COMPRESSIBILITIEB OF SILICATES : LizOSi02
May, 1957
The heat for the over-all reaction (equations 2a and 2b), as calculated from the slope of Fig. 2 is therefore equal to 26,000 3600 cal./mole. It is clear that this heat consists of two terms, the heat necessary to dissociate one mole of InP (eq. 2a), and the heat involved in dissolving some of the remaining InP in the indium resulting from the dissociation (eq. 2b). Since the solubility of InP in indium increases with temperature,u the heat of solution also increases, so that a linear relationship between log p and 1/T should not really be expected. It will be shown, however, that the heat of the reaction 2b is small over most of: the temperature range of Fig. 2, and in fact falls within the experimental error of the value calculated for the heat of the over-all reaction. The heat required for reaction 2b can be estimated from a knowledge of the phase diagram for the system In-InP.Io By plotting the logarithm of the liquidus composition on the InP side of the eutectic against the inverse of the freezing temperature, one can calculate the molar heat of solution of InP; if the melt behaves ideally this heat should equal the heat of fusion of InP. Only the points from about 800” down to the eutectic temperature can be used, however, since above that temperature the liquidus curve begins to flatten markedly, indicating increasing dissociation of the compound in the molten state; the interpretation of the data is then no longer simple. To calculate the heat for reaction 2b, it is only necessary to multiply the molar heat of solution of InP by the number of moles of InP soluble in one g-atom of indium a t a given temperature. It was found that up to 900” the heat of reaction 2b was less than the experimental error of the over-all heat of the reaction, as determined from Fig. 2. Above 900” the log p vs. 1/T curve should increase somewhat in slope but this effect apparently is obscured by experimental error. From the portion of Fig. 2 below 900” we can therefore calculate a value of 26,000 f 3600 cal./mole for the dissociation en-
*
(9) The phase diagram of the system In-InP has been determined by M. W. Shafer of the College of Mineral Industries, Penna. State Univ. (to be published). The system is simple, showing complete miscibility in the liquid state, immiscibility in the solid state, and a simple eutectic. The flatness of tho liquidus curve near the melting point of InP indicate8 dissociation of the compound in the molten state. (10) See. for example, ref. 7, chapter X.
515
ergy of indium phosphide into liquid indium and phosphorus. To find the cohesive energy it is necessary to add to this figure the heat of vaporization of liquid indium and one quarter of the heat of dissociation of PI molecules into phosphorus atoms. From published data, we find 56,000 cal./g. atom for the former* and one quarter of 288,000 cal./mole for the latter.” The cohesive energy of InP is thus 154,000 cal./mole in the temperature range investigated. It is of interest to compare this result to the cohesive energy of InP as calculated on the model of purely ionic bonding between the components, Msuming singly charged indium and phosphorus ions.12 Using the Madelung constant for the zinc blende structure and the known inter-atomic distance for InP, lo one obtains a value of S+,OOO cal./mole. In making this calculation the ionization energy of indium was taken as 132,000 cal./g. atom,bb while the electron affinity of phosphorus had to be estimated by Mulliken s rulela; a value of nine was taken for the compressibility parameter n. Any reasonable value for n and for the electron affinity of phosphorus yield a cohesive energy for InP, aa calculated on a purely ionic model, which is far smaller than that determined experimentally. One, therefore, reaches the not too surprising conclusion that the bonding in the compound is largely covalent. Comparing the cohesive energy of indium phosphide t o that of two gram atoms of germanium, ~ ’ finds that the former is namely, 178,000 ~ a l . , one somewhat smaller. This result seems to conflict with Welker’s prediction1‘ that 111-V compounds would have a greater bond strength than the bracketed Group IV element due to the partly ionic nature of the bond. It seems plausible, however, that this prediction would a ply more readily to “horizontal” 111-V compoundps (ie., both elements in the same Period) than to “diagonal” ones, in which the atoms differ markedly both in nuclear charge and in size. (11) (a) F. 8. Dainton, Tram. Faraday rSoc., 48, 244 (1947): (b) Q. Wetroff, Compl. rad., 906, QOa (1939). (12) See F. Seito, “The Modern Theory of Solids,” Ch. I , McUrawRill Book Co., New York, N. Y., 1940. (13) L. Pauling, “Nature of the Chemioal Bond,” Cornell Univ. Press, Ithaca, N. Y., 1948, Ch. 11. (14) R. E, Honig, J . C h s m Phys., 91, 1610 (1964).
