T H E LATTICE ENERGIES AXD PHOTOCHEMICAL DECOMPOSITION O F T H E SILVER HALIDES* BY S. E . SHEPPARD AND TV. VAXSELOW
I n a paper’ by one of the writers and A. P. H. Trivelli the following reaction scheme was proposed to represent the essential photochemical change in the production of the latent image:BF f
Ag
-
8 +Br (bromine atom)
+ e+hg
(silver atom)
the bromide ion in light losing an electron, which is then accepted by a silver ion to form a metallic silver atom. The same mechanism was independently postulated about the same time by K. Fajans.? Various subsequent hypotheses on the formation of the latent image have been chiefly concerned with the mechanism of concentration of the product t o give developable nuclei3 rather than with the primary photochemical reaction. However, very important investigations have been made by Eggert and 1Joddack4 and by F. Weigertj on the application of Einstein’s photochemical equivalence principle to silver halides. Eggert and Koddack concluded that the primary reaction agrees with this principle, in the sense that for each quantum of light absorbed, one silver atom is produced. a) B r b)
+ hv = Br + 8
+ Ag + 8 =
Ag.
Eggert and Noddack’s results point to absolute coupling of the reactions (a) and (b). Their experiments were carried out with gelatino-silver bromide plates. In view of the criticisms of TTeigert a redetermination of the quantum efficiency with pure silver halides free from binding materials seems very desirable.8 I n the meantime, a discussion of certain of the energy changes in the decomposition of the silver halides in terms of the lattice energies of the crystals appears of interest, because it affords a definite analysis of the steps involved in proceeding from silver and halogen to form silver halide crystals, and conversely from these crystals to metallic silver and free halogen. Communication S o . 360 from the Kodak Research Laboratories. S. E. Sheppard and A. P. H . Trivelli: Phot. J., 61, 403 (1921). * Chem. Ztg., 45, 666 (1921); Z. Elektrochern. 28, 499 (1922). Cf. 5. E. Sheppard, A. P. H. Trivelli, and R. Loveland: J. Franklin Inat., 200,76 (192j). Sitzungsber. preuss. Akad. Kiss., 1921,3 1 . 5Z. physik. Chem., 99,499 (1921); also Z. Physik, 18,232 (1923). “he writers are engaged upon an investigation of the quantum efficiencv using a modification of the method of Harturig in which silver halide is decomposed 6; light i / i L ’ Q C U O and the weight loss measured with a very sensitive micro-balance. 1
LATTICE ENERGIES O F THE SILVER HALIDES
Thermochemical Cycle for Calculation of Lattice Energies of Silver Halides The following reaction cycle for the silver halides is that proposed and used by AI. Born' and discussed by Foote and Mohler2 in regard to spectroscopic data. For a given silver halide AgX, where X is a halogen atom, we have the following cycles representing the formation and decomposition of the salt:
S f[&Xl+Qagx
T Tt-
(-%XI
T
+
[A& I / 2 (Xd + sag -k DX+ (&)(XI
,r
JAg
t
7
