mse 3050: thermodynamics and kinetics of materials

MSE 3050, Thermodynamics and Kinetics of Materials, Leonid Zhigilei

Instructor: Leonid ZhigileiOffice: Wilsdorf Hall 303DOffice Hours: 11:00 am to noon Wednesday & openTelephone: (434) 243 3582E-mail: [email protected]

Assistance with online sessions: Michael RedwineE-mail: [email protected]

Class web page:http://www.people.virginia.edu/~lz2n/mse305/

Class e-mail list: [email protected]

Contact Information:

Tuesday and Thursday, 9:30 – 10:45 amMechanical Engineering Building 341

MSE 3050: Thermodynamics and Kinetics of Materials


Research in Computational Materials Group:

impact resistance of carbon nanotube materials

nanofibrous and nanocrystalline materials

Group Web Site: http://faculty.virginia.edu/CompMat/

laser ablation

Development of computational methods for materials modeling atmultiple length & time-scales

Investigation of non-equilibrium materials processing, properties ofnanostructured materials, mechanisms of phase transformations

acoustic activation of surface processes:

acoustic pulse


Name:

E-mail:

Major:

Minor (if any):

Are you involved in a research project? If so, what is the topic? Who is your research adviser?

What is your objective for taking mse3050? What do you hope to learn from this course?

Have you had any course(s) on thermodynamics?

Have you taken mse2090? Any other MSE courses?

What computer language(s) do you know? Do you know how to write, compile, and run a code that does simple calculations and writes data to a file?

MSE 3050: Thermodynamics and Kinetics of Materials Questionnaire


Homework 30% Mid-Term tests 30% The final exam: 40%

Homework will be due at the beginning of class onthe due date. Homework solutions should be neat andstapled. Late homework is not accepted.

Discussions among students through the class e-maillist are permitted/encouraged at the conceptual level,but comparing the results and discussing/copyingsolutions is not allowed.

Mid-term tests and the final exam: pledged, closed-book and closed-notes

Grading:


Main (optional) text: D. A. Porter and K. E. Easterling,Phase Transformations in Metals and Alloys, 2nd edition,Chapman & Hall, London, UK, 1992 (TN690 .P597)

(reserve circulate at Science and Engineering Library).

can be bought at www.crcpress.com or www.amazon.com

Reprinted by CRC Press in 2003 & 2009 (3rd edition),but, aparently, with many typos and errors…Revised reprint of the 3rd edition fixes some of the errors

Lecture notes will appear at the class web page(http://www.people.virginia.edu/~lz2n/mse305) as courseprogresses.

Optional textbooks (placed on reserve circulate):

D. R. Gaskell, Introduction to the Thermodynamics of Materials, New York: Taylor & Francis, 1995, 2003, 2008, 2017 editions.

can be bought at www.amazon.com

Textbooks:


1. Review of classical thermodynamics needed forunderstanding of phase diagrams.

2. Application of the thermodynamic concepts to theanalysis of phase equilibria, phase transformations,and phase diagrams in one-component and multi-component systems.

3. Basic concepts of kinetic phenomena in materials.Mechanisms of diffusion in materials, analyticaland numerical methods to describe diffusion.Kinetics of phase transformations. Effect ofkinetics on microstructure.

Syllabus:

thermodynamic driving forces+

kinetics of mass and heat transfer=

complex microstructure of real materials


MSE 3050: Thermodynamics – Phase Diagrams – Kinetics

Review of classical thermodynamics

First Law - Energy Balanceo Thermodynamic functions of stateo Internal energy, heat and worko Types of paths (isobaric, isochoric, isothermal, adiabatic)o Enthalpy, heat capacity, heat of formation, phase

transformationso Calculation of enthalpy as a function of temperatureo Heats of reactions and the Hess’s law

Theoretical calculation of the heat capacity o Principle of equipartition of energyo Heat capacity of ideal and real gaseso Heat capacity of solids: Dulong-Petit, Einstein, Debye modelso Heat capacity of metals – electronic contribution

Entropy and the Second Law o Concept of equilibriumo Reversible and irreversible processeso The direction of spontaneous changeo Entropy and spontaneous/irreversible processeso Calculation of entropy in isochoric and isobaric processeso Calculation of entropy in reversible and irreversible processes



