J. Phys. Chem. 1995,99, 10609-10615
10609
Thermal Expansion Behavior of Zeolites and AlP04s P. Tschaufeser* and S. C. Parker School of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY, Great Britain Received: February 6, 1995; In Final Form: April 24, 1995@
Lattice dynamic calculations for zeolites and AlP04s were performed at elevated temperatures to evaluate the thermal expansion behavior of these materials. This has led to the interesting prediction in advance of experiments that many zeolites and A1po4s show a negative coefficient of expansion, which means a contraction of their cell volumes on heating. Recent experimental results support these predictions. The success that we had in predicting the expansion behavior of zeolites and AlP04s gives a measure of the reliability of the model and demonstrates the potential of computer simulation techniques.
I. Introduction This article aims to show that simulation techniques are having a profound impact on science, enabling us to understand and increasingly to predict the manner in which atoms in complex solids arrange themselves and interact with each other. This is especially true for the porous inorganic crystal structure zeolites and APo4S, which play a major role in the chemical and petroleum industry. Their technologically important properties are intimately related to their structure and are currently being intensively studied by both computational and experimental methods. Experimental structure determination methods, in particular X-ray diffraction studies, have provided a wealth of information on the structural properties of zeolites and AlP04s.I However, detailed atomistic and structural information at elevated temperatures within the zeolites and AlP04s is scarce. One of the primary motivations for computer simulation arises from the difficulties of obtaining this information through experimental investigation. For this reason, the possibility of modeling solids, with the aid of high-speed computers, is becoming an increasingly important complementary technique to experimental studies. It should be noted that information at elevated temperatures is of critical importance because the commercial chemical reactors and catalyst beds are run at high temperatures. It is just these high temperatures where experimental studies face the greatest challenge. In solid state studies computer modeling techniques have achieved a high degree of precision in calculating energetic and dynamic properties. Atomistic simulation techniques have been successfully used to predict, for example, crystal structures, lattice dynamics, and phase transitions for a range of ionic and semi-ionic materials (for example, see refs 2, 3, and 4). The major aim in this study was to simulate the structural changes, especially the thermal expansion behavior, of zeolites and AlP04s at different temperatures and gain insight into the factors which govern these changes. Such knowledge is essential if we want to understand the technologically important properties of these materials, but it is also fascinating from a fundamental viewpoint. Our studies predicted in advance of experiments that many zeolites and AlP04s actually contract on heating.
II. Simulation Technique The method described in this article is based on lattice dynamics which allows the calculations of free energies, @Abstract published in Advance ACS Abstracts, June 1, 1995
0022-3654/95/2099-10609$09.00/0
enabling lattice expansivities and the thermodynamic properties to be studied. To date the most reliable approach for predicting structural and thermodynamic properties of inorganic solids without recourse to experiment is atomistic simulation. Recent work has shown that computationally based lattice energy calculations can model detailed aspects of the structural properties of zeolites and AlP04s (for example, see refs 5-8). The main limitation of the lattice energy minimization is the neglect of temperature; that is, the simulation was performed effectively at 0 K and even neglects zero-point motion. Our extension to the static lattice simulation technique is to include effects of temperature, leading to the calculation of free energy and thermodynamic properties of zeolites and AlP04s. A new computer code, PARAPOCS,3 which includes entropic effects to calculate free energies has been used, enabling structure and properties at elevated temperatures to be calculated. Lattice dynamics incorporates temperature by calculating vibrational frequencies in periodic structures. We use the quasiharmonic approximation, in which the vibrational frequencies are assumed to be harmonic oscillators whose frequencies vary with the cell volume. The atoms in lattice dynamics are held fixed when evaluating the vibrational frequencies and thus sample the energy at specific lattice sites where the shape of the potential energy-well along each normal mode is assumed to be harmonic. It should also be emphasized that although the vibrational frequencies are assumed to be harmonic, the component interactions are often complex anhamonic functions. Free energy minimization is achieved by first calculating the Helmoltz free energy, which is comprised of the lattice energy and the vibrational free energy, and then adjusting the cell volume and coordinate positions until a minimum free energy configuration is obtained. The approach adopted is to calculate the free energy at a given volume and adjust the cell volume by a very small amount, and after the volume adjustment all ions in the crystal are moved so that they come to mechanical equilibrium. This reduces the possibility that ions are moved into unstable configurations, where the harmonic approximation will break down. The resulting change in free energy with volume is the internal pressure, which is used to guide further cell volume adjustment until the internal pressure is equal to the applied pressure. Thus, the effect of increasing the temperature will cause the equilibrium cell dimension to change. This apparent anomaly, assuming harmonic vibrations, can be resolved by considering two forms of anharmonicity; extrinsic and intrinsic anharmonicity. The first is extrinsic anharmonicity, where the vibrational 0 1995 American Chemical Society
10610 J. Phys. Chem., Vol. 99, No. 26, 1995
Tschaufeser and Parker
TABLE 1: Three-Body Shell-Model Potential Parameters
Z
Si
AI
+4.0
+3.0
long-range 0 K -2.0
Na
+1.0
Si-0
two-body short-range AI-0 0-0 K-0
Na-0
three-body 0-Si(A1)-0
shell-core 0
1283.907 0.320 52 10.661 58
A
P C
unit e
i-1.0 1460.3 0.299 12 0.149
22 764.3 0.149 27.88
1000.30 0.361 98 10.569
iv
5836.84 0.2387 0.0 109.47 2.097 24
0 0
k Y k
-2.86902 74.92
eV46 deg eV/rad2 e evIA
TABLE 2: Semiempirical Potential Parameters long-range Si ~
~~
Z
two-body short-range
0
AI
P
-1.2
f1.4
f3.4
Si-0
0-0
AI-0
P-0
unit
18 003.7572 0.205 204 8 133.5381
1388.7730 0.3623 188 175.0000
16 008.5345 0.208 477 9 130.5659
9034.2080 0.192641 8 19.8793
kveVA6
~~
+2.4
Z
v: C
frequencies and hence the vibrational free energy vary at a different rate than the internal lattice energy with the cell volume. This is the consequence of the quasi-harmonic approximation and leads to the ability to model thermal expansion. The second component of anharmonicity is intrinsic anharmonicity, in which the displacement of atoms along each normal mode describes an anharmonic potential energy surface. The reliability of this technique in modeling thermal expansion can be judged by comparing with experimental data for a number of minerals; that is, for alumina, olivine (Mg2Si04), and quartz at 300 K the calculated thermal expansivities are 11 x 20 x and 21 x 10-6,10respectively, while the experimental values are 9 x 27 x 10-6,'2 and 20 x 10-6.13 Thus, lattice dynamics currently provides an efficient method for determining thermodynamic properties and phase stabilities, provided intrinsic anharmonic effects are not significant, as is the case, of course, near the melting point.
