Tao Deng, dengtao@sjtu.edu.cn 1 1896 1920 1987 2006 Properties of Materials Chapter 3 Electrical Properties of Materials Tao Deng
Tao Deng, dengtao@sjtu.edu.cn 2 3. The electrical properties Electrical conductivity Dielectric property Thermoelectric Pyroelectric Piezoelectric Ferroelectric Photoelectric
3.1 Electrical conductivity Tao Deng, dengtao@sjtu.edu.cn 3 3.1.1 Introduction 3.1.1.1 Characterization of electrical conductivity Electrical conduction: when a voltage is applied between two ends of a material, there is a current flowing through the material. Ohm's Law Resistance: R I V R L S S R L Resistivity: 1μ cm=10-9 m =10-6 cm=10-2 mm 2 /m
3.1 Electrical conductivity Tao Deng, dengtao@sjtu.edu.cn 4 I=SJ(J is electrical current density ) V=LE(E is electric al field intensity ) 1 J E Electrical conductivity (-1 m-1 or S/m): 1 J E Relative electrical conductivity (IACS%): If the conductivity of the international standard soft copper (resistivity at 20 0 C: 0.01724 mm 2 /m) is 100%, a material s relative conductivity is defined as the percentage of its conductivity divided by soft copper's conductivity. For example, the IACS% of iron is 17%; The IACS% of aluminum is 65%.
Tao Deng, dengtao@sjtu.edu.cn 5 3.1.1 The electrical conductivity of typical materials at room temperature Room temperature values (Ohm-m) -1 = ( - m) -1 METALS conductors Silver 6.8 x 10 7 Copper 6.0 x 10 7 CERAMICS Soda-lime glass 10-10 Concrete 10-9 - 10-11 Iron 1.0 x 10 7 Aluminum oxide <10-13 SEMICONDUCTORS Silicon 4 x 10-4 Germanium 2 x 10 0 GaAs 10-6 semiconductors POLYMERS Polystyrene <10-14 Polyethylene 10-15 -10-17 insulators
3.1.1.2 Materials electrical conductivity Tao Deng, dengtao@sjtu.edu.cn 6 Conductor: ρ<10-5 Ω.m; Semiconductor: ρ=10-5 ~ 10 10 Ω.m; Insulator: ρ>10 10 Ω.m;
Tao Deng, dengtao@sjtu.edu.cn 7 3.1.1.3 Mechanism of electrical conduction (1) Carriers Current is the directional flow of electrical charge in space. In any matter, as long as there are free particles with charges (carriers), there will be current under electric field In metals, the carriers are free electrons (electronic conduction) In inorganic materials, there are two types of carriers: Ions, including positive/negative ions and vacancies (ionic conduction) Electrons, including negative electrons and holes (electronic conduction) In polymers, the carriers are solitons In superconducting materials, the carriers are two-electron Cooper pairs
3.1.1.3 Mechanism of electrical conduction 2)Mobility of carriers In the conductor with a cross-sectional area of the unit area, n is the number of carriers in the unit volume and q is the charge carried by each carrier. If the external electric field (E) is applied along the longitudinal direction, there is a force of qe acting on each carrier. Under the action of this force, each carrier moves along the direction of E, and its average speed is v. J nqv E J E nqv E Mobility of carrier is defined as : v E It is the average drift velocity of the carriers under the action of a unit electric field. Tao Deng, dengtao@sjtu.edu.cn 8
3.1.1.3 Mechanism of electrical conduction Tao Deng, dengtao@sjtu.edu.cn 9 nq If there are several carriers that contribute to the conductivity in the material, then the total conductivity is the sum of all individual carriers: nq i i i i i i Two key factors for material s conductivity: The concentration of carriers Carrier mobility. External conditions (such as temperature and pressure), bonding, composition, and other factors have an impact on the carrier concentration and carrier mobility.
Tao Deng, dengtao@sjtu.edu.cn 10 3.1.1.4 Band theory (1)Basic concept -The potential field from positive ions has a periodicity and it makes the movement of free electrons not completely free. -Study the energy distribution of electrons in the periodic potential field in metals.
Tao Deng, dengtao@sjtu.edu.cn 11 3.1.1.4 Band theory Arrangement of metallic atoms x 1 When the distance between atoms is large (x 1 ), electrons in atoms are mutually independent.
