Putting the theory into practice - thermodynamic modelling
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A former Materials World article (Dynamic Delivery, February 2010, p18-20) highlighted the applicability of software packages for predicting phase equilibria in multicomponent systems, such as MTDATA developed at the National Physical Laboratory, in engaging students’ interest in thermodynamics through examples of realworld applications. The use of such software does not, of course, stop in the classroom but underpins the design, optimisation and day-to-day troubleshooting of many industrial processes as well as the development of new, advanced materials and products, with specifically targeted properties. Here are some examples of predictive calculations used to address industrial problems and find costeffective solutions.
Operation calculations for copper smelter
The process flow sheet for the Kennecott Utah Copper Smelter features a two stage process in which copper-iron sulphides are oxidised first to white metal in an Outokumpu flash smelting furnace (FSF) and then to copper, ready for electrolytic refining, in a flash converting furnace (FCF). The FSF operates with a silica flux and an iron silicate (fayalite) slag, the FCF with a lime flux and a calcium ferrite slag. Phase equilibrium calculations have been used to determine suitable fluxing practises for the FSF and to investigate operational problems associated with the mixing of FSF and FCF slags.
Sections through the CaO-Cu-Fe-O-SiO2 system at constant copper concentration, for a range of temperatures and applied oxygen pressures applicable to the FSF, were calculated to identify saturation limits for the various crystalline phases, which might form from low temperature liquids. Results can be presented in the form of temperaturecomposition diagrams, liquidus contours and primary phase maps or rotatable liquidus surfaces, an example of which is shown left for compositions containing 10% Cu2O with a fixed oxygen partial pressure corresponding to that in air. A low temperature liquidus valley can clearly be identified extending through the centre of the diagram. Different primary crystalline phases are shown in different colours (see Figure 1, below).
Phase equilibrium calculations have also been used to investigate the consequences of possible carry-over of iron silicate slag from the FSF into the FCF, entrained with molten sulphide.
Figure 2 (black line) shows calculated equilibria for the CaO-Cu-Fe-O system with a fixed Cu2O level of 15 wt% at a typical O2 partial pressure of 10-5 atm. as CaO is substituted by Fe2O3. The liquidus valley, where normal operation occurs, is clearly apparent. If five wt% SiO2 is added (blue line) liquidus temperatures are raised, largely through the formation of a high melting crystalline phase, alpha prime dicalcium silicate. The practical consequence is an increase in slag viscosity, making the contaminated FCF slag difficult to tap.
Reliable solder joints?
During the transition to lead-free soldering it will be necessary to create joints soldered with alloys of mixed composition, for example during rework and repair. The mechanical performance of such alloys is determined by the phases formed on solidification and their compositions, both of which can be predicted from phase equilibrium calculations. Rapid assessments of joint reliability can be made on the basis of such calculations.
Figure 3 shows the masses of phases predicted to form under fast cool conditions for a tin/lead (Sn-Pb) joint repaired using a lead free tin/silver/lead (Sn-Ag-Cu) solder. Fast cooling is simulated in Scheil type calculations where crystalline phases calculated to form under equilibrium conditions at a series of stepped temperatures are excluded from subsequent calculations, assumed to have no further influence on the solidification process. Overall compositions with 75% Sn-Pb ‘electrician’s solder’ and 25% Sn-Ag-Cu and with 25% Sn-Pb and 75% Sn-Ag-Cu are considered.
Differences in the relative amounts of lead-based and lead-free solder clearly influence the final proportions of the major phases formed, Pb-rich FCC and Sn-rich BCT, the levels of intermetallics formed and the rate of solidification. With 75% Sn-Pb about 75% of the mass of the liquid phase is lost at the final solidification temperature, 453K. With 25% Sn-Pb there is a more gradual loss of liquid from 478K, about 25% being lost at the final solidification temperature, 451K.
The predicted temperature range over which solidification occurs corresponds to the ‘pasty’ range of the alloy, which has been shown to be important in defining its susceptibility to the fillet lifting phenomenon, the lifting of a solder joint from a PCB pad as the board cools and contracts after the soldering process. The ‘pasty’ range for each solder combination is more readily apparent from plots of heat capacity (Cp) versus temperature (see Figure 4).
Vehicle exhaust catalysts
Combustion, perhaps the most important industrial chemical reaction, is well suited to analysis based upon predictive phase equilibrium calculations. Chemicals and materials company Johnson Matthey, for example, has used MTDATA to investigate the subtleties of how vehicle exhaust composition affects performance under changing conditions, spanning all types of running including start-up.
Figure 5 shows the partial pressures of selected gaseous species calculated to form over a range of temperatures when a fuel, such as propane containing a small amount of sulphur as an impurity, is burnt in air. The full result would feature many hundreds of lines reflecting a very rich gas phase speciation. Only those species containing sulphur have been displayed here, to illustrate the fate of the impurity in the fuel.
Note that H2S is the major carrier of sulphur at the low temperature end of the partial pressure plot. Equilibration of combustion products at low temperatures, without use of a catalyst, is likely to result in the formation of H2S. Plots focusing on nitrogen or carbon containing species would show the suppression of CO and NOx, under the same conditions.
Combustion in a marine environment or when there is salt on the road can be simulated by adding NaCl to the overall composition of the previous calculation. The amounts of sulphur containing species calculated to form under such conditions are shown below. Amounts rather than partial pressures are shown in order to demonstrate the formation of condensed sodium sulphate (Na2SO4) (black line). Liquid sodium sulphate can dissolve the protective oxide layer on turbine blades, for example, and cause rapid corrosion to occur. A mixture of sodium chloride and sodium sulphate makes matters even worse by increasing the range of liquid stability.
These examples give just a glimpse of the wide range of applicability of predictive phase equilibrium calculations within industry, limited only by the availability of databases containing the model parameters, which underpin such calculations. Work at NPL to address the need for greater database coverage continues through active participation in projects involving the critical assessment of thermodynamic data.
Alan Dinsdale and John Gisby, National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, UK. Tel: +44 (0) 20 8943 7098. Email: firstname.lastname@example.org