Introduction to the Arrhenius Relationship

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Do curso por University of California, Davis

Materials Science: 10 Things Every Engineer Should Know

909 classificações

University of California, Davis

Materials Science: 10 Things Every Engineer Should Know

909 classificações

We explore “10 things” that range from the menu of materials available to engineers in their profession to the many mechanical and electrical properties of materials important to their use in various engineering fields. We also discuss the principles behind the manufacturing of those materials. By the end of the course, you will be able to: * Recognize the important aspects of the materials used in modern engineering applications, * Explain the underlying principle of materials science: “structure leads to properties,” * Identify the role of thermally activated processes in many of these important “things” – as illustrated by the Arrhenius relationship. * Relate each of these topics to issues that have arisen (or potentially could arise) in your life and work. If you would like to explore the topic in more depth you may purchase Dr. Shackelford's Textbook: J.F. Shackelford, Introduction to Materials Science for Engineers, Eighth Edition, Pearson Prentice-Hall, Upper Saddle River, NJ, 2015

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Course Overview / The Menu of Materials / Point Defects Explain Solid State Diffusion

Welcome to week 1! In lesson one, you will learn to recognize the six categories of engineering materials through examples from everyday life, and we’ll discuss how the structure of those materials leads to their properties. Lesson two explores how point defects explain solid state diffusion. We will illustrate crystallography – the atomic-scale arrangement of atoms that we can see with the electron microscope. We will also describe the Arrhenius Relationship, and apply it to the number of vacancies in a crystal. We’ll finish by discussing how point defects facilitate solid state diffusion, and applying the Arrhenius Relationship to solid state diffusion.

Crystallography and the Electron Microscope6:39

Introduction to the Arrhenius Relationship5:33

The Arrhenius Relationship Applied to the Number of Vacancies in a Crystal4:13

Point Defects and Solid State Diffusion3:15

The Arrhenius Relationship Applied to Solid State Diffusion2:38

Conheça os instrutores

James Shackelford
Distinguished Professor Emeritus
Department of Chemical Engineering and Materials Science

So now let's go to the short video lecture,

in which we introduce the great Swedish chemist Svante Arrhenius,

who quantified for us the important observation that

chemical reactions happen more rapidly as we go to higher temperatures.

And in fact, they happen more rapidly at an exponentially faster rate.

That concept is one that we're going to see helpful in

understanding solid state diffusion, but also in a number of other

similar applications throughout the remainder of this course.

And now we'll have a lesson on diffusion,

the transport of atoms within a solid material.

And to begin.

Let's acknowledge a very important relationship,

temperature relationship of chemical reaction rates,

originally identified in that regard in the late 19th century.

So, what this equation is telling us is at the rate at which chemical

reactions occur, increase exponentially with temperature.

We see temperature over here on the right side of the equation.

It's important to appreciate that that temperature

is in the denominator of this exponential term, but

it is also in an exponential term that is negative.

So if we think that through that means that ultimately as

the temperature increases, The rate will increase also, and

we'll see very specific examples shortly.

We call this the Arrhenius equation, because we're indebted to

Svante Arrhenius, a great Swedish chemist from the 19th century.

One of the great scientists of the 19th century, he very appropriately

won the second Nobel prize in chemistry for this work.

In spite of the fact that he was a personal friend of Alfred Nobel,

the benefactor for the Nobel prizes, he richly deserved this honor because again,

this equation is of

tremendous utility and understanding of the nature

of chemical reactions in general across a wide temperature range.

And very broadly gives us an expression

that allows us to appreciate that

exponential dependence on temperature for any thermally activated process and

again, we'll see in this chapter that diffusion is an excellent example.

And we begin to see how this somewhat complex looking small

equation becomes elegantly simply if we simply take

the logarithm of both sides of the previous form.

So we have the logarithm of the rate is equal to the logarithm of that

exponential term.

And of course the natural logarithm of the base e,

is the argument of that exponential and so that is -Q over RT.

And the logarithm of a product is the sum of the logarithms,

and so the right side of the equation becomes

the logarithm of the pre-exponential constant,

and the argument of the exponent.

So Q over R now becomes

the slope of a linear plot.

This is basically y is equal to mx

plus b, in the usual form, y is we think of y as mx plus b.

We have our mx over here and our b over here.

So we can look at a plot of this

equation, this now nicely linear equation.

So, we see as we look at a set of data points

with a typical experimental scatter along

a wide temperature range, that the best fit through that is a straight line slope.

And again, that slope is the minus q over r.

Also, because we're plotting this against 1 over temperature and

the 0 on that scale is going to correspond to the hypothetical case

of 1 over infinite temperature,

then we can simply extend this experimental spot to the intercept and

get the value then of the logarithm,

natural logarithm of the pre-exponential constant.

So we have the ability now to be very quantitative

about monitoring the rate of chemical reactions.

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