INTERNATIONAL
ZINION
I n view of the great d e m a n d for travel services in
N o r t h America at the time of the Congress it is strongly
recommended t h a t Congress participants m a k e immediate
a r r a n g e m e n t s for their transportation.
Living Accommodation
Provisional reservation of rooms in Montreal has already
been made. These will be allotted in the order of receipt
of the registration forms which a c c o m p a n y the general
information booklet. Because accommodation in Montreal
hotels and motels is m u c h in d e m a n d during the s u m m e r
m o n t h s it is strongly recommended t h a t these forms be
sent to the n e a r e s t American Express office or corres p o n d e n t as early as possible, a n d n o t later t h a n 15
F e b r u a r y 1957, to ensure the accommodation desired.
Excursions
OF CICYSTALLOGI~APHY
837
for the period following the Congress. F u r t h e r details a r e
given in t h e general information booklet.
Exhibition
I t is planned to arrange an exhibition of a p p a r a t u s a n d
books of crystallographic interest a t the Congress t t e a d quarters. Manufacturers and publishers wishing to receive
detailed information should write to Dr A. O. McINwosH,
Central Research Laboratory, Canadian Industries Limited, McMasterville, Quebec, Canada.
Free space will be m a d e available for a display of experimental devices, charts, models, a n d other noncommercial items of interest to the Congress. Details of
this exhibit m a y be obtained from the C h a i r m a n of the
Commission on Crystallographic Apparatus, Prof. A.
GtlI~IEI~, Conservatoire National des Arts et M6tiers, 292'
rue Saint-Martin, Paris 3, France.
.
An excursion of general interest to a n i m p o r t a n t section
of the St. Lawrence Seaway D e v e l o p m e n t is being arranged for the afternoon of Saturday, 13 J u l y 1957, a n d
a d a y ' s outing b y steamer on the St. Lawrence R i v e r is
being organized for Sunday, 14 J u l y 1957. Three trips
of mineralogical and geological interest will be available
P r o g r a m m e for Non-active Registrants
Several interesting tours a n d short excursions are b e i n g
arranged for non-active members during the technical
sessions of the Congress. Details a n d tickets will be available a t the time of registration in Montreal.
Book Reviews
Works intended for notice in this column should be sent direct to the Editor (P. P. Ewald, Polytechnic Institute of Brooklyn,.
99 Livingston Street, Brooklyn 1, N . Y . , U.S.A.). A s far as practicable books will be reviewed in a country differenC
from that of publication.
Dynamical Theory of Crystal Lattices. By M.
BOl~N a n d K . HuANO. P p . v i i i + 4 2 0 w i t h 28 figs.
O x f o r d : C l a r e n d o n P r e s s (Geoffrey Cumberlege).
1954. P r i c e 50s.
This book has an o u t s t a n d i n g value because of its coordinated account of the work b y Born a n d his collaborators on the t h e o r y of crystals. The last comprehensive
review of their work was the article b y Born & Maria
G6ppert Mayer, which appeared in 1933. Since t h e n m a n y
i m p o r t a n t contributions have been made. The aim of the
book is to deduce the macroscopic behaviour of crystals
from their microscopic properties, the latter being described in the general case b y t h e potential energy
corresponding to small displacements of the atomic nuclei
from the lattice points a n d b y t h e p a r a m e t e r s characterizing the behaviour of the atoms under the influence
of electromagnetic fields. As a rule, the q u a n t u m mechanical t r e a t m e n t of the s y s t e m of nuclei a n d electrons is
applied only in order to j u s t i f y those principles. Being
basic to the t h e o r y given in this book, the adiabatic
a p p r o x i m a t i o n is t h o r o u g h l y discussed. I n this approxim a t i o n the motion of the electrons is t r e a t e d as if t h e
nuclei were at rest a n d a corresponding potential energy
for their motion existed. F o r similar reasons, a t r e a t m e n t
is given of the behaviour of molecular systems under the
action of electromagnetic fields for long wavelengths. I n
the t h e o r y of optical phenomena, the case of X - r a y s is
accordingly omitted. Because of t h e special behaviour of
electrons in metals, which requires methods of their own
a n d makes t h e vMidity of t h e adiabatic a p p r o x i m a t i o n
questionable, the t h e o r y of metals is excluded. The scope
of the book is f u r t h e r confined to crystals w i t h o u t
imperfections. Likewise, surface p h e n o m e n a are excluded.
