Solid State Structure

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Solid State Structure

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Solid State Structure

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

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

Amorphous SolidsA solid substance with its atoms held apart at equilibrium spacing, but with no long-range periodicity inatom location in its structure is an amorphous solid. Examples of amorphous solids are glass and sometypes of plastic. They are sometimes described as supercooled liquids because their molecules arearranged in a random manner some what as in the liquid state. For example, glass is commonly madefrom silicon dioxide or quartz sand, which has a crystalline structure. When the sand is melted and the

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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, butrather soften gradually when they are heated. The physical properties of amorphous solids are identical inall directions along any axis so they are said to have isotropic properties, which will be discussed in moredetail later

.

Crystalline SolidsMore 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. Acrystal is a regular, repeating arrangement of atoms or molecules. The majority of solids, including allmetals, adopt a crystalline arrangement because the amount of stabilization achieved by anchoringinteractions between neighboring particles is at its greatest when the particles adopt regular (rather thanrandom) arrangements. In the crystalline arrangement, the particles pack efficiently together to minimizethe total intermolecular energy.

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

Courtesy: IBM Research, Almaden Research Center.

Crystal StructureCrystal structures may be conveniently specified by describing the arrangement within the solid of a smallrepresentative group of atoms or molecules, called the ‘unit cell.’ By multiplying identical unit cells inthree directions, the location of all the particles in the crystal is determined. In nature, 14 different typesof crystal structures or lattices are found. The simplest crystalline unit cell to picture is the cubic, wherethe 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 witheither an extra atom centered in the cube or centered in each face of the cube. Most metals form bcc, fccor Hexagonal Close Packed (hpc) structures; however, the structure can change depending ontemperature. 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 iseasier for planes of atoms to slide by each other if those planes are closely packed. Therefore, latticestructures with closely packed planes allow more plastic deformation than those that are not closelypacked. 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 cubiccrystal structure will exhibit more ductility (deform more readily under load before breaking) than abody-centered cubic structure. The bcc lattice, although cubic, is not closely packed and forms strongmetals. Alpha-iron and tungsten have the bcc form. The fcc lattice is both cubic and closely packed andforms more ductile materials. Gamma-iron, silver, gold, and lead have fcc structures. Finally, HCP latticesare 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 latticesare found in nature. However most metals and many other solids have unit cell structures described asbody center cubic (bcc), face centered cubic (fcc) or Hexagonal Close Packed (hcp). Since these structuresare most common, they will be discussed in more detail.

Body-Centered Cubic (BCC) StructureThe 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 ofanother cube so the corner atoms are shared among eight unit cells. It is said to have a coordinationnumber of 8. The bcc unit cell consists of a net total of two atoms; one in the center and eight eighthsfrom corners atoms as shown in the middle image below (middle image below). The image belowhighlights 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 lowertemperatures. 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 lessmalleable than close-packed metals such as gold. When the metal is deformed, the planes of atoms mustslip over each other, and this is more difficult in the bcc structure. It should be noted that there are otherimportant mechanisms for hardening materials, such as introducing impurities or defects which makeslipping more difficult. These hardening mechanisms will be discussed latter.

Face Centered Cubic (FCC) StructureThe 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 areshared among eight unit cells. Additionally, each of its six face centered atoms is shared with an adjacentatom. Since 12 of its atoms are shared, it is said to have a coordination number of 12. The fcc unit cellconsists of a net total of four atoms; eight eighths from corners atoms and six halves of the face atoms asshown 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 bccstructure. The atoms from one layer nest themselves in the empty space between the atoms of theadjacent layer. To picture packing arrangement, imagine a box filled with a layer of balls that are alignedin columns and rows. When a few additional balls are tossed in the box, they will not balance directly ontop of the balls in the first layer but instead will come to rest in the pocket created between four balls ofthe bottom layer. As more balls are added they will pack together to fill up all the pockets. The packingfactor (the volume of atoms in a cell per the total volume of a cell) is 0.74 for fcc crystals. Some of themetals that have the fcc structure include aluminum, copper, gold, iridium, lead, nickel, platinum andsilver.

