SPECIAL REPORT 96-2

Electromechanical Phenomena in Ice

Victor F. Petrenko February 1996
Abstract

This report examines the electromechanical effects in ice. This group of

physical phenomena, which was found and studied relatively recently,

broadens basic knowledge of ice and may have some practical applications. The electromechanical phenomena in this monograph are separated

into three groups: 1) Effects in which electromagnetic fields are generated by

means of mechanical actions such as elastic stress, plastic strain, fracture

or friction; 2) Effects in which an application of electric fields modifies such

mechanical properties of ice as its plasticity, elasticity and friction; 3) Effects

in which plastic strain changes electrical conductivity or dielectric permittivity

of ice. Experimental results and theoretical models are discussed and some

possible practical applications suggested.

For conversion of SI units to non-SI units of measurement consult Standard

Practice for Use of the International System of Units (SI), ASTM Standard E380-

93, published by the American Society for Testing and Materials, 1916 Race St.,

Philadelphia, Pa. 19103.
Special Report 96-2

Electromechanical Phenomena in Ice

Victor F. Petrenko February 1996

Prepared in cooperation with

THAYER SCHOOL OF ENGINEERING

DARTMOUTH COLLEGE

Approved for public release; distribution is unlimited.

US Army Corps


of Engineers

Cold Regions Research &


Engineering Laboratory
ii

PREFACE

This report was prepared by Dr. Victor F. Petrenko, Professor of Engineering, Thayer School

of Engineering, Dartmouth College, Hanover, New Hampshire. Funding was provided by the

U.S. Army Research Office through contract DAAL 03-91-G-0164 and by CRREL.

The author is most grateful to Dr. George Ashton, Dr. Erland Schulson and the late Dr. Andrew

Assur, for their help, support and collaboration, without which this report would have had little

chance to appear. He also expresses his special thanks to Dr. Robert Whitworth, Dr. John Glen

and Ivan Ryzhkin for their useful remarks and comments on the text. In many cases their suggestions improved the report in content and logic and identified errors that the author had overlooked. The author appreciates the help of Linda Dorr and Donna Withrow in editing and typing

the manuscript.

The contents of this report are not to be used for advertising or promotional purposes. Citation

of brand names does not constitute an official endorsement or approval of the use of such commercial products.
iii

CONTENTS

Preface ..................................................................................................................................... ii

Foreword.................................................................................................................................. v

Nomenclature .......................................................................................................................... vi

Introduction ............................................................................................................................. 1

Electrical phenomena in ice friction ....................................................................................... 1

Structure and electrical properties of the ice surface ......................................................... 1

Early works on asymmetrical rubbing ............................................................................... 2

Frictional electrification ..................................................................................................... 3

Effect of electrical fields on ice friction............................................................................. 7

Electro-elastic effects .............................................................................................................. 10

Is ordinary ice Ih piezoelectric? ......................................................................................... 10

Phonon-induced polarization of ice ................................................................................... 11

Polarization induced by nonuniform strain ........................................................................ 11

Other pseudo-piezoelectric effects ..................................................................................... 13

Electromagnetic phenomena in ice fracture ........................................................................... 13

Theory ................................................................................................................................. 13

Laboratory experiments...................................................................................................... 16

Field experiments ............................................................................................................... 20

Electroplastic effects in ice ..................................................................................................... 22

Dislocation currents in ice .................................................................................................. 24

Motion of charged dislocations in an electrical field ......................................................... 25

Effect of static electrical field on ice creep ........................................................................ 25

Effect of plastic deformation on electrical properties of ice ............................................. 26

Literature cited ........................................................................................................................ 28

Selected bibliography .............................................................................................................. 30

Abstract ................................................................................................................................... 31

ILLUSTRATIONS

Figure

1. Ice friction and ice electrification measurements in the laboratory and on snow in

the field................................................................................................................. 3

2. Experimental setup ........................................................................................................ 3

3. Potential difference across 75-μm-thick polyethylene film and its tension ................. 4

4. Potential difference between ice and a stainless foil .................................................... 4

5. Dependence of the potential difference between ice and stainless steel slider on

sliding velocity ..................................................................................................... 4

6. Dependence of the electric current through ice/metal slider interface on sliding

velocity at three different temperatures ............................................................... 4

7. Records of the potential difference across a capacitor built into a ski at three

sliding velocities .................................................................................................. 5
iv

Figure

8. Schematic dependence of the space charge density on the distance to the ice

surface .................................................................................................................. 6

9. Changes in tension of the polyethylene belt when a 3-kV bias is switched on and off 7

10. Changes in tension of the aluminum belt when a 3-kV bias is switched on and off .... 8

11. Changes in tension of the stainless steel foil belt when the ice cylinder direction of

rotation reverses ................................................................................................... 9

12. Generation of piezoelectric polarization in a crystal under the action of the uniform,

uniaxial compression ........................................................................................... 10

13. Application of Neumann’s principle to ice ................................................................... 11

14. Air bubble migration against a pressure gradient in water ........................................... 11

15. Some practical cases in which nonuniform strain generates electric polarization of

ice ......................................................................................................................... 12

16. Oscillograms of the electric field strength in the ice sample doped with 10–4

mole/L NH3 .......................................................................................................... 13

17. Representation of variations in ions’ concentration, electric field strength and

electric potential along the crack surface in granular ice .................................... 14

18. Three modes of cracks ................................................................................................... 16

19. Lines of force of the electric field induced by stable mode I and mode II cracks in

ice ......................................................................................................................... 16

20. Jumps of electric potential caused by nucleation of thermocracks .............................. 17

21. Signal recovery system used to detect emissions.......................................................... 17

22. Electrical signal of a microcrack in freshwater columnar ice ....................................... 18

23. Electrical signal of a large crack splitting many columns in freshwater columnar ice 18

24. Typical electrical signal captured from a microcrack in freshwater ice under the

action of an external electric field ....................................................................... 18

25. Schematic of experimental configuration used in measurements of electric fields

on the ice surface around a stable crack .............................................................. 19

26. Amplitude of electric potential on the surface of the ice sample measured in the

configuration shown in Figure 25 ........................................................................ 19

27. Synchronous records of the electromagnetic and seismic signals captured from

natural and artificially induced glacier tremors on 17 August 1977 ................... 20

28. Synchronous 3-day en route measurements of electric and magnetic fields ................ 21

29. Experimental configuration used in measurements of EME from cracks in lake and

sea ice ................................................................................................................... 21

30. Typical signal captured from a thermocrack grown in lake ice .................................... 22

31. Electromagnetic emission from a crack in sea ice ........................................................ 22

32. Section in the ( ) 1100 plane of a 60° dislocation on a plane of the shuffle set in the

structure of ice ...................................................................................................... 23

33. Directions of the principal stresses in the vicinity of an edge dislocation ................... 23

34. Change in activation energy of a charge carrier in ice in the vicinity of an edge

dislocation ............................................................................................................ 23

35. Dislocation currents in ice ............................................................................................. 24

36. Dependence of the relative change in strain rate on the applied dc voltage ................. 25

37. Effect of compressive strain on the electric properties of ice single crystals, measured at 1 Hz .......................................................................................................... 28

38. Effect of plastic deformation on dielectric permittivity and conductivity .................... 27
FOREWORD

At the present time, thousands and thousands of

people around the world deal with ice, snow and permafrost. They are scientists, educators, engineers, navigators, meteorologists and others. While a small fraction

of these people contribute to the knowledge base in ice

physics, all of them use knowledge from it frequently.

Moreover, successful applied research is based upon

fundamental science—one more reason for ice specialists to have a textbook on ice physics on their desks.

The first modern ice physics text was Fletcher’s

book on The Chemical Physics of Ice (1970). Fletcher’s

book is in typical textbook format: it is reasonably brief

and easy to understand. He touched on a few of the

most important topics, but not all of them.

The most comprehensive book on ice physics to

date was published by Hobbs in 1974. Hobbs considered almost all of the basic aspects of ice as understood

at that time. Moreover, he described and compared several (sometimes opposing) viewpoints. This fundamental and rather large (837 pages) book is commonly

known as the “Ice Bible” by specialists in the field. In

1974 and 1975, two CRREL Monographs on ice were

produced by John Glen. These were briefly and clearly

written and reviewed almost all ice-related subjects.

This work was (and in some respects still is) a magnificent introduction to ice.

Finally, in 1981 Maeno wrote a simple, popular

book for the express purpose of attracting people’s attention to the subject.

During the past 20 years, a significant amount of

new experimental and theoretical work has appeared,

dramatically changing our views on ice physics. As a

result, we are now able to formulate physical laws using

more simple and direct methods. We have found some

of the physical models used in the past to be completely

wrong. The physics of ice is a much better developed

subject than it was 20 years ago.

For the above reasons, I feel the time is ripe for a

contemporary book on ice physics, incorporating the

known and proven with almost 20 years worth of material not covered by previous works.

I have tried to prepare a “readable” book, and not

one that requires the reader to be a uniquely educated

person. It is my intent to present the material in such a

way that any reader attracted by the title Ice Physics

will be able to comprehend it. This is quite difficult for

a book dedicated, not to a particular field of knowledge,

but to a specific material. Indeed, for ice it means we

have to consider a wide variety of subjects, including

quantum chemistry, solid state physics, the theory of

elasticity, ionic conductivity, synchrotron x-ray topography, crystal growth, the physics of surfaces and more.

The primary goal is to produce as simple a book as

possible without sacrificing scientific accuracy. Experimental facts, physical ideas and theories will be

strongly organized and bound together cohesively. The

reader will be introduced to a wide variety of material

on a step by step basis. Then the picture will be whole.

To accelerate materials publication, this book will

appear first in the form of a series of joint CRREL–

Dartmouth reports, later to be published in CRREL’s

Monograph series, on:

1. The structure of ordinary ice

Part I: “Ideal” structure of ice. Ice crystal lattice

Part II: Defects in Ice

Volume 1: Point defects

Volume 2: Dislocations and planar defects

2. Electrical properties of ice

Part I: Conductivity and dielectric permittivity of

ice

Part II: Advanced topics and new physical phenomena

3. Optical properties

4. Electro–optical effects in ice

5. Thermal properties

6. Mechanical properties of ice. Elasticity and anelastic relaxation. Plastic properties. Fracture of ice

7. Electromechanical phenomena in ice

8. Surface of ice

9. Other forms of ice and their properties

10. Ice in space

11. Ice research laboratories

The reports will be prepared in a sequence convenient to the author. The present report is the sixth in the

series.

v
vi

NOMENCLATURE

α angle

a interatomic distance

αai deformation-potential constant of ith

type charge carrier

α0 fraction of water molecules on the ice

surface oriented with their dipole

moments (i.e., protons) pointing

outwards

C, C0 capacitance

χij susceptibility tensor

cmnij stiffness tensor

∆ thickness of the surface layer

∆I dislocation current

d interelectrode distance

Di diffusion coefficient of i

th defects

Dion diffusion coefficient of ions

dkmn piezoelectric strain tensor

E electric field strength

E⊥ component of electric field perpendicular to a crack surface

E Young’s modulus

ε dielectric permittivity

e proton charge

ε0 dielectric permittivity of a vacuum

Eai activation energy of a defect

Ei i

th component of the electric field

strength

ei defects’ electric charge (i = 1, 2, 3, 4)

eion electric charge of an ion

εij strain tensor

eijk piezoelectric stress tensor

εs static dielectric permittivity of ice

ε∞ high-frequency dielectric permittivity

of ice

F force

Φ ≅ 3 B oo .85k Tr

f frequency

g grain size

γai activation volume of a defect creation

H magnetic field

η amplitude of dislocation vibrations

I electric current

i 1, 2 ,3

jD diffusion flux

JDR drift flux

ji flux of i

th defects

φs surface potential

κ κ 1

1

2 − −1 , screening lengths

kB Boltzmann constant

KI intensity factor for a mode I crack

KII intensity factor for a mode II crack

L film thickness

l length of a crack

λ, λs, λski surface charge density

ld length of a dislocation segment

λsc screening charge density

Lt length of electrically charged track

μ friction coefficient

μi mobility of i

th defect

μion mobility of ions

n concentration

ν Poisson’s ratio

n1 H3O+ ion concentration

n2 OH– ion concentration

n3 D-defect concentration

n4 L-defect concentration

N water molecules’ concentration

P pressure

P0 normal pressure

Po polarization

Pel electrostatic pressure

Pi i

th component of the polarization vector

Q electric charge

θ angle between a crack plane and 

r

r

q linear density of dislocation charge

R resistance

r distance to a crack tip

ρ space charge density
vii

ρi dipole moment of water molecule

s surface area

σ(∞) tensile stress at infinity

σij stress tensor

smnij compliance tensor

σs ice static conductivity

σ∞ high-frequency conductivity of ice

T temperature

Td tension of a dislocation line

t time

τ(∞) shear stress at infinity

τ1 fast electric relaxation time

T1, T2 belt tension

τ2 slow electric relaxation time

τD Debye relaxation time

u potential energy of a defect

V potential difference or applied voltage

vcr crack velocity

v velocity

ωD Debye frequency

x distance to ice surface

 

r

E electric field strength

 

r

P polarization vector

 

r

r pointing vector drawn from a crack tip

to the point of observation

 

r

Ω configuration vector
Electromechanical Phenomena in Ice

VICTOR F. PETRENKO

INTRODUCTION

Among the numerous interesting properties of ice,

there is a group of physical phenomena in which electrical and mechanical properties correlate. That correlation can manifest itself in three ways:

1. Electromagnetic fields are generated by means

of mechanical actions, such as elastic stress, plastic

strain, fracture or friction.

