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Lidong Chen
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THERMOELECTRIC MATERIALS
AND DEVICES
THERMOELECTRIC
MATERIALS AND
DEVICES
LIDONG CHEN
RUIHENG LIU
XUN SHI
Shanghai Institute of Ceramics,
Chinese Academy of Sciences,
Shanghai, China
Elsevier
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Contents
1. General principles of thermoelectric technology 1

1.1 Introduction 1
1.2 Thermoelectric effects 2
1.2.1 Seebeck effect 2
1.2.2 Peltier effect 5
1.2.3 Thomson effect 6
1.2.4 Relations between thermoelectric effects and coefficients 7
1.3 Theory of thermoelectric power generation and refrigeration 8
1.3.1 Thermoelectric power generation 9
1.3.2 Thermoelectric refrigeration 14
References 18
2. Strategies to optimize thermoelectric performance 19

2.1 Introduction 19
2.2 Basic theory for transports in thermoelectrics 20
2.2.1 Band model for carrier transport 20
2.2.2 Scattering of carriers 26
2.2.3 Thermal transport and phonon scattering in solids 27
2.2.4 β factor as a performance indicator for thermoelectric materials 31
2.3 Approaches to optimize thermoelectric performance 33
2.3.1 Band convergence 33
2.3.2 Electron resonant states 35
2.3.3 Alloying 35
2.3.4 Phonon resonant scattering 37
2.3.5 Liquid-like thermoelectric materials 39
2.4 Thermoelectricity in nanoscale and nano-thermoelectric materials 40
2.4.1 Carrier transport in nanoscale 41
2.4.2 Heat transport in nanoscale 44
2.4.3 Nanocrystalline and nanocomposite thermoelectric materials 46
References 48
3. Measurement of thermoelectric properties 51

3.1 Introduction 51
3.2 Measurement for bulk materials 51
3.2.1 Electrical conductivity 51
3.2.2 Seebeck coefficient 53
3.2.3 Thermal conductivity 56
v
vi CONTENTS
3.3 Measurement for thin films 62

3.3.1 Measurement of thermal conductivity of thin films 62
3.3.2 Measurement of electrical resistivity of thin films 67
3.3.3 Measurement of Seebeck coefficient of thin films 70
3.3.4 Measurements of electrical conductivity and Seebeck coefficient of
nanowires 72
3.3.5 Measurement of thermal conductivity of nanowires 75
3.4 Conclusion 78
References 79
4. Review of inorganic thermoelectric materials 81

4.1 Introduction 81
4.2 Bismuth telluride and its solid solutions 82
4.3 Lead telluride based compounds: PbX (X 5 S, Se, and Te) 87
4.4 Silicon-based thermoelectric materials 93
4.4.1 Si-Ge alloys 93
4.4.2 Mg2X (X 5 Si, Ge, and Sn) 95
4.4.3 High manganese silicide 98
4.4.4 β-FeSi2 100
4.5 Skutterudites and clathrates 103
4.5.1 Filled skutterudites 104
4.5.2 Clathrates 110
4.6 Superionic conductor thermoelectric materials 112
4.7 Oxide thermoelectric materials 116
4.8 Others 118
4.8.1 Half-Heusler (HH) compounds 118
4.8.2 Diamond-like compounds 122
4.8.3 SnSe 126
4.8.4 Zintl phases 130
References 134
5. Low-dimensional and nanocomposite thermoelectric materials 147

5.1 Introduction 147
5.2 Superlattice thermoelectric films 148
5.2.1 Synthesis of superlattice thermoelectric films 148
5.2.2 Phonon transport and thermal conductivity in superlattice films 150
5.2.3 Carrier transport in superlattice structure 152
5.3 Nanocrystalline thermoelectric films 157
5.4 Thermoelectric nanowires 159
5.5 Synthesis of nanopowders 161
5.6 Nano-grained and nanocomposite thermoelectric materials 169
5.6.1 Preparation techniques for nanostructured materials 169
5.6.2 Skutterudite-based nanocomposites 171
5.6.3 Multiscaling structures in PbTe-based materials 172
5.7 Summary 174
References 176
CONTENTS vii
6. Organic thermoelectric materials 183

6.2 Doping and charge transport in organic semiconductors 184
6.3 Thermoelectric properties of typical conducting polymers 188
6.3.1 Polyaniline 188
6.3.2 P3HT 192
6.3.3 PEDOT 197
6.3.4 Other organic thermoelectric materials 200
6.4 Polymer-based thermoelectric composites 204
6.4.1 Interface-induced ordering of molecular chain arrangement 205
6.4.2 Interfacial scattering to phonons and electrons 207
6.4.3 Organic/inorganic nanointercalated superlattice 209
6.4.4 Charge transfer by the junctions 212
6.5 Summary 214
References 214
7. Design and fabrication of thermoelectric devices 221

7.2 Structures of thermoelectric devices 222
7.3 Fabrication and evaluation technologies of thermoelectric devices 225
7.3.1 Manufacturing process 225
7.3.2 Electrodes and interfacial engineering 227
7.3.3 Measurement of electrical and thermal contact resistances 234
7.3.4 Evaluation of conversion efficiency and output power 236
7.3.5 Harman method 238
7.4 Modeling and structure design of thermoelectric devices 240
7.4.1 Modeling approaches 240
7.4.2 Examples of module design by three-dimensional finite element
method 246
7.5 Thermoelectric microdevices 252
7.6 Device service behavior 256
7.7 Summary 261
References 263
Index 269
C H A P T E R
1
General principles of
thermoelectric technology
1.1 Introduction
The first thermoelectric effect, namely the Seebeck effect, was discov-
ered in 1821, which describes the electromotive force generated by the
temperature difference. In the following thirty years or more, Peltier
effect and Thomson effect were successively discovered. These effects
are the three main physical effects in thermoelectric technology that
describe the direct conversion between thermal and electrical energies
[13]. Although the discoveries of both Seebeck and Peltier effects were
made using a circuit composed of two different conductors and the
effects were only observed at the junctions between dissimilar conduc-
tors, they are actually the bulk properties of the materials involved, not
the interfacial phenomena. Solid state physics developed in the follow-
ing century reveals that all the three thermoelectric effects originate
from the energy difference of carriers in different materials and/or in
the different parts of materials under different temperatures.
Thomson built the relationship among the three effects, and devel-
oped the basic thermodynamic theories for thermoelectric effects [3].
Thomson’s work showed that a circuit composed of two conductors
with positive and negative Seebeck coefficients (usually called the ther-
mocouple) is a type of heat engine. Such heat engine can generate elec-
trical power by virtue of the temperature difference, or pump heat to
realize refrigeration. However, since the reversible thermoelectric effects
are always accompanied by the irreversible Joule heat and heat conduc-
tion, its energy conversion efficiency is principally low. Thermoelectric
effects have been widely used for temperature calibrations as thermo-
couples, but they had no practical application as heat engine, and there
Thermoelectric Materials and Devices Copyright © 2021 China Science Publishing & Media Ltd.
DOI: https://doi.org/10.1016/B978-0-12-818413-4.00001-6 1 Published by Elsevier Inc. All rights reserved.
2 1. General principles of thermoelectric technology
had been no useful theory to guide the design and fabrication of ther-
moelectric heat engines for a long time. Such situation did not change
until 1911, when Altenkirch, for the first time, analyzed the relationship
between the energy conversion efficiency and materials’ physical para-
meters (Seebeck coefficient, electrical conductivity, and thermal conduc-
tivity) in thermoelectric devices [4]. He pointed out that to enhance the
energy conversion efficiency, large Seebeck coefficient and electrical
conductivity, and low thermal conductivity are required. This outlines
the embryo for the criterion that is nowadays used to judge the thermo-
electric performance of materials—figure of merit (Z) or dimensionless
figure of merit (ZT).
This chapter will briefly illustrate the thermoelectric effects and the
relationship between the thermoelectric conversion efficiency and the
physical properties of materials.
1.2 Thermoelectric effects
1.2.1 Seebeck effect

The direct conversion from heat to electricity in solid materials was
discovered by a German scientist, Thomas Johann Seebeck, in 1821. It is
thus named as the Seebeck effect. In the next 2030 years, the research-
ers successively discovered the Peltier and Thomson effects. These three
effects as well as the Joule effect are the physical foundations during the
thermoelectric conversion processes.
Thomas Johann Seebeck connected two different metal wires end-to-
end to form a loop, and then he observed a magnetic field around the
circuit when heating one junction and holding the other at low tempera-
ture, as shown in Fig. 1.1A. He wrote in his paper that “From the above
described experiments, it follows that the main and important condition
for the emergence of magnetism in these metal circuits is the presence
of temperature difference in the circuit links” [1]. Therefore, he named
it as thermomagnetism. Soon after that, this phenomenon was reex-
plained by Hans Christian Oersted. Oersted’s experiment demonstrated
that the magnetic field around the circuit was not directly contributed
by the temperature difference. Instead, the temperature difference gen-
erated a voltage Vab and thus an electric current in the circuit to provide
magnetism observed in experiment. Accordingly, he proposed the con-
cept of thermoelectricity. Nonetheless, since the phenomenon was firstly
discovered by Seebeck, it was named as the Seebeck effect until today.
As shown in Fig. 1.1B, when two conductors (a) and (b) connect each
other with cold-end temperature T and hot-end temperature T 1 ΔT, the

FIGURE 1.1 (A) Experimental phenomenon and (B) equivalent diagram of Seebeck
effect.
electrical potential difference Vab in the circuit can be measured at the

free ends (having the same temperature) of (b), which is expressed as
Vab 5 Sab ΔT (1.1)
where Sab is the differential Seebeck coefficient of the two conductors

with the unit of μV/K. Vab is directional, which depends on the intrinsic
properties of two constituting materials and the direction of tempera-
ture gradient. Sab is defined as positive when the thermoelectric current
flowing from hot end to cold end in conductor (a). Seebeck coefficient is
also called thermopower or thermal EMF coefficient.
The generation of thermoelctric potential can be simply but principally
explained by the fluctuation of charge distribution under a temperature
gradient. As shown in Fig. 1.2, taking the p-type semiconductor (holes are
majority carriers) as an example, when the temperature field is uniform,
the distribution of carriers (concentration, energy, and velocity) is also
uniform and the material as a whole is electrically neutral. When there is
a temperature difference between the two ends of material, the hole car-
riers at the hot end (the temperature is T 1 ΔT) gain higher energy
(E 1 ΔE) than the cold end (the temperature is T), and thus become more
prone to diffuse toward the cold end. Driven by the temperature/energy
difference, more holes diffuse to and accumulate at the cold end, and the
distribution of charges becomes nonuniform anymore, forming an inner
electric field. The inner electric field yields a reversed drift charge cur-
rent. When a dynamic equilibrium is established between the thermal
activated diffuse and inner field driven drift charge flows, a steady volt-
age V is formed.
Based on the definition of thermoelectric potential described earlier, the
absolute Seebeck coefficient of a material at temperature T is defined as
V
S 5 lim (1.2)
ΔT-0 ΔT

FIGURE 1.2 Schematic depiction of Seebeck effect.
The relation between the differential Seebeck coefficient Sab and the
absolute Seebeck coefficients Sa, Sb is
Sab 5 Sa 2 Sb (1.3)
The absolute Seebeck coefficient is independent with the direction

of temperature field and thus it is an intrinsic property of material. In
p-type semiconductors, the majority charge carriers (holes) diffuse
from hot end to cold end driven by the energy gradient, which has
the same direction as thermoelectric potential inside the material.
According to Eqs. (1.1)(1.3), the absolute Seebeck coefficient is posi-
tive. Correspondingly, the direction of the thermoelectric potential in n-
type semiconductors is from cold end to hot end, and the absolute
Seebeck coefficient is negative. Normally, the Seebeck coefficient of
metals is very small with the values about several microvolts per Kelvin
(μV/K), while the Seebeck coefficient of semiconductors can reach sev-
eral tens or hundreds of microvolts per Kelvin (μV/K).

