ENERGY ADDITIVITY IN CRYSTALS AND GLASSES
319
REFERENCES (1) ADAM,N. K., AND JESSUP, G.: J. Chem. SOC.127, 1863 (1925). (2) ANDREAS, J. M., HAUSER, E. A., AND TUCKER, W. B.: J. Phys. Chem. 42, 1001 (1938). F. E.: In J. Alexander’s Colloid Chemistry, Vol. 111, p. 41. The Chemical (3) BARTELL, Catalog Company, Inc., New York (1931). (4) BARTELL, F. E., AND OSTERHOFF, H. J.: Colloid Symposium Monograph 6, 113 (1927). : mechanique de la chaleur. Paris (1869). (5) D U P R ~Theorie (6) EDSER,E.: Fourth Report on Colloid Chemistry, p. 263. British Association for the Advancement of Science, His Majesty’s Stationary Office, London (1922). (7) HARKINS,W. D.: I n J. Alexander’s Colloid Chemistry, Vol. I, p. 192. The Chemical Catalog Company, Inc., New York (1926). (8) HARKINS, W. D., AND ANDERSON, T. F.: J. Am. Chem. SOC.69,2189 (1937). (9) HARKING, W. D., AND BROWN,F. E.: J. Am. Chem. SOC.41,499 (1919). (10) MACK,G. L.: J. Phys. Chem. 40, 159 (1936). (11) MILLER,N. F.: J. Phys. Chem. 46,1025 (1941). (12) PEASE, D. C.: J. Phys. Chem. 49,107 (1935). (13) SULMAN, H. L.: Bull. Inst. MiningMet. No. 182 (1919). (14) WARE,I. W.: J. Phys. Chem. 37,023 (1933). (15) YOUNG,T.: Phil. Trans. Roy. Soa. 96, 65 (1805).
ENERGY ADDITIVITY IN OXYGEN-CONTAINING CRYSTALS AND GLASSES1v2 MAURICE L. HUGGINS AND KUAN-HAN SUN Kodak Research Laboratories, Rochester, New York Received March 6 , 19.46
In correlating the properties of solid oxides with the properties of their component atoms or ions it is useful to compare their molal energies of formation, not from the elements in their usual “stahdard” states, but from dilute gases composed of the simple (metal and oxide) ions. The purpose of this paper is to present and discuss values of such energies, computed from data in the literature. Both simple oxides and “complex oxides” (e.g., silicates, sulfates) are considered. For our data we use the values (Qf) of molal heats of formation (from the elements in their standard states) of the oxides and gaseous ions collected by Bichowsky and Rossini (1). These are all for a temperature of 18°C. The molal energy of formation of a compound from the simple gaseous ions we shall designate by the symbol Ei. For a simple crystalline oxide, M,O,, Ei is related to the Qf values according to the equation: Communication No. 1074 from the Kodak Research Laboratories. Presented before the Division of Physical and Inorganic Chemistry at the 107thMeeting of the American Chemical Society, Cleveland, Ohio, April 5, 1944. A preliminary paper dealing with this subject has already been published (M. L. Huggins and K.-H. Sun: J. Am. Ceram. SOC. 28,149 (1945)).
320
MAURICE L. HUGGINS AND KUAN-HAN SUN
Ei[M,O,, crystal]
=
e)+,
Qf [M,O,, crystal] - m Qf [M
- n Qf
[Ow-, gas]
gas]
- (m + n) RT
(1)
The corresponding relations for vitreous oxides and for complex oxides (containing more than one non-oxygen element) are obvious. It may be noted that the sign of Ei is so chosen as to wake Ei greater the greater the stability of the substance, that is, the lower its actual content of energy. This convention as to the sign conforms to the convention adopted by Bichowsky and Rossini with regard to Qf values and to the universal custom in calculating and using “bond energies.” We realize that for some purposes f r e e energies are of more interest than total energies, but calculation of the former involves complications with regard to the entropy contributions, into which we do not care to go a t this time. From the results of x-ray diffraction studies of crystals and glasses it seems certain that, with very few exceptions, each non-oxygen atom or ion, in any of t h e oxides we are considering, is surrounded by oxygen atoms or ions. Most of the ionic formation energy, E d ,of such a solid results from the attractions between closest neighbors-that is, from the attractions between each positive atom (Na, Ca, Si, P, . . .) and the surrounding oxygens. One might expect the attraction energy between positive atoms and the surrounding shell of oxygen atoms to vary but little from compound to compound or from glass to glass. This is especially likely if the coordination number stays the same, but even with a change of coordination number the energy change should not usually be large. The energy contributions of pairs of atoms which are not closest neighbors are relatively small, and the summation of these may be assumed to be roughly the same in the compounds being considered. It is reasonable, therefore, to expect approximate additivity of energies, the Ei values being the sum of energy contributions resulting from the attraction of each positive atom for its surroundings. The calculations reported here show this to be the case. Significant departures from additivity do occur, however. In most cases they can be attributed to differences in the number or arrangement of closest neighbors. The additivity assumption can be expressed mathematically in the following way. For a glass or compound of formula M,MbtML#t . . . . On,
Ei
=
mMcM M
(2)
The mM values are the relative numbers of metal (non-oxygen) atoms, as expressed by the formula. The eM values are constants characteristic of these elements, deduced from the experimental E , values. Each eM is a measure of the decrease in energy when one gram-atom of the ion M and the equivalent number of oxide ions [O--) are transferred from the gaseous state to an average simple or complex oxide in the solid state, in which each M has as near neighbors only oxygens and each oxygen has as near neighbors only more electropositive atoms (M, M’, M”. . . . ). The individual eM values deduced are listed in table 1and many of them are plotted in figure 1.
321
ENERGY ADDITIVITY IN CRYSTALS AND GLASSES
TABLE 1 Energy constants for various ions in simple and complex oxides AVERAGE 3EVIATION
COMPOUNDS USED IN COMPUTING cM
hi
ks.-cal.
Ca++
839
CaO
0
MgCI.
912
MgO - CaO, Mg(OH)z - &(OH),, MgC03 - CaCOs, MgSO4 - CaSO4, Mgs(PO4)z - Cas(P04)z, M ~ , ( A S O~ )Cas(As04)z, ~ MgwO4 - Caw04
9
Sr++
800
SrO - CaO, Sr(OH)z- Ca(OH)z, SrCOa- CaC03, SrSO4 - CaSO4, Sr3(P04)z - Caa(PO4)z, Sra(AsO~)z- Cas(AsO&, SrWO4 - Caw04
5
Be++
768
BaC03- SrC03, BaO - SrO, Ba(OH)zBas04 - SrSO4, Bas(PO4)z - Sra(P04)~, ~ ) ~ , - SrWO4 Bas(As04)z- S ~ ~ ( A S OBaWO4
5
Li+
351
LizO - BaO, LiOH - Ba(OH)z, LizS04 - BaSO4, LiN03 - Ba(NO&
7
Na+
322
NazO-LizO, NaOH -LiOH, NazSO4 - LizS04, NaN03 - LiN03
6
I(+
299
KzO - NazO, KOH - NaOH, KzSO4 - NazSO4, KNOs - NaNOs
4
Rb+
295
RbzO - KzO, RbOH RbNO3 - KNOs
Cs+
288
CSZO - RbzO, CSOH - RbOH, CszSOa - RbzSO4, CShTOa - RbNOs
c1*7
9948
NaCIO4, KClO4, Ba(Cl04)~
6
S+0
7195
LizSO4, Na&O4, K2S04, RbnSO4, CszS04, MgSO4, CaSO4, SrSO4, Bas04
9
C1+6
5030
NaC103, KClOa, Ba(C103)~
4
N+6
6831
LiNOs, NaNOs, KNOa, RbNOs, C'sNOa, Ca(NO&, Sr(NOsh, Ba(N0s)z
6
P+6
4737
Na3P04, Mgs(PO&, CasPOdz, Srs(POl)z, B a d P 0 ~ h
2
- KOH, RbzSOc - KzS04,
1
.
