1
24 February 2021
Lecture 1- Experimental Methods for the Study of Nanostructured Materials, Chiara La Guidara
When you want to understand essentially the properties of a material and especially you want to
program the function of the material so you need to indict some characterization of material which
means you need to know mostly actions of different properties of the material. Among them we could
mention:
-Chemical composition: for example
- Size, shape (proteins, nanoparticles...)
- Interactions, Structural Arrangement
- Surface properties (roughness, charge, magnetic properties..)
- Transport (thermal, mechanical, electric..)
In this lecture we will essentially not look at the composition of the material but we will look into the
other properties.
Direct and indirect Methods
We can have 2 characterization methods:
1. Direct methods: which is the microscopy technique and in this method we can use many
different radiation types, so for example: Light that is the most traditional, Electrons that is also
quite traditional, X-Rays, Neutrons are very penetrant in materials and the very funny thing is that
metals are essentially transparent to neutrons but water, for example, has a significant scattering.
So essentially you can use neutrons to study the interior of metallic objects. We can do
microscopy with many different radiations. The advantage of this direct technique is that we have
an image of the sample, and this means that the interpretation of experiment is typically easier
because we directly observe our materials. Another advantage is that in a microscopy we can see
if there are variations in the properties of the material at the local scale so we can compare
different bits of the same material. Therefore we can have informations about eterogeneting in the
properties of the material and so on. This is the mains advantages of the direct method but there
are some this disadvantages, one is which directly related to what we just mentioned that we only
typically see a bit of our material in a microscopy image and therefore if we want to obtain a
statistic on the properties typically is not excellent with microscopy because we will need to a
quier really many different images of the samples to have a example of statistics properties of the
materials. And also there is a intrinsically limitation of a microscope technique which is affected
(defected) that we need to use lenses, so if you want to have a image of material with whatever
radiation in any case we have to use of lenses -> the use of lenses imposes some limitations on the
resolution of this tecniques.
2. Indirect methods: Is essentially scattering, but also Spectroscopies. The radiation that we use
is basically the same (Light,Electrons,X-Rays, Neutrons..) but I was saying that the concept is
different: we don’t form an image of the sample but we essentially see how the radiation is
deviated or its also affected to reduce by the interaction with the sample. The advantage of the
indirect method is that, contrary to microscope, we have typically a big portion of the sample
( made by millions of particles) and therefore we acquire very good statistics in a short time so in
that sense we have very good statistics. And the other advantage is typically that we don’t have to
use lenses and therefore we have less limited in the resolution which is essentially governed by
, 2
the wavelength of the radiation. Of course, this technique has disadvantages: first we get indirect
information and we get information about the intensity of radiation which we need to model to
extract the information and so we can’t directly extract the information like from an image. We
really need to build a theorical model to extract the information from the experiment. And the
second kind of limitations of this tecnique is the opposite again of microscopy, because due to ?
we avarege over so many particles or a big portion of the system,we easily missing in this case
eterogenetis so local properties. In this sense the two techniques are very complementary: with
one we can get very good information on the avarage properties but we miss details oh local
variations, while in the other one we can see that but the satistics on the avarege properties are
essentially most limited. So in most of the cases actually the best approach when you characterize
a material, is a combination of microscope and scattering tecniques to get a very detailed
informations on your system.
Direct and Indirect methods
Direct observation: Optical Microscopy, Trasmission and Scanning Electron, Microscopy,
Atomic force microscopy.
Indirect Methods: Opctical correlation techniques, small angle scattering.
Optical Microscopy
The basic element of optical microscopy is the microscope which traditionally is called the compoud
microscope because indeed it is basically the combination of many different elements in order to build
an object that you can use to form images of samples. There are typically two kinds of optical
microscope which are used:
1. Upright microscope:
2. Inverted microscope
The advantage of the inverted is that? For example when you have a big object , they are typically
subject to gravity and so it’s very difficult to see with the upright microscope because the focal lens of
an object is very limited and therefore at one point you will not be able to see it. It’s more developed.
It’s the most used in research because it has a very flexible design.
