J. Phys. Chem. 1985, 89, 1695-1699
1695
6. Summary
2. A method of calculating the variation of bond length with coordination number for a crystalline binary compound with a given stoichiometry (eq 5 ) . 3. A set of internally consistent equations for the prediction of W W ) ,W , and M W ) / W . 4. An equation for the Madelung component of the lattice energy (eq 8) which is more reliable than Kapustinksii's familar relationship (eq 11).
The arguments presented here lead to four significant results. 1. A simple geometrical model for the estimation of Madelung constants for crystalline binary compounds.
Acknowledgment. We are grateful for the generous financial support provided by the Robert A. Welch Foundation (Grant No. F08 1).
The factor 0.8738 is one-half the Madelung constant for the NaCl structure and is only slightly larger than the factor given in eq 8 (0.8571). However, eq 11 does not consider the effect of the ratio a / b and gives predictions which are generally less reliable (mean absolute error = 8.6% for the crystals in Tables I and 11) than those of eq 8.
MgO of Very High Energy Content from Decomposition of Mg(OH), Dario Beruto,t* P. F. Rossi,t and Alan W. Seamy** Istituto di Chimica, Facolta di Ingeneria, Universita di Genova, Genoa, Italy, and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, and Department of Materials Science and Mineral Engineering, University of California, Berkeley, California 94720 (Received: September 11, 1984)
In an effort to determine the reason that the H 2 0 produced by decomposition of Mo(OH)~in effusion cells approaches apparent equilibrium pressures only -lo4 times the expected equilibrium pressures, the heat of solution of MgO in HC1 solutions was measured as a function of the area of the surface accessible to N2 gas. Excess heats of formation of MgO as great as 73 kJ (17 kcal) per mol of MgO were measured for particles of N2-accessiblesurface areas of -300 m2/g, but of probable total surface areas of -600 m2/g or more. The activities calculated for the MgO from the excess heats are high enough to account for the low equilibrium H 2 0 pressures.
Introduction In 1958 Kay and Gregory' reported the surprising observation that when a well-established method2*,for obtaining equilibrium pressures from Knudsen effusion measurements was applied, the reaction Mg(OH),(s) MgO(s) + H,O(g) (1) yielded apparent equilibrium pressures of H20(g) which were only lo-" times the clearly reliable equilibrium pressures that Giauque and Archibald had measured by a static t e c h n i q ~ e . A ~ similar observation has since been made for MgCa(C03)2decompo~ition.~ For C a C 0 3 decomposition, the measured pressures of C 0 2approach the expected equilibrium pressures in a Knudsen effusion cell, but the pressure established in a C a C 0 3 powder bed heated in an open crucible under vacuum is that characteristic of an equilibrium source for which the C 0 2 pressure is less than times the expected equilibrium pressure for the rea~tion.~,' Kay and Gregory called this kind of apparent equilibrium behavior a pseudoequilibrium. We will call it an anomalous equilibrium to emphasize that although the phenomenon has not been understood, its origin is almost certainly not experimental error or flawed theory; some kind of equilibrium must have been approached in each of these decomposition reactions. The tests for approach to equilibrium both in open crucibles' and in effusion cell^^^^^* depend upon the same straightforward principle. In an open cell, the flux of molecules supplied to the vapor phase by the solid reactant must increase in direct proportion to its surface area. If the reaction is completely irreversible, the weight lost by the crucible will be directly proportional to that surface area. The fact that the rate of weight loss of an open cell that contained CaCO, was almost unchanged when the surface area of C a C 0 , was increased more than a factor of 10 implies that the COz pressure must be determined by a reaction that approaches equilibrium in the powder bed. In an effusion cell
-
-
f
Instituto di Chimica, Universita di Genova. Lawrence Berkeley Laboratory.