1.2.2 Peltier effect

Peltier effect is the inverse process of Seebeck effect, which describes
the phenomenon of directly pumping heat by carriers (holes and/or
electrons). When applying a current in the circuit composed of two dif-
ferent conductors, in addition the generated Joule heat, extra heat will
be released or absorbed at these two junctions (Fig. 1.3). This effect was
firstly discovered by a French scientist, J.C.A. Peltier, in 1834 and thus
was named as the Peltier effect. Peltier connected Bi and Sb wires and
observed the freezing of the water droplets in one of the junctions of the
two metals when applying an electric current on the circuit. After the
current was reversed, the ice was melted (Fig. 1.3A).
As shown in Fig. 1.3C, when two pieces of conductors with different
Fermi levels are connected and if an electric current is applied on this
link, the electrons will jump either from the high energy level to the low
energy level or in the opposite direction across the interface potential bar-
rier, and therefore either release heat or absorb heat at the junctions. For
example, in the metal/n-type semiconductor link, when the electrons
flow from latter to the former driven by the electric field, the electrons
jump from high energy level to low energy level accompanied with heat
release at the junction. Experimental results show that the heat absorbed
or released per unit time is proportional to the electric current
dQ
5 πab I (1.4)
dt
when current flows from a to b. Here πab is the differential Peltier coeffi-
cient with the unit of V, t is the time, and I is the current. When current
FIGURE 1.3 (A) Experimental phenomenon and (B) schematic depiction of Peltier effect.

flows from metals to p-type materials (electron flows from low-energy-

level conductor to the high one), heat is absorbed, and πab is negative.
Apparently,
πab 5 πba (1.5)
In analogy to Seebeck coefficient, the differential Peltier coefficient at

the junctions is related to the absolute Peltier coefficients of the two con-
stituting materials via
πab 5 πa 2 πb (1.6)
1.2.3 Thomson effect

The fact that both the Seebeck and Peltier effects occur only at junc-
tions between different conductors might suggest that they are interfa-
cial phenomena, but they are really dependent on the bulk properties of
the materials involved. It is known nowadays that these two effects
stem from the different properties of the materials connected together,
that is, the difference in electron energies between the two conductors.
The correlation between Seebeck and Peltier effects had not been real-
ized until William Thomson (later became Lord Kelvin) recognized this
issue in 1855. He analyzed the relationship between Seebeck effect and
Peltier effect and then proposed that there must be the third effect, that
is, when an electric current passes through a piece of uniform conductor
with a temperature gradient, reversible heat absorption or release
should occur through the whole piece beside the Joule heat. This effect
was experimentally verified in 1867 and was termed as Thomson effect.
When an electric current I passes through a piece of conductor with
temperature difference ΔT along the current direction, the heat released
or absorbed per unit time is
dQ
5 βΔTI (1.7)
dt
where β is the Thomson coefficient with the unit of V/K. If the direction
of current is consistent with that of the temperature gradient (from cold
side to hot side) and the conductor absorbs heat, β is positive and vice
versa. Considering the analogy of this expression with the definition of
material’s specific heat, Thomson vividly called β as “specific heat of
the current.” The origin of the Thomson effect is similar to the Peltier
effect. The difference is that the potential difference in the Peltier effect
comes from that of the carriers in different conductors, while it is
caused by the temperature gradient in a single conductor for the
Thomson effect. Compared to the aforementioned two effects, the

Thomson effect contributes little to thermoelectric conversion and is

therefore often neglected in the analysis of energy conversion processes
and device design.
1.2.4 Relations between thermoelectric effects and coefficients

The Seebeck, Peltier, and Thomson effects are the intrinsic properties
of bulk materials and these three coefficients are related to each other.
Thomson derived the relations among these three coefficients according
to equilibrium thermodynamics [3]
πab 5 Sab T (1.8)
TdSab
βa 2 βb 5 (1.9)
dT
These are called the Kelvin relations. The exact derivation of the
Kelvin relations should rely on irreversible thermodynamics [5]. These
two equations are verified by the experimental investigations on numer-
ous metals and semiconductors. For a single conductor, Eq. (1.9) can be
rewritten as
TdS
β5 (1.10)
dT
It can be also rewritten as
ðT
β
S5 dT (1.11)
0 T
The thermoelectric coefficients in Eqs. (1.8) and (1.9) are the differen-
tial values of two conductors. As demonstrated in Eqs. (1.3) and (1.6),
the absolute Seebeck (or Peltier) coefficient becomes equal to the differ-
ential Seebeck (or Peltier) coefficient if the second material in the circuit
is regarded as having zero Seebeck (or Peltier) coefficient. This can be
realized in practice by using a superconductor as the second material,
because both the Seebeck and Peltier coefficients are zero at the super-
conducting state. Generally, the absolute Seebeck coefficient of lead is
calibrated by measuring the differential Seebeck coefficient in the circuit
composed of lead and superconductor. If the absolute Seebeck coeffi-
cient of a material at low temperature is determined by connecting a cir-
cuit using a superconductor as the reference material, by using the
Eq. (1.11), one can find the values at higher temperatures above the crit-
ical superconducting temperature after measuring the Thomson coeffi-
cient [6,7]. Absolute Seebeck coefficients of other materials can be
calibrated by measuring the differential Seebeck coefficients in the

circuit composed of lead and the target materials. The Peltier coefficient
is difficult to measure in the experiment, and therefore it is often calcu-
lated via the Kelvin relation by using the measured Seebeck coefficient.
It is clear that, the Thomson effect is a spontaneous phenomenon as
the Seebeck coefficient changes along a temperature gradient inside a
conductor. Obviously, all the thermoelectric effects take place through-
out the whole material caused by temperature gradients and/or electric
current, though the Seebeck and Peltier effects are observed macroscop-
ically at the junctions.
1.3 Theory of thermoelectric power generation and

refrigeration
A practical thermoelectric device is usually constituted by n- and

p-type materials (legs) connected electrically in series and thermally in
parallel. A pair of n- and p-type legs, conveniently called as π-shape ele-
ment, is the basic unit of a thermoelectric device. Usually, a number of
π-shape elements make up a practical thermoelectric module via a par-
allel or series connection. The working principle of thermoelectric
power generation and refrigeration can be schematically shown in
Fig. 1.4.
Thermoelectric devices can be designed into several configurations
such as plate-like, cascaded, film, and ring-shaped devices for different
applications and/or working environment. Among them, the plate-like
device is the most typical one (Fig. 1.5), which has been widely used as
FIGURE 1.4 Schematic depiction of thermoelectric (A) power generation and

(B) refrigeration.

FIGURE 1.5 Structure and photo of plate-like thermoelectric devices.
power generation and refrigeration. Taking this type of device as an

example, this chapter will describe the relationship between energy con-
version efficiency and material performance (thermoelectric coeffi-
cients). To simplify the model and obtain a concise relation, the
materials’ physical parameters are taken as temperature-independent
constants. In addition, it is assumed that heat flows in the one way from
the hot end to the cold end through thermoelectric legs, and there is no
heat exchange (such as thermal radiation, conduction, and convection)
between the legs and the surrounding medium. However, practically,
the physical parameters (thermal conductivity, electrical conductivity,
and the Seebeck coefficient) of thermoelectric materials are usually
dependent on temperature, and it is not easy to keep unidirectional heat
flow from heat source and sink because the heat exchange between ther-
moelectric legs and surrounding medium cannot be completely pre-
vented. The performance prediction and design of practical devices are
much more complex and will be discussed in detail in Chapter 7,
Design and Fabrication of Thermoelectric Devices.
1.3.1 Thermoelectric power generation

1.3.1.1 Efficiency η
Thermoelectric devices can generate electric power and drive the
load when there is a temperature gradient between the two ends. The
energy conversion efficiency is the most important performance indica-
tor for thermoelectric devices. Giving the temperatures at the hot and
cold ends of the π-shaped device as Th and Tl (shown in Fig. 1.6),
respectively, the thermoelectric energy conversion efficiency (η) is
defined as
P
η5 (1.12)
Qh

FIGURE 1.6 Thermoelectric power generation.
where, P is the output power on the load, and Qh is the heat input at
the hot end (supplied by heat source). Here we do not consider the ther-
mal and electrical resistances at the interfaces as well as the Thomson
heat within the legs. On the assumption of unidirectional heat flow
without side heat dissipation, the net income heat at the hot junction
will be transferred from hot end to cold end by thermal conduction [K
(Th 2 Tl)] and Peltier pump. According to the Peltier effect, when taking
a p-type conductor as example, heat will be absorbed at the current-in
end (hot end in Fig. 1.6) and be released at the current-out end. The
amount of Peltier pumped heat from hot end to cold end in Fig. 1.6 is
πpnI, where I is the current and πpn is the total Peltier coefficient of the
two legs. On the other hand, the net heat income at the hot junction is
composed of two parts, the heat input (supplied from heat source) at
the hot end (Qh) and the Joule heat (I2R/2, where R is the total electrical
resistance of the two legs). Here, it is reasonable to assume that the
Joule heat I2R transfers equally to the hot end and cold end, therefore
only half of the Joule heat (I2R/2) reaches to the hot end. Then, we can
obtain the following equation
1 2
πpn I 1 KðTh 2 Tl Þ 5 Qh 1 I R (1.13)
2

Combining Eq. (1.8), the heat input is

1 2
Qh 5 Spn Th I 2 I R 1 KðTh 2 Tl Þ (1.14)
2
where Spn is the total Seebeck coefficient of n and p legs. The Seebeck
voltage in the circuit is
V 5 Spn ðTh 2 Tl Þ (1.15)
Giving the resistance of the load as Rl, the loop current and output
power are
Spn ðTh 2 Tl Þ
I5 (1.16)
R 1 Rl

Spn ðTh 2TÞl 2
P5 Rl (1.17)
R1Rl
Eq. (1.12) can be refined as

P I 2 Rl
η5 5
Qh 1
Spn Th I 2 I 2 R 1 KðTh 2 Tl Þ
2
(1.18)
S2pn ðTh 2 Tl ÞRl
5
1 2
S RðTh 1 Tl Þ 1 S2pn Th Rl 1 KðR1Rl Þ2
2 pn
Here it is convenient to define a parameter Z, called thermoelectric

figure of merit, as
S2pn
Z5
RK
where Z is mainly determined by the properties of the thermoelectric
lp Ap
legs; R 5 ln
An ρn 1 Ap ρp , K 5 An
ln κn 1 lp κp in which ρ and κ are the electri-
cal resistivity and thermal conductivity, respectively; A and l are the
sectional area and length of the thermoelectric legs. Then the efficiency
can be expressed as
T h 2 Tl Rl =R
η5 (1.19)
Th ð11R1 =RÞ
2
1 1 R1 =R 2 Th2T2hTl 1 ZTh
Th 2 Tl
where Th is the Carnot cycle efficiency. One can define ε 5 Rl/R and
@η @η
obtain the p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi value of η when @ε 5 0. In Eq. (1.19), when @ε 5 0,
maximum
ε 5 Rl =R 5 1 1 ZT (T is the average temperature of the hot and cold

ends, T 5 ðTh 1 Tl Þ=2). Then the thermoelectric generator exhibits the

maximum energy conversion efficiency
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Th 2 Tl 1 1 ZT 2 1
ηmax 5 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (1.20)
Th 1 1 ZT 1 T1 =Th
It is seen from Eq. (1.20) that the maximum efficiency is only related
to the temperature difference and the ZT value. Like other heat engines,
thermoelectric generator takes the Carnot cycle efficiency as the up limit
of its energy conversion efficiency.
As discussed earlier, the parameter ZT of a device is a dimensionless
value, which is determined by the properties of the thermoelectric mate-
rial. It is conventionally to define the dimensionless figure of merit (ZT)
of a material to evaluate its thermoelectric performance
S2 σ
ZT 5 T (1.21)
κ
Clearly, for a given operation temperature range, a larger ZT will
produce higher efficiency. Fig. 1.7 demonstrates the relationship
between the efficiency of thermoelectric power generation and the aver-
age ZT of the material for a given Tl 5 300K and different Th. For exam-
ple, if we want to obtain a 25% efficiency using thermoelectric
technology, a comparable level to the conventional heat engine, the
average ZT of the constituent materials should be larger than 2.0 even
under a hot side temperature of 1000K. Nowadays, for most of the
state-of-the-art thermoelectric materials, the average ZT over wide tem-
perature range is smaller than unity, and thus the conversion efficiency
of practical device is much inferior to the conventional heat engines
(Fig. 1.8). Therefore, enhancing materials’ ZT takes always priority in
field of thermoelectricity.
1.3.1.2 Output power

The Seebeck voltage produced in a device under a temperature gradi-
ent (Th 2 Tl) is V 5 Spn(Th 2 Tl) as shown in Eq. (1.15). Obviously, this
voltage is the sum of the internal voltage drop and the voltage drop on
the road. The latter is the output voltage V0
Rl
V0 5 Spn ðTh 2TÞl (1.22)
Rl 1 R
The current is
Spn ðTh 2 Tl Þ
I0 5 (1.23)
Rl 1 R

FIGURE 1.7 Dependence of ηmax on ZT when the temperature of the cold end is fixed
at 300K.
FIGURE 1.8 Dependence of ηmax on the temperature difference when the temperature
of cold end is fixed at 300K.