2. Mechanical properties, such as plasticity, elasticity and friction, are modified by the application of

electrical fields.

3. Electrical conductivity or dielectric permittivity

are changed by strain.

We will refer to such effects as electromechanical

phenomena (EMP). Most of the experimental results

described in this report were discovered recently, during the last decade. Of course, ice is not unique in

exhibiting electromechanical effects. Similar phenomena were previously found in semiconductors, ferroelectric and piezoelectric materials, where EMP may

have a much greater intensity—electrical fields are

much stronger, for instance. Nevertheless, EMP in natural ice may have quite a large total magnitude, such as

electrical potential difference, owing to the large size

typical of ice sheets. In addition, since ice is one of the

most widespread materials on Earth, the electromechanical effects described below may have important

practical applications.

ELECTRICAL PHENOMENA

IN ICE FRICTION

This section describes two recently discovered

effects in friction on ice and snow. The first one is a

strong frictional electrification (Petrenko and Colbeck

1995), and the second is an effect of electrical fields on

ice friction (Petrenko 1994a). These phenomena illustrate the important role that ice electrical properties

plays in ice friction. It is most likely that these effects

result from the special structure and electrical properties of the ice surface. Since the physical properties of

the ice surface were discussed in detail in a previous

report (Petrenko 1994b), we will only briefly review

the information necessary to the following discussion.

Structure and electrical properties

of the ice surface

The physical properties of the ice surface differ significantly from those of bulk ice. In the temperature

range from 0°C to approximately –4°C, there is a thin

liquid or liquid-like film on the ice surface, which has

optical properties very similar to those of ordinary

water (Furukawa et al. 1987, Elbaum et al. 1993). The

film’s thickness depends on temperature, surface crystallographic orientation and ice purity. The film is also

sensitive to environmental conditions and it is about 50

nm at –1°C. A special layer remains on the ice surface

even at temperatures down to –100°C. This layer exhibits a diffusion coefficient, electrical conductivity,

structure and viscosity that are quite distinct from

those of bulk ice (see Maeno 1973, Barer et al. 1977,

Golecki and Jaccard 1978, Mizuno and Hanafuza

1987).

One of the best-known theoretical models developed to explain ice surface structure and properties

was invented by Fletcher (1962, 1963, 1968). The key

idea in Fletcher’s model is the assumption that at the

ice surface a significant fraction of molecules (denoted

as αο) is oriented with their dipole moments (i.e., protons) pointing outwards, as opposed to the bulk where

molecules are oriented randomly. This would result in

the buildup of a large positive polarization charge at

the surface. Fletcher came to his conclusion about
molecule orientational ordering by analyzing the interaction between dipole and quadruple moments of water molecules close to the surface. Such an orientation

of water molecules implies a high density surface electrical charge λs. Though this charge was predicted by

Fletcher many years ago, its existence was proven

experimentally only recently during experiments on

the frictional electrification of ice and snow.

All other predictions of Fletcher’s model are consequences of the molecular ordering in the surface layer.

In fact, since in the bulk there is no ordering between

the surface and the bulk, there should be a transitional

layer with a large concentration of hydrogen bond defects allowing molecules to reorient. This transitional

disordered layer, according to Fletcher, is the liquidlike layer. Besides the Fletcher model, there have been

several others designed to explain the unique physical

properties of the ice surface. No one of them is able to

account for all of its known properties.

One important surface property is ice friction. The

bibliography on ice and snow friction is vast (see reviews by Hobbs[1974] and Colbeck [1992]). Here, we

can examine only the major ideas available in the literature on this subject. In doing so, we will underscore

the facts that make ice different from most other materials. In static friction, the strong and universal adhesion of ice to almost any solid is one such difference.

Depending on temperature, ice/slider interface roughness and slider materials, it takes from a fraction of a

second to hours to produce mechanically a very strong

ice/solid interface. Intensive mass transport via the liquid-like surface film accelerates this process at temperatures above –10°C. The nature of the strong bonding

between ice and solids is not quite understood yet and

perhaps originates from the special arrangement of

water molecules on the ice surface mentioned above.

The coefficient of kinetic friction of ice in the temperature interval from –3 to –40°C strongly depends

on sliding velocity v, varying from 0.9 at v = 10–5 m/s

to 0.05 at v > 10–1 m/s (Barnes et al. 1971, Evans et al.

1976, Jones et al. 1991). For granite-on-ice friction,

Barnes et al. (1971) distinguish three ranges of sliding

velocity characterized by the different mechanisms

that govern the friction: ice creep, when v < 10–6 m/s;

ice plastic flow and fracture, when 10–3 m/s > v > 10–6

m/s; and frictional melting, when v > 10–3 m/s, T =

–11.75°C. The velocity at which the transition to frictional melting takes place may depend on the initial ice

temperature, normal pressure and ice and slider roughness, but the occurrence of melting and liquid lubrication of the ice friction have been proven many times.

Yet, for a precise quantitative description of such friction, we need more data on both the film thickness and

the real contact area. At temperatures close to the melting point and at high normal pressure, the pressure

melting of ice can also contribute to the formation of a

liquid film between the ice and a slider.

The study of the surface potential of ice and electrical charges at the ice surface has quite a long history

and continues to attract the attention of numerous

scholars. Such interest in the electrostatic properties of

the surface of ice is stimulated by both the fundamental problems associated with it and certain practical issues. Fundamental questions, which the study of the

surface potential and ice surface might help to resolve,

include the issue of the structure of the surface of ice.

For instance, if all the molecules at the ice surface are

oriented “proton-outwards” as Fletcher’s model suggests, this must lead to a positive charge at the surface

λs and a positive potential of the ice surface φs. Both λs

and φs are determined by the thickness of the surface

layer ∆ and the fraction of the oriented water molecules contained in this layer. Thus, measurement of λs

and φs in conjunction with other data (∆ for example)

might provide valuable information on the microscopic structure and nature of the ice surface layer.

The practical issues stimulating the study of the

electrical properties of the ice surface, include, first of

all, the problem of atmospheric electricity (see review

in Hobbs 1974) as well as the problem of adhesion and

friction of ice and snow (Petrenko 1994a,b).

Among physical mechanisms suggested to explain

ice surface charge and thunderstorm electricity were

surface electronic states (Buser and Jaccard 1978), a

thermoelectrical effect (Latham and Mason 1961,

Latham 1963), charge separation on freezing (Workman and Reynolds 1949, 1950), and the motion of

charged dislocations produced by rubbing one piece of

ice against another (Takahashi 1969a).

Early works on asymmetrical rubbing

Until recently, asymmetrical rubbing of ice on ice

was the only phenomenon studied in connection with

ice frictional electrification. Chalmers (1952) measured an electrical charge from small snow fragments

when two handfuls of snow were rubbed together,

finding a negative electrical charge of 2–8 × 10–10 C on

the ice fragments. Yoshida (1944), Reynolds et al.

(1957), Latham and Mason (1961) and Latham (1963)

studied charge separation during asymmetrical rubbing of ice on ice. In such an experiment, the constant

rubbing point becomes warmer than the variable rubbing point. The electrical potential differences generated in such experiments were very small and did not

exceed tens of millivolts. Such weak electrification is

attributable to the rubbing piece being heated more

than the rubbed one, with the potential difference arising from the thermoelectrical effect. Since the thermo2
electrical power of ice does not exceed 4 mV/°C (Bryant and Fletcher 1965), this effect is always small.

Takahashi (1969a) measured the electrical potential

difference between a vibrating metal plate and the surface of pure single crystals of ice, both before and after

the ice was rubbed with another single crystal or with

a plane. He found changes in the potential difference

ranging up to 0.2–0.3 V after the rubbing. Unfortunately,

he did not realize that he simply produced an ice–metal

contact potential or, in other words, he measured a difference in electron work functions between the metal

plate and the ice. The observed relaxation time was

very long (hours at –10°C) and had nothing in common

with the dielectric relaxation time in ice, which is 5 ×

10–5 seconds at that temperature. The effect that Takahashi found is likely ascribable to a difference in the

structure and thickness of the surface charge double

layer on fresh and aged ice surfaces. The layer slowly

changed by adsorption of impurities from the air and

diffusion of the impurities in ice. We will discuss such

an electric double layer in the next section.

Frictional electrification

This writer (Petrenko and Colbeck 1995) studied

frictional electrification on cylindrical samples of

polycrystalline ice grown from very pure, deionized

and degassed water. A polycrystalline ice layer, of

about 2 cm thickness and a typical grain size of 5–12

mm, was frozen onto the outside of a stainless steel

cylinder (Fig. 1). The cylinder was mounted on a lathe

located inside a coldroom where temperature could be

controlled within ±0.2°C. All ice samples were machined with a cutter to an outer diameter of 10 cm and

then subsequently polished with sandpaper. The ice

static conductivity σs was 10–9 Ω–1 m–1 at T = –30°C

and 10–7 Ω−1m–1 at T = –10°C. The measurements of

σs were made both with the apparatus at rest and during experiments. No difference was found among σs

values measured before, during and after the friction

experiments. This showed that possible local melting

and refreezing of the ice surface does not significantly

change the ice conductivity. When the cylinder rotated,

a frictional force changed the belt tension (T2 – T1).

Then, the friction coefficient μcould be calculated as

μ

α = −+













1 1

2

arcth 2

1

T T

T T (1)

where α is an angle shown in Figure 1.

A schematic of the experimental setup is shown in

Figure 2. Reverse rotation of the cylinder allowed us to

measure T2 instead of T1. Polyethylene, aluminum and

stainless steel belts of 2.5-cm width were used as the

sliders, and measurements were made at temperatures

from –5 to –35°C and at sliding velocities from 0.5 to 8

m/s.

To determine whether friction causes melting, a

thin thermocouple (0.1 mm) was attached to the outer

Figure 1. Ice friction and ice electrification measurements in the laboratory (top) and on snow in

the field (bottom) (after Petrenko and Colbeck

1994).

1-mm plastic plate

C

metal plates

13-mm-thick dielectric plate (2μF)

to the data logger

d

T1 T2

a

Electric ground

metal foil

dielectric film

stainless steel

 cylinder

ice

to an electrometer 

Figure 2. Experimental setup (after Petrenko

and Colbeck 1994).

3

Load cell

Electrometer

Keithley 616

Digital storage

oscilloscope

Computer

Ice

spring T

T1

2
4

0 20 40 60 80 100

50

40

30

20

10

0

Time (s)

Voltage (V)

Tension (arb. units)

5

4

3

2

1

0

on

off

V

T1

0 20 40 60 80 100

300

240

180

120

60

0

Time (s)

Voltage (V)

on on on

off off

off

0 1 2 3 4 5 6

0

10

20

30

40

50

V (volts)

v (m/s)

Figure 5. Dependence of the potential difference between ice and stainless steel slider on

sliding velocity (after Petrenko and Colbeck

1994). T = –10°C.

Figure 4. Potential difference V between ice

and a stainless foil. Sliding velocity was 1 m/s

(after Petrenko and Colbeck 1994). Temperature is –30°C. The arrows indicate when the

lathe was switched on and off.

side of the thin (75-μm) metal and dielectric belts sliding on the ice. The maximum heating by friction did not

exceed 1°C; hence, general melting of the ice cylinder

surface did not take place, although there may have been

some local melting at a few points of direct ice–slider

contact.

