Electrical and Magnetic Properties of Materials

Properties of a material which determine its response to an electric field.
Materials are classified based on their electrical properties as conductors, semiconductors and insulators and newly super conductors.

1. School of Multidisciplinary Engineering Center for Materials Engineering Essentials of Materials Science and Engineering Instructor: Tesfaye Refera ( Associate Prof. PHD ) Electrical and Magnetic Properties of Materials By: Abenezer Mengistu

2. Introduction Engineering materials are important in everyday life because of their versatile structural properties. Other than these properties, they do play an important role because of their physical properties. Prime physical properties of materials include: electrical properties ; thermal properties; magnetic properties ; and optical properties .

3. ELECTRICAL PROPERTIES OF MATERIALS Properties of a material which determine its response to an electric field . Materials are classified based on their electrical properties as conductors , semiconductors and insulators and newly super conductors. Electrical conductivity of a material is defined in terms of ease of charge flow through it. Charge that flows comprised of either electrons, ions, charged holes, and their combinations. Ohm’s law relates the current and applied voltage : OHM’S LAW where is the resistance of the material.  

4. Material’s electric resistance is NOT an intrinsic-property, i.e . it depends on object geometry. Electrical resistivity , defined as follows, is an intrinsic property, inverse of which is conductivity . Electrical resistivity: Electrical conductivity: One way of classifying solid materials is according to the ease with which they conduct an electric current; within this classification scheme there are three groupings: conductors , semiconductors , and insulators.  

5. Energy band structures in solids (Band Theory) Electrons in Solids are arranged into shells and sub-shells in accordance with Pauli exclusion principle with distinct energy state/level. As the atoms of a bulk solid material come within close proximity of one another, electrons are acted upon, or perturbed , by the electrons and nuclei of adjacent atoms. This influence is such that each distinct atomic state may split into a series of closely spaced electron states in the solid, to form what is termed an electron energy band . The electrical properties of a solid material are a consequence of its electron band structure: that is, the arrangement of the outermost electron bands and the way in which they are filled with electrons.

6. For 12 atoms

7. The energy corresponding to the highest filled state at 0 K is called the Fermi energy, E f . Four types of band structures are possible at 0 K as shown in the following figure . Band structures (a) some metals, in particular those that have a single s valence electron (e.g., copper) and (b) are found in metals / conductors e.g (Mg) . Band structures (c) and (d) are distinguished by the size of energy band gap . Narrower energy band gap i.e. size < 2 eV , is found in semiconductors , while the broader energy band gap i.e. size > 4 eV, is found in insulators.

8. Conduction in terms of band and atomic bonding models O nly electrons with energies greater than the Fermi energy may be acted on and accelerated in the presence of an electric field. These are the electrons that participate in the conduction process, which are termed free electrons. Another charged electronic entity called a hole is found in semiconductors and insulators. Holes have energies less than E f and also participate in electronic conduction. As the ensuing discussion reveals, the electrical conductivity is a direct function of the numbers of free electrons and holes .

9. Metals For the metallic bonding model, it was assumed that all the valence electrons have freedom of motion and form an electron gas, which is uniformly distributed throughout the lattice of ion cores. Although these electrons are not locally bound to any particular atom, nevertheless, they must experience some excitation to become conducting electrons that are truly free. Generally, the energy provided by an electric field is sufficient to excite large numbers of electrons into these (Empty) conducting states . The reason why metals are highly conductive at low temperatures!

10. Insulators and Semiconductors For insulators and semiconductors, empty states adjacent to the top of the filled valence band are not available . Electrons become free only by taking the energy which is approximately equal to the band gap energy E g and be excited to the conduction band. T he distinction between semiconductors and insulators lies in the width of the band gap; for semiconductors it is narrow, whereas for insulating materials it is relatively wide.

11. For electrically insulating materials , interatomic bonding is ionic or strongly covalent . Thus, the valence electrons are tightly bound to or shared with the individual atoms. In other words , these electrons are highly localized and are not in any sense free to wander throughout the crystal . The bonding in semiconductors is covalent (or predominantly covalent ) and relatively weak , which means that the valence electrons are not as strongly bound to the atoms. Consequently, these electrons are more easily removed by thermal excitation than they are for insulators.