Therefore, the output power P0 is derived as

S2pn ðTh 2Tl Þ2 Rl
P0 5 (1.24)
ðRl 1RÞ2
or
ε Spn ðTh 2Tl Þ

2 2
P0 5 (1.25)
ðε11Þ2 R
When the load resistance Rl is equal to the internal resistance R, that

is, ε 5 Rl/R 5 1, the output power reaches the maximum value Pmax
S2pn ðTh 2Tl Þ2 S2pn ΔT2
Pmax 5 5 (1.26)
4R 4R
The corresponding efficiency at the maximum output is

Th 2 Tl
Th
η5 h i (1.27)
Th 2 Tl
22 1
2 Th 1 4
ZTh
Let Al 5 An 1 Ap, the sum of the sectional areas of the two thermo-
electric legs. And then the output power per unit area is
P0 ε S2pn ðTh 2Tl Þ2

5 (1.28)
Al ðε11Þ2 ðAn 1 Ap Þðρn ln =An 1 ρp lp =Ap Þ
1.3.2 Thermoelectric refrigeration

1.3.2.1 Coefficient of performance
Fig. 1.9 shows the working principle of thermoelectric refrigeration.
The main parameters describing the refrigeration performance include
coefficient of performance (COP), maximum refrigerating capacity, and
maximum temperature difference. COP is defined as
Qc
COP 5 (1.29)
P
where Qc is the amount of heat absorbed at the cold end (refrigeration
capacity) and P is the input electric power. As described in Fig. 1.3,
when a current I flows from the n-type leg to the p-type one at the
upper junction in Fig. 1.9, heat absorption and heat release will take
place at the upper junction and the lower junction, respectively, result-
ing in the formation of a temperature drop (ΔT 5 Th 2 Tl) between the

FIGURE 1.9 Working principle of thermoelectric refrigeration.
two ends. The heat pumped from the upper to the lower end per unit
time by Peltier effect is πpnI. At the same time, thermal conduction is
inevitable against the Peltier heat pumping due to the temperature gra-
dient. Giving the total thermal conductance of the legs K, the heat flow
driven by temperature difference is KΔT. Similar as in power generator,
Joule heat will be generated when the current is passed through the
refrigeration device. The Joule heat I2R transfers equally to the hot end
and cold end, therefore only half of the Joule heat (I2R/2) reaches the
cold end. Based on the aforementioned analyses and assumptions, the
thermal balance equation at the cold end can be established:
1 2
QC 1 I R 5 πpn I 2 KðTh 2 Tl Þ (1.30)
2
The refrigerating capacity per unit time at the junction Qc is
1
QC 5 πpn I 2 I 2 R 2 KðTh 2 Tl Þ (1.31)
2
or
1
QC 5 Spn Tl I 2 I 2 R 2 KðTh 2 Tl Þ (1.32)
2

l A
where R 5 Alnn ρn 1 App ρp , K 5 Alnn κn 1 lpp κp . Here the subscripts n and p
represent n- and p-type thermoelectric legs, respectively.
The voltage applied on the two thermoelectric legs is the sum of the
internal voltage drop (VR 5 IR) and the “anti-Seebeck voltage” to over-
come the thermoelectric voltage induced by temperature difference
[VS 5 Spn(Th 2 Tl)]:
V 5 VR 1 VS 5 IR 1 Spn ðTh 2 Tl Þ (1.33)
Therefore, the input power P (the rate of expenditure of electrical

energy by the thermoelectric legs) is
P 5 IV 5 I 2 R 1 Spn ðTh 2 T1 ÞI (1.34)
where the first term is the internal resistive loss and the second term is
the rate of working to overcome the thermoelectric voltage. Substituting
Eqs. (1.32) and (1.34) into the definition of COP, Eq. (1.29), we obtain
Spn Tl I 2 12 I 2 R 2 KðTh 2 Tl Þ
COP 5 (1.35)
I 2 R 1 Spn ðTh 2 Tl ÞI
Apparently, if fixing temperature difference Th 2 Tl, the COP varies

with the applied current. Let d(COP)/dI be zero, one can find the opti-
mum current ICOP at which the COP reaches the maximum value

Sp 2 Sn ðTh 2 Tl Þ
ICOP 5 hpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i (1.36)
R 1 1 ZT 2 1
or
ðSp 2 Sn ÞðTh 2 Tl Þ
ICOP 5 lp
hpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i (1.37)
ln
An ρ n 1 Ap ρ p 1 1 ZT 2 1
where Z holds the same definition as that in Eq. (1.20). Under this opti-
mum current, the maximum efficiency COPmax is
Tl 1 1 ZT 2 Th
COPmax 5 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Tl (1.38)
Th 2 Tl 1 1 ZT 1 1
Correspondingly, the applied voltage and input power are

ðTh 2 Tl Þ 1 1 ZT
ðVCD ÞCOP 5 Spn pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (1.39)
1 1 ZT 2 1
1 1 ZT ðTh 2Tl Þ 2
PCOP 5 Spn pffiffiffiffiffiffiffiffiffiffiffiffiffiffi (1.40)
R 11ZT 21

respectively, where T 5 ðTh 1 Tl Þ=2 is the average temperature of the

thermoelectric elements. Further, one can obtain the released heat per
unit time at the hot end
1 2
Q 5 Qc 1 P 5 Spn Th I 1 I R 2 KðTh 2 Tl Þ (1.41)
2
Similarly, the COP of a thermoelectric device at heating mode is
Spn Th I 1 12 I 2 R 2 KðTh 2 Tl Þ
COP 5 (1.42)
I 2 R 1 Spn ðTh 2 Tl ÞI
1.3.2.2 Maximum depression of temperature ΔTmax

Another key parameter of thermoelectric refrigerator is the tempera-
ture difference that can be established between the two ends
ΔT 5 Th 2 Tl. Obviously, this temperature difference is related to the
refrigerating capacity and current. Based on the thermal balance equa-
tion [Eq. (1.30)], it is obtained that
Spn Th I 2 12 I 2 R 2 Qc
ΔT 5 (1.43)
K
When the cold end is adiabatic, that is, Qc 5 0, let dΔT/dI be 0 under
which ΔT reaches the maximum value, and the optimum current IT is
Spn Tl
IT 5 (1.44)
R
The corresponding maximum temperature depression ΔTmax is
1
ΔTmax 5 ZTl2 (1.45)
2
This can also be used to know the minimum temperature that can be
reached at the cold end of the refrigerator
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 1 2ZTh 2 1
ðTl Þmin 5 (1.46)
Z
ΔTmax or (Tl)min is usually used to evaluate the performance of ther-
moelectric device as refrigerator. They are determined by the figure of
merit (Z) of the constituent thermoelectric materials and the tempera-
ture of heat sink (Th).
1.3.2.3 Maximum refrigerating capacity Qc,max

The heat absorbed per unit time by the refrigerator (or called the
refrigerating capacity) is given by Eq. (1.31). Obviously, for giving

thermoelectric materials, Qc, is related to the current (I) and the tem-
peratures at the two ends (Th, Tl). Similarly, let dQc/dI be 0, one can
obtain the optimum current Iq which satisfies Qc reaching the maximum
value at a certain temperature,
Spn Tl
Iq 5 IT 5 ; (1.47)
R
The corresponding Qc is
S2pn Tl 2
Qc 5 2 KðTh 2 Tl Þ (1.48)
2R
Next, the maximum refrigerating capacity Qc,max is obtained when
the temperature difference is 0, that is,
S2pn Tl 2
Qc;max 5 (1.49)
2R
Apparently, Qc,max is independent of the thermal conducting proper-
ties of the thermoelectric material. In addition, based on Eqs. (1.48) and
(1.49) as well as (1.43) and (1.45), the relationship between the refrigerat-
ing capacity and temperature difference is
Qc 5 KðΔTmax 2 ΔTÞ (1.50)
1
ΔT 5 ðQc;max 2 Qc Þ (1.51)
K
It is seen that Qc varies with ΔT in a linear way. To plot Qc against
ΔT, one can easily find ΔTmax and Qc,max from the intercepts onthe
A
two axes, and the total thermal conductance K K 5 Alnn κn 1 lpp κp of
the thermocouple from the slop. It is convenient to estimate the thermal
conductance of the constituting thermoelectric materials in a device
from the experimental variation of Qc with ΔT.
References
[1] J. Seebeck, Magnetische Polarisation der Metalle und Erze durch Temperatur-
Differenz Abh, Akad. Wiss. Berl. (1822) 289346.
[2] J.C.A. Peltier, Nouvelles Expériemences sur la Caloricite descourants électriques, Ann.
Chim. Phys. 56 (1834) 371386.
[3] W. Thomson, On a mechanical theory of thermo-electric currents, Proc. R. Soc. Edinb.
(1851) 9198.
[4] E. Altenkirch, Elektrothermische Kalteerzeugung, Phys. Z. 12 (1911) 920.
[5] I. Muller, Thermodynamics of Irreversible Processes, North-Holland Pub.Co-distribu-
tors for USA, Interscience Publishers, New York, 1951.
[6] G. Borelius, W.H. Keesom, C.H. Johansson, J.O. Linde, Establishment of an absolute
scale for the thermo-electric force, Proc. K. Akad. Wetensch. Amst. 35 (1932) 1014.
[7] J.W. Christian, J.P. Jan, W.B. Pearson, I.M. Templeton, Proceedings of the royal society
of London series a-mathematical and physical sciences (1958) 213245.