The compound microscope
The essentials elements of any compound microscope are:
- The illumination systems: at the bottom of the microscope. The first microscope
observations were done with ambient light , but typically is not sufficient and you need more
intense light. The illumination source can be from many different kinds from a simple lamp (like
more less that one that you use at home), but it can be more complex especially for the advanced
techniques (lasers, LD lamps). So the illumination source which depends on the different
techniques more or less complex. Then you have a set of lenses and aperture which are used to
convey the light on the stage where we have the sample and focus essentially the light in direction
of the sample
- The lenses system: Then you have to collect the light which is going to the sample which is
on the stage and what is used to collect the light and then to form an image of the light is the
objective. The objective is the most important thing and the lens of the objective is what
determines the resolution of the optical image. But typically in modern microscopes you have
another lenses system: a tube lens. Here in figure you have simple lenses but in reality you have
, 3
systems of lenses because you have to correct some parameters. Thanks to that you form the
image which is determining mostly the magnification (ingrandimento) of the image.
- The oculars or nowadays a camera connected to a computer: to really form the image and look
at it.
These are the three blocks which compose the compound microscope.
Objective-Tube lens system
Here i want to show to you it’is what essentially determines the magnification of the object that you
are observing in the microscope. So you are illuminating our object and forming an image to the
system of objective lens and thug lens. This system nowadays is constructed in such a way that
microscopes are called infinity optics and let’s say the optics of the microscope are called infinity
optics. Why that? They are called infinity optics because if we look at the simple scheme: the object
is positioned in the focal plane of the objective lens, so essentially the distance from the lens to the
object is equal to the focal lens of the object. So my object is completely on the focal plane.
Therefore if i would not have any other lenses (quindi se non ci fosse l’ulteriore lente in fig), since my
object is in the focal plane, you know that the image of this object will be at infinity. But then the
addition of the tube lens is used to bring back the image of the object on a plane which is at the focal
lens of the tube lens. Why is the image at the focal lens of the tube lens? It is simple because anyway
which comes from infinity, which is the situation for the first lens (..) and it will form an image on the
focal plane of the other lens. So essentially the advantage of the system is that the size of the image
object it’s only dependent on the two focal lengths of the lenses (like you can see in the formula
so=size of the object and si= size of image). Then essentially the magnification , which is given by the
microscope, is si/so that is equal to the ratio between the focal lens of the tube lens and the focal lens
of the object. I can put these lenses at any distance between them and this doesn’t change. So it is a
construction’s advantage of the infinity optics system that essentially consists in the fact that the
magnification only depends on these 2 parameters and I can build the system with any distance
between the objective lens and the tube lens. Typically the focal lens of the tube lens is fixed (fissata)
for a certain manufacture (costruzione). Actually the bad thing is that typically different
manufacturers have differentes tube lenses and this is why you can not use for example the objective
of nikon for example on a ? microscope because these numbers (fTL) are different.
So the magnification that I tell you is specific to the construction that is used. Instead the f(obj) is
what typically tells you the overall magnification of the objective and in detail you can see that the
higher the magnification closer you have to get to the sample. Typical values that you find for the
magnification is: 2.5-100.
Eyepiece
If you look at the image to the oculars then you have an additional magnification which is given by
the lens of the ocular. The magnification of the ocular depends on the focal lens of the ocular only
and the typical values are between 10 and 25. The total magnification of the object that you see on the
oculars or on the camera is the product of Mot (magnification of the object) and Mep (magnification
of the ocular).
Diffraction,Interference and Resolution
One very important thing is that we have to deal with distraction fenomena. In all the very simple
schemes that we saw in the other pages we used to calculate the image’s formation ( we called it
geometrical optics) and we essentially see that the image of one point in the object corresponds to one
point in the image. So we have a simple corresponder between one point in the object and one point in
the image. In reality it isn’t so simple so whenever you form an image of an object using a lens, the
image of one point of the object is not one point. So due to the effect called diffraction the image of
, 4
one geometrical point of the object is bigger than a point and this is which gives rise to the limits to
the resolution in the microscopy techniques. The diffraction phenomena is what happens in general
when light is encountering an obstacle and the fact that the light cannot propagate without any
perturbation, then as the consequence that the radiation interacting with the object is altered in 2 ways.
The intensity of the radiation can be altered and in addition also ?propagation of light. The elements
that can generate driffaction in a microscope is:
-Apertures: so in any microscope we have some apertures which are used to direct the light and these
apertures can have an obstacle to the propagation of light and it can induce diffraction. There are
lenses in which the finite size of course perturbes the propagation of the light because the propagation
is not the same on the lenses and on the borders of the lenses (?).
- Elements in the specimen (the sample itself): when the light encounters particles in our sample, these
particles diffract light, at least their size is moreless comparable with the wavelength of the light that
we are using to illuminate.
