materiale final cursuri

7/28/2019 Materiale Final Cursuri

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CHAPTER 3

- CONDUCTIVE PROPERTIES OF MATERIALS -

Conductivity & Ohms Law

Conductivity the ease with which a material is capable of conducting anelectric current ().

According to this property, there are 3 types of materials:

- conductors;

- semiconductors;

- insulators;

Metals are the best conductors, typically having

Insulators have the conductivity low

Semiconductors have intermediate conductivity

Ohms Law: states that the ratio of U to I remains constant

independent of the magnitude or direction of I.

Some ceramic materials called varistors (thermistors) do not obey Ohms law.

Any material with a non-linear U(I) characteristic is called non-ohmic.

density of current (

Where:

l length of the sample

A cross section area of the sample, perpendicular on the direction of I


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This form of Ohms law has the following advantages:

1. It is expressed in terms of a material parameter (

) that, unlike R, doesnt

depend on sample dimensions.2. Its a local expression (i.e. its valid in every point of the material)

3. Its a vector relation, showing that 2 vectors quantities are parallel andproportional everywhere in the material.

In anisotropic material (usually in non-cubic crystal structure) is a 9-

component tensor.

Conductivity in metals. Classical free electrons theory

The first model: the electrons have a particle nature.

We can explain the resistance of a material by means of collision of the drifting

electrons and certain lattice atoms. The more collisions we encounter, thegreater the resistance is.

The second model: the electrons have a wave nature.

This model considers that the matter waves are scattered by lattice atoms.

scattering process of radiation (dissipation on small particles in all directions).

It can be coherent or un-coherent.

Coherent scattering: the scattering senders are periodically arranged and there

is a slight phase relationship between the scattered waves.

The first theory is the classical free electron theory of conductivity in metals.

The idea on which Drude theory is based is that many electrons in metals are

nearly free. Thats why he postulated the existence of a free electron gas or

plasma, composed of the valence electrons of the individual atoms in a crystal.

If we have a monovalent element (Li, Na, K, Rb, Cs, Fr), it is assumed that each

atom contains 1 electron to this plasma.


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- friction (damping force)Due to this 2 forces, the electrons will be accelerated until the velocity will be

saturated.

[ ( )]

The relation time can be interpreted as the average time between 2

consecutive collisions.

t

v

vd


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This equation shows that conductivity is large for large number of free

electrons in a large relaxation time.

The relaxation time is proportional to the average time between 2 consecutive

collisions.

- mean free pathAdvantages

- for metals is in very good accordance with experimental results

- for insulators and semiconductors we need more precise theory (quantic)

Conductivity in metals and non-metals

- in equilibrium no electric field- when an electric field is applied

At equilibrium the valence electrons perform random motions with no

preferred velocity in any direction.

If an electric field is applied

V(k)x

V(k)x


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The Fermi sphere/circle is displaced in a direction opposite to the electric field.This displacement takes place because some electrons propagating in opposite

direction to the field E receive from it a maximum increase in their energy,

thats represented by the electrons in the double shaded crescent in the right

part having higher energy.

These electrons are those which contribute to the electric conductor.

Therefore, the Drude classical theory of conduction must be modified.

The main difference between Drudes theory and quantum theory is that Drude

assumed that all electrons drift under the influence of an electric field with a

relatively modest velocity.

Quantum mechanics shows instead that only specific electrons participate in

conduction and these electrons drift with a higher velocity, named Fermi

velocity .

The conductivity in quantum mechanics

This equation shows that the conductivity depends according to the quantum

mechanical model on the Fermi velocity , the population density per unitvolume and relaxation time.

This equation is more meaningful than the one in classical theory, showing that

not all free electrons are responsible for conduction (shown by the fact that depends on and not merely on any v) and instead the conductivity in metalsdepends to a large extend on the population density of the electrons near the

Fermi surface (or sphere in 3D).

