THE TRANSFORMATION OF ENERGY IN SOLIDS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78-04861A000400030019-6
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 21
• Document Creation Date: December 20, 2016
• Document Release Date: June 6, 2006
• Sequence Number: 19
• Publication Date: July 1, 1955
• Content Type: REPORT

25X1
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THE TRANSFORMATION OF ENERGY IN SOLIDS
F. Moglich and R. Rompe
Zeitschrift fUr Physik, I.,!j (1940) 707-728
. ( From German)
Ju4y t955
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T71311 TR NSFO1dQ-'1.TI0NNT 01' :1: ERGf IN dOLIDI
s~
F. NloQlich and R. Ronipe
Zeltschrif t fur Physik, 115 (1;1+0) 707-26
(From German).
The el e on s of a crystal aria the crystal lattice are coupled
with ca oh other as regards energy. fence:, energy can be taken up from the
electron ,as by t'.e lattice and vice versa. Apart from the simple
collisions between electrons and the lattice, observed by BLOCH, there are,
cspccially at high temperatures, processes (multiple collisions) in
which the amountcf transferred energy is very great. The temperature
dependence of the of fec-dive cross section.is shown. Finally it, is shown
horn vory fast electrons inside the; crystal place themselves in thermal
equilibrium with the; electron gas. Calculations are mu,_de to find the
time required to roach this equilibrium.
When considering the; forms of energy of a solid, we are accustomed
to make a sub-division into two parts: the energy of the lattice and the
energy of the electron gas. Itetur_lly these two are not independent of
each other. Idi conditions are similar to the case of xn.olecul.:s, where
the energy of nuclear oscillation, or rotation, and of electrons can be
separated from each other. Those three forms of energy, also, arc not
without interaction ainorigst each other: the rotation, through centrifugal
force, iinf'lucnccc the binding-force of the molecule, the amplitude of
nuclear oscillation affects the moment of inertia and finally, the electron
jump is a decisive factor in the binding strength of the molecule and it is
known that a a,issociation of the molecule can be brought about by the
excitation of higher electron jumps.
In the case of solic.s also it will have to be assumed that the
excitation of igher electr~7n en.rgi.s will cause a change in the lattice
stability. Nevertheless, in every case resulting from the radiation of
visible and ultraviolet light of not too small wave length, it is probable
that the variation in lattice stability may be neglected: obviously there
is no strong coupling; of the two forms of energy of solids. For this
reason we think that the follow:,-ing considerations can be regarfed as
valid, for instance.for .the excitation of the electron into the first band
above the ground state.
There is, moreover, an analogy here to diatomic molecules, in
the ca?c where for the e,_citeci and, unoxcitue. state the two potential
curves are nearly identical, the minima lie one over the other, etc.
Therefore, it is clear, from two Franck-Condon principle, that to a first
approximation no conversion of el.ctron energy into energy of nuclear
oscillation can take place. he consider the corresponding assumption to
be all the more justified! since the elevation of one or several electrons
from the lower to the upper band represents an incomparably smaller
interference with the b,ondin stability of the solid than is the cxcitr_tion
of a molecule-electron, since the number of the electrons constituting
the cohesion of the solid is very gnat. We consider ourselves entitled,
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thoruforc, to rugloct the consiae;rati:ms of v. ;'1PFEL (1 )
for our p zrposes.
At thin point vro.must Discuss the objections which have been raised
recently against the rigid application of the band model of the solid.
More especially,,- :re would ref or to the works of FRENKEL (2) and SLATER
(3) who have called the band model "sophisticatcc_". Thus, Slater holds
that a t,c;ory of solids must reproduce the follo:rin three energy states,
which result from the quitu primitive conception of a solid as a
con_lomcrate of single atoms or molecules: 1. citation of the electron
into ac state in which the electron possesses a certain energy above the
ground state, without being free, but where this condition may be tr-nsferred
from one atom to any neighbouring atom (F renkcl excitons); 2. Complete
ionisation, the electron becoming freely mobile; 3. Ionisation with
immediate recombination or ad ition to neighbouring atoms.
A criticism of the band model is that it makes no allowance for
cListinction between these three types of behaviour. An excited electron
is practically always freely mobile and has no possibility of recombination
or ad.;itio:a which can be loc_.1ise d. ?'ro cannot support this criticism of
the band model because, for oxample, the objection that the electrons in
the conduction band must alrr.ys exhibit an infinitely great conductivity
disappear? at once on taking into account the interaction with the
lattice. Neither do we quito see to what extent consideration of the
Coulomb force between electron and ion is supposed to give a better
approximation, because this is already included in a first approximation;
the periodic potential of course depends above all on the ions of the
lattice and it would be superfluous to take this into account a second time.
Moreover, in our view, the formation of solid and liquid substances,
and, also of molecules, is pre-eminently connected with the existence of
non-coulomb electron forces, viz. the chemical linkage forces which give
rise to a very intimate fusion of the individual atoms. It is not
surprising, therefore, that these structures exhibit properties widely
divergent from those of single atoms and we do not think there is any
special lurposu, when describing absorption in a solid, to refer to the
behaviour of an electron with respect t: one, of the partners in the
combination. In those cases, ho-,rever, whore the actual chef ical linkage
forces are not so important, as for exuiple in molecule lattices and perhaps
also in the poly naric~es studied by SCHEIBE and his collaborators
the fronkel exciton idea can be profitably used.
