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478 Part C Materials Properties Measurement

bulb that contains the sensing liquid should be much

larger (by a factor of at least 1000) than the volume

of the indicating capillary due to the small relative ex-

pansion coefﬁcients



mercury: 0.00016

◦

−1

; ethanol:

0.00104

◦

−1



. The bulb and capillary are the container

for the sensing liquid but, as they have a temperature

coefﬁcient different from zero, they are an integral part

of the sensor and are the origin of nonlinearities in the

reading. Finally, the scale, which is needed for the user

to read the indicated temperature by comparison with

the liquid level in the capillary, shows a temperature-

dependent length dilatation. It can easily be seen, that

this complicated temperature dependence causes uncer-

tainties, especially due to the level of immersion of the

thermometer in the bath to be measured. Therefore, the

depth of immersion during calibration is usually marked

on the thermometer and should preferably be used again

when measurements are made.

There are other sources of errors, some of which are

similar to issues in other thermometers. Thermal con-

tact through the glass walls and the heat capacity of

the liquid in the bulb lead to time-constant effects and

errors if there is not enough time for the system to equal-

ize. Particular errors of liquid-in-glass thermometers

result from pressure effects. High external pressure may

change the bulb volume and consequently the level of

the liquid in the capillary. The gas in the capillary, which

should compensate for the vapor pressure of the liquid

at higher temperatures to avoid interruptions of the li-

quid column and the formation of bubbles, will affect

the indication. Linearization of the scale may not be per-

fect or the scale may be misplaced or misaligned. Also,

parallax errors may occur due to refraction by the glass

tubes if the reading is not taken exactly perpendicular to

the surface.

The advantages of liquid-in-glass thermometers

remain their immunity to chemical attack and electro-

magnetic interference and their low cost. Instruments

are available with a maximum error of 0.1

◦

Cinthe

range from the ice point to about 50

◦

C. This error in-

creases to 1

◦

Cor2

◦

C near the limits of the application

range at −80

◦

C and 500

◦

8.5.5 Thermocouples

Thermocouples nowadays have the widest ﬁeld of ap-

plication of all temperature sensors. They generate an

electrical readout similar to resistance thermometers,

but the measuring principle is quite different. In re-

sistance thermometers a sensor’s property, namely the

temperature-dependent resistance of the material, is

measured at the location of the sensor. With thermo-

couples, their basic principle, the Seebeck effect (one

of the thermoelectric effects, discovered in 1821), is

a property of the whole wiring between the measur-

ing and the reference junction. The principle circuit of

a thermocouple is presented in Fig. 8.12.

The Seebeck effect means that within a conduct-

ing wire exposed to a temperature gradient a voltage

difference is generated between its ends depending

on their temperature difference. The simpliﬁed picture

considering the electrons within the conductor as free

particles explains that they tend to move to the low-

temperature side because on the high-temperature side

the electron gas contains more kinetic energy and ex-

pands to the other end of the wire. This expansion

causes a negatively charged low-temperature end. The

voltage difference generated in this way ﬁnally stops

the electron motion at an equilibrium state. If the con-

ductor, named A for distinction, is homogeneous along

its length with respect to its geometrical cross sec-

tion, chemical composition, and lack of defects, the

Seebeck voltage depends only on the temperature dif-

ference between the ends. To measure this voltage

one connects a second wire B of a different mater-

ial to the temperature-measuring end of wire A and

leads it, via a contact stabilized to a reference tem-

perature, to the other input terminal of a voltmeter.

Due to the fact that disturbing effects can only be

excluded from the temperature measurement for homo-

geneous parts of the circuit, all inhomogeneous parts of

the wiring, such as the measuring junction, the refer-

ence junction and other contacts within the measuring

voltmeter circuit, should be strictly kept isothermal.

