The Lattice Energies of the Silver Halides and their Photochemical

T H E LATTICE E S E R G I E S OF T H E SILVER HALIDES ASD THEIR PHOTOCHEMIChI, DECORIPOSITIOS. 11* BY S. E. SHEPPARD A S D TV. V.4NSELOW

I n a previous paper under this title’ the authors drew attention to the problem of the energies necessary for the photodecomposition of the silver halides. They pointed out that if the primary process of this photolysis consisted in the liberation of electrons from halide ions, as suggested independently by Sheppard and Trivelli, and by Fajans, in 1921, then apparently there must first be provided energy sufficient, in one quantum of light, to overcome the lattice energy of the silver halide, together with sufficient energy to release the electron from the halide ion. The quanta corresponding to these, separately or in one quantum, are very much greater than correspond to the wave lengths of light which are photochemically active. In the meantime, the investigations of Sheppard and Vanselow2 on the photopotentials of silver: silver halide electrodes have given rather convincing evidence that the primBry reaction in light, does consist, in the simultaneous separation of halide ions into electrons and bromine atoms. The investigation also showed that: a. the electrons move to a considerable extent in the direction of the light ray; b. the electrons can traverse, or behave as if they can traverse, a thickness of silver bromide up to 80 m p without being captured by Ag+ ions; c. that this permits the bromine to travel an equal distance, without being captured by Ag atoms; d. that the space-charge of unbalanced AgT atoms thus produced soon restrains the electrons, so that an almost stationary stat,e ensues. Again, the investigations of Toy and his collaborators’ have shown very definitely that the wavelength limits of the photoconductance effect-the primary photocurrent of Crudden and Pohl-are identical with those producing the photographic latent image. These inner photoelectrons must be the same as those revealed in Sheppard and Tanselow’s work. There appears no reason to doubt, therefore, at present that the primary photochemical event is that symbolized as X hv+S 0 and the question proposed by Sheppard and Vanselow in the preceding paper is definitely to be answered. In discussing the problem, these authors pointed out that there were two principal mays of meeting the difficulty. One consisted in an application of the principle of “energy on credit,” i.e., in supposing the elementary act to have available the energy released in subsequent stages, such as the forma-

+

-+

* Communication KO.360 from the Kodak Research Laboratories.

2720

S. E . SHEPPARD A S D W. VASSELOW

tion of silver metal. I t was pointed out that if this were extended to the final state-of metallic silver and gaseous bromine-the quanta required would be too small, compared with observation, instead of too large, The other suggestion was based on the evidence for “lattice loosening’’ or disorientation in the silver halides. I t was pointed out that if the reaction occurred primarily in surfaces and “loosened” ions, smaller energy quanta would be sufficient. This conception was shown to be in accordance with Gndden and Pohl’s views on the origin of the inner photoelectric effect in isolated special ions. The Problem of Light Absorption This latter conception is not entirely satisfactory for the following reason. It would mean that the characteristic spectral absorption of the crystalline silver halides was dependent upon just these “loosened” ions. It is true that experiments by Fromherz4 indicate that adsorption of certain ions, e . g . , Ag+, T1+, does shift the spectral absorption toward the longer wave lengths. This then agrees with t’he previous work of Fajans and Frankenberger which showed that such adsorption shifted the spectral sensitivity in the same way. Since such adsorption is a purely surface effect, this might be regarded as supporting the conception described. Sone the less, the general features of the spectral absorption, very clearly shown in the case of silver iodide by Schel1,j and by Hilsch and Poh16 are not in harmony with such a view. The absorption would depend in much greater degree upon the state of division than actually appears.* There is a paucity of data on the actual spectral absorption of the silver halides. The data available will be noticed later, but the necessity for fuller and more exact measurements is emphasized. h very important contribution to the problem has been made recently by Linus P a ~ l i n g . He ~ takes as point of departure Sommerfeld’s modification of the “electron gas” theory of the metallic state.8 As in the older theory, Sommerfeld still assumes that the conductance electrons are assimilable to a gas, but this assemblage of free electrons does not hare velocities distributed according to hlaxwell’s principle, but is subject to the Fermi statistics, the gas being “degenerate” to a large degree. An important deduction from this theory is an expression for the work required to get an electron out of the metal. The expression obtained for this work is A = ITo - w i where Wois the true external work of expulsion (or admission) and Wi is the inner kinetic energy of the electron in the metal-corresponding to a “Sullpunkt” pressure-and A = lTJi -Wois the effective “outer field” of the electron. The physical meaning of the W,, (the true work of expulsion) is that it represents the attractive forces of the positive metal atoms (ions), whose * It is, however, noteworthy that when the silver halides are produced in a state having no free surface, as by dissolving in saturated alkaline halides, or in solid crystalline alkaline halides,O the absorption edge regresses to the ultraviolet. This will be discussed later as an effect of ionic deformation and dipole orientation.

LATTICE ENERGIES O F SILVER HALIDES

2721

action on the electron compensates for itself in the interior of the metal, but comes into play as soon as any electron tends to pass a surface. “The high ‘Nullpunkt’ pressure which obtains inside the metal is therefore only compensated for by the surface of the metal.”lo W, equally affects, as a retardation potential, the admission of electrons into a metal, and hence affects the dzfraction of electrons in electronic bombardment. Therefore the de Broglie equivalent wavelength A, in vacuo

x,

=

h mv

h becomes

x m = v f z i G

VTT-K

where V is the potential connected with the velocity v by the relation

volt-electrons and V,, the lattice potential corresponding to W, = V,e”. lattice potential, can be determined experimentally, since

A,, lI

=

~

4

=

2

x.

Hence V,, this

h ___ m e t/V V,

= [

+

I

T

Arne

by measurements of p , the refractive index for electrons.’? On the other hand, Wi can be calculated on Sommerfeld’s theory, as wi =

E(3/8n)?/~/~/a

zm where v = number of metal atoms per volume unit, n = number of conductance electrons per atom. If N = Avogadro’s number and a is atomic volume (atomic weight) then v = N/a. From an application of Pauli’s exclusion density principle, n falls in the valency range of the metal, as I , 2 , or 3 , and so on. This expression reduces to W. - C.n2/3. a-2/3 I and if W, is expressed in volt-electrons Wi = n2r3X 26.07 X

On the basis of Rupp’s first values of W, by electronic diffraction, and Sommerfeld’s Wi values for the metals used, Rosenfeld and Witmer“ obtained values of A of the order 4 to 6 volts, which were of the order to be expected

S. E. SHEPFARD AND W. VANSELOW

2722

for the thermionic work-function. These values were, however, only rough preiiminary ones. Furthermore, Bethel3 showed that this lattice potential V,--W, can be calculated as ir =, 2 / 3 rive

where when p (r) is the wave-mechanics charge-density of electrons of the single atoms (in a spherical shell at distance r from nucleus); assuming the bound electrons have spherical symmetrical configurations, the free electrons are uniformly distributed in the crystal. Kow 0, the “moment of inertia of charge,” it was pointed out by Rosenfeld,14 is related to the diamagnetic susceptibility by Pauli’s relation:-

whence by substitution into Bethe’s result for Yo el’,

Xd =

or Mro

=

3

4~rnc‘Xd

which reduces to W, = -6.43 X IO%, X d being the atomic or molar susceptibility per unit volume. Rosenfeld points out that the observed experimental value of X for metals Hence, is the difference of the para and dia values, Xerp = X,,,, - &a. experimental values of $J can be compared with the calculated values of A. Again, recent work identifies C$ with the long-wave (red) limit hv, of the photoelectric effect, i . e . , with the term p in the Einstein equation 112

mv?

=

hv - p .

where v is the incident frequency, (The identification of the thermionic and photoelectric work functions is disputed by E. H. Hall.15 It has been confirmed for platinum and tungsten.) This gives another source of experimental values which can be compared with the X values of Sommerfeld’s expression. The Lattice Potential V, It appeared to us that the lattice potential V, (V,e = W,) might be identical with the electrostatic lattice potential part of the crystal lattice energy. This can be calculated in some cases from the structure by the methods of Born, Madelung, etc., in others from the lattice energy determined thermochemically, but assuming also a structure. For the metals, the lattice energy u = Imt elnet,

+

.