Electrical resistivity in metals and alloys

Metal Electrical Conductivity


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Silver

Copper

Gold

Aluminum

Iron

Alloy Electrical Conductivity Brass (70% Cu, 30% Zn)

Platinum

Plain steel

Stainless Steel

Mothiessens Rule

1. - where constants2. Influences of the temperature

A constant; function of both impurity and host metal.

CHAPTER 4

- SEMICONDUCTOR MATERIALS -

Semiconductors are materials that have electrical conductivity between the

conductivity of a conductor and the conductivity of an insulator

.The electric properties of these materials are extremely sensitive to the

presence of even small concentration of impurities.

Intrinsic semiconductors are those in which the electric behavior is based on

the electronic structure inherent to the pure material. When the electric charge

is dictated by impurity atoms the semiconductor is said to be doped or

extrinsic.

Intrinsic semiconductor

Structure


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At 0 K it has a completely filled valence band, separated from an empty

conduction band by a relatively narrow band gap (smaller than 2 eV).

Elemental semiconductors

Si (1.1 eV)Ge (0. eV)

Compound semiconductor materials having intrinsic behavior can be:

- III-V compounds: GaAs, InSb

- II-VI compounds: CdS, ZnTe

- ternary compounds: HgCdTe, GaAsP

Material Band Gap(eV)

Electron

Density

Hole

Mobility

Elemental

Si 1.11 0.14 0.05Ge 0.67 2.2 0.38 0.18

III-IV

Compounds

GaP 2.25 - 0.05 0.002

GeAs 1.42 0.85 0.45InSb 0.17 7.7 0.07

II-VI

Compounds

CdS 2.40 - 0.03 -

ZnTe 2.26 - 0.03 0.01

Ternary elements dont have a precise value of the band gap because the

proportion of the elements may differ (x = 0.20.4) so the properties differ too.

Intrinsic semiconductors, for every electron excited into the conduction band a

missing electron is left behind in the valence band. This missing electron is

treated as a positively charged particle called hole. The charge of a hole is

.Intrinsic conductivity

|| ||N, P concentration of electrons/holes

mobility of electrons/holesThe mobility of holes is smaller than the mobility of electrons in a

semiconductor.


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In intrinsic semiconductors if an electron jumps in conduction band, a hole

remains in valence band.

In extrinsic semiconductors if an electron jumps to the impurity level, number

of electrons will be smaller than the number of holes.

Extrinsic semiconductors

The electrical behavior of an extrinsic semiconductor is determined by

impurities. These impurities, when they are present (even in small

concentration) introduce excess electrons or holes.

Doping means addition of controlled amount of impurities in order to increase

the number of charge carriers in a semiconductor.

There are 2 types:

n-type extrinsic semiconductor

In order to obtain a n-type semiconductor we need an impurity atom with a

valence of V to be added as a substitution impurity (P, As, Sb).

Only 4 of the 5 valence electrons of impurity atom can participate in the

bounding. The 5th

electron is loosely bound and therefore it can be easily

removed from the impurity atom, becoming a free electron (conduction

electron). For each of these loosely bounded electrons there exists a single

energy level or energy state located within the forbidden band gap just below

the bottom of the conduction band.

For each excitation event a single electron is supplied or donated to the

conduction band. Since each electron is excited from an impurity level, no

corresponding hole is created within the valence band.

||The electrons in a n-type extrinsic semiconductor are majority carriers and the

holes are minority carriers.

p-type extrinsic semiconductor

An opposite effect is produced by the addition to Si or Ge of trivalent

substitution impurity (group III Al, Br, Ga).

One of the covalent bands around each of these atoms is deficient in an

electron. Such a deficiency can be viewed as a hole that is weakly bound to the

impurity atom. This hole can be illustrated from the impurity atom by the

transfer of an electron from adjacent band.

Each impurity atom of this type introduces an energy level within the band gapalone, but very close to the top of the valence band.


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A hole is created within valence band by the thermal excitation of an electron

from the valence band into this impurity electron state. With such a transition

only one carrier is produced, a hole in the valence band, a free electron is not

created in either impurity level or conduction band. The impurity of this type is

called acceptorbecause is capable of accepting electrons from valence band,leaving behind holes.

||Holes are majority carriers and electrons are minority carriers.