Hexagonal Close Packed (HPC) StructureAnother common close packed structure is the hexagonal close pack. The hexagonal structure ofalternating layers is shifted so its atoms are aligned to the gaps of the preceding layer. The atoms fromone layer nest themselves in the empty space between the atoms of the adjacent layer just like in the fccstructure. However, instead of being a cubic structure, the pattern is hexagonal. (See image below.) Thedifference 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 thatarrange 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. Notethat there are six of these "grooves" surrounding each atom in the hexagonal plane, but only three ofthem 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 thecorners of the top and bottom layers contribute 1/6 atom to the unit cell, the two atoms in the center ofthe 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 alarger lattice.

The coordination number of the atoms in this structure is 12. There are six nearest neighbors in the sameclose 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 someexamples include beryllium, cadmium, magnesium, titanium, zinc and zirconium.

Similarities and Difference Between theFCC and HCP Structure

The face centered cubic and hexagonal close packed structures both have a packing factor of 0.74, consistof closely packed planes of atoms, and have a coordination number of 12. The difference between the fccand hcp is the stacking sequence. The hcp layers cycle among the two equivalent shifted positionswhereas the fcc layers cycle between three positions. As can be seen in the image, the hcp structurecontains only two types of planes with an alternating ABAB arrangement. Notice how the atoms of thethird plane are in exactly the same position as the atoms in the first plane. However, the fcc structurecontains three types of planes with a ABCABC arrangement. Notice how the atoms in rows A and C are nolonger aligned. Remember that cubic lattice structures allow slippage to occur more easily than non-cubiclattices, 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.

Metal Crystal Structure Atomic Radius (nm)

Aluminum FCC 0.1431

Cadmium HCP 0.1490

Chromium BCC 0.1249

Cobalt HCP 0.1253





Copper FCC 0.1278

Gold FCC 0.1442

Iron (Alpha) BCC 0.1241

Lead FCC 0.1750

Magnesium HCP 0.1599

Molybdenum BCC 0.1363

Nickel FCC 0.1246

Platinum FCC 0.1387

Silver FCC 0.1445

Tantalum BCC 0.1430

Titanium (Alpha) HCP 0.1445

Tungsten BCC 0.1371

Zinc HCP 0.1332

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 singlecrystal. 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 turbineengine 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 nucleationpoint. At the solidification temperature, atoms of a liquid, such as melted metal, begin to bond together atthe nucleation points and start to form crystals. The final sizes of the individual crystals depend on thenumber of nucleation points. The crystals increase in size by the progressive addition of atoms and growuntil they impinge upon adjacent growing crystal.





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

In engineering materials, a crystal is usually referred to as a grain. A grain is merely a crystal withoutsmooth faces because its growth was impeded by contact with another grain or a boundary surface. Theinterface formed between grains is called a grain boundary. The atoms between the grains (at the grainboundaries) 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 theunaided eye. The spangles that are seen on newly galvanized metals are grains. Rapid cooling generallyresults in more nucleation points and smaller grains (a fine grain structure). Slow cooling generallyresults in larger grains which will have lower strength, hardness and ductility.

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

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

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





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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 ambienttemperature.

Shrinkage can sometimes cause cracking to occur in component as itsolidifies. Since the coolest area of a volume of liquid is where itcontacts a mold or die, solidification usually begins first at this surface.As the crystals grow inward, the material continues to shrink. If thesolid surface is too rigid and will not deform to accommodate theinternal shrinkage, the stresses can become high enough to exceed the tensile strength of the materialand 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 spaceand a void is left.

Anisotropy and Isotropy

In a single crystal, the physical and mechanical properties often differ with orientation. It can be seenfrom looking at our models of crystalline structure that atoms should be able to slip over one another ordistort in relation to one another easier in some directions than others. When the properties of a materialvary 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 beisotropic. 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, theproperty 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 materialanisotropic. Material forming will be discussed later but let’s continue discussing crystalline structure atthe atomic level.





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Solid State Structure

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