Tao Deng, dengtao@sjtu.edu.cn 12 3.1.1.4 Band theory Arrangement of metallic atoms within Bulk Metals x 3 When the spacing is less than x 2, the originally independent energy levels of an atom spread into a band consisting of a discrete series of energy levels; the energy difference between these levels is small (about 10-23 ev.)
Tao Deng, dengtao@sjtu.edu.cn 13 3.1.1.4 Band theory Arrangement of metallic atoms within Bulk Metals x 4 When the atomic spacing is further reduced (x 4 ), the band is broadening.
Tao Deng, dengtao@sjtu.edu.cn 14 Energy band The highest energy band partialy occupied by some electrons is called the valence band Core band band energy is lower than that of the valence band Conduction band band energy is higher than that of the valence band Band gap ( E g )- the forbidden energy gap between the valence band and the conduction band
The energy band of three typical materials Tao Deng, dengtao@sjtu.edu.cn 15 Empty band Valence band Conduction Band Overlap region Overlapping of Valence band and the empty band conduction band Valence band is half full E g 0.2~2.5eV Semiconductor E g >2.5eV Insulator Metallic conductor For example Si: E g =1.1eV Ge:E g =0.71eV For example : diamond E g =6.0eV
3.1.1.5 Theory of the electrical conductivity Tao Deng, dengtao@sjtu.edu.cn 16 (1)The classical electron theory Free electrons are considered as "electron gas - - analyze with classic gas molecules kinetic theory. The interaction within the free electrons and between them and the positive ions are treated as the mechanical collision. 2 ne l 2mv 2 ne 2m t l -mean free path of the electron;m -mass of the electron;v -average speed of the electron;e - charge of the electron ;t - the average time between twice collisions;n -the number of free electrons per unit volume;
The influence of the temperature and the point defects on electron movement Tao Deng, dengtao@sjtu.edu.cn 17 3 collisions 6 collisions The influence of temperature The model of an electron moving in the lattice 8 collisions The influence of point defects
3.1.1.5 Theory of the electrical conductivity Tao Deng, dengtao@sjtu.edu.cn 18 (2)Quantum theory of free electrons Basic assumptions: In metals, the electric field formed by the positive ions is uniform; The electrons in the valence band belong to the entire metal; they have no interaction with ions, and can move freely; The electrons in the inner bands of each atom have the same energy states with those in the original single atoms, while the electrons in the valence band have different energy states that are quantalized to different energy levels.
(2)Quantum theory of free electrons Tao Deng, dengtao@sjtu.edu.cn 19 Wave-Particle Duality: h mv h p 2 2mv 2p h h For monovalent metal, the kinetic energy of free-electron: Where, K 2 E 1 2 mv 2 2 h K 8m wave frequency (wave number or wave vector) 2
The relationship between electronic energy and wave vector Tao Deng, dengtao@sjtu.edu.cn 20 E E E e E -K O +K -K O +K -K O +K E - K curve of free electrons The effect of the electric field on the E-K curve
Tao Deng, dengtao@sjtu.edu.cn 21 The interference of electronic wave The electrical resistance is caused by the scattering of electronic waves through: Ion lattice; Static lattice distortion generated by defects or impurities; Dynamic lattice distortion generated by thermal vibration.
3.1.1.6 Ionic conduction Tao Deng, dengtao@sjtu.edu.cn 22 (1) Conductive mechanism of ionic crystals a) Conduction through intrinsic ions Due to the increase of thermal vibration, ions leave the lattice site to form interstitial ions and vacancies (thermal defects). Such thermal defects can move under the electric field to generate current. Concentration of thermal defects increases with in temperature, so the ionic intrinsic conductivity increases with temperature as well: Where E s - The activation energy of ions. 2) Conduction through impurity ions E s s As exp kt im Aexp B T B E k s
(2)The conduction mechanism in glass Tao Deng, dengtao@sjtu.edu.cn 23 Glass is usually an insulator -- at high temperature, some glasses can become a conductor. Glass is also a conductor of the electrolyte. Its conductivity comes from the movability of ions in the structure. For example, in the silica network of a soda glass, a sodium ion jumps from one structural gap to another to generate the current. This conduction is similar to the conduction from interstitial ions in the ionic crystals. The composition of the glass has a great impact to the resistance.
3.1.1.7 The conduction in polymers Tao Deng, dengtao@sjtu.edu.cn 24 In 1977, Shirakawa from Japan and MacDiamid from the United States found that the conductivity of polyacetylene, doped with I 2 or AsF 5, increases from 10-9 S / cm to 10 3 S/cm.