THE COMPRESSIBILITIES OF THE SILICATES : THE LizO-SiOz SYSTEM BY HARRYBLOOMAND JOHNO’M. BOCKRIS The John Harrison Laboratories of Chemistry, The University of Pennsylvania, Philadelphia, Pa. Received Augus: S, 1068
Two models for the liquid silicates indicate different courses for the compressibility isotherms as B function of composition. An apparatus is described which permits measurement of the compreseibilities of liquids up to T = 1350’. Compressibilities have been measured for the LizO-SiOp system over the composition range 2455% L&O. Results are in disagreement with the classical model and give some support t o the discrete anion model.
Introduction In the classical view of the structure of liquid silicates1it is assumed that the orthosilicate compo(1)
Cf.H. Stanworth, “The Propertiesof Glass,” Oxford, 1950, p. 89.
sition (66.7 mole % Mz0)2 consists of 4M+ and Si0.i4- ions. Addition of silica t o this composition results in the formation of ailicon-oxygen chains in (2) Throughout this paper, compositions are given in mole %.
616
HARRY BLOOM AND JOHN O’M. BOCKRIS
which each Si atom has attached to i t two charged 0 atoms. The M + is assumed to be located in wells of minimum potential energy near an 0atom. This theory requires lengthening of the chains as the proportion of Si09 increases, the length tending to increase indefinitely as the composition of the mixture approaches 60% SiOz. Further addition of Si08 causes the structure to become two dimensional, the extent of the ionic sheets increasing until the Si02 content is 66.7%, when further addition causes the sheets to give way to a threedimensional structure. This threedimensional structure becomes more extensive with further addition of SiO, tending eventually to the three-dimensional structure of pure silica. A model for the liquid silicate lattice has recently been which differs from the classical one in that instead of the infinite chains and two-dimensional sheets of this theory, it postulates the existence of discrete cyclic silicate anions, essentially polymers of the ion SiaOp6-, which exist a t compositions between 50% M20 and about 10% MzO in the alkali oxide-silica systems. At compositions near to 1070, three-dimensional bonding is supposed to be taken up throughout the structure which in these low Mg0 contents then becomes identical to that of the classical theory. These two theories of the liquid silicate structures therefore differ essentially in the composition at which the three-dimensionally bonded lattice is supposed to be taken up. As the extent of continuously bonded areas of Si-0 becomes larger in the liquid lattice, the compressibility of the liquid silicate should become less. Thus, if the classical theory were correct, inflections should occur on the compressibilitycomposition isotherm at the 50% M80 composition (where a rapid increase of S i - M i chain length occurs), and again a t 33% MrO, where the structure commences to exhibit three dimensional bonding. Because from a composition of 33% M z O to pure SiOz, the three-dimensional bonding 18 gradually taken up, there should be no particular inflection in the compressibility isotherm a t composition of less than 33% M20. Conversely, according to the discrete ion theory, the ion type and shape is supposed to remain una1tered between the compositions 50 and 10% MzO; the size of the cyclic anion uniformly increasing until this latter composition. The compressibility would be expected to decrease smoothly over the range 50-10% and undergo a rapid decrease at compositions of less than 10% MzO, where, according to the discrete anion theory, there commences a rapid spread of three-dimensional (silica-like) bonding. The compressibility isotherms thus proffer a clear diagnostic in distinction between classical and discrete ion theories.
Experimental Ultrasonic velocity measurements were made by the method of Richards, Brauner and Bockris.’ Use is made (3) J. O’M. Bockris and D. C. Lowe, Proe. R o y . Soc. ( L o n d o n ) ,PPBA, 423 (1954). (4) J. O‘M.Bockrin, J. W. Tornlinnon and J. L. Wbite, Trans. Faraday Soc., 61, 299 (1956). (5) J. O’M. nockris, J. D. Mackonzie and J. A. Kitchener, ibid.. 61, 1734 (1055).