12. Electron Mobility When an electric field is applied, a force is brought to bear on the free electrons; as a consequence, they all experience an acceleration in a direction opposite to that of the field, by virtue of their negative charge . But there are scattering of electrons by imperfections in the crystal lattice, including impurity atoms, vacancies, interstitial atoms , dislocations, and even the thermal vibrations of the atoms themselves. Each scattering event causes an electron to lose kinetic energy and to change its direction of motion.

13. There is, however, some net electron motion in the direction opposite to the field, and this flow of charge is the electric current. The scattering phenomenon is manifested as a resistance to the passage of an electric current. Several parameters are used to describe the extent of this scattering; these include the drift velocity and the mobility of an electron . The drift velocity ν d represents the average electron velocity in the direction of the force imposed by the applied field. The constant of proportionality is called the electron mobility , which is an indication of the frequency of scattering events; its units are square meters per volt second.

14. Resistivity ( Mathiessens rule) Lattice vibrations and phonon scattering play a role in disrupting the mean free path of electrons. In addition, crystalline defects and impurity atom affect the conductivity. These scattering mechanisms act independently on one another. Thus the effective resistivity of metals can be represented as follows: (Mathiessens rule) With increase of temperature, thermal vibrations increase so the resistivity, and vice versa. In the same manner, with increase of either defects or impurities, resistivity increases. For pure metals, the resistivity approaches zero at absolute zero temperature.

15. Super Conductivity Some metals lose all resistivity abruptly and completely at some low temperatures, above 0 K. - phenomenon is called superconductivity , and the materials that exhibit it are called superconductors . The temperature at which the resistivity vanishes is called the critical transition temperature , T c . Many metals, solid-solution alloys, some ceramics and intermetallic compounds exhibit superconductivity. Ex.: Ti , V, Zn, W, Al, Hg, NbTi , Nb 3 Sn, MgB 2 , La- Sr -Cu oxide, YBa 2 Cu 3 O 7-x , carbon nanotubes, etc.

16. Semiconductivity Electrical properties of semiconductors are unique, in the sense that their electrical properties are extremely sensitive to even minute concentrations of impurities. Two kinds of semiconductors – intrinsic and extrinsic . For intrinsic semiconductors, their electrical behaviour is based on inherent electronic structure of the pure material. On the other hand, if the electrical properties are dominated by impurities, they are called extrinsic semiconductors. In semiconductors, the valence and conduction bands do not overlap as in metals, but they possess enough electrons in the valence band those can be promoted to the conduction band at a certain temperature.

17. Electronic and Ionic conduction Within most solid materials a current arises from the flow of electrons, which is termed electronic conduction . In addition, for ionic materials a net motion of charged ions is possible that produces a current; such is termed ionic conduction .

18. Electrical conduction in ionic ceramics Charge can also be conducted via ions - called ionic conduction. This may occur either in conjunction with or separately from electronic conduction. A mobility I may be associated with each of the ionic species as follows : (where n I and D I represent, respectively, the valence and diffusion coefficient of a particular ion; e, k, and T denote the same parameters as explained earlier) The diffusion constant is given by Einstein’s equation, , Where Z is the charge on the ion Then where, N I is the number of predominant mobile ions.  

19. Electrical conduction in ionic ceramics Several types of compounds show exceptionally high ionic conductivity. Such phases fall into three broad categories: halide and chalcogenides of silver and copper; oxides with β -alumina structure; and oxides of fluorite structure. Ex.: La 2 CuO 4 ( T c = 30 K), YBC compounds – yttrium doped perovskite structure, YBa 2 Cu 3 O 7 ( T c = 92 K). By properly engineering the point defects, it is possible to convert ceramics into semiconductors. Ex.: Indium tin oxide (ITO ).

20. Electrical conduction in polymers Polymers are, in general, insulators. They can be made conductors (Conductive Polymers) in two ways: (1) introducing an additive to the polymer to improve conductivity, and (2) creating polymers with inherent conductivity. (1) Adding ionic compound or Introducing conductive fillers such as carbon black. (2) Inherent conductivity by doping. Ex.: polyparaphynylene, polypyrole, polyaniline, acetal polymers .