C H A P T E R
2
Strategies to optimize
thermoelectric performance
2.1 Introduction
The dimensionless figure of merit (ZT) is the key criterion that quan-
tifies thermoelectric (TE) performance of materials. According to the
definition ZT 5 S2σT/κ, high-performance TE materials should possess
a large Seebeck coefficient S, a high electrical conductivity σ (S2σ
is termed as power factor), and a low thermal conductivity κ. Fig. 2.1
qualitatively outlines the dependence of the three TE parameters on car-
rier concentrations. σ and S change in crosscurrent with the increase of
carrier concentrations. For most semiconductors, the optimal carrier
concentration corresponding to the highest power factor usually lies
within the range of 10191020 cm23, a value in the heavily doped or
degenerate semiconductors. The thermal conductivity is majorly com-
posed of two parts: lattice thermal conductivity (κL) and electronic ther-
mal conductivity (κe). The latter is proportional to σ, so high electrical
conductivity will directly result in a high κe, which is unfavorable for
high ZT. Due to the correlation and interaction of carriers and phonons,
the strategies aiming at reducing κL by intensifying phonon scattering
usually also influence S and σ. Therefore the three parameters S, σ, and
κ that determine TE performance are basically dependent on each other.
This is the primary cause of why enhancing TE performance is
extremely difficult. The independent and synergetic regulation of
electrical and thermal transports has been the long-term goal in
thermoelectrics.
Based on semiconductor physics and transport theory in solids, this
chapter will outline the basic theory on tuning transport properties of
TE materials and focus on the correlation among the key transport
Thermoelectric Materials and Devices Copyright © 2021 China Science Publishing & Media Ltd.
DOI: https://doi.org/10.1016/B978-0-12-818413-4.00002-8 19 Published by Elsevier Inc. All rights reserved.
20 2. Strategies to optimize thermoelectric performance
FIGURE 2.1 Dependence of electrical conductivity, Seebeck coefficient, power factor,

and thermal conductivity on carrier concentrations.
parameters. The strategies to explore and design high-performance TE

materials based on the developed theoretical models and proposed mul-
tiscale structure modulation in the recent decades will also be
summarized.
2.2 Basic theory for transports in thermoelectrics

2.2.1 Band model for carrier transport
Most of the TE materials are semiconductors. The electrical conduc-
tivity and Seebeck coefficient are mainly determined by material’s
intrinsic parameters, such as carrier concentration, mobility, and scatter-
ing processes. According to the band structure theory of semiconduc-
tors, as considering a single-carrier system with a parabolic band,
carriers are in the equilibrium state and obey the FermiDirac distribu-
tion when the external electrical field is zero. The carrier concentration
is the integral of the density of state (DOS) g(E) at the band edge

2.2 Basic theory for transports in thermoelectrics 21
multiplied by occupancy probability f(E), while g(E) and f(E) can be

expressed as [14]
4πð2m Þ3=2 1=2

gðEÞ 5 E (2.1)
h3
1
fðEÞ 5 (2.2)
1 1 exp Ek2B TEF
where m* is the effective mass of carriers, h is the Planck’s constant, EF

is the Fermi level, kB is the Boltzmann constant, and f is the
FermiDirac distribution function.
When considering the movement of electrons under external electri-
cal field and temperature gradient, the steady state is statistically
described by the Boltzmann equation
@f f 2 f0
1
h̄

ðΔk E ΔTÞ
@T
e
2 ε Δk f 5 2
h̄ τ
(2.3)
where f is the distribution function at the nonequilibrium state, f0 is the

distribution function at the equilibrium state, ε is the external field, rT
is the temperature gradient, τ is the relaxation time, and h̄ is the
reduced Planck’s constant. When the deviation from the equilibrium
state is small, the distribution function is
df ðEÞ f ðEÞ 2 f0 ðEÞ

5 (2.4)
dt τ
For a certain scattering process, a corresponding scattering parameter
λ is introduced, so the relaxation time is related to the carrier energy via
τ 5 τ 0 Eλ21=2 (2.5)
In the one-dimensional (1D) case, it is derived that

fðEÞ 2 f0 ðEÞ d EF E dT
5 Ux eεx 1 T 1 (2.6)
τ dT T T dx
where Ux is the drift velocity along x-direction. Considering the defini-

tion of the current density and the features of parity function integral,
the 1D current density (charge flux) is expressed as
ÐN
ix 5 6 8
0 eUx f ðEÞg0
ðEÞdE
1 9
< d @EF A dT = e dT (2.7)
5 6 e eεx 1 T K1 6 K2
: dT T dx ; T dx

22 2. Strategies to optimize thermoelectric performance
in which 1 and 2 correspond to holes and electrons, respectively. The

heat flux contributed by carriers is
ÐN @f0
jx 5 ϕðEÞdðEÞ
ðE 2 EF ÞUx gðEÞ
0 @E
2 0 1 3
(2.8)
d @EF A dT 5K2 1 1 dT K3 2 EF ix
5 4eεx 1 T
dT T dx T dx e
where
ðN
@f0
Km 5 τUx2 gðEÞEm21 dE ðm 5 1B3Þ (2.9)
0 @E
When rT 5 0, the electrical conductivity is

ix
σ5 5 e2 K1 (2.10)
ex
Based on Eqs. (2.7) and (2.8), the Peltier coefficient can be derived
based on its definition

jx 1 K2
π5 57 2 EF (2.11)
ix e K1
The Seebeck coefficient is

π 1 K2
S5 57 2 EF (2.12)
T eT K1
In fact, Seebeck coefficient can be also derived directly using Eq. (2.7)
under the condition εx 5 0 and ix 5 0. The result is the same with Eq. (2.12).
The carrier thermal conductivity can be calculated based on the defi-
nition under the condition ix 5 0

jx 1 K2
κe 5 2 5 K3 2 2 (2.13)
dT=dx T K1
where the minus sign means that heat transports from high temperature
to low temperature.
Now we have derived three parameters related to ZT by solving the
Boltzmann equation. All of them contain the integral Km that is related
to the distribution of carriers, physical properties of semiconductors,
and the relaxation time. For the spherical iso-energy surface, the drift
mobility is
2E
Ux2 5 (2.14)
3m

