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[Slide 1] Welcome everyone to the nanoHUB-U course,
from atoms to materials, Predictive Theory and Simulations.
I'm Ale Strachan, professor of materials engineering at
Purdue and I'm excited to spend the next
five weeks working with you on learning how
material properties can be understood in terms of
fundamental physics that govern atomic and electronic properties.
[Slide 2] So materials and challenges associated with
materials appear in multiple applications and at multiple
scales, from large structural applications like what you
see here in the Boeing 787. This is
the latest plane from Boeing and it's the
first commercial plane made almost entirely out of
a composite material, as opposed to aluminum. So
using a new material for such an application
opens up lots of opportunities but also a
lot of challenges that have to be overcome
during the development of the plane. At the
other spectrum of land scales in the microelectronics
industry they' are critical materials that are only
a few atoms thick, in which you see
here is the gate oxide that has to
perform in the billions of transistors that we
have in our laptops, yet as I said,
it's only a few atoms thick. Now materials
challenges also appear in industries that are not
traditionally associated with material science and engineering and
here's an example from the pharmaceutical industry where
developing a drug required manipulating the active ingredient
at the molecular scale in order to increase
its bioavailability. So in all of these industries
and in many other industries and applications, an
understanding of how materials behave in terms of
fundamental physics is enabling this development, this progress,
and more is needed, we need more predictive
tools and tools with higher accuracy that allow
us to make more quantitative predictions about materials.
[Slide 3] So in this course what we're
going to do is learn the fundamental physics
that allow us to understand how materials perform
from first principles and also relate these phenomena
at atomic and electronic scales with the macroscopic
world and we're going to complement what we
learned in the lectures with hands-on online simulations
using density functional theories and molecular dynamics simulations
of small molecules and crystals to develop a
more intuitive understanding of how materials look and
behave at atomic scales and how to relate
that to the macroscopic world. [Slide 4] So
speaking of how materials look at the atomic
scale, well they look very different. We have
molecular materials, these are where the interaction between
molecules is very weak, Vander boss bonds and
the interactions inside each molecule are very strong
covalent bonds. We have ceramic and semiconductors which
in many cases exhibit ionic type of bonding
and metals succeeded yet another class or character
of bonding. And all of these cases materials
can be crystalline with long-range order or amorphous
and their properties depend on their composition and
the way the atoms arrange themselves. So materials
look very different. [Slide 5] And they also
have very different properties and one way materials
scientists like to look at materials properties is
with these materials properties charts like the one
I'm showing here. So in this chart we
relate the strength of the material as a
function of density and each class of material
appears here as the little oval or circle
and we can go from foams that are
low density and low strength to some metallic
atoms that are high-strength and high density. So
what I find striking about this plot is
the fact that materials properties change by such
a huge margin. This is a log-log plot
so materials properties like strength can change by
many, many orders of magnitude, five or six
orders of magnitude, that's an amazing number and
it tells us and this type of plots
show the dispatches bonding and composition that matters
in the tears and microstructure, how you make
a material whether I'd have more defects or
less defects, that effects properties very, very significantly,
and all that need to be understood ,
needs to be understood in order to build
to predict how materials behave. [Slide 6] So
the quest for predictive materials simulations considered, predictive
materials capabilities, is long and illustrious, and can
be traced all the way back to Paul
Dirac who in 1929 right after most of
the development of quantum mechanics said in a
paper that essentially we have all the fundamental
knowledge for most of physics and all of
chemistry and I would add all of materials
science, but that the equations are difficult to
solve and so the focus should be on
understanding approximations and how to actually solve these
equations for problems that we're interested in and
that's going to be the path that we're
going to take in these five weeks .
[Slide 7] So as the Dirac mentioned, we're
going to start the quantum mechanical level and
if have a material and it is composed
of the collection of atoms and for us
and to mean a set of nuclei and
electrons and the state of such a system
of a bunch of atoms is completely governed
by its wave function. So probably all of
you have heard of a wave function before,
we're going to discuss that throughout the course.
But the wave function describes the state of
a collection of ions and electrons. and we
have an equation that describes the time evolution
of the wave functions. So if I know
the state of a system I can solve
this equation and predict the future and understand
how the material will behave. Now that's easier
said than done. This equation is called the
time- dependent Schrodinger equation and is very easy
to write, as you can see here, but
it's almost impossible to solve for most of
the problems that we're interested in. So even
with supercomputers we cannot solve these equations- this
equation- for most of the materials that we
would be interested in. Now fortunately we can
make approximations are very well controlled that allow
us to simplify the questions that need to
be solved and make a lot of progress
and that's what we'll discuss in the course.
So when we're dealing with electrons and electrons
are too small to be treated classically and
we do need a quantum mechanical description, however
for most applications we can get away with
the time independent Schrodinger equation that you see
here as opposed to the time dependent Schrodinger
question and that's because atoms and ions tend
to move very slowly with respect to electrons
so electrons kind of see their environment as
static and they can equilibrate instantaneously to the
instantaneous positions of the ions. So we're going
to work quite a bit with the time
independent Schrodinger question. Now ions on the other
hand are heavier and for the most part
can be described classically with Newton's equations of
motion F=ma, so using F=ma, we can predict
how a group of atoms will move. Now
that's not always the case and throughout the
course were going to discuss where and when
a classical approximation for atomic dynamics is not
appropriate and what we can do about it.
