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]