(Ag)'(X)Ex ___ (XI (Agf) (e) In the discussion of these cycles, all heat and work units are expressed in kg. cal. The symbols used have the following ~ignificance.~ denotes crystalline solid state, 0 denotes gaseous state, D = heat of dissociation per gram atom (% gm. molecule of XJ, s = heat of sublimation a t absolute zero of I gram mol metal or salt, Q = heat of formation of the salt from the elements in the ordinary state, J = work in kg. cal. necessary to ionize I gram-mol salt or metal, E, = electron affinity of I gram atom halogen gas, in kg. cal., e = I gram atom electron gas. In these cycles, we can obviously start from any state of combination and aggregation of the material, and proceed to any other, evaluating the energy changes. The normal course in the photographic process is from ion pairs Ag+ and X- in a dissolved state to the solid crystalline lattice AgX. Making allowance for the hydration of the ions,4 this will be equivalent to the passage from the gaseous state (Ag') (X-) and correspond to the lattice energy U. To determine this lattice energy we can proceed either by the left or right cycle indicated, but data for the former are lacking. On the right hand cycle work is counted as absorbed by the system for movement against the direction of the arrows, and uforded for changes in the opposite direction. Starting from (Xg+) (X-) equivalent grain atoms of the ionized gases, the first step is (Ag+) (X-) + (Ag+) (X)e. This requires energy equal to the electron affinity of the halogen. This might be determined directly from the convergence limit of a spectrum correspond8 = X- or by determination of the ionization potening to the reaction X tial of the at0rns.j Indirect determination of the electron affinity is possible:J.hgx
+--
+ -
[I
+
Verh. deutsch. physik. Ges., 21, 13, 679 (1919). "Origin of Spectra," 180 (1922). Ci. Foote and Nohler : op. cit. Fajans: 1-erh. deutsch. p h p i k . Ges., 1, 45 (1920); Grimm and Herzield: Z. Physik, 19. I41 (1923). Cf. Angerer: Z. Physik, 11, 167 (1922); Gerlach and Gromann: 18. 239 (1923);Oldenberg: 2 5 , 136 (1924); 31, 914 (192j); B. Ludlam: Trans. Faraday S O C . , ' 610; ~ ~ , J. Franck: 612 (192j-6). >
2
S. E. SHEPPAFCD AND W . VANSELOW
252
a. By taking Born’s values for the lattice energies of the alkali halides, and solving for E, in the equation for the cycle. b. Similarly, but using the lattice energies of the alkali halides deduced by Fajans from their heats of solution. e. By using values for the ionization potentials of the hydrogen halides. The data may be divided into two groups, corresponding to the direct and indirect methods. TABLE I Direct Values of E’ in kg. cals.
S
c1
Br
I
89.3
67.5
59.2
von Angerer: Z. Physik, 19, 149
I925
86.6 89.6
79.1 81.3
71.3
von Angerer and Muller: Physik. Z.,
1926
89
77
66
Ludlam: Trans. Faraday SOC., 21,
Year 1922
P e C
Obseration
(1922)
t
26, 643 (1925)
r 0 S
616 (1926).
C 0
P i C*
* The validity of the spectroscopic data as relevant to the electron affinity of the halogens has been questioned by J. Franck: Trans.Faraday SOC., 21,612 (1925-6)
I.
Year
c1
1919
86
TABLE I1 Indirect Values of E, in kg. cals. Br
I
86
79
Observation
&I.Born: T’erh. deutsch. physik. Ges., 21, 679; K. Fajans: 714 (1919).
1920
118.8
88.6
80.7
1920
119
84
77
4.
1922
116
87
81
5.
I923
88
89
82
6.
1922
81
73
66
2.
3.
Methods (a) and (b) von Weinberg: Z. Physik, 3, 340 (1920) M. Born: Die Naturwiss., 8 , 373 (1920). Foote and Mohler: “Origin of Spectra,” p. 182. Grimm and Hertzfeld: Z. Physik, 19, 149 (1923).
von Wartenberg and Henglein: Ber., 55, 1003 (1922).
L.4TTICE ENERGIES O F THE SILVER HALIDES
On considering this last table, it will be seen that the series
253 (2),
(3), and
(4) all give notably high values for the electron affinity of chlorine.
We find that this results from a value for the dissociation heat Cl, + 2 C1 having been used in these calculations (see next section) which is probably considerably too great. This value is C1, + 2 C1 2 Dcl = 113 kg. cal. due to 31. Pier’ concerning which Lewis and Randall2 have the following to say: “His data did not give directly either the heat of dissociation or the degree of dissociation; but a t each temperature the product of the two was found. Then, employing the thermodynamic requirement for the change of the degree of dissociation with the temperature, he solved simultaneously for both unknowns. Thus he found 0.026 for the degree of dissociation a t the highest temperature (2067’ IC.) and AH, = 113 kg. cal. for reaction C1, (g) = 2 Cl(&]. Such a procedure greatly exaggerates the large errors which are inevitable in work bf this character.]’ Csing Pier’s data, and their own heat capacity and entropy equations, they find for this heat of dissociation AH, = 70 kg. cals. It will be seen from the spectroscopic data cited in the next section that this value is still somewhat high, but it confirms the conclusion that the values ( 2 ) , (3), and (4) for the electron affinity of chlorine are too large. If we except these and give the other values cited equal weight, we obtain for the electron affinities of the halogens
+
Direct Indirect
c1
Br
I
88.6
76.2 84.6
65.5
8j.o
77.6
Ionization Work of Silver The next step required is J A ~the , ionization work of silver. The only datum for this is the determination of first ionization potential of silver vapor by P i ~ c a r d i . ~This gave 7.34 volts, equivalent to 174 kg. cals. per gram atom. Dissociation Heats of Halogens The term D, corresponds to the heat of dissociation of the halogen molecules per gram atom C1, + 2C1 - 2 Dcl Brz+2Rr - P D B ~ I*--+ 21 - 2 I ) I Here again, the values may be determined more or less indirectly from thermodynamical calculations,4 or more directly spectroscopically from the short wave-length limit of the molecular band ~ p e c t r u r n . ~We have tabulated the significant data as follows:‘2. physik. Chem , 62, 38j (1908), quoted by Landolt and Bornstein, p. 906, with the parenthetic comment (Geschatxt!) * “Thermodynamics,” p. 490 (1923). G a m , 56, 512 (1926). Cf. Lewis and Randall: op. cit. Franck: Trans. Faraday Soc., 21, 536 (1925-6).
S. E.
2 54
SHEPPARD AND W. VASSELOW
TABLE 111 Dissociation Heats of Halogens in kg. cals. per gram atom I.
Year 1908
2.
1910
c1
Br
I
Observation
>I. Pier: Z. physik. Chem., 26,
j6. j
385 (1908)
3 . 1914 4 . I919
17.15
Starck and Bodenstein: Z. Elektrochemie, 16, 961 (1910)
17.8 17.2
0. Stein: Ann. Physik, (4) 44, 497 (1914)
K. F. Herzfeld: Ann. Physik, (4)
23*5
59, 635 (1918)
5 . I923
35
20.8
15.8
Lewis and Randall: “Thermodynamics”
6 . 1923
27
23
18
Grimni and Herzfeld: Z. Physik, 19, I49 (1923)
7 . I924
28.5
K. Wohl: Z. Elektrochemie, 30, 36 (1924)
8 . 1924
35
17.
20
K.H. Gerke: J. Am. Chem. SOL. 46, 953 (1924).
9 . 1926
17.25
J, Koenigsberger: Saturwiss., 14,
17.6
H. Kuhn: Yaturwiss., 14, 600
779 (19261 I O . 1926
28.5
22.6
(1926)
Of these data, the value Dcl = 56.5 kg. cal. of Pier has already been discussed and dismissed as too high. The value 3 j kg. cal. calculated by Lewis and Randall also appears high according t o the spectroscopic data. Gerke’s value DCI = 35 (KO. 8 ) appears to be taken from Lewis and Randall. The other values, for Br and I, are consistent enough, so that we may provisionally accept the evaluation of Kuhn, and take DCI = 28.5, DB*= 22.6, D I = 17.6. Heat of Sublimation of Silver For corresponding to [Ag] --+ (hg) we have the following:H. C. Greenwood 5 5 . 8 kg. cal., 1911 Z. physik. Chem., 76, 484 (1911)
Z. Physik, 19, 149 (1923) Sitzungsber. preuss. Akad. Wiss., 30, 506 (1919) The values of Grimm and Herzfeld, and of Haber based on thermodynamics and compressibility are in fairly good agreement, and provisionally the value 65 kg. cal. will be used Grimm and Herzfeld F. Haber
63.3 66.0
kg. cal., 1923 kg. cal., 1919
LATTICE ENERGIES O F THE SILVER HALIDES
255
Heats of Vaporization of Bromine and of Sublimation of Iodine In the cases of I 2 Br2 -+Br and I 2 Iz -+I the heat effects of change of state should be included. For the former we have taken 3 . 7 0 kg. ca1.l and for the latter 7 . 2 7 kg. caL2 Heats of Formation of Silver Halides Finally, for the heats of formation of the solid silver halides, according to h g I ’2 (X?) = Ag X Qkgxwe have the following data:-
+
TABLE IT’ Heats of Formation of Silver Halides Pear
AgCl
‘914
AgBr
Observation
AgI
30.41
Braun and Kauf: Z. angew. Chem., 87,
30.61
L. Wolff: Z. Elektrochemie, 20, 19 (1914)
1 8 6 (1914)
Taylor: J. Am. Chem. SOC.,38, 2295 (1916)
1916
192j
calc.