So we have these 2 sources of diffraction, then when the light encounters an object like a lens, an
aperture or a sample it indict propagating (...) and this diffracted a light then will interfere at
sufficiently long distance from the sample and this interference generates a diffraction pattern of the
light on a far away screen. And essentially now we will see in the example of diffraction from a circle
aperture of light coming from a point source that the effect of this is that the image of this point
diffracted by the aperture becomes, due to this interfering phenomena, an object of a finite size and
they have a specific shape that we will see it’s in a plane?.
Diffraction by an aperture
In the example which we consider there is the example of a point source in front of a circular aperture.
Plane wave from the point source is diffracted by the aperture and the diffraction pattern is formed on
the screen which is at a distance R from the center of the aperture. We look at the intensity of the light
which is collected on the screen a the distance 𝜉 from the center of the screen, of the reference
system. If we want to measure the intensity of light I(𝜉), we find the formula in the slide. Where I(0)
is the initial intentensity, the intensity which comes from the source of light; J1? is not even an
analytical function. 𝜉 is the wave vector of incident light multiplied for the radius of the aperture a
and for the sin of the angle. When you make a plot : in the central part it’s a gaussian more and less
and then there are some minima and maxima. So this is the image of one point source and due to
diffraction is not one point (if it could be one point we will have just the central spike), it’s instead
this object which has a finite size. A finite size depends on the ratio between the size of the aperture
and the wavelength of radiation. In fact the 𝜉 is proportional to 2p over lambda. We can determine
the size of this region so from the maximum to the first minimum, which is the relevant size of the
object and we obtain: 𝜉=3.83 and if we substitute 𝜉 we obtain the radius of the Airy disc (the
distance from 0 to?) which is the size of one point which is from to diffraction on a screen. In the
formula R is the distance between the screen and the aperture.
Diffraction-limited resolution
Why is this thing limiting what we can distinguish in an image? Because if you think of 2 points in
the object from which you want to form an image,these 2 objects when you look at the object through
the lenses and the apertures of the microscope, these 2 points in the image give rise to this
distribution, so there are not any more points in the image . So as soon as these 2 airy functions are
sufficiently far one to each other, I don't have any problem in distinguishing one point from the other
(a). If there isn't a superimposition between these 2 distributions of light of 2 points, i can resolve
24 February 2021
Lecture 1- Experimental Methods for the Study of Nanostructured Materials, Chiara La Guidara
When you want to understand essentially the properties of a material and especially you want to
program the function of the material so you need to indict some characterization of material which
means you need to know mostly actions of different properties of the material. Among them we could
mention:
-Chemical composition: for example
- Size, shape (proteins, nanoparticles...)
- Interactions, Structural Arrangement
- Surface properties (roughness, charge, magnetic properties..)
- Transport (thermal, mechanical, electric..)
In this lecture we will essentially not look at the composition of the material but we will look into the
other properties.
Direct and indirect Methods
We can have 2 characterization methods:
1. Direct methods: which is the microscopy technique and in this method we can use many
different radiation types, so for example: Light that is the most traditional, Electrons that is also
quite traditional, X-Rays, Neutrons are very penetrant in materials and the very funny thing is that
metals are essentially transparent to neutrons but water, for example, has a significant scattering.
So essentially you can use neutrons to study the interior of metallic objects. We can do
microscopy with many different radiations. The advantage of this direct technique is that we have
an image of the sample, and this means that the interpretation of experiment is typically easier
because we directly observe our materials. Another advantage is that in a microscopy we can see
if there are variations in the properties of the material at the local scale so we can compare
different bits of the same material. Therefore we can have informations about eterogeneting in the
properties of the material and so on. This is the mains advantages of the direct method but there
are some this disadvantages, one is which directly related to what we just mentioned that we only
typically see a bit of our material in a microscopy image and therefore if we want to obtain a
statistic on the properties typically is not excellent with microscopy because we will need to a
quier really many different images of the samples to have a example of statistics properties of the
materials. And also there is a intrinsically limitation of a microscope technique which is affected
(defected) that we need to use lenses, so if you want to have a image of material with whatever
radiation in any case we have to use of lenses -> the use of lenses imposes some limitations on the
resolution of this tecniques.
