In this module we're going to continue exploring the ionic bonds and the bond for
some bond energy curves, but
this time we're going to see how the behavior of these materials that's
influenced by these curves will affect the properties of materials.
We're going to begin looking at the materials
behavior with respect to our bond energy behaviors and
in the last lesson we describe two materials A and B.
A has the stronger bond the deeper energy well than does material B.
The other point that we want to
emphasize in this comparative plot is the asymmetry of the curve.
The higher the melting temperature of the material, the less asymmetry
that that material has with respect to the vibrations back and forth.
Once we understand that we can relate this bond
energy curve to the behavior of the material,
we can look at characteristics that we know of the metals on the periodic chart.
What's plotted along here is, along the x axis, is the melting temperature
of the elements, on the periodic chart that crystallize into solids.
Along the y axis, we're looking at the coefficient of thermal expansion.
And what you can clearly see from this behavior is that if you look at all
the atoms,
what you will see is that as the melting temperature of the element increases,
there will be a corresponding decrease in the thermal expansion of that material.
And it goes hand-in-hand with the picture that we see to the left where we have
two materials, material A and B, with different melting temperatures.
Now when we are considering another property and
the one we're going to focus on here is the bond force curve.
When we look at the bond force curve, we can evaluate the behavior of the bond
force curve by taking the derivative at the equilibrium spacing.
So in the case of material A, it's going to have a steeper slope.
And when we look at material B, it's less steep at its equilibrium position.
So remember now what we're doing is we're taking the derivative
at their equilibrium positions.
We're now going to go back and consider the bond force curve.
We can consider the bond force in terms of
the attraction that's associated with these two masses.
Each mass is connected through a spring and the spring constant is going to be
a measure of the stiffness of the bond that's holding these two masses together.
So when I extend this into materials behavior in general,
what I recognize is as the material vibrates with increasing
thermal energy, you can see that the mass is vibrating back and forth.
And what you're doing in effect Is to stress the spring ever slightly.
And we're going to assume that all this stretching that we're seeing
is fully reversible, in other words, we haven't gone and
destroyed the spring by stretching the spring too far.
Now, what we can do, is to further our understanding,
we can consider the relationships between the derivatives of
these various behaviors and we can look at the force.
And that's, of course,
related to the derivative of the energy with respect to position.
Then what we can do is we can consider the stiffness of the particular
bonds that we're looking at.
And that stiffness is going to be related to the elastic modulus of the material.
Once again, we can Look at metallic materials from the periodic chart and
we can begin to look at the behavior of the elastic modulus.
Which again,
remember that the elastic modulus is an indicator of stiffness of the material.
What we see is as the melting temperature of the material goes up,
what were beginning to see is an increase, the elastic modulus of the material.
I have in front of me a very simple space model that describes the three dimensional
nature of what we have been looking at in this lesson where we've been
describing the two dimensional behavior of two masses that are connected by a spring.
Here we have three dimensional structure where
each one of the spheres inside represents either a cation or an ion.
Notice that they're all in it black and white to make sure that we maintain
the electrical neutrality associated with the structure.
We're going to be using this model in subsequent lectures to describe
the coordination number that is associated with this particular type
of three dimensional structure in a material like sodium chloride.
Thank you.