28.94
obs.
29.94
B. H. Wilsden: Phil. Mag., 49, 900 (1925) 23.0 14.0 23.81 k . o j 1 4 . 9 7 1 . 0 5
T. J. Wells: J. Phys. C h e m . , 2 9 , 8 1 6 (1925)
In view of the greater uncertainty in several of the other values involved, it appears sufficient t o take the following round number values for our purpose :Q A g C i 3 0 , o kg. cal. QAgBr 2 4 . 0 kg. cal. Q A ~ II j.0 kg. cal. For the calculation of the lattice energies we have U = Q - (E - J) D S S. If we take the direct, spectroscopic values for Ex (Table I) this gives U A ~ C209 I kg. cals. U A ~ 2B1 3~. I kg. cals. U A ~ Iz 1 3 . 6 kg. cals.
+ + +
‘Andrews: J. Chem. Soc., 1, 27 (1849) gives 3.65; Lewis and Randall: op. d., p. 5 1 2 give 3 75, Thomsen: Thermochemical Investigations (1905) gives 3.28 kg. cal. (It must be remembered that this will vary with the temperature.) Lewis and Randall find AH = 10450 - 9.6T, where T is temperature absolute, for the heat per gram molecule, H which agrees almost precisely with the heat of vaporization determined by Berthelot a t 60°, and is a trifle higher than the value obtained by Thomsen. Baxter, Hickey and Holmes: J. Am. Chem. Soc., 2 9 , 127 (1907); recalculated by Le+ and Randall: op. cit., p. 522; cf. particularly, Lewis and Randall: “Free Energy of Iodme Compounds,” J. Am. Chem. Soc., 36, 2259 (1914). Favre and Silbermann: Comptes rendus, 2 9 , 450 (1889) gavc 6.08 kg. cal.
2 56
S. E. SHEPPARD A S D TV. VASSELOW
If we take the indirect values for Ex, then U A ~ C2I I z kg. cals. U A ~ 2B0 5~ kg. cals. UAgl 2 0 1 . 5 kg. cals. The latter values agree better with those of Grimm and Herzfe1d.l U A ~ C I = 2 0 5 kg. cals. UA~B = ~198 kg. cals. Uagr = 192 kg. cals. and we might perhaps regard the former somewhat with suspicion, as making the lattice energy of AgI greater than that of AgC1. There enters here, however, the question as to how far lattice energies computed on the assumption of purely ionic lattices from rigid ions are correct, when there may be deviation from this premise, in the sense of deformation of the ions2 and approach to less heteropolar, more homopolar lattices. As will be noticed shortly, this tendency increases on passing from AgCl to AgI. Concerning this, Grimm and Herzfeld remark as “Finally, let us take into consideration the possibility that the assumed crystal lattice of rigid ions is so altered, that the ions are ‘deformed,’ indeed, that the lattice does not remain an ionic lattice, and that the ionic deformation leads to the ‘heteropolar’ union passing over into a more or less ‘homopolar’ union. In this case, which, for example, would present itself in the passage of the salt Xenon chloride XeCl into a compound of the type IC1, we have to consider a ‘deformation’ energy outside the limits of the theoretical Born lattice theory, the magnitude of which remains unknown to us. Since, however, the laitice energzes of exzstzng compounds used by u s later are based o n experimental data and not on theoretzcal values, the deformation energzes are already contained in them, and it only remains questionable, whether the difference of the ‘deformation energies,’ for example of XeCl and KaC1, or of Mg12 and can strongly falsify our estimated lattice energies. I n the most extreme case, with HCl, the deformation ‘energy‘ amounts to some I O O kg. caL4 As, however, with Hfthere is an extreme case, and in our calculations only the dzfferences of the deformation energies is important, we conclude, that the deformation will not falsify our results.” The conclusion is somewhat different when, as in the present case, it is the absolute magnitude of the lattice energy which is important. A principal issue raised in the present communication is the following. In the photodecomposition of the solid silver halides, is the lattice energy something which has to be overcome by radiation? If not, what becomes of this energy? If so, how is it effected, directly or indirectly? Before specifically taking up these questions, we may refer to the direct calculation of the lattice energies in Born’s theory, by way of compressibility values. ‘ Z . Physik, 19, 141 (1923). See later. ~ L o ccit., . p. 147. ‘Cf. Grimm and Herzfeld: 2 . Physik, 19, 147 (1923); P. Knipping: Z. Physik, 7, 328 (1921).
LATTICE ESERGIES O F THE SILVER HALIDES
257
Determination of Lattice Energies from Electrostatic Theory' If the ions are assumed to be infinilely hard rigid charged spheres, the (attraction) potential for any two according to C'oulomb's law is given by Q0 = &e?,r, where e = ionic charge, and r = distance between atomic centers. This picture is inadequate, since the substances formed are not incompressible, and instead there is postulated a force of repulsion which is infinitely small at great distances, but does not increase infinitely rapidly. By analogy with Coulomb's law, the potential energy of this force is given by 4 = Plr" where /3 and n are constants. The total potential energy for any two ions is therefore 4 = =te', r /3 'I". I n calculating the potential energy of a whole lattice from the mutual interaction of pairs of ions in different orientations, it is evident that 7' becomes 6, the lattice constant, i.e., the distance from one ion to the next similar ion on the edge of the unit cube.? The solution will be of the form
+
+
@ = -a, 6
+ b,:6"
where n and b are constants obtained by summation over e' and /3. Calculation of the constant a of the electrost,atic term has been facilitated by 1 1 a d e l ~ n g : ~ For a lattice of the XaC1 type, where @ is the potential energy for each elementary cube of edge 6, a = 13.94 @. The reaction below 6, the equilibrium value of the lattice constant and the corresponding energy of unit cube is obtained from the condition that for 6; the value of d@J/d6is zero. This gives *o
=
-a/&,
(I
-
I,
n).4
The lattice constant 6, for the undeformcd crystal can be determined by X-ray spectrographic methods, or can be calculated. If m and in' be the m + m'. atomic weights of the tiyo ions, then ___ is the weight of one "molecule," 5 XgX, and since in this type of crystal there are four of these in the unit cube, the mass of this is 4(m im') = p A 3 , where p is the density of thr crystal,
Ii
and A 1
2
3
=
&!2
AI. Born: "The Constitution of Matter," j o (1923). Born: "The Constitution of Jlatter," jo (1923). Physik. Z., 19, 524 (1918).
'e d6
=
-"2 - nb = 6
an-1
Hence%
6;"
b
Hence
= 7
=
for *=, 8,.
a? 6,
1
n
0
gon-r,
-a = 63
,n-1 + na-6__ 6,"
2
S. E. SHEPPBRD A X D W. VANSELOW
j8
The exponent n is connected with the slope of the curve relating the repulsive force with r. Crystal movement from equilibrium involves diminution of the lattice constant, i.e., a compression. The exponent n is closely connected with the compressibility K of the crystal. It is found that
+
If K , the compressibility, is determined experimentally, n can be obtained from this formula. For the alkali-halides of the type NaCl the value n = 9 has been found sufficiently accurate. For the calculation of the lattice energy, we have to multiply CP, by -N/4 because the elementary cube contains 4 ion-uairs. Hence
Inserting the values for a and 6, and for A' (Avogadro number) we have
U
=
54jq3/kg. m m'
+
cals.