0022-3654/85/2089-1695$01.50/0
the sample surface area is held constant and the orifice area is varied; the fact that the flux per unit area that escapes through the orifice approaches a constant value as the orifice area approaches zero is evidence that the vapor is undergoing a reaction in the cell that approaches equilibrium. One kind of unstable equilibrium in an effusion cell has been demonstrated by Lau et al.9 Under the conditions they established, the equilibrium reaction is MgS04(s) MgO(s) S02(g) + '/202(g). But when relatively large orifices are used, the principal reaction is MgSO,(s) MgO(s) SO,(g), and extrapolation of large-orifice data to zero area yields the correct equilibrium pressure for this second reaction. The apparent approach to equilibrium is unstable in the sense that some SO2and O2are formed even when SO3 is the principal product, and as the orifice area is decreased the relative quantities of SO2 and O2 continuously increase. With sufficiently small orifices the equilibrium pressures of SO2 and O2 are approached. For carbonate or hydroxide decompositions, the only significant gaseous product is C 0 2 or H 2 0 , so the anomalously low gas pressures in a carbonate or hydroxide decomposition imply that the gaseous product is in equilibrium with the reactant and with the solid oxide component in some form of high chemical activity. That is, in a two-component system of the kind described by reaction 1, the chemical activity of the gaseous reaction component,
-
-
+
+
(1) Kay, E.; Gregory, N. W. J . Phys. Chem. 1958, 62, 1079. (2) Whitman, C. I. J . Chem. Phys. 1951, 20, 161. (3) Motzfeld, K. J . Phys. Chem. 1955, 59, 139. (4) Giauque, W. F.; Archibald, R. C. J. Am. Chem. SOC.1937, 59, 561. (5) Powell, E. H.; Searcy, A. W. J. Am. Cerum. SOC.1978, 61, 216. (6) Knutsen, G. F.; Beruto, D.; Searcy, A. W. J. Am. Cerum. SOC.1982, 65, 219. ( 7 ) Searcy, A. W.; Kim, M. G.; Beruto, D. In 'High Temperature Materials Chemistry-11"; Munir, Z. A., Cubicciotti, D., Eds.; The Electrochemical SOC.:Pennington, NJ, 1983; p 133. (8) Searcy, A. W.; Buchler, A,; Beruto, D. High Temp. Sci. 1974, 6, 64. (9) Lau, K. H.; Cubicciotti, D.; Hildenbrand, D. L. J . Chem. Phys. 1977, 66, 4532.
0 1985 American Chemical Society
1696 The Journal of Physical Chemistry. Vol. 89, No. 9, 1985 ug,and that of the solid reaction component, a,, are related by
up, = K,and if the activity of each component is defined as unity when the stable equlibrium pressure P, is established, then when the anomalous equilibrium pressure P,, is established, us = (1 /u8) = P,/P,,. Thus, because Pae= 10-4P,, for reaction 1 a, = IO4 a t about 670 K. If this is the activity of the solid reaction component, its molar free energy content is calculated to be 670R In IO4 = 51.3 kJ/mol(12.3 kcal/mol) greater than that of the solid oxide in its standard state. Such a high free energy content would be expected only if the solid product is amorphous or is a metastable crystal modification. But X-ray diffraction observations1-1b12 and transmission electron microscope (TEM) studies13J4 indicate only the stable NaC1-type MgO to be produced. Earlier reports of solid products other than MgO in its stable NaC1-type crystalline form have been shown to be consequences of i m p ~ r i t i e s . ' ~ Reis has confirmed the anomalous pressure measurements of Kay and Gregory and has measured as functions of the extent of completion of the reaction the total surface area, the X-ray patterns, and the heats of solution in hydrochloric acid of mixtures of MgO and Mg(OH)* produced in an effusion ce11.16 None of these measurements showed evidence that anything other than NaCI-type MgO of constant small particle size was produced during the course of the