CHAPTER 5

- DIELECTRIC MATERIALS -

Dielectric materials are insulators, as they have a large energy gap between thevalence and conduction band. Thus, the electrons in the valence band cant

jump in the conduction band. Therefore the resistivities for these materials are

very high. Dielectric materials exhibit or can be made to exhibit an electric

dipole structure, that is a separation between positive and negative electrically

charged entities on a molecular/atomic level.

The 2 important applications are:

- capacitors for the storage of electrical charges

- electrical insulators for preventing electricity transfer

The most important properties

- Relative permittivity (dielectric constant)- tangent of loss angle Other important properties:

- feroelectricity

- piezoelectricity- electrostriction

- piroelectricity;

Capacitors

When a voltage is applied across a capacitor, one plate becomes positively

charged, the other one negatively charged with a corresponding electric field

directed from the positive to negative.

The capacity C is related to the quantity of charge stored in each plate and V isthe voltage applied across the capacitor.


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For the case of the plane capacitor with vacuum between the plates thecapacity will be

A the area of the plates

l distance between the plates

- permittivity of vacuumWhen introducing a dielectric between the plates, the capacity will become

where is the material permittivity.

represents the increase in charge storing capacity by insertion of thedielectric medium between the plates.

Field vectors and polarization

For each dipole an electric dipole moment is associated. q magnitude of each dipole charge

d the distance between charges

In the presence of the electric field a force will act on the dielectric dipole inorder to orient it in the direction of the field.

The surface charge density D or the quantity of charge per unit area of capacity

plates

- +

-

+


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PolarizationThe increase of charge density above the value of vacuum because of the

presence of dielectric

Types of polarization

Polarization the alignment of permanent or induced atomic or molecular

dipole moments with an externally applied electric field.

There are 3 types of induced polarization:

- electronic displacement

- ionic displacement- bipolar orientation

Dielectrics are materials characterized by states of electric polarization.

The state of electric polarization can be:

a) temporary (induced) depends on local b) permanent does not depend on A.

1. Electronic displacement polarization

The limited and elastic motion the electron shells on the dielectric atoms

It is a general property of materials. Generally materials which show only

electronic displacement polarization are called non-polar materials.

+

-


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2. Ionic displacement polarization

The limited and elastic motions of the ions of the dielectric under the action of

the electric field.

This polarization mechanism is specific for dielectrics with prevailing ionic

bonds.

3. Bipolar orientation

The orientation of the existing electric moments on the direction of the applied

field.

When , only under the influence of thermal energy, the electric momentsare random.

The dipolar orientation polarization is specific for materials which have electric

moments,polarmaterials.

Total polarization

Not all three mechanisms are present in a material. For example, Pi wont exist

in a material with covalent bonds (no ions are present).

B.

1. Spontaneous (Pyroelectric)

Represents the ordering of the electric moments of the dielectric on

temperature domains in the absence of the electrical external field.

2. Piezoelectric

Represents the phenomenon that appears under the action of the mechanical

strains applied on the structure.

Complex relative permittivity and tangent of loss angle

Complex relative permittivity can be expressed as


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D complex representation of the electric flux density

E complex electric field intensity

The real part of the complex relative permittivity characterizes the dielectricfrom the point of view of polarization ability whereas the imaginary part characterizes the dielectric from the point of view of energy losses in the

material.

Tangent of loss angle

The inverse of is called the quality factor of the dielectric

Frequency dependence of the dielectric constants

In many practical situations the current is alternatively, that is an applied

voltage on electric field changes direction with time. With each direction

reversal the dipoles attempt to reorient with the field.

This process requires some finite time. For each polarization type a minimum

reorientation time exists, which depends on the ease with which the dipoles

are capable of realignment.

A relaxation frequency is the reciprocal of this minimum reorientation time.

When a polarization mechanism ceases to function there is an abrupt drop in

the dielectric constant. Otherwise for each polarization mechanism isvirtually frequency independent.