3.1.1.7 The conduction in polymers Tao Deng, dengtao@sjtu.edu.cn 25
Polyacetylene H atoms on both sides of the double bond H atoms at the same side the double bond. Trans-form Cis-form Carbon atoms are bonded with each other through double bond single bond double bond to form a quasi-one-dimensional carbon chain,;every hydrogen atom bonds with a carbon atom located on the carbon chain; Each carbon atom is adjacent to two carbon atoms and one hydrogen atom ; Each carbon atom has four valence electrons. In polyacetylene, neighboring carbon atoms using their sp2 hybrid orbitals to form carbon - carbon σ bonds, and at the same time, they also use their sp2 orbitals to interact with hydrogen s s orbitals to form carbon hydrogen σ bonds; Each carbon atom has a valence electron (p z orbitals) and it becomes a π electron in the molecular bond of polyacetylene. Tao Deng, dengtao@sjtu.edu.cn 26
The band structure of one-dimensional carbon chain of polyacetylene Tao Deng, dengtao@sjtu.edu.cn 27 The energy band of onedimensional equidistant carbon chain Should be like a metal?? The energy band of onedimensional dimerized carbon chain Like a semiconductor!
Tao Deng, dengtao@sjtu.edu.cn 28 The soliton model In a certain range of the doping concentration, trans-polyacetylene has a high electrical conductivity. The conductive carriers of polyacetylene carry charge without spinning. The Soliton model: Trans-polyacetylene has two lowest dimerization states: A-phase and B-phase, with the same energy and symmetrical structure. If the A- phase and B-phase coexist in the same molecular chain, there will be a domain wall between them, which is called soliton. The alternating single bond-double bond structure is destroyed at the soliton. A phase, the soliton and B phase in trans-polyacetylene
3.1.2 The electrical conductivity of the metal Tao Deng, dengtao@sjtu.edu.cn 29 3.1.2.1 The electrical conductivity of the elements
Analysis of element conductive band theory 3s valence band is half-filled. High electrical conductivity The outermost s band is full, but the outermost s overlaps with the outermost p to form the conduction band. The conductivity is higher than IA family. The outermost p is filled with a small amount of electrons. Most of it is empty, with some overlapping with the main shell s. Higher conductivity. Similar to the alkali metal, there is non-overlapping band and valence band is half-filled. Higher conductivity. Sp hybrid orbital caused by covalent bond; involving the 2s electrons(4 valence electron) to form two hybrid bands, where one is filled, and the other is empty, but there is a band gap between the two hybrid band. The conductivity is poor. The outermost s band is full, partially overlapping with the half-filled d-band to form a conduction band with less empty level. Conductivity is relatively poor. Tao Deng, dengtao@sjtu.edu.cn 30
3.1.2.2 Matthiessen Law The resistance of ideal metals are based on only two scatterings- phononic scattering and electronic scattering. This resistance is reduced to zero at absolute zero. The third scattering (electrons scattered by impurities and defects) can be observed in the non-ideal crystal with defects, which still exists even at absolute zero. The scattering coefficient is composed of two parts: T Where, the scattering coefficient v T is proportional to the temperature T, ν is proportional to the concentration of impurities and independent of temperature. Matthiessen law T Where, (T) is the basic resistance of pure metals; is the residual resistance determined by chemical and physical defects, regardless of the temperature. Tao Deng, dengtao@sjtu.edu.cn 31
3.1.2.3 The relationship between electrical resistivity and temperature in metals T 2 1 0 T T T 3 where,ρ 0 - electrical resistivity at 0 ;α-temperature coefficient of resistance;β γ- High-order coefficient; Generally, ρ increases as T increases. T 2 5 T T In the very low temperature: Electron - electron scattering; In the higher Temperature: Electron - phonon scattering -T<Θ D 时,ρ T 5 ; -T> Θ D 时,ρ T Usually, in the case of temperature 1 T higher than the room temperature: 0 Tao Deng, dengtao@sjtu.edu.cn 32
Temperature coefficient Tao Deng, dengtao@sjtu.edu.cn 33 The average temperature coefficient of resistance: T 0 T 0 True temperature coefficient of resistance: T 1 T d dt Except the transition metals, for all other pure metals α 4 10-3 Transition metals, especially ferromagnetic metals, have a high α. For example, iron has a α= 6 10-3.