2723

LATTICE ESERGIES O F SILVER HALIDES

where Imetis the work of ionization, and Smetis the heat of sublimation. For face-centered cubic structures, @e =

U ~

I

- 1/q

where q is the slope of the compressibility curve. H. E. Ives and A. R. Olpin16 find from measurements on monatomic layers of the alkali metals that the maximum excursion of the red limit, corresponding to the most sensitive condition of these layers, corresponds to the first line o f t h e principal series, i.e., to the chief resonance line in absorption.

TABLE I Element

Li Ka

Monatomic

5230

6700i

(5000)

K Rb Ca

1st

A0

Tkk

(5400)

I

series

s-P

Res. Pot.

5900

6708 5896

2.10

7700

7899

I

.60

7950 8950

7947 8943

I

.56

1

40

I

.84

Ives points out that this indicates “When the film is in its most sensitive condition, the process of photoelectric emission occurs when sufficient energy is given to the atom to produce its first stage of excitation. I n the Einstein equation 112 mv2 = hv - p, it has been considered that p consists of two parts, zzz., hv, the energy newssary to release the electron from the atom, and p’ the energy necessary to carry it out from the surface.” For monatomic films of maximum sensitivity, the result implies that “the photoelectron comes from the atom of the alkali metal, that the energy necessary to bring this to resonance is sufficient, and that the term p’ is zero.” If the external and internal photoelectric effects with salts are to be interpreted by reference to Sommerfeld’s theory of metals, then the following question arises. Is the term p or the term p’ (in the foregoing expression for the external photoelectric effect) to be identified with the A = KO- JVi of Sommerfeld’s theory? It would seem from this theory that h should equal h u o p’ = p since it is supposed to give the whole work to get the electron out of the metal. Furthermore, if p’ is “the work to get the electron through the surface,’] then this should be the \To of Sommerfeld’s theory, whence

+

hv,

and

+ Wo

=

KO- Wi

jhu,j= -

Wi

which appears meaningless, because with JVo eliminated, no applied energy is necessary for electron emission, this being supplied by ITI.

S. E. SHEPPARD

2724

AND Fv. VANSELOW

I t is possible also that p’ is a purely empirical term, reflecting the experimental uncertainty of hv,, the threshold energy, and that for pure metals

A

=

W, -

TVi =

hv,

It may then be noted, that if it be assumed for monatomic layers, W,, the lattice potential, equals zero, again hv, = - Wi

It appears that Sommerfeld’s theory does not apply, either where a specific surface factor other than lattice potential is assumed, or when the metal is in a monatomic layer. The conditions for the alkali metals are rather disconcerting for the equation of Sommerfeld :

a. From C. T. Lane’s work” the observed magnetic susceptibilities of the alkali metals equal the para-magnetism of Pauli’s theory, and the diamagnetic value is zero. Hence the lattice potentials of Rosenfeld are zero. But, in this case there appears no reason why the red limit for monatomic layers should differ from that of more massive metal. b. From thermochemical and electrostatic considerations, definite lattice potentials can be calculated for the alkali metals. The thermochemical values agree fairly well with those calculated assuming body centered cubic structures (CsC1 type) as suggested by the lattice energy for CsCl type as 673/a, where a. is the side of elementary cube.’* The thermochemical values were obtained by calculating U from the heat o j sublimation and the ionization potential, and dividing by I - I/n = 8 / 9 . The value 9 for n, the slope of the compressibility coefficient is probably too high for R b and Cs.

TABLE I1 Element

4~

4c

Na K

6.95 5.82 5.56 5.25

6.77 5.86

Rb

cs

4x

Wi calcd.

o o o

3.16 2.06

0

1.12

1.18

4=Wi

IP

RP

3.80

j.13

2.10

3.76 4.38 4.13

4.32 4.16 3.88

1.60

I,

=

ionization potential

R,

=

resonance potential.

1.57 1.45

It might perhaps be natural to assume for a monatomic layer that W, = 0, but in that case, Wi seems to lose significance also. If the other values of @ = W, are assumed then the calculated values of No = Wi are higher than the observed values of hv, for thick layers of the metals, which, for A, =


2725

jooo to j400, are of the order 2.35 to 2.18 volts. It may be noted that the alkali metals are poorly crystalline a t ordinary temperat~res.~g It appears reasonable to conclude that Sommerfeld’s theory does not properly apply to monatomic layers, where one cannot speak of a surface and an interior of the metal.*

Other Metals If we turn to other metals than the alkali metals, we find that it is rather difficult to check the proposals that

h whence

=

Wo-

W i

=

hvo

Wi

=

hv,

+ p’ = hv, + W o

A = Wo - Wi = hv,

or

The fact is known that experimentally the red limit of photo-electric action depends upon gas layers, while the best values for thoroughly outgassed metals are for such where W, is not always readily determinable.?O We give in the following table summarized data showing:a. V, experimentally by elect,ron diffraction, b. q5x = V, calculated from diamagnetic susceptibiMy by Rosenfeld’s relation, corrected for xpars, c. dt = lattice potential calculated from thermochemical data = U / ( I - I/n), d. lation.

+M

U

=

lattice potential as electrostatic value by Madelung’s calcu-

=

lattice energy, is taken as

=

sublimation heat

+ ionization potential

=

S,

+ I,.

e.

Wi calculated from Sommerfeld’s expression, taking n

f.

W, - Wi or

I

= S’,e - Wi = 4; - Wi = q5M - w i

= I, 2,

etc.,

as indicated by colineation,

g. bP = red limit of photoelectric effect in volts,

h.

VR = resonance potential,

T’I = ionization potential.

Data used taken from Critical Tables, unless otherwise specified. * It may be noted that the view that the process of photo-electric emission depends primarily upon excitation of atoms to resonance followed by second order collisions of excited atoms and slow electrons has already been expressed.21 The original expectation was that hu, at limit would equal the ionization potential. The theory based on resonance potential# and second order collisions suggests that not the xhole of Wi, the electron inner pressure, is available, but only a lower level value corresponding to low velocity electrons.

2726

S. E . S I I E P P A R D AKD W. VAKSELOW

V,

Element g

V R

n = ~ 1 3 ~ 2 n=2

3.65 3 .i6

A1 n=3

j .63

1ii3

AS

n=3

I4

4.27

4 47

Bi n=3

11.5

4.40

4

02

I

.90

C n=4

13.4

Ca n=2

6.09

6.6

2.92

Cd n=z

10.6

3

3.i8

Cu n=2

14.2

I .38 3 .80

Examination of these results appears to shoiy: a. That in a number of cases Ives' conclusion, that X, is given by the resonance potential rather than the zonzzatzon potential, is confirmed.

K,.

Li, Xa, K, Rb, Cs, Ag, (Al), Bi, (C), Ca, Ba, Cd, Cu.

I,. As. Arsenic appears at present to be an exception. b. The Sommerfeld relation, that A = hv, = \To - \Ti, gives agreement in some cases with the experimental threshold, hut not in others. This is brought out more explicitly in the following table.


2727

TABLE Is’ A,

obs.

Element

‘4g n = z n =

hv, obs. in

W,-W,

Volt9

Ionization Potential

Resonance Potential

4.70

4.27

~

A1

4iiO

2.4j

3595

3 .26

2360

4.65

n = 3 AS

n = 3

4.40

Bi n = 2

4.02

8 .o

n = 3

Ca n = z

4000

2.92

3.02

2.73

2

.24

6.60

6 . IO

Cd n = z

3140

3.59

3.65

8.2j

3.78

cu n = 2

3000

3,62

3 .oo

7.69

3.86

There appears no definite reason, on the “electron gas” theory, why JVo - Js’, should give either the ?esonance potenttal of the atoms, or the ionization potential The fact that data for non-alkali metals freshly distilled and outgassed give support to Ives’ contention indicates that it tends to hold for all freshly formed, presumably imperfectly crystallized surfaces, even of massite metals (not monatomic layers) In the case of hg, Cu and Au, the agreement betn een the electrostatically calculated potentials, the thermochemically, the magnetically calculated, and the potentials observed by electron diffraction is quite good (Table T ) TABLE T’ v o

Element

Ag AU

cu

4T

obs.