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order to make and repair the highways; and by a peculiar irony,
although the great thoroughfares were thus maintained solely at the
peasants' expense, the roads which the peasants really needed, the
cross-roads in agricultural districts, were left to ruin and neglect.
More odious still were the demands of the militia service. Every
unmarried man up to forty years of age could be called upon for this
oppressive duty. No substitution was allowed. Although for the
wealthy the exemptions were innumerable, for the poorest class no
exemption was permitted. Improvident marriages offered the only
means of escape. The approach of the Government's agent was the
signal for panic and disorder, and the miserable villagers fled for
concealment to the woods.
Even more grievous than the Corvée and the militia were the abuses
which pervaded the whole system of taxation. The heaviest of all the
taxes was the terrible burden of the Taille, a direct tax levied
sometimes on property and sometimes on income, falling almost
entirely on the poor—alike on the struggling landowner and on the
landless labourer—assessed without order or method, constantly
varying and constantly increased. Every year in the rural districts
some unfortunate villager was selected to act as collector of the
Taille. He alone had to decide how much each of his neighbours was
worth, and how much he must extort from them to satisfy the
Government, and if his efforts or his calculations failed, his own
property and person were responsible for the amount. The
opportunities for abuse in such a system, for the satisfaction of
personal jealousies and grudges, are as obvious as its unfairness
towards those on whom the office was inflicted. 'The office of
collector,' cried Turgot, 'drives to despair and frequently to ruin all
those on whom it is imposed.' In order to escape the Taille, the
peasant strenuously concealed his savings. If, in spite of his
Government, he prospered, he dared do nothing to give an air of
comfort to his home. We find him in one case entreating his landlord
not to tile the roof of his cottage, because such a sign of prosperity
would mean for him an increase of taxation. It was the object of
every man to seem desperately poor. Then besides the Taille, the
peasant had to pay the accessory taxes, which in process of time
had been assimilated with it; the Poll-tax and the Vingtièmes,
imposts imposed by Louis XIV on all alike, but the weight of which
the powerful classes had contrived to shift on to the shoulders of the
weak; the road-tax, when the Corvées were abolished; the tax of the
franc-fief, whenever he happened to own lands which had once been
the lands of nobles; and always, apart from the demands of the
Exchequer, his seigneur's dues and his pastor's tithe. Statistics may
sometimes be misleading, but an able statistician has calculated,
upon evidence which it is difficult to deny, that, allowing for all these
direct charges, the peasant in many parts of France paid away four-
fifths of his income to the Treasury, the seigneur, and the Church,
and out of every hundred francs he earned, retained little more than
eighteen francs himself[4].
But the record of his troubles did not end there. The Gabelle,
perhaps the most exasperating impost ever devised by an empty
Exchequer, compelled all citizens over seven years of age to
purchase yearly seven pounds of salt from the agents of the State.
But this salt was reserved for cooking and eating alone, and if salt for
any other purpose were needed, the agents of the State had the
right to make its subjects purchase more. The whole system of
indirect taxation was conceived in the same spirit as this monument
of fiscal folly. The face of the country was covered by barriers and
custom-houses, occupied by an army of revenue officers, who
purchased from the Government the right of collecting the customs
and excise. Twelve hundred leagues of artificial frontiers separated
the various provinces of France, impeded trade, and played havoc
with prices. The small vine-growers were almost ruined by the excise
levied upon wine, which even in those days was conspicuous for its
severity and for the inquisitorial practices of those who enforced it.
Calonne declared that the salt tax alone produced every year nearly
four thousand sentences, of imprisonment, flogging, exile and the
galleys. Under such auspices smuggling multiplied, and the
Government retorted by heavy punishments. Bodies of armed
banditti were organised in disturbed districts, and carried on for
years together a guerilla war against the forces of the Crown.
Unemployed labourers and ruined peasants found a livelihood in
swelling the ranks of disaffection, and in the absence of any poor-law
administration, mendicancy and vagabondage rapidly increased.
The records of the last years of the Ancien Régime are consequently
full of evidence of alarming and growing disorder. Townspeople
complained that the beggars, driven from the country, flocked into
the cities for shelter. The Intendants reported to the Council that the
chief highways of the kingdom were infested with dangerous
vagrants. In vain the Government multiplied its corn-laws and
arrests, and endeavoured to stifle the clamours of indigence by
feeding some and by punishing others. In 1767, fifty thousand
beggars were arrested; but in 1777, the numbers of that unfortunate
class had risen to nearly a million and a quarter. In Paris the census
of 1791 declared that out of a population of six hundred and fifty
thousand, over one hundred and eighteen thousand were without the
means of regular subsistence. It is easy to understand how, pressed
by hunger, and pursued by a rigorous penal code, many of these
wandering mendicants crossed the thin line which separates
extreme want from crime, and how, when the Old Monarchy
suddenly collapsed, and when in the search for freedom law was for
the moment lost, this large group of miserable beings, armed with
brief power and long-accumulated hatred, exacted a terrible revenge
for the wrongs of the labouring community in France, from whose
ranks they and their ancestors had been driven by a system
politically and socially unjust.
Such, in the eighteenth century, were some of the conditions of life in
France. Each class lived apart, entrenched in its own chilling
traditions. 'Nobody,' cried Turgot, 'cares for any interest but his own.'
Local patriotism, common intercourse, friendly feeling, no longer
drew men of different ranks together. The sense of citizenship had
generally died out. Below the others the peasant stood alone. His
poverty clung to him as a garment of shame. His commonest
impulses were want and fear. His love of legend made him
superstitious. His ignorance made him credulous, bigoted,
suspicious, easily persuaded to believe in evil. Isolated from the
world, conscious of belonging to an inferior caste, encountering on
all sides the privileges of his masters, and yet with no superior to
care for him and no wise counsellor to guide him, blunted in feeling
by long endurance, gentle, submissive, often gay, but more often
brooding on the indignities which he suffered, and resenting the
injustice even more than the hardship of his lot, he heard and
welcomed with passionate illusion the new doctrine of human
dominion, which proclaimed that men were equal, whatever their
station, whatever their distress, and from that moment the attainment
of equality, so easy to imagine, so hard to approach, became the
commanding ideal of the poor.
FOOTNOTES:
[1] It will be understood that in the Pays d'État, the powers of the
Intendants, as regarded taxation and public works, were limited
and controlled by the rights of the local assemblies.
[2] The expenses of the royal table amounted to nearly three
hundred thousand pounds a year.
[3] I have taken all these figures from M. Taine's Ancien Régime,
and have reduced them roughly to their equivalents in English
money of our own day. I have, however, throughout calculated the
livre at 10d., although Arthur Young puts it as high as 10-1/2d.; so
that the amounts in the text are, if anything, understated.
[4] One part of the taille, that which fell upon the cultivator,
reached the privileged orders indirectly through their farmers, but
even then there were certain exemptions in their favour. The
franc-fief was the tax of one year's revenue levied every twenty
years on non-noble holders of noble lands. The calculation of
income given here I take from the note on the subject contained
in the appendix to M. Taine's volume on the Ancien Régime,
which is founded on the procès-verbaux of the provincial
assemblies. On an income of 100 francs, he estimates the taille
(with its accessories), the poll-tax, and the road-tax together, at
42 fr. 15 c.; the two vingtièmes at 11 fr., the tithe at 14 fr. 28 c.,
and the feudal dues at 14 fr. 28 c.; total 81 fr. 71 c.
CHAPTER II.
The Last Years of the Ancien Régime.
The decay of the old society was accompanied in France by a decay
of the ideas which were inseparably associated with it, and which,
long kept alive by authoritative sanctions, had exacted, not always
without violence, the reverence of men. As the State had usurped
the control of every department of action, so the Roman Catholic
Church had usurped the control of every department of thought.
Resting serenely upon authority and dogma, it had dictated and
circumscribed the knowledge of its subjects, had directed their
intellectual interests, and had aimed at supplying not only a religion
to govern their conduct, but also a complete theory to govern their
lives. Against this monopoly, and the conceptions on which it was
established, the best minds of the eighteenth century rose in revolt,
and their revolt was celebrated by an outbreak of active and intrepid
thought. Beginning in the mysterious domain of physical science,
with great discoveries in astronomy, chemistry, physics, geology and
mathematics, the new spirit of enquiry spread like a flame to illumine
other topics. Its votaries, rejecting ancient tradition and immemorial
habit, turned with sudden enthusiasm to observation and analysis,
and built up for themselves step by step new systems of knowledge,
based, not on what their teachers taught them, but on positive facts
which they had ascertained and tested for themselves. The vivid
curiosity thus aroused woke in them distrust of all preconceived
notions, banished the reverent awe which had restrained earlier
generations, and broke down the old barriers of belief.
Before long the passion for investigation passed beyond the limits of
physical science, and ranging far afield, entered the domain of
theology, of economics, of politics and social laws. In all fields alike
there appeared the same disposition to repudiate opinions previously
held, to examine afresh, under no restrictions, the principles which
lay at the root of religion and government, the general laws which
regulated human institutions, the origin of existing conceptions of
society and property, of justice and right. Tradition was dethroned,
and reason was set up in its seat, as the only test by which opinions
could be determined, without regard to the subordinate place which
reason fills in the conduct of men. The classical spirit, with its finish,
its artificiality, its limitations, already dominant in France, set its
stamp upon the new philosophy, and afforded the vehicle for
conveying it to the world. In successive generations of polished
intercourse, the French language had acquired extreme nicety and
clearness of expression; it was admirably fitted for criticism, analysis,
argument, definition; and it thus rendered the new ideas at once
popular and lucid. A passion for philosophical discussion took hold of
the educated world, and carried them past the facts which they ought
to have noticed, to theories which seemed more distant and
consequently more profound. All alike began to speculate, to
generalise, to enquire into the meaning of many things, the current
interpretation of which they had determined no longer to accept;
while the necessity, from which all Frenchmen suffer, of never being
dull, encouraged superficiality in the new search for truth, and
checked the close study of history, which alone could have avoided
error.
As the secrets of the universe unfolded, and as men learned how
clear and simple were the laws of physical nature, they determined
that there must be other laws of nature, equally clear and simple, to
explain society and politics; and finding this theory lamentably
contradicted by the confusion of institutions and abuses round them,
they began to assail those institutions and abuses with the audacity
which science gives. Law and religion in their actual forms were so
corrupt that the shocked imagination of these dreamers fell back
upon ideals of natural religion and natural law. Far aloof themselves
from actual politics, untrained by that wisdom of many voices which
free political discussion bestows, dissatisfied with their own political
customs, but disdaining to study thoroughly the political customs of
others and the origin of all, they proceeded to formulate, by the aid of
pure reason, theories which would satisfy their newly roused
emotions, and fit in with some apparently more simple and scientific
formula of life. All those for whom politics in practice were a sealed
book, took refuge in these politics of the imagination, and the political
world in France found itself presently divided into two camps, one
consisting of those who governed, the other of those who
discoursed, the latter perpetually establishing principles, which the
former perpetually broke. A society devoted to letters and to
conversation embraced and disseminated the speculative literature
of the age, and thus the great literary men of the eighteenth century
became in France what politicians sometimes strive to be in happier
lands, the fountains of political inspiration, and the real leaders of
public thought.
Among the pioneers of the new doctrines two men stand out
conspicuously in each half of the century,—Montesquieu and Voltaire
in the first half, Diderot and Rousseau in the second. Montesquieu,
the earliest of the philosophers, was a polished and eminent lawyer,
well versed in history, serious, acute, a profound student of human
institutions, and the master of a terse and pointed style. His writings,
generally speaking, were no mere flights of pert fancy, but the result
of systematised and careful thought, weighty, luminous, moderate in
tone, and scientifically sane. It was Montesquieu, who, in his Lettres
Persanes, initiated the philosophic movement, and unmasked the
batteries of criticism and satire, which for two generations were to
play so effectively upon the foundations of the old monarchy in
France. It was Montesquieu, who, twenty seven years later, when he
produced the great work of his life, the Esprit des Lois, analysed with
clear and wide sagacity the laws which regulate human governments
and customs, and thus destroyed the mysterious prestige which had
never till then been stripped from the ancient institutions of France. It
was Montesquieu, who first exposed those institutions to a ruthless
analysis which they could not stand. But the slow and careful
method, which was Montesquieu's distinction, was less popular with
his successors. It involved too much trouble. It ran the risk, except in
a master's hands, of being dull. The classical spirit, the French
temperament, the love of amusement combined to guide criticism
into an easier groove, and the philosophic movement, without
altogether deserting the studious atmosphere of facts, adopted a
more becoming garment in the exquisite raillery of Voltaire.
Voltaire's life extended long past the middle of the century, and its
closing years were the years of its greatest triumphs. But he yet
belongs to the generation of Montesquieu rather than to that of
Rousseau. Under him, the tone of the new movement altered. It
became lighter, and bolder too. Its reserve vanished. Its intrepidity
increased. It entered every field. It illumined every subject. In verse,
in prose, in history, in drama, in romance, Voltaire assailed traditions,
beliefs, abuses, exposing mercilessly their shortcomings and shifts,
laughing aloud over their absurdities, denying the pretensions which
they boasted, denouncing the iniquities to which they led. Voltaire's
rare and versatile wit, his light touch, his unabashed scepticism, his
brilliant common-sense, appealed irresistibly to the minds of his
countrymen. He made the philosophic movement popular. He
identified it with many errors, and with the gravest faults of taste. But
with it all he taught men to despise many follies and to impeach
many wrongs.
It was Voltaire who gave to the literary movement that decisive tone
of irreligion, which it so long retained. The Church stood in the van of
the opponents whom the philosophers had to encounter, and to
attack the Church, her practice and her creeds, was to Voltaire an
intellectual delight. More than any other institution the Church in
France represented the spirit of tradition, of authority, of submission
to formulas, of reverence for the past. As such, she was certain to
view with alarm the new spirit of independent enquiry. Of all forms of
political power, the political power of the Church was the most
unpopular. She stepped in to support with mysterious sanctions the
civil institutions which many felt were unjust. As the censor of the
Press, she represented the Government at the very point where the
Government and the philosophers came into conflict. Of all the