Consequently, the number of junctions in the wiring

should be reduced to an absolute minimum. In ad-

dition, current-induced voltage drops along the leads

should be excluded by the use of a high-impedance

voltmeter.

meas

917 35

DVM

ref

(Ice point)

Wire A (copper)

Wire B (copper

nickel alloy)

Fig. 8.12 Principle design of a thermocouple

Part C 8.5

Thermal Properties 8.5 Temperature Sensors 479

Table 8.6 The eight internationally adopted types of thermocouples

Type Materials max. Temp. Sensitivity (μV/

◦

C) at

(

◦

C) 20

◦

C 100

◦

C 500

◦

B Platinum 30% rhodium/platinum 6% rhodium 1700 0 0.9 5.1

E Nickel-chromium alloy/copper-nickel alloy 870 60.5 67.5 81.0

J Iron/another slightly different copper-nickel alloy 760 51.5 54.4 56.0

K Nickel-chromium alloy/nickel-aluminium alloy 1260 40.3 41.4 42.7

N Nickel-chromium alloy/nickel-silicon alloy 1300 26.6 29.6 38.3

R Platinum 13% rhodium/platinum 1400 5.9 7.5 10.9

S Platinum 10% rhodium/platinum 1400 5.9 7.4 9.9

T Copper/copper-nickel alloy 370 40.3 46.7

For the temperature of the reference junction in

most cases the ice point is used, since it can be real-

ized simply and provides sufﬁcient temperature stability

and homogeneity. Alternatively, an isothermal reference

junction at a stabilized temperature different from 0

◦

can be applied, if its temperature is accurately measured

and the Seebeck voltage of the reference-junction tem-

perature read from standard tables (see below) is used

for correction.

For different measuring purposes, different mater-

ials are used for thermocouples. In Table 8.6 standard

commercially available devices are listed including

their maximum temperature.

There are mathematical deﬁnitions for the response

of each leg material or material composition to tempera-

ture changes. Manufacturers guarantee tolerance classes

1 to 3 for the agreement of their products with those

formula-based tables (class 1: 0.4%; class 2: 0.75%;

class 3: 1.5% within certain temperature limits).

Most errors when using thermocouples are simi-

lar to those with other thermometers concerning heat

capacity, time constants, immersion and radiation. Par-

ticular errors due to material properties or construction

principles are avoided by obtaining the instrument from

a well-known supplier.

The type of thermocouple appropriate for a cer-

tain application should be selected ﬁrst according to

the temperature range speciﬁed by the manufacturer.

For low-accuracy demands in industrial environment

uncertainties of 1% are reached with standard devices.

For higher demands, rare-metal thermocouples such as

type B, R and S should be chosen because of their im-

proved uncertainty of 0.1%.

8.5.6 Radiation Thermometers

Radiation thermometers determine the surface tem-

perature of an object by measuring its temperature-

dependent radiation. They are noncontact thermometers

and are suitable for remote sensing. This makes them

a superior or even only choice, if the objects are far

away, moving fast or if they are too hot or dangerous

to achieve direct contact, e.g. hot furnaces, the blades

of a spinning turbine or the sun and other stars in the

universe.

Radiation thermometers rely on fundamental ther-

modynamic physical laws, e.g. Planck’s law, and they

can easily be modeled in great detail. A measurement at

a certain temperature can be related to the measurement

of the temperature of the triple point of water or an-

other temperature ﬁxed point by direct comparison and

is, by this means, directly traceable to the ITS-90. The

measured radiance has to be corrected, however, due to

the quality of the sample’s surface, characterized by its

spectral emissivity and the stray light reﬂected into the

detector from the surroundings.

A radiation thermometer observes only the tem-

perature of the object’s surface, which may even be

considered as the sensing element of the method, and

not the sample’s temperature deep in the bulk. This is

a disadvantage for the determination of bulk tempera-

tures, but it turns out to be an exclusive advantage if the

surface temperature is the quantity of interest.

The most common type of radiation thermometers

are spectral band radiation thermometers (for the de-

sign principle and a photograph, see Fig. 8.13). The

main components are focusing optics with a set of two

apertures deﬁning the observed part of the target sur-

face and the ﬁeld of view. Within the optical path a band

ﬁlter selects the wavelengths of interest. Finally a radi-

ation detector converts the collected light ﬂux into an

electrical current which is ampliﬁed and indicated on

the display.

Although everything radiates, only for certain ge-

ometric conﬁgurations can the radiance be calculated

ab initio, so that they can be used for calibration

Part C 8.5

480 Part C Materials Properties Measurement

Shutter Plano-convex lens Pilot laser

Field stop

Focussing Translation stage

Aperture

Interference filter

Detector

Motor drive

Temperature

controlled housing

Fig. 8.13 Principle design and photograph of a radiation thermo-

meter

of electromagnetic radiation detectors, especially for

radiation thermometers. Those calculable sources are

blackbodies, which radiate according to Planck’s law

(Table 8.3), and electron storage rings, which deliver

synchrotron radiation at higher energies following the

Schwinger formula. Because the wavelengths used in

radiation thermometry mainly coincide with the regime

of Planck’s law, blackbodies operating at the ﬁxed point

temperatures of ITS-90 are the natural devices for tem-

perature calibrations.

