332
DOC.
13
ELASTIC BEHAVIOR AND SPECIFIC HEAT
Doc.
13
A
Relationship
between
Elastic Behavior
and
Specific
Heat in
Solids
with
a
Monatomic
Molecule
by
A.
Einstein
[Annalen
der
Physik
34
(1911): 170-174]
My colleague,
Professor
Zangger,
drew
my
attention
to
an important
note
published
[1]
recently
by
Sutherland.1
Sutherland asked himself whether the
elastic
forces of
solids
are
forces of the
same
kind
as
the forces that
drive
the carriers of infrared
proper
oscillations
back
to
their
position
of
rest,
and hence
give
rise to
their
proper
frequencies.
He found that the
question
should
very
probably
be
answered in
the
affirmative
on
the
basis
of the
following
fact:
the infrared
proper frequencies
are
of the
same
order of
magnitude
as
the
frequencies
one
would have to
apply
in
order
to
send
through
the
body
elastic transverse vibrations whose
half-wavelength
is
equal
to
the
distance
between the
[3]
neighboring
molecules of the
body.
Notwithstanding
the
importance
of Sutherland's
analysis,
it
is
clear that
this
way
leads
at
best
to
a
rough order-of-magnitude
relation,
particularly
because
it must
be assumed
that the
known
infrared
proper frequencies are
chiefly
to
be
viewed
as
oscillations
of
differently charged
ions
of
a
molecule
with
respect
to
one
another,
while elastic
[4]
oscillations
are
to
be
viewed
as
oscillations
of
whole molecules with
respect
to
one
another. It
seems
to
me
therefore that
a more
exact test
of Sutherland's idea
is
possible
only
for
substances with
monatomic
molecules, which, according
to
both
experience
and
the theoretical
model,
do
not
manifest
optically
detectable
proper
oscillations
of the
[5]
known kind.
However, according
to
my
theory
of the
specific
heat of
solids,2
which I
based
on
Planck's
theory
of
radiation, it is
possible
to
determine the
proper frequencies
of
heat-carrying
monatomic bodies from the
dependency
of the
specific
heat
on
the
temperature.
These
proper frequencies can
be used
to test
Sutherland's
conception
by
comparing
them
with
those obtained from
elasticity.
One
way
in which this
can
be
done
is
given below,
and let
me say
here
right
away
that,
in this
way,
Sutherland's
conception
of the essential
identity
of the
elastic forces
and those
determining
the
proper frequency
was
satisfactorily
confirmed
in
the
case
of
silver.
An
exact
calculation
of
the
proper
oscillation
frequencies
from
the
elasticity
constants
is
out
of the
question
for the time
being.
Instead,
we are using
here
a
rough
method of
[2]
1
W.
Sutherland,
Phil.
Mag.
20
(1910):
657.
[6]
2 A. Einstein, Ann. d.
Phys.
22
(1907):
180.