2. Indirect methods: Is essentially scattering, but also Spectroscopies. The radiation that we use
is basically the same (Light,Electrons,X-Rays, Neutrons..) but I was saying that the concept is
different: we don’t form an image of the sample but we essentially see how the radiation is
deviated or its also affected to reduce by the interaction with the sample. The advantage of the
indirect method is that, contrary to microscope, we have typically a big portion of the sample
( made by millions of particles) and therefore we acquire very good statistics in a short time so in
that sense we have very good statistics. And the other advantage is typically that we don’t have to
use lenses and therefore we have less limited in the resolution which is essentially governed by
, 2
the wavelength of the radiation. Of course, this technique has disadvantages: first we get indirect
information and we get information about the intensity of radiation which we need to model to
extract the information and so we can’t directly extract the information like from an image. We
really need to build a theorical model to extract the information from the experiment. And the
second kind of limitations of this tecnique is the opposite again of microscopy, because due to ?
we avarege over so many particles or a big portion of the system,we easily missing in this case
eterogenetis so local properties. In this sense the two techniques are very complementary: with
one we can get very good information on the avarage properties but we miss details oh local
variations, while in the other one we can see that but the satistics on the avarege properties are
essentially most limited. So in most of the cases actually the best approach when you characterize
a material, is a combination of microscope and scattering tecniques to get a very detailed
informations on your system.
Direct and Indirect methods
Direct observation: Optical Microscopy, Trasmission and Scanning Electron, Microscopy,
Atomic force microscopy.
Indirect Methods: Opctical correlation techniques, small angle scattering.
Optical Microscopy
The basic element of optical microscopy is the microscope which traditionally is called the compoud
microscope because indeed it is basically the combination of many different elements in order to build
an object that you can use to form images of samples. There are typically two kinds of optical
microscope which are used:
1. Upright microscope:
2. Inverted microscope
The advantage of the inverted is that? For example when you have a big object , they are typically
subject to gravity and so it’s very difficult to see with the upright microscope because the focal lens of
an object is very limited and therefore at one point you will not be able to see it. It’s more developed.
It’s the most used in research because it has a very flexible design.
The compound microscope
The essentials elements of any compound microscope are:
- The illumination systems: at the bottom of the microscope. The first microscope
observations were done with ambient light , but typically is not sufficient and you need more
intense light. The illumination source can be from many different kinds from a simple lamp (like
more less that one that you use at home), but it can be more complex especially for the advanced
techniques (lasers, LD lamps). So the illumination source which depends on the different
techniques more or less complex. Then you have a set of lenses and aperture which are used to
convey the light on the stage where we have the sample and focus essentially the light in direction
of the sample
- The lenses system: Then you have to collect the light which is going to the sample which is
on the stage and what is used to collect the light and then to form an image of the light is the
objective. The objective is the most important thing and the lens of the objective is what
determines the resolution of the optical image. But typically in modern microscopes you have
another lenses system: a tube lens. Here in figure you have simple lenses but in reality you have
, 3
systems of lenses because you have to correct some parameters. Thanks to that you form the
image which is determining mostly the magnification (ingrandimento) of the image.
- The oculars or nowadays a camera connected to a computer: to really form the image and look
at it.
These are the three blocks which compose the compound microscope.
Objective-Tube lens system
Here i want to show to you it’is what essentially determines the magnification of the object that you
are observing in the microscope. So you are illuminating our object and forming an image to the
system of objective lens and thug lens. This system nowadays is constructed in such a way that
microscopes are called infinity optics and let’s say the optics of the microscope are called infinity
optics. Why that? They are called infinity optics because if we look at the simple scheme: the object
is positioned in the focal plane of the objective lens, so essentially the distance from the lens to the
object is equal to the focal lens of the object. So my object is completely on the focal plane.
Therefore if i would not have any other lenses (quindi se non ci fosse l’ulteriore lente in fig), since my
object is in the focal plane, you know that the image of this object will be at infinity. But then the
addition of the tube lens is used to bring back the image of the object on a plane which is at the focal
lens of the tube lens. Why is the image at the focal lens of the tube lens? It is simple because anyway
which comes from infinity, which is the situation for the first lens (..) and it will form an image on the
focal plane of the other lens. So essentially the advantage of the system is that the size of the image
object it’s only dependent on the two focal lengths of the lenses (like you can see in the formula
so=size of the object and si= size of image). Then essentially the magnification , which is given by the
microscope, is si/so that is equal to the ratio between the focal lens of the tube lens and the focal lens
of the object. I can put these lenses at any distance between them and this doesn’t change. So it is a
construction’s advantage of the infinity optics system that essentially consists in the fact that the
magnification only depends on these 2 parameters and I can build the system with any distance
between the objective lens and the tube lens. Typically the focal lens of the tube lens is fixed (fissata)
for a certain manufacture (costruzione). Actually the bad thing is that typically different
manufacturers have differentes tube lenses and this is why you can not use for example the objective
of nikon for example on a ? microscope because these numbers (fTL) are different.