3.1.2.4 The impact of stress and deformation caused by cold processing Tao Deng, dengtao@sjtu.edu.cn 34 Cold processing will increase the lattice distortion, thus increase the resistivity: Fe Cu Al Mg.etc., may increase by 2~6%; W Mo Sn.etc., may increase by 15~90%. 99.8% 97.8% 93.5% The amount of deformation during cold processing 80% Recrystallization annealing may cancel the increase of the resistance 44% Annealing temperature/ o C
3.1.2.5 The conductive property of the alloys Tao Deng, dengtao@sjtu.edu.cn 35 (1) The resistivity of the solid solution Generally, with the increase of the concentration of the solute, the resistivity also increases because of the lattice distortion. When solute concentration is small, the resistivity follows Matthiessen's law: T r ρ T - Base resistance of pure base metal ρ r -The additional resistance caused by the concentration of solute (impurity) point defects, dislocations, etc., independent of temperature.
Tao Deng, dengtao@sjtu.edu.cn 36 (2)The resistivity of ordered alloys With the increase of order in the solid solution The chemical interaction among the alloy components is strengthened, and number of conductive electrons decreases, so the residual resistance increases; The ionic potential field become more symmetrical, so that the probability of the electron scattering is greatly reduced and the residual resistivity decreases; The second factor is usually dominant, so the resistivity of the alloy is normally reduced with increased structural order Quenching state Annealed state Au, % (atom)
3.1.2.6 The influence of pressure on the metal conductivity Tao Deng, dengtao@sjtu.edu.cn 37 Normal metal : The resistivity decreases as the pressure increases: iron, cobalt, nickel, copper, silver, gold, niobium, vanadium, lead, etc. Abnormal metal : The resistivity doesnot follow the normal trend as the pressure increases: alkali metal, alkaline earth metal and rare earth metals;
Tao Deng, dengtao@sjtu.edu.cn 38 The effect of pressure on the conductivity of nonconductive materials High pressure can often lead to the metallization of the substance, causing the changes of the conductivity type, enabling the transform of insulator semiconductor metal superconductors. The critical pressure required for certain semiconductor and dielectric materials transformation into the metallic state Element P C /MPa ρ/(μω.cm) Element P C /MPa ρ/(μω.cm) S 40,000 - H 200,000 - Se 12,500 - Diamond 60,000 - Si 16,000 - P 20,000 60±20 Ge 12,000 - AgO 20,000 70±20 I 22,000 500 - - -
Tao Deng, dengtao@sjtu.edu.cn 39 3.1.2.7 The influence of geometric dimensions on the electronic resistivity When the size of material is reduced to the same order of magnitude of the free path of the conduction electron, the scattering of electrons in the surface of the sample creates a new additional resistance. In this case, the effective scattering coefficient L eff is 1 L 1 L eff L d Where, L L d, respectively, is the free path of the electrons scattered in the bulk sample and the surface. 1 The resistivity of thin film is: L d 0 1 d where,ρ 0 -The resistivity of bulk sample ; d - The thickness of film;
3.1.3 The electrical properties of the semiconductors Tao Deng, dengtao@sjtu.edu.cn 40
3.1.3 The electrical properties of the semiconductors Crystalline semiconductor Elemental semiconductor:si, Ge, Se, Te and so on solid solution semiconductor:ge-si, Bi-Sb, GaAs-GaP and so on ; compound semiconductor :GaAs, CdS, SiC, GeS, AsSe 3 and so on ; Noncrystalline semiconductor noncrystalline silicon(α Si) polycrystalline silicon ; chalcogenide glass ; Organic semiconductor Polymer semiconductor Tao Deng, dengtao@sjtu.edu.cn 41
The electronic energy states in semiconductor Tao Deng, dengtao@sjtu.edu.cn 42 The sharing of valence electrons in semiconductor crystals splits the original atomic electron energy states into a series of levels with very small difference of energy between them to form a energy band. Energy Empty band (conduction band) The distance between atoms in Covalent Crystals single atom Forbidden band Filled band (valence band) 3p 3s 2p 2s 1s n=3 n=2 n=1 The distance between atoms The evolutional process of silicon covalent crystals
3.1.3.1 Intrinsic semiconductor Tao Deng, dengtao@sjtu.edu.cn 43 Intrinsic semiconductor: pure, single crystal, no structural defects. The number of free electrons in the conduction band=the number of holes in the valence band The process of intrinsic excitation Stimulated by the electric field, temperature, or light