Significant frictional electrification was found for all

sliding materials used (e.g., Fig. 3 and 4). The potential

differences V observed were comparable both when the

belt slid on its own circular track on the ice cylinder’s

surface and when it slid continuously on a fresh surface

(spiral track). The electrification of the ice surface was

not homogeneous. Normally, it was possible to find two

positions along the 30-cm-long cylinder where V differed by a factor of two. Since the belt covered many ice

grains, contributions from individual grains were not

significant and added only a small oscillating component to V.

Typically, the potential differences generated between ice and metal were about 300 V (ice/Al, –31.5°C,

2 m/s). Under the same experimental conditions, the

electrical field generated by the friction of ice on polyethylene reached E = 2.1 × 106 V/m. This magnitude

was calculated as the ratio of the potential difference

across the film to the film thickness L. When the electrification was measured in the temperature interval from

–4.5 to –35°C and for sliding velocities from 0.5 to 8

m/s, the sliders always received a positive charge. The

electrification increased with decreasing temperature

and increasing sliding velocity (Fig. 5). The maximum

V = 1.6 kV was found at the lowest temperature

T = –35°C and the highest sliding velocity ν = 8 m/s.

From the measurements of a current I passing

through the electrometer when it was used as a current

meter, we found that the coupled ice–slider acted as a

charge generator (Fig. 6). Moreover, at temperatures

above approximately –12°C, the current is proportional

Figure 6. Dependence of the electric current

though ice/metal slider interface on sliding

velocity at three different temperatures (after

Petrenko and Colbeck 1994).

–1 0 1 2

–2

–1

0

1

2

3

4

T = –10 °C

T = –14 °C

T = –25 °C

ln[v(m/s)]

ln[I(10 A)] –8

Figure 3. Potential difference V across 75-μm-thick

polyethylene film and its tension T (after Petrenko

and Colbeck 1994). Sliding velocity was 1 m/s. The

arrows indicate when the lathe was switched on and

off. Temperature was –19°C.
5

160 480 800 1120 1440

2.2

1.6

1.0

0.4

-0.2

Time (s)

Voltage (V)

11 m/s

8.3 m/s

5.5 m/s

Figure 7. Records of the potential difference V

across a capacitor built into a ski at three sliding velocities (after Petrenko and Colbeck 1994).

Temperature was –4°C. Skier started at t = 0 and

slowed at the moments marked with the arrows.

to sliding velocity. Thus

I dQ

dt

ds

dt == ∝ λ v (2)

where Q = electrical charge

λ = surface charge density that the slider

picked up from the ice surface

s = area swept

v = sliding velocity

t = time.

When the input impedance of a measuring device is

much larger than the resistance of ice R, the charge

generated flows through the ice, resulting in a potential

difference V

V = IR . (3)

Since R for ice increases exponentially with decreasing temperature (see the Electrical Properties of

Ice [Petrenko 1993b]), the observed electrification rises rapidly at low temperatures. The charge density

λ found at T = –10°C was about 1.6 × 10–6 C/m2 and

10–5 C/m2 at –35°C. An even higher charge density

of about 10–4 C/m2 accumulated at the ice/dielectric

slider interface. Since it is unlikely that a slider picks

up all the surface charge from the ice, these values of λ

appear to be a lower limit.

At temperatures below –10°C, the density of charge

collected from the surface becomes nonlinearly dependent on the sliding velocity (see Fig. 6). While at T =

–10°C, I is proportional to v, at –14°C I increases as

v1.5 and at T = –25°C it increases as v2.

In the field experiments, we used an alpine ski as a

slider on snow (Fig. 1). The ski itself acted as a flat

capacitor C0 to measure an electrical field of strength E

generated by charge density λski that accumulated on

the bottom ski surface. A larger capacitor C = 2 μF,

connected in parallel with C0, reduced the potential

difference V to a magnitude that could be measured by

a portable data logger carried by the skier in a backpack. It is easy to show that

V d C

C C = +

λ

ε ε

ski

2 0

0

0 (4)

where ε0 and ε are the dielectric permittivities of a vacuum and of the material between the metal plates in the

ski respectively. The reduction factor C0/(C + C0) was

5.1 × 10–4.

The field measurements of snow frictional electrification were made in deep powder snow in British

Columbia. Figure 7 shows a typical record of V taken

at –4°C at three different velocities. The general character of the electrification observed in the field experiments agrees well with the laboratory results. One of

the most noticeable differences is that, in the field, V

first becomes negative and only then positive. At the

highest speed, V reached 2.2 V, which corresponds to

λ = 3.6×10–7 C/m2. This charge density was comparable with a value of 1.6 × 10–6 C/m2 found on ice. In the

absence of the buffer capacitor C, V would have been

4.4 × 103 V if there had been no electrical breakdown

of the air or the ski dielectric material. And this is not

yet at saturation. According to the laboratory results,

we can expect even higher voltages at lower temperatures. A reader interested in ski electrification can find

more details in Colbeck’s (1994) publication.

Possible reasons for electrification by friction, i.e.,

the accumulation of the electrical charges transferred

from the ice surface onto the slider, can be classified

into two categories:

1. The slider sweeps up the charge already present

at the ice surface.

2. Friction somehow produces a spatial separation

of the charge, which is then swept up by the slider.

After analyzing our data and the known ice surface

properties, we favor mechanism 1. Figure 8 shows a

very general electrical charge distribution in ice near

the surface. In a thin subsurface layer, a charge layer of

an extremely high density λs is formed. The major factor leading to its formation is the ordering of dipole

moments of the water molecules in the upper monomolecular layer, resulting in polarization Po. Such

ordering was initially suggested by Weyl (1951) for

water and was later used by Fletcher in his model of

the ice surface structure. Other evidence for the existence of such an ordered layer of water molecules at the
6

ρ

κ κ 1 2 –1 –1

d

surface charge

screening charge

D

Lsc

ice surface comes from the high adsorption coefficient

of ice at temperatures above –40°C (Ocampo and

Klinger 1983), and the results of computer simulations

carried out by Bush and Devlin (1991). At the same

time the polarization of water molecules in the bulk is

zero. Therefore, the polarization 

r

P drops from 

r

P0 at

the surface (x = 0) to 0 (x = ∞). This nonuniform polarization results in a surface charge of a high density

λ ∂

∂ s =− =

∞

∫ P

x

dx P0

0

. (5)

An estimation using eq 5 gives λs ≈ 2 × 10–1 C/m2.

Other possible reasons accounting for the formation of

λs could be adsorption of ions from the air and the

presence of the surface electronic states.

In thermal equilibrium the surface charge λs must

be neutralized by the opposite screening charge λsc,

equal to the former in magnitude, which is distributed,

however, in a much thicker screening layer. The

screening of the surface charge in ice was considered

in Petrenko and Ryzhkin (1984a), and in Petrenko and

Maeno (1987). The screening charge is composed of

protonic charge carriers (Bjerrum D- and L-defects

and H3O+ and OH– ions). There are two screening

lengths in ice κ1

−1

 and κ2

−1

1

1

3

2

30 40

1

2

κ εε

≅

 ( ) +











 ∞ 

− en n

0 Bk T (6)

1

2

2

10 20

1

2

κ εε

≅

 ( ) +















− en n

k TB 0s

(7)

where ε0 = dielectric permittivity of vacuum

ε∞ = 3.2, the high-frequency permittivity of ice

εs ≈ 100 = static dielectric permittivity of ice

kB = Boltzmann constant

e3 = 0.38e = charge of Bjerrum defects

n10 = concentrations of H3O+ ions

n20 = concentrations of OH– ions

n30 = concentrations of D-defects

n40 = concentrations of L-defects.

At the screening length κ1

−1, which is determined by the

concentration of majority carriers (n30 + n40) and coincides with the well-known expression for the Debye

screening length κ1

−1, the field drops down from the

original value λs/ε0ε∞ to λs/ε0εS. As we have seen, εS ≈

102, that is, κ1

−1 is a characteristic length at which εS

attains a steady-state value. At larger x the field drops

down to zero because of screening by minority charge

carriers, i.e., ions with a larger characteristic screening

length κ2

−1 determined by ion concentrations (n10 + n20).

Substitution of charge carrier concentrations in pure ice

(Petrenko 1993b) into eq 7 and 8 gives at T = –5°C

1 3 4 10

1

8

κ

≅ × − . m (8)

1 3 10

2

5

κ

≅ × − m. (9)

Figure 8. Schematic dependence of the space charge density ρ on the distance to the ice surface x (after Petrenko and Colbeck 1994). Scales are arbitrary. d is the thickness of liquid-like layer, D is the thickness of the ice layer

rubbed off by a slider from the ice surface, and κ1

–1 and κ2–1 are the length of

screening by Bjerrum defects and ions correspondingly.
But at –35°C they are longer than eq 8 and 9 predict

owing to the exponential dependencies of the charge

carrier concentrations on temperature. At –35°C

1 8 10

1

8

κ

≅ × − m (10)

1 1 6 10

2

4

κ

≅ × − . m. (11)

Notice that both the liquid-like layer and the principal screening length κ1

−1

 are very small. That makes it

likely that a slider, when rubbing ice, sweeps off the

surface charge together with the most of the screening

charge. That leaves just a small fraction of all λs on the

ice surface (see Fig. 8). This may explain why the density of the surface charge taken away by the sliders (λ ≤

10–5 C/m2) was much smaller than the theoretically

predicted λs ≈ 2 × 10–1 C/m2. Another factor decreasing λ is that the real contact area is much smaller than

the slider surface, and hence the slider does not sweep

off the whole area of the interface as assumed in eq 2.

The described mechanism of electrification by friction, thus, though hypothetical, is based on firm and

clear deductions from the surface physics of ice and

can be tested experimentally in the future, since it implies characteristic dependencies on temperature, sliding velocity, thickness of the “erased” layer and doping of ice.

Other mechanisms that may in principle contribute

to the frictional electrification of ice are the motion of

charged dislocations during the plastic deformation of

ice subsurface regions (Takahashi 1969a, Petrenko and

Whitworth 1983), a charge separation by microcracks

in ice during cleavage of surface layers (Petrenko

1993a) and the Workman-Reynolds (1949, 1950) effect (charge separation during refreezing of ice). It is

unlikely that any of these phenomena is able to account

for the large magnitude of the potential difference, 1.6

kV, observed in our research. Under the most favorable

conditions, the first two mechanisms generated V values that are much less then 1 V and the Workman-Reynolds effect generated about 100 V. Also, the Workman-Reynolds effect reaches a maximum in doped ice

samples while frictional electrification decreases with

doping. As discussed in the previous section, the thermoelectric effect can add only a negligible contribution.

The fact that at higher temperatures (–5 to –10°C)

the electrification is proportional to the sliding velocity (V ∝ v) while at lower temperatures (≤ –25°C) V is

proportional to v2 can be explained in terms of the

length of the electrically charged track on the ice surface Lt that a slider leaves behind. When the slider is

moving at constant velocity, any electrical charge

picked by it has to relax, flowing over the distance Lt to

the location of the opposite electrical charge behind the

slider. Then the resistance R in eq 3 is proportional to Lt

= τD . v and V is proportional to v2. (τD is the Debye

relaxation time of the ice.) Measurements of τD revealed that Lt ≈ 0.1 mm at –5°C but Lt ≈ 1 cm at –35°C.

Hence, at the high temperature the discharge takes place

locally under the slider since Lt is much less than the

slider dimensions (2.5 cm). In that case R does not depend on v and V ∝ v. But when at the low temperatures,

Lt becomes comparable with the slider dimensions, and

R ∝ Lt ∝ v and V ∝ v2.

Effect of electrical fields on ice friction

Earlier (Petrenko 1994a), it was demonstrated that

the application of an external dc bias to the ice/slider

interface can double the force of dynamic and static

friction between ice and metals and between ice and dielectrics. The experimental techniques, the ice samples

and experimental conditions used were similar to the

ones described in the previous section (see Fig. 1 and

2). The measurements were performed at temperature

intervals from –5 to –30°C, with sliding velocities from

0.5 to 8 m/s and the dc bias within the range from –3 to

3 kV. All slider materials created a strong increase in

apparent friction coefficient when the bias |V | ≥ 1 kV

was applied. Owing to the high dc impedance of pure

ice, the electrical power consumed from the power supply was very small (about 10–3 W at –30°C for metal

sliders and even less for dielectric ones).

Figure 9 depicts the changes in polyethylene belt

tension T2 when a 3-kV bias was applied to the ice cylinder and the foil electrode attached to the outer surface

7

Figure 9. Changes in tension of the polyethylene belt (T2) when a 3-kV bias is switched on

and off (after Petrenko 1994a). Temperature is

–30°C. Sliding velocity is 2 m/s. The friction coefficient μ ≈0.3 at V = 0 and μ ≈ 0.5 at V = 3 kV.