21. A dielectric material is one that is electrically insulating ( nonmetallic ) and exhibits or may be made to exhibit an electric dipole structure; that is, there is a separation of positive and negative electrically charged entities on a molecular or atomic level. As a result of dipole interactions with electric fields, dielectric materials are used in capacitors. Polarization ( P ) is orientation of permanent or induced dipoles under externally applied electric field . At high enough frequencies, the dielectric will experience electrical breakdown initiated by the field-induced excitation of a number of electrons into the conduction band, and the insulator become a conductor. The magnitude of the electric field required to cause dielectric breakdown is called the dielectric strength or breakdown strength. Dielectric Behavior

22. Ferro-electricity Ferro-electricity is defined as the spontaneous alignment of electric dipoles by their mutual interaction in the absence of an applied electric field. It arises from the fact that the local field increases in proportion to the polarization. Thus, ferro -electric materials must possess permanent dipoles. Ex.: BaTiO 3 , Rochelle salt (NaKC 4 H 4 O 6 .4H 2 O), potassium dihydrogen phosphate (KH 2 PO 4 ), potassium niobate (KNbO 3 ).

23. Piezo-electricity ( pressure electricity ) electric polarization(i.e., an electric field or voltage) is induced in the ceramic crystal when a mechanical strain (dimensional change) is imposed on it. The inverse piezoelectric effect is also displayed by this group of materials; that is, a mechanical strain results from the imposition of an electrical field. Hence piezo-electric materials are useful as transducers – devices that convert mechanical stress into electrical energy and vice versa. Application for these materials includes microphones, ultrasonic generators, sonar detectors, and mechanical strain gauges. Ex: Barium titanate, lead titanate, lead zirconate, ammoinium dihydrogen phosphate

24. Piezo-electricity ( recent research focus ) T he application of piezoelectric nanostructures to energy harvesting has expanded rapidly in the last decade leading to a huge range of reported devices. Most studies focus on zinc oxide , as its nanostructures are formed relatively easily using low temperature methods. In addition, the nanostructures are crystallographically aligned and non-ferroelectric, and therefore do not require poling. However , more recently other well-known materials have been investigated for nanostructured energy harvesters including lead zirconate titanate (PZT) and barium titanate , with the potential for higher power outputs due to their higher piezoelectric coefficients.

25. MAGNETIC PROPERTIES Magnetic properties refer to the response of a material to an applied magnetic field. Magnetism is a phenomenon by which a material exerts either attractive or repulsive force on another. Basic source of magnetic force is movement of electrically charged particles. Thus magnetic behaviour of a material can be traced to the structure of atoms. Electrons in atoms have a planetary motion in that they go around the nucleus. This orbital motion and its own spin cause separate magnetic moments, which contribute to the magnetic behaviour of materials. Thus every material can respond to a magnetic field. However, the manner in which a material responds depend much on its atomic structure, and determines whether a material will be strongly or weakly magnetic.

26. Bohr Magneton Magnetic moment due to spin of an electron is known as Bohr magneton, M B Where, q – the charge on the electron, h – Planck’s constant, m e – mass of electron . Bohr magneton is the most fundamental magnetic moment .  

27. Why not all materials are magnets? As every material consists spinning electrons , each of them could be a magnet. Fortunately, not so! There are two reasons for it. First : according to Pauli exclusion rule, two electrons with same energy level must have opposite spins – thus so are their magnetic moments, which cancel out each other. Second : orbital moments of electrons also cancel out each other – thus no net magnetic moments if there is no unpaired electron(s). Some elements such as transition elements, lanthanides, and actinides have a net magnetic moment since some of their energy levels have an unpaired electron.

28. Magnetic Dipole A magnetic dipole may be thought of as small bar magnet composed of north and south poles. (instead of positive and negative charges in electric dipoles). Within a magnetic field, the force of field exerts a torque that tends to orient the dipoles with the filed. Magnetic forces are generated by moving electrically charged particles. These forces are in addition to any electrostatic forces that may already exist. It is convenient to think magnetic forces in terms of distributed field, which is represented by imaginary lines. These lines also indicate the direction of the force .