The spectral radiance L

meas

measured by a spectral-

band radiation thermometer is given by (8.30)for

sample temperatures higher than 200

◦

meas

=ε(λ)L



λ, T



. (8.30)

This is the spectral radiance of a blackbody L

(λ, T

)

at the sample temperature T

corrected by the emissivity

ε(λ) of the sample surface. Applying Wien’s radiation

law

(λ, T ) =



/λ



exp



−c

/λT



(8.31)

as a valid approximation for the blackbody radiation at

the wavelengths shorter than λ

max

commonly used in ra-

diation thermometry the true temperature of the sample

surface T

can be estimated from the measured radiance

temperature T

meas

according to

1/T

=1/T

meas

+(λ/c

)ln[ε(λ)] . (8.32)

meas

is the temperature derived from the spectral ra-

diance L

meas

by Wien’s law. If the sample temperature

is below 200

◦

C, the detector’s own radiance must be

compensated.

Calibration of a radiation thermometer is performed

by comparison with a source of known radiance. This

can be done by measuring the emission of a tungsten

strip lamp or, as mentioned, of a blackbody at a cer-

tain temperature known from a calibrated, e.g., platinum

thermometer or preferably of a temperature ﬁxed point

blackbody. If only an uncalibrated light source is avail-

able, one may compare the thermometer under test with

a reference radiation thermometer when they both ob-

serve the radiance of a light source with stable emission.

There are several other types of radiation thermome-

ters, such as the disappearing-ﬁlament thermometer, the

ratio thermometer, and the multispectral radiation ther-

mometer, which are not described here [8.53]. Based

on a different physical law, the Stefan–Boltzmann law

(Table 8.3), total radiation thermometers measure a sig-

nal proportional to T

. They often collect the radiation

of the target incident on a hemisphere. Therefore, the

distance to the object has to be quite short. Further ther-

mometers use optical ﬁbres to conduct the light to their

detector. In some cases the other end of the ﬁbre is

covered by a sort of small blackbody, the temperature

of which is changed by thermal contact with the tar-

get. Its temperature is then determined from its spectral

radiance as described above.

8.5.7 Cryogenic Temperature Sensors

Temperatures near absolute zero seem to be of inter-

est only to specialists in ultra-low temperature physics.

However, a lot of important material properties, which

are of increasing interest for technical applications,

change with decreasing temperature, superconductivity

and superﬂuidity being the most prominent examples.

There are further macroscopic quantum phenomena,

such as the Josephson effect, that are essential for

the highest sensitivity magnetic-ﬁeld sensors (supercon-

ducting quantum interference devices or SQUIDs) or

the quantum Hall effect as basis for the international

standard for the resistance unit ohm. As a consequence

the CIPM recently adopted an extension of the in-

ternational temperature scale from the lower end of

ITS-90 near 1 K down to below 1 mK, the Provisional

Part C 8.5

Thermal Properties 8.5 Temperature Sensors 481

Low Temperature Scale of 2000 (PLTS-2000). It is

given by the deﬁnition of the relation between pressure

and temperature along the melting curve of

He. This

solid–liquid phase transition can be described by the

Clausius–Clapeyron equation in principle. But, since

the molar volumes and entropies of the solid and the

liquid phase are not known with sufﬁcient accuracy,

a polynomial with internationally agreed coefﬁcients is

used [8.54].

Before cooling the sample and the thermometer

is ﬁlled from the gas-handling system into the mea-

suring cell (Fig. 8.14) via a capillary. The pressure in

the cell at low temperatures varies within the range

2.9–4.0 MPa and is determined capacitively. One of

the cell walls is shaped as a membrane and responds

to pressure changes by changing the distance between

the moving plate glued to it and the ﬁxed counter plate

(center plate). The center plate and the reference plate

represent a stable reference capacitor at low tempera-

tures. The resolution of the capacitance bridge indicates

distance changes between the plates of the order of only

fractions of an atomic diameter, which yields a temper-

ature resolution of some μK at 1 mK up to some 100 μK

at 1 K.

