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3.012 Fundamentals of Materials Science Fall 2003

Lecture 1: 09.08.03 Introduction to fundamental concepts

Today:

THERMODYNAMICS AS A BASIC TOOL FOR MATERIALS SCIENCE & ENGINEERING...............................................2Energy and entropy..............................................................................................................................................................................2

WHAT IS THERMODYNAMICS?..............................................................................................................................3Changes of state and equilibrium........................................................................................................................................................3Defining our mission............................................................................................................................................................................7

References............................................................................................................................................................9

Reading: Bent, The Second Law, pp. 1-5

Supplementary Reading: -

PLANNING NOTES:

Need shorter first lecture – we’ll have to do course admin stuff on first day

Lecture 1 – introduction 1 of 9 5/8/23


Thermodynamics as a basic tool for materials science & engineering

Energy and entropy

Materials scientists seek to tune the structure and synthesize materials with properties that provide optimum performance in every type of materials application – the structure-properties-performance triangle

propertiesstructure

performance

In order to design materials with optimum performance in various applications, we need to know how properties change in response to their environment

o These responses determine how we can synthesize/fabricate materials, build devices from materials, and how the devices will operate in a given application:

Raw materials –(synthesis, processing, fabrication)-> final devices Materials are exposed to a variety of forces (mechanical, chemical, electrical, magnetic, etc.)

during synthesis, processing, and in their final applications

Heat Electrostatic potentialMechanical stress concentration gradientsChemical reaction intermolecular forcesElectric fields surface forcesMagnetic fields etc.

synthesisprocessing

application



What is thermodynamics?

2 points of view

Thermodynamics provides the theory to understand how materials respond to all types of forces in their environment- including some forces you may have not thought about or recognized as ‘forces’. We will introduce two different points of view during this term:

Classical thermodynamics

Classical Thermodynamics (or what most people just call thermodynamics) is the theoretical framework via which we can understand and predict how materials will tend to change internally in response to forces of many types on a macroscopic level.

Statistical mechanics

Statistical mechanics (or statistical thermodynamics) is the calculation of thermodynamic properties starting from molecular models of materials- either simple lattice models or quantum mechanical models.

Why 2 approaches?o Useful in different applications

Changes of state and equilibrium

A sentence of new concepts

Thermodynamics is concerned with describing how internal energy, entropy, and free energy dictate changes in a materials’ state at equilibrium.

o …ok, so what do each of these terms mean? Let’s proceed in (mostly) reverse order:

o State A unique set of values for the variables that describe a material and the forces to which it is

exposed. For example:

o Volume (V)o Pressure (P)o Number of molecules (N)o …and more that we will begin to describe in the coming lectures

The molecules in materials heat up, react, rearrange, change shape, form and break bonds with one another, and undergo myriad other changes in response to changes in their environment.



The changes in macroscopic properties that occur due to these internal molecular interactions are changes in the state of the material.

State AMaterial

Thermodynamic forces

PressureTemperatureMagnetic fieldsLight(more later)

State B State C State D

(V0, N0)

(V < V0, N0) (V > V0, N0) ( V0, N > N0)

Let’s continue to define the italicized terms, as a brief introduction to the concepts we will focus on for much of the term:

Equilibrium

Equilibrium is defined as a state from which the material has no tendency to undergo a change. Analogy to potential energy: a ball rolling on hills and valleys:

V(x)

x

(1)

(2)

(3)

(4)

(1) Unstable state - system is actively tending toward a new equlibrium state(2) Metastable equilibrium state - system can change to a lower total energy state(3) Unstable equilibrium state - any perturbation will cause the material to change to a new equilibrium state(4) Stable equilibrium state - material does not change its state in response to small perturbations

We will return to define the different types of equilibrium states in mathematical terms later in the term. In physics, you learn that stable equilibrium is achieved when the potential energy is at its lowest level- when the

potential energy is minimized. Similar minimization laws will come into play in reaching internal equilibrium in materials.

Internal energy (U)



Internal energy is a quantity which measures the capacity to induce a change which would not otherwise occur.

In freshman physics you learned:o Total energy E = V + KEo Potential energy + kinetic energyo this leaves out changes which occur internally in a material

Total energy E = U + V + KE Typically in thermodynamics we are calculating internal changes in the absence of external bulk

motion, so we focus on U and assume V = KE = 0o How do these energies relate to the bonding ‘energies’ you learned about in freshman chemistry?

Internal energy in a material is ‘stored energy’- energy is transferred to a material via all the possible forces that act on it- pressures, thermal energy, chemical energy, magnetic energy, etc.

Entropy (S)

Entropy is a non-intuitive but absolutely critical parameter of materials- along with the more common extensive parameters like volume and number of molecules. We will introduce a rigorous thermodynamic definition for entropy in the coming lectures, but let’s start with a physical interpretation of entropy to aid in our grasp of what entropy is:

If I drop a crystal of table salt (NaCl) into a beaker of pure water, the salt will dissolve quite rapidly. This is common knowledge, but why should it happen?

o STRENGTH OF BONDS IN NACL, STRENGTH OF BONDS BETWEEN WATER AND NACL – SHOW BOND ENERGY IS WEAKER BETWEEN WATER AND IONS THAN BETWEEN IONS IN THE CRYSTAL

Dissolution of a salt crystal

It is equally common experience that once dissolved, the salt crystal will never spontaneously re-form- even though the bonding energy between ions in the crystal would be quite strong.

So what drives the dissolution and non-resolidification of this crystal in water? The answer is that dissolution increases the entropy of the system, while resolidification would decrease the entropy. Entropy on a microscopic scale is a measure of randomness or disorder in a system, and one of the fundamental axioms (the second law) of thermodynamics is that the entropy of the universe always increases in spontaneous processes. When table salt dissolves, the entropy of the system (salt + water) significantly increases, as the ions go from a highly ordered state in the crystal to the highly disordered state in solution. In contrast, re-formation of the crystal would decrease the entropy of the system and so it is extremely unlikely to happen.