1) The concentration of the intrinsic carrier Tao Deng, dengtao@sjtu.edu.cn 44 Based on the probability of the intrinsic carrier occupying the energy level: n i p i K T 1 3 2 exp Eg 2kT Where n i - the concentration of free electrons; P i - The concentration of holes; T-The absolute temperature; k - Boltzmann constant;k 1 = 4.82 10 15 K -3/2 ; The concentration of the carriers increases with increasing temperature; The concentration of carriers decreases when the forbidden band becomes wider. For example:when T =300K,E g Si =1.1eV, n i Si =1.5 10 10 cm -3 ; E g Ge =0.72eV, n i Ge =2.4 10 13 cm -3 ;
(2)The mobility and the electrical resistivity of intrinsic semiconductors Tao Deng, dengtao@sjtu.edu.cn 45 Under the external electric field, the average speed of the directional drifting of carriers is a constant value that is proportional to the electric field strength ε: v n n v p p where,μ n and μ p, respectively, are the average drifting velocities (cm / s) of free electrons and holes under the unit field strength (V / cm); they are called the mobility For Ge:μ n =3900 cm 2 /Vs;μ p =1900 cm 2 /Vs For Si: μ n =1400 cm 2 /Vs;μ p =500 cm 2 /Vs The resistivity of intrinsic semiconductor is: i j qn qn i n i p qn where,q -The absolute value of the electronic charge. i 1 n p
3.1.3.2 The electrical properties of the semiconductor containing impurities (1)N-type semiconductor (extra electrons) N-type semiconductor doping the intrinsic semiconductor (with 4 valence electrons) with the pentavalent elements, such as P, As, Sb, etc. E C -E D <<E g,so, it is easy to excite the free electron. n 1 qn D n where,n D -The dopant concentration n i >>n p The energy band and the Fermi distribution of the N-type semiconductor Tao Deng, dengtao@sjtu.edu.cn 46
(2)The P-type semiconductor (extra holes) Tao Deng, dengtao@sjtu.edu.cn 47 P-type semiconductor doping the intrinsic semiconductor (with 4 valence electrons) with the trivalent elements, such as Al, Ga, etc. n i <<n p +3 The structure of the P-type semiconductor The energy band and the Fermi distribution of the N-type semiconductor E A -E V <<E g,electrons in the valence band can enter the E A level at room temperature, as a result of some vacancy generated in the valence band.
3.1.3.3 The impact of the temperature on the resistance of semiconductor Tao Deng, dengtao@sjtu.edu.cn 48 The influence of temperature depends on the competition of the resulting change in concentration of carriers and the mobility of carriers. All Impurities are ionized. The intrinsic excitation has not yet started, the concentration of carriers almost remains constant, and the phonon scattering dominates, so the resistivity increases. Phonon scattering is weak, but number of the ionic impurity donors increases with temperature, and therefore the resistivity decreases. The dependence of the resistivity of N-type semiconductor on temperature The intrinsic excitation starts with a temperature rise, the carrier concentration increases dramatically, far more than the phonon scattering, and therefore the resistivity decreases.
Tao Deng, dengtao@sjtu.edu.cn 49 3.1.3.4 Conduction in semiconductor (1)The effect of temperature Under the normal circumstances, the dependence of the electrical conductivity (resistivity) of temperature is e B T 0 0 e B T Where, B - The conductive activation energy of material. The higher B, the greater the change of resistivity with temperature.
(2) The effect of light Tao Deng, dengtao@sjtu.edu.cn 50 Photoconduction: The irradiation of the light makes the resistance of some semiconductors decrease. The energy of photons is transferred to the electrons in valence band, and the excited electrons jump to the empty band. Application of photosensitive effect : Photosensitizing effects: automatic control systems, lighting automation.
(3)The effect of voltage Tao Deng, dengtao@sjtu.edu.cn 51 The relationship between the current and voltage of some semiconductors (such as the ceramic semiconductor of zinc oxide ) is not linear, i.e. the resistance varies with the change of voltage. This effect can be used to make varistors, which can be applied for voltage absorption, high-pressure regulator, and surge arresters.
(4)The effect of pressure Tao Deng, dengtao@sjtu.edu.cn 52 In addition to generating the structural deformation, some semiconductors under pressure have a change of the energy band structure., which results in the change of electrical resistivity. The relationship of semiconductor piezoresistive effect with stress is: 0 T where,ρ 0 - the resistivity without stress;δρ-the change of resistivity when stress is added; β-piezoresistive coefficient;tthe applied stress (the tension is positive; the compress is negative).
