Solid State Structure

In the previous pages, some of the mechanisms that bond together the multitude of individual atoms or molecules of a solid material were discussed. These forces may be primary chemical bonds, as in metals and ionic solids, or they may be secondary van der Waals’ forces of solids, such as in ice, paraffin wax and most polymers. In solids, the way the atoms or molecules arrange themselves contributes to the appearance and the properties of the materials.

Atoms can be gathered together as an aggregate through a number of different processes, including condensation, pressurization, chemical reaction, electrodeposition, and melting. The process usually determines, at least initially, whether the collection of atoms will take to form of a gas, liquid or solid. The state usually changes as its temperature or pressure is changed. Melting is the process most often used to form an aggregate of atoms. When the temperature of a melt is lowered to a certain point, the liquid will form either a crystalline solid or and amorphous solid.

Amorphous Solids
A solid substance with its atoms held apart at equilibrium spacing, but with no long-range periodicity in atom location in its structure is an amorphous solid. Examples of amorphous solids are glass and some types of plastic. They are sometimes described as supercooled liquids because their molecules are arranged in a random manner some what as in the liquid state. For example, glass is commonly made from silicon dioxide or quartz sand, which has a crystalline structure. When the sand is melted and the liquid is cooled rapidly enough to avoid crystallization, an amorphous solid called a glass is formed. Amorphous solids do not show a sharp phase change from solid to liquid at a definite melting point, but rather soften gradually when they are heated. The physical properties of amorphous solids are identical in all directions along any axis so they are said to have isotropic properties, which will be discussed in more detail later

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Crystalline Solids
More than 90% of naturally occurring and artificially prepared solids are crystalline. Minerals, sand, clay, limestone, metals, carbon (diamond and graphite), salts ( NaCl, KCl etc.), all have crystalline structures. A crystal is a regular, repeating arrangement of atoms or molecules. The majority of solids, including all metals, adopt a crystalline arrangement because the amount of stabilization achieved by anchoring interactions between neighboring particles is at its greatest when the particles adopt regular (rather than random) arrangements. In the crystalline arrangement, the particles pack efficiently together to minimize the total intermolecular energy.

The regular repeating pattern that the atoms arrange in is called the crystalline lattice. The scanning tunneling microscope (STM) makes it possible to image the electron cloud associated individual atoms at the surface of a material. Below is an STM image of a platinum surface showing the regular alignment of atoms.

Courtesy: IBM Research, Almaden Research Center.

Crystal Structure
Crystal structures may be conveniently specified by describing the arrangement within the solid of a small representative group of atoms or molecules, called the ‘unit cell.’ By multiplying identical unit cells in three directions, the location of all the particles in the crystal is determined. In nature, 14 different types of crystal structures or lattices are found. The simplest crystalline unit cell to picture is the cubic, where the atoms are lined up in a square, 3D grid. The unit cell is simply a box with an atom at each corner. Simple cubic crystals are relatively rare, mostly because they tend to easily distort. However, many crystals form body-centered-cubic (bcc) or face-centered-cubic (fcc) structures, which are cubic with either an extra atom centered in the cube or centered in each face of the cube. Most metals form bcc, fcc or Hexagonal Close Packed (hpc) structures; however, the structure can change depending on temperature. These three structures will be discussed in more detail on the following page.

Crystalline structure is important because it contributes to the properties of a material. For example, it is easier for planes of atoms to slide by each other if those planes are closely packed. Therefore, lattice structures with closely packed planes allow more plastic deformation than those that are not closely packed. Additionally, cubic lattice structures allow slippage to occur more easily than non-cubic lattices. This is because their symmetry provides closely packed planes in several directions. A face-centered cubic crystal structure will exhibit more ductility (deform more readily under load before breaking) than a body-centered cubic structure. The bcc lattice, although cubic, is not closely packed and forms strong metals. Alpha-iron and tungsten have the bcc form. The fcc lattice is both cubic and closely packed and forms more ductile materials. Gamma-iron, silver, gold, and lead have fcc structures. Finally, HCP lattices are closely packed, but not cubic. HCP metals like cobalt and zinc are not as ductile as the fcc metals.

Primary Metallic Crystalline Structures
(BCC, FCC, HCP)

As pointed out on the previous page, there are 14 different types of crystal unit cell structures or lattices are found in nature. However most metals and many other solids have unit cell structures described as body center cubic (bcc), face centered cubic (fcc) or Hexagonal Close Packed (hcp). Since these structures are most common, they will be discussed in more detail.