The t h e o r y given in the book originated in several'
papers from 1912 a n d 1913 b y Born a n d Th. von K a r m a n
where the mathexnatieal foundation of the t h e o r y of t h e
vibrations of simple crystal lattices was given t o g e t h e r
w i t h its application to the problem of the specific h e a t
of crystals. I n these papers the so called periodic b o u n d a r y
condition was also introduced. These two principles form
basic features of the present book a n d have there been
worked out a n d applied in a generM a n d systematic way.
The book consists of two parts called ' E l e m e n t a r y
theories' a n d 'General theories', respectively. The first
p a r t gives an easily readable account of the e l e m e n t a r y
aspects of crystal forces a n d binding energies, elastic a n d
t h e r m a l properties, infra-red vibrations, a n d also of the
stability of lattice structures. The repulsive overlap forces
acting between pairs of atoms in the crystal are discussed
on the lmsis of the T h o m a s - F e r m i statistical model a n d
are also, a s in the older theories, introduced as power or
exponential functions of the interatomie distances. The
aspects of the distribution function for the vibrational
frequencies specifically connected w i t h the lattice structure are discussed w i t h reference to B l a c k m a n ' s investigations. The t h e o r y of the elasticity a n d s t a b i l i t y of lattice
structures is based on the special assumption of central
two-body forces.
838
BOOK
REVIEWS
I n t h e whole of this p a r t of the book, a n d also in t h e
second part, t h e deeper, purely q u a n t u m mechanical
calculations from f u n d a m e n t a l constants of the cohesive
a n d elastic properties (as given b y ttylleraas, Landshoff
a n d LSwdin for some simple ionic crystals) are, unfort u n a t e l y , only briefly referred to. The corresponding calc u l a t i o n b y S c h m i d t for d i a m o n d is n o t m e n t i o n e d .
A l t h o u g h these calculations refer to rather special cases
t h e y give useful insight into the n a t u r e of t h e forces in
crystals a n d h a v e also, as L u n d q u i s t has recently found,
a n i m p o r t a n t bearing on the t h e o r y of the infra-red
vibrations considered in t h e book. The necessity of
i n t r o d u c i n g an 'effective' ionic charge t h e n follows witho u t ad hoc assumptions like those used in t h e book, thus
e m p h a s i z i n g t h e value of t h e q u a n t u m mechanical approach.
The second p a r t of t h e book contains in its first chapter
t h e investigations of t h e adiabatic a p p r o x i m a t i o n a n d
of the optical t h e o r y of molecular systems, a n d includes
also a general t r e a t m e n t of t h e statistical mechanics of
such systems u n d e r external forces. A n interesting new
t r e a t m e n t of this problem is given b y Born in an Appendix. The following chapter forms a central part of the
book. The authors give here a general t h e o r y of crystal
vibrations a n d deduce t h e elastic a n d piezoelectric
properties as limiting cases for long wavelengths a n d small
frequencies. The m e t h o d s used are those laid d o w n b y
Born a n d v. K a r m a n in their original papers a n d by
B o r n in his book Dynamilc der Kristallgitter of 1915.
These m e t h o d s are s u p p l e m e n t e d by those introduced
b y E w a l d for t h e field caused b y vibrating dipoles,
w h e r e b y ionic lattices w i t h their long-range Coulomb
forces are incorporated in a consistent way. As shown in
t h e book, t h e t h e o r y of elastic a n d piezoelectric properties
can t h e n be based on t h e m o s t general quadratic expression for t h e p o t e n t i a l energy corresponding to the
short-range forces if t h e macroscopic elastic a n d piezoelectric equations, including the s y m m e t r y properties of
t h e elastic constants, are assumed to be valid.
The reliance on macroscopic equations should be
avoided in a consistant microscopic theory. For this
purpose a different approach to t h e problem would
a p p a r e n t l y be required.
After t h e n e x t chapter, where t h e t h e r m a l properties
are considered in detail on the basis of the t h e o r y of
finite deformations, there follows t h e i m p o r t a n t final
chapter where an exposition is given of crystal optics,
including applications to infra-red absorption, t h e R a m a n
effect a n d t h e t h e r m a l scattering of light. H e r e the t h e o r y
has m e t w i t h considerable success in t h e i n t e r p r e t a t i o n of
t h e m e a s u r e m e n t s on t h e Ram. an effect.
