NENG 301 Thermodynamics and Kinetics of Nanomaterials Prof. Y. Alex Xue CNSE, SUNY Polytechnic Institute office: CESTM B230C phone: 956-7220 e-mail: yxue@sunypoly.edu office hours: Monday 3 4 PM Course Website: http://www.albany.edu/~yx152122/neng301-17.html
From the course catalogue Applications of first, second, and third laws of thermodynamics to open and closed systems. Thermodynamics of multicomponent, multiphase chemical and biological systems are reviewed. Applies the concepts of reaction rate, stoichiometry and equilibrium to the analysis of materials systems. Rate expressions from reaction mechanisms and equilibrium or steady state assumptions are used. Design of reactions via synthesis of kinetics, transport phenomena, and mass and energy balances are covered. Introduction to diffusional processes. Prerequisite(s): satisfactory completion of MAT 260, NENG 120/122
What is Thermodynamics? Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, it doesn't bother you any more. -- Arnold Sommerfeld
Course learning objectives The overall learning objectives for this course are the following: The student will demonstrate understanding of the basic structure of thermodynamics, including state functions and process variables; extensive and intensive properties; and the First, Second and Third Laws of Thermodynamics The student will be able to develop, manipulate, and utilize relationships between thermodynamic variables and apply these relations to gases, liquids and solids The student will demonstrate understanding of how thermodynamic processes determine the equilibrium structures of materials at the macroscale, the microscale, and the nanoscale The student will learn how the kinetics of physical and chemical processes are dictated by thermodynamic driving forces The student will learn how to address important scientific and engineering problems by thermodynamic and kinetic analyses At the beginning of each book chapter covered I will provide you with a list of specific learning objectives for that chapter
Subjects to be covered Background Why Study Thermodynamics The Structure of Thermodynamics The Laws of Thermodynamics Thermodynamic Variables and Relations Equilibrium in Thermodynamic Systems Unary Heterogeneous Systems Multicomponent Homogeneous Non-reacting Systems Solutions Multicomponent Heterogeneous Systems Thermodynamics of Phase Diagrams Introduction to Kinetic Processes: Diffusion, Oxidation,
Textbook and other readings Textbook: R. DeHoff, Thermodynamics in Materials Science (Second Edition, CRC Press, Taylor & Francis Group, 2006) available at the University Bookstore Homework problems will be assigned from the textbook. Extra readings on kinetics will be provided: D.A. Porter and K.E. Easterling, Phase Transformations in Metals and Alloys Other readings may be distributed from time to time All non-textbook readings will be made available on the course web site
Homeworks (12) Homeworks, exams and grading Assigned each week Due on the following Thursday in class unless otherwise noted Check the homework due date in the course website NO LATE-SUBMISSION AND NO MAKE-UP homework There will be one midterm and one final written exams Grades will be based on the midterm exam (20%), final exam (20%), and homeworks (12 x 5%). By definition, do not ask for instructor help for homework!
Academic dishonesty Academic dishonesty refers to plagiarism, cheating, multiple submission, forgery, sabotage, falsification, unauthorized collaboration, and bribery Academic dishonesty will not be tolerated in this course Any incidence of academic dishonesty will result in an automatic failure of at least the assignment/exam if not the course and will be reported in writing to the CNSE Office for Student Services
Some comments on subject matter Classes on thermodynamics have a certain reputation for being difficult If you have never seen this stuff before, it can be somewhat challenging However, it is not rocket science or advanced quantum mechanics: thermodynamics and kinetics are founded in real-life experiences Also: thermodynamics and kinetics are important foundations for a wide variety of scientific and technical subjects If you are in nanotechnology, you will see this stuff for the rest of your career you must know this!!