Body-Centered Cubic (BCC) Structure
The body-centered cubic unit cell has atoms at each of the eight corners of a cube (like the cubic unit cell) plus one atom in the center of the cube (left image below). Each of the corner atoms is the corner of another cube so the corner atoms are shared among eight unit cells. It is said to have a coordination number of 8. The bcc unit cell consists of a net total of two atoms; one in the center and eight eighths from corners atoms as shown in the middle image below (middle image below). The image below highlights a unit cell in a larger section of the lattice.

The bcc arrangement does not allow the atoms to pack together as closely as the fcc or hcp arrangements. The bcc structure is often the high temperature form of metals that are close-packed at lower temperatures. The volume of atoms in a cell per the total volume of a cell is called the packing factor. The bcc unit cell has a packing factor of 0.68.

Some of the materials that have a bcc structure include lithium, sodium, potassium, chromium, barium, vanadium, alpha-iron and tungsten. Metals which have a bcc structure are usually harder and less malleable than close-packed metals such as gold. When the metal is deformed, the planes of atoms must slip over each other, and this is more difficult in the bcc structure. It should be noted that there are other important mechanisms for hardening materials, such as introducing impurities or defects which make slipping more difficult. These hardening mechanisms will be discussed latter.

Face Centered Cubic (FCC) Structure
The face centered cubic structure has atoms located at each of the corners and the centers of all the cubic faces (left image below). Each of the corner atoms is the corner of another cube so the corner atoms are shared among eight unit cells. Additionally, each of its six face centered atoms is shared with an adjacent atom. Since 12 of its atoms are shared, it is said to have a coordination number of 12. The fcc unit cell consists of a net total of four atoms; eight eighths from corners atoms and six halves of the face atoms as shown in the middle image above. The image below highlights a unit cell in a larger section of the lattice.

In the fcc structure (and the hcp structure) the atoms can pack closer together than they can in the bcc structure. The atoms from one layer nest themselves in the empty space between the atoms of the adjacent layer. To picture packing arrangement, imagine a box filled with a layer of balls that are aligned in columns and rows. When a few additional balls are tossed in the box, they will not balance directly on top of the balls in the first layer but instead will come to rest in the pocket created between four balls of the bottom layer. As more balls are added they will pack together to fill up all the pockets. The packing factor (the volume of atoms in a cell per the total volume of a cell) is 0.74 for fcc crystals. Some of the metals that have the fcc structure include aluminum, copper, gold, iridium, lead, nickel, platinum and silver.

Hexagonal Close Packed (HPC) Structure
Another common close packed structure is the hexagonal close pack. The hexagonal structure of alternating layers is shifted so its atoms are aligned to the gaps of the preceding layer. The atoms from one layer nest themselves in the empty space between the atoms of the adjacent layer just like in the fcc structure. However, instead of being a cubic structure, the pattern is hexagonal. (See image below.) The difference between the HPC and FCC structure is discussed later in this section.

The hcp structure has three layers of atoms. In each the top and bottom layer, there are six atoms that arrange themselves in the shape of a hexagon and a seventh atom that sits in the middle of the hexagon. The middle layer has three atoms nestle in the triangular "grooves" of the top and bottom plane. Note that there are six of these "grooves" surrounding each atom in the hexagonal plane, but only three of them can be filled by atoms.

As shown in the middle image above, there are six atoms in the hcp unit cell. Each of the 12 atoms in the corners of the top and bottom layers contribute 1/6 atom to the unit cell, the two atoms in the center of the hexagon of both the top and bottom layers each contribute ½ atom and each of the three atom in the middle layer contribute 1 atom. The image on the right above attempts to show several hcp unit cells in a larger lattice.

The coordination number of the atoms in this structure is 12. There are six nearest neighbors in the same close packed layer, three in the layer above and three in the layer below. The packing factor is 0.74, which is the same as the fcc unit cell. The hcp structure is very common for elemental metals and some examples include beryllium, cadmium, magnesium, titanium, zinc and zirconium.

Similarities and Difference Between the
FCC and HCP Structure

The face centered cubic and hexagonal close packed structures both have a packing factor of 0.74, consist of closely packed planes of atoms, and have a coordination number of 12. The difference between the fcc and hcp is the stacking sequence. The hcp layers cycle among the two equivalent shifted positions whereas the fcc layers cycle between three positions. As can be seen in the image, the hcp structure contains only two types of planes with an alternating ABAB arrangement. Notice how the atoms of the third plane are in exactly the same position as the atoms in the first plane. However, the fcc structure contains three types of planes with a ABCABC arrangement. Notice how the atoms in rows A and C are no longer aligned. Remember that cubic lattice structures allow slippage to occur more easily than non-cubic lattices, so hcp metals are not as ductile as the fcc metals.