reaction. The possibility remains that during decomposition an unstable solid intermediate is present in quantities too low for ready detection by X-ray diffraction or TEM. If, for example, a layer of a high-activity intermediate transforms irreversibly to the stable solid product as a consequence of accumulated strains when its layer thickness is only 1 nm, the intermediate could go unobserved; yet the gaseous product and reactant could be in equilibrium with the intermediate rather than the stable product. Additional TEM studies have been undertaken to evaluate this possibility.'' Decomposition of Mg(OH)z, MgCa(C03)2,and CaCO, under vacuum are alike in that the solid product oxides have high surface areas. The MgO which Giauque and Archibald4 produced by reaction 1 had an enthalpy of formation about 4 kJ/mol more positive than expected from other careful measurements. Giauque18 suggested that this difference must arise from a high (but unknown) surface area. Natarajan et al.19confirmed by solution calorimetry the fact that the molar enthalpy of MgO increases with decreasing particle size, but they concluded that their data supported the suggestion of Rao and Pitzerm that the high enthalpy reflected high concentrations of internal defects. Liveyzl and co-workers, who measured differences of as much as 7-8 kJ between heats of solutions of MgO samples of high surface areas (1 53-267 m2/g) and a sample of 4.5 m2/g surface area, pointed out that the various samples retained enough water to form almost a monolayer of water on the MgO surface, and they suggested that this water may significantly reduce the measured heats of solution. Furthermore, Thomas and Baker lo measured X-ray diffraction line broadening for the samples of Livey et al. and concluded that the measured variations in heats of solution are primarily consequences of variations in surface energy, not of strain. The enthalpies of solution that have been measured for MgO prepared by reaction 1, whatever their origins, are far too low to indicate that the chemical activity of the MgO is IO4. But it seemed possible that the surface energies of MgO in the calorimetric experiments so far carried out were substantially reduced (IO) Thomas, D.; Baker, T. W. Proc. Phys. SOC.,London 1959, 74, 673. (1 1) Cemino, A.; Porta, P.; Valigi, M. J . Am. Ceram. SOC.1966, 49, 152. (12) Librant, 2.;Pampuch, R. J . A m . Ceram. SOC.1968, 51, 109. (13) Anderson, P. J.; Horlock, R. F. Trans. Faraday SOC.1%2,58, 1993. (14) Gordon, R. S.;Kingery, W. D. J . Am. Cerarn. SOC.1966, 49, 654. (15) Brett, N. H.; Anderson, P. J. Trans. Faraday SOC.1967, 63, 2044. (16) Reis, T. Ph.D. Thesis, University of California, Berkeley, 1983. (17) Kim, M. G.; Dahmen, U . ; Searcy, A. W. Lawrence Berkeley Laboratory, Berkeley, CA. LBL Report No. 18972. (18) Giauque, W. F. J. A m . Chem. SOC.1949, 71, 3192. (19) Natarajan, M.; Sarma, T. S.; Ahluwalia, J. C.; Rao, C. N. R. Trans. Faraday SOC.1969, 65, 3088. (20) Rao. C . N. R.: Pitzer. K. S. J . Phvs. Chem. 1960. 64.,~ 282(21) Livey, D. T.; WanMyn, B. M.; Hewitt, M ; Murray, P. Trans. Br. Ceram. SOC.1957, 56, 217. 1
Beruto et al. TABLE I: Spectroscopic Analysis of Mg(OH)2 Powders elements
wt %
elements
Si AI B
0.25 0.01 0.20 0.02 0.15
Ba Na
Fe Ca
cu
Mn C
,
wt % 0.001 0.07 0.02 0.02 0.27
by adsorbed water. Infrared spectra indicate that water is adsorbed as OH- ions.22 These ions, like C032-on Ca0,23may be formed by a reaction that is more exothermic than the reaction of the gas with the solid to reverse the decomposition reaction. We undertook the present study to determine whether for high surface area MgO samples of reduced water content the enthalpies might be high enough to account for the anomalous H 2 0pressures of reaction 1.