NENG 301 Week 1 Basic concepts of thermodynamics (DeHoff, Chaps. 1-2) & mathematical preliminary 10
Learning objectives for Chapter 1 At the end of this chapter you will be able to: Understand the breadth of thermodynamics as an essential subject in science and engineering Understand the concept of equilibrium as it pertains to thermodynamics Understand the meaning of terms such as system, surroundings, boundary, and properties from a thermodynamics viewpoint Understand the concept of phase in a thermodynamics sense Understand the concept of a unary phase diagram and how it can be used to predict structure as a function of the state of a system Appreciate the concept of equilibrium maps as products of thermodynamic analyses 11
What is Thermodynamics? The study of energy transformations and the relationships among physical properties of substances which are affected by these transformations. -- K. Wark, Thermodynamics, 5th Edition (1988) Classical (phenomenological) thermodynamics Deals with macroscopic systems, without recourse to the nature of the individual particles and their interactions Requires no hypothesis about detailed structure of matter on the atomic scale, thus laws are not subject to change as knowledge concerning nature of matter is discovered Statistical thermodynamics Based on statistical behavior of large groups (ensembles) of individual particles, and postulates that values of macroscopic properties merely reflect some sort of statistical behavior of enormous ensembles Quantum thermodynamics: properties and interactions depend on the distribution of electrons and their energies 12
Why is the study of thermodynamics important? 1. Thermodynamics is pervasive 2. Thermodynamics is comprehensive 3. Thermodynamics is established 4. Thermodynamics provides the basis for organizing information about how matter behaves 5. Thermodynamics enables the generation of maps in equilibrium states that can be used to answer a prodigious range of questions of practical importance in science and industry 13
How is thermodynamics pervasive? Thermodynamics applies to every volume element of all systems at all times How is thermodynamics comprehensive? Systems: metals, ceramics polymers, composites, solids, liquids, gases, solutions, crystals with defects Applications: structural materials, electronic materials, corrosion-resistant materials, nuclear materials, biomaterials, nanomaterials Influences: thermal, mechanical, chemical, interfacial, electrical, magnetic 14
How is thermodynamics established? J. Willard Gibbs: On the Equilibrium of Heterogeneous Substances was a 300-page paper published between 1875 and 1878 You flip through the pages and it reads, more or less, like a modern physical chemistry textbook Just about everything that we are covering in this course can be traced to Gibbs A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts. (A. Einstein) 15
How does thermodynamics provide a basis for organizing information on how matter behaves? Thermodynamics provides a mechanism for describing the properties of scientifically and technologically important systems It allows you to take database information and apply it to an even wider collection of real-life problems A huge amount of information has been collected, is stored in databases, and is available for use 16
What do we mean by equilibrium Thermodynamic equilibrium a condition in which the thermal (temperature), mechanical (pressure), and chemical (concentration) characteristics do not change with time No net flows of matter, no phase changes, no unbalanced potentials (a.k.a. driving forces ) within a system Characteristics of a system at thermodynamic equilibrium no changes with respect to time: dx/dt = 0 when a system is in thermodynamic equilibrium it will not change when it is isolated from its surroundings? Note the distinction with steady state no changes with respect to time, but the system changes when it is isolated from its surroundings T high T low 17
Kinds of Equilibrium Equilibrium A system is in thermodynamic equilibrium if it is not capable of a finite spontaneous change to another state without a finite change in the state of the environment Thermal: equality of temperature across the system boundary Mechanical: equality of pressure across the system boundary Phase Equilibrium: no tendency for net transfer of one or more species from one phase to another Chemical: no tendency for chemical reaction 18
Some important (if obvious) concepts System: any region of the universe, large or small, that is being considered in our analysis Boundary: the interface between the system and its surroundings Surroundings: regions outside the boundaries of the system but can alter the system by interacting with it Properties: Physical characteristics that define the condition of the system and its surroundings 19
What is a phase (a really important concept) A phase is a physically distinctive form of matter, such as a solid, liquid, gas or plasma A phase of matter (a region of materials) is characterized by having relatively uniform chemical and physical properties Phases are separated from each other by a (usually) distinct boundary or interface A single phase may or may not have regions separated by surfaces or interfaces, but two phases are always separated by a surface or interface The phases that develop due to materials synthesis or processing can have a huge impact on the properties and/or performance of those materials 20
Unary phase diagrams These simple unary (single component) phase diagrams show the stability of a particular phase under different conditions (P and T) Water (left) can exist in at least three phases depending on temperature and pressure -- thermodynamics can predict behavior when conditions change Molybdenum (right, atomic number 42) shows qualitative behavior that is similar, but there are major quantitative differences 21
Equilibrium Map #1a: Phase Diagram (Ge/Si) Liquid (L) L+S Solid (S) 22
Equilibrium Map #1b: Phase Diagram (Al/Si) 23
Aluminum-rich side of the Al-Si phase diagram A simple binary eutectic with limited solubility of aluminum in silicon and limited solubility of silicon in aluminum. Eutectic point indicates The chemical composition and temperature corresponding to the lowest melting point Of the solid mixture. 24
Equilibrium Map #1c: Phase Diagram (Ag/Mg) 25
Exercise: multi-variable calculus 1. dz =? dx +? dy If 2..?
