, a monotectic is formed where two liquid phases of different compositions exist in equilibrium with a solid phase. The separation of polymers from polymer-solvent solutions can often be understood in terms of underlying monotectic behaviour. With a more negative Gibbs energy of interaction in the liquid phase, a simple eutectic between two effectively immiscible solids results. Potassiumchloride-lithium chloride is an example of such a system. Molten salt mixtures exhibiting low temperature eutectics are widely used as solvents in extracting and processingmetals, such as uranium, during nuclear fuel reprocessing.
To the left of the original lens shaped Ge-Si diagram, a negative Gibbs energy of interaction in the solid phase results in acongruently melting maximum. This type of phase diagram is most often encountered in liquid-gas systems where the maximum is known as an azeotrope or constant boiling mixture.
The final course (year three) considers the wide variety of diagram types that itis possible to generate from phase equilibrium calculations, with practical examples of their uses. Projections from and sections through multicomponent systems andgeneralised x-y plots, where the x and y variables can be phase properties such as, compositions or thermodynamic properties, are showcased along with binary phase diagrams and ternary isothermal sections.
Aqueous systems are discussed in terms of pH plots for acid-base titrations and Pourbaix diagrams, used to identify the main carrier species for selected elements as afunction of EH (oxidation potential) and pH.
Case studies based onpublished scientific work include calculating mercury’s partial pressure in the gas phase above a bismuth-indium-mercury (Bi-In-Hg) amalgam. These amalgams, rather than pure mercury, are used in compact fluorescent lamps to provide adesired mercury pressure of around 0.8Pa necessary to generate a luminous flux stable over the, potentially wide range of lamp operating temperatures. Phase equilibrium alculations are now widely used as a guide to determine suitable amalgam compositions. The calculated partial pressure of Hg(g), above an amalgam containing Bi, In and Hg in the molar ratio 53:47:2, is shown as afunction of temperature in the diagram.