Vol. 61
of phaae interference of two wave trains, one passing through the liquid, and the other, a reference signal. For measurements on liquid silicates, several modificatione to the technique of Richards, et al., were made. Heating waa carried out in a carbon tube resistance furnwe similar to the one described by Mackenaie.’ Control of furnace temperature could be obtained by manual adjustment of the over 30 minutes. As the time m “Powerstat” to quired to take 5 duplicate measurements of wave length ie of this order, such temperature control is satisfactor Tern erature was measured by means of calibrated 20% R h d t v8. 40% Rh-Pt thermocouplee in Alundum sheaths. The crucibles for containing the melt were manufactured by a process described by Todinson, el ai.,@from mol bdenum sheet of thickness 0.006”. Specially ductile b o sheet waa used for the bottoms. The crucibles were 1.5” in diameter and 6” tall. The rods used for propagatin the ultrasonic vibrationa were high density Alundum. h e y wefe circular in crosssection, 0.6” diameter by 18” long, m t h flat ends. The accuracy of measurement de ends largely on the flat nature of the ends of these rods. the alumina waa rapidly attacked by the liquid the end in the melt became eeriously corroded after two or three hours and did not allow accurate measurement after that time. The ends were therefore ground flat after each run. During a run, the alumina rods were supported in two clamps, which were attached by means of a long screw to the upper end and lower parts of the frame, respectively. The rods could be advanced or retracted in the furnace by meana of knurled nuts working in the clamps. To the cool end of each rod, a barium titanate, pieaoelectric transducer waa cemented. The transducers were 0.5” in diameter. The crucible containing the weighed mixture of lithium carbonate and owdered uarta waa supported on the top face of the lower d n d u m ro8. The furnace waa waembled, helium assed in and the tempefature brought up to just about the iquidus temperature within 6 houra. Heating waa continued at this tem erature overnight so aa to decompose all the carbonate an$ meaaurernents of sound velocity were begun. Ultrasonic vibrations generated by the bottom transducer pasaed viu the bottom of the crucible into the melt and after being pro agated thmu h it, were picked up by the upper alumina r o z conducted i o n g the rod to the transducer at the top and converted by this transducer into electrical impulses. The wave train from the upper transducer was mixed with the attenuated direct signal In the electronio apparatus as described by Richards, et al., and complete interference resulted when the two wave trains wgre out of phase. When this took place, a null was observed at a celc tam position on the cathode ray tube detector. The upper rod was advanced or retracted until a second complete null xpeared in the same position on the cathode ray screen. e distance traversed b the upper rod between the two nulls w a then ~ the wave %ngth of the ultrasonic vibration In the melt. During this process the attenuation wm checked to ensure that the direct signal waa reduced in amplitude to the same amount as that of the transmitted eignal. The frequency ( v ) was measured by a frequency meter and was checked during each reading for constancy. From the frequency and wave length (A) the velocity of the ultrasonic vibrations in the melt was calculated from the equation JI = Y X. The displacement of the up er rod waa made to cover three or four complete wave len tg, EO that a more accurate measure of wave length coufd be made The dis lacement of the upper rod was measured by mean; of a cattetometer. At least six readings were taken a t each temperature. The first measurement was taken at 20’ above the liquidue tem erature. The temperature was increased by amounts of &out 20’ and measurements taken at each new temperature up to 1300’. This upper limit was the tem erature at which absorption of the ultrasonic vibrations by t i e alumina rods became too great to enable further measurements to be made.
1s
f!
(6) N. E. Richarda. E. Brauner and J. O’M.Bockris, British J . Applied Phya., 6, 387 (1955). (7) J. D. Mackeneio, The&, London, 1954. (8)-1. W. Tornlinson. D. C. Lowe,G. W. hfellors and -1. O’M.Bockria, J . Sci. In&., 81, 107 (1954).
t
May, 1957
COMPRESSIBILITIES OF SILICATES: Ili~OSiOz
617
TABLE I
RESULTS I N THI LilOSiO, SYSTEM Composition mole % LirO
Velocity, tu. sec. 1150'
12600
1300°
1150'
25 .. .. 2850 ... 30 3000 2890 2725 2.179 32.8 3000 2900 2700 2.171 37 3000 2850 2475 2.159 .. 2490 2120 ... 43 55 .. 1930 1500 ... The reproducibility of velocity measurements at each tem erature was &lo0 meters/sec., i.e., 3-651,. dxtures were made up by weighing calculated quantities of lithium carbonate and powdered quartz into a bottle which was shaken for 30 minutes. The uarts was washed with boiling, concentrated HCI, followed\y distilled water, and dried. The lithium carbonate (A. R. Quality) had been heated in an oven at 200' for 4 hours and cooled in a desiccator. Duplication of measurementswaa carried out on several compositions. Reproducibility wm obtained to within
Denaity 12000
...