The Statistical Interpretation of Entropyo Physical meaning of entropyo Microstates and macrostateso Statistical interpretation of entropy and Boltzmann equationo Configurational entropy and thermal entropyo Calculation of the equilibrium vacancy concentration

Fundamental equationso The Helmholtz Free Energyo The Gibbs Free energyo Changes in compositiono Chemical potentialo Thermodynamic relations and Maxwell equations

Phase Transitions and Phase Diagrams

One-component systemso Enthalpy and entropy dependence on P and To Gibbs free energy dependence on P and To Clapeyron equationo Understanding phase diagrams for one-component systemso Polymorphic phase transitionso Driving force for a phase transitiono First order and second-order phase transitions



Introduction to Solution Thermodynamics

o Ideal solution: Entropy of formation and Gibbs free energyo Chemical potential of an ideal solutiono Regular solutions: Heat of formation of a solutiono Activity of a componento Real solutions: interstitial solid solutions, ordered phases,

intermediate phases, compoundso Equilibrium in heterogeneous systems

Binary phase diagrams

o Binary phase diagrams and Gibbs free energy curveso Binary solutions with unlimited solubilityo Relative proportion of phases (tie lines and the lever principle)o Development of microstructure in isomorphous alloyso Binary eutectic systems (limited solid solubility)o Solid state reactions (eutectoid, peritectoid reactions)o Binary systems with intermediate phases/compoundso The iron-carbon system (steel and cast iron)o Gibbs phase ruleo Temperature dependence of solubilityo Multi-component (ternary) phase diagrams



Diffusion in solids - phenomenological description

o Driving force for diffusion in ideal solutionso Flux, steady-state diffusion, Fick’s first lawo Diffusion coefficient, Einstein relationo Nonsteady-state diffusion, Fick’s second law

Thermodynamics of diffusion

o Driving force for diffusion revisitedo Diffusion in ideal and real solutionso Thermodynamic factoro Diffusion against the concentration gradiento Spinodal decomposition

Solutions to the diffusion equation

o Numerical integrationo Analytical solutiono Applications

Chemical homogenization Carburization of steel

Kinetics

Basic concepts in kinetics

o Kinetics of phase transformationso Activation free energy barriero Arrhenius rate equation



Atomic mechanisms of diffusion

o Substitutional diffusiono Interstitial diffusiono Temperature dependenceo High diffusivity paths (grain boundaries, surfaces,

dislocations)

Kinetics of phase transformations

o Supercooling and superheatingo Driving force for phase transformationo Homogeneous nucleationo Critical radius, nucleation rateo Heterogeneous nucleationo Nucleation in melting and boilingo Growth mechanismso Rate of phase transformationso Solidification and growth morphologieso Kinetics of solid-state transformations


Application of thermodynamics and kinetics to materials

Component - chemically recognizable species (Fe and C incarbon steel, H2O and Sucrose in sugar solution in water). Abinary alloy contains two components, a ternary alloy - three, etc.

Materials consist of phases or mixtures of phases. A phase is aportion of a system that has uniform properties and composition.The phase may or may not be in an equilibrium state.

Two distinct phases in a system have distinct chemical orphysical characteristics (e.g. liquid water and ice) and areseparated from each other by definite phase boundaries. A phasemay contain one or more components.

A single-phase system is called homogeneous, systems with twoor more phases are mixtures or heterogeneous systems.

Equilibrium – the state in which the system parameters nolonger evolve (there are no fluxes of matter or energy, smalldisturbances decay, …).

The phases that are not in equilibrium can undergo aspontaneous phase transformation to an equilibrium phase ormixture of phases.

Definitions: Components and Phases



Thermodynamics can be used to predict weather the system isin equilibrium and to analyze the phase stability and phasetransformations.

Questions thermodynamics can answer: Is a particular processpossible? Is a spontaneous evolution in a particular directionpossible? What is the final/equilibrium state of the system?

Thermodynamics of phase stability and phase transitions

Equilibrium is the state that is achieved given sufficient time.But the time to achieve equilibrium may be very long (thekinetics can be slow) and a state along the path to the equilibriummay appear to be stable. This is called a metastable state.

In thermodynamics, the equilibrium is described as a state of asystem that corresponds to the minimum of thermodynamicfunction called the free energy. Thermodynamics tells us that:

• Under conditions of a constant T, P, and composition, thedirection of any spontaneous change is toward a lower Gibbsfree energy.