I3 147 3 1 5 F 3

’

+E

I2 0

12.2

I4 3 14.0

12.2

13 . 8

2728

S. E. SNEPPARD AND W. VANSELOW

There appears then some reason for identifying the lattice potential V, of Sommerfeld’s theory, calculated from the diamagnetic susceptibility, with the electrostatic part of the lattice energy, determined from thermochemical relations as $T = V/(I - r/n) where n is the compresssib;lity gradient, or calculated electrostatically as

$E

=

for r

face-centered and simple

cubes. I t may be noted that Herzfeld and Wolf??give 1152

$E

= -kg

a,

cals. for NaCl type

=

kg cals. for CsCl type a, and that the latter relation gives values for $E for the alkali metals agreeing well with those calculated as $T.

Photoionization of Halides L. Pauling has applied considerations drawn from Sommerfeld’s theory of metals to the absorption of light by solutions and crystals of the halides of the alkali metals and of silver. He states initially “In Sommerfeld’s electron theory of metals, the energy of a met,allic electron or “free” electron is represented as the difference of two energy qualities, Wi - W,. W,is the average potential energy of the electron as it moves around in the metal, and Wi is its average kinetic energy. W, = V,e where V, is the acerage potential within the metal.” I n this connection, it may be noted that in Sommerfeld’s papers, and in the related work of Rosenfeld, Houston, etal. the difference of the two energies is usually written U’, - Wi, since W, is > Wi. As already stated W, - W i should equal the work-function 4 of the thermionic relation 1 = -&TZe-+/kT where I = current A = universal constant for pure metals k = Boltzmann’s constant, and hence the value hv,(+p’) for the long wave limit of the external photoelectric effect. Pauling refers to Bethe’s (9. v,) and Rosenfeld’s work as showing that V, can be calculated from the diamagnetic susceptibility as

- 6.43

x

Io‘Xd

where ~d is the magnetic susceptibility per unit volume. The expression for t h e total energy of the electron is restated as T. - W, ( = Wi - W.,), where


2729

T. is the average kinetic energy. “It is probable that even in the lowest st,ate T.( =Wi) is not zero for a free electron in, say, a crystal of sodium chloride. The electron as it wanders from ion to ion penetrates into each ion, traversing an orbit which in part is similar to a Kepler orbit. For a Kepler orbit T.( =Myi) is equal to one half the average potential energy with the sign changed, that is to - I,!Z W, (otherwise, in this case, -Wi = 1 / 2 Wo), On the other hand, an electron moving in a region of constant potential, such as Sommerfeld assumes in his electron theory of metals, has in the lowest state T.( =Wi)= 0.” I n this connection it may be remarked that Sommerfeld appears rather to consider that inside the surface of the metal, W, = 0,but when the electron tends to leave the surface, Myo assumes abruptly its full value. “Hence, the total energy of the free electron in the lowest state is to be expected to lie somewhere between -W, and -I/Z W,,in other words, the electron affinity E of the liquid or crystal should lie between 1 / 2 W, and W,. I t will be shown in the following sections that a number of observed phenomena indicate that it is uniformly equal to about 0.8 W,.” If it is permissible to assume that Pauling’s Eorystalis essentially Sommerfeld’s A = IT, - Wi,then the relation A = 0.8 W, is not confirmed for metals: TABLE VI Element vo A Vo - Vi 0.8 Vo 4b Ag I2 6.5 9.6 3.6 A1 17 6.4 13 . 6 6.4

+

+

AS

Bi Ca cu

14 11.5 11 ..?

14.2

4.27

11.2

4.40 6.6 3 .o

9.2 9.0 11.4

4.i 4 .o

(6.1) 3.8

I t is possible that Pauling’s “total energy” for lowest state, = Ecrystsl,is not identical with Sommerfeld’s W o - Ri but logically Sommerfeld’s UTo - ITi = A is “the electron affinity of the metal crystal,” since it is the stopping potential, or work just necessary to allow an electron t o pass in or out, and for metals, A is not equal to 0.8 I n fact, as pointed out by Houston, Wi is more nearly a constant fraction of IT,,, indicating possibly a common origin. Absorption of Light by Solutions of Alkaline Halides Following this general argument, Pauling makes a specific application to the photoionization of halides in water as origin of their characteristic absorption in the ultraviolet. I n this he follows Franck and ScheibeZ3but with modified reasoning and results. The argument is that “Both the initial state and the final state are different for a free halogen ion in aqueous solution [from that’ in ~ a c u o ? ] . ‘The final state, consisting of a halogen atom and an electron, lies lower [than in z,acuo] by an a m o u n t equal to EH~o, equal to the electron affinity of water. I t is assumed that the ‘free electron’ is in its

2730

6. E. SHEPPARD AND W. VANSELOW

lowest state; hence the absorption frequency which corresponds is that of the long-wave limit of absorption.” (Franck and Scheibe calculated from the absorption maximum.) I n addition, the upper level is shifted by an amount equal to the heat of hydration of the neutral halogen atom, estimated by Franck and Scheibe as 5 kg. cals. per mol, but which Pauling prefers to disregard. It will be noted that this assumes in certain degree the “energy on credit” principle discussed previously, but with a very explicit limitation noted later. “‘ heIlower level is shifted by an amount equal to the potential energy of the electron in the electrical field of the water dipoles about the ion.” The following argument is important, because it explains the difference between Franck and Scheibe’s result and Pauling’s and also because it appears equally applicable in another connection not so considered by Pauling. “The following argument shows that this is equal to tuice the contribution of the water dipoles to the heat of hydration of the halide ion: “Let @ebe the potential produced a t the center of the ion by the charge E. The work done in adding the element of charge de due to the charge already present is then Pede, and the total work involved in moving a charge e from a region outside the liquid to the liquid is

But the potential energy of the charge e in the potential @e,due to the surrounding dipoles, is @e2,and thzs much energy must be supplied if the charge is to be removed so rapidly as not to allow the water dipoles time for reorientation. Since the hydration energy of a halide ion is due almost entirely to the ortentatton of the water dipoles (the contribution of electronic deformation making only about 3 per cent of the dielectric constant) we may take z H z (twice the heat of hydration) as the shift of the lower level.” I n a footnote he states that we might equally regard the lower level as shifted by Hz, and the upper level by -Hz, giving the same results. This leads to the equation hv = E x HxHx- - EH,O

+

+

to represent the energy change of the single elementary process of shifting the electron from the (hydrated) halide ion to a state of self-hydration by water, when E x = electron affinity of free chlorine atom, Hx- = heat of hydration of halide ion, EH,O= electron affinity of water. Whereas Franck and Scheibe take the hydration heat only once, obtaining hv = E x Hx- - H x - E H ~ O

+

where H x is the heat of hydration of the halogen (neutral) atom, this latter term is disregarded by Pauling, in keeping with the argument that the water dipoles have not time for reorientation. Hence while Franck and Scheibe get 18.5 kg. cals. = 0.8 volt-electron for EH~O, Pauling gets 88 kg. cals. = 3.81

2731


volt-electrons. From Rosenfeld’s equation, taking x water as - 0 . 7 2 X IO-^, V, = 4.63 and hence E H ~= O 0.82 Wo.In this connection, if we assume that EH*O represents, as TVo - \Vi, the energy required to remove an electron from water, it should equal the lo2g wave limit of the photoelectric effect. For water this is given as 2030 A.U., which makes EH,O= 5.86 volt-electrons, or 133 kg. cals., for ice about the same ( O b o l e n ~ k y ) . ~The ~ agreement is not very gqod, but it might be objected that the water surface (or ice surface) was contaminated with air or oxygen. The present argument is important, because on passing to the photoionization in crystals, the instantaneous acceptor for the electron released from the halide ion is taken as the “crystal” as a whole, as the mechanism producing a “field” like the water dipoles in solution, and not the metal cation.