29. Magnetic Field Strength (H) If a magnetic field is generated by passing current through a coil of length and number of turns , then the magnetic field strength is given by: Magnetic flux density (induction) represents the magnitude of the internal field strength within a substance that is subjected to an field , is called the permeability ,   B H  

30. Magnetization ( ) of the a solid, is defined by the expression : (Analogy to Polarization in E field) Magnetic susceptibility( ) is given as: is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field.  

31. Types of Magnetisms A material is magnetically characterized based on the way it can be magnetized. This depends on the material’s magnetic susceptibility – its magnitude and sign. Dia-magnetism : very weak; exists ONLY in presence of an external field. Para-magnetism : slightly stronger; When an external field is applied dipoles line-up with the field, resulting in a positive magnetization. However, the dipoles do not interact. Ferro-magnetism : very strong; dipoles line-up permanently upon application of external field . Anti- ferro -magnetism : dipoles line-up, but in opposite directions, resulting in zero magnetization. Ferri -magnetism : similar to anti- ferro -magnetism, BUT dipoles of varying strength cannot cancel each other out .

32. Diamagnetism Diamagnetism is a fundamental property of all matter, although it is usually very weak. It is due to the non-cooperative behavior of orbiting electrons when exposed to an applied magnetic field. Diamagnetic substances are composed of atoms which have no net magnetic moments ( ie ., all the orbital shells are filled and there are no unpaired electrons). However, when exposed to a field, a negative magnetization is produced and thus the susceptibility is negative. If we plot M vs H, we see: 34

33. Para-magnetism This class of materials, some of the atoms or ions in the material have a net magnetic moment due to unpaired electrons in partially filled orbitals. One of the most important atoms with unpaired electrons is iron. However, the individual magnetic moments do not interact magnetically, and like diamagnetism, the magnetization is zero when the field is removed. In the presence of a field, there is now a partial alignment of the atomic magnetic moments in the direction of the field, resulting in a net positive magnetization and positive susceptibility. 35

34. Ferro-magnetism When you think of magnetic materials, you probably think of iron, nickel or magnetite. Unlike paramagnetic materials, the atomic moments in these materials exhibit very strong interactions. These interactions are produced by electronic exchange forces and result in a parallel or antiparallel alignment of atomic moments. Exchange forces are very large, equivalent to a field on the order of 1000 Tesla, or approximately a 100 million times the strength of the earth's field. 36

35. Magnetism Examples sign magnitude Dia - Small, Constant Organic materials, superconducting materials, metals like Bi Para + Small, Constant Alkali and transition metals, rare earth elements Ferro + Large, Function of H Transition metals (Fe, Ni, Co), rare earth elements ( Gd ) Anti-Ferro + Small, Constant Salts of transition elements ( MnO ) Ferri + Large, Function of H Ferrites (MnFe2O4, ZnFe2O4) and chromites Magnetism Examples sign magnitude Dia - Small, Constant Organic materials, superconducting materials, metals like Bi Para + Small, Constant Alkali and transition metals, rare earth elements Ferro + Large, Function of H Transition metals (Fe, Ni, Co), rare earth elements ( Gd ) Anti-Ferro + Small, Constant Salts of transition elements ( MnO ) Ferri + Large, Function of H Ferrites (MnFe2O4, ZnFe2O4) and chromites

36. Temperature E ffect With rising temperature, magnitude of the atom thermal vibrations increases. This may lead to more randomization of atomic magnetic moments as they are free to rotate. Usually, atomic thermal vibrations counteract forces between the adjacent atomic dipole moments, resulting in dipole misalignment up to some extent both in presence and absence of external field. As a consequence of it, saturation magnetization initially decreases gradually, then suddenly drops to zero at a temperature called Curie temperature , T c . The magnitude of the Curie temperature is dependent on the material: For cobalt – 1120 ˚C, for nickel – 335 ˚C, for iron – 768 ˚C, and for Fe 3 O 4 – 585 ˚C .