Experimental Section Spectroscopic analysis of the Mg(OH)2 powders are given in Table I. Scanning electron microscope pictures showed most powder particles to have cross sections of 0.1-0.2 pm. Powders were pressed into disks in a stainless-steel holder at a pressure of 400 kg/cmz for 1 min at room temperature, although some MgO was prepared from loose powders. The Mg(OH)z samples were heated in a Pt open crucible inside a symmetrical t h e r m ~ b a l a n c e . ~Sample ~ weights ranged from 50.5 to 50.7 mg, usually made up of 6-8 small pressed pieces of 4 X 4 X 0.3 (mm3) average dimension. Surface areas of the initial samples were measured in the same thermobalance by the BET method using N z as the adsorbant at 78 K.25*26 No significant difference was measured between loose powders and pressed specimens. The surface areas averaged 30 m2/g. The samples were heated under a vacuum of the order of 5 X IO" torr at 275 "C until -85% of the theoretical weight change of reaction 1 was obtained. Then the samples were heated at 600 "C for 12 h, when no further weight change was recorded at a sensitivity of 4 X lo4 mg/min. This treatment is sufficient to decompose MgCO,, the probable phase in which carbon is present. If silicon and boron (see Table I) are assumed to be present as MgSi03 and MgBZO4and the B2O3 is assumed to remain in the sample, the heating expels 100% of the water. If silicon is present as S i 0 2 and all the B203escapes on heating, up to 2% of the H 2 0 is calculated to remain in the sample. Surface areas were measured without opening the apparatus to air. But even if cooled under vacuum to room temperature, the samples gained up to 0.3% of the original weight. This problem was overcome by introducing liquid nitrogen containers around the quartz furnace tube when the temperature was 250 "C. To produce samples with lower surface areas, high surface area specimens were sintered at 550 OC in the presence of water vapor at 345 Pa. The water vapor was removed by heating at 600 OC under vacuum, and the initial weight of MgO was recovered to within 0.01%. Surface areas of the sintered oxides were measured again without exposure to air. The MgO samples were removed from the thermobalance, and a part of each was weighed into a Pyrex bulb 7 mm in diameter. As soon as possible (- 10 min) each bulb was put in a vacuum line and heated to 500 "C for 16 h to drive out the water absorbed during exposure to air. The bulb was sealed and introduced into the calorimeter. To determine the influence of the heating time, some samples were heated at 500 "C under vacuum for only 4 h before they were sealed and put into the calorimeter. The other part of the sample was returned to the thermobalance, and the amount of water taken up was determined quantitatively. After (22) Anderson, P. J.; Horlock, R. F.; Oliver, J. F. Trans. Faraday SOC. 1965. 61. 2754.
(23) Beruto, D.; Botter, R.; Searcy, A. W. J . Phys. Chem. 1984.88, 4052. (24) Beruto, D.; Barco, L.; Searcy, A. W.; Spinolo, G. J. Am. Ceram. SOC. 1980, 63, 439. ( 2 5 ) Brunauer, S.; Emmet, P. H.; Teller, E. J . Am. Chem. SOC.1938, 70, 309. (26) Brunauer, S. "The Adsorption of Gases and Vapors";Oxford University Press: New York, 1943.
MgO from Decomposition of Mg(OH)2
I-
-1
I I
I I
4 I 3 I I I
I
y '
I
The Journal of Physical Chemistry, Vol. 89, No. 9, 1985 1697 TABLE 11: Heats of Solution of MgO and Water Content as a Function of Surface Area water content heats of soh, water as % of monolayer surface area kJ/mol content, capacity of SBEP, m2/g 2 N HCI 12 N HCI mol % (100) MgO planes 48 152.2 1.2 5.7 54 180" 86 156.5 1.2 5.7 1.7 8.1 90 157 106 164.6 193 1.5 7.2 150 172 20 1 1.8 8.6 158
5
I I I I
I
!-T
I
202
196
195.5 205
233 263
220.8
288
2.0 2.0 2.2
230.9 240.7
9.6 9.6
10.5
2.2
205
10.5 10.5
2.2
" Made from Mg(OH), for which a chemical analysis is not available.