Absorption Limits of Solid Halides Passing to the alkaline halides, the argument is applied in the form

+

hv = +e E, - Ecrystal where +e is the electrostatic part of the lattice energy, Ex = electron affinity = electron affinity of crystal. of halogen, and Eorysta~ Pauling’s results are summarized in Table T7I.

TABLE VI1 Ecrystal

Crystal

KaC1 KCl RbCl KBr KI

hu

Ex

e+

Ecrystai

-xxros

W, 7.3

1%0

7.11 6.81

3.90

5.69

3.90

8.90 7.98

29

5.07

38

6.8

,78

6.j1

3.90

7.6j

5.04

3.51

7.59

5.12

6.4 6.7

‘79

5.98

43 45

4.94

3.12

7.11

5.29

j8

7.0

.75

0.82

--

‘ / I

The values of x are averages of Landolt and Bornstein and P. Pascal,*b while the values of hv are taken from the data of R. Hilsch.*6 If the values of the hypothetical “EorysLs?’ are determined from the equation

+

Ecrysta1 = e$ EX - hv and the values of JVo determined from x, then the ratios of Ecrystal to JTo approach as shown to 0.80. I n the case of the metals it was shown that Wocalculated from x, with the exception of the alkali metals, was equal to e$, the electrostatic lattice potential. I n the case of the alkali halides it would appear from Pauling’s data that W, comes out considerably less than Q. But this depends considerably on the uncertainty of x. Recent data on the susceptibilities of the halides by Ikenmeyer” and by ReichenedeP show that the susceptibility is quite accurately additive for the two ions, and give values which differ from Pauling’s, being mostly greater.

S. E. SHEPPARD AND W. VANSELOW

2732

TABLE VI11 Salt

KaCl KCl RbCl KBr

KI

X,

(Pauling)

Xm

(Ikenmeyer) 32.3

Pauling W,

Ikenmeyer W.

+e

7.66 6.90

8.90 7.98

7.92 7.82 8.10

7.65 749

38

38.8

7.3 6.8

43 45 58

53.2 52.6

6.4 6.7

67.3

.O

29

7.11

It will be seen that the values of W, calculated from Ikenmeyer’s data for give values approaching the e. s. lattice potentials except for NaC1 and KCI. Other salts show a similar relation, the ,$e W, values sometimes approaching closely, in other cases differing by about I volt, the differences being in both directions. If this is not due to the errors of the experimental values on either side, then it appears that it must have significance for some finer differentiation in the structure of the crystals, whether connected with ionic deformation, or deviation from the ideal lattice type. It is perhaps noteworthy that the differences are of the same order, for the alkaline halides, as those between the ionization and resonance potentials of the metal atoms. In any case, the W,, values obtained differ noticeably in most cases from those given by Pauling, and give also less consistent results for the semi-empirical value Ecrystal= 0.8 Wo.

x

-

Available Energy on Credit The basic conception that the light absorption and photoionization in salts involves the shifting of the electrons to new lower levels not identical with the final value possible, but intermediately consistent with the rapidity of the process, is perhaps capable of expression in ways other than the one proposed by Pauling. S o t all the energy finally available is immediately available, and the question is, what constitutes this margin? The most obvious term, of the later energy terms, is the ionization potential of the metal atoms, L e . , supposing the electrons accepted by the cations. Before testing this the data available may be scrut’inized. The values of ,$e for these salts given by Pauling are acceptable; indeed, there are no others available. They are consistent both with thermochemical and electrostat,ic results. The values of E, may be queried, as not being the best available.29 But it mus, be presumed that the value of hv,, the long wave absorption limit, is subject to considerable uncertainty. To comply with the assumption of lowest electron state, it should be the value when the absorption is zero. The curves of absorption do not cut the axis of wave-lengths sharply, but, owing partly to impurities, asymptotically. We have selected the values from Hilsch’s observations where the extrapolated absorption edge cuts the wave length axis. These values differ appreciably from those given by Pauling, but appear to us to be reasonable in view of the data. Using these values, and the more recent values of X , it will be seen that values of Errystsl,/Wo deviate considerably more from 0.8 than do Pauling’s results.

LdTTICE ENERGIES O F SILVER HALIDES

2733

TABLE IX Salt

NaCl KC1 RbCl KBr KI

hv

A,

1900

5.86 6.18 6.18

2050

j .7 2

2500

4.68

2000

1900

Csing these values of X, process by the equation

EX

+e

8.90 7.98 7.65 7.59

3.90 3.90 3.90 3.51 3.12

-

Calc.

W,’

6.94

8 .7 0 7.14 6.70 6.j o 6.92

7.66 6.90 7.65 7.59 8.10

5.70

5.37 5.38 5.55

7.11

R o

Ecwstai

W,’/Ecrystal

0.91 .82 .jo

.71 .68

he, the attempt may be made to represent the

he

=

+e

+ E,

-

Ihle

where 1~~is the ionization potential of the metal. The results do not support. this hypothesis. TABLE X Salt

NaCl KC1 RbCl KBr XI

+e

8.90 i .98

7.65 7.59 7 . I1

EX

3.90 3.90 3.90 3.51

3,12

I3le

5.13 4.32 4.16 4.32 4.32

hv, calc.

hv, obs.

7 .67 j.j6 7.39

5.86 6.18 6.18 5 72 4.68

6.78 5.91

I t will be seen that the calculated values are all too high by a large amount. An alternative possibility is to suppose that the formation of “free” electrons is equivalent to the formation of the metal lattice (of cations plus free electrons), so that the counteracting field to +e i s that of the corresponding metal. The value of + M ~for the alkali metals were obtained thermochemically (vide i n f r a ) and check fairly well for those deduced electrostatically from the potential. TABLE XI Salt h a i t Ex +are hv, calc. hv, obs. XaC1 8.90 3.90 5.85 5.86 6.95 6.06 6.18 KC1 7.98 3.90 5.82 6 .oo 6.18 5.56 RbCl 7.65 3.90 KBr 7.59 3.5’ j .82 5.28 5.72 KI 7.11 3 .I2 5.82 4.41 4.68 The correspondence between hv, calc. and he, obs. is quite good, and indeed can be slightly improved by taking different values (3.65and 3.35) for EB? and EI.~O I n either case, it lends empirical support to the conception advanced, which implies that the interaction schematized by the equations

~b

+ hv - + X + 8 + e hfe -+


2734

is equivalent to an “initial virtual field” of the metal, somewhat in the manner supposed by StoneP to account for certain magnetic phenomena. Photolysis of Silver Halides Pauling has applied the same equation hvo = +e

+ E,

- Ferssral

used for the photoionization of the alkali halides to the absorption and photolysis of the silver halides, assuming, with Fajans, and Sheppard and Trivelli, that the first occurrence in this photodecomposition is the freeing of an electron from the halide ion. In view of the results of Toy and his collaborators, in showing the agreement of spectral sensitivity of silver bromide vith its photoconductance, it may be well agreed that the primary event in absorption, photoconductance, and photodecomposition is the same. For few of these, however, is the threshold, or wave length limit well established. The best data for absorption are those of Schellj and of Hilsch and PohP for AgI. For AgCl and AgBr the values are not very concordant.

TABLE XI1 Salt

AgCl

A0

Light Absorption

(E. & N.) (H. c t P.)

4100

+ (C.)

4800 (E. & K.) 4700 (H. cC: E‘.) 4800 (T.)

5800

-k (C.)

5200

(T.)

4000

4100

AgBr

AgI

A0

Photo-conductance

s200

(1-1. & x j

j 3 0 0 ((?.‘I

A0

Photographic

ljoo

(H.

ct

31.)

E. S- IC’. = Eggert and Soddack: 2. Piiysik, 31,922 (192j ) ;20, 299 (19231, H. 8: P. = Hilsch and Pohi: Zoc. cit. C. = Coblentz: B u y . Stand. Sci. Pnp., S o . 456. T. = Toy: Proc. Severith Inlcrnat. Congr. Phot.. p. 33, 1928. H. 8: hf. = Huse and Meulendyke: Phot. J . , 66, 306 (1926).

