36
METHODS OF MEASURING PROPERTIES
factor responsible for the nanotechnology revolution has been the improvement of
old and the introduction of new instrumentation systems for evaluating and
characterizing nanostructures. Many of these systems are very large and expensive,
in the million-dollar price range, often requiring specialists to operate them. The aim
of the present chapter is to explain the principles behind the operation of some of
these systems, and to delineate their capabilities.
In the following sections we describe instruments for determining the positions of
atoms in materials, instruments for observing and characterizing the surfaces of
structures, and various spectroscopic devices for obtaining information of the
properties of nanostructures [see e.g., Whan (1986)l.
3.2. STRUCTURE
3.2.1. Atomic Structures
To understand a nanomaterial we must, first, learn about its structure, meaning that
we must determine the types of atoms that constitute its building blocks and how
these atoms are arranged relative to each other. Most nanostructures are crystalline,
meaning that their thousands of atoms have a regular arrangement in space on what
is called a ciystal lattice, as explained in Section 2.1.2 (of Chapter 2). This lattice
can be described by assigning the positions of the atoms in a unit cell, so the overall
lattice arises from the continual replication of this unit cell throughout space.
Figure 2.1 presents sketches of the unit cells of the four crystal systems in two
dimensions, and the characteristics of the parameters a, b, and 19 for these systems
are listed in the four top rows of Table 3.1. There are 17 possible types of crystal
structures called space groups, meaning 17 possible arrangements of atoms in unit
cells in two dimensions, and these are divided between the four crystal systems in
the manner indicated in column 4 of the table. Of particular interest is the most
efficient way to arrange identical atoms on a surface, and this corresponds to the
hexagonal system shown in Fig. 2.4a.
In three dimensions the situation is much more complicated, and some particular
cases were described in Chapter 2. There are now three lattice constants a, b, and c,
for the three dimensions x, y , z, with the respective angles a, p, and y between them
(a is between b and c, etc.). There are seven crystal systems in three dimensions with
a total of 230 space groups divided among the systems in the manner indicated in
column 4 of Table 3.1. The objective of a crystal structure analysis is to distinguish
the symmetry and space group, to determine the values of the lattice constants and
angles, and to identify the positions of the atoms in the unit cell.
Certain special cases of crystal structures are important for nanocrystals, such as
those involving simple cubic (SC), body-centered cubic (BCC), and face-centered
cubic (FCC) unit cells, as shown in Fig. 2.3. Another important structural arrangement is formed by stacking planar hexagonal layers in the manner sketched in
Fig. 2.4b, which for a monatomic (single-atom) crystal provides the highest density
or closest-packed arrangement of identical spheres. If the third layer is placed
directly above the first layer, the fourth directly above the second, and so on, in an
A-B-A-B- . . . type sequence, the hexagonal close-packed (HCP) structure results.
METHODS OF MEASURING PROPERTIES
factor responsible for the nanotechnology revolution has been the improvement of
old and the introduction of new instrumentation systems for evaluating and
characterizing nanostructures. Many of these systems are very large and expensive,
in the million-dollar price range, often requiring specialists to operate them. The aim
of the present chapter is to explain the principles behind the operation of some of
these systems, and to delineate their capabilities.
In the following sections we describe instruments for determining the positions of
atoms in materials, instruments for observing and characterizing the surfaces of
structures, and various spectroscopic devices for obtaining information of the
properties of nanostructures [see e.g., Whan (1986)l.
3.2. STRUCTURE
3.2.1. Atomic Structures
To understand a nanomaterial we must, first, learn about its structure, meaning that
we must determine the types of atoms that constitute its building blocks and how
these atoms are arranged relative to each other. Most nanostructures are crystalline,
meaning that their thousands of atoms have a regular arrangement in space on what
is called a ciystal lattice, as explained in Section 2.1.2 (of Chapter 2). This lattice
can be described by assigning the positions of the atoms in a unit cell, so the overall
lattice arises from the continual replication of this unit cell throughout space.
Figure 2.1 presents sketches of the unit cells of the four crystal systems in two
dimensions, and the characteristics of the parameters a, b, and 19 for these systems
are listed in the four top rows of Table 3.1. There are 17 possible types of crystal
structures called space groups, meaning 17 possible arrangements of atoms in unit
cells in two dimensions, and these are divided between the four crystal systems in
the manner indicated in column 4 of the table. Of particular interest is the most
efficient way to arrange identical atoms on a surface, and this corresponds to the
hexagonal system shown in Fig. 2.4a.
In three dimensions the situation is much more complicated, and some particular
cases were described in Chapter 2. There are now three lattice constants a, b, and c,
for the three dimensions x, y , z, with the respective angles a, p, and y between them
(a is between b and c, etc.). There are seven crystal systems in three dimensions with
a total of 230 space groups divided among the systems in the manner indicated in
column 4 of Table 3.1. The objective of a crystal structure analysis is to distinguish
the symmetry and space group, to determine the values of the lattice constants and
angles, and to identify the positions of the atoms in the unit cell.
Certain special cases of crystal structures are important for nanocrystals, such as
those involving simple cubic (SC), body-centered cubic (BCC), and face-centered
cubic (FCC) unit cells, as shown in Fig. 2.3. Another important structural arrangement is formed by stacking planar hexagonal layers in the manner sketched in
Fig. 2.4b, which for a monatomic (single-atom) crystal provides the highest density
or closest-packed arrangement of identical spheres. If the third layer is placed
directly above the first layer, the fourth directly above the second, and so on, in an
A-B-A-B- . . . type sequence, the hexagonal close-packed (HCP) structure results.