For the silver halides the following data were used: P
AgCl AgBr (&I
5.jjo 6.473
5.674
m 107.88
107.88 107.88
m'
G
35.46 79.92 126.92
184 178
j,78
150)
6.49
..lQ.U./a, 5.56
The corresponding values of U are given in the last column. The value for AgI is based on the assumption of a cubic lattice, which is correct only above 140'C. But from the lattice constant given for this1 6.493-Ao.U. t'he calculated value of U A ~isI 130 kg. cals. These values are low compared with those obtained indirectly from thermochemical considerations. This is possibly due to the value of n = 9 being too high. Although deformation of the anion by the cation, such as occurs in silver salts (vide inf.),is not assumed to affect the compressibility, it might affect the slope of the compressibility curve. Relation of Lattice Energy to Photochemical Change It was stated already that the primary photochemical change in the silver halides has been represented by the equation S + h v = S + e
followed by
+
hg
+ e = xg.
Xou- this means, either that we can disregard the lattice energy, and assume that the light acts on the halide ions as if they were independent gaseous
+
ions, or that st'arting with the system [XgX] solid we pass by the action of Cf. K. Wyckoff: "The Structure of Crystals," 319 (1927).
LATTICE ESEECIES OF THE SILT-ER HALIDES
2 59
light to the system iAg) (S)e. I n the latter case, according to the cycle installed, and the values obtained, this would imply that there must be afforded the energies
r + Ex.
From the values obtained, it will be seen that these quantities would be for the three silver halides of the following order:Silver Halide AgC1 AgBr AgI
U 212
zoj 201. j
++ 8Exj
kg.cals.
+;
kg. cals.
+ 8 4 . 6 kg. cals. j .6
Let us suppose that each step requires absorption of an equivalent molar quantum Khv of radiation. The following graph represents the relation of wave-lengths to quanta and molar quanta. h molar quantum Khv = kg. cals. would correspond t o a wave-length of about 130 mop, a molar quantum K hv = 86 kg. cals. to a wave-length of about 3200 A.U.' Both these values, notably the first, are far shorter than the wave-lengths active in the photochemical decomposition of the silver halides, which are comprised in the known absorption spectra of these bodies. The apparent contradiction may be made clearer perhaps by considering a diagram of the energy levels (Fig. 2 ) . The question arises, is this apparent contradiction a real problem? For example, is it necessary to assume the electron separation as the mechanism? If a direct decomposition, corresponding t,o t,he heat of formation Q.k,s were assumed, (e.g., in homopolar 1
Cf. also yon Xngerer. loc. cit.
2 60
S. E. SHEPPARD AND
W. VASSELOW
molecules) than no contradiction to the wave-length thresholds would exist, since the wave-lengths corresponding to these heats of formation are well in the range of visible and even infra-red radiation (cf. Table Itr), But there exists independent evidence that the inner photoelectric effect postulated by Fajans and by Sheppard, actually occurs. The first piece of evidence is the phenomenon of photo-electric conductivity, particularly of the primary photo-current distinguished by Gudden and Pohl.' The correlation of this with the photochemical change is only assumptive and not directly proved. I t will be shown that it might be possible to regard this effect as occurring independently of the photochemical AFflNlW-8;Kg.C4LS. E, = EECTPON
1
d
U L A P I C E ENERGY
(xz) + [A81 SOLID SILVER AND MOLECULAR HALOGEN
a SHEAT
[As XI
OF FORMATION
FIG. 2
Energy Level Diagram
change, and perhaps as not necessitating a n y demand by the lattice energy. But it is evidence of an inner photo-electric effect. The second piece of evidence consists in the production of photo-electric potentials a t electrodes of silver : silber halide : electrolyte. The authors d l show in another communication that their experimental evidence with this system strongly confirms the simultaneous production of free electrons and atomic halogen, by light acting on the silver halides. We shall assume for the present, therefore, that the assumption of the inner photo-electric effect, is justified, and consider the apparent contradiction with lattice energy requirements. One way of meeting the difficulty, which is raised by the quantum theory of energy changes, is suggested by the theory itself. It may not be necessary to supply the full quanta of energy corresponding to U and Ex, in view of the free energy liberated in the subsequent stages leading t o 1/12(X2) [hgl. This implies that the electron i s released, at a cost less than the true electron affinity by an amount corresponding to these subsequent gains. The argument that the free energy of a subsequent reaction phase should be available for an earlier one has usually been rebutted, as teleological. Yet it is
+
' Z . Physik, 6,248 (1921).