[Slide 8] So let's see how this plays
out, how in principle we can use these
equations to predict how materials will behave. So
I'm going to start out with a collection
of atoms, these are the blue dots that
you see here. They are classical so their
condition and their state is given by their
positions, R and velocities, V of a collection
of atoms so given that they're classical sol
I can describe it their time evolution using
Newton's equations that I've written here in Hamilton's
form. So the dot here represents time derivative,
so R dot equals V, equals the time
derivative of position equals velocity and time derivative
of velocity equals force over mass. Now the
question is- where does this force come from?
And it's going to come from the bonding
and the bonding is done by electrons so
to characterize this force, to obtain this force,
we need to solve for the elections and
that requires solving time dependent-independent- Schrodinger equation that
you see here. So once I solve this
equation what this equation tells me is how
the electrons organize and react to the presence
of the ions and once I solve that
equation, I have an energy- this number here,
E- is the energy of the system and
if I know an energy, you know from
classical mechanics that the gradient negative the gradient
of the energies of force I can compute
the force on every single atom and then
I can feed that back into Newton's equations.
[Slide 9] So if we put all of
this together what would have is a molecular
dynamics code actually, and evolutionary molecular dynamics code,
and I'm going to tell you how this
works. So I have initial conditions, positions and
velocities. I'm going to compute energy and forces
based on these positions so I solve the
Schrodinger equation that tells me where the atom-
the electrons- sit around the atoms. I compute
the forces from that energy expression and with
those forces I can predict the future, I
can move my positions, I can update my
positions at time- ahead of time, if I'm
at the time t, at time Delta t,
and I can also update my velocities because
I know the time derivative of velocity so
I can calculate the velocity in the future
a little bit. So I move my atoms
,okay, and now my atoms are at different
positions so what I have to do is
go back and re- optimize my elections resolve
the Schrodinger equation so that the electrons are
able to respond to these new atomic positions.
So basically by putting all of this together
you have an evolution molecular dynamics code that
shows conceptually up how you can predict how
a material will behave from first principles .
Okay, okay in the equations that I've shown
here, nothing changes if I have a metal
or semiconductor or a polymer. the equations always
the same, the parameters that go into the
equations are always the same and I have
the same description regardless of what material I
have with some caveats that we're going to
discuss throughout the course but in principle with
this knowledge I can predict how materials will
behave. [Slide 10] Now so fine, I can
do simulations, I can look at how atoms
move and that's called molecular dynamics, I'm going
to show you two examples of molecular dynamics
simulations where I take a piece of aluminum
bulk on the left and a nanoparticle on
the right and I'm heating them up, okay,
so I'm running dynamics and I'm increasing the
energy that they have and what she sees
that as they warm-up they vibrate more and
more and we'll also see in a little
bit- take a look at the Nano cluster
here- that the displacements are becoming larger and
larger and at some point it melts. So
the Nano cluster has melted, the bulk material
hasn't melted yet but if you wait a
little bit more it will melt as well.
So this simple simulation is a simulation that
you'll be able to do in the course
in the next few weeks. and it shows
a couple of important things. The simulation itself
predicts that a Nano cluster melts at a
lower temperature than a bulk aluminum, that's observed
experimentally and just by solving this equation that
we just described we can capture these nontrivial
phenomena without tuning in the solution. Now the
other important aspect is that if I'm interested
in melting of aluminum say, I'm really not
interested in saying well when the cluster melts
the atomic positions are in such and such
coordinate. So I'm interested more in an average
response of the system. For example I might
be interested in knowing at what temperature the
system melts so in order to do that,
in order to relate the atomic level processes
that we can describe with molecular dynamics to
the macroscopic world of thermodynamics, things like temperature,
what we're going to do in the class
is we're going to learn statistical mechanics allows
us to make the connection between the microscopic
and macroscopic world. [Slide 11] So that's all
I wanted to discuss with you in this
first lecture, it's an overview lecture, but before
I finish Id to go over the course
outline in a little bit of detail on
a week by on a weeknight week basis,
so the first week , the week we're
on, were going to discuss quantum mechanics and
how quantum mechanics allows us to understand the
electronic structure of atoms in the second week
we're going to build on this knowledge and
we're going to talk about bonding, how when
I bring atoms together they create chemical bonds,
or don't create chemical bonds, how they form
molecules and crystals, and we're going to be
able to do some best functional theory calculations
of small molecules and crystals. On week three
were going to discuss how atoms move according
to classical mechanics and we're going to talk
about collective dynamics and we're going to complement
the lectures with actual online simulations. In in
week four we're going to discuss statistical mechanics
and the connection between the atomic and electronic
world, the microscopic world and the macroscopic world.
And we're going to learn how to make
thermodynamic predictions out of atomistic simulations. And finally
in week five were going to go over
test case, study cases and we're going to
learn to apply what we've -we learned in
the first four weeks to current areas of
research that are of interest to us. So
that's all I wanted to say in the
first lecture. In in every week we're going
to have six lectures, each lecture is going
to be about 20 minutes long, and we're
going to complement that, as I said with
online simulations, homework assignments and quizzes and exams.
So thank you very much and I'll see
you in lecture two.