Conductivity of Metals

8 Key excerpts on "Conductivity of Metals"

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  Materials NQF3 SB

  TVET FIRST

  • Sparrow Consulting(Author)
  • 2013(Publication Date)
  • Macmillan

    (Publisher)

  Unlike other substances, the atoms that make up metals are held together by metallic bonds. This means that the outer electrons flow easily from one atom to another, which makes metal a good conductor. Because metals are solids, their atoms lie fixed in a regular crystal lattice structure . However, not all metals behave in the same way because their behaviour depends on the strength of the bonds between the atoms of the metal and the crystalline structure. Electrical conductivity Electrical conductivity is the ability of a material to conduct an electric current. This means that when an electrical potential difference is applied to a material, its moveable charges flow through the material, creating an electric current. Materials such as glass or wood have low electrical conductivity. These materials have a high resistance to the flow of electrons, and are called insulators. Silver, copper and gold are good examples of high-conductivity metals. Did you know? Water is a conductive material. Ocean water is more conductive than drinking water because the salt makes it easier for electrical charges to flow through the water. 49 Module 2: Describe, select and use metals for construction purposes Heat conductivity Heat or thermal conduction occurs when heat energy is transferred through a material. Heat will be transferred until all of the material has reached the same temperature. This is called thermal equilibrium. Malleability Malleability is the ability of metal to be hammered or shaped into thin sheets without breaking. The easier it is to hammer a metal into a thin sheet, the more malleable it is. Ductility Ductility is the ability of metal to be drawn out into a wire. The easier it is to draw a metal out into a wire, the more ductile it is. It is important to note that ductility and malleability do not always correlate with each other although they are very similar. Gold is both ductile and malleable, but lead is only malleable.

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  Engineering Materials Science

  • Milton Ohring(Author)
  • 1995(Publication Date)
  • Academic Press

    (Publisher)

  Semiconductor Devices: Physics and Technology , Wiley, New York (1985). reprinted by permission. AT&T;

  Descriptions of electrical conductivity are concerned with the magnitude and attributes of the materials constants in Eq. 11-4 . Corollary issues revolve about how n and μ vary as a function of temperature, composition, defect structure, and electric field. An alternative complementary approach to understanding electrical properties is via electron band diagram considerations. We adopt this approach at times but also make extensive use of charged carrier dynamics to provide a balanced portrait of electrical conduction and related phenomena.

  In addition to high resistivity, some insulators possess important dielectric properties that are exploited for use in capacitors. Electrons and ionic charge in dielectrics tend to oscillate in concert with the applied ac electric field frequency; this is distinct from the migration and net displacement carriers undergo in a dc field. The implications of this in assorted applications are addressed later.

  11.2 ELECTRONS IN METALS

  11.2.1 Free Electrons Revisited

  The description of electronic structure in Chapter 2 suggests that metals contain a typical distribution of atomic core levels topped by a densely packed continuum of conduction or free electron levels. Their energies were derived assuming the electrons were confined to a well from which they could never escape. A more realistic picture of a metal was suggested in Section 2.4.3.2 . Instead of walls extending to infinite energy there is now a finite well that confines the free electrons as shown in Fig. 11-4 . The energy possessed by electrons in the highest occupied level is known as the Fermi energy , E F . But electrons at energy E F still have to acquire the

  work function energy, q

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  Materials Science and Engineering

  An Introduction

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  Will the electri- cal conductivity of the noncrystalline metal be greater or less than its crystalline counterpart? Why? [The answer may be found in all digital versions of the text and/or at www.wiley.com/college/callister (Student Companion Site).] 18.8 Electrical Resistivity of Metals • 657 metals and alloys.) Again, metals have high conductivities because of the large numbers of free electrons that have been excited into empty states above the Fermi energy. Thus n has a large value in the conductivity expression, Equation 18.8. At this point it is convenient to discuss conduction in metals in terms of the resistiv- ity, the reciprocal of conductivity; the reason for this switch should become apparent in the ensuing discussion. Because crystalline defects serve as scattering centers for conduction electrons in metals, increasing their number raises the resistivity (or lowers the conductivity). The concentration of these imperfections depends on temperature, composition, and the de- gree of cold work of a metal specimen. In fact, it has been observed experimentally that the total resistivity of a metal is the sum of the contributions from thermal vibrations, impurities, and plastic deformation—that is, the scattering mechanisms act indepen- dently of one another. This may be represented in mathematical form as follows:  total =  t +  i +  d (18.9) in which  t ,  i , and  d represent the individual thermal, impurity, and deformation resistiv- ity contributions, respectively. Equation 18.9 is sometimes known as Matthiessen’s rule. The influence of temperature and impurity content on total resistivity is demonstrated in Figure 18.8, a plot of resistivity versus temperature for high-purity copper and several copper–nickel alloys. For all four metals, resistivity increases with increasing tempera- ture.