Time (s)

T (arb. units)

on on off

off

0 10 20 30 40 50

100

95

90

85

80

75

2
8

of the dielectric film, as shown in Figure 1. In a static

electrical field, ice behaves as a conductor so that the

entire bias is applied across the dielectric belt and the

air gap between the belt and the ice cylinder. Since T2

increases when frictional force increases, the effect

shown in Figure 9 corresponds to greater friction with

the applied voltage. Within the limits of experimental

error (±20%, determined by oscillations of T2), there

was no difference in the effects of positive and negative biases on the apparent ice friction coefficient μ. At

higher temperatures (from –5 to about –10°C), (T2 –

T1) becomes comparable with oscillations in the belt

tension because of the small magnitude of ice friction.

This results in the fact that while the effect of a dc bias is

noticeable at these temperatures, it becomes much more

pronounced only when the temperature decreases.

The change in the frictional force can be explained

by means of electrostatic pressure Pel , which increases

the normal pressure of the belt on ice

P E V

L el = = ε ε 0

2

0

2

2 2 2 (12)

where V = applied voltage

E = electrical field strength at the ice/slider interface

ε0 = dielectric permittivity of a vacuum

L = thickness of the belt.

Pel reaches a maximum in the absence of an air gap

between the ice and the slider. In this case and under

conditions indicated in Figure 9, Pel = 4 kPa, which

exceeds the average normal pressure P0 of the belt on

ice by a factor of four. Under the experimental conditions described, we can expect a fivefold increase in

the apparent friction coefficient. Since we see a smaller

effect, we assume that there was an average (and dynamic) air gap between the ice and the slider of about 0.2

mm, sufficient to reduce the effect on the observed

magnitude. Also, Pel should not depend upon the bias

polarity, in agreement with the experimental results.

When metallic belts made of aluminum or stainless

steel foils were used, the effect of dc bias on friction

was comparable to the results obtained with dielectric

sliders (see Fig. 10). In this case the dc bias was applied across the entire thickness of the ice between the

central metal cylinder and a metal slider. The effects of

positive and negative bias on friction were similar to

each other but not quite reversible. Namely, when the

bias was switched off, it took a long time (several minutes at –30°C) to restore the initial frictional force.

Since the electrical field vanishes during the much

shorter time of about 0.1 second (this was a time constant of the electrical circuit used), the observed effect

of the electrical field on ice–metal friction cannot be

explained in terms of electrostatic pressure. However,

even more serious evidence in favor of disregarding

the importance of electrostatic pressure comes from a

quantitative comparison of Pel and P0. While P0 remained the same, as in experiments with dielectric

sliders (about 1 kPa), Pel has not exceeded 0.18 Pa (see

eq 12). This smaller electrostatic pressure comes from

a larger L, across which the dc bias V was applied. In

this case L was equal to the ice thickness (1.5 cm) since

the central metal cylinder and the metal belt acted as

two electrodes attached to a poor conductor (ice). The

absence of any sizable potential drop at the ice/metal

interfaces was proven by perfectly linear current voltage characteristics. The field effect was more pronounced at low temperatures for the same reason as in

the case of the dielectric sliders, that is better signal-tonoise ratio.

The application of electrical fields also increased

static friction between ice and metals (see Fig. 11).

This phenomenon was very noticeable at temperatures

above –15°C, at which it takes just a few seconds for a

metal belt to freeze to the ice cylinder. At lower temperatures, when a slider rested just few seconds beTime (s)

3 kV off

3 kV on

0 5 10 15 20 25

30

29

28

27

26

25

T (arb. units) 1

Figure 10. Changes in tension of the aluminum belt

(T1) when a 3-kV bias is switched on and off (after

Petrenko 1994a). The smaller T1 is, the larger friction is (see Fig. 1). Temperature is –30°C. Sliding velocity is 2 m/s. The friction coefficient μ ≈ 0.34 at V =

0 and μ ≈ 0.47 immediately after V = 3 kV is turned

on.
tween sliding, there was usually no pronounced difference between static and dynamic friction, and the electrical field affected friction in the manner shown in

Figure 10. Once again, a strong field effect such as that

shown in Figure 11 cannot be explained in terms of

electrostatic pressure.

As working hypotheses accounting for the phenomena observed, I considered electrostatic pressure (see

eq 12), the effect of static electrical fields on the plastic

deformation of ice and expansion of the contact area

caused by electrical fields.

Electrostatic fields externally applied to the interface between ice and a dielectric slider are able to significantly alter normal pressure and, consequently, the

friction force (eq 12). Perhaps a more important and

interesting fact is that such electrostatic attraction between ice and a slider always occurs by itself owing to

the frictional electrification. Under certain conditions,

such electrification can contribute to the formation of

the friction force.

The effect of electrical fields on plastic deformation

of thin ice monocrystals (Petrenko and Schulson 1993)

was used to explain the action of an external electrical

field on the dynamic friction of metal sliders against

ice. It appears that an application of relatively small dc

electrical biases, on the order of 50 V, to an ice/metal

interface reduces by nearly an order of magnitude the

plasticity of a layer of ice of 50–100 μm thickness adjacent to the metal. This in turn is caused by the extraction of the major charge carriers (Bjerrum defects)

from the region near the electrode by the electrical

field (Petrenko and Schulson 1992). Depletion of Bjerrum defects from the subsurface layer of ice alters the

conditions of dislocation motion, which results in the

reduction of plasticity. When ice slides, there is a plastic shear deformation in the contact zones between the

ice and slider. Therefore, a reduction in the plasticity

of ice when a voltage V is applied results in an increase

9

10

8

6

4

2

0

Time (s)

Tension (arb. units)

0 20 40 60 80 100

V = 0 V = 2 kV

T

T1

2

Figure 11. Changes in tension of the stainless

steel foil belt when the ice cylinder direction of

rotation reverses (after Petrenko 1994a). Temperature is –10°C. Peaks correspond to static

friction. The two sets of dashed lines indicate the

average magnitude of the belt tension T1 and T2

when 2-kV dc bias between ice and steel was

“on.” The static friction coefficient μ ≈ 0.267 at V

= 0 and μ ≈ 0.312 at V = 2 kV.

of resistance to shear stress, or in other words results in

an increase of frictional force.

The effect of an electrical field on the plasticity of

ice may also contribute to the observed effect of a field

on static friction (see Fig. 11). In addition to that mechanism, there is the possibility that the applied field

changes the contact area between the ice and metal.

The following grounds support this assumption: the effect of an electrical field on static friction was observed only when the temperature was high enough

that a quasi-liquid film, characterized by low viscosity

and a large self-diffusion coefficient as compared to

ice, existed at the ice surface. When a strong electrical

field is present in the voids between ice and metal, ice

is attracted into these regions by the electrostatic pressure and tends to fill them. Since the static dielectric

permittivity of ice is quite large (εs ≈ 100), the driving

force of electrostatic pressure is also quite large

P

E = ε ε 0 ( ) − 2 1

2

s . (13)

A mass transfer at high temperatures can efficiently

occur along the quasi-liquid film, filling air gaps between the ice and the metal slider and increasing the

ice adhesion.

The above experimental facts and discussion show

the importance of electrical effects on ice friction.

Physical mechanisms of the phenomena are not determined yet. We have considered here only a few obvious mechanisms that are known to be applicable under

similar experimental conditions and can be easily estimated. Other mechanisms, such as electrolytic effects

caused at the metal/ice interface, the role of thin local

liquid patches, modification of the mechanical properties

of ice surface by multiple local melt–refreeze, etc.,

should also be analyzed. This is an extensive field for

future study.
10

stress tensor in eq 14 should be of the order of P

eijk ≈ P ≈ 2×1010 C/m2. (19)

The reader can check that eq 19 gives the correct order

of magnitude for strong piezoelectric crystals such as

segnet salt (4.2 × 1010 C/m2). In quartz, which is a weak

piezoelectric, eijk is about 1.5 × 109 C/m2.

Figure 12 illustrates generation of the electrical

polarization 

r

P under the action of uniform compression. Looking at the figure, we can easily realize that

the piezoelectric effect is incompatible with a center of

symmetry. Otherwise, the vector 

r

P would not know

which direction to go: to the left or to the right. According to Neumann’s principle, the symmetry of any

physical property of a crystal cannot be less than the

symmetry in the atomic structure of that crystal. In our

case this means that crystals with a center of symmetry

in the atomic structure cannot exhibit a piezoelectric

effect.

Let us apply Neumann’s principle to ice. Ice is a

molecular crystal consisting of water molecules. While

the centers of the water molecules are arranged into a

regular wurtzite lattice, the molecular dipoles may have

one of six allowed orientations and are not ordered (see

Hobbs 1974 and Petrenko 1993c). Such a random orientation of the dipoles results in zero polarization of ice

as it is shown in Figure 13b. In other words, ice has a

kind of statistical center of symmetry. An application of

uniform strain, as shown in Figure 13c, may cause

some reorientation of a small fraction of the molecules

but without distortion of the center of the symmetry

(Petrenko and Ryzhkin 1984b). The reorientation of

water molecules in ice under strain is responsible for

the ice anelastic relaxation. We can conclude now with

confidence that ordinary ice Ih cannot be an ordinary

piezoelectric. Though some early papers reported observation of a piezoelectric effect in ice (see, for instance, Rossman 1950), it is likely that this resulted

ELECTRO-ELASTIC EFFECTS

Is ordinary ice Ih piezoelectric?

Perhaps the most well-known electromechanical

phenomenon is piezoelectricity. Application of uniform elastic strain to a piezoelectric crystal causes its

electrical polarization. The electrical polarization is

characterized by a vector 

r

P . Crystalline quartz is a

well known example of a piezoelectric material. Mathematically, the direct piezoelectric effect is described

P Ee i ij j ijk jk = +× εχ ε 0 (14)

where Pi = ith component of the polarization vector

eijk = piezoelectric stress tensor

χij = electrical susceptibility tensor

εjk = strain tensor.

The inverse effect produces a contribution to the strain

εmn = cmnijσij + dkmn Ek (15)

where cmnij = stiffness tensor

σij = stress tensor

dkmn = piezoelectric strain tensor.

Two piezoelectric tensors relate

dkmn = smnij ekij (16)

where smnij is the compliance tensor.

The physical mechanism of piezoelectric polarization is very simple and can be explained in the following

way. The atomic structure of all piezoelectric crystals

may be thought of as consisting of pairs of positive and

negative ions. Since one such pair makes an electric

dipole, we can say that the whole structure of a piezoelectric crystal is composed of such elementary

dipoles. Now, using this simplified interpretation of

piezoelectric polarization, we can easily estimate its

absolute magnitude, which can later be compared with

the magnitude of pseudo-piezoelectric effects in ice.

Let us take a typical length of an elementary dipole a =

10–10 m and the dipole concentration N = 3 × 1028 m.

Then

P Nae≈ ≈×

ε ε0

10 2 2 10 C/m . (17)

Application of a strain εii varies the length a by the

factor of εii. The piezoelectric polarization is described

with the change in the polarization vector

∆P ≈ εiiP. (18)

Hence, the components eijk of the piezoelectric

Figure 12. Generation of piezoelectric polarization in a crystal under the action of the uniform,

uniaxial compression.

σ

σ

P

special axis and

special direction

P = e ε +(ε χ E ) i ijk jk 0 ij j
11

Figure 14. Air bubble migration against a pressure gradient in water. grad (P)

P = Σ pi = 0

σ

In ice Ih:

water molecule

+

+

_ pi

P = Σ p = 0 i

b. Chaotic orientations of water

molecules in ice before stress.

a. Electric dipole moment

of a water molecule.

c. Partial ordering of the water molecules in ice after stress was applied.

Figure 13. Application of Neumann’s principle to ice.

from some of the pseudo-piezoelectric effects discussed later in this report.

Phonon-induced polarization of ice

Whalley and Klug (1984) noticed that while a

macroscopic bulk of ice does not have a dipole moment, at the microscopic scale of about of tens of angstroms, the ice lattice may be polarized by statistical

fluctuations in the small statistical ensembles. That

means that at the microscopic scale ice can behave as a

piezoelectric. As Whalley and Klug showed, this can

affect propagation of elastic waves with a wavelength

comparable to the size of the polarized micro-regions.

The same phenomenon should also result in additional

absorption of infrared light.

