DOC.
21
MOLECULAR MOTION IN
SOLIDS
365
Doc.
21
Elementary
Observations
on
Thermal Molecular Motion
in Solids
by
A.
Einstein
[Annalen
der
Physik
35
(1911):
679-694]
I have shown in
a
previous
paper1
that
a
connection
must exist
between the
law
of
radiation
and
the
law
of
specific
heats of
solids
(deviation
from
the
Dulong-Petit
law).2
The
investigations by
Nernst and
his
students
have
now
shown
that, on
the
whole,
specific
heats indeed
display
the behavior deduced from the
law
of
radiation,
but that the
true
law
of
specific
heats
deviates
systematically
from the
law
established
by theory.
One of
the
first
goals
of
this
paper is
to
show
that
these
deviations
are
due to
the
fact
that the
[2]
oscillations
of
molecules
are
far from
being
monochromatic oscillations.
The heat
capacity
of
an
atom
of
a
solid is similar to
that of
a
strongly
damped
oscillator in
a
radiation
field
and
not like
that of
an
oscillator that
is
only slightly
damped.
For that
[3]
reason
specific
heat decreases
less
rapidly
toward
zero
with
decreasing temperatures
than
the earlier
theory
would have
it;
the
body
behaves
similarly
to
a
mixture
of
resonators
whose
proper
frequencies are
distributed
over a
certain
region.
Further,
it will be shown
that Lindemann's
formula, as
well
as my
formula for the
calculation
of the
proper
frequencies
v
of
atoms,
can
be
derived
by
dimensional
arguments,
with
the latter also
[4]
yielding
the order of
magnitude
of
the
numerical
coefficients
appearing
in
these
formulas.
Finally,
it will
be
shown
that the
laws
of
heat
conduction
in
crystallized
insulators
are
not
in accord with
molecular
mechanics,
but
that it
is
possible
to
derive
the order
of
magnitude
of the
actually
observable
thermal
conductivity by
means
of
a
dimensional
argument,
and
thereby
simultaneously
to find out how
the thermal
conductivity
of
monatomic
substances is
probably
related
to
their atomic
weight,
atomic
volume,
and
proper
frequency.
§
1.
On the
Damping
of
Thermal Oscillations
of
Atoms
I
showed
in
a
recently published
paper3
that
one
arrives at
approximately
correct values
for the
proper frequencies
of
the
thermal
oscillations
of
atoms
if
one
starts out
from the
following assumptions:
1
A.
Einstein, Ann.
d.
Phys.
22
(1907):
184.
2
Thermal motion
in solids
was
conceived
there
as
consisting
in
monochromatic
oscillations
of
atoms. Cf.
§2
of
this
paper.
3
A.
Einstein,
Ann.
d.
Phys.
34
(1911):
170.
[1]
[5]
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