LATTICE ENERGIES O F THE SILVER HALIDES
261
definitely used in the quantum theory of spectra. For example, Sommerfeld’ states: “Consider two atoms, which differ from each other, only in t’hat the L-shell in the first is present as an L1 level, in the second as an L? level. Should an electron be raised from the K-shell t o thesurface of the atom, then the effective nuclear charge of the L-shell is increased by I ; this, therefore, contracts together. Since in this contraction, energy is set free, the Lshell contributes part of the work for the K-excitation: the excitation-energy is therefore lessened by the presence of the L-shell-and naturally also by the presence o j the others.”
It may be objected that there is no way of picturing the over-coming of the lattice energy L7 by a quantum process. The individual ions do not possess lattice energy, as individuals, but only collectively, as a space relation of positive and negative ions. It appears none the less true, that the lattice energy must ipso jacto exist as a resistance to the freeing of a negative charge. In point of fact, a direct photomechanical action of radiation upon matter has been suggested by one of the writers,2 and more specifically worked out by F. Weigert for paired systems (atoms or atom groups) of electron donors and electron acceptor^.^ The latter has adduced as further specific evidence for such a process the phenomena of phototropy in solids.‘ The latter is shown chiefly by crystal lattices of complex deformable molecules; it is not explicable as an isomeric or tautomeric molecular change, but only as an affair of pairs or gr0ups.j In view of the problem of disposing of the lattice energy in heteropolar lattices of relatively rigid ions, it appears that the evidence for direct (primary) photomechanical disintegration of the silver halides may have to be reconsidered.6 Many examples have been cited to demonstrate a direct mechanical disintegration by light acting on solids. Bredig and Pemse17 suggested that the developable “latent image” was due to a photomechanical disintegration of the silver halide crystals. Actual disintegration can be observed in the case of silver iodide, as first noticed by C. Schultz-Sellacks and studied more fully by H. Scholl.9 h very thin continuous layer of silver iodide is obtained by exposing a silver mirror to iodine vapor. This becomes turbid and vari-colored by exposure to intense light, and can be shown by rubbing to be actually mechanically disintegrated. “Atombau und Spektrallinien.” 3rd. Ed., Chap. 8 On Theory of Fine Structures, p, 614 (1924). S. E. Sheppard: “Photochemistry,” 331 (1914). b-erh. deutsch. Physik. Ges., 21, 479, 61j, 639 (1919); Z. Physik, 2 , I (1920);3,437 (1920); 5 , 410 (1921). Z. Elektrochemie, 24, 2 2 2 (1918). S. E. Sheppard: Chem. Rev., 4, 319 (1927). Discussed in a forthcoming article by S. E. Sheppard on “Colloids and Photochemistry” in J. Alexander’s “Colloid Chemistry, Theoretical and Applied.” Arch. wiss. Phot., 1, 33 (1899). 8 Pogg. Ann., 143,.442 (1871). Ann. Physik, 16, 193, 417 (1905).
262
S. E. SHEPPARD AXD W. VAXSELOW
Luppo-Cramerl at one time maintained the view that these phenomena, and the “developability” by ammonia induced in silver bromide by light2 were due to direct photomechanical disintegration. I n 1910-11, The Svedberg3 observed that a number of metals-mercury;,silver, lead, copper, tin-would be disintegrated quite rapidly by ultraviolet light, more slowly by ordinary light. He obtained colloid sols in water or alcohol in this way. The investigations of Xordenson4 were held to show that the mechanical disintegration of the metals is a consequence of a preliminary photochemical preoxidation, while Luppo-Cramer also abandoned6 the view of primary photomechanical disintegration of the silver halides in favor of regarding it as a consequence of photochemical liberation of halogen and disruption by halogen pressure. The importance and magnitude of the lattice energy of silver halide crystals forces a restatement of the question, however. Thermodynamic consideraton of the lattice formation already discussed (p. zoo) and the tensor character of the radiation in the newer wave-theories6 suggest that it is neither necessary nor sufficient to regard the mechanical disintegration of the crystal as the consequence of a primary photochemical change. It appears that a t the least there is an initial synergy of the photomechanical and the photo-electric actions of light. Synergy in the sense that the lattice loosening (Gitter-Auflockerung) and electron liberation and transfer are closely coupled prophases of a n y photochemical change in solids. It is probably much too soon to speak here of one aspect as usually preceding the other. Lattice Disorientation and Ionic Deformation We saw that there was another thermodynamic cycle leading from the solid lattice to the gaseous ions, uw., by way of the sublimation heat S,,, and the work of ionic dissociation J A g ~ .Hence Is one t o suppose that radiation has t o furnish two equivalent quanta before valency electrons can be removed from the independent gaseous negative ions by yet a third quantum? This appears even more improbable than a dzrect photomechanical sublimation into gaseous ions. Moreover, even if we could treat the lattice ions as equivalent to independent gaseous ions, the quantum required to overcome the electron affinity Kolloid-Z., 17, 51 (1915);Zl,28, I j 4 (1917). Cf. “The Silver Bromide Grain of Photographic Emulsions” by A. P. H. Trivelli and S.E. Sheppard. Monographs on the Theory of Photography, No. I (1921). 3Kolloid-Z., 6, 129 (1910);also 11. Kimura: Memoirs Kyoto Coll. Sci. (Japan), 5, 252 (191.1). ‘Koliidchem Beihefte, I., 91 (1915);cf. also The. Svedberg: “The Formation oE Colloids,” p. 81 (1921). “Kolloid Chem. Kolloid-Chemie und Photographie,” zd Edit Swann: J . Franklin Inst., 205, 323 (1928).
2 63
LATTICE ENERGIES O F THE SILVER HALIDES
is still much larger than that experimentally found effective. Provisionally, it appears that a way out is to be found in a “loosening” disorientation of the lattice itself-equivalent to a reduction of the lattice energy-correlated with a deformation of the ions, equivalent to a reduction of the electron affinity. Some of the evidence for this will be considered. Lattice loosening or disorientation has been discussed in relation to dlffusion and electrolytic conduction in solid crystals. G. von Hevesy’ has pointed out that a t the melting point the magnitude of the conductance of fused salts changes abruptly. Assuming that the electronic condition does not change a t the melting point, the number of free ions must have increased in the melt. Conversely, the fall in conductance on solidification must be due to the immobilization of the ions in the lattice. However, in the neighborhood of the melting point the lattice is relatively loosened or disoriented, so that a notable number of ions can still wander. As a rough measure of this tendency to lattice disorientation he suggests the ratio Y =
conductance of liquids conductance of solids
taken just below and above the melting point. The following table shows how this varies with different salts:
TABLE T’ Conductance of liquids x = Conductance of solids
x = Conductance of liquids
Conductance of solids X
Y
KaS03 KN03 LiN03 IiCl PbClz SnClz XaCt
TlCl TlBr T1J AgCl -4gBr x gJ
20000
20000 10000
9000 jooo 4000 3 000
I 60
130 IO0
30
5 0.9
Of great importance for the present argument is the parallelism indicated by vonHevesy between lattice disorientation, as indicated by this coefficient, and the inclination of the ions lo pass to the neutral state. Aiccordingto von Hevesy, if [K+Cl-] is to be converted to [K] [Cl] then the electron affinity of (’1 must be overcome.2 This demands 89 kg. cal. per gram atom, while the + ionization work of K e + I< which is gained is 99 kg. cal.,’gram at’om, giving the slight excess only of i o kg. cal. Then in the case of [hg-I-], von
+
+
-
Hevesy takes the corresponding values, of I - e
4
-
I as
jg
kg. cal. {gram
Uber Gitter-Auflockerung,” Z. physik. Chem., 101, 337 i 1 4 2 2 the lattice energy itself, nor whv the decomposition t o [I