1
I
As+6
4507
Na3As04, Mg,(As04)~,Caa(AsO&, Srs(AsOa)?,Baa(AsO4)z
3
Sb+6
4250
Na3Sb04
0
s+4
3343
Na2S03, KzSOa, MgSOs, BaS03
7
c+4
4208
Li?COa,NazCOs,K2COs,Rb~C03,CSZCOS, MgCOs, CaCOs, SrCOs, BaCOs
1
322
MAURICE L. HUGGINS I N D KUAN-H.4N SUN
TABLE 1-Continued ~
M
COYPOUNDS USED IN COMPUTING t M
AVEBAGE DEVIATION
kg.-cal.
Si+‘
3129
8
33-
2047
8
Sl*+
1878 1793
39 5
1721
7
H+
515
3
H+
501
1
H+
490
3
H+
489
6
cu+
295
0
Ag+
346
6
TI+
309
4
KH4+
151
Bei+
1141
22
v++
901
0
hfn++
895
14
Fe++
919
17
co++
1118
16
Ni++
929
18
cu++
860
17
Znu
941
11
Pdt+
978
28
Cd++
883
23
- C’
3
323
ENERGY ADDITIVITY I N CRYSTALS AND GLASSES
TABLE I-Concluded M
COkE'OUNDS USED IN COYPUTING
AVERAGE JEWTION
-
kg.- cal.
Sn++
882
4
Hgf+
907
26
Pb++
829
9
2555
0
1563
0
V+++
1691
0
Cr+++
1695
43
Gaff+
1827
0
As-
1767
0.
Y*+
1566
2
In-
1722
0
Sb+++
1614
46
Tl+++
1734
0
Bi*+
1526
69
Ti+4
2882
0
Ge+4
3055
0
zr+4
2637
1
Sn+d
2769
58
Pb+4
2835
3
V+6
4564
0
Se+6
6886t
5
Te+B
61671
0
Nsc-
'
* c denotes the heat of formation (Qf)of NH4+ from hypothetical NH4 metal. Assuming Qf[Se+Bl = -6100 kg.-cal., estimated with the aid of ionization potential data from Latimer (3) and Sherman (4). $ Assuming Qj [Te+'l = -5317 kg.-cal., estimated with the aid of ionization potential data from Latimer (3) and Sherman (4).
,
324
MAURICE L. HUGGINS AND KUAN-HAN SUN
An idea of the deviations from additivity can be obtained from the average deviations of the eM values computed for a given ion (from different compounds) from the average of these values. These are given in the last column of table 1. The average of these average deviations, weighted according to the number of compounds involved in its calculation, is about 10 kg.-cal. This is a rough measure of the average departure from the additivity assumption, the experimental data tabulated by Bichowsky and Rossini being assumed to be correct. In many instances the departures from constancy of the eM values are certainly beyond the probable experimental error. For most elements, however, the data on these departures are so meager as not to warrant discussion a t this time. However, for phosphorus and silicon compounds, the data suffice to show a distinct trend of the experimental ep or esi values with the ratio, Np or Nsi, of the number of phosphorus (or silicon) atoms to the number of qxygen Variation of
ey
TABLE 2 in phosphates and silicates
Np OR Nsi
0.250
4737
4737
0.286 0.333 0.400 0.250 0.333 0.500
4719 4696 4658 3141 3129 3110
4719 4693 4658 3141 3131 3110
atoms in the crystal or glass. This is shown in table 2. Theexperimental values are fairly well represented by the following equations: ~p
= 4870
- 530Np
(3)
= 3172
- 123Nsi
(4)
These equations would of course not be expected to hold in crystals containing more than one kind of ion of large charge ( > 2). Another way of representing the variation is shown in table 3. As an approximation, we may consider adjacent silicon and oxygen atoms to be joined by electron-pair bonds, with only ionic forces between the oxygens and other adjacent atoms (ions), such as sodium, potassium, calcium, etc. Five types of Si04 groups can then be distinguished, differing in the number of oxygens which are shared with other silicons. To each of these types one can assign a definite esi value, consistent with equation 4. If this point of view and the numerical values deduced are correct, it follows that instability results if a crystal or glass contains Si04 groups of two types which are not adjacent in table 3. For example, a glass of composition inter-
ENERGY ABDITIVITY IN CRYSTALS AND GLASSES
b
b
b
... .
.
...
325
326
MAURICE L. HUGGINS AND KUAN-HAN SUN
kcal.
kcol.
7000-
- 7000
6500-
- 6500
>
Te
~ -
1500t
I
Be
1000-
Zn ,.