The test of Pauling’s hypothesis in this case he takes as the agreement between calculated x d values and observed x d values for the silver halides. The published values differ considerably, and in order to check them it appeared well to calculate the values from the additivity principle for ions32 using for the halide ions the recent determinations of ReichenedeP which agree well with those of Ikenmeyer. For the Ag’ ion, the observed value for silver corrected according to Rosenfeld, gives x d (corr.) = - 19.1 as the diamagnetic value of Ag+ ion. The values given in Landolt-Bornstein are the original values of Stefan 1Ieyer:-(S.31.) He took Ag 0.151 X IO& = x whereas later values of Honda,


2735

and of Owen, give 0.191 X IO^. Hence Critical Tables gives S . hf. values of .Ag halides X 19 ' I j. L. & B.

Critical Tables

Pascal (calc.)

,\gc1 IgBr

- 40 - 49

-46.7 - 62

-j1.1

AgI

-j8

- 86

-15.7

-61.7

Pascal's values (quoted by Pauiing) are obtained by assumed additivity of Ag (atom) Halogen (atom).33

+

He gives

- 3 1 , I X IO-^

Ag

=

c1

= - 20.1

Rr I

=

AgCl = - 5 1 . I AgBr = - 6 1 . 7 AgI = - 75.7

Xhence

- 30.6 - 13.6

=

Certainly it is more accurate to calculate for the additivity of the ions, correcting for the para-magnetism of the metal atom. Hence

= X, - xd

x0b3

(xp

x,

= -

Xobs

= xd)

-

XoGs

-

Taking .I& X, (Rosenfeld) x o b s

= =

=

-

=

Xd

=

-

xd

0 . 8 6 X IO-^ X IOS X 108

0.20

21.6 X IO-^ 21.6 - 9.3 3 0 , 6 X IO-^ (cf. Pascal)

and taking Reicheneder's halogen ion values we get :

TABLE SI11 Salt

XAg+

AgC'1 AgBr

-30

AgI

xx-

6

Xsalt

-30.6

-21.9 -32. j

-30.6

-51.2

XPaacaI

-jI.I

-b3.1

-81.8

- 86

-75.;

-

This makes Rosenfeld's value for Ag+ X d and makes the TT, ITo value calculated

V,,= 6

&it.

-36.7 -62 . O

j

-52,

=

-

19

I

-61.7

considerably too low,

43 X Kd (calc.)

=

30.6 6 43 X - X 10.j3 108

=

19 . 2 volts

very high. At the same time, it gives better agreement for Pauling's values.

S. E . SHEPPARD A S D W . VANSELOW

2736

TABLE

Calcd, 11y Pauling

Salt

AgC1 AgBr xgi’

*

XIV

Calcd.

Crit. Tables

by Addition

-19-9 -j3 .6

--52.5

-63.1

-46.7 -62 . o

- jj , 7

-81.8

- 86

Recalcd. Pauling

Pascal

-55 - 60 -81

-j1.1

-61,7 -75.7

(-iI )* Calculated by Sheppard and Vanselow from Pauling’s data.

So that taking the additive values of XM,we get for Eerystal Eerysta1= 0.80 W o= 6.43 K X 0.80 TABLE

K

xM

AgCl AgBr AgI Vsing for

K

-j2

j

-63

I

W O

0.36;

13.1 ‘3.9 12 7 5

- 82 =

Ecrystal

10.48 11.10 10.20

Xhi X d -

M. 15’.

-

These values of Wo V,, are considerably greater than the electrostatic values, or the thermochemical values.

TABLE XVI +T

AgCl AgBr AgI

9 96

V, (magnetic) 13 I O

I3 90 12 7 5

9 60 9 46

a + 3 14 volts + 4 30 volts +3 29 volts

But, taking &, as with Pauling, and the values of E, of Pauling, we get hv = +e E, - Eerystal

+

TABLE XYII hvoba.

AgCl AgBr AgI

2.86 2.44 2.25

This indicates that Pauling’s values with the best assumptions for Xd, give discordant results. If, however, the thermochemical #e values are used, (including the deformation energy),

LATTICE ENERGIES OF SILVER HALLIDES

2737

TABLE XVIII hvcalc.

3.38 2 .or 2.25

then a better agreement is obtained, though not convincing. It is apparently a fair question why W, calculated from for PoryaLsl = Jvi W,,but e@electrostatic in the equation

-

xd

is to be used

+

hv = d Ex - Eeryatel I n the Sommerfeld theory, on which Pauling's theory is based, W, is used as the term for the potential restraining the electron. Does W, in this case (halide crystal) = e@ E,? The values agree with this fairly well.

+

e+

AgCl AgBr AgI In this case, hv = W, =

also and

+ EX

wo 13,I O 13.9

13.86 13.17 12.58

=

-

'2.75

hv, = external photoelectric limit.

Ecryatal

W, - 0.8 IT,, )To - (Re- IT))

= w i

hv, = But, this gives

W o - Wi

hv, = e@

+ E,

=

-

ITo - hv hv

which is found to be discordant with observation, giving much too high values of hvO. Moreover, reverting to the alkali halides, these do not show any surh agreement as the silver salts.

TABLE XIX

+

e+ 8.90 7.98 7.65 7.59

Salt

NaCl KC1 RbCl KBr KI

7.11

EX 3.90 3.90 3.90 3 .SI 3.12

=s

WO (calcd. from

12.80 11.88

7.66 6.90

11.55

11.10

7.92 7.82

10.23

8.10

Xd)

Obviously in these cases, Wo, calculated from x d , is much more nearly equal to eqb than to e@ E, and, since the term E, has already been allowed for

+

5. E. SHEPPARD AND W. VANSELOW

2738

in developing the tnner photoelectric effect, it does not appear necessary to consider it again for the outer effect. Hence, while for salts, or generally heteropolar crystals, W, of Sommerfeld’s metal theory probably is analogous to e#~ E,, there appears no reason to identify this with the total magnetically calculated lattice potential. To conserve the application of Sommerfeld’s theory to the photoionization of salts, it appears that one must either: ( I ) identify W, with e+ E,-which gives grave discrepancy with the alkali halides and does not give the right magnitude for the external photoelectric effect with the silver halides. disregard any relations of 17,to e+ or e+ E,, and any relation of (2) hu (internal limit) to hv, (external limit). Rut this actually is in serious disharmony with Sommerfeld’s whole theory. Discussion: While Pauling’s results show support for the hypothesis, i t must be noticed that the agreement becomes much less imposing if certain quite permissible variations are made in the values of +e, efc. First, as already pointed out, the values of A,, or hv., are rather uncertain, but the consensus of observed data is to raise the values somen-hat above those given by Pauling, Le., to lessen the corresponding value of hv. Further, the values of +e used by Pauling are calculated from the lattice interval a, by the equation of Xadelung

+

+

+

- 17476e?

@ e = +-

(r

=

r a0:’2, distance between adjacent ions)

Now the lattice energies computed in this way, assuming rigid ions, are considerably lower than those computed by the Born cycle from thermochemical data. If the electrostatic potentials are computed from these lattice energies by the relation +T = U,’( I - I / n ) There n is the slope of the compressibilitypressure curve, then values of +e are obtained which are greater than those calculated directly, the differences being upwards of I volt-electron, proceeding from AgCl to AgI. This difference is disregarded by Pauling in the matter of the light absorption and photolysis of the silver halides, but is adduced by him, in connection with a later section on the shift of x-ray absorption edges in the halides, as explaining the disagreement of the results of his hypothesis in the case of A4gCland CuC1. “In CuCl and XgCl the cation is an eighteen shell ion, and as a consequence is expected to exert a large deforming action on the outer electrons of neighboring anions. The deformation will reduce the external screening of the outer electrons of the anion, and so will cause a shift to shorter wave lengths. This effect is to be added to those already considered. Some idea of its magnihde can be obtained from a discussion of the crystal energy. The crystal energy of dgC1 as obtained therniochemically is about I volt-electron greater than that given by the Born formula, based on a lattice of non-deformed ions. This suggested that a similar change h C v is to be expected, which corresponds to about AA = - 2 S.C . Just such a


2739

shift is required to cause agreement between the calculated values of AXLicl and the observed values. It seems probable that a measurable deformation effect in addition to the effect of the crystal potential and the crystal electron affinity is to be anticipated in every crystal containing a deformable anion and an eighteen shell cation.” I t is not clear why this effect is to be considered in the case of a shift of an inner electron and not in the case of an outer electron. If it is taken into consideration, and the values of @efor the silver halides used which are obtained from the thermochemically calculated lattice energy, then the following table is obtained: TABLE XX -xd

-xd

Salt

e+,

Xm

AgCl AgRr AgI

9 96 9 60

4100

2

86

11.0

5;

41

49 9

52

4800

2

44

IO

j

60

51 6

53.6

9 46

5200

2 2;

IO

3

81

69 3

71

63 I 81 8

Eoryatal calc.

hv

obs.