supports of the old order, she was in many ways the most open to
attack. Consequently, the philosophic movement from the first
brought its forces to bear upon the Church, and Voltaire led the
onslaught with the irreverent vivacity of his nature, and the rich
splendour of his information and literary resource.
In the middle of the eighteenth century, however, the conduct of the
philosophic movement passed to a large extent into younger hands.
In 1751, the first volume of the celebrated Encyclopaedia
concentrated public attention on a group of writers of no common
range and understanding, all inspired with the new spirit, and
combined to carry it into every field of economic, political, and social
action. The Encyclopaedists numbered among them many
distinguished men. On the roll of their contributors we find the names
of Turgot, Rousseau, Buffon, Marmontel. D'Alembert, the
accomplished mathematician, brought to the work his trained
abilities, his admirable style, and the wisdom acquired by a student
during a life spent in frugality and independence. But the greatest of
the staff, the most original in genius, the most reckless in expression,
and the most intense and imaginative in thought, was the brilliant,
perverse, impetuous Diderot, with his extraordinary, magnetic
conversation, his indomitable perseverance, his genuine
consciousness of his own shortcomings, his ardent desire for the
improvement of mankind. It is significant that nearly all the prominent
members of the Enyclopaedic party had been brought up as pupils of
the Jesuits, and unquestionably, as a party, they associated
themselves with a pronounced attack upon the chief tenets of the
Catholic Church. But it is difficult and not very profitable to attempt to
assign definite names of obloquy to the varieties of disbelief within
their ranks, and it is a grave mistake to regard that aspect of their
writings as the most characteristic or important. What gave to the
enterprise its force and success was the fact that it travelled far
beyond the barren conflicts of theology, and brought the new ideas,
the new habit of enquiry and analysis, the new fearlessness of social
comment, and the new humanitarian zeal, to investigating political
and economic phenomena, to preparing the way for practical reform.
The glory of the Encyclopaedists lies not in their contempt for things
holy, but in their hatred of things unjust, in their denunciation of the
trade in slaves, of the inequalities of taxation, of the corruption of
justice, of the wastefulness of wars, in their dreams of social
progress, in their sympathy with the rising empire of industry, which
was beginning to transform the world.
Posterity is more familiar with the defects than with the virtues of this
strange episode in human thought. Its ideals were disfigured by
many faults—by unreality, political ignorance, dangerous license,
violent extremes. In its anxiety to escape from conventions, it relaxed
necessary codes. It made impiety obstreperous. It hastily adopted a
belief in the perfectibility of man, to fill the niche where once had
rested a belief in the perfection of God. In place of the traditions and
systems which it uprooted, it taught its followers to look for guidance
to their own instincts, and to vague aspirations after imaginary
systems of natural law. It planted in the French people an
inextinguishable desire to abolish everything which reminded it of the
past, however much they might suffer in the attempt. Its teaching
seemed to discourage the impulses of virtue, and to offer no
satisfaction for the spiritual needs of man. Helvetius' famous treatise
De l'Esprit laid down, amid much shallow commonplace, the
depressing doctrine that self-interest dictates both the conduct and
the views of men, and that the attainment of pleasure is their only
final aim. Holbach's not less famous Système de la Nature touched
the climax of a century of philosophical commotion, in its passionate
indictment of the vices of kings and the slavery of men, in its direct
demand for revolution, in its remorseless rejection of every form of
faith, in its insistence upon atheism and materialism as the only true
philosophy of life. 'Religious and political errors,' cried Holbach, 'have
changed the universe into a valley of tears.'
Beside the contributors to the Encyclopaedia, and sometimes among
them, were men of different schools of thought, allied with them in
advocating change. Quesnai and Turgot were conspicuous in the
ranks of an eminent sect termed by some Economists, by others
Physiocrats. The Economists shared with Diderot and his colleagues
the zeal for reform, the contempt for the past, the democratic temper
of the times. They were prepared to enforce equality even at the cost
of despotism. They insisted on the subordination of all private rights
to the public interest. They preached the necessity of national
education as the first essential of national prosperity, and urged that
the burden of taxation should be thrown upon the land, which they
regarded as the sole source of wealth. They advocated free trade,
free agriculture, free industry, while they cared little for freedom itself.
Others like Morelly, the author of the Code de la Nature, accepted
the Economist theory of the omnipotence of the State, but added
other theories of their own. Morelly proposed to establish community
of goods and uniformity of all conditions. He denounced the
institution of private property, and he shadowed forth in their earliest
shape many of those suggestions for the readjustment of the world,
which have since assumed the name of Socialism and acquired the
dimensions of a spectre in minds intolerant of change.
But far above the sound of other voices rose the lofty tones and the
sonorous rhetoric of Rousseau. Rousseau disdained the study and
analysis of the past, in which Montesquieu had sought laborious
wisdom. He cared nothing for the diffusion of knowledge and art, of
which Voltaire was the brilliant representative. He hardly understood
the wide, ambitious projects, by which Diderot and Turgot hoped to
benefit humanity. He resented the utilitarian theories of Helvetius. He
hotly denied the material philosophy of the school of Holbach. To
Rousseau's angry discontent with life, study, knowledge, cultivation,
seemed to be only steps in the degradation of man. To his inflamed
vision all society was artificial, all accepted forms of political
organisation were tyranny and abuse. Man, he protested, was
naturally good and just and loving, created by a just and loving God,
until art, the bane of life, invaded his simplicity, tainted his virtue, and
brought him face to face with suffering and sin. Sweep away
therefore, he exhorted his hearers, all the false fabric of society, the
world of ugly want and insolent riches miscalled civilization, the
oppression miscalled order, the error miscalled knowledge! Level its
inequalities, repudiate its learning, break its conventions, shatter its
chains! Let men return to the simplicity of ancient days, to the idyllic
state, when uncorrupted instinct only ruled them, and there once
again, innocent and ignorant, as Nature made them, and guided only
by the 'immortal and celestial voice' of reason, seek the high paths of
felicity of life.
In a generation full of privilege and hardship, and weary of its own
artificial ways, such teaching as this struck a resounding chord. It did
not matter that the teacher reconciled a rather sordid practice with a
gorgeous theory, and was himself too often morbid, egotistical,
unmanly, mean. The disciples, who drank in his doctrines, did not
enquire critically into his motives. They did not ask—and possibly we
have not the right to speculate—whether he assailed society,
because he failed to shine in it, or whether he inveighed against
riches, because he lacked the patient industry to earn them for
himself. They did not know or care whether his quarrel with the
world, his indictment of its usages and laws, his eloquent defence of
human instinct, and his sensuous love for Nature, were or were not
dictated by the feverish longing which possessed the man to follow
every impulse of his mind, and to submit his impulses to no control.
They did not see that the example of a master, who, whatever
shameful faults he might commit, could still maintain that civilization,
and not he, deserved the blame, and could still gravely describe
himself to his friends as one of the best men that he had ever known,
was only too well calculated to enable his disciples to persuade
themselves that they were instruments of virtue, purity and justice,
while they were permitting iniquity and palliating crime. They knew
that his denunciation of oppression coincided with the bitter lessons
which their experience taught. They found that his eloquent words
renewed their self-respect, and raised their ideal of the dignity of
man. They felt that he pleaded the cause of the unfortunate in tones
and with a genius which made the fortunate attend, and that he
brought to that exalted service the widest compassion, the readiest
sympathy, and the most majestic language which the eighteenth
century had heard.
In 1762, Rousseau published one of the most famous, and, in its
consequences, probably one of the most important books ever
written. 'Man was born free,' ran the prologue to the Contrat Social,
—'man was born free, and is everywhere in chains.' In the Contrat
Social Rousseau rejected altogether the historic method—that wise
process of political philosophy, which patiently studies the
circumstances of the past, in order, by the experience so obtained, to
modify and to improve the present. Relying on the unsafe methods
of abstract, a priori speculation, he proceeded to develop, out of his
ardent and imaginative brain, an ideal theory of society, which should
establish by logical and conclusive argument the opinions which his
sentiments had already espoused. The result of the enterprise was
the celebrated doctrine of the Sovereignty of Peoples. The origin of
every human society, argued Rousseau, was this:—At some remote
epoch in the dawn of days, men, living in a state of nature, virtuous,
rational, equal and free, had resolved to enter into an association to
defend the persons and property of all, while every individual in it
remained free. Accordingly, they had formed a Social Compact,
under which each individual had submitted himself to the direction of
the general will, and had been received as an inseparable part of the
whole. The body formed by this Social Compact was the Sovereign.
All citizens who belonged to it—and all did—had an equal share in
the common sovereignty, and were bound to one another by a
fraternal tie. Its sovereignty consisted in the exercise of the general
will, and that sovereignty could not be alienated to any individual or
group, nor could it be divided up into different parts and distributed
among different officials. The will of the sovereign body was
expressed in laws, and every member of it must take his part
personally, and not by delegation, in the making of those laws. If he
delegated that right to representatives, he surrendered his share of
sovereign power. For the sake of convenience, the sovereign body
might delegate to governments certain executive powers for a limited
time; but the sovereign body still retained the right of resuming or
modifying those powers at will, and must from time to time assemble,
in order to enforce its right. When the whole sovereign people was
thus assembled, the power of governments ceased, and all
executive authority was suspended. If any government usurped the
sovereignty, the Social Compact was thereby broken; all citizens
resumed their liberty to act, and might rise in rebellion to assert it.
Lastly, in religion, the sovereign body was entitled to impose a civil
profession of faith, and to compel all its citizens, under penalties of
banishment and death, to believe in the existence of a beneficent
God, in an immortal life, in the reward of the just and the
chastisement of the wicked, in the obligation of the Social Contract
and of the laws.
It is easy in these days to criticise the Contrat Social. The mistaken
idea of compact as the basis of society; the rejection of
representative legislatures, and the insistence on a principle which
could only apply in a miniature State—the personal participation of
every citizen in the making of the laws; the sanction given to the right
of insurrection, when the imaginary compact was broken; the
absence of any method of ascertaining whether the compact were
broken or not;—these are flaws in its argument which will readily
occur. It is easy also to point to certain characteristics which disfigure
it throughout—to its disregard of facts, to its sophistry and
inconsistencies, to the narrow intolerance of its sentimental theology,
to its aloofness from the region of practice, to its reliance on dogma
and on the logic of words. But it is not so easy to appreciate the
extraordinary impression which in those days it produced, or the
enthusiasm aroused in all who looked for liberty, by the fearless
splendour of its phrases, by the fused argument and passion of its
style, by its generous democratic temper, by the spiritual
earnestness which inspired it, by its fine exaltation of patriotism and
freedom. The Contrat Social supplied the text and lit the fire of
revolution. It became the gospel of the Jacobin party, and of that
party Robespierre constituted himself high-priest.
The seed sown by these remarkable writers fell upon fruitful soil. The
years which immediately preceded the outbreak of the Revolution in
France were years of vague but widespread agitation. An
enthusiasm for the natural greatness of man, and a boundless
contempt for the age and society in which he lived, pervaded the
thought of the time. In almost every European country, observers
noticed the same presentiment of impending change, and of a
change which, on behalf of humanity, most people were prepared to
welcome. Thinkers and talkers alike were full of illusions, full of
curiosity, full of unselfishness, full of hope. Outside France, as within
it, everyone plunged into philosophical debate. In the trading cities of
Germany, merchants and manufacturers would gather, after the
day's work, to discuss the condition of the human race. Sovereigns
like Frederick, Catherine, and Joseph affected the secure radicalism
of despots. In Spain, in Portugal, in Tuscany, as well as in England
and France, statesmen echoed the new humanitarian maxims.
Aranda, Pombal and Manfredini exhibited the spirit, and emulated
the reforms, of Turgot and Necker, of Fox and Pitt. The outbreak of
the American Revolution roused the deepest interest in Europe.
Volunteers from France poured over to America, to fight for the
political ideals, about which they had for so long been dreaming, and
the realisation of which in the New World seemed to bring home
conviction to the Old. The tidings of the triumph of the American
colonists were received with acclamation in the roadsteads of
Elsinore. Strangely enough, the feverish unrest of the time produced,
in an age which professed to have undertaken a war against
superstition, a revival of the mysticism of an earlier day. On the eve
of the French Revolution, the best educated classes in Europe were
engrossed by secret societies and brotherhoods, like the Illuminati,
the Swedenborgians, the Mesmerists, the Rosicrucians, dabbling on
all sides in necromancy and occult science, and frequently the dupes
of ridiculous impostors, who, catching the temper of the times,
proposed to effect by charlatanism the regeneration of the world.
This vague perturbation of spirit did not, it is true, penetrate to the
lowest or unlettered class. But in all above that rank it was
conspicuous. The years of the reign of Louis XVI were in France, as
in nearly all parts of Europe, years of national expansion. The trade
of the country was advancing by leaps and bounds, and the
commerce of Bordeaux already exceeded, in the sober judgment of
Arthur Young, that of any English port save London. At the same
time the wealth of the middle classes was increasing with similar
rapidity. Year after year they lent more money to the Government;
and year after year, as they saw the Government wasting it with
reckless profusion, and falling steadily deeper into debt, they ranged
themselves more decidedly in the ranks of opposition, and became
more emphatic in their discontent. The gross mismanagement of the
finances became a matter in which they felt they had a right to
interfere. Their stake in the game of politics made them politicians,
and not only that—it made them reformers too. And thus the growing
wealth of the country tended indirectly to multiply the enemies of the
Court, and to throw on to the side of revolution that important
financial interest, which is generally a stable, sometimes an
obstructive, element in a State.
In other ways also, by the end of the century, in their style of living, in
their education, in their enlightenment, the middle classes had
become the equals of the nobles. They had imbibed the same
philosophy; they had cultivated the same tastes; they contemplated
with the same sublime ignorance of history and politics the
philanthropic ideas of the age; and they resented, even more bitterly
than before, the exclusive and exacting privileges of caste. At the
same time, the nobles, on their side, were losing, under the benign
influence of philosophy, a great deal of the apathetic insolence,
which had made their privileges hateful. The Court of Louis XVI was
very different from that of his predecessors. It was less pompous,
less artificial. The rules of etiquette were relaxed. A better tone