Learning objectives for Chapter 2 At the end of this chapter you will be able to: Understand the general statements of the laws of thermodynamics Understand the basic terminology of thermodynamics as presented and used in this chapter and be able to give examples of each: system, surroundings, state of a system, state function Understand the classification of thermodynamic systems into different categories Know the meaning of the terms heat and work from a thermodynamic perspective Understand the difference between exact and inexact differentials Understand the classification of thermodynamic relationships: the laws of thermodynamics; definitions; coefficient relationships; Maxwell relations; and conditions for equilibrium 27
General statements of the laws of thermodynamics as applied to the universe There exists a property of the universe, called its energy (U), which cannot change no matter what processes occur in the universe There exists a property of the universe, called its entropy (S), which can only change in one direction no matter what processes occur in the universe A universal absolute temperature scale exists and has a minimum value, defined to be absolute zero, and the entropy of all substances is the same at that temperature Don t worry for now: we will have a lot to say about these in Chapter 3 28
Again: important (if obvious) concepts System: any region of the universe, large or small, that is being considered in our analysis Boundary: the interface between the system and its surroundings Surroundings: regions outside the boundaries of the system but can alter the system by interacting with it Properties: Physical characteristics that define the condition of the system and its surroundings 29
This is a system. The subset of the universe in focus in a particular application of thermodynamics is usually called the system At any given instant of observation the condition of the system is described by an appropriate set of properties Limitations on changes in these properties are set by the nature of its boundary 30
System, surrounding, boundary and universe
This is a system that goes through a process The subset of the universe in focus in a particular application of thermodynamics is usually called the system At any given instant of observation the condition of the system is described by an appropriate set of properties Limitations on changes in these properties are set by the nature of its boundary 32
Classification of systems Thermodynamic systems can be classified into several categories: 1. unary (one chemical component) versus multicomponent (two or more chemical components in multicomponent systems, the chemical composition may vary 2. homogeneous (single phase) versus heterogeneous (two or more phases, eg. ice/water) 3. closed (no exchange of matter by the system across its boundary with the surroundings) versus open (exchange of matter by the system with the surroundings) [notealso: isolated] 4. non-reacting versus reacting (specifically chemical reactions) 5. simple versus complex o simple: only energy exchanges involve thermal, mechanical or chemical changes o complex: gravitational, electrical, magnetic or surface factors 33
A typical thermodynamic system Cross-section through a MOSFET (metal oxide semiconductor field effect transistor) thin film device shows it to be a multicomponent, multiphase system in which chemical reactions and the influence of an electric field are important 34
State Functions State functions (or state variables): a system is said to be in a certain state when all of its properties have these specific values depend on the current condition of the system and not on how the system got there temperature pressure volume chemical composition (internal) energy entropy others. 35
Still more definitions Process: processes are described by quantities that only have meaning for changing systems Consider a transition from state A to state B: represented by a curved path in the X-Y plane The change in Z (or DZ) is independent of the path There are two very important types of processes: work done on the system as it changes heat absorbed by the system as it changes 36
What is Thermodynamics? The study of energy transformations and the relationships among physical properties of substances which are affected by these transformations. -- K. Wark, Thermodynamics, 5th Edition (1988) Thermodynamics is mainly concerned with transformations of heat into mechanical work and the opposite transformations of mechanical work into heat. -- E. Fermi, Thermodynamics (1937) 37