-Xp0

5

There is, therefore, a considerable discrepancy when comparing Pauling’s original values, and what we regard as the best values for Xd. This discrepancy becomes somewhat greater if we take Pauling’s values for hv, since this increases Eeryatsland therefore x d . This makes it desirable to test the hypothesis of substituting in place of Eeryatal, a . e . , the equation hv

=

+ E,

e$

- @ag

This gives

TABLE XXI hv calc.

hv obs.

A

86

z 86

I 00

I1

2

44

I 33

58

2

2;

1

Salt

e%

EX

XgCl BgBr XgI

9 96

3 90

I2 0

I

9 60

3

51

I2 0

I

9 46

3

12

I2 0

+Ag

67

The discrepancies here are very considerable and increase in passing from the chloride t o the iodide. The possibility that @ A value ~ is incorrect could, therefore, only correct one value, but not this trend Effect of Polarization (Deformation) According to Fajans, the increasing shift of the absorption edge toward the red in the series AgCl-+AgBr-+AgI is due to the increasing deformation of the anion by the silver cation. I n the equation hv =

L i t

+ Ex -

@Me

no apparent account is taken of this. But, since the bsslt values were calculated from thermochemical data, they contain this energy. Hence if we


2740

used the potentials calculated from nondeformed ions, we should have the equations proposed.

+

Pauling hv = +E Ex (+ p) - Eerystal Sheppard & Vanselow hv = 4~ E, (+ p)

+

- qhe

where p is the deformation energy. But, contrary to Fajans’ conception, this would tend to shorten the wave length of the absorption limit, and in increasing degree passing from C1 to I. The deformatzon in this case may be considered to stand in the same relation as the hydration of the halide ion in aqueous solution. It is a polarization effect between halide and silver ions. Pauling’s argument on the necessity of taking z H, seems applicable in this case also, in the sense that that field of the deformed ion pairs introduces a dipole moment,* and the relation of the electron to this field is similar to that of the electron to the water dipoles. becomes either If this is admitted, the equation using

+ + + +

hv = +E 2p Ex -4 ~ e or hv = +T p Ex - he I n the first case, the crystal potential is taken as for nondeformed ions, and the deformation energy taken twice. In the second, the deformation energy is included once, in the potential calculated from thermochemical data. The imperfection of the data for the silver halides makes a further control of this deformation energy desirable. One possible measure, suggested by Fajans, is the difference between the lattice energies of the silver halides and the corresponding sodium halides.34 This gives AKg cals.

AgC1-Sac1 AgBr-NaBr AgI-KaI

Ve

25.6 31.4 39.2

1.11

I

.36

I .70

It will be seen that these are of just the same amounts as the values of A in Table X I X or, in other words, if we add the deformation energy p thus found we get the following:

TABLE XXII Salt

I

+ + 1.36 0.58 +

AgCl AgBr AgI

1.86

1.11

1.11

1.70

+ p = calc.

hv

2.98 2.47 2.28

hv obs.

.86 2.44

2

2 .25

The agreement is as close as could be expected, especially considering the uncertainty of the measures of the deformation. But that these are of the

-

* Perhaps degenerating to quadrupoles.


2741

right order seems confirmed by comparison with the molar refractions, and the reciprocal temperature coefficients of conductivity of the salts a t their melting point.35 The argument for making the deformation responsible for a shortening of the critical wave length, instead of lengthening, as suggested by Fajans, must, of course, be considered for itself apart from these results. The effect was apparently so considered by Pauling in relation to x-ray absorption edges of the anions. Moreover, if deformation is a step toward homopolar binding, then it must be noted that Franck’s observations on the spectra of vaporized silver halides show these to have absorptions falling short of the solid silver halides.36 Discontinuous band

AgCl AgBr AgI

3485 .O 3393 6 3500

Continuous

3400-3500 A.V. 3050-3 1 5 0 A.U.

It is also noteworthy that solutions of silver halide in alkaline halide, whether as aqueous or solid solutions, show no extension of absorption into the visible but cut short in the ultra-violet (cf. Fromherz and hlenschick).3’ This indicates that the transition to complex ions of types Ag+ ( A d ) Br- (Brilg) where parts are in homopolar binding, has the effect of shortening the absorption or increasing the electron affinity. The effects of adsorption discussed by Fajans3* in this connection are not conclusive for deformation in the crystal, and can be otherwise interpreted, e.g., as increase of total absorption, any extension to the red being consequent on this. I n general, actual midening of a spectral band by reason of increase of total (maximum) absorption, must be carefully distinguished from true shift of the locus of maximum absorption, and of associated absorption limits.

Criticisms of the Virtual Metal Field In the foregoing some evidence is. given that the absorption limits of the halides are better expressed by the relation hv = e4Jsslt than by Pauling’s equation

+ Ex - e4Jmetal + E, - Eoryatal

hv = e&.lt At the same time it is realized that if the theoretical basis of Pauling’s Eoryatal is not unobjectionable, the introduction of as the compensating term is also open to criticism. In the first place, of course, it introduces a product of the final reaction as virtually present. But in this case this is not purely teleological. If the pure

S. E. SHEPPARD AND

9742

W. VANSELOTV

metal consists of metal cations plus more or less “free” electrons, then s ~ m z t l taneously wtth the ‘:freeing” o j electrons, by light or otherwise, from the anion, the “pure” metal is present, since the system cation free electron comes into being. From this point of view, therefore, the virtual field of the metal is not without logic. I t may be remarked also that it meets the requirement of the Phase Rule, that change (decomposition) of a solid body (crystal) can only occur in the presence of, and at the interface with, a solid product of the reaction. (I. Langmuir.)39 But, even if, qualitatively, the virtual field of the metal lattice is admitted, a serious quantitative objection is voiced in the following argument from Pauling on the consequence of the rapzdzty of light absorption (q.v.): “in the very rapid process of the absorption of a quantum of radiation by an electron, theJinaZ state of the electron is not the equilibrium level of the entire system, but rather a quantized electronic level for the system with the atomzc nudea in thear orzganal poszttons.’J40 If this be applied to the present conception, it would mean that the virtual metal lattice potential considered would be that of the metal atoms, t.e., cations zn situ in the crystal, of salt, not as present in the final metal. But, evidently, this means that the lattice potential, the coulomb part of the energy, is reduced in the ratio of r/a, : r/a where

+

= distance between metal atoms in metal lattice a = distance between metal atoms in salt lattices.

a.

And, evidently this means simply an exact compensation of e+, since this value equals e+, the coulomb part for the salt. That internally the tn.0 fields should compensate in this way, as far as movement of electrons is concerned, is arguable since the potential term is

Practically, this reduces the equation for light absorption and action limits to hv = e$

+ E,

- e$

=

Ex,

yet in general this simple equality does not seem to hold

TABLE SXIII Halide

hv

NaCl KC1 RbCl AgCl

5.86 6.18 6.18 2.86

KBr AgBr

5.72

KI AgI

Ex

3.90

A(hv - E x ) + I .96 +2.28 +2.28 - I .04 +2.21

2.44

3

-1.07

4.68

3.12) > 3.12 j

+I&

2 . 2 j

-0.87

LATTICE EA‘ERGIES OF SILVER HALIDES

2743

Here it is at once evident that for the alkaline halides hv is greater than E,, for the silver halides, less. If this be attributed simply to deformation by the silver cation, this neither explains why there is the large positive difference for alkaline halides, nor why hv - E, decreases with the silver halides from C1 to I, whereas the deformation should increase. Hence, if some kind of internal compensation is to be admitted, it is evident that there is incomplete compensation, and in fact, undercompensation for the alkali halides, overcompensation for the silver halides. Pauling’s E,,,.,t,l at present supplies the most flexible term for this compensation. 13ut, if the equality of e+ = W, be = 0.80 W,, = 0.80 e+, and a less flexible, morerigidcomverified, then Ecrvetal pensation is given. I t is not at first evident how two dzferent lattice potentials, or corresponding energies e+ electrostatic energy W, = eVo electromagnetic energy are to be interpreted. The value \To = eV,, however, may be identified with the electrodynamic potential of crystal optics-discussed hy P. P. E ~ a l d . ~ ’ The electrostatic lattice potential of an ionic lattice is e . y.

where by p’ is understood an atom of the crystal lattice, by its charge, and by Rpp,its distance from the point P, and the numerator extends to all the atoms p‘. If P coincides with an atom of the lattice, this becomes for t,he total energy €,I

e$5 =

I,‘2

z,

€

E ’

2,’ 2 . 2 (where r

lattice intervalj

=

which corresponds t o the form already noted: Ae2/r. On the other hand, electrodynamic potentials in crystal optics are characterized by sums of the type Fpr I @ !(t! F(P) =

Ep,

C

Rpp,

representing the (Hertzian vectorial) potential a t a time t at the point P, produced by the individual actions of the moments F,,! of thepfatoms. Compared with the electrostatic potential, the essential difference is the appearance

of the “retardation” (t - k ) , corresponding to the finite velocity of the C

wave disturbance. I t is possible that in the case of light absorption and photoionization, the effective potentials are not the electrostatic ones, but the electrodynamic. I t is not certain that these are necessarily to be identified with the lattice potentials calculated from magnetic susceptibilities.

S. E. SHEPPARD A S D W. VASSELOW

2744

The theoretical basis of Pauling’s Eerystal has been discussed. I t is based primarily on the conception that the total energy kinetic-potential should be between 1/2 and I W,,and empirically approaches 0.8 W,,.If W, from x d is actually the same as e#, then Pauling’s equation cannot be equally valid for the alkali halides and the silver halides. The data available at present are not sufficiently accurate to decide. Electron Affinity of Crystal and the External Photoelectric Effect In so far as Pauling’s Efryetal is identifiable with the value of the total energy W, - Wi Wi - W ofor the lowest state of the electron, it should correspond to the thermionzc work functzon and to the long wave limit of the external photoelectric effect. The values for water have already been discussed. For the silver halides, reliable values of A, are not available. In the most recent work of Toy, Edgerton and S’ick 42 it is stated that, confirming Duna, the “activities” are of the order iodide > bromide > chloride, and that the effect is du? to radiation shorter than 2800 A.U. and as long as or longer than 1800 A.U. In fact Wilson43notes specifically the sensitivity of AgI a t 1800 b.U. as I O times greater than that of hl. This would give a value of hu, between 4.88 and 7 . 2 6 volts; Pauling’s values of Ecryetslare: 10.00v.e. AgCl AgBr 9 . 5 2 v.e. 8.86 v.e. On the other hand, on the hypothesis of a virtual “metallic” field in light, the value of hv, for external effect should be either hv, = e$ 2 p E, - ITl where JVi is the kinetic energy for the electron in the “virtual” silver metal field. This also gives values too high. An alternative possibility on this assumption is that the value for hv, would be given by IT, - W i for Ag metal. This gives 6.5 volts, which is of the right order, but, as already pointed out, metallic silver actually shows a considerably lower value. I n any case, proceeding from Sommerfeld’s theory, it appears that a definite relation should exist between the external and internal photoelectric effects. A feasible relation, for the halides, would be that in light the value hu for the inner photoelectric effect gives the quantum making electrons just freedom enough to move within the lattice, and that to get out they must overcome the lattice potential W,. If we identify W,,with e+, this gives h u , = e+ - hv

-

+

+

TABLE XXIV Whence

AgCl AgBr Ad

hvo

9.96 - 2 . 8 6 = 7 . 1 o v . e . 9.60 - 2 . 4 4 = 7.16 ” I’ 9 . 4 6 - 1.6; = 7.79

or, if we assume that the deformation energy was taken care of in the equation for hv,.


2745

TABLE XXV hv. 9 . 0 3 - 2 . 8 6 = 6 . 1 7 v. e. 8.68 - 2.44 = 6 . 2 4 ” 8.35 - 7.67 = 6.68 ”

AgCl = AgBr = AgI =

These values are also, totally, of the right order, between 5 and 7 volts, and are close to the values of W, - Wi for silver. A recent article by F. Kriiger and A. Bal144 however, cites wave length limits or the external photoelectric effect at much lower values than these of Toy et. al.

TABLE XXVI AgCl AgBr AgI Ag2S

3 1 2 0 R.V. 3320 R.V. 4070 R.V. 4070 R.U.

3 . 7 5 volts 3.53 ” 2 . 8 8 ’’ 2.88 ”

But, it is noted that the curves approach the axes asymptotically, so it is questionable how far these values represent the true work functions. I n particular, t,he question of possible displacement by formation of metallic silver composition X, 3 I 50) by photodeposition deserves consideration. The other question in this connection is the extent to which the results indicate the surface potential of the metal as being less than that calculated for the massive crystal. If the same treatment is applied to Kriiger and Ball’s data as to Pohl and Hilsch’s measurements for the ultraviolet absorption, viz., to neglect the asymptotic part of the curve, and to take the intersection of the “edge” as the true threshold, the values obtained are:

TABLE XXVII Salt

AgCl AgBr Ai31

A0

254 269 271.2

m!J ”

’’

hv, in volt-electrons 4.60 4.36 4.32

Even these are about 2 volts lower than suggested by the lattice potential theory, and appear difficult to explain except by the hypothesis of “local action,” ie., of local lattice loosening, already discussed.45 The calculations made of the surface energy of crystals from lattice theory may assist this.46 Important to notice in this connection is the later work on deformation of ions in the surface layer. Lennard- Jones and his collaborator^^^ have shown that it is the deformability of the surface ions which controls the contraction of the surface. While the contraction for alkali halides is only 5 per cent of the interplanar spacing, the surface energy for alkali halides of the IOO plane is diminished by about 20 per cent owing to the deformability of the surface ions.

2746

S. E. SHEPPARD AND W . YANSELOW

If we suppose that it is the potential energy of the siirjace which controls the exit of electrons in the photoelectric effect with salt, and also that it is the change of thzs which permits the effect of deforming ions adsorbed to extend the photochemical and photo-absorbent threshold for silver salts, it may be possible to correlate the inner and outer photoelectric effects Thus taking the value of 9 electrostatic, for a single layer of atoms, we get, according to hfadelung, I 612e2/r. Hence TABLE XXYIII #

hgC1 AgBr

8.30 8.19 7.70

hv 2.86 2.44 2.25

hvo

hv, obs.

5.44

4.60 4.36 4.32

5.68 5.45

The values for the surface layer are uncorrected for deformation, whereas according to Lennard- Jones and Dent, considerable deformation must exist. It appears probable, in view of the behavior of monatomic metal layers, that the external photoelectric threshold is much more affected by “lattice loosening” than the internal value.