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  Materials Science for Engineers

  • J.C. Anderson, Keith D. Leaver, Rees D. Rawlings, Patrick S. Leevers(Authors)
  • 2004(Publication Date)
  • CRC Press

    (Publisher)

  part III Electromagnetic properties and applications Electrical conduction in metals 14.1 Introduction: role of the valence electrons Many readers may have learned quite a lot about electricity and electric currents without knowing just why it is that some materials will conduct readily while others are insulators, although these can acquire a static electric charge. In the foregoing chapters we have seen how all matter is built up of charged constituents, both positive and negative, and obviously conduction of electricity must be associated with motion of those charges. Because the protons in the nucleus of an atom are firmly fixed they can only move when the whole atom moves. Now when electrical conduction occurs in metals, we know that no matter is transported, so that the motion of protons cannot be involved and the loosely bound electrons must be responsible for the passage of current. In contrast, we saw in Chapter 10 that electrolytic conduction involves the movement of both positive and negative ions. For the moment we confine ourselves to metals, and remember that, when discussing metallic bonding in Section 5.6, we pointed out that only the valence electrons could be readily removed to take part in bonding. Similarly, we would expect only the valence electrons to be able to take part in conduction. Thus the number of conducting electrons per atom is determined by the atomic structure. Looking at Table 14.1 we can see that copper, silver and gold have only one such electron per atom, zinc and cad-mium have two, while aluminium has three. The Group I metals sodium and potassium are far too reactive to be of much engineering importance. If there are more than three valence electrons both the character of the bonding and the electrical properties change completely, except in the case of the heavy metals such as Sn and Pb. These two are included in the table, because when they are alloyed together they are used as solder.

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  Introduction to Engineering Materials

  • George Murray, Charles V. White, Wolfgang Weise(Authors)
  • 2007(Publication Date)
  • CRC Press

    (Publisher)

  309 10 Electrical Properties of Materials 10.1 INTRODUCTION The electron conductivity of solid materials gives an almost unambiguous way to classify them. Simply put, on the basis of electrical conductivity, materials are either insulators, semiconductors, conductors, or superconductors. Superconduc-tors are a special class of materials that exhibit zero resistance below a certain temperature. They will not be considered here. The conductivity of all of the more common and widely used materials is shown in Figure 10.1. The range of conductivities is quite large. Where we draw the lines for these materials appears to be somewhat arbitrary, but we can define these three categories fairly precisely in terms of the number of electrons available for conduction. This number can be computed using the energy band structure for the valence electrons, a subject covered in the following section. Insulators and most polymers have a low conductivity because of their strong covalent bonds and the absence of free electrons, but in some polymers a conducting powder is mixed with the polymer to form a conducting composite. In a few others of the so-called conducting polymers, there exist some free electrons within the polymer structure, creating conductivity on the order of that found in crystalline semiconductors, and in some conducting polymers the conductivity approaches that of metals. There is a tremendously large variation in the conductivity of solids, being about a factor of 10 25 from conductors to insulators. Ohm’s law can be used to express conductivity and its reciprocal, resistivity, which are not functions of specimen dimensions, and the conductance and resis-tance, which are functions of specimen dimensions. Resistance is related to resistivity by: R = ρ l /A where R = resistance ρ = resistivity (usually expressed in Ω · m) l = specimen length A = specimen area and in terms of conductivity, σ , σ = l /RA units are ( Ω · m) − 1

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  Electronic, Magnetic, and Optical Materials

  • Pradeep Fulay, Jung-Kun Lee(Authors)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  For example, annealing metals and alloys probably will increase their electrical conductivity because dislocations, a type of atomic-level defect in the arrangement of atoms, are annihilated. Similarly, if we bend an annealed copper wire or deform a metal or an alloy in some manner, the resistivity will increase. This is because of an increase in the dislocation density (see Section 2.11). The conductivity of pure metals decreases with rising temperature because of the increased scat-tering of electrons off the phonons. Adding alloying elements or the presence of impurities causes a disruption in the periodic order of atoms and introduces a strain (see Section 2.11). This causes a sudden change in the potential energy of conduction electrons as they approach the atoms of foreign Scattering off impurity atoms or atoms of alloying elements added Scattering off vibrations of atoms of the host material Scattering off intrinsic defects such as dislocations and vacancies FIGURE 2.8 Schematic showing the sources of the scattering of conduction electrons in a metallic material. Temperature ( T ) Resistivity (ρ) Pure metal ρ R Superconductor ρ T ρ FIGURE 2.9 The temperature dependence of the conductivity of a typical metal and a superconductor. 59 Electrical Conduction in Metals and Alloys elements (the alloying elements and/or impurities). The scattering of electrons from these foreign atoms then increases, thereby causing increased resistance. Therefore, we expect the conductivity of alloys generally to be lower than that of essentially pure metals. The conductivity of alloys is con-trolled by extrinsic factors, that is, the concentration and nature of the added alloying elements (see Section 2.12). Thus, in alloys, mobility is limited by the scattering of electrons off impurity atoms. We refer to the mobility that is limited by this effect as impurity-scattering limited drift mobility .