So the magnification that I tell you is specific to the construction that is used. Instead the f(obj) is
what typically tells you the overall magnification of the objective and in detail you can see that the
higher the magnification closer you have to get to the sample. Typical values that you find for the
magnification is: 2.5-100.
Eyepiece
If you look at the image to the oculars then you have an additional magnification which is given by
the lens of the ocular. The magnification of the ocular depends on the focal lens of the ocular only
and the typical values are between 10 and 25. The total magnification of the object that you see on the
oculars or on the camera is the product of Mot (magnification of the object) and Mep (magnification
of the ocular).
Diffraction,Interference and Resolution
One very important thing is that we have to deal with distraction fenomena. In all the very simple
schemes that we saw in the other pages we used to calculate the image’s formation ( we called it
geometrical optics) and we essentially see that the image of one point in the object corresponds to one
point in the image. So we have a simple corresponder between one point in the object and one point in
the image. In reality it isn’t so simple so whenever you form an image of an object using a lens, the
image of one point of the object is not one point. So due to the effect called diffraction the image of
, 4
one geometrical point of the object is bigger than a point and this is which gives rise to the limits to
the resolution in the microscopy techniques. The diffraction phenomena is what happens in general
when light is encountering an obstacle and the fact that the light cannot propagate without any
perturbation, then as the consequence that the radiation interacting with the object is altered in 2 ways.
The intensity of the radiation can be altered and in addition also ?propagation of light. The elements
that can generate driffaction in a microscope is:
-Apertures: so in any microscope we have some apertures which are used to direct the light and these
apertures can have an obstacle to the propagation of light and it can induce diffraction. There are
lenses in which the finite size of course perturbes the propagation of the light because the propagation
is not the same on the lenses and on the borders of the lenses (?).
- Elements in the specimen (the sample itself): when the light encounters particles in our sample, these
particles diffract light, at least their size is moreless comparable with the wavelength of the light that
we are using to illuminate.
So we have these 2 sources of diffraction, then when the light encounters an object like a lens, an
aperture or a sample it indict propagating (...) and this diffracted a light then will interfere at
sufficiently long distance from the sample and this interference generates a diffraction pattern of the
light on a far away screen. And essentially now we will see in the example of diffraction from a circle
aperture of light coming from a point source that the effect of this is that the image of this point
diffracted by the aperture becomes, due to this interfering phenomena, an object of a finite size and
they have a specific shape that we will see it’s in a plane?.
Diffraction by an aperture
In the example which we consider there is the example of a point source in front of a circular aperture.
Plane wave from the point source is diffracted by the aperture and the diffraction pattern is formed on
the screen which is at a distance R from the center of the aperture. We look at the intensity of the light
which is collected on the screen a the distance 𝜉 from the center of the screen, of the reference
system. If we want to measure the intensity of light I(𝜉), we find the formula in the slide. Where I(0)
is the initial intentensity, the intensity which comes from the source of light; J1? is not even an
analytical function. 𝜉 is the wave vector of incident light multiplied for the radius of the aperture a
and for the sin of the angle. When you make a plot : in the central part it’s a gaussian more and less
and then there are some minima and maxima. So this is the image of one point source and due to
diffraction is not one point (if it could be one point we will have just the central spike), it’s instead
this object which has a finite size. A finite size depends on the ratio between the size of the aperture
and the wavelength of radiation. In fact the 𝜉 is proportional to 2p over lambda. We can determine
the size of this region so from the maximum to the first minimum, which is the relevant size of the
object and we obtain: 𝜉=3.83 and if we substitute 𝜉 we obtain the radius of the Airy disc (the
distance from 0 to?) which is the size of one point which is from to diffraction on a screen. In the
formula R is the distance between the screen and the aperture.
Diffraction-limited resolution
Why is this thing limiting what we can distinguish in an image? Because if you think of 2 points in
the object from which you want to form an image,these 2 objects when you look at the object through
the lenses and the apertures of the microscope, these 2 points in the image give rise to this
distribution, so there are not any more points in the image . So as soon as these 2 airy functions are
sufficiently far one to each other, I don't have any problem in distinguishing one point from the other
(a). If there isn't a superimposition between these 2 distributions of light of 2 points, i can resolve