Polarization induced by nonuniform strain

Though ordinary ice Ih is not a conventional piezoelectric, under some special conditions elastic strain

can induce an electrical polarization in it. Such special

conditions are gradients of strain, temperature or impurity concentration and also an externally applied

electrical field. All these factors destroy the statistical

center of the symmetry, whose existence imposes a

ban on the conventional piezoelectricity of ice.

Let us start the consideration of such pseudo-piezoelectricity from an electrical polarization of ice caused

by nonuniform strain. This phenomenon was first observed by Evtushenko et al. (1984), who have studied

electrical fields generated by bending vibrations in

thin pure single crystals of ice. Later (Evtushenko et al.

1987, Evtushenko and Petrenko 1991) such polarization was measured in a wide temperature range, from 0

to –80°C, on ice doped with HF, HCl and NH3. The

wide temperature range and the doping were used to

study the phenomenon of ice having different types of

majority charge carriers. Also, a theoretical model of

the pseudo-piezoelectric effect was developed, which

is explained below.

It was suggested that in ice under a nonuniform

strain, protonic charge carriers migrate along the pressure gradient in the same way as an air bubble moves

upwards in water (Fig. 14). The reason for such migration of the defects is that their specific volume differs

from that of a water molecule. As the result, point defects larger then a water molecule will migrate in the

direction opposite to the pressure gradient, while those

with a smaller specific volume will migrate in the direction of the gradient. Some important practical cases in

which nonuniform strain causes the protonic defect’s

migration and an associated electrical polarization are

shown in Figure 15. Also, since there is an oscillating

gradient of pressure in a longitudinal wave, such a wave

is followed by a wave of weak electrical polarization in

ice.

The formation of any protonic point defect results in

deformation of the surrounding lattice. In the case of

Bjerrum defects, the defective hydrogen bonds are

weaker than the normal ones, and therefore they will be

longer. This is obvious in particular for a D-defect,

where there exists an extremely strong repulsion between two protons on one hydrogen bond. Accordingly,

we can assume that Bjerrum defects “expand” ice,

increasing its volume. If ice is under pressure P, then the

formation energy of the i

th defect Eai is increased by the
12

b. Crack. c. Bend.

* Normally, in solids pressure is not hydrostatic, i.e., σ11 ≠ σ22 ≠ σ33.

Then, instead of eq 20 we should use

Eai(σij) = Eai(0) + γai(σ11 + σ22 + σ33) = Eai(0) + γaiσjj (20a)

or

Eai(εij) = Eai(0) + αaiεjj (20b)

where αai is a deformation-potential constant of ith type charge carrier.

amount of work against this pressure

Eai(P) = Eai(0) + Pγai (20)

where γai is the so-called activation volume.* For the

defects that increase volume, γai is positive, and their

formation energy is raised proportionally to the applied

pressure. This results in an exponentially decreasing

concentration of such defects with increasing pressure.

Since the formation energy of defects Eai depends on

the applied pressure P according to eq 20, in the presence of a pressure gradient, there is a force 

r

Fi acting

upon the defects

 

r

FE P i ai ai = −grad grad ( ) = −γ ( ). (21)

To find a resulting flux of the defects 

r

ji, we have to

add this force to the transport equation

 

r r r j eE n D n i i i ii i i = − ( ) η μ ΦΩ − grad (22)

where ei = electric charge of the defects

E = electric field strength

ni = defect concentration

μi = defect mobility

Di = defect diffusion coefficient

 

r

Ω = configuration vector

c) bend

b) crack

a. Indentation.

 

r rrrr Ω= − − + ∫( ) j j j j dt

t

1234 0

. (23)

The quantities ηi are given by

ηi = 1,–1,–1,1 for i = 1,2,3,4 (24)

and

Φ

T = 3 85 . k r B oo (25)

where roo = 2.76 Å is the oxygen–oxygen distance in

ice (Jaccard 1964). To find the electrical field strength

caused by the pressure gradient ∇P, we should solve

the system of eq 22–23 under particular initial and

boundary conditions. Thus, in the case of one dominating carrier type and static ∇P

 

r

E P

e e

= ∇

+ ⋅ ∞

γ

ε ε

ai

i

i

0 Φ

(26)

while for two types of charge carriers, for example

H3O+ ions and L-defects, and static pressure gradient

the electrical field is

 

r

E

P

e = ( ) γ γ a4 a1 − ∇

(27)

(see Evtushenko et al. [1987] and Evtushenko and Petrenko [1991]). Electrical polarization of ice caused by

stable and growing cracks was calculated in another

publication (Petrenko 1993a). Electromagnetic emission generated by such cracks will be described in the

section on electro-fracture effects.

Equations 26–27 show how the defect’s activation

volumes can be determined from measurements of the

Figure 15. Some practical cases in which nonuniform strain generates electric polarization of ice. The

arrows indicate the direction of motion of charge carriers.
strain ω >> ωD, where ωD is a Debye frequency, the

charge carriers in ice have no time to get redistributed

in the bulk of the deformed ice and, in the first approximation, the oscillating part of the polarization ≈εijp.

At the lower frequencies ω = ≤ ωD, we have to allow

for the ac bias arising at the elastic oscillations being

applied to the bulk of ice, whose electrical conductivity and dielectric permittivity have a complicated frequency dependence (Hobbs 1974, Petrenko 1993b).

Such electrical polarization induced by elastic strain in

ice with temperature or impurity gradients, or both,

was reported by Evtushenko et al. (1987).

ELECTROMAGNETIC PHENOMENA

IN ICE FRACTURE

At present we know of several electromagnetic

phenomena that are associated with the presence or

appearance of cracks in ice. They are electromagnetic

emissions (EME) from growing cracks and stable

cracks under varying stress, and also crack-induced

changes in electrical conductivity and apparent dielectric permittivity of ice.

The most interesting and intriguing of these phenomena, EME from cracks, was primarily found under

poorly controlled field conditions when a low signalto-noise ratio left doubts and uncertainty about the

phenomenon’s existence. Later, EME from cracks in

ice were reproduced and studied in a well-controlled

laboratory environment. The laboratory results made it

possible to develop physical models that explained that

electromechanical effect. When the researchers were

equipped with these models, they succeeded in obtaining reliable and well-reproducible detection of EME

from cracking in lake and sea ice. At the present time,

the EMP described below in this section are well understood and have even been found useful, both in ice

mechanics and remote sensing of stress in ice. That is

why we first start with a theoretical consideration of

the physical processes that cause EME from cracks in

ice and other associated phenomena. Then, we will

discuss laboratory and field data and their interpretations.

Theory

Cracks splitting pre-polarized ice

The main cause of EME from cracks in natural ice is

the so-called “frozen-in” or “intrinsic” electrical field

that is always presents in both sea and freshwater ice.

This electrical field is generated by spatial nonuniformity in the concentration of ions dissolved in the ice

bulk (Petrenko 1992a, 1994b). Figure 17 shows schematically such an electrical field inside granular ice.

The electrical field originates from the nonuniform

13

pseudo-piezoelectric effect. Indeed, that method was

used (Evtushenko and Petrenko 1991) to determine γai.

By varying temperature and doping, we determined

activation volumes of all four types of protonic defects

in ice. Figure 16 shows time dependencies of an electrical bias generated across a thin ice sample when a

step-shaped pulse of bending was applied to the sample. The ice was doped with NH3 in such concentration

that D-defects were majority charge carriers above

–30°C, but below –35°C OH– ions dominated. The observed decay of the signals is mainly attributable to a

final input impedance of the measuring circuit used.

Since the electrical charges of OH– ions and D-defects

are opposite, so are the electrical biases caused by their

migration.

Other pseudo-piezoelectric effects

There are more trivial pseudo-piezoelectric effects.

They can be observed when ice is already electrically

polarized for some reason. For example, because of the

thermoelectric effect (Brook 1958), ice is always polarized when there is a temperature gradient in it. The

electrical potential difference generated is usually

small since the thermoelectrical power of ice is low

∆

∆

V

T

=± − ( ) 2 4 mV/ C° (28)

(see Bryant and Fletcher 1965, Takahashi 1966). More

pronounced electrical polarization of ice can be induced by nonuniform distribution of impurity ions in

ice. In this case ∆V can reach hundreds of millivolts

and even 1 V (Brook 1958, Petrenko 1992a). Hence,

we can say that a piece of ice acquires an electrical

polarization if there are either temperature or impurity

gradients in it. Elastic strain εij (even uniform) changes

the dimensions of the ice sample, changing its dipole

moment. When a characteristic frequency of applied

1. –20°C.

2. 30°C.

3. 40°C.

4. 50°C.

2

3

4

1

10

t (ms)

0

–0.1

0.1

E (V/m)

Figure 16. Oscillograms of

the electric field strength E

in the ice sample doped with

10–4 mole/L NH3.
14

g

n

E

φ

Figure 17. Schematical representation of variations

in ions’ concentration n, electric field strength E and

electric potential φ along the crack surface in granular ice.

distribution of impurities in ice. Namely, when ice

grains grow, impurities are pushed out by the phase

boundary from grain centers to their peripheries, so

that more impurities get trapped near grain boundaries.

This process is common for most materials and is ascribable to lower solubility of foreign atoms and ions

in a solid phase as compared with a liquid phase. Mobile ions trapped in the ice bulk then diffuse against the

gradient of their concentration, generating electrical

charge transport and an intrinsic electrical field in ice.

In thermal equilibrium, that diffusion flux jD is canceled with a drift flux of the ions jDR

jDR + jD = 0 (29)

where

j e

e

DR n E i

i

= μi i (30)

j Dn k T

e

D ii n i B

i

=− ∇ =− ∇ i

μ (31)

where μi = ion mobility

Di = ion diffusion coefficient

ni = ion concentration

ei = ion electric charge.

Equalizing the right-hand sides of eq 30 and 31, we

find the intrinsic electrical field

E k T

e

= ∇ ( ) n B

i

i ln . (32)

Such an electrical field oscillates from grain to

grain in the ice bulk following grain configurations

and is very significant even in non-doped ice grown

from distilled water, E = 100 – 1000 V/m. In doped ice

E can locally be as large as 104 V/m (Petrenko 1992a,

1994b).

When an ice mass is split by a crack rapidly growing in the direction perpendicular to the electrical field,

the field generates two surface charges of the opposite

sign ±λs on the opposite surfaces of the crack

λ εε s s = − 0 ( ) ⊥ 1 E (33)

where E⊥ is a component of the electrical field perpendicular to the crack surface. Inside the crack the same

component, Ecr

⊥ , exceeds E⊥ by two orders of magnitude

E E cr

⊥ = ⊥ εs (34)

since εs ≈ 102. Taking E⊥= 102–103 V/m, we obtain a

potential difference ∆φ across a 1-mm wide crack

∆φ ≈ 10 – 100 V. (35)

Such a large potential difference can easily explain

why the intrinsic electrical field dominates among the

causes of EME from cracks in ice.

The processes of dielectric relaxation causes the

density of crack surface charges to decay with time. In

the case of a growing crack, this density, thus, decreases as the distance from the crack tip increases. Hence,

eq 33–35 are applicable only in a crack tip’s vicinity.

To calculate λs far from the tip, we should take into

account two processes of relaxation of electrical

charges in ice (Jaccard 1964, Gluschenkov and Petrenko 1993, Petrenko 1993a). In the first relaxation process, λs decays exponentially with time from its initial

value λs to

ε

ε

λ λ ∞ ≈

s s s

1

30 .

The relaxation time of this fast process is

τ

ε ε

σ

1

0 ≈ ∞

∞

. (36)

At T = –10°C in pure ice, τ1 ≈ 10–6 seconds and is

even shorter in natural ice. Since the crack velocity in

freshwater ice varies in the range from 102 to 103 m/s

(Petrenko 1992a, Sato and Wakahama 1992), the

length of a high-density surface charge train behind a

crack tip is about 10–6 s ×(102–103) m/s = 0.1–1 mm.
15

The constants αaj are usually called the deformation

potential constants and for a quite wide variety of materials these constants are about 10 eV.

The force acting on charge carriers in the presence

of a strain gradient is

 

r

F U =− = = ∇ grad grad( ii ii () ) . α ε αε (42)

This force initiates a flux of the charge carriers, i.e.,

electrical currents, and as a consequence an electrical

potential difference appears, as in the case of the bending of ice samples (Evtushenko et al. 1984, 1987).