The table below shows the stable room temperature crystal structures for several elemental metals.

A nanometer (nm) equals 10^-9 meter or 10 Angstrom units.

Solidification

The crystallization of a large amount of material from a single point of nucleation results in a single crystal. In engineering materials, single crystals are produced only under carefully controlled conditions. The expense of producing single crystal materials is only justified for special applications, such as turbine engine blades, solar cells, and piezoelectric materials. Normally when a material begins to solidify, multiple crystals begin to grow in the liquid and a polycrystalline (more than one crystal) solid forms.

The moment a crystal begins to grow is know as nucleation and the point where it occurs is the nucleation point. At the solidification temperature, atoms of a liquid, such as melted metal, begin to bond together at the nucleation points and start to form crystals. The final sizes of the individual crystals depend on the number of nucleation points. The crystals increase in size by the progressive addition of atoms and grow until they impinge upon adjacent growing crystal.

a) Nucleation of crystals, b) crystal growth, c) irregular grains form as crystals grow together, d) grain boundaries as seen in a microscope.

In engineering materials, a crystal is usually referred to as a grain. A grain is merely a crystal without smooth faces because its growth was impeded by contact with another grain or a boundary surface. The interface formed between grains is called a grain boundary. The atoms between the grains (at the grain boundaries) have no crystalline structure and are said to be disordered.

Grains are sometimes large enough to be visible under an ordinary light microscope or even to the unaided eye. The spangles that are seen on newly galvanized metals are grains. Rapid cooling generally results in more nucleation points and smaller grains (a fine grain structure). Slow cooling generally results in larger grains which will have lower strength, hardness and ductility.

Dendrites
In metals, the crystals that form in the liquid during freezing generally follow a pattern consisting of a main branch with many appendages. A crystal with this morphology slightly resembles a pine tree and is called a dendrite, which means branching. The formation of dendrites occurs because crystals grow in defined planes due to the crystal lattice they create. The figure to the right shows how a cubic crystal can grow in a melt in three dimensions, which correspond to the six faces of the cube. For clarity of illustration, the adding of unit cells with continued solidification from the six faces is shown simply as lines. Secondary dendrite arms branch off the primary arm, and tertiary arms off the secondary arms and etcetera.

During freezing of a polycrystalline material, many dendritic crystals form and grow until they eventually become large enough to impinge upon each other. Eventually, the interdendriticspaces between the dendrite arms crystallize to yield a more regular crystal. The original dendritic pattern may not be apparent when examining the microstructure of a material. However, dendrites can often be seen in solidification voids that sometimes occur in castings or welds, as shown to the right..

Shrinkage
Most materials contract or shrink during solidification and cooling. Shrinkage is the result of:

• Contraction of the liquid as it cools prior to its solidification

• Contraction during phase change from a liquid to solid

• Contraction of the solid as it continues to cool to ambient temperature.

Shrinkage can sometimes cause cracking to occur in component as it solidifies. Since the coolest area of a volume of liquid is where it contacts a mold or die, solidification usually begins first at this surface. As the crystals grow inward, the material continues to shrink. If the solid surface is too rigid and will not deform to accommodate the internal shrinkage, the stresses can become high enough to exceed the tensile strength of the material and cause a crack to form. Shrinkage cavitation sometimes occurs because as a material solidifies inward, shrinkage occurred to such an extent that there is not enough atoms present to fill the available space and a void is left.

Anisotropy and Isotropy

In a single crystal, the physical and mechanical properties often differ with orientation. It can be seen from looking at our models of crystalline structure that atoms should be able to slip over one another or distort in relation to one another easier in some directions than others. When the properties of a material vary with different crystallographic orientations, the material is said to be anisotropic.

Alternately, when the properties of a material are the same in all directions, the material is said to be isotropic. For many polycrystalline materials the grain orientations are random before any working (deformation) of the material is done. Therefore, even if the individual grains are anisotropic, the property differences tend to average out and, overall, the material is isotropic. When a material is formed, the grains are usually distorted and elongated in one or more directions which makes the material anisotropic. Material forming will be discussed later but let’s continue discussing crystalline structure at the atomic level.