(i) outline the methods used by the Braggs to determine crystal structure

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1 9.4.4 Investigations into the electrical properties of particular metals at different temperatures led to the identification of superconductivity and the exploration of possible applications (i) outline the methods used by the Braggs to determine crystal structure Year 11 When two different sources of waves are producing waves that are passing through each other the two waves will interfere with each other and produce constructive interference and destructive interference. The diagram above shows how two slits act as separate sources of waves and how these waves interfere with each other constructively and destructively. This is a picture that shows constructive and destructive interference of water waves produced from two separate sources CONSTRUCTIVE INTERFERENCE DESTRUCTIVE INTERFERENCE Braggs Experiment Outline Braggs used x-rays and directed them through A crystalline material. X-rays were used since they have a very short wavelength and comparable to the interatomic spacing in which they were investigating. The individual atoms acted as a separate source of the x-rays as they were scattered of them. As the x-rays travelled away from the crystalline solid they interacted with each other and produced constructive and destructive interference. A photographic plate was placed in the path of these scattered x-rays. The film was developed and the resulting wave interference pattern analysed In this analysis the angle in which constructive interference occurs (ie. a bright spot) was determined. The wavelength of the x-rays was known. The spacing between the atoms could then be determined using n 2d sin see below With more complex analysis of diffraction spacing af all atoms in the material could be determined and an overall picture of the arrangement of atoms could be deduced. n 2d sin

2 Ex. X-rays with a wavelength of 5 angstroms ( 0.5 nm) were incidented upon a crystalline structure and the first order of consructive interference (first bright spot) occurred at angle of 30 degrees. Calculate the spacing between the two atoms that caused this constructive interference. n=1, 0.5 nm = 0.5 x 10-9 m, 30 0, d=? n 2d sin d= 5 x m A photograph showing the pattern formed from x-ray diffraction. Each spot represents constructive interference Today, detectors can instantly measure the angles at which constructive interference occurs (ii) identify that metals possess a crystal lattice structure X-ray diffraction has been used to investigate how the atoms are arranged in metals. Metals have been found to possess a crystal lattice structure. This means that the atoms are arraged in a pattern that is:- 3 dimensional Repeating Ordered The diagram to the right shows some examples of the crystal lattice structure that metals have. Examples of different crystalline structures found in metals

3 (iii) describe conduction in metals as a free movement of electrons unimpeded by the lattice Metals have a large number of free electrons (charge carriers) that are loosely bound to their nucleus and thus can drift through the crystal lattice. This gives metals good electrical conductivity (iv) identify that resistance in metals is increased by the presence of impurities and scattering of electrons by lattice vibrations The electrons flowing through a lattice are impeded in two main ways:- Electrons colliding with phonons (packets of lattice vibrational energy) produced by the vibrating lattice. Electrons colliding with imperfections in the crystal lattice such as impurities or spaces in the lattice where an atom should be. Below are examples of impurities/imperfections that may occur in a crystal lattice of a metal.

4 Heat is generated Each time there is a collision between an electron & either an imperfection or a lattice vibration (phonon) the electron loses some kinetic energy. This energy is transformed into increased vibrational energy of the crystal lattice Increased Vibrational energy = Heat The substance gets hotter. This produces more vibration in the lattice (more phonons) An increase lattice vibration (increase in the number of phonons) means an increases in the number of collisions and an increase in resistance This explains why an increase in temperature of metals increases the resistance and A current flowing through a conductor heats the conductor What about resistance at low temperatures??? If we decrease the temperature we would expect the electrical resistance of a metallic conductor to decrease to a low but non-zero value as the temperature approaches absolute zero. However, we would still expect a residual resistance even near absolute zero due to crystal lattice imperfections. The fact is, however, the electrical resistance of some metals disappears completely at sufficiently low temperatures (v) describe the occurrence in superconductors below their critical temperature of a population of electron pairs unaffected by electrical resistance Materials that can exhibit superconductivity have crystal lattices :- that have impurities/imperfections that are vibrating & producing phonons. Packets (quanta) of vibrational energy that exhibit normal conductivity at high temp. s HOWEVER Superconductors will allow the transmission of electrons unimpeded and with no energy loss when bougfht to a temperature equal to or below their critical temperature, which is above absolute zero = 0K They do this by having there electrons pair up. These electron pairs interact with the crystal lattice. This interaction allows these pairs to move through the crystal lattice with zero resistance