The easiest way to discuss work is through classical mechanics Consider the application of a force F: if the point of application of the force moves, then the force does work The increment of work done by the displacement is: w F dx F=P ext A w P A dx P dv ext ext Work 38
Work Work, like energy, can take various forms: mechanical, electrical, gravitational, etc. All have in common the fact that they are the product of two factors, an intensity term and a capacity term. the simplest form of mechanical work arises when an object moves a certain distance against an opposing force. example: electrical work is done when a body having a certain charge moves through a potential difference Type of work intensity factor capacity factor formula mechanical force change in distance f Δx gravitational gravitational potential (a function of height) mass mgh electrical potential difference quantity of charge QΔV surface surface energy/tension change in area g DA 39
Heat Heat and work are both measured in energy units, so they must both represent energy Energy can take many forms: mechanical, chemical, electrical, radiation (light), and thermal, or heat Heat is a form of energy, but it differs from all the others in one crucial way: complete conversion of heat into other forms of energy is impossible Thermal energy can be transferred from one body (i.e., one system) to another (we often refer to this as a "flow" of heat) Heat can only flow spontaneously from a system at a higher temperature to one at a lower temperature 40
Heat and Work Consider a gas in a cylinder that is subjected it to two processes: compress from P i, V i to P f, V f heat from T i to T f Mass Piston Mass Piston P i, V i T i T f P f, V f mechanical stops
Exact and inexact differentials An ordinary (exact) differential, when integrated, yields a finite difference given by the limits of integration: x x 1 2 dx x x Dx 2 1 In other words: an exact differential integrates to a finite difference, independent of the path of the integration In contrast, an inexact differential integrates to a total quantity which depends on the path of integration taken: 2 Q Q 1 The cyclic integration of an exact differential is exactly zero for all cycles, while the cyclic integral of an inexact differential is usually non-zero: dy 0 (all cycles) Q 0 exact inexact 42
Exact and inexact differentials Quantities of heat Q and work W are path dependent and hence depend on the path taken by a given process The terms DQ and DW in this case are meaningless If DW meant anything it would mean W 2 - W 1 The system in either the initial state or the final state does not have any work W 1 or W 2, nor does it have any heat Q 1 or Q 2 Work and heat appear during a change in state; they are not properties of the state, but instead are properties of the path Properties of the state of the system (T, P, V, U) have differentials which are exact, while differentials of properties of the path (Q and W) are inexact 43
Peculiarities of heat, work and energy Heat and work both appear at the boundary of a system Work can be completely converted into heat (by friction, for example), but heat can only be partially converted to work conversion of heat into work is accomplished by a heat engine Heat and work are best thought of as processes by which energy is exchanged Energy is measured in terms of its ability to perform work or to transfer heat The basic unit of energy is the joule one joule is the amount of work done when a force of 1 newton acts over a distance of 1 m; thus 1 J = 1 N-m The newton is the amount of force required to accelerate a 1-kg mass by 1 m/sec 2, so the dimensions of the joule are kg m 2 s 2 The other two units in wide use: the calorie and the BTU (British thermal unit) are defined in terms of the heating effect on water 44
Mathematical Preliminary: multi-variable calculus Partial Derivative Total Differential
Mathematical Preliminary: multi-variable calculus Total Derivative along a particular path y(x) in the x-y plane:
Mathematical Preliminary: multi-variable calculus Path-independent integral for state functions: z = z(x,y) Total Differential: a differential that yields a path-independent integral Conditions for Total Differential
Mathematical Preliminary: multi-variable calculus If dz = xdx + ydy, is dz exact? If so, what is z = z(x,y)?