Cd -
H!-
CO
Sr
Bo
-
--
500 JH
1000
0
-
89
500
ci
Rb
mediate between NazSizOs and Na2SiOa would contain SiO, groups of the second and third types shown in this table, but not (if thermodynamically stable) any of the first, fourth, or fifth types. Any of the fourth type, if present, would tend to react with some of the second type, to give more of the third:
I
0-
I I
-0-si-0-
0
+
I
-0-si-0-
0
I
AI
3137
3123
-
I
0 2 -0-di-0-
A' 2(3131)
327
ENERGY ADDITIVITY IN CRYSTALS AND GLASSES
This reaction would result in an increase in stability of about 1kg.-cal. per “mole” of each SiOc group reacting. It seems reasonable t o assume that this is an example of a general principle of silicate chemistry (2): If true, it enables one to determine from the over-all composition alone (provided no other ions of charge > 2 are present) the types of SiOc groups (table 3) present and the relative amounts of each type. Many
A“ 2.8
2.6
2.4
2.2
2.0
I.8
1.6
\. 4
S A U
COORDINATION
NUMBERS:
02
a3
04
0s
08
FIG.2. Interatomic distances in oxides, plotted so as to show the relationship to the Periodic System.
of the properties of silicate glasses (e.g., viscosity and its temperature dependence) are doubtless closely related to composition, in terms of those Si04 types. Similar remarks are applicable to phosphate systems and probably also t o aluminates, borates, etc. The available data on hydrogen-containing compounds seem also to warrant classification into several subdivisions-hydroxyl compounds, bicarbonates, bisulfates, (solid) acids. Separate values have therefore been computed and included in table 1.
328
MAURICE L. HUGGISS AND KUAN-HAN SUN
Examination of the numerical values in table 1 shows, as mould be expected, a primary dependence of the eM values on the number of units of charge on the ion M. Next in importance seems to be the interatomic distance between M and 0 atoms. For a given charge on M, the smaller the M-0 distance the greater is the eM value. This is shown by a comparison of figure 1, showing many of the eM values, with figure 2, showing observed interatomic distances in corresponding oxides. A third factor is doubtless the coordination number of M-that is, the number of oxygens around it in the glass or crystal. Variations in coordination number are probably responsible for some of the irregularities shown in figure 1, and also for many of the differences between the experimental eM values computed for different compounds of the same element. In conclusion we wish to emphasize the fact that the eM values computed in this paper are only approximate average values and that theoretically they should not and experimentally they do not give accurate energies of formation by simple additivity. Nevertheless, the approximate constancy and additivity of the eM values are useful, and comparisons of their magnitudes show correlations with the structures of atoms, crystals, and glasses which, in our opinion, are not as well shown in any other way. SUMMARY
1. Values have been computed for the energies of formation of a large number of oxygen-containing inorganic crystals and glasses from their component ions in the gaseous state. 2. These energies of formation can be computed approximately by the addition of energy constants characteristic of the component positive “ions” (elements other than oxygen). 3. These energy constants depend primarily on the ionic charge, but also on the interatomic distance between positive and negative ions, on the coordination numbers, and on other factors. 4. Minor deviations from constancy of the energy constants for phosphorus and silicon can be related to variations in the phosphorusloxygen or siliconloxygen ratio stnd so to the proportion of oxygens in the POI or Si04 groups which are shared with other phosphorus or silicon atoms. 5. Si04 or .PO4 groups differing by more than one in the number of shared oxygens tend to react together and so probably exist together only rarely, if a t all, in the same substance. BEFERENCES (1) BICHOWSKY, F. R., AND ROSSINI,F. D.: The Thermochemistry of the Chemical Substances. Reinhold Publishing Corporation, New York (1936). (2) HUGGINS, M. L., SUN,K.-H., AND SILVERMAN, A . : In J. Alexander’s Colloid Chemistry, Theoretical and Applied, Vol. V., p. 308. Reinhold Publishing Corporation, New York (1944). (3) LATIMER, W. M.: The Oxidation States of the Elements and their Potentials in Aqueous Solutions. Prentice-Hall, Inc., New York (1938). (4) SHERMAN, J.: Chem. Rev. 11,97-170 (1932).
,
