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APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
ON THE POSSIBILITY OF FORMATION OF A NUCLEAR URANIUM

LATTICE AT VERY HIGH TFMPFMTURES

B. T. Feld and E. Teller

At very high temperatures, U metal can be considered to consist of almost

completely ionized nuclei, surrounded by a gas of electrons. Under these circumstances, there will be strong Coulomb forces between adjacent U nuclei.~and as

?&ariaG. Mayer has pointed out, a “tendency for the nuclei to form a lattice.

We have attempted to estimate the possibility of occurence of this phencmeuon by two simple, very rough calculations. In both cases, we have compared U with a

number of other metals, since the lattices formed by most metals are cubical, And thus~

of a simplo nature.

First, we have

tude of vibration r of

lattice spacing a. For

considered as a criterion for melting the ratio of the ampli.

the atoms at the melting temperature of the metal to tho

the U, we have looked at two cases. In the first case, the

U atoms have an energy of 5 kev and normal density. For this case, the net charge on

the U nucleus was considered to be 88. In the ~econd case the U is compressed 1~-fold

.

and the nuolei, with an effective charge of 16, are considered to have an energy of

1 kev. The average frequencies of vibration for the metal lattices are calculated

from the Debye temperatures @ of these metals, and the amplitude of vibration oomputed at the melting temperatures. The comparison is shown in Table I.

APPROVED FOR PUBLIC RELEASE

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Substance

w

Au

Al

Ag

Pb

Cu

Ca

M.

Mo

Fe

K

Na

TABLE I

--iir310° K

190

390

215

88

315

230

370

379

395

100

159

T melt.

3&3° K

15$

933

1233

600

1356

K183

1728

2893

1808

335

. 371 _

U, 5 kev, density 19

U. 1 kev. densitsr15 x 19

-yzi-

.069

.081

.091

●W3

0W5

●@

.@

.100

0112

.118

.133

.43

.418

.656

We note that, since the amplitudes of the U vibrations are, in both cases,

relatively greater than those of any of the other metals at their melting points, the

U will have, by this oriterion, a greater tendencyto form a liquid.

The seoond c~terion for melting compares the energy of the atom or nucleus

(kT) with the work required to remove it completely frm the lattice, to leave a hole

in its former place, and to attach the nucleus at the surface of the lattioe. In the

case of Us this work was considered to be given by the energy required to remove the

U nucleus from its surrounding uniformly distributed electron gas. Attaching the

nucleus at the surface does not liberate energy in the limiting case of high electron

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APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
“ixmperatures. This

uniform density and

FMd9US iS balanced

is so because the eleotrons are distributed in the lattice with

the energy gained from their interaction with the newly attaohed

by their decreased interaction with the other nuclei. In the

case of’the other metals, this work was taken as the energy of vaporization, (energy

of removal = 2 x energy of vaporizations energy on the aurfaoe = energy of vaporization; the difference has to be taken) and was compe.redwith kT at the melting point.

This comparison is

metal

Pb

Al

Na

h.u

x

Cu

Ni

Ag

R

Fe

MO

Ca

shown in Table 11.

energy of vaporization - E

3020x10”12ergs/atm

4.73

1.81

5.70

6.80

Ij.80

4.1

6.75

10.8

2*W

la/x3 ‘

.0270

.0273

00283

.o@

.0302

.0528

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.0394

.0356

00370

.0370 “

.0501

U, 5 kev, density 19 I.02x10-7 .0785

U, 1 kev, density 15 x 19 0083 .193

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APPROVED FOR PUBLIC RELEASE
n

● -

.

*

1

The ratio of

for the II than for the

energy to work of removal is seen to be greater, in both cases,

other metals at their melting points. Again~ this indic~tes

that the U will not form a lattice under the conditions we

the margin of’6afety, acoording to the above calculations,

have considered. However$

is not very large, 80 that

further investigations using better criteria for melting seem to be called for.

APPROVED FOR PUBLIC RELEASE

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APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE