Coordination Number And Atomic Packing Factor example essay topic

The materials used in solar hot water systems must be carefully chosen to ensure that the unit will be efficient but also affordable. The efficiency of the conversion of sunlight energy to heat energy of the water depends on the materials of construction and the efficiency of heat transfer of the materials. Solar hot water systems use the processes of conduction to transfer the heat absorbed from the sun to the water and convection to move water through their structure. This assignment discusses the materials used in construction of solar hot water systems and their heat transfer properties. 2.0 Conduction Conduction is the process of transferring energy through a material from one point to another. Conductivity (k) is the rate at which the energy is transferred and its units are Watts per metre Kelvin or (W / mK).

The higher the rate of conductivity the faster energy is transferred through the material. Conduction can occur in two different ways in solids; the first is by crystal vibration waves (photons) where particles of high kinetic energy vibrate rapidly and bump into other particles to transfer energy from one point to another. The second way is by de localised electrons or free moving electrons which transfer energy throughout materials much better than atoms do, as their energy to mass ratio is much higher than that of atoms. This allows the electrons to travel much faster throughout a substance and transfer energy faster. For a material to be a good conductor of kinetic or electrical energy it requires both methods of conduction, which is found in metals and some other materials (i.e. graphite). The conductivity of a solar hot water system's materials are important ie. adequate insulation is required to prevent energy being lost to the unit's surroundings.

Materials for the pipes should not resist the transfer of thermal and kinetic energy being passed through the pipes to the water in the collector panel (shown in Fig 1. ). The conductivity (k) of a material can be described by the following equation. The contribution of ke increases with free electron concentration. Copper is an abundant, cheap metal with great thermal and electrical conductivity. It is strong, malleable and ductile making it an ideal material for water pipes.

Copper has a thermal conductivity (k) value of 398 W / mK, which is below silver's thermal conductivity of 428 W / mK however still much larger than other metals such as Aluminium (247 W / mK) or steel (60 W / mK). This makes copper useful in transferring kinetic energy as it means that is will not use energy whilst transferring water i.e. it is an efficient transfer medium. Resistivity is the inverse of conductivity and is a measure of how much energy is lost in transfer over a particular length. If a material has a high conductivity it will have a low resistivity like silver and copper.

Why does copper have such a high value of conductivity? Copper is a heavy metal with a density of 8.69 g / cm 3. This high density indicates that the atoms of copper are very closely packed in their crystalline structure allowing thermal energy to be conducted at a faster rate and more efficiently. Copper's crystal packing is called face centred cubic, which is one of the two densest ways of packing atoms in all of the possible packing schemes. Some other metals with the face centred cubic packing include Ag, Al, Au, Ca, Co, Ni, Pb and Pt. Fig 2. shows how atoms are structured in a unit cell of face centred cubic (fcc) structure.

There are a total of 4 atoms in fcc unit cell. A unit cell is defined as the smallest unit of a crystal lattice which can be multiplied to produce an entire lattice. There is half an atom at each face of a cube and an eighth of an atom at each of the eight corners. In total there are 4 atoms per unit cell. There is only one other packing scheme which allows atoms to be packed at the same ratio as it does in fcc and that is hexagonal close packed (hop). Fig 3. shows how atoms are structures in a unit cell of hop.

Fcc has a stacking pattern of A, B, C, A, B, C. The atoms in every fourth layer are in line whereas the hop stacking pattern is A, B, A, B and atoms in every third layer are in line. Although the stacking patterns for fcc and hop are slightly different the coordination numbers are both 12. Fig 4. and Fig 5. show how the orientation of layers for face centred cubic is slightly different to that of the hexagonal closest packed structure. A coordination number is based on the number of other spheres a single sphere contacts anywhere in the lattice or joins with strong bonds.

In fcc each sphere is in contact with six spheres in the same plane, three in the plane above and three in the plane of atoms below. In hop each sphere is in contact with the same number of spheres in each different plane as fcc is. Some elements, which are hexagonal close packed are Zinc, Magnesium and Titanium. Body Centred Cubic (bc c) is the most common packed structure adopted by metals.

Group 1, group 2 and some early transition metals are structured like body centred cubic (see Fig 6. ). The coordination number of bc c is 8. The atoms aren't as closely packed in bc c so the metals aren't as dense as fcc and hop metals. Bcc metals don't conduct as well as others so they would not be suited for use in piping of solar hot water systems. The coordination number plays a very important role in conductivity.