(5)Magnetic effect Tao Deng, dengtao@sjtu.edu.cn 53 Hall Effect When a semiconductor with current is placed in the uniform magnetic field, a lateral electric field perpendicular to the direction of the external electric field and magnetic field will be generated. The magnetoresistant effect The current density is reduced as a magnetic field, perpendicular to the current inside the semiconductor, is applied. Due to the presence of the magnetic field, the resistance of the semiconductor increases.
Tao Deng, dengtao@sjtu.edu.cn 54 3.1.4 Superconductivity Phenomenon At a temperature below a certain critical temperature T c, the specific resistance of a material suddenly drops to very low (<10-25 Ω. cm). Potential applications Superconducting thermonuclear reaction Lossless superconducting transmission Super electromagnet Superconducting maglev train Magnetic resonance imaging The dependence of the resistivity of mercury on temperature(1911-onnes)
3.1.4.3 The physics of the superconductivity Tao Deng, dengtao@sjtu.edu.cn 55 In the superconducting state, there are attractive force between the electrons near the Fermi surface (rather than the electrostatic repulsion in the normal state), the electrons with opposite momentum and spin are paired together to generate Cooper pairs. It is the result of the interaction between the electrons and crystal lattice. Positive ion e 1 e 2 The total momentum and the average speed of Cooper pairs remain constant during their movement. They don't consume energy and can move through the lattice with no resistance.
3.1.4.4 The superconducting tunneling effect (Josephson effect) Tao Deng, dengtao@sjtu.edu.cn 56 In the 1960s, Josephson effect in weakly connected superconductors is one of the significant breakthroughs in the research of superconductivity. Weakly connected superconductors have a sandwich structure of superconducting - insulator - superconductor (SIS) with a nanometer insulating film in the middle of the two superconductors. Josephson junction Josephson effect:for the S-I-S structure with current < I C,there is no voltage through the dielectric layer. The weakly connected superconductors have a zero resistance, i.e. the insulating (vacuum, normal) layer between two superconductors can also pass the superconducting current.
Josephson junctions Possible Josephson junctions: (1) Superconductor- insulator - Superconductor; (2) Superconductor - normal metal - Superconductor; (3) Superconductor - vacuum - Superconductor (STM); (4) two superconductors contacted by point; (5) Two superconductor contacted by microbridge; (a) Tunnel junction (b) Proximity effect bridge (c) One-dimensional micro-bridge (d) Twodimensional micro-bridge (e) Three-dimensional micro-bridge (f) the micro-bridge with thickness changing (g) Point contact Tao Deng, dengtao@sjtu.edu.cn 57
3.1.5 Measurement of electrical resistance Tao Deng, dengtao@sjtu.edu.cn 58 3.1.5.1 (1) Measurement of resistance in metals Adjusting the current and four variable resistors, so that the electric potentials of point f and point c in the bridge circuit are equal. The bridge is in equilibrium: R x R n I I 1 1 R R 1 2 I I 2 2 R R 3 4 If R1 = R3, then R2 and R4 can be adjusted with R2 = R4 in the double bridge measurement. In other words, the equilibrium of the bridge can be achieved by adjusting R3 and R4 only: R x R n R R 1 2 Measurement through double bridge
Tao Deng, dengtao@sjtu.edu.cn 59 2)The resistance measurements of semiconductors V I S l 3 2 2 1 3 1 1 1 1 1 2 l l l l l l V I lv I 2 The two-probe method The four-probe method
3) The resistance measurements of insulators Ballistic galvanometer can be used in the measurement of the resistance of an insulator. When the switch K is switched to 1 and after a time of t: R x Ut Q Where U is the voltage of DC supply ; t is the charging time; Q is the electric charge on the capacitor after a charging time t, which can be measured by ballistic galvanometer. When the switch K is switched to 2, we have Q C b m where C b is the impact constant of ballistic galvanometer; α m is the maximum offset of the galvanometer (direct readout). Therefore : R x Ut C b m Tao Deng, dengtao@sjtu.edu.cn 60
3.1.5.2 The application of resistance measurement Tao Deng, dengtao@sjtu.edu.cn 61 Measuring the solubility curve of the solid solution Studying of alloy aging Studying the order - disorder transition in alloys Investigating material fatigue process