Mathematical Preliminary: multi-variable calculus If dz = xdx + ydy, is dz exact? If so, what is z = z(x,y)?
Simple Exercise If Z is a state function that depends on other state functions X and Y, Z = Z (X,Y), show: ( 50
The Zeroth Law of Thermodynamics Equilibrium is characterized by a function of thermodynamic state variables. This function specifies the equation of state. 51
Classification of relationships Just wait and see: you will become familiar with a large number of thermodynamic relationships! In order to sort through the coming confusion it will be useful to classify these relationships 1. Laws of thermodynamics these form the physical basis for all subsequent relationships There exists a property of the universe, called its energy (U), which cannot change no matter what processes occur in the universe There exists a property of the universe, called its entropy (S), which can only change in one direction no matter what processes occur in the universe A universal absolute temperature scale exists and has a minimum value, defined to be absolute zero, and the entropy of all substances is the same at that temperature 52
Classification of relationships 2. Definitions new parameters, quantities and variables based on prior ones Energy: U = U(S,V) du = T ds P dv Enthalpy: H = U + PV dh = T ds + V dp Helmholtz free energy: F = U TS df = S dt P dv Gibbs free energy: G = U + PV TS = H - TS dg = S dt + V dp 3. Coefficient relationships describe how the value of state variable changes during an infinitesimal step in a process: dz MdX NdY X, Y, Z are all Z Z dx dy state variables X Y Y X 53
Coefficient relationships between state functions If Z is a state function that depends on other state functions X and Y, then we can related a change in Z with respect to X and Y: dz MdX NdY Z Z dx dy X Y Y If Z = f(x,y) represents a surface in (X,Y,Z) space, then dz is the sum of the components in the X and Y directions X 54
Coefficient relationships between state functions apply to an ideal gas Z Z dz MdX NdY dx dy X Y Y X Consider a mole of an ideal gas: PV = RT or V = f(p,t) Express V as a function of T and P: RT 1 V R( T ) P P Determine the partial derivatives: V RT ; V R 2 P T P T P P So the final relationship for dv is: RT R dv dp dt 2 P P 55
Classification of relationships (con t) 4. Maxwell relationships provide descriptions of partial derivatives involving state functions M N dz MdX NdY Y X X Where did this come from? Go back to: Z Z M and N X Y Y X Now take the derivatives: M Z N Z Y X Y X and Y X X Y X Y X Since the order of differentiation doesn t matter: M Z Z N Y Y X X Y X 56 X Y X X Y Y Y Y
Classification of relationships (con t) As stated previously: Maxwell relationships provide descriptions of partial derivatives involving state functions Some are entirely unimportant, while others are extremely important, for example: S V dg SdT VdP P T the isothermal pressure dependence of entropy is given by the easily-measured thermal expansion 5. Conditions for equilibrium sets of equations that describe the relations between state functions that must exist when a system is at equilibrium; these are the relationships that are used to calculate equilibrium maps We ll have a lot of these! T P 57
More definitions equations of state or state functions: relationships between dependent variables of state and independent variables of state intensive property: a property that is independent of the quantity of matter in a system (temperature, pressure, concentration, etc.) extensive property: a property that is dependent of the quantity of matter in a system (volume, heat capacity) Note that we can derive intensive properties from extensive properties (example: mole fraction) 58
Chapter 2 So what have we learned? We have three laws of thermodynamics: energy is conserved entropy is created temperature has a zero We can classify thermodynamic systems into categories: number of components number of phases nature of the system boundary chemical reactivity complexity with respect to non-mechanical forces Thermodynamic relations can be classified as well: the laws of thermodynamics definitions coefficient relationships Maxwell relations conditions for equilibrium 59
Homework 1 2.5. Write the total differential of the function a. Identify the coefficients of the three differentials in this expression as appropriate partial derivatives. b. Show that three Maxwell relations hold among these coefficients. 60