• The state of stable thermodynamicequilibrium is the one withminimum free energy.

• A system at a metastable state istrapped in a local minimum of free

energy that is not the global one. metastable

equilibrium

Fre

e E

nerg

y

Arrangement of atoms


Fre

e E

nerg

y

Structure (arrangement of atoms)


A phase diagram is a graphical representation of all theequilibrium phases as a function of temperature, pressure, andcomposition.

Phase diagrams can be predicted (calculated) throughanalysis of free energies of phase and their mixtures. They canbe used to describe gas - liquid - solid transitions, polymorphicsolid-to-solid transitions, stable phases in alloys of differentcomposition, etc.

Application of thermodynamics and kinetics to materialsPhase diagrams

Pressure-temperature phase diagram for H2O:



Phase diagrams do not predict all the possible structures

Pressure-temperature phase diagram for carbon:

We can see graphite, diamond, liquid carbon on the phasediagram… but where are fullerenes and nanotubes?


Example of a binary phase diagram: steel iron–iron carbide (Fe–Fe3C)

In their simplest form, steels are alloys of Iron (Fe) and Carbon(C). The Fe-C phase diagram is a fairly complex one, here weare only looking at the steel part of the diagram, up to ~7 wt.%Carbon.


Fe3CFe

-Fe + Fe3C

-Fe

-Fe

-Fe + Fe3C

L +

C (graphite)

L

-Fe + L


Another example: phase diagram for chocolate and vanilla

Credit: Kenneth A. Jackson, University of Arizona.



Example of ternary phase diagram: oil – water – surfactant system

Surfactants are surface-active molecules that can form interfacesbetween immiscible fluids (such as oil and water). A largenumber of structurally different phases can be formed, such asdroplet, rod-like, and bicontinuous microemulsions, along withhexagonal, lamellar, and cubic liquid crystalline phases. Ternaryphase diagram shows compositional ranges for different phases.


Drawing by Carlos Co, University of Cincinnati



Crossing a boundary on a phase diagram does not result in an immediate phase transformation

We have to consider how the non-equilibrium (but metastable)phase transforms to the equilibrium one → kinetics



Thermodynamics can be used to predict the equilibrium phasesfor different conditions as well as the phase transformations thatcan occur.

“When or how fast does a phase transformation occur?” is not aright question for classical thermodynamics.

Thermodynamics tells us what should happen - not how fast itwill happen . “How fast?” is the question addressed by kinetics.

Most kinetic phenomena in materials involve diffusion.Therefore we will consider mechanisms of diffusion in materialsbefore discussing kinetics of the nucleation and growth of a newphase.

Kinetics

AtomVacancyEm

Distance

Ene

rgy

Tk

Eexp~τ1rate

B

m


Analysis of both the equilibrium phase diagrams and the kineticsof phase transformations will help us to understand and predictcomplex microstructures like the one shown below

Microstructure of cast Iron

The long gray regions are flakes of graphite.

The matrix is a fine mixture of BCC Fe and Fe3C compound.


http://www2.umist.ac.uk/material/research/intmic/


Formation of eutectic layered microstructure in the lead-tinsystem during solidification at the eutectic composition.Compositions of and phases are very different solidification involves redistribution of Pb and Sn atoms byatomic diffusion.

In the micrograph, the dark layers are lead-reach phase, the light

layers are the tin-reach phase.


Compositions of and phases are defined bythermodynamics and can be determined from the phasediagram, the size and arrangement of the layers in themicrostructure is defined by the kinetics of solidification.



Analysis of phase diagrams for brass helps to understand theconnections between the evolution of the brass productionmethods and changes in composition of brass pipes used inhistorical organs. It is also essential for conservation andcorrosion prevention in old organ pipes.

Baroque-style organ reconstructed in Örgryte Nya Kyrka, Gothenburg, Sweden

MRS Bulletin Vol 32, March 2007, 249-255

MRS Bulletin Vol 42, Jan. 2017, 55-60



Buffett, Nature 473, 292, 2011Gubbins et al., Nature 473, 361, 2011

T. Duffy, Nature 506, 427, 2014

mse 3050: thermodynamics and kinetics of materials

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