2.166 2.169 2.148 2.128 2.066
-Compressibility-
laow 2.17 2.10 2.15 2.13 2.11 2.04
(am.*dyne-') iaooo
ll6O0
0.3 5.1 5.1 5.1
.. ..
.. 6.5 5.5 5.7 7.0 13.0
1300O
5.7 6.3 6.4 7.7 10.0 21.8
I
3-6 yo.
Results Velocity ( u ) , density ( p ) and adiabatic compressibility (0) are given a t 1150, 1200 and 1300" in Table I. Figure 1 shows velocity isotherms as a function of composition a t the same three temperatures and Fig. 2 shows isotherms of the adiabatic compressibility (calculated from the general equation u = as a function of composition. Discussion Figure 2 shows clearly that there are no breaks in the compressibility isotherms corresponding to the changes in nature of the silicate groups present in the liquid according to the classical theory.' The isothermal compressibility does, however, decrease uniformly, as required by the discrete anion Fig. 1.-Velocity of eound in meters r second 88 a function model, over the composition range 55% M20-25% of the molar percentage of Ghium oxide. M,O. That this change of isothermal compressibility (p.) with composition is consistent with the form expected according to the discrete ion model for liquid silicates may be demonstrated in two specific ways. Firstly, the discrete ion theory indicates that a t any given composition of the silicate between 66% M,O and 10% MzO, the predominant silicate anions should have a characteristic length. Further, between CM,O = 50% and CM,O = lo%, the crosssection of the silicate anion should be constant, whilst the length, I , should increase with decrease of CM,O. If pa (exptl.) is plotted against the theorctical value of 1 calculated6on the basis of the discrete anion theory, it is found that
dim
8.
1
e
*fly
(1)
over the composition range 50%-24% M,O. Hence, as, over this range according to the discrete anion
theory, the cross-sectional area of the silicate anions is supposed to be constant, the empirical result (1) is equivalent to the relation
Fig. 2.-Compressibilit in cm.* dyne-' as a function of the molar composition o t t h e molar percentage of lithium oxide.
where VA is the molar volume of the silicate anion. However, according to the theory of liquids in terms of holese
where AVM is the change of volume on melting and V M is the molar volume of the liquid. The change of AVM on composition would not be expected to be great in a series of similar liquid6 such a8 the lithium silicates between the composition range 50-
81
(9)
R. Furth, Proc. Camb. Phil. Soc., 87, 252 (1941).
0:
u (A
vM/v~)
(3)
518
E. A. MOELWYN-HUGHES AND R. W. MISSEN
2401, LLO. Let it be assumed here to be negligible. VM for a pure electrolyte C+A- can be regarded as having effectively the value (VCVA)'/~, where Vc is the molar volume of the cation, which in the system a t present under consideration is VLI, and is constant for the series of liquids examined (whilst VA va.ries, if the discrete anion theory is correct). Hence, for a system such as the lithium silicates over bhc range of compositions stated, V M a VA'/*. It follows that for the systems considered equation 3, based on the general theory of holes in liquids, takes t8hespecial form
Vol. 61
that an inflection in the compressibility-composition relation occurs between CM!O = 25 and CM,O = 0%. If the inflection im lied in Fig. 2 is assumed to occur approximately alf way between 0 and 25% L&O, the composition a t which it takes place is about 12% LizO. However, it is just at a composition near to this, namely, 10% LiaO, that, according to the discrete ion theory,a there is a radical change in the structure of the liquid, the discrete ion structure becoming, for compositions containing cLilo < lo%, a partially broken down threedimensional lattice. The latter structure would be expected to have a considerably lemer compressi(4) bility (Le,, fewer holes per cc.) than that of a series of if A V M is assumed independent of composition and discrete ions of nearly the same Si/O ratio (where tho discrete anion theory is applicable. The theo- holes and free space exist), so that the compressiretical equation 4 therefore has the same form as bility would indeed be expected to undergo a sudthe empirical equation 2, thus lending support to den decrease in just that region of composition where the assumptions made in the deduction of 4. the experimental results of Fig. 2 suggest that such Secondly, the dotted line in Fig. 2 (obtained by a decrease occurs. extrapolating the experimental relation shown by Acknowledgments.-The authors are grateful to the solid line to the value for the compressibility of vitreous Si02 at the same temperature'O) suggests the Atomic Energy Commission for a grant in support of this work under Contract Number AT (10) W. G. Cady," Piezoeleotricity," Academia Praas, New York, (30-1)-1769. N. Y., 1946, p. 140.