5 (i) process information to identify some of the metals, metal alloys and compounds that have been identified as exhibiting the property of superconductivity and their critical temperatures (vi) discuss the BCS theory BCS Theory to explain Low Temperature Superconductivity This theory was thought up by three scientists working together (John Bardeen, Leon Cooper, and John Schrieffer BCS theory) in The theory states that the supercurrent in a superconductor is carried by many millions of bound electron pairs, called Cooper pairs.

6 These pairs form when one electron passing between adjacent positive ions distorts the lattice slightly due to electrostatic attraction. This distortion is associated with the release of phonons. These phonons create a trough of increased positive charge density around the electron. Before the electron passes by and before the lattice springs back to its normal position, a second electron is drawn into the trough. It is through this process that two electrons, which should repel one another, link up. The forces exerted by the phonons overcome the electrons' natural repulsion By pairing off two by two in cooper pairs the electrons pass through the superconductor unobstructed. WHEN, and only when, THE TEMPERATURE OF THE SUPERCONDUCTOR IS EQUAL TO OR BELOW THE CRITICAL TEMPERATURE (T C ). Phonons When one of the electrons that makes up a Cooper pair, passes close to an ion in the crystal lattice, the attraction between the negative electron and the positive ion cause a vibration to pass from ion to ion until the other electron of the pair absorbs the vibration. The net effect is that the electron has emitted a phonon and the other electron has absorbed the phonon. It is this exchange that keeps the Cooper pairs together. Discuss for and/against FOR The BCS theory is very useful in explaining low temperature superconductivity HOWEVER AGAINST The BCS theory cannot, in it s current form, be used to explain high temperature superconductivity (vii) discuss the advantages of using superconductors and identify limitations to their use Advantages of Superconductors Low energy wastage Low heat build up Faster transmission of information via electricity (faster switching)

7 Limitations of Superconductors In most superconductors temperatures need to be kept far too low for practical purposes. New high temp. superconductors are :- brittle difficult to make into wires difficult to manufacture chemically unstable in some environments (ii)perform an investigation to demonstrate magnetic levitation The Meissner effect is an expulsion of a magnetic field from a superconductor during its transition to the superconducting state. Eddy currents are induced in the surface of the superconductor. These induced currents set up a magnetic field to oppose any field that would otherwise penetrate the surface (iii) gather and process information to describe how superconductors and the effects of magnetic fields have been applied to develop a maglev train MAGLEV Train Propulsion and Levitation is achieved by the attractive and repulsive forces of magnetism. There are superconducting magnets on the carriage. These electromagnets are made from a superconductor and the temperature is kept under the critical temperature. The superconductor allows huge currents and hence huge magnetic fields to be achieved by these electromagnets on the train. The movement of these superconducting magnets as the train moves along the track induces a current in levitation coils in the track. These coils will then become electromagnets themselves, repelling the train upwards. This counteracts the downward force of gravity or weight force & thus the carriage will levitate. Other coils in the track are responsible for propelling the carriage along. Superconductors are essential to produce the huge magnetic fields required for levitating a train.

8 MAGLEV Track Propulsion Forces on a MAGLEV train Levitation (iv) process information to discuss possible applications of superconductivity and the effects of those applications on computers, generators and motors and transmission of electricity through power grids Computers Further reduction in size of Si chips is limited to heat build up from the resistance in connections to the chip. Conventional connections to chip are slower in conducting information (several magnitudes) than superconductors Using superconductors will allow more densely packed chips and higher processing speeds (250x) faster & smaller computers Generators & Motors Motors & Generators using superconductor magnets would not require an iron core The would become smaller & lighter Requiring lower energy input from fossil fuels Cheaper for consumers & better for the environment (greenhouse gases) Transmission of electricity through power grids Traditionally electricity is transmitted at high voltages and through thick copper wires to minimise energy waste in the form of heat from resistance. Using superconductors to transmit power there would not be any resistance and hence lower voltages, larger currents and thinner wires could be used. This would reduce cost to consumers.