The absorption of electric energy by the dielectric material under an alternating

field is called dielectric loss. This loss can be significant for electric field

frequencies close to the relaxation frequency.

At the frequency of utilization a low dielectric loss is desired.


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Dielectric material types

A number of ceramics and polymers are used as insulators or in capacitors.

Many of the ceramics including mica, porcelain, have the electric constants

within range of 6 10. These materials also exhibit a high degree ofdimensional stability and mechanical strength.

Typical applications

- power line and electric insulation

- switches

- light receivers

The titanate ceramics such as barium titanate (

) can be made to have

extremely high dielectric constants which render them especially useful for

some capacitors applications.

The magnitude of the dielectric constant for most polymers is smaller than for

ceramics, generally between 2 and 5. These materials are commonly used for

insulation of wires, cables and motors, and in addition for some capacitors.

Other electrical charge of dielectric materials

Dielectrics can be classified according to their properties in the following

categories:

1. - insulating materials2. - capacitor materials, electricity storage3. Ferroelectrics, piezoelectrics, piroelectrics and electrostriction used for

their special functions

a) Ferroelectricity

Some dielectrics present a behavior of polarization vs. applied electric field verysimilar to the behavior of B vs. H for ferromagnetic materials. This type of PE

graph is called ferroelectric hysteresis loop.

Ferroelectricity takes place in this material below a temperature called Curie

temperature.

Examples of materials displaying ferroelectricity:

- barium titanate - - Rochelle salt

- potassium di-hydrogen-phosphate

- potassium niobate


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- lead zirconate-titanate (PZT)

Ferroelectrics have extremely high dielectric constants, even at relatively low

applied field frequencies (at room temperature for is almost 5000).Consequently capacitors made from these materials can be significantly smallercompared to capacitors made from other materials.

b) Piezoelectricity and electrostriction

When an electric field is applied to a dielectric material, the polarization may

modify the dimensions of the material. This dimension change is called

electrostriction.

On the other hand when a dimensional change (mechanical strains) is imposed

on some dielectrics polarization occurs and a voltage field is created.

Dielectric materials displaying this type of behavior are called piezoelectric,

which means pressure electricity.

Piezoelectric materials are used in transducers which are devices that convert

electrical energy into mechanical strains or vice versa. Familiar applications

include microphones, pick-ups, ultrasounds generators, sonar detectors.

(the pick-up cartridge, as the stylus traverses the grooves on a record, a

pressure variation is imposed on a piezoelectric material located inside the

cartridge which is then transformed into an electric signal and amplified before

going to the speaker)

Examples of piezoelectric materials

- lead zirconate

- ammonium di-hydrogen-phosphate

- quartz

Generally this property is characteristic for materials having crystal structures

with a low degree of symmetry.

c) PiroelectricityPiroelectric materials are a special class of piezoelectric materials. By heating

the material, external expansion creates a deformation which produces a

change in the extend of polarization and thus, a voltage results across the

sample.

PROPERTY CAUSE EFFECT

Ferroelectricity Physical property of a material plus

electrical field applied and

removed

Polarization that remains

after the electric field is

removed


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Electrostriction Electric field Dimensional change

Piezoelectricity Dimensional change Electric field plus

polarization

Piroelectricity Temperature change, dimensional

change

Polarization plus electric

field

CHAPTER 6

- MAGNETIC MATERIALS -

Magnetism is the phenomenon by which the materials assert an attractive or

repulsive influence on other materials.

Examples of materials:

- iron

- steel

All substances are influenced to a certain degree by the presence of the

magnetic field. The externally applied magnetic field is designated by H. If the

magnetic field is generated by means of a solenoid or a cylindrical coil

consisting of N closely spaced turns having the length l and carrying a current ofmagnitude I

The magnetic induction denoted by B represents the magnitude of the internal

field strength within a substance that is subjected to an H field.

H: applied field

B: internal field induced by applied field

is called permeability, which is a property of a specific moment throughwhich the H field passes and in which B is measured.