K
I:
t
THERMODYNAMIC PROPERTIES OF METHYL ALCOHOLCHLOROMETHANE SOLUTIONS BY E. A. MOELWYN-HUGHES AND R. W. MISSEN Department of Physical Chemistry, University of Cambridge, Cambridge, England Received August 10, I066
Exccss frec energies and heats of mixing have been measured at 35' for binary solutions of methyl alcohol and methylene dichloride, chloroform and carbon tetrachloride, respectively. The excess entropies of mixing obtained from them show that the systems are very irregular. The abnormal behavior is most marked for solutions dilute in alcohol. For these solutione the partial molar properties of the alcohol become very large as dilution is increased. This behavior requires exponent!af equatiow for an adr, irate description of the compsitional de endence of the thermodynamic functions, but wer-aeries efractive ingces of the solutions have also been measured a g o ' equations are apppliea%lc a t most compositions.
Several theories have been advanced recently of binary solutions of which one component is an alcohol.' The experimental data with which any of them can be compared, however, are often inadequate in that the entropy changes which occur on mixing are not obtained from free energy and thermal changes measured at the same temperature. As part of a program2 of investigating properties of solutions, we have measured free energies and heats of mixing of solutions of methyl alcohol with methylene dichloride, chloroform and carbon tetrachloride, respectively, at 35". The free energy changes for methyl alcohol and carbon tetrachloride solutions at this temperature have been well defined by Scatchard and his co-worke r ~ and , ~ those ~ ~ for methyl alcohol and chloroform solutions by Kireov and Sitnikov; but the See, for example, J. A. Barker, J . Cham. Phys., SO, 1526 (1052); Kretschmer and R. Wiebe, ibid., 82, 1607 (1954). E. A. Moelwyn-IIiighos and R. W. Missen, Trans. Faradnfl Soc., in preaa. (3) 0.Scatchard, 8.E. Wood and J. M. Mochcl, J . Am. Chen. Soc., 68, 1960 (1946). (4) G. Scatchtlrd and J,, R. Tioknor, ibid.. 74, 3724 (1952). (6) V. A. Kireev and I . 1'. Sitnikov, J . P h y s . Chem. (U.S.R.R.), 16, 492 (1041).
thermal changes have not been similarly treated. It is known, however, that these solutions have large, non-zero excess entropies of mixing, and are thus far from regular in Hildebrand's sense.e As far as we know, there is no other available information about the behavior of mixtures of methyl alcohol and methylene dichloride. Experimental Purification and Physical Properties of the Liquids.The purification and physical properties of the methylene dichloride, chloroform and carbon tetrachloride used have been described.* A. R. methyl alcohol waa purified by fractionation, the roduct being removed over a temperature range of 0.0f to 0.04" It had a refractive index (+D) of 1.3287 and a density'(d26,) of 0.7867. Vapor ressures measured at 5" intervals in the e uilibrium still from 25 to 65' are reproduced by equation ?l) with a standard deviation of 0.4 mm. loglo p0 = 17.3506 - 2.9314 logio T 2383.7/T (1) in which p0 is the vapor pressure, mm. and T the absolute tem erature, and the constants were determind b the mettod of least squares. The boiling point calcuIateJfrorn this equation is 64.59". Apparatus.-Excess free energies of mixin were calculated from equilibrium data measured in a modkfied Gilespie,
b1
-
(6) J. H. IIildebrand, J . Am. Chem. Boc., 61, 66 (1929); Faraday SOC.Disc., 16, 3 (1953).
c+ I
I I