The temperature values related to the

He pres-

sure were determined by primary thermometry based

on a noise thermometer with a resistive SQUID as

the temperature-sensitive element (Table 8.3). It was

cross-checked by several magnetic thermometers de-

scribed later on. Nuclear orientation thermometry is

a further primary method at millikelvin temperatures.

It relies on the temperature-dependent ordering of the

magnetic moments of radioactive nuclei indicated by

the anisotropy of their emitted γ radiation. The prob-

4.0

3.8

3.6

3.4

3.2

3.0

2.8

0 0.2 0.4 0.6 0.8 1

p(MPa)

T (K)

Phase transition 0.902 mK

Minimum 315.24 mK

Solid

Liquid

Reference plate

Centre plate

Moving plate

Diaphragm

Silver sinter

He fill line

I 3 Pa

1μK

3 Pa

Fig. 8.14 The melting pressure of

He and the capacitive pressure sensor to measure it

lem of this thermometer is its narrow temperature range

depending on the activation of the sensor. There is

a danger of overheating at low temperatures with high

activities, and of insufﬁcient sensitivity at high temper-

atures with low activities.

For practical temperature measurements, different

resistance thermometers are used. The principle of

these measurements is described in Sect. 8.5.3. The

RhFe resistors mentioned there are suitable for tem-

peratures down to 1 K. Below that, germanium and

carbon resistors have been the favourites for a long time.

These are semiconducting materials with a temperature-

dependent resistance caused by the carriers being frozen

with falling temperature. Over recent years further types

of resistors have been developed by different manufac-

tures (carbon-glass resistors, carbon-ceramic resistors,

ruthenium-oxide sensors).

Magnetic thermometers show a temperature-depen-

dent magnetization. If the magnetic moments of either

the electronic shell of the thermometer’s atoms or of

their nuclei are exposed to a homogeneous and static

magnetic ﬁeld, they order to a certain extend depend-

ing on the lattice or nuclear temperature according to

the Boltzmann distribution. The resulting macroscopic

magnetization is inversely proportional to temperature

(Curie or Curie–Weiss law) and can be probed by sus-

ceptibility or magnetic resonance measurements. The

ﬁrst case is realized with the electronic moment of,

e.g., cerium magnesium nitrate (CMN), which is a use-

ful thermometric substance and workhorse from above

1 K to about 10 mK. For the measurement of tempera-

tures from about 30 mK down to the μK region pulsed

NMR with pure platinum (Pt-NMR) is the standard

method. For both thermometers a precise calibration at

Part C 8.5

482 Part C Materials Properties Measurement

their high-temperature end is essential, where the sig-

nal amplitude unfortunately is low. In addition, both the

construction of the device and the purity of the sens-

ing substance should produce a strictly linear behavior,

because only extrapolation to their respective lowest

temperatures is possible. A detailed description how to

generate very low temperatures and how to measure

them is given in [8.55]and[8.56].

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Part C 8

485

Electrical Prop

9. Electrical Properties

Electronic materials – conductors, insulators,

semiconductors – play an important role in to-

day’s technology. They constitute electrical and

electronic devices, such as radio, television,

telephone, electric light, electromotors, com-

puters, etc. From a materials science point of

view, the electrical properties of materials char-

acterize two basic processes: electrical energy

conduction (and dissipation) and electrical energy

storage.

•

Electrical conductivity describes the ability of

a material to transport charge through the

process of conduction, normalized by ge-

ometry. Electrical dissipation comes as the

result of charge transport or conduction.

Dissipation or energy loss results from the

conversion of electrical energy to thermal

energy (Joule heating) through momen-

tum transfer during collisions as the charges

move.

•

Electrical storage is the result of charge storing

energy. This process is dielectric polarization,

normalized by geometry to be the material

property called dielectric permittivity. As po-

larization occurs and causes charges to move,

the charge motion is also dissipative.

In this chapter, the main methods to char-

acterize the electrical properties of materials

are compiled. Sections 9.2 to 9.5 describe the

measuring methods under the following headings

•

Electrical conductivity of metallic materials

•

Electrolytical conductivity

•

Semiconductors

•

Dielectrics.

As an introductory overview, in Sect. 9.1 the ba-

sic categories of electrical materials are outlined

in adopting the classiﬁcation and terminology

of the chapter Electronic Properties of Ma-

terials of Understanding Materials Science by

Hummel [9.1].