,
Hg / 6 -
5
2
5
2 C
,Sample
1
Figure 1. Calorimeter cell equipped for heat of solution studies: (1) lid; ( 2 ) silicon rubber gasket; (3) brass guide; (4) solid Pyrex piston; (5) Pyrex test tube; ( 6 ) stainless steel cell; (7) thin Pyrex sample holder. each thermal treatment under vacuum, surface areas were remeasured. S E M observations were made at up to 30 000 magnification on samples of MgO by procedures that minize rehydratiom6 Heats of solution were measured in a heat-flow, Tian-Calvet type microcalorimeter essentially like that described in the literature (Figure l).27 Outgassed samples of MgO of weights between 1 and 4 mg were opened under an HC1 solution in the calorimeter. High-purity HCl solutions, either 2 or 12 N, were used at 298 K. The calorimeter was calibrated by using the Joule effect in air, under vacuum, and in water. The results agreed with J mm-2, to within 1%. The heat the measured value, 6.68 X J. The cell was released by breaking the Pyrex bulbs was so designed that 4 cm2 of HC1 solution filled the entire space when a bulb was broken. The system was tested with ZnO. For both 2 N and 12 N HCI, the measured values, -97.78 and -121.29 kJ/mol, agreed within 1% with values derived from heats of f o r m a t i ~ n . ~The ~ , ~heat ~ of solution of the initial M B ( O H ) ~in 2 N HCI was -1 18.04 kJ/mol. From this value a heat of formation of -925.98 kJ/mol for Mg(OH)2 can be derived. The accepted value at 298 K is -924.7 kJ/mo1.28
Results SEM examination of the initial Mg(OH)2 particles and of low surface area MgO samples obtained by vacuum decomposition of M o ( O H ) ~and subsequent sintering showed no evident change in external particle shapes. But decomposition increases the area of surface which is accessible to N2from 30 m2/g to as much as 300 m2/g. These observations show that the particles have become microporous. We point out later reasons for thinking that only (27) Calvet, E.;Pratt, H.'Recent Progress in Microcalorimetry", Oxford University Press: New York, 1963. (28) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.;Nuttal. R. L. "The NBS Tables of Chemical ThermodynamicProperties. Selected Value for Inorganic and C, and C2Organic Substances in SI Units". J . Phys. Chem. Ref.Data Suppf. No. 2 1982, I I . (29) Stull, D. R.; Prophet, H. et al. "JANAF Thermochemical Tables", 2nd Ed.; Natl. Stand. Ref. Data Ser. (US. Natl. Bur. Stand.) 1971, NSRDS NBS 37.
I
0
I
I
IO0
I
S ~ E T(m2/gr)
I
200
0
Figure 2. Standard heat of formation AIYH~O~~~ (kJ mol-'(MgO)) derived from heat of solution data vs. apparent surface area of MgO measured by the BET method. (0) points derived from Natarajan and co-worke r ~ ;(0, ' ~ h 0 ) points derived from this study. about half of the internal pores may be accessible to N2. Certainly the measured areas are lower limits to the actual areas. Surface area measurements, calorimetric measurements, and residual water contents are summarized in Table 11. Linear extrapolation of the heats as a function of surface areas in the 100 m2/g range after the heats were corrected for the heat of dilution of HC1 gave -149.1 kJ/mol for the heat of solution at infinite dilution at 298 K. From this value -608.58 kJ/mol can be derived for the heat of formation of MgO with negligible surface. Data obtained with loose powders agreed with those obtained with disks to within 4%. The value reported in the literature is -601.24 kJ/mo1.28 Accordingly, we added 7.33 kJ/mol to our values to normalize the data to the standard, and we corrected the heats of solution measured by Natarajan et al.I9 with 0.1 N HC1 in the same manner for comparison (Figure 2). In the time required for weighing in air, the high surface area MgO took up weights equivalent to 9 mol % water. Heating under vacuum to 250 O C reversed about 40% of this weight gain. Heating under vacuum at 500 O C for 16 h caused no significant change in surface areas but caused the weights to decrease to the equivalent of 1 mol % more water than was present when the MgO samples were first exposed to air. Because those samples contained from 0 to 2% water, depending on interpretation of the analyses (see Experimental Section), the water content of the samples introduced into the calorimeter can be identified as from 0.015 to 0.039 mol of H20/mol of MgO. Water contents in Table I1 are averages of those calculated from the range of analytical uncertainty. The fractional coverages of surface sites were calculated by using the assumptions22that the MgO is formed of uniform cubes with (100) planes exposed and that each 02-ion
1698 The Journal of Physical Chemistry, Vol. 89, No. 9, 1985
