Summer School for Integrated Computational Materials Education 2018 Thermodynamics Module Q&A

Thermodynamic Properties CALPHAD Methodology Fundamental Theory Empirical Rules Experimental Data Models Experimental Determination Ab Initio Calculation Parameter Optimization Database Thermodynamic Properties Equilibrium States Phase Diagrams

Thermodynamic Modeling Gibbs energy per mole for a solution phase is normally divided in: excess term reference surface physical contribution configurational contribution Ideal solution model Regular solution model Real solution

Different Models (Binary) Ideal solution Regular solution Real solution Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

Q1. Which model to use? For teaching, simple models are sufficient and instructive Ideal solution term has a single well Preferred interactions between the same species penalizes mixing Single phase to two phase transition For scientific & engineering predications, accurate models & parameters are required Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

Q2. How is extrapolation done There are many parameters that comes with the models As the number of components increases, so does the number of parameters Fits to experimental data sets the parameters, but the range is limited Interpolation if within the range; extrapolation if outside Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

Q3. How can the concentration be different if the chemical potential is the same? Q4. Phase diagrams/minimum free energy

Phase Stability: Common Tangent Const.  +  Thermodynamics in Materials Engineering - R.E. Napolitano

Chemical Equilibrium When chemical potential of each species is constant throughout, the system is in chemical equilibrium In single phase material, the chemical potential is constant when the concentration of all species are constant. When multiple phases are present, the equilibrium concentration must be constant in each phase, but they can be different from one phase to another so that the chemical potential of each species are constant. Thornton

Phase Stability: Common Tangent Const.  +  Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G   T  XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G   T  XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G   T XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G   T XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G   T XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G   T XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G  T  XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G   T  XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G  T  XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G  T  XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Phase Stability: Const. of Phase Diagram GA vs T GB vs T G   T   XB Thornton MSE 454 F15 Used with permission Thermodynamics in Materials Engineering - R.E. Napolitano

Double-Well Free Energy Case Ag-Cu system: Free energy & phase diagram Thornton MSE454 F16

Q5. Isopleth Q6. Multicomponent system

Isotherm & Isopleth Ternary phase diagram is actually 3D To plot on paper quantitatively, you need to cut in some direction Isotherm (T=constant) Isopleth (one composition = constant) Figure by Elmer Prenzlow http://129.89.58.197/mediawiki/index.php/File:Ternary_Cooling.JPG Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

Systems with more than 3 components In order to visualize, additional concentration must be fixed If there is a component that has low solubility, they precipitate out (so fix it at the solubility limit) Multiple sections are needed to fully represent the phase diagram Isothermal sections are also made along constant concentration (isopleth) Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018

Drawing common tangent electronically My students typically use power point to do this. Summer School for Integrated Computational Materials Education Ann Arbor, MI June 4-15, 2018