Discussion and Conclusion The theory of light absorption and photoionization for the silver halide. put forward 6y L. Pauling recognizes the importance of the lattice energy in determining the absorption limit, and suggests partial compensation for this by “the electron affinity of the crystal.” It renders unnecessary, therefore, the hypothesis of Sheppard and Tanselow, that the photodecomposition might be initially limited t o locally loosened regions of the crystal, which had a lower lattice energy. This hypothesis was in line with the conceptions of A. Smeka14’ concerning the mechanical and electric properties of crystals, and also with the views of Gudden and Pohl on the inner photoelectric effect with salts. The weakest point of this conception is in relation to spectral absorption. If the photochemical sensitivity corresponds to the absorption (wave length distribution) then the latter should depend similarly on lattice loosening, and the variation of absorption with the dispersity of the halides would be very considerable. For these reasons, Pauling’s quantitative theory is very welcome. We have produced some evidence to show that it is not entirely adequate. One difficulty which has not been noticed is indicated in a very recent paper on * used ionic “Electron Diffraction in Ionic Crystals,” by E. R ~ p p . ~He crystals (NaC1, KCl and KBr) to determine the refractive index for electrons. Whereas for a metal v

+ V,

where v = velocity-voltage of electrons V, = lattice potential of metal


2747

with these salts, the diffraction agreed precisely with the de Broglie relation X =

:’l

i-

Io-8cm.

when n X = 2 d m @ (Bragg). This means that these crystals showed no refractive index for electrons, and that an inner lattice potential similar t o the metals does not seem to be present. Rupp remarks, “This absence is comprehensible from the nature of the ionic crystal. All ionic charges are compensated; free electrons are not present.” This result throws some doubt upon the validity of Pauling’s application of Sommerfeld’s “electron-gas” theory to ionic crystals, and hence on the “electron affinity of the crystal.” If these alkali halides possessed intrinsically such an electron affinity-corresponding to Pauling’s hypothesis of Kepler orbits of the valence electrons-it would seem that it should be effective for slon~ bombarding electrons. On the other hand, the hypothesis that the “field” operative on the electrons loosened by light is the virtualmetal field due to themetal atoms simultaneously produced, is not affected by Rupp’s results. This “field” is not inherently present, but comes into being in virtue of the interaction of light and valence electrons. Experiments on electron diffraction by crystals simultaneously exposed to light within their absorption region should prove of interest. Meanwhile, a complete theory of photoionization should lead to a definite correlation of the external and internal photoelectric effects, as well as account for the photodecomposition. The relation of photodecomposition to “lattice loosening” in the light of the preceding discussion, appears to be more restricted than previously indicated. I t seems likely that the photodecomposition can take place irrespective of “lattice loosening” for waves within the absorption band. Lattice loosening, however, increases the probability of its commencing a t a given point, and extends the active wave length region by lowering the crystal lattice potential. This will be discussed in a later paper.

Summary The importance of lattice energy for light absorption and photo(I) decomposition of crystals is affirmed. The application of Sommerfeld’s “electron gas” theory of metals (2) to photoionization in ionic crystals (polar lattices) is discussed and criticized. (3) Pauling’s conception of an “electron affinity of the crystal,” based on the electron gas theory, is analyzed, and certain objections raised. (4) Replacements of “the electron affinity of the crystal” by the virtual field (lattice potential) of the metal released by photoionization is suggested as giving better concordance of observed and calculated wave length limits of absorption.

2748


( 5 ) It is suggested that deformation of anions by cations with large external electron sheaths tends, p e r .se, rather to shorten t,he wave length limit of light absorption than to extend it. Adsorption effects supporting the opposite view are ascribed to lattice loosening.

References S. E. Sheppard and W.Vanselow: J. Phys. Chem., 33, 250 (1929). S. E. Sneppard: Phot. J., 68 (Sew series 5 2 ) , 402 (1928); W.Vanselow and S. E. Sheppard: J. Phys. Chem., 33,331 (1929). F. C. Toy: Proc. Seventh International Congress of Photography, p. 14 (1928); F. C. Toy and G. B. Harrison: Nature, 123,679 (1929). H. Fromherz: 2. physik. Chem., lB,324; H. Fromhere and G. Karagunis: 346 (1928). l

C. Schell: Ann. Physik, 35, 69- (1911). R. Hilsch and R. W. Pohl: 2. Shysik, 48,384 (1928). ‘L. Pauling: Phys. Rev., (2) 34,954 (1929). A. Sommerfeld: Naturwissenschaften, 15, 82j (1927). Cf. A. Smakula: 2. Physik, 45, I (1927). 10 A. Sommerfeld: loc. cit. 11 Cf. L. Rosenfeld and E. E. Witmer: 2. Physik, 49, j34 (1928); H. Bethe, Naturwissenschaften, 15, 787 (1927). 12 Cf. E. Rup Ann. Physik, 85,981 (1928). l 3 H. Bethe: I n n . Physik, 87, 55 (1928). I4 L. Rosenfeld: Naturwissenschaften, 17, 49 (1929). I s E . H. Hall: Proc. Kat. Acad. Sci., 15, 504-14 (1929). l e H . E. Ives and A. R. Olpin: Phys. Rev., (2) 34, 1 1 7 (1929). C. T. Lane: Phil. Mag., 8, 354 (1929). K. F. Herzfeld and K. L. Wolf: Ann. Physik, 78, 195 (1925). I9 Cf. R. Wyckoff: “The Structure of Crystals,” 232. 2 o Cf. R. Suhrmann: 2. Physik, 33, 63 (1925). 21 A. W. Uspensky: 2. Physik, 40, 56 (1926) 22K. F. Herzfeld and K. L. Wolf: i n n . Physik, 78, I96 (I92j). 23 J. Franck and G. Scheibe: 2. physik. Chem., 139,22 (1928). 24 Obolensky: Ann. Physik, 77, 644 (1925). 25 P. Pascal: Compt. rend., 158,37 (1914). 2 6 R .Hilsch: 2. Physik, 44,4 2 1 , 860 (1927). 27 K. Ikenmeyer: Ann. Phvsik, 1, 169 (1929). Reicheneder: Ann. Physik, 3,58 (1929). 2 g Cf. S. E. Sheppard and W.Vanselow: op. cit. Cf. S. E. Sheppard and W. Vanselow: loc. cit. 31E.C. Stoner: Phil. Mag., 8, 251 (1929). 32 Cf. K. Ikenmeyer: loc. cit. 33 P. Pascal: Com t rend., 158, 37 (1914). 34 K. Fajans: 2. g y s t . , 66, 337 (1927-8). 36 W. Bilte and W. Klemm: Z. anorg. Chem., 152,267 (1926); 131, 2 2 (1923). 35 Cf. J. Franck and H. Kuhn: Z. Physik, 44, 607 (1927). 3’ H. Fromherz and W. Menschick: Naturwissenschaften, 17,274 (1929). 38 K. Fajans and G. Karagunis: Naturwissenschaften, 17, 274 (1929). 19 I. Langmuir: J. Am, Chem. Soc., 38,2263 (1916); B. Topley and J. Hume: Proc. Roy. SOC.,120,2 1 1 (1928); J. Hume and J. Colvin: Phil. Mag., 8, 589 (1929). 4 0 Cf. J. Franck: Trans, Faraday Soc., 21,236 (1925); J. Franck and G. Scheihe: op. cit. M. Born and R. Oppenheimef: Ann. Physik, 84,457 (1927). 41 P. P. Ewald: Ann. Physik, 64, 253 (1921). 42 F. C. Toy, H. A. Edgerton and J. 0. C. Vick: Phil. Mag., 3, 482 (1927). 43 W. Wilson: Ann. Physik, 23, 10; (1907). 4( F. Kruger and A. Ball: 2. Physik, 55, 28 (1929). ‘5 S. E. Sheppard and W. Vanselow: op. cit. ( 8 J. E. Lennard-Jones, and P. A. Taylor: Proc. Roy. Soc., 109;476 (1925); J. E. Lennard-Jones and B. M. Dent: 121,247 (1928); J. Biemiiller: 2. Physik, 38, 759 (1926); J. Biemuller and B. M. Dent: Phil. Mag., 8, 530 (1929). 4’A. Smekal: Anz. Akad. Wiss. Wien, 1926, 195; also Phys. Ber., 8, 1379 (1927); z. angew Chem., 42,489 (1929). 48 E . Rupp: Ann. Physik, 3, 497 (1929). Rochester, N . Y. June 25. 19.30.

The Lattice Energies of the Silver Halides and their Photochemical

Recommend Documents