To find the electrical field in the area around a crack,

we first find a vector of polarization 

r r Prt ( ) , . Let us consider ice with four types of charge carriers. Then

 

∂

∂

ε

r

P r r

t

P j

j

= =

=

∑  ̇ j j

1

4

(43)

where fluxes 

r

jj are determined by the transport equation

 

r r r j eE

e

D n j j j aj ii

j

j

= − +∇ ( ) η αε − ∇j j

σ

ΦΩ 2 (44)

whereσj = |ej| μj nj are the partial conductivities and Dj

are the diffusion coefficients.

Inside the bulk material

 

div div r rE P = − / . ε ε ∞ 0 (45)

Taking into account that curl 

r

E = 0 (quasi-stationary

approximation) and that at infinity (r = ∞) 

r r

E P = = 0 ,

we can find

 

∇ =− = φ εε∞

r r

E P / . 0 (46)

If for a particular crack, the deformation εii

r

( ) r t, is

known, then the system of eq 43–46 is complete. In the

presence of dielectric/conductor or conductor/conductor interfaces, we have to join the proper boundary conditions to this system of equations. The system of eq

43–46 has analytical solutions for many cases of practical interest that will be shown in the following sections.

Figure 18 illustrates three types of elementary

cracks. Notice that the mode III crack does not produce

an electrical field since, for an isotropic material, εii = 0

(see for example Hellan 1984).

For a mode I crack

ε

ν

θ

π

ii I = ( ) − K ⋅ r

1 2

E 2

cos

(47)

The rest of the surface charge relaxes very slowly

with a relaxation time τ2

τ

ε ε

σ

2

0 ≈ s

s

(37)

which is about 0.1 second in pure ice. That means that

a crack moving with 103 m/s velocity can have a 100-

m long electrically charged tail.

Since the intrinsic electrical field is an oscillating

function of the crack length (see Fig. 17), so is the surface charge and the resulting electrical dipole moment

of the crack. When a crack grows, its total dipole moment oscillates and generates an EME. An average frequency of EME f relates to the crack velocity vcr and an

average grain size g as

f v

g = cr . (38)

This relationship provides an investigator with a

simple method of crack velocity determination using

measurements of f and g (Petrenko 1992a, Gluschenkov and Petrenko 1993). The dielectric relaxation reduces λs and should be taken into account. Readers can

find more details of the theory of such EME in some

previous papers (Petrenko 1992a, Gluschenkov and

Petrenko 1993).

EME from the pseudo-piezoelectric effect

The second important mechanism resulting in crackinduced electrical polarization of ice is the pseudopiezoelectric effect discussed above (see eq 20–27 and

Fig. 15b). A theoretical description of such polarization was developed earlier (Petrenko 1993a).

When a crack appears and expands, it generates

strains in the surrounding material that we define as

 

εij

r

( ) r t, , which depend upon coordinates 

r

r and time t.

We have to find the electrical field strength 

r r Ert ( ) , and

electrical potential φ r

( ) r t, that are caused by these elastic strains. The charge carriers have to move because

their energy U depends on strains

U = U0 + U1 (εij) . (39)

In a linear approximation for an isotropic material

UU U

i

− − = − ⋅ <<  ̃ ,

=

0 aj ii 0 aj ii ii α ε αε ε ∑

1

3

1 (40)

where we use the Einstein summation convention

ε ε ii ii

i=

∑ =

1

3

. (41)
where τ1 is the fast relaxation time from eq 36 and the

jth type of charge carriers are majority charge carriers.

Laboratory experiments

Today, we have an ample collection of experimental data on the generation of EME and electrical signals by cracks in ice. To the best of our knowledge, the

first laboratory measurements of electrical signals

from cracks were performed by Takahashi (1969b). He

measured an electrical charge generated by the breaking of frost under a temperature gradient. The frost was

grown either between two ice hemispheres or between

two metal plates. Significant charge separation was

observed only under a temperature gradient, which

generates an electrical field E⊥ in the direction perpendicular to the cracks in the frost. The strength of electrical field E⊥ of about 20 V/m at –15°C was generated

by the thermoelectric effect in ice. The density of the

electrical charge separated by cracks in frost was estimated by Takahashi as 10–6 C/m. That value exceeds

by about one order of magnitude the charge density

predicted by eq 33. The discrepancy may be explained

by the break in the frost occurring at the narrowest

neck, where the temperature gradient, and hence E⊥ ∝

∇T, exceed their average magnitudes.

Takahashi (1983) expanded his study of charge separation by cracks in single-crystalline ice samples.

During those experiments, both sample cross section

and the temperature gradient were well defined. Again,

MODE I

MODE II

Figure 19. Lines of force of the electric field induced by stable mode I and mode II cracks in ice

(after Petrenko 1993a).

0

16

MODE I MODE II MODE III

Figure 18. Three modes of cracks.

where ν is Poisson’s ratio, E is Young’s modulus and KI

is an intensity factor

K l I = ∞ βσ π ( ) (48)

where σ(∞)is tensile stress at infinity and l is the crack

length. The numerical coefficient β depends on boundary conditions and is about 1. For the mode II crack

ε

ν

θ

π

ii II = ( ) − K ⋅ r

1 2

E 2

sin

(49)

K l II = ∞ βτ π ( ) (50)

where again β is about 1 and τ(∞) is shear stress at infinity (Hellan 1984).

For stable cracks or cracks that move “slowly,” i.e.,

cracks for which the time of their motion is longer than

the electrical relaxation times, the system of eq 43–46

has a solution (Petrenko 1993a)

 

r

E

e

eD n

e =

−∇ ⋅ + ∇ 







































+













ε

α σ

σ

εε

ii

j j

j

jj j

j

o

j

2 1 Φ .

(51)

Figure 19 shows force lines of an electrical field generated by mode I and mode II cracks in ice. Estimates

made using eq 47–51 show that a typical electrical

potential difference between infinity and a crack increases from 10–100 mV at the crack’s tail to about 1 V

at the crack’s tip.

The electrical field generated by a rapidly growing

crack can be calculated as

(52)

 

r r

r

E tr t

e r d

t

= ( ) =− −( )

[ ] ( ) ∇ ( ) ∫

, exp / 

exp / ,

1

0

εε

τ

ξ τ

α σ

εξ ξ

0

1

1

j j

j

ij
17

though there was large scattering in the data, significant charge separation was observed only in the presence of a temperature gradient ∇T and, hence, E⊥. An

average of that set of the results fits well to the prediction given by eq 33.

Electrical signals from thermocracks in ice singleand polycrystals were studied by del Pennino et al.

(1974). Their ice specimens were frozen on the top of a

massive copper substrate that was also used as the first

electrode. The second electrode, connected to a lock-in

amplifier, was vibrated above the ice surface to measure the ice–metal contact potential (Kelvin method).

Thermocracks were produced during intensive cooling

of the copper substrate because of the difference in the

thermal expansion coefficients of copper and ice. The

cracks in the ice (which were assumed to be mode I

type) grew in prismatic planes of ice single crystals,

starting from the copper substrate toward the mobile

electrode. Figure 20 depicts several such events. The

potential jumps associated with crack nucleation

measured from one to several volts and were

characterized by very long relaxation time. The relaxation time varied from 102 seconds at –20°C to 104

seconds at –100°C. While the signals’ amplitude can

be explained in terms of the pseudo-piezoelectric polarization of ice induced by cracks, their too-long relaxation time does not correspond to any electrical relaxation time known for ice. That time may correspond, as the authors suggested, to relaxation of elastic

stress in ice.

Fifolt (1990, 1991) and Fifolt et al. (1992, 1993)

found and investigated electrical signals from cracks

in freshwater columnar and granular ice under uniaxial

compression. Temperature gradients and other possible sources of external electrical fields were absent in

these well-controlled experiments. The measurements

were performed in a temperature range from –10 to –

33°C. Electrical signals from cracks appeared as an

–40 –80 –120 –120 –80 –40

20

15

10

5

0

V (V)

T (°C)

Figure 20. Jumps of electric potential V caused by

nucleation of thermocracks (after del Pennino et al.

1974). Open circles show V during freezing at a constant rate of 0.5°C/min; solid circles show V under

warming at a rate of 0.35°C/min.

Figure 21. Signal recovery system used to detect emissions (after Fifolt et al. 1993).

d

+ -

Ice

b

a

c

e

f

Storage

Scope

computer

Preamp.

Electrode

Shielded box

MTS

+ -

-

-

-

-

-

-

+

+

+

+

+

+ a. Ice sample and electrodes.

b. Synthane endcaps.

c. RF shielded enclosure.

d. High input impedance preamplifier.

e. Digital storage oscilloscope.

f. Computer.

electrical potential difference between two metal electrodes, which were either attached to an ice specimen

(thin foil electrodes) or placed at some distance from

the specimen surfaces (see Fig. 21).

Observed signals ranged in amplitude from 4 to 70

mV and lasted from 1.5 × 10–4 to 10–2 seconds. Most

commonly, the signals exhibited an exponentially

decaying form (Fig. 22). Independent measurement

showed that the signals’ delay time coincided with the

slow dielectric relaxation time τ2 (see eq 37). The signal

type shown in Figure 22 was typical for small cracks

that either split one ice grain or were located on one

intergranular boundary. Oscillating, sinusoidal type signals were characteristic for large cracks that split many

single-crystalline grains or columns (Fig. 23).

The nature of such signals was understood after the

discovery of the frozen-in, intrinsic electrical field in

polycrystalline ice (Petrenko 1992a). Cracks in such ice
18

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

Amplitude (volts)

Time, ms

0 1 2 34

Figure 22. Electrical signal of a microcrack in freshwater columnar ice (after Fifolt et al. 1993). T =

–33°C, σ = 6.3 MPa.

Figure 23. Electrical signal of a large crack

splitting many columns in freshwater columnar ice (after Fifolt et al. 1993). T = –30°C,

σ = 3.78 MPa.

1 0 0

0

8 0

0

6 0

0

4 0

0

2 0

0

0

Time (μs)

Amplitude (volts)

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

split electrically pre-polarized ice, causing the appearance of growing or oscillating electrical dipoles (see

the theoretical section above). This mechanism was

later proven in experiments in which a strong external

electrical field was applied to ice samples with growing cracks (Petrenko 1993d). It was shown that in this

case the magnitude of electrical signals from cracks is

proportional to the external electrical field E⊥, in accordance with eq 33. An example of a signal generated

by a microcrack in the presence of an external electrical field is shown in Figure 24. Again, the decay time

of the signals coincided with the slow dielectric relaxation time τ2.

Electrical polarization of ice, induced by a stable

crack, attributable to the pseudo-piezoelectric effect,

was studied using the scheme depicted in Figure 25 to

determine electrical field distribution around the crack

(Petrenko 1992a). Narrow cracks prepared by a thin

Figure 24. Typical electrical signal captured from a microcrack in freshwater

ice under the action of an external electric field E⊥= 10 V/cm. T = –10°C, crack

dimensions 2 × 2 cm (after Petrenko

1992a).

0 1 2 3

0

0.6

0.9

1.2

1.5

0.3

t (ms)

V (V)
19

Ice

Shielded box

Ice

s

MTS

testing machine

Lock-in

amplifier

Preamplifier

Figure 25. Schematic of experimental configuration used in

measurements of electric fields on the ice surface around a

stable crack (after Petrenko 1992a).

bandsaw (1 mm thick) were located in the middle of

the samples, perpendicular to their long side. Sample

dimensions were 15 × 6 × 6 cm3 and the crack length

varied from 5 to 30 mm. An oscillating sine wave, of

frequency from 1 to 300 Hz, was applied to the samples by an MTS testing machine. In this set of measurements, a sine potential difference was measured by

a lock-in amplifier between one remote electrode

mounted into the ice and one electrode placed near the

crack tip. This latter electrode in some cases was

mounted into the ice to a depth of 2 mm, by careful

heating of the electrode, or was attached to the ice surface with slight pressure. The electrodes were made of

stainless steel wire of 0.1-mm diameter.

Figure 26 shows the distribution of the amplitude of

an oscillating electrical potential φ measured around

an artificial mode I tearing crack. To compare these

experimental results with the theory, φ was calculated

using eq 51

φ

ε α

εε =

+

ii j

j

0

j

e e

Φ (53)

where εii must be taken from eq 47 and αj = α4 = 6.2

eV (Evtushenko et al. 1987). There is satisfactory

quantitative and qualitative agreement between theory

and experiment in the vicinity of the crack tip for r =

1–10 mm. At r = 1 mm, φ = 0.8 mV. Yet, at larger distances φ remains almost constant instead of decreasing

to 0 as the theory predicts (φ ∝ r –1/2; r is the distance

–30

–20

–10

0 10

20

30

–30

–20

–10

0

10

20

30

0.2

0.4

0.6

0.8

1.0

y (mm)

x (mm)

φ (mV)

Figure 26. Amplitude of electric potential φ on the surface of

the ice sample measured in the configuration shown in Figure 25; large grains of ice grown from deionized water (after

Petrenko 1992a).