Beruto et al. From cleavage experiments, Gilman31arrived at a recommended value of 1200 mJ/mz for MgO. Values of 2000-3000 mJ/mz have been measured at room t e r n p e r a t ~ r e , ~but ~ . ,Gilman ~ concluded that plastic deformation increases these values over those measured at 78 K. Several theoretical calculations of surface energies have been reported, but Benson and McIntosh33concluded that the calculated values are too sensitive to the values chosen for repulsive and van der Waals potentials to be reliable. If the area of pores not accessible to N2 are assumed to be negligible and if the MgO samples are assumed to be composed of cubes with (100) faces, the maximum change in slope of Figure 2 at 120 m2/g surface occurs when the particles have 10-nm edge lengths. For such particles, the ratio of the number of edge molecules to surface molecules is -0.1. The difference between measured enthalpies at high surface areas and enthalpies predicted by linear extrapolation of the low surface area data might for that reason be interpreted as the excess enthalpy of crystal edges. But it is unlikely that the excess enthalpy of molecules in edges would exceed H, (6 - 4)/(6 - 5) = 2H,, where 6 is the number of nearest neighbors for ions in the bulk, 4 is the number for ions in an edge, 5 is the number for ions in a (100) surface, and H , is the excess enthalpy of a (100) surface. The change in slope, therefore, for high surface area samples is improbably great. We think it is so because the MgO aggregates contain pores that are inaccessible to the N z used for BET measurements. The surface enthalpies of any closed pores that may be present in the MgO would be measured in the calorimetry experiments, but their surface areas would not be measured by the BET method. As part of a study of the H20-catalyzed sintering of MgO, we have found the volume of pores in the submicron MgO aggregates of 158 mz/g surface area to be only about one-half the volume calculated from the difference between the molal volume of Mg(OH)2 and Mg0.34 Possibly, the pore volume is so much less than the theoretical value because the MgO formed from each initial Mg(OH), particle has collapsed into an aggregate of substantially reduced volume. But for CaO formed from CaCO, powder decomposition the internal porosities have been demonstrated to be near the value predicted from the difference in CaC03 and CaO molar volumes.35 It seems probable that for MgO from Mg(OH)2 the total internal porosity is also near that expected from the difference in reactant and solid volumes, but that the residual water closes narrow passages between MgO crystallites and blocks access to some of the pores. We plan to measure heats of solution for MgO from MgC03 decomposition. For that MgO, surface areas as high as 700 m2/g have recently been measured.36 If, as we believe, the apparent surface areas reported in the present work are systematically low because some pores are closed, the 700 m2/g MgO will have enthalpies of solution per mole which are little higher than the highest values measured in the present study. The samples of highest surface area had approximately 73 kJ/mol excess enthalpy, more than enough the account for the low H 2 0 pressures measured by Kay and Gregory. Unfortunately, a quantitative comparison of their measured HZOpressures to pressures predicted from alternate interpretation~l~.~' of the influence of surface enthalpy on particle activity is not possible. Water in the effusion cells reduces both the measured surface areas and measured enthalpies by unknown amounts. The water can only be removed by heating to higher temperatures, a process that reduces the surface area. The existence of high enthalpy contents in small MgQparticles is clearly a matter of exceptional fundamental and practical interest. We expect that all very small solid particles will prove
5g 1 1 -
1
/
/
-I
I
-
0
20
40
s,
60 (m2/gr)
00
100
Figure 3. Standard heat of formation AHfo298 (kJ mol-'(MgO)) for low surface MgO samples vs. surface area measured by the BET method. ( 0 ) Natarajan and co-worker~;'~ (0,0 ) data from this study.
is converted to two OH- ions with complete coverage corresponding to 11 molecules per nmz.
Discussion It is well established that the last several percent of water from Mg(OH), require much more stringent conditions for removal than does the bulk of the Furthermore, we have found that when the water has been nearly all removed, it is readsorbed and strongly bound even during cooling to room temperature in a reasonably high vacuum. Manipulations in an ordinary drybox, as the reported water contents in the samples of Livey et aLZ1demonstrate, leave a major fraction of a monolayer in the samples. Our observations support the suggestion of Livey and co-workers that measured heats of solution of MgO are significantly influenced by that water: when we heated an MgO sample of 263 m2/g accessible surface area after brief exposure to air for 4 h at 500 OC the sample retained 3.5% water compared to 2.2% for a sample heated 16 h, and the heat of solution was -183 kJ/mol for the sample of higher water content compared to -220 kJ/mol for that with the lower water content. As shown in Figures 2 and 3, our measured variations in the heats of formation with surface area are in good agreement with those reported by Natarajan and c o - w ~ r k e r swhose '~ data were taken with surface areas of less than 100 m2/g. Our samples of