9.1 Electrical Materials ............................... 486

9.1.1 Conductivity

and Resistivity of Metals ............... 486

9.1.2 Superconductivity ........................ 487

9.1.3 Semiconductors ........................... 488

9.1.4 Conduction in Polymers ................ 490

9.1.5 Ionic Conductors .......................... 490

9.1.6 Dielectricity ................................. 491

9.1.7 Ferroelectricity and Piezoelectricity 492

9.2 Electrical Conductivity

of Metallic Materials ............................. 493

9.2.1 Scale of Electrical Conductivity;

Reference Materials ...................... 493

9.2.2 Principal Methods ........................ 494

9.2.3 DC Conductivity, Calibration

of Reference Materials .................. 496

9.2.4 AC Conductivity, Calibration

of Reference Materials .................. 496

9.2.5 Superconductivity ........................ 497

9.3 Electrolytic Conductivity ........................ 498

9.3.1 Scale of Conductivity..................... 498

9.3.2 Basic Principles ............................ 499

9.3.3 The Measurement

of the Electrolytic Conductivity....... 501

9.4 Semiconductors .................................... 507

9.4.1 Conductivity Measurements........... 507

9.4.2 Mobility Measurements................. 510

9.4.3 Dopant and Carrier Concentration

Measurements ............................. 513

9.4.4 I–V Breakdown Mechanisms ......... 518

9.4.5 Deep Level Characterization

and Minority Carrier Lifetime ......... 519

9.4.6 Contact Resistances

of Metal-Semiconductor Contacts... 523

9.5 Measurement

of Dielectric Materials Properties............ 526

9.5.1 Dielectric Permittivity ................... 527

9.5.2 Measurement of Permittivity ......... 529

9.5.3 Measurement of Permittivity

Using Microwave Network Analysis . 532

9.5.4 Uncertainty Considerations............ 536

9.5.5 Conclusion .................................. 537

References .................................................. 537

Part C 9

486 Part C Materials Properties Measurement

9.1 Electrical Materials

One of the principal characteristics of materials is

their ability (or lack of ability) to conduct electrical

current. According to their conductivity σ they are di-

vided into conductors, semiconductors, and insulators

(dielectrics). The inverse of the conductivity is called re-

sistivity ρ that is ρ =1/σ . The resistance R of a piece of

conducting material is proportional to its resistivity and

to its length L and is inversely proportional to its cross-

sectional area A: R = Lρ/A. To measure the electrical

resistance, a direct current is applied to a slab of the ma-

terial. The current I through the sample (in ampere), as

well as the voltage drop V on two potential probes (in

volt) is recorded as depicted in Fig. 9.1.

The resistance (in ohm) can then be calculated by

making use of Ohm’s law V = RI. Another form of

Ohm’s law j =σ E links current density j = I/A,that

is, the current per unit area (A/cm

), with the conduc-

tivity σ (Ω

−1

or siemens per centimeter) and the

electric ﬁeld strength E = V/L (V/cm).

The conductivity σ of different materials at room

temperature spans more than 25 orders of magni-

tude as depicted in Fig. 9.2. Moreover, if one takes

the conductivity of superconductors, measured at low

temperatures, into consideration, this span extends to

40 orders of magnitude (using an estimated conduc-

tivity for superconductors of about 10

−1

This is the largest known variation in a physical

property.

9.1.1 Conductivity and Resistivity of Metals

For metallic materials it is postulated that they contain

free electrons which are accelerated under the inﬂuence

of an electric ﬁeld maintained, for example, by a battery.

The drifting electrons can be considered, in a prelimi-

nary, classical description, to occasionally collide (that

is, electrostatically interact) with certain lattice atoms,

thus losing some of their energy. This constitutes the

electrical resistance.

Semiconductors or insulators which have only

a small number of free electrons (or often none at all)

display only very small conductivities. The small num-

ber of electrons results from the strong binding forces

between electrons and atoms that are common for in-

sulators and semiconductors. Conversely, metals which

contain a large number of free electrons have a large

conductivity. Further, the conductivity is large when

the average time between two collisions τ is large.

Obviously, the number of collisions decreases (i. e.,

τ increases) with decreasing temperature and decreas-

ing number of imperfections. The simple free electron

model describes the electrical behavior of many mater-

ials reasonably well.

Electron Band Model

Electrons of isolated atoms (for example in a gas)

can be considered to orbit at various distances about

their nuclei. These orbits constitute different energies.

