Thermodynamic data A tutorial course Session 1: Introduction and unary data (part 1) Alan Dinsdale...

Thermodynamic dataA 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:

FundamentalsUnary 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

𝐺=𝐻−𝑇 𝑆+𝑃𝑉

Other properties related to Gibbs energy

• Entropy • Enthalpy • Heat capacity • Molar Volume • Expansivity = • Compressibility =

Problems• Entropy has a defined value

while S(0 K) is zero• Enthalpy, and therefore Gibbs energy, has no absolute value

– We can only talk about differences in Enthalpy or Gibbs energy– If we give a value of a Gibbs energy it has to be relative to

something else– Enthalpies are commonly referred back to the enthalpies of the

elements in their standard states at 25°C– It is convenient also to reference Gibbs energies back to the

standard state of the elements at 25°C– This gives us G-Hser– Note: SER means Standard Element Reference and not Stable

Element Reference. For most elements this would be the same. However for P, S and B the crystalline form stable at 25°C is not very well characterised.

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

ΔfH, S298, Cp, Ttrs and ΔHtrs

• In general all that is required for a pure substance is – ΔfH : the enthalpy of formation at 298.15 K from the

elements in their standard states– S298 : the standard entropy of the substance at 298.15 K– Cp as a function of temperature from 298.15 K upwards– Ttrs : the temperature of any transformations eg solid to

solid, solid to liquid– ΔHtrs : the enthalpy change associated with this

transformation

Expression for G, H, S and Cp

• Normally the Gibbs energy is expressed in terms of one or a number of overlapping power series expressions of the form:

where n typically might take the values 2, 3 and -1

• From this expression for other thermodynamic

properties can be derived:

Saturday, April 3, 2010 13

Example : Data for Sn


Heat capacity of Sn for different phases

Tfus = 505.078Ttrs

• Three phases: • Diamond• Bct_a5• Liquid

• Quite different variation of Cp

• Can convert Cp data to give variation of H with temperature


Enthalpy of Sn relative to 298.15 K

ΔfusH

ΔtrsH

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Entropy of Sn

ΔfusS

ΔtrsS


Gibbs energy of phases of Sn relative to BCT_A5

Tfus

Ttrs


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


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

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 KClDeltaf H S298

-436684.1 82.555

a b T c T^2 dT-2 Upper Temperature Limit Enthalpy change

50.47661 0.005924377 7.49668E-06 -144173.9 700 0

143.5698 -0.1680399 9.9657E-05 -8217836 1044 26283.9

73.59656 0 0 0 2000 0

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 = 26284-25.17624521*T+3.69441e-6*P• CSCL:G = 3207.841581-0.078831938*T-1.592096e-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

Thermodynamic data A tutorial course Session 1: Introduction and unary data (part 1) Alan Dinsdale...

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