There are many cases when the increase in entropy occurring for a given process is not obvious, but for any spontaneous process ever analyzed, entropy increases have been found.

A puzzle: can I minimize energy and conserve energy at the same time? Consider this example:o You drop a rubber ball from your hand, and it falls, bounces off the floor a few times, then lies still. You

could repeat this many times- the ball might not always bounce the same way, but it would always fall toward the ground and end lying on the ground. On the other hand, you have probably never seen a rubber ball begin spontaneously bouncing and jump into your hand. Why not?1 You may answer that the ball is minimizing its potential energy. But the ball started with a higher potential energy than it has at the end of this process- where did that energy go, if energy is conserved? And if the energy can flow out of the ball to bring it to rest on the floor, why can’t it flow the opposite direction and cause the resting ball to jump back into your hand?

o Energy is lost from the ball in the form of thermal energy- friction and perhaps sound waves as the ball moves through the air. This transfer of energy increases the microscopic disorder in the ball’s surroundings (down at the atomic/molecular level!- thermal energy increases the random motion of molecules), thus increasing the entropy of the universe. In order for the ball to jump back into your hand, the reverse process would have to occur- thermal energy from the floor and air would have to spontaneously accumulate and pass into the ball. This would reduce the random ‘thermal motion’ of the surroundings and decrease the total entropy of the universe. Such a process has never been observed to happen.

Returning to the example of the salt crystal, on a molecular level, once the atoms are released from the crystal, their thermal energy will scramble them thoroughly (and randomly) through the solution- and because this thermally-driven process is random, it extremely unlikely that it will ever randomly reverse. Finding the balance between energies (like bonding between molecules, or forces induced by an electric field) and entropy (random thermally-induced disorder) is what defines equilibrium states. Thermal energy drives materials to randomize- vibrating molecules, rotating molecules, and mixing molecules, while other types of energy have non-random effects (e.g. positively charged molecules are pulled directionally toward negative charges in an electrostatic potential). We will discuss the microscopic description of entropy in more detail when we introduce statistical mechanics in the second portion of the term.

Free energy

As described above, the internal energy and entropy are two functions whose behavior in a material in spontaneous processes is dictated by the laws of thermodynamics. Free energies may be thought of as thermodynamic functions that include both the internal energy and entropy and help define the conditions for equilibrium under common laboratory conditions. Their important role in thermodynamic calculations will be clear later in the term.

So what’s fundamental about it?

Thermodynamics has many practical uses. It provides the theory to answer the following sorts of practical materials questions:2

o Is it possible to make such-and-such a material and, if so, what processing variables make it possible?o If I have a given material and I put it in service in a particular environment, will it remain that way?o What are the limiting properties of such a material? What is the maximum response?o What processes make the material unstable?o How do I formulate a prediction for how a material will change in time?

Thermodynamics in Materials Science

Thermodynamics explains many phenomena in the natural world:o Why does heat flow from ‘hot’ objects to ‘cold’ objects?



o Why do some chemical reactions occur, while others do not?o How is heat related to mechanical work and other forms of work?

…and it continues to be a fundamental part of new materials discoveries.

Thermodynamics in Materials Engineering

The interpretation of a material’s response to the forces in its environment is the basis of many many many technologies. Some examples:

Thermodynamic Driving Force: Technology Based Upon It:

Heat engines of all typesElectrostatic potential batteriesMechanical stressconcentration gradientsChemical reactionsintermolecular forcesElectric fieldssurface forcesMagnetic fields

Defining our mission

The connection between energies, entropy, and equilibriumo Our goal for the term is to learn how energy, entropy and free energy dictate the state of materials

Thermodynamics provides 4 laws that contain all the necessary rules for predicting the equilibrium state of materials. Much of the term will be devoted in fact to understanding the most important of these- the second law, which dictates how the entropy must change in a spontaneous process.

o As a preview, these 4 laws of thermodynamics can be summarized as follows: zeroth: two systems in thermal contact that are in thermal equilibrium with a third system are in

thermal equilibrium with one another . first: the sum of the heat transfer and work done on a system provide the change in internal

energy to a system. second: the entropy of the universe always increases in a spontaneous process. third: the entropy of a system at absolute zero temperature is zero.

o the laws have not been proven, only never disproveno The laws provide a description of how the universe works, not an explanation.o perhaps the most important (and useful) concept we will teach this term is the use of the second law: the

second law dictates how materials respond to their environment. We will see that the second law ‘translates’ into rules governing equilibrium. These rules depend

on the conditions of the system (are we at constant temperature and pressure? Or constant temperature and volume?), but are of the form:

At equilibrium, entropy is maximized



o Or At equilibrium, internal energy is minimized

o Or At equilibrium, free energy is minimized

These rules are part of the real power behind thermodynamics- they allow us to predict how a material will alter its state if exposed to a given set of conditions.

A closing word about complicated phrasing

From http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heat.html:

"Teaching thermodynamicsIs as easy as a song:

You think you make it simplerWhen you make it slightly wrong.

Zemanzky's plea

You’ll notice that we have already used some involved phrases defining ideas in this first lecture (‘behavior in a material in a spontaneous process…’). This is because thermodynamics depends on very careful definitions and descriptions of the conditions under which laws should be applied. If at any point any of these phrases are not clear to you, ask for an explanation! These concepts are not simple, but they are important tools for your future as a materials scientist/engineer.



References

1. Bent, H. A. The Second Law (Oxford University Press, New York, 1965).2. Carter, W. C. (2002).


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