# Week 8 Notes.docx

7/28/2019 # Week 8 Notes.docx

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MECHANICAL BEHAVIOUR OF SOLIDS

Crystals are held together by interatomic or intermolecular bonds.Covalent bonding occurs in crystals like diamond. Ionic bonding

occurs in crystals like sodium chloride. Secondary bonding(hydrogen bonding, van der Waals forces) is primarily responsiblefor crystal formation in molecular crystals. All these bonds establishan equilibrium length and can be thought of as springs. The atomsand molecules of a crystal vibrate about their equilibrium positions

just as a mass on a spring can oscillate around its equilibriumposition.

If one were to try and stretch or compress the crystal, many bonds of the crystal would have to deformslightly at the same time. A strain ( ) is a percentage measure of how much a material deforms in aparticular direction due to a stress ( ) applied to it.

YOUNG'S MODULUS


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Youngs Modulus also depends on the direction of the stress. The more bonds that lie in the direction of the

stress, the higher Youngs Modulus will be in that direction. For example, applying stress in the [110]direction in the silicon lattice results in a higher Youngs Modulus than when stress is applied in the [100]


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direction because there are more bonds lying in the [110] direction that need to be stretched orcompressed.

The material property that describes the amount of strain that appears in the direction perpendicular tothe applied stress is Poissons ratio ( ):

Bonding and crystal structure determine the magnitude of Poissons ratio for a material. Crystal structurealso determines how the ratio varies with direction.

STRAIN ENERGY


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POINT DEFECTS

An impurity atom that occupies anormal lattice site is called asubstitutional impurity atom and animpurity atom found in the intersticebetween matrix atoms is called aninterstitial impurity atom. Whether aforeign atom will occupy asubstitutional or interstitial site usuallydepends largely on the size of the atomrelative to the size of the site.

The energy distribution in a solid(Maxwell-Boltzmann distribution)suggests that a number of individualatoms may acquire enough thermal

energy to be displaced from the equilibrium lattice site, leaving behind a vacancy .

( ) For most materials, the proportionality constant . is the change in energy due to the creation of a vacancy (

).

is the total number of lattice sites


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On cooling, the vacancy density is lowered by diffusion of vacancies to grain boundaries and dislocations,which act as sinks. However, on very rapid cooling (quenching) from a high temperature near the meltingpoint most of the vacancies do not have time to diffuse to sinks and are said to be frozen in. This gives aconsiderably greater non-equilibrium concentration of vacancies than that indicated by the thermalequilibrium value.

Some materials lattice type will change as a result of defects. For example, iron changes from an FCC to aBCC crystal at high temperatures or if enough impurities are introduced into it.

POINT DEFECTS IN IONIC SOLIDS

A Schottky defect is a vacancy where the leaving atom repositions itself on the surface of the crystal. Inionic solids, two vacancies are created, one by the anion and one by the cation, with the anion-cation pairmoving to the surface together. The vacancies left behind become partially charged holes in the lattice.Those holes will move in reaction to an applied electric field. Thus, Schottky defects affect a materialsconductivity.

( ) is the energy required to produce a Schottky defect is the total number of lattice sites


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LINE DEFECTS


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Impurities in the vicinity of dislocation cores tend to reduce the local distortion energy of the dislocationsand thus stabilize the system against slip. Substitutional impurities that are a mismatch in size to the hostprevent dislocations from migrating smoothly along a plane. Generally, the higher the concentration of impurities, the more effectively they block migration, the stronger the material.

If an interstitial impurity forms polar covalent bonds to the host atoms, the layers are prevented fromsliding past one another, even when only a small amount of impurity is present. For example, because ironforms polar covalent bonds with carbon, the strongest steels need to contain only about 1% of carbon bymass to substantially increase their strength.

Also, intersecting dislocations in a solid make it harder for them to move by increasing the length of thedislocations (which increases the strain energy). This is called strain hardening or work hardening and it

results in a mechanically stronger material which is less prone to plastic deformations, but is more brittle.


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SLIP SYSTEMS


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INTERFACIAL IMPERFECTIONS

Because of their finite size, all solid materials have free surfaces , which are interfaces between solids andgases. The arrangement of atoms at a free surface differs slightly from the interior structure because thesurface atoms do not have neighbouring atoms on one side. Usually the atoms near the surface have thesame crystal structure but a slightly larger lattice parameter than the interior atoms.

Surface energy ( ) quantifies the disruption of intermolecular bonds that occur when a surface is created.It is defined as the increase in energy per unit area of new surface formed. In crystalline solids, surfaceenergy depends on the crystallographic orientation of the surface those surfaces that are planes of densest atomic packing are also the planes of lowest surface energy. This is because atoms on thesesurfaces have fewer of their bonds broken or, equivalently, have a larger number of nearest neighbourswithin the plane of the surface. Surface energies can be reduced by the adsorption of foreign atoms ormolecules from the surrounding atmosphere. Impurity atom adsorption makes it almost impossible tomaintain atomically clean surfaces.

Grain boundaries separate regions of different crystallographic orientation. Solids with grain boundariesare referred to as polycrystalline, since the structure is composed of many crystals each with a differentcrystallographic orientation.

Grain boundaries have an interfacial energy because of the disruption in atomic periodicity in the vicinity of the boundary and the broken bonds that exist across the interface. The interfacial energy of grainboundaries is generally less than that of a free surface because the atoms in a grain boundary aresurrounded on all sides by other atoms and have only a few broken or distorted bonds.


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A phase is defined as a homogeneous, physically distinct and mechanically separable portion of thematerial with a given chemical composition and structure. Phases may be substitutional or interstitial solidsolutions, ordered alloys or compounds, amorphous substances or even pure elements.

Solids composed of more than one element may consist of a number of phases. For example, a de ntistsdrill consists of a mixture of small single crystals of tungsten carbide surrounded by a matrix of cobalt. Here

the cobalt forms a continuous phase. Polyphase materials such as the dentists drill are generally referredto as composite materials .

Boundaries between two phases of different chemical composition and different crystal structure aresimilar to grain boundaries, while boundaries between different phases with similar crystal structures andcrystallographic orientations may be analogous to low-angle grain boundaries in both energy and structure.

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