Quantum size effects in the redox potentials, resonance Raman spectra, and electronic spectra of CdS crystallites in aqueous solution

K.

Kalyanasundaram

,

E.

Borgarello

,

D.

Duonghong

, and

M.

Grätzel

, , ().

A.

Henglein

, , ().

R.

Rossetti

and

L.

Brus

, , ().

J.

Kuczynski

and

J. K.

Thomas

, , ().

A.

Henglein

, , , ().

D.

Duonghong

,

J.

Ramsden

, and

M.

Grätzel

, , ().

We use a JEM 200 electron microscope at 200 KV. The limiting resolution is $∼6 Å.$

Our pulsed Raman apparatus is described by

S. M.

Beck

and

L. E.

Brus

, , ().

A thin layer of $∼100 Å$ CdS particles has been previously investigated. [

G. C.

Papavassiliou

, , ().]An enhancement of Raman scattering at 454 mm was reported and explained qualitatively in terms of an exciton blue shift.

Extremely broad Raman scattering from 15–30 Å grains in $ZrO2$ powder has been reported [

V. G.

Keramidas

and

W. B.

White

, , ()].

Slab or cylinder surface modes have been reported for small grains in polycrystalline CdS films [

J. F.

Scott

and

T. C.

Damen

, , ()].

G.

Kanellis

,

J. F.

Morhange

, and

M.

Balkanski

, , ().

S.

Veprek

,

Z.

Iqbal

,

H. R.

Oswald

,

F. A.

Sarott

,

J. J.

Wagner

, and

A. P.

Webb

, , ().

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 13, Eqs. (119) and (85).

R. K.

Cook

and

R. W.

Christy

, , ().

A review is given by R. M. Martin and L. M. Falicov, in Light Scattering in Solids (Topics in Applied Physics), edited by M. Cardona (Springer, New York, 1975), Vol. 8, Chap. 3.

R. H.

Callendar

,

S. S.

Sussman

,

M.

Selders

, and

R. K.

Chang

, , ().

T. C.

Damen

and

J.

Shah

, , ().

R. M.

Martin

, , ().

P. P.

Lotici

and

C.

Razzetti

, , ().

S.

Permogorov

and

A.

Reznitsky

, , ().

P. J.

Colwell

and

M. V.

Klein

, , ().

We do not attribute the optical changes upon aging to the fact that the initially cubic structure becomes partially hexagonal. The band gaps of the two forms are extremely close [

M.

Cardona

,

M.

Weinstein

, and

G. A.

Wolff

, , ()]. The vibrational frequencies, dielectric properties, and strength of the Frohlich interaction should also be quite similar in the two phases.

R.

Dingle

,

W.

Wiegmann

, and

C. H.

Henry

, , ().

R. C.

Miller

,

D. A.

Kleinman

,

W. T.

Tsang

, and

A. C.

Gossard

, , ().

H. Gerischer, in Physical Chemistry: An Advanced Treatise (Academic, New York, 1970), Vol. KA, Chap. 5.

T.

Inone

,

A.

Fujishima

,

S.

Konishi

, and

K.

Honda

, , ().

Note that the sign of the charge must be considered; $Vi−$ is negative and $Vi+$ is positive. For a cube of edge 2R, this expression is multiplied by 0.75. This expression is for an infinite barrier at the crystallite edge. Localization energies for real, finite barriers are somewhat smaller. There is also a polarization term. These ideas will be described in a forthcoming publication.