Finally attention must also be dra-,--in to the fact that there is no
ground for supposing that there is any contradiction between the
ex_pcrimrntal facts which are known today and the band model explanation
with its consequential observation of the reaction with the lattice.
It must also be remcmboror course, that the character of the crystals
is by no means perfect and that they continually exhibit the presence of
impurities and deviations from the stoichiometrically correct state.
The importatin.ce of these facts, especially the strong influence exerted by
impurities, internal stre;.s;es, loose spots, and similar conditions, on the
electron spectrum of the crystals, has boon discussed. systematically by
S1 1tAL (5). There seems to be not the sli,,htest 'doubt that a development
of the band model in this direction is both necessary and. profitable.
Even though in this work we do not digress from the case of the ideal
crystal, yet we shall frogently indicate the necessity for generalisations
of this kind, Besides this, from the theoretical point of view, we have
See references at end
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devoted two special papers to the application of the present conceptions
to actual crystals. (6).
LJ TTIOE E[c
electrons capo.b e of tall i.ng u1: ener:_;y. Caring to the Pa ..li prohibition,
ho:=never, there are at best only as C lcectrons of 'this in the
lover b G"c Z'C are hole T main t i.n , from absorption. Consic.eration
of the tot'. X 10 r " wwuld thin, in r'oduce a factor 2 In the of,, Llebriu.in time,
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-18-
It is only if the fact electrons possess energy which is great
compared with the energy gap between the two bands (for instance
in the case of radiation of short wave ultra viol:t ), that there could
be a greater participation of the electrons of the lower band
because these could then absorb enough energy to enable them to get
past the forbidden zones. Of course such fast electrons would
probably fall within the range of the strong activity of the multiple
collisions (L: by very large ) and return to the lower band without
radiation. Nevertheless it cannot be proved. quite so easily that it
is just such processes which are respon4ible for the excitation of
insulators by means of fast electrons or alpha particles.
On the other hand, w th metals. a large number of electrons can
always participate in plasma interaction because of course the lover
band is only half full, so that very short relaxation times may be
expected f or them.
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{ 1) A. v. HIPPEL, ZS. f. Phys. 101 0936) 680 , Phys. Rev. 5 (1938) 1.096;
see also R.J. SEEGER, E. ' ELLER, Phys. Rev. 51+
(1938) 575.
? (2) J. FRE,NKEL, Phys. Rev. 2 (1931) 17,1276. Phys. ZS, d.
Sowjetunion 2 (1936) 158,
(3) J.C. SLATER, Trans. Faraday Soo, 34 (1938) 828.
(4) See the combined report of C. SHEIBE, A SCHONTAG, F. KATHEDER,
Naturwissensoh. j (1939) 499.
(5)
A. SI KAL, Handb d. Phys. XXIV 2. 2nd. Edition, p.886.
ZSf.Phys. 101 (1936) 661.'
(6) F. MOGLICH and R. ROMPE, " Phys. Z. (y 91+0) 236.
F . MOGLICH, N.. RIEHL. ? and R. ROMPE, ZS. f. techn. Phys. 21 (1940) R.8,
(7) We refer here to R. RQMPE and M. STEENBECK, Ergebn. d. exakt. Naturvo.188
(1939) 257-
(8)
(9)
A. SMEKAL, loc. cit.
B. GUDDEN, Ber. Phys. Math. Soc. Erlangen 62, (1930) 289.
A.H. WILSON. Proc. Roy. Sr---. London (A) j 1931) 2+8.
134 1931-32) 277.
1933) 1+87.
W. M ER,, ZS.f.Phys. a (1933) 278.
Phys. ZS. .16-- (1935) 749.
W. MEYER, H. NELDEL, Phys. ZS. (1937) 1014;
W.SCHOTTKY, F. WAIBEL, ZS. (1935) 912-
u
F. MOGLICH , ZS. f.Phys.10 (1938) 503.
(10) M. SCHON, ZS.f.techn. Phys. j (1938) 369;
11
N.REIHL, M.SCHON, ZS.f,Phys. 114. (1939) 682;
W.de.GROOT, Physica 6 (1939) 275;
T.H.GISOLF, Physica 6 (1939) 84;
R.P. JOHNSON, J.O.S.A. 29 (1939) 387-
(11) H. FRO=CH , Elektronentheoric der Metalle (Electron Theory of
metals) (book) Berlin 1930.
(12) See in this connection F. MUGLICH, N. RIEHL and R. ROMPE,, ZS.f.techn.
Phys. loo, cit,
(13)
M.SCHON, ZS.f.techn. Phys. i.2 (1938) 361.
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REFERENCES (Contd).?
N. REIHL and M. SCHON,
See iri this connection
A. CRAVATH, Phys.
ZS.f.Phys. 114 (1939) 682.
F. MOBLICH and R. ROMPE, Phys. Z.4i(1940)236.
Rev. 6 (19.36) 24.8.
41
H.FROHLICH and N.F. MOTT, Proc. Roy. Soc.
F,. BLOCH,.ZS.f.Phys. ~2 (1928) 555.
171 (1939) 496.
R.. PEIERLS, Ann. d. Phys. (1930) 121; 1 (1930) 244, 12 (1932)154..
A. SOMMERFELD and H. BETHE,. Handb.d.Phys. XXIV/2.?2nd edition.
See in this connection R. ROMPE and M. STE VBECK, Ergebn. d. exakt.
Naturw. 18 (1939) 257.
. it
(22) F. MOGLICH and R. ROMPE, Phys, ZS. t (191F0) 2360
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