37. Domains Any ferromagnetic or ferrimagnetic material that is at a temperature below T c is composed of small-volume regions called Domains in which there is a mutual alignment in the same direction of all magnetic dipole moments giving rise to a permanent net magnetic moment per domain. Each of these domains is separated from the rest by domain boundaries / domain walls. Boundaries, also called Bolch walls , are narrow zones in which the direction of the magnetic moment gradually and continuously changes from that of one domain to that of the next. The domains are typically very small about 50μm or less, while the Bloch walls are about 100nm thick. For a polycrystalline specimen, each grain may have more than one microscopic sized domain .

38. When a magnetic field is imposed on the material, domains that are nearly lined up with the field grow at the expense of unaligned domains. This process continues until only the most favourably oriented domains remain . In order for the domains to grow, the Bloch walls must move, the external field provides the force required for this moment. When the domain growth is completed, a further increase in the magnetic field causes the domains to rotate and align parallel to the applied field. At this instant material reaches saturation magnetization and no further increase will take place on increasing the strength of the external field .

39. Magnetic H ysteresis Once magnetic saturation has been achieved, a decrease in the applied field back to zero results in a macroscopically permanent or residual magnetization, known as remanance , M r . The corresponding induction, B r , is called retentivity or remanent induction of the magnetic material. This effect of retardation by material is called hysteresis . The magnetic field strength needed to bring the induced magnetization to zero is termed as coercivity , H c . This must be applied anti-parallel to the original field. A further increase in the field in the opposite direction results in a maximum induction in the opposite direction. The field can once again be reversed, and the field-magnetization loop can be closed, this loop is known as hysteresis loop or B-H plot or M- H plot .

40. Hysteresis Loop

41. Application Of Magnetic property Electronic Motor and Generator An electric motor that uses electromagnets in the spinning stator to turn. There is an electrical 'slip-ring' on the stator that directs the power to a different magnet section of the stator to achieve rotation. 43 In real world there many operation of magnetic property . This property is use as two form as Electromagnetic field and magnetic field .

42. Magnetic storage Magnetic storage and magnetic recording are terms from engineering referring to the storage of data on a magnetized medium. Magnetic storage uses different patterns of magnetization in a magnetizable material to store data and is a form of non-volatile memory. The information is accessed using one or more read/write heads. 44

43. Magnetic bearing A magnetic bearing is a bearing which supports a load using magnetic levitation. Magnetic bearings support moving machinery without physical contact, for example, they can levitate a rotating shaft and permit relative motion with very low friction and no mechanical wear. 45 Magnetic properties of Materials

44. Magnetic separator Magnetic separator for particle size less than 3mm magnetite, pyrrhotite , ilmenite and other materials, wet magnetic separation, but also for coal, non-metallic minerals, building materials and other materials in addition to iron work . Available downstream, semi-reflux, reflux-type and other forms of magnetic separator, cylinder surface magnetic field strength can be produced according to the actual use of the special. 46

45. Magnetic property in Medical The Attraction of Magnet Therapy Some magnets are multipolar , with both the north and south poles facing the patient/desired body part, often with manufacturers touting that their circular or checkerboard or triangular pattern is in some way superior. But this also further limits how far the magnetic field reaches. Any effect inside the body must be limited to a few millimeters, only skin deep. 47

46. Magnetic Resonance Angiogram (MRA) A magnetic resonance angiogram (MRA) is a type of magnetic resonance imaging (MRI) scan that uses a magnetic field and pulses of radio wave energy to provide pictures of blood vessels inside the body. In many cases MRA can provide information that can't be obtained from an X-ray, ultrasound, or computed tomography (CT) scan. 48

47. An eddy current brake , like a conventional friction brake, is responsible for slowing an object, such as a train or a roller coaster. However, unlike electro-mechanical brakes, which apply mechanical pressure on two separate objects, eddy current brakes slow an object by creating eddy currents through electromagnetic induction which create resistance, and in turn either heat or electricity. 49 Eddy current brake

48. Thank you for your attention!!