No m e n t i o n is m a d e in this chapter of t h e original
w o r k b y E w a l d in which t h e foundations of this t h e o r y
comparisons w i t h experiments would h a v e b e e n of great
use. The book would certainly also h a v e b e e n m o r e
valuable if the references given h a d been m o r e complete
a n d appropriate. I n spite of this, however, t h e book is of
great value in giving a t h o r o u g h exposition of a w e a l t h
of m e t h o d s of f u n d a m e n t a l importance in crystal theory.
I. WALLER
Imstitute of Mechanics and Mathematical Physics
Upsala, Sweden
Dielectric Behavior and Structure. By C. P.
SMYTH. Pp. 441. New York ; Toronto; London;
McGraw-Hill. 1955. Price $9.00; 64s. 6d.
This book has been published in a chemical series a n d
has b e e n w r i t t e n primarily for chemists. ~[t deals w i t h
m a n y aspects of dielectrics, b u t its principal subject is
the relation b e t w e e n dielectric behaviour and molecular
structure, in particular t h e elucidation of t h e structure
of molecules w i t h t h e help of dielectric m e a s u r e m e n t s .
The two first chapters deal with the t h e o r y of dielectric
constant and loss. These are v e r y well w r i t t e n and give an
excellent i n t r o d u c t i o n to t h e theory. The a u t h o r himself
is n o t a theoretician, a n d in some parts of these chapters
he follows other authors v e r y closely, b u t this is to t h e
a d v a n t a g e of t h e book, as t h e material Has b e e n judiciously selected. The theoretical physicist will find those
passages of considerable interest where t h e validity of
t h e various theories is tested b y comparison w i t h experiment.
Concerning t h e t r e a t m e n t of dielectric loss, one criticism can be m a d e which, however, applies equally to
m a n y other treatises on this subject. The loss is t r e a t e d
on a purely macroscopic basis a n d the concepts used are
those of macroscopic physics a n d electrical engineering.
These concepts are well established and easy to use, a n d
as t h e y are often encountered in papers on dielectric
t h e o r y it is essential t h a t t h e s t u d e n t become familiar
w i t h t h e m . Nevertheless, t h e chemist, or, in fact, a n y
reader who is interested in atoms a n d molecules r a t h e r
t h a n in electric condensers, voltages a n d charging currents, will find t h a t these concepts alone do n o t satisfy
him. To h i m the s t a t e m e n t t h a t the loss is due to t h e
charging current h a v i n g a c o m p o n e n t in phase w i t h t h e
voltage will appear n o t an explanation of t h e loss b u t
merely a formalism to describe it. I t h i n k t h a t , in addition to the macroscopic theory, an atomistic explanation
of t h e dielectric loss should also be given, at least in a
qualitative way. Many readers would u n d e r s t a n d t h e
n a t u r e of t h e dielectric loss m u c h b e t t e r if t h e y were told
were given. Important generalizations and simplifications
something about the atomic and molecular processes
of the t h e o r y have, however, been achieved in t h e book.
The second p a r t of Born & H u a n g ' s book is n o t easy
to read, particularly because t h e authors write their
formulae in a form as general as possible. I t is h a r d n o t
to get lost in t h e jungle of formulae a n d notations, a l t h o u g h
t h e authors h a v e been careful in choosing their symbols.
The i n t e n t i o n of t h e authors in this p a r t of t h e book
has e v i d e n t l y b e e n to give the general m e t h o d s r a t h e r
t h a n to apply t h e m to definite problems. E v e n so, a
n u m b e r of special assumptions have, however, been unavoidable and, in order to test t h e m , more complete
which lead to t h e transfer of energy from t h e electric
field to the r a n d o m internal m o t i o n of t h e dielectric.
The two i n t r o d u c t o r y chapters are followed b y several
chapters dealing with the dielectric properties of gases,
liquids a n d solids, a n d b y one discussing measuring
techniques.
This is followed b y a v e r y detailed discussion of t h e
connexion b e t w e e n dipole m o m e n t , molecular structure
and electronic configuration in t h e molecule, a n d b y a
n u m b e r of chapters illustrating t h e conclusions concerning
molecular structure which can be d r a w n from dielectric