Thermodynamic data A tutorial course Session 2: unary data (part 2) Alan Dinsdale “Thermochemistry of Materials” SRC

Review The aim was to give you some experience in handling data – Conversion of data from one format to another – Calculation of unary phase diagram – Estimation of lattice stabilities

Heat capacity data for KCl Deltaf HS ab Tc T^2dT^(-2) Upper Temperature LimitEnthalpy change E E Convert these data to G-Hser Hint : Start with the low temperature range. Use the equations for Cp given in slide 11 and equate them to the coefficients in the above table. Then include Δ f H 298 and S 298 Then go to the second temperature range. Adjust the first and second coefficient to make sure that H and S are the same as line 1 at the temperature limit Then go to the third range but this time include also the enthalpy and temperature of transition

AB TC T ln(T)d T^2e T^3f T^(-1) Upper temperature limit E E E E E E E E E E E E E E E The answers

Phase diagram for KCl Calculate the phase diagram for KCl between 300 to 1800 K, 0 to 3 GPa We have three phases: HALITE, LIQUID and CSCL We can take the HALITE phase as the reference phase. The data for the other phases will be relative to that and will take the form A+BT+CP HALITE:G = 0 LIQUID:G = *T e-6*P CSCL:G = *T e-6*P what value do you calculate for the triple point when all three phases are in equilibrium ? Hint: The boundary between HALITE and the LIQUID and CSCL phases is given by setting the appropriate Gibbs energy expression to zero and then expressing T as a function of P

Lattice stability data for bct Ga Bct_a5 is the phase labelled as II on the next slide Derive lattice stability data for this bct_a5 phase Hint: extrapolate the phase boundaries between phase II and liquid, and phase II and phase I (ortho_Ga). These temperatures can be marked on the next diagram and a straight line can drawn between them to show how the Gibbs energy of this bct_a5 phase varies with temperature

Phase diagram for Ga

Gibbs energy differences for Ga

This session will be concerned with: Unary data (part II) – Magnetic model – Pressure dependence – Lattice stabilities – Unstable phases

Magnetics

Magnetic materials Bcc Fe (T C = 1043 K) – therefore all ferritic steels Fcc Ni (T C = 633 K) – therefore most austenitic steels and superalloys Co (hcp, fcc), Mn (cbcc, fcc, bcc), Dy (hcp), Gd (hcp), Fe 3 O 4

Entropy contribution

Enthalpy contribution

Heat capacity contribution

Heat capacity of bcc Fe

Gibbs energy differences for Fe

Enthalpy differences for Fe: ref fcc

Pressure dependence

T-P phase diagram for Fe

Lattice stabilities: Difference in Gibbs energies between phases Often we are interested in the thermodynamic properties of phases outside the region where they are stable – Eutectics – we would like to have data for liquid Ag and Cu at 780°C – well below the melting points of the elements – Solubility – in order to model the Fe-Cr phase diagram we need data for Cr in austenite (fcc). The only stable solid phase of Cr is bcc. Therefore we need to derive data for fcc Cr

Extrapolation of P-T phase diagrams

Extrapolation of binary phase diagrams

Cr-Ni

Cr-Ni thermodynamic properties

Trends in entropies of fusion: fcc

Trends in entropies of fusion: hcp

Trends in entropies of fusion: bcc

Trends across transition metal series

Trends down a series in the periodic table

Use of ab initio calculations The present set of element data were derived largely from experimental data. Ab initio calculations were not thought to be sufficiently accurate in 1991 Now we have much more confidence in ab initio calculations. They can be used for calculation of enthalpy differences between phases and entropy of phases at 25°C However ab initio has also told us that some phases of elements are mechanically unstable eg. Fcc Cr, fcc W, even bcc Ti at low temperatures This calls into question the very basis behind lattice stabilities

Next session This will be concerned mainly with the liquid phase Exercise: The data for fcc and liquid Ag are given by: T T ln(T) E-3 T E-6 T T -1 (fcc) T T ln(T) (Liquid) Calculate the melting point, the heat capacity and the difference in Gibbs energy and entropy between the two phases between 50 K and 5000 K assuming that it is valid to extrapolate the data. Can you explain the odd behaviour ? What should the curves look like ?