# Unit 1: Section 3 Designer Materials

Summary of chapter 4 and 5 from Advancing Physics AS

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• Created by: R_Hall
• Created on: 05-04-13 15:10

## Hooke's Law

• Hooke's Law (named after Robert Hooke) says that extension is proportional to force
• The extension or compression of a spring is proportional to the force applied- so Hooke's Law applies
• On a graph of load against extension, there is a straight line region, followed by a curve. The point where the line starts to curve marks the elastic material of the material. If load is increased past the elastic limit, the material will be permanently stretched.
• A stretch can be elastic or plastic-
• 1. Elastic deformation- the material returns to original shape after forces are removed. Happens for as long as Hooke's law is obeyed
•  When put under tension, the atoms within an elastic material are pulled apart. They can move small distances relative to their equilibrium positions without changing position within the material, Once load is removed, the atoms return to equilibrium position
• 2. Plastic deformation- the material is permanently stretched. Happens after elastic limit is exceeded
• Some atoms move in relation to one another. When load is removed, the atoms don't return to original positions
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## Stress, Strain and the Young Modulus

• If forces stretch a material- they are tensile. If they squash the material- they are compressive
• Stress (Pa or Nm-2) is force applied/ cross sectional area
• Strain is extension/ original length
• A stress causes a strain
• As a greater tensile force is applied to material, the stress increases. The atoms start to get pulled apart. Eventually, the atoms separate completely and the material breaks. The stress at which this occurs is the fracture stress
• Up to a point called the limit of proportionality, stress and strain are proportional. Stress/ Strain gives the Young Modulus (Nm-2 or Pa) of a material. It is used by engineers to make sure their materials can withstand sufficient forces
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## Structures of Solids

• Metals- form a crystalline lattice. Electrons which have left the metal atoms form a 'sea' of free electrons, leaving a lattice of +ve ions. The free electrons make metals good conductors of heat and electricity.
• Electrostatic attractions forms a metallic bond- makes metals stiff. The strongly bonded lattice makes it tough. The ions are free to move when force is applied- ductile
• Ceramics (eg. pottery, brick or glass)- Atoms arranged crystalline or polycrystalline (many regions of crystalline structure). Some ceramics (eg. glass) are amorphous- no overall pattern
• Atoms arranged in a ionically or covalently bonded  giant, rigid structure. Strong bonds make ceramics stiff, while the rigid structure makes them brittle
• Polymers- molecular chain of single monomers covalently bonded together. The monomers are hard to separate-> strong
• Polymer chains can unfold and rotate -> flexible. The strength and number of bond between chains varies. Lots of strong cross-linking bonds means high rigidity
• Scanning Electron Microscopes (SEM) and Atomic Force Microscopes (AFM) are used to estimate and measure sizes of atoms. Only show the surface (need X-ray crystallography to see beneath).
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## Mechanical Properties of Solids

• Brittle- brittle materials (eg. ceramics) break suddenly without deforming plastically
• Ductile- ductile materials (eg. copper) can be easily drawn into wires, while keeping their strength
• Malleable- malleable materials (eg. gold and brass) can change shape easily through hammering and rolling, but won't necessarily keep their strength
• Hard- hard materials (eg. hardened steel and diamond) are resistant to cutting, indentation and abrasion
• Stiff- stiff materials have a high resistance to bending and stretching
• Tough- tough materials (eg. polymers) are difficult to break, as they absorb a lot of energy before breaking
• Stress-strain graphs for ductile materials curve
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## Electrical Properties of Solids

• Resistance depends on- Length (longer- harder to make a current flow), Area (greater area- easier for electrons to pass) and Resistivity
• Resistivity depends on the material- the structure may make it easy or difficult for a charge to flow. Defined as the resistance of a 1 m length with a 1 m2 CSA (measured in Ωm, ohm-metres)
• Conductors have really small resistivity's
• Conductivity is the conductance of a 1 m length with a 1 m2 CSA (measured in Sm-1, siemens per metre)
• Charge carrier density- how many charge carriers there will be per unit volume of material
• In metals, the charge carriers are the free electrons- the charge carrier density is high. Increasing the temperature decreases the conductivity slightly- as the lattice vibrates more, increasing the scattering of electrons from the lattice, so they are less free to move
• In semi-conductors, the charge carriers are the free electrons- the density is low (lower conductivity). As temperature increases, more electrons are free to conduct. Increase in temperature= increase in conductivity
• Insulators have no charge carriers
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