Thermodynamic data A tutorial course Session 1: Introduction and unary data (part 1) Alan Dinsdale “Thermochemistry of Materials” SRC

Outline of course The aim is – Present the underlying basis behind the calculation of phase equilibria from critically assessed thermodynamic data – To show how thermodynamic data are represented in terms of temperature, pressure and composition – To describe the experimental techniques and ab initio methods used to provide raw materials for us to use in our thermodynamic assessments – To show the basis behind critical assessments – To give you some experience in handling data and datafiles

Topics This is what we aim to cover during the course: – Fundamentals and equations of state – Data for 1 component systems – Data for 2 component systems – Experimental methods – Thermodynamic databases – Extrapolations to ternary and higher order systems – Calculations of thermophysical properties There is a lot of material to cover so the course will be broken into a number of sessions. Each session will conclude with questions and issues for you to consider at your leisure

This session will be concerned with: Fundamentals Unary data (part 1)

1. Fundamentals For most practical purposes in Inorganic Materials Thermodynamics we express the stability of a material in terms of the Gibbs energy which represent as a closed equation in terms of the sort of variables that we have some control over eg temperature, pressure and composition. G = f(T, P, x) This is essentially our basic equation of state The stable state is the one which has the minimum Gibbs energy Unfortunately we can’t measure Gibbs energy, we can only measure or have some understanding about, properties which are related to the Gibbs energy

Basic equation of State

Other properties related to Gibbs energy

Problems

Basic Plan To derive an expression for the Gibbs energy of each phase in a system as a function of temperature, pressure and composition This will involve extrapolation of the data from regions where they can be measured to ranges of temperature and composition where we have no information This mean that we will have to use reliable, well tested and (hopefully) physically sound models

2. One component systems (Part 1) A number of publications with standard tables of thermodynamic functions of substances – JANAF – IVTAN, from TCRAS – Barin & Knacke – Pankratz – Hultgren These will generally give, over a range of temperature, values for Cp and S. Also they will provide information about H and G but the reference states for these will often be different from one compilation to another and therefore they must not be mixed

Δ f H, S 298, Cp, T trs and ΔH trs In general all that is required for a pure substance is – Δ f H : the enthalpy of formation at K from the elements in their standard states – S 298 : the standard entropy of the substance at K – Cp as a function of temperature from K upwards – T trs : the temperature of any transformations eg solid to solid, solid to liquid – ΔH trs : the enthalpy change associated with this transformation

Expression for G, H, S and Cp

Saturday, April 3,

Example : Data for Sn

Saturday, April 3, Heat capacity of Sn for different phases T fus = T trs Three phases: Diamond Bct_a5 Liquid Quite different variation of Cp Can convert Cp data to give variation of H with temperature

Saturday, April 3, Enthalpy of Sn relative to K Δ fus H Δ trs H

17 Entropy of Sn Δ fus S Δ trs S

Saturday, April 3, Gibbs energy of phases of Sn relative to BCT_A5 T fus T trs

Saturday, April 3, Volumes of phases If we have molar volume data as well as Gibbs energy as a function of temperature we can calculate unary phase diagrams

Saturday, April 3, Unary phase diagrams : Sn

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

End

For you to work on Conversion of Cp data into G-Hser: KCl Calculate unary phase diagram for KCl Derive lattice stabilities for Ga from a unary phase diagram

Heat capacity data for KCl Deltaf HS ab Tc T^2dT-2Upper Temperature LimitEnthalpy change E E Convert these data to G-Hser

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 ?

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 Use the following slide for the Gibbs energy difference between the liquid phase and the stable orthorhombic phase

Phase diagram for Ga

Gibbs energy differences for Ga