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The relative permeability of a material is a measure of the degree through

which the material can be magnetized or the ease with which a B field can be

induced in the presence of an external H field.

The magnetic moment (magnetic dipole moment) is a vector that characterizesthe magnets over all the magnetic properties.

For a bar magnet the direction of a magnetic moment points from the magnets

north pole to its south pole.

Magnetization is another magnetic quantity and is defined

The magnetization of the magnetized material is the local value of its magneticmoment per unit volume. It is a vector field rather than just a vector (like the

magnetic moment) because different areas in the magnet can be magnetized

with different directions and strengths.

In the presence of an H field, the magnetic moments tend to become aligned to

the field and to reinforce it because of the magnetic field. The term is ameasure of this contribution.

is called magnetic susceptibility

Analogy between electric and magnetic parameters

B D

H E ...

M P

Origins of magnetic moments

Each electron in an atom has magnetic moments that originate from 2 sources:

- one is related to the orbital motion around the nucleus

- the second one: the electron may also be thought of a spinning around an axis


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This second magnetic moment originates from this electron spin. Spin magnetic

moments may be only in up direction (spin up) or in down direction (spin

down).

The fundamental magnetic moment is the Bohr-Procopiu magnet

For each electron in an atom the spin magnetic moment is .The first orbital magnetic moment is Magnets

Description of magnet behavior

Ferro and ferrimagnetic materials are the ones normally thought as magnets.

They are attracted to a magnet strongly enough that the attraction can be felt.

They are the only ones that can retain the magnetization and become magnets.

Ferrimagnetic materials are similar, but weaker. The susceptibility is verylarge: .Paramagnetic materials (Al, Pt) are weakly attracted to a magnet. This effect is

hundreds of thousands weaker and it can only be determined by using very

sensitive instruments or by using very strong magnets.

Diamagnetic materials are the ones that are repelled weakly by both poles of a

magnet. Compared to para and ferromagnetic substances, diamagnetic

substances Ca, Cu and plastic are even more weakly repelled by magnets.

The permeability of diamagnets is smaller than .All substances not possessing one of the other types of magnetization are

diamagnetic. This includes most substances. In order to emphasize this weak repulsion force one must use extremely strong

super conducting magnets.

Diamagnetism

Is a very weak form of magnetism that is not permanent and persists only whilean external field is being applied. The magnitude of the induced magnetic


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moments is extremely small and in a direction opposite to that of the applied

field. Thus the relative permeability is less than 1 (slightly) and the magneticsusceptibility is less than 0.

It was found bay Lenz that a current is induced in a wire loop whenever a barmagnet is moved towards or from this loop.

The current thus induced causes in turn a magnetic moment which is opposite

to the current one.

Diamagnetism may be explained by postulating that the external magnetic field

induces a change in the magnitude of the inner atomic currents, that is the

external field accelerates (decelerates) the orbital electron so that their

magnetic moment is in the opposite direction to that of the external magnetic

field.

In other words, the responses of the orbit electron counteract the external

field.

So far, we considered only electrons that are bounded to the ?. However

metals also have free electrons, which are forced to move in a magnetic field in

a circular path. This leads to a ? contribution to the diamagnetic moment the

circulating free electrons cause a magnetic moment.

Paramagnetism

In a paramagnetic material there are unpaired electrons, that is atomic or

molecular orbitals with exactly 1 electron in them. The unpaired electron is free

to align its magnetic moment in any direction. Where an external magnetic

field is applied, these magnetic moments will tend to align themselves in the

same direction as the applied field, thus reinforcing it.

For a diamagnetic material, in the absence of the magnetic field no dipoles

exist. In the presence of a field, dipoles are induced and there are aligned

opposite to the field direction.

For a paramagnetic material, in the absence of a paramagnetic field, the

orientations of diatomic magnetic moments are random, such that the material

as a whole presents no net macroscopic magnetization. When an external field

is applied the dipoles align themselves with the external field; they enhance it

giving rise to a relative permeability

and to a relatively small but

positively magnetic susceptibility.