prevailed in its society. The haughtiest nobles opened their doors
freely to lowborn genius. They debated republican theories in their
drawing-rooms. They applauded republican sentiments in the
theatres. They began dimly to realise their public duties, and in a
tentative way to perform them. They awoke to the distress of the
poor about them, and endeavoured to alleviate it with a generous
hand. Some of the nobility proposed to surrender their immunity from
taxation. Others, headed by the King, emancipated the serfs who still
remained on their estates. The Marquis de Mirabeau established a
gratuitous office for the settlement of law-suits. The Duchesse de
Bourbon rose early in the morning, to visit with alms the garrets of
the poor. The Queen laid out a village at the Trianon, where, attired
in a muslin gown and a straw hat, she could fish in the lake and see
her cows milked. The King multiplied his private charities, and, one
severe winter, commanded that all the poor, who came, should be
fed daily in the royal kitchens. On all sides, among the upper classes
of society, the same symptoms showed themselves. Extravagant but
kindhearted sensibility became the mainspring of their actions;
reform was their passion, limitless, radiant hope their creed. 'With no
regret for the past,' says one of their number, looking back from the
sere contemplation of later years on that entrancing morning of his
life,—'with no regret for the past and no apprehensions for the future,
we danced gaily along a carpet of flowers stretched over an abyss.'
The same spirit animated the Government of the time. In spite of his
want of strength, his lamentable irresolution, and his well-intentioned
lethargy of mind, Louis XVI possessed not a few of the qualities in
which good kings excel—a high standard of morality and duty, a
large fund of quiet simplicity and courage, a readiness to listen to the
advice of wiser men, a marked sensitiveness to public opinion, and a
genuine desire to serve his people. Louis had not been long upon
the throne before he gave proof of his benevolent intentions by
appointing to the office of Comptroller-General the greatest practical
reformer of the day. Under Turgot the new spirit penetrated rapidly
into every department. The extravagances of the Court were cut
down. Useful changes were introduced into the system of farming
and collecting the taxes. The Corvées were converted into a regular
impost, from which the privileged classes were not exempt. The
guilds, which monopolised and fettered trade, were suppressed.
Fresh encouragement was offered to agriculture and commerce.
Free trade in corn was established within the kingdom. The minister
talked of commuting feudal dues, and dreamed of abolishing the
inequalities of taxation. A spirit of gentleness and consideration
came over the administration. The Government not only introduced
reforms; it condescended to recommend them to the public, to point
out their necessity, to explain their intention. 'The burden of this
charge,' said the Royal edict which abolished the Corvées, 'falls
solely upon those who possess nothing but the right to toil.' 'The right
to work,' ran the preamble to the edict which suppressed the guilds,
'is the most sacred of all possessions, and every institution which
infringes it, violates the natural rights of man.'
In the same way, Necker, when he succeeded Turgot, appealed for
support to public opinion. He recognised the 'invisible power which
commanded obedience even in the King's palace,' and endeavoured
to justify his policy by publishing an account of the state of the
finances. In the same way, though Turgot and Necker fell, and their
schemes perished with them, the reforming spirit continued to affect
the Government all through Louis' reign. Change after change,
experiment after experiment, attested the readiness of the Crown to
bend before the forces of the time. The measures taken, first of all to
suppress, and afterwards partly to restore the guilds, destroyed the
old relations between employers and workmen, while they did little to
establish a more complete or satisfactory system in their place. And
thus, when the Revolution came, there reigned generally among the
artisans of the great towns a sense of uncertainty and discontent,
which rendered discipline impossible and mischief easy.
Again, only a year before the Revolution, one royal decree
transformed the administration of justice in France; while a year
earlier, in 1787, another bold and memorable measure completed
the reform begun as an experiment some years before, and
established provincial assemblies in all the Pays d'Élection. The
importance of this step, which has been sometimes overlooked
among the graver changes of a later day, can hardly be
exaggerated; for it introduced, almost without warning, a new
principle into the government of the country. By the side of the
autocratic Intendants, new provincial assemblies were created,
which stripped the Intendants of most of their powers, or, if they
resisted, entered into active competition with them. By the side of the
autocratic Sub-Delegates, new district assemblies were formed, to
pursue a similar course of action in a smaller sphere. In place of the
ancient parochial assemblies, and in the midst of the inequalities and
privileges, of which French villages were the familiar scene, and
which in themselves remained unaltered, new, elective, municipal
bodies sprang up to assert democratic methods, among conditions
wholly irreconcilable with democratic ideas. When one considers the
scope of these important changes, their novelty, their
inconsistencies, and the suddenness with which they were made,
one realises something of the confusion and paralysis which they
must have produced in the public service, and one begins to
understand why the agents of the Government proved so powerless,
in spite of their prestige, when they had to face the crisis in 1789. On
the very eve of the Revolution, Louis and his advisers, forgetful of
the salutary maxim that the most dangerous moment for a bad
Government is the moment when it meddles with reform, had
deliberately destroyed the old, despotic, administrative system,
which, at the end of the eighteenth century, formed the only certain
mainstay of the throne.
It is not necessary to linger here over the episodes of Louis' reign.
Turgot and Necker fell in turn; but Necker carried with him from office
a reputation for sound finance, for disinterestedness, and for honest
liberality of opinion, which won for him a name out of all proportion to
his powers. He left behind him a problem of ever-increasing difficulty,
and a deficit alarmingly enlarged by the intervention of France in the
American war. For a time, after the overthrow of Necker, reactionary
influences had their way. The wastefulness of the Treasury
continued. The spectre of reform was for the moment laid. And at the
head of that splendid and light-hearted Court, which combined the
profuse traditions of the Grand Monarque with the gay philanthropy
that was the fashion of the day, and resented all economies as
mean, and radical innovations as thoroughly ill-bred, there stood,
conspicuous in brilliancy and beauty, the figure of the Queen. Wilful
and proud, unthinking and extravagant, intolerant of disagreeable
facts, because she was wholly ignorant of their truth, already widely
calumniated and misjudged, but destined to face far worse
calumnies, which partisanship, in the mask of history, has repeated
since, Marie Antoinette has never ceased to command the interest
and attention of posterity, as her tragic story, and the fall to which her
errors partly led, have never ceased to move its pity and respect. In
1783, Calonne took office as Comptroller-General, and for four
years, encouraged by the favour of the Queen and Court, and
helped by his own surprising agility and resource, Calonne
maintained his place. Money was found at ruinous expense to supply
the necessities of the Government and the rapacious claims of
courtiers. Every day bankruptcy came more distinctly into view. At
last Calonne, unable to carry on his system any longer, fell back
upon a desperate expedient. He summoned, in February, 1787, an
extraordinary assembly of Notables, consisting of nobles, bishops,
magistrates and officials, laid before them frankly the situation of
affairs, and gaily informed them that within the last ten years the
Government had borrowed no less than fifty millions sterling.
It is curious to notice the attitude of this assembly, and the way in
which its action was received by the country. As might be expected,
the Notables, consisting almost entirely of members of the privileged
orders, were not prepared to make large personal sacrifices to save
the state. When Calonne audaciously proposed to them the abolition
of privileges and exemptions, and asked them to submit to a heavy
tax, he fell, amid a storm of reproaches from the courtiers, who
regarded him as a deserter from their ranks. But instead of carrying
popular sympathy with him, Calonne found that his opponents,
although they were resisting reform, had usurped the popularity of
reformers. The Notables adroitly shifted the ground of attack to the
conduct of the Government. They demanded the public accounts.
They censured the acts of the Administration. And simply because
they assailed the Government, and ventured to criticise and oppose
the Crown, they suddenly found themselves, to their own surprise,
transformed into popular heroes, and their conduct and courage
applauded all over the kingdom. The same thing happened after
Calonne's fall. Loménie de Brienne, the Archbishop of Toulouse,
succeeded to Calonne's office, and found himself compelled to take
up many of Calonne's plans. Thereupon the Parlement of Paris
stepped to the front, and following the example of the Notables,
accepted some of the Minister's reforms, and particularly the edict
for the establishment of provincial assemblies, while they rejected
the new taxes, which were an inseparable part of the Government's
scheme. In vain the King threatened and punished the members of
the Parlement. The Parlement, borrowing the language of the times,
and forgetting that they themselves were only a privileged and
exclusive corporation, posed as the representatives of the nation,
and demanded that the States-General should be summoned to
express the national will.
The Government attempted to carry its schemes through with a high
hand. All over the kingdom, the local Parlements, the judicial
magistracy of France, took up the cause of the exiled Parlement of
Paris, echoed its tones, and even threatened dangerous rebellion. In
Dauphiné, in particular, the clergy, nobles, and commons of the
province, gathering at Vizille, and led by the courageous eloquence
of Mounier, protested against the policy of the Minister, and defied
the Crown. The nation, caring little for the rights or wrongs of the
quarrel, but delighted to see the all-powerful Government baffled and
assailed, welcomed the Parlements as national deliverers, and
proclaimed them the champions of popular freedom. For a moment
the strange spectacle offered of the privileged orders in France
defending their privileges, with the enthusiastic support of the nation,
against the Government, which wished to destroy them in the
interests of all. In face of this extraordinary union, the Government
recoiled. Alarmed by the increase of riots and disorder, by the high
price of food, by the disaffection in the army, by the Ministry's total
loss of credit, and by the prospect of bankruptcy in the immediate
future, the King decided to consult the nation. He announced that the
States-General, the ancient, representative Parliament of France,
would again, after the lapse of a century and three-quarters,
assemble to debate the destinies of the kingdom. Then the
popularity of the privileged bodies died as suddenly as it had begun.
In August, 1788, Necker was recalled to office, and a general
outburst of rejoicing celebrated the astonishing surrender of the
Crown.
A wise minister would have endeavoured by prompt and decisive
action to allay the vague excitement of the time. Every day the
feeling of restlessness was spreading in the country. Paris had
become a great debating club. The tension in the public mind was
already extreme. Instead, however, of hurrying on the elections,
instead of showing a resolution to face the crisis with enlightenment
and calmness, the Government hesitated, procrastinated, wavered,
and allowed all the world to see that it had formed no policy, and
hardly knew what its intentions were. The meeting of the States-
General was delayed until the following spring, and in the meantime
the Government stimulated the fever of opinion. All through the
winter of 1788-9, France was flooded with political addresses and
with democratic pamphlets—among which the audacious pamphlet
of the Abbé Sieyès excited general remark—calculated to raise as
high as possible the hopes and pride of the Tiers-État. To add to the
war of words, the Government invited all classes to draw up Cahiers
or petitions of grievances, to be laid before the States-General, when
they met, and thus, by its own action, it focussed the attention of its
subjects on the many abuses which had been borne silently so long.
Moreover, when the important question of the constitution of the new
States-General arose, the Government found it impossible to make
up its mind. In the electoral arrangements, as might be expected
from the innumerable local and personal rights still existing in the
country, there was very great complexity and confusion. But the
general principle, at any rate in the Pays d'Élection, was this. The
nobles and clergy of each Bailliage, as a rule, elected their
representatives directly, though the rule was subject to a good many
exceptions. In the election of the commons, on the other hand, the
voting was in no case direct, but had two, or even three or four
degrees. All Frenchmen over twenty-five, who had paid even the
smallest amount of direct taxes, had votes. They might vote for any
representatives they pleased, for there was no property qualification
for candidates. But they could not vote for them directly. The
electoral assembly of each Bailliage thus consisted of the nobles and
clergy of the Bailliage, and of a number of representatives of the
commons, who had been previously elected by primary assemblies
of voters in the different towns and villages of the Bailliage. When
the electoral assembly of the Bailliage had been formed, the nobles,
the clergy, and the electors of the Tiers-État, who composed it,
separated into three distinct bodies[5], and each order chose a
certain number of deputies to represent it in the States-General at
Versailles. The number of deputies allowed to each Bailliage varied
according to circumstances, but was mainly determined by its
population and wealth.
It was arranged without opposition that the nobles and the clergy in
the States-General should have, according to usage, three hundred
representatives each; but then the difficult question arose, how many
deputies were the Tiers-État to elect. The advocates of democracy
urged, amid enthusiastic applause from the public, that the commons
infinitely out-numbered the other two orders, and ought therefore to
have at least double the number of representatives. On this point
Louis and Necker alike wavered undecided, besieged by the
importunities of the democratic feeling which they had let loose in
France. In vain Necker, in November, 1788, gathered another
assembly of Notables, and tried to shift his responsibility on to them.
The Government at last made up its mind to concession, and
announced that the commons were to have 'the double
representation'—six hundred representatives in the new Parliament.
But the genius of irresolution still dogged its steps. It could not even
then bring itself to decide whether the three orders should sit and
vote in separate Houses, or whether they should all sit in one
Chamber and vote together. The timidest intelligence must have
perceived that, unless the three orders were to vote in one body, the
numerical superiority which the commons had obtained would be
without significance, and the Government's concession to popular
feeling would be merely a delusion. And yet to the last this important
question was left undecided by the Crown, as a fruitful source of
quarrel out of which the troubles of the Revolution might begin. So,
with a Government perplexed by fears, with a local administration
paralysed by a variety of recent changes, with signs of disorder
multiplying upon every side, with innumerable difficulties requiring
settlement, and with the fixed spirit of old traditions vainly attempting
to assimilate the new, the monarchy prepared to meet the
representatives of the nation, who, already flushed with triumph, and
intoxicated with self-confidence and hope, advanced to realise their
long-delayed millennium, and with the aid of freedom and philosophy
to readjust the destinies of France.
FOOTNOTES:
[5] In three cases only, in Langres, Péronne, and Montfort
l'Amaury, the three orders sat and voted together in the electoral
assembly.
CHAPTER III.
The Early Days of the Revolution.
On the 5th May, 1789, the States-General were opened by Louis at
Versailles. From the first the Government betrayed its helplessness,
and its total inability to appreciate the situation. The Commons'
deputies had come to Versailles for the most part with the largest
expectations. They were fully alive to existing evils. They were full of
schemes and ideals of reform. They foresaw, and were willing to