Speciﬁcally, the larger the radius of an orbit, the larger

the excitation energy of the electron. This fact is often

represented in a somewhat different fashion by stating

that the electrons are distributed on different energy

levels, as schematically shown in Fig. 9.3.

These distinct energy levels, which are characteris-

tic for isolated atoms, widen into energy bands when

atoms approach each other and eventually form a solid

as depicted on the left-hand side of Fig. 9.3. Quantum

mechanics postulates that the electrons can only reside

within these bands, but not in the areas outside of them.

The allowed energy bands may be noticeably separated

from each other. In other cases, depending on the ma-

terial and the energy, they may partially or completely

overlap. In short, each material has its distinct electron

energy band structure. Characteristic band structures for

the main classes of materials are schematically depicted

in Fig. 9.4.

The band structures shown in Fig. 9.4 are somewhat

simpliﬁed. Speciﬁcally, band schemes actually possess

a ﬁne structure, that is, the individual energy states

Battery

Ampmeter

Voltmeter

–

Fig. 9.1 Principle of the measurement of the resistance of

a conductor

Part C 9.1

Electrical Properties 9.1 Electrical Materials 487

Quartz

Dry wood

Rubber

NaCl

Mica

Glass

GaAs

Doped Si

SiO

porcelain

Insulators

Semiconductors

Metals

–20

–18

–16

–14

–12

–10

–8

–6

–4

–2

Ω cm

Fig. 9.2 Conductivity scale of materials

(i. e., the possibilities for electron occupation) are often

denser in the center of a band (Fig. 9.5).

Some of the bands are occupied by electrons while

others remain partially or completely unﬁlled. The de-

gree to which an electron band is ﬁlled by electrons

is indicated in Fig. 9.4 by shading. The highest level

of electron ﬁlling within a band is called the Fermi

energy E

. Some materials, such as insulators and semi-

conductors, have completely ﬁlled electron bands. (They

differ, however, in their distance to the next higher band.)

Metals, on the other hand, are characterized by partially

ﬁlled electron bands. The amount of ﬁlling depends on

the material, that is, on the electron concentration and the

amount of band overlap.

According to quantum theory, ﬁrst only those ma-

terials that possess partially ﬁlled electron bands are

capable of conducting an electric current. Electrons can

then be lifted slightly above the Fermi energy into an al-

lowed and unﬁlled energy state. This permits them to be

accelerated by an electric ﬁeld, thus producing a current.

Second, only those electrons that are close to the Fermi

energy participate in the electric conduction. Third, the

number of electrons near the Fermi energy depends on

the density of available electron states (Fig. 9.5). The

conductivityin quantum mechanical terms yields the fol-

lowing equation: σ =1/3e

τ N(E

), where v

is the

velocity of the electrons at the Fermi energy (called the

Fermi velocity) and τ N(E

) is the density of ﬁlled elec-

tron states (called the population density) at the Fermi

energy. Monovalent metals (such as copper, silver, and

gold) have partially ﬁlled bands, as shown in Fig. 9.4.

Their electron population density near the Fermi energy

is high which results in a large conductivty. Bivalent met-

als, on the other hand, are distinguished by overlapping

upper bands and by a small electron concentration near

the bottom of the valence band. As a consequence, the

electron population near the Fermi energy is small which

leads to a comparatively low conductivity. For alloys, the

residual resistivity increases with increasing amount of

Energy

Electron band

Forbidden band

Energy levels

Solid Gas

Distance between atoms

Fig. 9.3 Schematic representation of electron energy levels in ma-

terials

solute content. Finally, insulators have completely ﬁlled

(and completely empty) electron bands which results in

a virtually zero population density as shown in Fig. 9.4.

Thus, the conductivity in insulators is virtually zero.

9.1.2 Superconductivity

The resistivity in superconductors becomes immeasur-

ably small or virtually zero below a critical tempera-

ture T

. About 27 elements, numerous alloys, ceramic

materials (containing copper oxide), and organic com-

pounds (based, e.g., on selenium or sulfur) have been

found to possess this property (Table 9.1).

It is estimated that the conductivity of superconduc-

tors below T

is about 10

−1

. The transition

temperatures where superconductivity starts range from

0.01 K (for tungsten) up to about 125 K (for ceramic su-

perconductors). Of particular interest are materials with

above 77 K, that is, the boiling point of liquid nitro-

Part C 9.1