Question

Establish a relationship between atomic structure, crystal structure, imperfections and mechanical properties of materials.

Answer 1

Atomic Structure

Atoms are composed of electrons, protons, and neutrons. Electrons and protons are negative and positive charged particles respectively. The magnitude of each charged particle in an atom is 1.6 × 10-19 Coulombs. The mass of the electron is negligible with respect to those of the proton and the neutron, which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10-27 kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A the number of neutrons. Neutrons and protons have very similar masses, roughly equal to 1 amu each. A neutral atom has the same number of electrons and protons, Z. A mol is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus, a mole of carbon has a mass of 12 grams.

The number of atoms in a mole is called the Avogadro number, Nav = 6.023 × 1023. Note that Nav = 1 gram/1 amu. Calculating n, the number of atoms per cm3 of a material of density δ (g/cm3 ): M Nn av δ = where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with a density δ = 1.8 g/cm3 , M =12, we get 6 × 1023 atoms/mol × 1.8 g/cm3 / 12 g/mol) = 9 × 1022 C atoms/cm3 . For a molecular solid like ice, one uses the molecular mass, M(H2O) = 18. With a density of 1 g/cm3 , one obtains n = 3.3 × 1022 H2O molecules/cm3 . Note that since the water molecule contains 3 atoms, this is equivalent to 9.9 × 1022 atoms/cm3 .

Most solids have atomic densities around 6 × 1022 atoms/cm3 . The cube root of that number gives the number of atoms per centimeter, about 39 million. The mean distance between atoms is the inverse of that, or 0.25 nm. This is an important number that gives the scale of atomic structures in solids.

Crystal structures

All metals, a major fraction of ceramics, and certain polymers acquire crystalline form when solidify, i.e. in solid state atoms self-organize to form crystals. Crystals possess a long-range order of atomic arrangement through repeated periodicity at regular intervals in three dimensions of space. When the solid is not crystalline, it is called amorphous. Examples of crystalline solids are metals, diamond and other precious stones, ice, graphite. Examples of amorphous solids are glass, amorphous carbon (a-C), amorphous Si, most plastics.

There is very large number of different crystal structures all having long-range atomic order; these vary from relatively simple structures for metals to exceedingly complex structures for ceramics and some polymers. To discuss crystalline structures it is useful to consider atoms as being hard spheres, with well-defined radii. In this scheme, the shortest distance between two like atoms is one diameter. In this context, use of terms lattice and unit cell will be handy. Lattice is used to represent a three-dimensional periodic array of points coinciding with atom positions. Unit cell is smallest repeatable entity that can be used to completely represent a crystal structure.

Thus it can be considered that a unit cell is the building block of the crystal structure and defines the crystal structure by virtue of its geometry and the atom positions within.

Important properties of the unit cells are

• The type of atoms and their radii R.

• Cell dimensions (Lattice spacing a, b and c) in terms of R and

• Angle between the axis α, β, γ • a*, b*, c* - lattice distances in reciprocal lattice , α*, β*, γ* - angle in reciprocal lattice

• n, number of atoms per unit cell. For an atom that is shared with m adjacent unit cells, we only count a fraction of the atom, 1/m.

• CN, the coordination number, which is the number of closest neighbors to which an atom is bonded.

• APF, the atomic packing factor, which is the fraction of the volume of the cell actually occupied by the hard spheres. APF = Sum of atomic volumes/Volume of cell.

Imperfections:

There is no such thing as a perfect crystal. Crystalline imperfections (or defects) are always present. In addition, impurity atoms are always present. Many of the properties of materials are sensitive to the presence of imperfections, and not necessarily in an adverse way.

So, what kind of imperfections exist in solids? One way to classify imperfections is by their dimensionality. Point defects exist by definition as a point (0 – dimensional) and include vacancies, interstitial atoms, and substitutional impurity atoms. These point defects are shown in the two figures below and will be discussed further in the reading.

Mechanical Properties of Material:

Strength

It is the ability of a material to resist the externally applied forces without breaking or yielding. The internal resistance offered by a part to an externally applied force is called stress.

Stiffness

Stiffness is the ability of a material to resist deformation under stress. The modulus of elasticity is the measure of stiffness.

Elasticity

It is the property of a material to regain its original shape after deformation when the external forces are removed. This property is desirable for materials used in tools and machines.

It may be noted that steel is more elastic than rubber.

Plasticity

Plasticity is a property of a material which retains the deformation produced under load permanently. This property of the material is necessary for forgings, in stamping images on coins and in ornamental work.

Ductility

Ductility is the property of a material enabling it to be drawn into a wire with the application of a tensile force. A ductile material must be both strong and plastic. The ductility is usually measured by the terms, percentage elongation and percentage reduction in area. The ductile material commonly used in engineering practice are mild steel, copper, aluminum, nickel, zinc, tin and lead.

Brittleness

It is the property of breaking of a material with little permanent distortion. Brittleness of a material is opposite to ductility property.

Brittle materials are withstanding compression load. When subjected to tensile loads snap off without giving any sensible elongation. Cast iron is a brittle material.

Malleability

It is a special case of ductility which permits materials to be rolled or hammered into thin sheets, making wire. A malleable material should be plastic but it is not essential to be so strong. The malleable materials commonly used in engineering practice are lead, soft steel, wrought iron, copper, and aluminum.

Toughness

Toughness is the property of a material to resist fracture due to high impact. It is measured by the amount of energy that a unit volume of the material has absorbed after being stressed up to the point of fracture.

This property is desirable in parts subjected to shock and impact loads. Normally the toughness of the material decreases when it is subjected heat.

Machinability

It is the property of a material which refers to a relative ease with which a material can be cut. The machinability of a material can be measured in a number of ways such as comparing the tool life for cutting different materials or thrust required to remove the material at some given rate or the energy required to remove a unit volume of the material. For example, that brass can be easily machined than steel. That means the machinability property of brass is high when compare to steel.

Resilience

It is the property of a material to absorb energy and to resist shock and impact loads. It is measured by the amount of energy absorbed per unit volume within elastic limit. This property is essential for designing the spring materials.

Creep

When a material is subjected to a constant stress at high temperature for a long period of time, it will undergo a slow and permanent deformation called creep. This property is considered in designing internal combustion engines, boilers, and turbines.

Fatigue

Fatigue is the repeated loading and unloading of metal due to direct load variation, eccentricity in a rotating shaft and differential thermal expansion of a structure. Even substantially below the yield point (elastic limit) of a metal or alloy this repeated loading can lead to failure, usually measured in terms of the number of cycles (repeated load applications) to failure.

Some studies have suggested that well over 80% of all mechanical failures of metal are attributable to fatigue.

This property is considered in designing shafts, connecting rods, springs, gears, etc.

Hardness

Hardness is a very important property of the metals and has a wide variety of meanings. It also embraces many different properties such as resistance to wear, scratching, deformation and machinability etc.

Also, it is the property of a metal, which gives it the ability to resist being permanent, deformed (bent, broken, or have its shape changed) when a load is applied. The greater the hardness of the metal, the greater resistance it has to deformation.