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  An Introduction to Electronic Materials for Engineers

  • Wei Gao, Zhengwei Li;Nigel Sammes;;(Authors)
  • 2011(Publication Date)
  • WSPC

    (Publisher)

  Assuming only electrons are responsible for both the electrical and thermal conduction in metals, and free electrons behave like an ideal gas. At a constant temperature, the ratio of the electrical and thermal conductivities should be a constant for metal conductors. This is called the Wiedemann -Franz law. For an ideal gas, thermal conductivity K can be treated as K = 1/3 × C v ⋅ l m ⋅ v th , (2.33) where C v = specific heat at constant volume l m = mean free path v th = thermal speed of electrons C v can be taken as 3/2 nK B for a monatomic ideal gas, so now K = 1/2 × n ⋅ K B ⋅ l m ⋅ v th , (2.34) where n = number of free electrons, and K B is Boltzmann’s constant = 1.38 × 10 -23 J/K. Electrical conductivity is given by Eq. (2.14) σ = n ⋅ e 2 ⋅ τ / m , (2.14) τ redefined as 2 τ = l m / v th , K / σ = m ⋅ K B ⋅ v th 2 / e 2 . (2.35) Using m T K B th 3 = ν , (2.36) 28 Introduction to Electronic Materials for Engineers Eq. (2.35) can be written as K / σ = 3 K B 2 ⋅ T / e 2 , (2.37) or K /( σ ⋅ T ) = 3 K B 2 / e 2 , (2.38) 3 K B 2 / e 2 is a constant, therefore, the left side of Eq. (2.38) is also a con-stant. 3 K B 2 / e 2 = L = 2.23 × 10 -8 W ⋅ Ω /K 2 . (2.38a) Table 2.3 Lorenz numbers of some metals and alloys at 293 K. Metal or Alloy Lorenz number ( L × 10 -8 W Ω /K 2 ) Aluminium 2.18 Cadmium 2.26 Copper 2.30 Indium 2.4 Lead 2.49 Lithium 2.48 Magnesium 2.38 Molybdenum 2.41 Nickel 2.15 Niobium 2.29 Palladium 2.60 Potassium 2.16 Rhodium 2.27 Tantalum 2.40 Tin 2.47 Uranium 2.77 Stainless steel (18/8) 3.33 Phosphor bronze (1.25%) 2.46 Yellow brass 2.50 Constantan (55Cu45Ni) 3.56 Source: Electronic Materials by L.A.A. Warnes, Macmillan Education Ltd. 1990. L is called Lorenz number, which can also be measured by experi-ments. Some results are listed in Table 2.3. Metals with good conductivity Classical Theory of Electrical Conduction and Conducting Materials 29 generally obey Wiedemann-Franz law.

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  An Introduction to Electronic and Ionic Materials

  • Wei Gao, Nigel M Sammes;;;(Authors)
  • 1999(Publication Date)
  • WSPC

    (Publisher)

  Two Classical Theory of Electrical Conduction and Conducting Materials In this chapter, the free electron conduction theory is described. This description is then used to explain the conduction properties of materials. Finally, materials which are used for electrical conduction in electrical and electronic industries are introduced. In classical electron conduction theory, an electron is treated as a very small particle with certain mass and electric charge: Electron mass m e = 9.1 x 10~ 31 kg Electron charge e = -1.6 x 10 19 C. Because electrons behave like particles in this theory, they obey Newton's Laws of motion. In Sections 2.3 to 2.5, we will apply this theory to describe the electron conduction behaviour in conductors. 2.1. Resistivity and Temperature Coefficient of Resistivity (TCR), Matthiessen's Rule 2.1.1. Resistivity The electrical resistance, R, of a material is defined as R oc l/A (2.1) 8 Classical Theory of Electrical Conduction and Conducting Materials 9 or R = pi IA , (2.2) where I is the length, A is the area of the cross-section of the conductor and p is called electrical resistivity. Equation (2.2) indicates that p is the resistance of a material in unit length and unit cross-section area. 2.1.2. Matthiessen's Rule and TCR For pure metals, resistivity p is the sum of two items: a residual part, p r , and a thermal part, p t (see Fig. 2.1). This is called Matthiessen's rule: P(total) = Pr + Pt P = Pr(l+Pt/Pr) Pt/Pr = f(T) P = /V[1 + /(T)]. (2.3) (2.4) (2.5) (2.6) For most metals and alloys, p is approximately proportional to temperature T and can be written as (see Fig. 2.2) p = p 0 (l + aAT), (2.7) where a is called the temperature coefficient of resistivity (TCR). Temperature, K Fig. 2.1. Resistivity versus temperature for a typical metal, Matthiessen's Rule. 10 An Introduction to Electronic and Ionic Materials -273 -200 0 100 200 Temperature. C Fig.2.2. The effect of temperature on the resistivity of selected metals.

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