As you increase the number of contact points between the atoms you increase the number of pathways for energy to be transferred along to other atoms. Thus the rate of conductivity increases with number of contact points and the coordination number. Fig 7. Comparing the Conductivity of face centred cubic packed structures to body centred cubic. Metal (fcc) Conductivity W / mK Metal (bc c) Conductivity W / mK Silver 428 Iron 80 Copper 398 Tungsten 155 Aluminium 247 Molybdenum 142 Gold 315 Tantalum 54.4 As can be identified in Fig 7. metals which are face centred cubic have on average a higher conductivity than metals which are body centred cubic. The atomic packing factor is a measurement of the amount of space utilised by atoms in a unit cell (see Fig 8.

). The more atoms which are in a unit cell will indicate a larger atomic packing factor. Fig 8. Calculation for atomic packing factor. Different crystalline structures have different atomic packing factors and this is related to their coordination number. In Fig 9. there is a positive correlation between coordination number and atomic packing factor.

Both fcc and hop have 12 coordination and also have an atomic packing factor of 0.74 and because of this they have similar metal conductivities and densities. 0.74 is the highest atomic packing factor achievable and from this it is easy to see why copper is such a great conductor and why it is used in solar hot water systems in piping and collector panels. The density (ρ ) of crystal structure of a metal solid can be calculated when the following are known: Fig 10. Density Computations (below) From the formulae involved in this density calculation it is evident that the packing scheme has a direct impact upon the density of a metallic lattice or monatomic lattice. The density is the number of atoms in a unit cell relative to the volume of the unit cell.

Materials that have a larger atomic weight are more likely to form fcc or hop crystals and therefore have a higher density. 3.0 Convection Copper is used in the collector panel for the parallel collector pipes and other water pipes. In the collector pipes it is important that the material used has a high conductivity so that the largest quantity of kinetic energy possible can be transferred to the water from the sun. It is also important the metal has a fairly low specific heat capacity so that the metal doesn't require too much energy to heat up and therefore allow the majority amount of energy to heat up the cold water.

Copper has both high conductivity and a low specific heat capacity for a metal. Copper has a specific heat capacity of 386 J / kg K so it takes 386 joules of energy to raise 1 kg of copper through a temperature change of one degree or Kelvin. The energy used to heat the water comes from the sun. The light enters the panel as electromagnetic radiation and is absorbed by the collector pipes, which conducts the kinetic energy to the water. Cold water enters the parallel collector at the bottom (see Fig 11. ), as the water gains kinetic energy it displaces colder water above it and the water makes it's way through the pipes and comes out of the collector panel warm to be stored in the storage tank until use (see Fig 11. ).

The process called convection is responsible for the upward displacement of a warmer liquid or gas. Convection currents occur when the heat source is below the substance to be heated. Having the collector panel placed below the storage tank allows the use of convection to transfer water once heated to the storage tank instead of having to use a small water pump, which saves unnecessary use of energy. The use of convection currents to move water around the solar hot water system is called thermosiphon.

4.0 Surface absorption and the glass house effect To ensure that energy is absorbed the layer of material in the collector panel below the glass panel needs to be dark in colour. Being dark in colour allows the medium to heat up faster as it is able to absorb energy at a faster rate than other mediums. Being dark however means that the medium will also radiate at a higher rate. Emissivity is a unit of measurement between zero and one. It is a measurement of how easily a surface will emit or absorb radiation.

A dark matt surface has an emissivity (e) value of nearly one and a white shiny object close to zero. The electro magnetic radiation which is radiated by the panel is in the form of infrared radiation. Most of the infrared radiation which is re-emitted by the system is contained beneath the glass. The layer of glass on the collector panel prevents this infrared radiation escaping; this uses the green house effect to an advantage.

The Stephan-Boltzmann equation is applicable in this situation however most of the radiation emitted from the surface of the panel is infrared which stays below the glass and eventually ends up heating the water leading to a higher overall efficiency. 5.0 Conclusion Copper is a very common metal used in solar hot water systems as it has many favourable properties. These include a great conductivity due to its face centred cubic structure and de localised electrons, a high density, a fairly low specific heat capacity, abundance in availability, strength and cheap price relative to other metals. The crystalline structure that a metal may exist in, can affect many of its properties. The coordination number and atomic packing factor, both affect the conductivity of the lattice. Other important processes which need to be understood to be harnessed and used in appliances such as solar hot water systems are conduction and convection, the green house effect and surface absorption..