Sample dimensions 13 × 6.5 × 6.5 cm

Crack length l = 3 cm

Width d = 1 mm

T = –10°C

Stress amplitude 0.12 MPa

Frequency 90 Hz
20

to the tip). This discrepancy could arise from small oscillations of the crack surfaces if there is a constant

potential difference between them.

Similar EME from cracks were observed by Thiel

(1992). He recorded EME in the vicinity of ice cracks

created by breaking rods of ice, scouring the ice surface, applying uniaxial pressure to a cylindrical ice

core and using a bore-hole jack in an ice sheet. The

observations were made in the frequency band from

50 Hz to 15 kHz, using a two-channel audio cassette

recorder and wire probes inside or outside the ice.

Thiel found that EME events correlate with acoustic

emissions events that arise during crack formation.

Field experiments

At present we have several reports on observations

of EME from lake ice, glaciers and sea ice sheets. Kachurin et al. (1979) reported the detection of electrical

and magnetic signals from ice and snow under field

conditions. Radio waves emitted by the motion of

snow avalanches were recorded by a set of radio-frequency receivers working in the frequency ranges of

0.1 to 30 Hz, 900 Hz to 2 kHz, 2.5 MHz, 40 MHz and

760 MHz. The electrical component of EME was recorded at 760 MHz, and the magnetic component at

the other frequencies. The sensitivity of the detectors

over all frequencies was 1 to 2 μV/m. Broadband EME

with a maximum near 1 kHz were recorded for avalanches of freshly fallen snow and near 2.5 MHz for

packed snow. The amplitudes of the electromagnetic

signals investigated were one to two orders of magnitude higher than that of background noise in the same

corresponding range. The authors did not provide information either on the distance from the receiver to the

avalanches nor on the types of antenna used. While all

the mechanisms of EME from ice considered above are

applicable for numerous cracks in a snow cover during

an avalanche, there may be some additional phenomena, such as frictional electrification, responsible for the

EME from snow avalanches.

The same authors reported detection of magnetic signals captured from a mountain glacier (Malyy Azau glacier in the Caucasus Mountains) during various natural

and artificially induced dynamic processes. The EME

and seismic signals were recorded in the 0.1- to 30-Hz

frequency range. The magnetic component was captured with a single-turn loop with a diameter of 100 m

and with an induction coil with a Permalloy core. Figure

27, taken from the paper by Kachurin et al. (1979),

shows the correlation between EME and seismic signals

captured from the glacier. Later, Kachurin et al. (1984)

reported EME from freshwater lake ice and sea ice

sheets. To measure the horizontal component of the

magnetic field, they used an induction coil with a resonance frequency of 10 Hz. The EME from lake ice were

detected during air cooling at night and during ice hummocking. In the same study Kachurin and his co-authors

measured quasi-static (10–2 to 1 Hz) electrical fields

generated in first-year sea ice during its loading. When

the load was applied they detected an electrical potential

difference of a few millivolts between two electrodes

mounted into the ice at a distance of 50 m from each

other. The corresponding bend of the ice sheet was

about 10–4 radian.

They also made a very interesting attempt to detect

sea ice EME from an airplane flying at an altitude of 100

*

* * *

0 20 40 60 0 20 40 60 80 100 120 140

0

-5

5

0

10

20

30

Figure 27. Synchronous records of the electromagnetic (top) and seismic (bottom) signals captured from natural and artificially induced glacier tremors on 17 August 1977 (after Kachurin et al. 1979). The pass

band of the electromagnetic and seismic signals is 0.1 to 30 Hz.
21

30000

3000

300

30

E (V/m)

H (nT)

100

10

0

12 16 20 00 04 08 12 16 20 00 04 08 12 16

t (hours)

(1) (2) (3) (4) (5) (6) (7) (8)

Figure 28. Synchronous 3-day en route measurements of electric (top) and magnetic (bottom) fields (after Kachurin

et al. 1988).

1. Fast 1-year ice, 100–130 cm, snow 20 cm,

hummocks

2. Marine ice 60–80 cm, hummocks, snow 20 cm,

compression

3. Ice fields with open pools

4. Fresh, snow-free ice 30–40 cm, compression

5. Large open pools, ice-free water, tow vessel

released and 180° turn made

6. Fresh ice with open pools

7. Ice fields with open pools

8. Passage into solid ice.

m using a magnetic ferrite antenna connected to a selective amplifier. The amplifier was tuned to the frequency

of 100 kHz. An equivalent sensitivity of the measuring

system equaled 2 μV/(mV/m), and an equivalent noise

level was 0.3 mV/m. The plane flew above various regions such as open water, thin ice and thick ice during

different wind conditions. Strong wind loads the ice,

causing intensive cracking, hummocking and deformation. They found that the strength of the electromagnetic field increased to 5–8 mV/m above the regions with

intensive ice deformation, while without wind loading

or above open water, variations of EME did not exceed

0.5 mV/m as measured on different days.

During the navigation period of 1986, the electrical

and electromagnetic fields arising from a fracturing of

the ice cover during ship passage were measured from

the nuclear icebreaker Arktika (Kachurin et al. 1988). A

dynamic electrometer was used for the measurements

of electrostatic fields in the range of 10 to 105 V/m. The

electrometer was on a movable arm mounted 11 m

above the waterline at the bow of the icebreaker. Electromagnetic pulses were recorded with an induction

transducer having a ferrite core with a resonance frequency of about 1 kHz. The signals were amplified by a

selective microvoltmeter in the frequency range from

Figure 29. Experimental configuration used in measurements of EME from cracks in lake and sea ice (after

Gluschenkov and Petrenko 1993).

Amplifier Filters

Digital

oscilloscope

Computer

Ground

Ice field Crack

Cable 100 m

Antenna

Pre-amplifier

200 Hz to 2 kHz. The researchers picked this frequency

range to minimize the level of natural and industrial

electromagnetic interference and to allow subsequent

satellite measurements through the ionospheric radio

propagation window in the ELF range. An equivalent

ambient noise was about 10–10 T while the signals usually measured from ice fracture exceeded 10–9 T.

Figure 28 shows the results of synchronous measurements of the electrical and electromagnetic fields made

in ice sheets of various thicknesses and ages. Icebreaker

velocity and electrical and magnetic field strengths correlated over a much shorter time scale of several minutes. The electrical and magnetic fields measured in

these experiments may be caused by both EME from

cracks and frictional electrification of ice and snow generated by the icebreaker passing through the snow-covered ice.

Petrenko and Gluschenkov (1995) reported field

measurements of EME from individual cracks in freshwater lake ice, and Gluschenkov and Petrenko (1993)

did the same with first-year sea ice. The electrical component of the EME from cracks was measured with an

experimental setup shown schematically in Figure 29.

A 10-m-long dipole antenna was stretched horizontally

1 m above the ice surface. The antenna was connected to

an input circuit with a high input impedance (1014 Ω)

preamplifier. The high input impedance together with

the electrical capacitance of the antenna (~10–11 F) enabled us to measure electrical fields in a wide frequency
22

0 280 560 840 1120

t (ms)

0

10

20

–10

–20 mV

0 0.005 0.01 0.015

0

3.3

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

t, s

V, volts

I II

V (volts)

t (s)

Figure 31. Electromagnetic emission from a crack in

sea ice (after Petrenko and Gluschenkov 1995). The

crack was 60 cm long and 10 cm wide. Area I corresponds to the crack propagation and area II corresponds to electrical relaxation of the electric field after

crack arrest.

Figure 30. Typical signal captured from a thermocrack grown in lake ice (after Gluschenkov and

Petrenko 1993). T = –5°C.

range, from about 10–3 Hz to 1 MHz. Additional filtering was used to cut off the common industrial (60 Hz)

and ionospheric (ƒ ≥ 100 kHz) noise.

Most of the signals captured from identified cracks

were very similar to those found in the laboratory (Petrenko 1992a, Fifolt et al. 1993). A typical signal captured from a thermocrack in freshwater columnar lake

ice is depicted in Figure 30. The crack appeared 10 m

from the antenna and split several single-crystalline

columns of ice. As in the laboratory experiments, the

oscillation of the electrical field can be interpreted in

terms of an oscillating electrical charge on the crack

surfaces.

An electrical signal captured by a dipole antenna

from a larger crack splitting a cold (–35°C) plate of sea

ice is shown in Figure 31. The crack surface was normal to the direction of the gradient of salinity of the ice,

and hence the crack grew perpendicular to the frozen-in

intrinsic electrical field. Again, as in corresponding laboratory experiments, the signal increases during crack

propagation and then relaxes after crack arrest.

ELECTROPLASTIC EFFECTS IN ICE

Several electromechanical phenomena in ice are

associated with the motion of electrically charged dislocations. They are all of quite small magnitude. Nevertheless, their significance is determined by their contribution to the study of the physical mechanisms that

govern motion of dislocations and, hence, plastic deformation of ice. Electrically charged dislocations

were found in many materials such as ionic crystals

(see review by Whitworth 1975); covalent semiconductors (see review by Alexander and Teichler 1991);

and crystals with mixed covalent–ionic bonding (see

review by Osip’yan et al. 1986). In these materials the

electrical charge on a dislocation core appears when a

dislocation captures either charged point defects (such

as vacancies and interstices in ionic crystals) or electrons (or holes), as happens in semiconductors or when

both point defects and electrons (holes) are captured.

Significant theoretical efforts have been applied to

clarify the formation of the dislocation charges in ionic
23

materials and semiconductors. Though there are no

theoretical papers on the electrical charge of dislocations in ice, some reasons for formation of such a

charge are obvious.

First, the charge may originate from electrical activity of dangling hydrogen bonds in the dislocation

core. Figure 32 illustrates a dangling bond in the core

of a 60° dislocation. A dangling bond may or may not

have a proton on it. In the first approximation, the

probability of finding a proton on a dangling bond is

50%, since when a regular hydrogen bond breaks into

two dangling bonds, one proton is shared between two

bonds. It is generally acknowledged that a regular hydrogen bond is electrically neutral. The dangling

bonds of a dislocation core introduce electron energy

levels or narrow energy bonds located in the forbidden

band of ice. Depending on the relative position of a

Fermi level and the dislocation levels (bands), the exchange of electrons between the dangling bonds and

the bulk ice will result in a net negative or positive

charge of the dislocation. It is not known at present if

Figure 33. Directions of the principal stresses in the

vicinity of an edge dislocation. The dislocation line is

directed perpendicularly to the figure’s plane.

x

b

Figure 32. Section in the ( ) 1100 plane of a 60° dislocation

on a plane of the shuffle set in the structure of ice, illustrating the dangling bond in the core.

such dangling bonds may exchange protons with an

ice bulk.

Second, a mechanism that may result in a net dislocation charge is strong elastic interaction between a

protonic charge carrier—i.e., ions and Bjerrum defects—and strain generated by a dislocation. Figure 33

illustrates stress patterns in the vicinity of an edge

dislocation. As is seen from this figure, the dislocation

generates compression in the upper quadrants and tension in the lower ones.

The specific volumes of protonic charge carriers

(ions and Bjerrum defects) exceed that of a water molecule (Evtuschenko et al. 1987, Evtuschenko and

Petrenko 1991). Thus, all these charged defects should

accumulate in the lower quadrant and escape from the

upper one. Figure 34 shows schematically the change

in defect activation energy as a function of the x coordinate, also shown in Figure 33. Since for the protonic

defects in ice αi ranges from 1.2 to 6.8 eV and εii is

about 0.1 in the vicinity of a dislocation core, the binding energy, αi εii, of the defects on an edge dislocation

Figure 34. Change in activation energy αεii of a charge

carrier in ice in the vicinity of an edge dislocation.

x

αεii
24

c) d)

electrometer

0 100

time (s)

2

0

–2

–4

I (pA)

50

30

0

c. Ice specimen mounted for tensile deformation experiment.

Figure 35. Dislocation currents in ice (after Petrenko and Whitworth 1983).