foresee, no obstacles. They were prepared to transform the country;
and they confidently expected, under the guidance of a benevolent
King and of a liberal and experienced Minister, to begin without delay
the work of national regeneration. But from the outset they
encountered a series of checks and disillusionments, which
increased in gravity as time went on. They found that the
Government, instead of taking the lead with vigour, met them with no
definite proposals for reform, and with little but vague philanthropic
intentions over and above its desire to restore the finances. They
found that the King and his advisers had not even made up their
minds as to the constitution of the new Parliament, and could not
bring themselves to decide whether the three orders were to sit and
vote together or apart. They found themselves in an atmosphere
new to most of them, set to do work new to all, conscious in their
own minds that a new era had begun and that they must assert
themselves to mark it, but yet accustomed from immemorial habit to
regard the nobles as their superiors, the King as their master, and
the Government as irresistibly strong.
Accordingly, at first, the attitude of the Commons was one of great
embarrassment. They had as yet no recognised leaders of their own,
and the Ministers, to whom they looked for leadership, were silent
and appeared to be as much perplexed as themselves. On one point
only they were clearly resolved and determined to yield to no
pressure. They insisted that the deputies of the nobles and clergy
should join them, and should form one chamber with themselves. On
their side, the nobles and clergy refused to listen to this innovation.
The Commons steadily rejected a compromise, and on that point the
deadlock arose. Instead of the States-General setting to work to
repair the finances and to carry reforms, six weeks went by,
occupied only with this preliminary quarrel, while all the time the
excitement in Paris and in the country deepened, the conflict of class
interests became more apparent and acute, and the reactionary
courtiers rejoiced at the fiasco and used their influence to widen the
breach. The Commons, growing more confident as they felt their
strength, and as they realised the power of the forces behind them,
held their ground, disregarded the pressure and the innumerable,
little, social slights, to which they were daily exposed at Versailles,
and became more and more pronounced in their policy of self-
assertion; and the Government revealed more strikingly than ever,
alike to the States-General and to the public, its entire lack of
purpose and resolve.
At last, after six weeks of waiting, the Commons took matters into
their own hands, and from that moment events moved fast. On the
17th June, the deputies of the Tiers-État resolved on a momentous
step, and on the motion of Sieyès, constituted themselves alone the
National Assembly of France. The Government, alarmed at this
usurpation of power, determined to reassert its authority and, while
offering a large programme of reform, to insist on the separation of
the three orders. On the 20th, the Commons found themselves
excluded from their hall, and their sittings consequently interrupted;
but they persevered in the policy which they had adopted, and
adjourning simultaneously to the Tennis Court, swore solemnly never
to separate till they had given a constitution to France. On the 23rd,
the King came down in state to the Assembly Hall, and while offering
large concessions, annulled the resolutions of the Commons. But the
Commons, inspired by the courageous words of Mirabeau, rejected
the programme which Louis had laid before them, adhered to their
resolutions, and defied the Crown. Within a few days, the nobles and
the clergy were requested by Louis to abandon the struggle, and the
union of the three orders was complete.
But the Court party bitterly resented the usurpation of the Commons.
The disorder in Paris was increasing fast. Necker held ostentatiously
aloof from his colleagues. The King, distressed and embarrassed,
suffered himself to be persuaded by the haughtier spirits at Court,
helped by the direct influence of the Queen, to make an attempt to
recover the authority which he had allowed to slip from his grasp.
The old Maréchal de Broglie, a veteran of the Seven Years' War, was
summoned to the royal counsels. Great masses of troops, composed
chiefly of Swiss and German regiments in the service of France,
were concentrated, in spite of the protests of the Assembly, around
Paris and Versailles. On the 11th July, Necker and three other
Ministers were dismissed, and their places in the Government filled
by decided adherents of the reactionary party. On the 12th, the news
reached Paris, and the people, scared, famished and indignant,
burst into revolt. On the 14th, that revolt culminated in the decisive
movement which destroyed the Bastille, which shattered the plans of
the Court party, and which completed the triumph of the Revolution
and the humiliation of the Crown.
'With the 14th July,' said a wise and enlightened witness of the time,
'the terror began.' The rising in Paris was the signal for the first
general outbreak of violent disorder in France, which proved that the
distressed classes had taken the law into their own hands, and that
the Government was utterly unable to cope with or control them. The
strongest motive for disorder was unquestionably material want. For
many years past, the condition of the poorer peasants and labourers,
both in the towns and in the country side, had been almost
intolerable, and in 1789, the chronic distress of this large class
reached an acute stage. In 1788, a severe drought had been
followed, on the eve of the harvest, by a hail-storm of extraordinary
violence and extent, which had destroyed the crops for sixty leagues
round Paris. That, in turn, had been followed by the severest winter
known for eighty years, which had completed the ruin which the
drought and the storm had begun. The consequence was that, in the
spring and summer of 1789, the price of bread rose as in a siege,
and on all sides the cry of famine spread. From all parts of France, in
the spring of 1789, came the same alarming rumours of scarcity and
distress. From all parts of France, in the months preceding the
capture of the Bastille, came the same reports of disturbances and
riots occasioned by the want of food. Discontented peasants,
unemployed labourers, rapidly reduced to criminals by hunger,
passed from patient misery to despair, and broke out into resistance.
Compromised or defeated in the country, they took refuge in the
towns; and thus, in April and May, observers noticed that 'frightful
numbers of ill-clad men of sinister appearance,' many of them
foreigners, all more or less destitute and dangerous, were pouring
into Paris, where already bread was exorbitantly dear, and where
already the number of unemployed and paupers bore a dangerous
proportion to the population of the city.
The trouble caused by the scarcity of food was stimulated by another
motive second to it only in importance—the feverish excitement of
political hope. Depressed and ignorant as they were, the labouring
class in France had, nevertheless, grasped the idea that in some
vague way the meeting of the States-General marked an era in their
lives, and was somehow or other destined to ease the intolerable
burden of their lot. With them political freedom and constitutional
reform took the immediate shape of food, work, and relief from
feudalism and taxation. Once the idea had been implanted in them,
their restless anticipations rapidly increased. Every week of delay
rendered them less manageable. Every check experienced by the
Assembly was a spur to their impatience. Every step taken by the
Government to assert its authority or to overawe the reformers filled
them with indignation, suspicion and panic. In the poorer districts of
Paris, and especially in the gardens of the Palais Royal—the
headquarters of Bohemians, idlers, mischief-makers, crowds—the
political excitement of the time found expression in perpetual
demonstrations, not unmixed with rioting and outbreaks. The regular
authorities of the city, unused to the spectacle, looked on, unable to
control it. The police force of Paris under the Ancien Régime was so
small as to be practically useless. The garrison, formed of the
Gardes Françaises, who were responsible for the maintenance of
order, sympathised with the citizens, who spared no hospitality or
flatteries to gain them, and finally, mutinying against their officers,
went over to the popular side. The other regiments in the
neighbourhood showed a marked inclination to follow the example of
the Gardes Françaises. The Government, deserted by its own
agents, drew back; and the spirit of disorder, produced by the desire
for food and the desire for freedom, obtained the mastery of Paris,
and took command of the Revolution too.
The example set by Paris was immediately followed in the provinces.
At Strasbourg, Lyons, Dijon, Troyes, Besançon, Rouen, Caen, all
over the country, spontaneous risings occurred, directed against the
authorities or practices of the Ancien Régime, and often
accompanied by violence and bloodshed. The people, stimulated by
the pressure of famine and by the feverish excitement of the time,
and believing that the hour of their deliverance had come,
determined to deliver themselves. In different places the outbreak
took a hundred different forms. In garrison cities the people, imitating
the Parisians, attacked the nearest fortress or castle, and, as in
Paris, the troops generally fraternised with the assailants. In some
quarters popular indignation was directed against the tax-offices and
custom-houses, in some against the local magistrates, in some
against the tithes, in some against the newly-introduced machinery,
in some against the Jews, in most against corn-dealers and all
concerned in trafficking in grain. In the towns the distressed
workmen rose against the bourgeois, and against the unjust
economic system, which had long rendered their condition
unbearable. In the country districts the peasants rose against the
iniquities of feudalism, and burned the monasteries and châteaux,
where the court-rolls, the records of their hated liabilities, were kept.
No doubt, with the desire to redress abuses there mingled, in the
minds of an ignorant and embittered peasantry, a great deal of
ferocity and crime. In many places indiscriminate war was declared
against all kinds of property, and the outbreak took the form of a
struggle between rich and poor. But the most notable features of the
revolutionary movement were, first, its universality, and secondly, the
powerlessness of the authorities to confront or to suppress it.
Everywhere the agents of the administration collapsed. The
Intendants, the law-courts, the police, completely paralysed,
abdicated or disappeared, and the inhabitants of town and country
alike, recognising the helplessness of the Government, gave way to
an inevitable panic.
The consequence was that the months of July and August were
signalised by a sense of insecurity amounting to terror. The wildest
rumours pervaded the country, and the most extraordinary instances
are found of places where the people, panic-stricken by some vague,
unfounded report of the approach of brigands, who had no existence
out of their imagination, rushed to arms or fled into concealment to
protect themselves against their own alarm. One result of the 'great
fear' was that volunteer forces of citizens, interested in restoring
order, sprang up on all sides, in imitation of the National Guard just
organised in Paris, to which they were destined before long to be
assimilated; and these volunteer forces, though sometimes used by
the bourgeois to repress the movements and to maintain the
subjection of the labouring class, were still invaluable in restoring
peace. Moreover, in place of the authorities of the Ancien Régime,
there sprang up, to exercise the duties of administration, informal
municipal committees composed of electors, which, usurping the
powers abdicated by the Government, rapidly organised themselves,
secured the obedience of their fellow-citizens, and set to work, as
best they could, to reconstruct the administration of the country. The
rapidity and skill with which these municipal committees and their
volunteer forces organised themselves, clearly illustrate the
readiness of the provinces to act on their own initiative and to take
over the responsibilities of the Revolution, and show how completely
the people of France at first kept pace with, if they did not outstrip,
their leaders in Paris and Versailles.
The most obvious and the wisest course for the National Assembly
to adopt, would have been to legalise as rapidly as possible the
changes so suddenly effected, and to set to work without delay to
organise the new administrative system. After the 14th July, the King
had completely surrendered, and the Assembly had only to act in
order to be obeyed. The task before it was, it is true, difficult and
almost endless. It was imperatively necessary to restore order. But it
was also imperatively necessary—and this the Assembly did not see
—to construct, as quickly as it could be done, some form of local
government, to replace the old order which had disappeared. It was
imperative to provide by some means for the necessities of the
revenue, until a permanent financial system could be organised, in
place of the old taxes which people would no longer pay. It was
imperative to take steps to convince, not only the bourgeois and the
peasants, but the distressed artisans in the towns as well, that the
Assembly was alive to the urgent necessities of the moment, had a
real grasp of the situation of affairs, and would do all that could be
done to protect their interests, and to save them from the starvation
which they imminently feared. These were the measures which
Mirabeau urged upon his colleagues, but unfortunately, there were
few men in the Assembly who possessed the gift of practical
statesmanship, which genius, lit by experience, had conferred on
Mirabeau.
The character of that famous Assembly, read in its own day by the
critical but far-seeing eyes of Burke, has excited the wonder of
posterity. Its most notable feature was its want of practical
experience. Among the upper clergy and the nobles, there were, it is
true, certain deputies, who from their position had obtained some
knowledge of affairs, but these men were liable to be distrusted by
their colleagues, because the moderation which their experience
taught them, obviously coincided with their interests. Among the
Commons there were not a dozen men who had held important
administrative posts. There was only one deputy, Malouet, who had
held the great office of Intendant, and was in consequence really
familiar with the working of the old administrative system. The great
majority of the deputies of the Commons consisted of lawyers of little
celebrity, who brought to the Assembly all the facility of expression,
but little of the utilitarian caution, which in England is associated with
their profession. The place of experience, in the case of most
members of the Assembly, was taken by a large imagination, a
boundless optimism, a vast store of philosophic tags and democratic
phrases, a fatal fluency of speech, a fine belief in logic, an academic
disregard of the rude facts of practical existence. Never was any
body of men so much inspired by hope and confidence, so full of
honourable enthusiasm, so convinced of its own ability, or so fixed in
its honest desire, to regenerate the world.
Accordingly, the early history of the Assembly is marked by a series
of strange scenes, only possible in a nation with whom extreme
versatility of temperament takes the place of humour, illustrating the
susceptibility, the emotion, the feverish excitement, the liability of the
whole body to act on the impulse of the moment, regardless of what
the consequences might be. A happy phrase, a witty saying, a burst
of declamation, would carry it off its feet, and settle the fate of a
division. The prodigious quantity of written rhetoric declaimed from
the tribune wasted a prodigious quantity of time, but there was
always an audience ready to applaud it. The debates were
conducted with very little order. The entire absence of method in the
Chamber often frustrated the business-like work done by its
committees. In vain Mirabeau urged his colleagues to adopt the
procedure of the English House of Commons. The French people,
newly emancipated, disdained the example of any other nation. In
the great halls at Paris and Versailles, where the Assembly
successively sat, the process of legislation continued to be attended
by a constant clatter of talk and movement, interrupted by noisy
shouts and gestures, by obstruction and personal abuse, and
aggravated by the presence in the galleries of large numbers of
strangers, whom at first the Assembly welcomed, and whose
turbulence it afterwards vainly attempted to control. The noisy

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Thermoelectric Materials and Devices

Publisher: Matthew Deans

1. General principles of thermoelectric technology 1

2. Strategies to optimize thermoelectric performance 19

3. Measurement of thermoelectric properties 51

3.3 Measurement for thin films 62

4. Review of inorganic thermoelectric materials 81

5. Low-dimensional and nanocomposite thermoelectric materials 147

6. Organic thermoelectric materials 183

7. Design and fabrication of thermoelectric devices 221

1.2 Thermoelectric effects

1.2.1 Seebeck effect