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Both (dia and para) are considered to be non-magnetic because they exhibit

magnetization only in the presence of the external field.

Ferromagnetism

Certain metallic materials posses a permanent magnetic moment, in the

absence of an electric external field and have very large and permanent

magnetization. These are the characteristics of ferromagnetism and they are

displayed by the transition metals (Fe, Co, Ni) and by the rare earth metals (Gd

Gadolinium).

Magnetic susceptibility can be as high as and we can write

because No net magnetic moment is associated with the ions. However, each ion possesses a non-zero magnetic moment predominantly of spin origin.

These ions are arranged in the crystal structure in such way that themoments of adjacent ions are antiparallel and thus cancel one another. As a

consequence the solid as a whole possesses no net magnetic moments.

Ferrimagnetism

Some ceramics also exhibit a permanent magnetization called ferrimagnetism.

The macroscopic magnetic characteristics of ferromagnetic and ferromagnetic

are similar.

The distinction lies in the source of the net magnetic moments.

Cubic ferrites - The ions are magnetically neutral. The spin moments of all ions areantiparallel as in ferromagnetic so they cancel one another and have no net

contribution to the magnetization of the solid. All the ions have theirmoments aligned in the same direction and this total moment is responsible for

the net magnetization.

Cubic ferrites having also other composition may be produced.


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Cation Net spin magnetic moment (Bohr-Procopiu mg)

5 4 5 3 2 1

The saturation magnetizations for ferromagnetic materials are not so high as

for ferromagnets. On the other hand, ferrites having ceramic materials are

good electrical insulators. For some magnetic application such as frequency

transformers, a low electrical conductivity is most desirable.

The influence of temperature on magnetic behavior

Raising a temperature of a solid results in an increase in the magnitude

vibration of atoms. The increased thermal motion of atoms tends to randomize

the direction of any moment that may be aligned, resulting in a decrease of the

magnetic spin for both ferro and ferri magnetic materials.

The saturation magnetization is maximum at 0 K where the thermal vibrations

are minimum. With increasing temperature, the saturation magnetizationdiminishes gradually and then abruptly drops to 0 at Curie temperature.

Domains and hysteresis

Any ferro and ferri magnetic material that has a temperature below Curie

temperature is composed of small volume regions in which all magnetic dipole

moments are aligned in the same direction.

Such a region is called domain and each one is magnetized to its saturationmagnetization. Adjacent domains are separated by domain boundaries or walls

(block walls).

For ferrimagnets and ferromagnets the flux density B and the field density H

are not proportional. If the material is initially unmagnetisez, then varies as a

function of H.

The curve begins at the origin and as H is increased, the B field begins to

increase slowly, then more rapidly, finally leveling off and becoming


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independent of H. This maximum value of B is the saturation induction Bs. The

slope of B vs. H curve at H=0 is specified as a material property and is called the

initial permeability .

As the external field is applied, the domains are oriented in directions favorableto the applied field (or nearly aligned to it) grow at the expense of those that

are unfavorably oriented. This process continues with increasing field intensity

until the specimen becomes a single domain, thus saturation being achieved.

From saturation as the H field is reduced by reversal field direction, the curve

does not retrace its original path. A hysteresis effect is produced. At 0 H field

there exists a residual B field called remanence for the remanent induction Br.

The material remains magnetized in the absence of the external H field. The

explanation for this phenomenon is the resistance to moment of domain walls

that occurs in response to the increase of the magnetic field in the opposite

direction. When the applied field H reaches 0, there is still some net volume,

fractions of domains oriented in the former direction which explains the

existence of the remanence Br. In order to reduce the B field of the specimen

to 0, an H field of magnitude Hc must be applied. Hc is called coercitivity (or

coercitive field). Upon continuation of the applied field in this reverse direction

saturation is achieved in the opposite sense. A ? reversal of the field up to the

point of initial saturation completes the symmetrical hysteresis loop.

This B vs. H curve represents a hysteresis loop ? to saturation.

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