[0001]

in Figure 35a. A smaller ice sample was then cut off

the bent specimen for tensile tests (Fig. 35b and c). The

electrodes were formed from an Hg-In amalgam,

which adheres well to the surface of ice but remains

liquid down to –30°C, so that it does not interfere with

deformation. Dislocation currents were measured with

an electrometer at T = –20°C during tensile creep of

the ice samples. A typical recording of both the current

I and the tensile elongation ∆l are shown in Figure

35d. The abrupt changes in the current ∆I were caused

by the starts and stops of charged dislocations. It was

shown that q can be calculated as

 

q

Ib

d = ∆ z

p

 ̇

l (54)

where bz= component of the Burgers’ vector along

the length of the specimen

d= interelectrode distance

∆I= dislocation current

 

 ̇

lp = rate of the tensile plastic deformation.

The dislocation charge may be expressed in terms of

qa/e, i.e., in the number of elementary charges per intermolecular distance a. We found that the dislocation

charge in ice was positive, with an absolute magnitude

of qa/e = 2 × 10–3. That corresponded to two proton

a)

b)

E1

[0001]

E2

b. How the tensile specimen is cut from the bent crystal.

a. Bent crystal containing an excess of dislocations of one sign. When deformed by tension the

majority of dislocations move toward the upper

electrode E1.

is about tens of electronvolts and is comparable with the

defects’ activation energy. That should result in significant buildup of defects near a dislocation and in total

electrical charge if αi differs for positive and negative

defects. Such a mechanism of dislocation charge creation was first suggested and estimated in Petrenko and

Ryzhkin (1986a,b), but has never been accurately calculated.

Electrically charged dislocations can manifest themselves in three different electromechanical phenomena.

First, their motion during plastic deformation can result

in an electrical current, a so-called dislocation current.

Second, application of an external electrical field may

cause the dislocation motion and, hence, small plastic

deformation. Third, the introduction of dislocations

may change concentrations of charge carriers and, as

a result, cause a change in electrical conductivity and

dielectric permittivity of ice. We will consider below all

three groups of phenomena.

Dislocation currents in ice

Dislocation currents in ice were measured and used

for determination of the linear density of dislocation

charge q (Petrenko and Whitworth 1983). We used

specimens of very pure single crystals of ice in which

the majority of edge dislocations of one mechanical

sign was introduced by preliminary bending, as shown

d. Recordings of change of length ∆l and

current I during tensile deformation. Load is

applied and removed at times indicated by the

arrows. ∆l was measured in micrometers.
25

pected. This should increase the estimated upper limit

of qa/e somewhat.

We can conclude that there is no significant discrepancy among different authors and the techniques

applied and that most probably the magnitude of qa/e

should be somewhere in the range from 2 × 10–3 to 2 ×

10–2. If the above-described accumulation of point defects in the region of tension near a dislocation core is

responsible for the dislocation charge, then the small

linear density of this charge does not reflect the real

number of the defects captured, but rather shows a difference in concentrations of positive and negative

defects near the dislocation.

Effect of static electrical field on ice creep

In ionic crystals and some semiconductors, qa/e is

so large (0.1–1.0) that the application of high external

electrical fields of E ≈ 104 V/cm is able to accelerate or

halt creep, depending on the relative directions of qE

r

and the predominant velocity of dislocations (Whitworth 1975, Osip’yan et al. 1986). Such an effect of

electrical fields on plastic deformation in ice has not

been observed so far. However, the application of even

smaller static electrical fields of 103 V/cm can significantly suppress plastic creep of thin ice specimens having a thickness of 1 mm or less (Petrenko and Schulson

1993).

We examined the effect of dc and ac electrical fields

on the plastic deformation of pure and doped (with HF

and KOH) single crystals of ice in the temperature

range of –10 to –45°C. The basal plane (0001) was a

slip plane for dislocations. We found that a relatively

small (about 10–50 V) dc voltage applied across thin

single crystals decreased both the creep strain rate ε ̇

and the high-frequency conductivity of ice σ∞. Figure

36 depicts the dependence of the creep strain rate on the

dc voltage applied to a 50-μm thick ice specimen. At

the same time, the application of an ac electrical field of

the same strength as the dc field or the application of a

dc field to thick specimens (1–3 mm) did not reveal

changes in the creep rate. We felt that the observed

changes in the plastic deformation were ascribable to a

decrease in the concentrations of Bjerrum defects

caused by the strong static electrical fields. The concentration of Bjerrum defects is proportional to σ∞ and

can be easily monitored.

charges per thousand intermolecular distances along

the dislocation core. This charge magnitude was estimated as a lower limit because of the use of blocking

(non-ohmic) electrodes, so that the charge flow within

the ice produced polarization at the surface and the full

current may not be recorded by the electrometer.

Motion of charged dislocations

in an electrical field

Itagaki (1970) used a different technique to determine the dislocation charge density q. Using X-ray topography to observe dislocation lines in ice, he found

that some dislocations vibrated when an external ac

electrical field was applied. At the low-frequency limit,

the amplitude of vibrations η depends only on the

length of a dislocation segment ld, external electrical

field E and the tension of a dislocation line Td. Namely

 

η =

l ⋅ ⋅ 2

8

E q

Td

. (55)

This equation enables us to estimate q if l, η and E are

known.

Itagaki measured the amplitudes of vibrations η in

pure single crystals of ice taken from the Mendenhall

glacier. The ac field strength ranged from 3 to 600

V/cm, and three frequencies of 60, 1.33 and 0.33 Hz

were used. The linear density of a dislocation charge

estimated by Itagaki ranged from qa/e = 3.6 × 10–3 to

qa/e = 2 × 10–2.

Later, Joncich et al. (1978) tried to explore a similar

idea to estimate q for dislocations. They applied a

strong electrical field across a low-angle title boundary

consisting of edge dislocations. Their tests were performed at T = –15°C. No measurable displacement of

the boundary was observed. Based on their experimental precision, Joncich et al. concluded that qa/e

cannot exceed 3.3 × 10–3. Since they used a dc electrical field and blocking electrode, the real E in the ice

bulk in their experiment could be lower than they ex-

∆ ̇  ̇/ ε ε

0 100 200 300 400

V

Figure 36. Dependence of the relative change in strain

rate ε ̇ on the applied dc voltage V (after Petrenko and

Schulson 1993). ε ̇ is the strain rate at V = 0. T = –20°C,

sample thickness L = 50 μm.
26

–100 –90 –80 –70 –60 –50 –40 –30

Temperature (°C)

Compression

1.0 C.P.S.

1.0 C.P.S.

Compression

–100 –90 –80 –70 –60 –50 –40 –30

Temperature (°C)

30%

15%

0%

30%

15%

0%

600

400

200

0

Dielectric constant

2.0

1.0

0

Conductivity (10–9

Ω–1 cm–1) Figure 37. Effect of compressive strain on the electric properties

of ice single crystals, measured at 1 Hz (after Higashi 1969).

of ice that had undergone 15 and 30% plastic deformation (Fig. 37). These changes were confirmed later by

Mae and Higashi (1973), after they conducted very detailed and careful investigations on the effect of plastic

deformation on ice electrical conductivity and dielectric

permittivity in wide temperature (–10 to –100°C) and

frequency (0.5 to 103 Hz) ranges. During plastic deformation of pure single crystals of ice, the dislocation

density in their experiments rose from 104 to 107 cm–2.

Mae and Higashi found that plastic deformation left unchanged the high-frequency conductivity σ∞ but induced significant changes in low-frequency conductivity σs. This can be easily explained, as the plastic deformation generated a concentration of new charge carriers

that was comparable with the minority charge carrier

concentration but was much less than the majority

charge carrier concentration. That would also explain

the failure of Brill and Camp, who measured ε in the

region of majority charge carrier frequency.

A typical change in σs found by Mae and Higashi,

after introducing a dislocation density of 107/cm2, was 2

× 10–10/Ω . cm. Notice that this number, when recalculated into the number of elementary charges per intermolecular length on a dislocation, gives 5×10–3, which

is in the range of the experimental magnitude of qa/e.

to be replaced with “original” printout

Effect of plastic deformation on

electrical properties of ice

Dislocations introduced during the process of plastic deformation can affect the electrical properties of

ice (as well as other materials) in a variety of ways.

They can generate new point defects such as vacancies, interstitials and Bjerrum defects; they can also

capture point defects by their elastic field and make

defects immobile. All this can change the charge carrier concentrations. But this is not the whole story yet.

Owing to their long-range elastic and electrical fields,

dislocations can effectively scatter charge carriers. As

a result the charge carrier mobility usually decreases

after plastic deformation. Moreover, charged dislocations may, in principle, move under the action of these

electrical fields, contributing to both electrical conductivity and dielectric permittivity.

The first known, but unsuccessful, attempt to find

the effect of plastic deformation on the electrical properties of ice was made by Brill and Camp (1957). They

reported no changes induced by plastic deformation in

the dielectric properties of ice at 1 kHz. On the contrary, Higashi (1969) reported preliminary results obtained by Mae, who found a very profound increase in

low-frequency conductivity and dielectric permittivity
Mae and Higashi also analyzed separately changes

in the mobility and concentration of minority charge

carriers caused by plastic deformation. They used for

this purpose their experimentally obtained frequency

dependencies of σ and ε, but exploited a theory

by MacDonald (1953), which is not applicable to ice.

Their results showed unrealistic magnitudes for an

ion mobility of 0.6 cm2/V s. Nevertheless, when the

same experimental technique is combined with a specific theory for ice (Petrenko and Ryzhkin 1984a),

it gives a correct value for mobility of ions, of a few

10–3 cm2/V s (Zaretskii 1991).

Noll (1978) studied the influence of plastic deformation on electrical properties during and after deformation. He measured σ and ε at T = –3 and –10°C in a

frequency range from 10–2 to 105 Hz, a strain rate range

from 2 ×10–5 to 10–3 s–1, and a strain range from 0.03

to 0.6. He found that plastic deformation reduces the

electrical conductivity in the space-charge dispersion

frequency range (Fig. 38). The decrease depended

strongly on the strain rate, while the strain magnitude

27

had little effect. After deformation takes place, recovery processes have been observed that restore the original conductivity if the total strain was small. Rapid

and large deformation, however, causes permanent

changes in the conductivity and dielectric permittivity.

Itagaki (1978, 1982, 1983) conducted a very interesting series of experiments and theoretical calculations aimed at determining the contribution of electrically charged dislocations to the electrical properties

of ice. In 1978 he carried out an exciting experiment in

which he compared the electrical properties of dislocation-free areas of ice pure microcrystals with areas

having a high density of dislocations. He used hoarfrost crystals as the specimens and X-ray topography

to visualize dislocations in them. Use of tiny liquidmercury electrodes prevented damage to the ice crystals. Itagaki did not observe the Debye dispersion of σ

and ε in dislocation-free regions, while it was present

in the regions with high dislocation density and in the

initially dislocation-free regions after introduction of

dislocations by surface scratching. On the basis of

these observations, he concluded that the main reasons

known for the polarization process in ice, the Debye dispersion and hence the high-frequency conductivity σ∞, are related to the motion of charged

dislocations in an ac electrical field.

 He later developed a theoretical model supporting this idea (Itagaki 1982, 1983). However, Itagaki’s model was not accepted by the ice physics

community. While dislocations in ice can contribute to and modify the electrical properties of ice,

they cannot account completely for those electrical properties. There may be other reasons for the

absence of Debye dispersion found by Itagaki in

very thin and pure specimens of ice. One possibility is that the specimen thickness was comparable

with or less than a screening length. Conventional

theories of electrical properties of ice (Jaccard

1964) predict an absence of the Debye dispersion

in this case (Petrenko and Ryzhkin 1984a).

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February 1996

Electromechanical Phenomena in Ice DAAL-03-91-G-0164

Victor F. Petrenko

U.S. Army Cold Regions Research Thayer School of Engineering

and Engineering Laboratory Dartmouth College Special Report 96-2

Hanover, New Hampshire 03755 Hanover, New Hampshire 03755

U.S. Army Research Office

Research Triangle Park, North Carolina

Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161.

This report examines the electromechanical effects in ice. This group of physical phenomena, which was found

and studied relatively recently, broadens basic knowledge of ice and may have some practical applications. The

electromechanical phenomena in this report are separated into three groups: 1) Effects in which electromagnetic

fields are generated by means of mechanical actions such as elastic stress, plastic strain, fracture or friction; 2)

Effects in which an application of electric fields modifies such mechanical properties of ice as its plasticity, elasticity and friction; 3) Effects in which plastic strain changes electrical conductivity or dielectric permittivity of

ice. Experimental results and theoretical models are discussed and some possible practical applications suggested.

Cracks in ice Ice mechanics

Electrical properties Ice physics

Ice defects

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