111. Potential Models A key component of all simulation studies is the choice of the interatomic potential models. In this work use has been made of a model which has been very successful in calculating the structural and defect properties of a wide range of ionic and semi-ionic solids (for example, see refs 5 and 14-16). The basic form for the potential describing the interaction of a pair of ions is given below:
where qi and % represent the full or partial charges of the interaction, re is the interatomic distance between ion i and j , and A, Qij, and CQare variable parameters in the description of the short-range component of the potential. In the simulation studies for zeolites we employed the fully ionic potential model of Cat10w.I~ The parameters describing the interatomic forces were obtained by fitting to experimental data of quartz. The model also includes the effects of polarizability on the oxygen ions by using the shell mode1,I4*l7 in which an ion is represented by a core and shell coupled by a harmonic spring. The shell model has only been used for oxygen ions, since the polarizability of the cations is small. Additionally, a three-body term is included to take account of the directionality of bonding of oxygen ions with silicon or aluminum ions.
We used the potential model recently derived by Kramer et al.5 for AlPO4s. They have developed the potential using abinitio quantum mechanical methods. The parameters were determined from the potential energy surface of a cluster and then fitted to the bulk properties of berlinite. Al, P, and 0 are assigned to partial atomic charges. This model is a two-body rigid ion model and does not include ionic polarizability and a bond-bending force. These potential parameters have previously been shown to be capable of modeling silicates and aluminophosphates very a ~ c u r a t e l y . ~The - ~ ~interatomic '~ potentials used in the calculations are summarized in Tables 1 and 2. We first investigated the thermal expansion behavior of different siliceous and nonsiliceous zeolites, and then we studied this behavior on several AlP04s at elevated temperatures.
IV. Results A. The Structure and Thermal Expansion Behavior of Zeolites. The structural parameters and the thermal expansion coefficients have been calculated for 18 different zeolite structures at elevated temperatures. The most surprising aspect and result of these calculations was that with increasing temperature the cell volume contracts significantly for all zeolites considered, except sodalite and cancrinite. This result is surprising, as one intuitively believes that the crystal should expand on heating. The thermal expansion coefficients of some siliceous zeolites at elevated temperatures are shown in Figure 1. The results show that most zeolites have a negative thermal expansion, which means a contraction of the cell dimensions on heating. In contrast, cancrinite and sodalite show the expected behavior; their lattice parameters show expansion on heating. Interestingly, cancrinite and sodalite are the most stable and dense structures, when compared to the other zeolites considered. Additionally, the thermal expansion behavior of some nonsiliceous zeolites was calculated. In Figure 2 the thermal expansion coefficients of nonsiliceous zeolites (their Si:Al ratios are listed in Figure 2 ) and, as a comparison, their siliceous analogues are illustrated. As with the siliceous zeolites, all the nonsiliceous analogues show a negative thermal expansion on heating with the exception of nonsiliceous sodalite and cancrinite. Comparing the thermal expansion behavior of siliceous and nonsiliceous zeolites, the contraction or expansion of nonsiliceous zeolites is much smaller compared to the siliceous zeolites. However, the effect of the aluminum and the chargecompensating cations is complex. If the filling of a zeolite with
Thermal Expansion Behavior of Zeolites and AlPO4s
J. Phys. Chem., Vol. 99, No. 26, 1995 10611 TABLE 3: Unit Cell Parameters (A) for Siliceous and Nonsiliceous Zeolite L at Several Temperatures (the Si:Al Ratio of Nonsiliceous Zeolite L Is 3:l) zeolite L K-zeolite L temp W) U C U C
8,00e-5
-&
6.00~-5
h
d
.Y
E 8
4n00c-51/
50 100 200 300 400 500
2.00~-5
O,OOe+O
-2,OOe-5
-4,We-5
!
.
I
0
IO0
.
, 200
,
,
300
fempcrarure
,
,
400
,
I 500
(K)
Figure 1. Predicted thermal expansion coefficient for several siliceous zeolites.
6.0e-5
2
&” .-9
5.0e-5 4.0e-5
11
f
$
3.0e-5
C
.-
‘ij
5
2,Oe-5
1
l,Oe-5
! i o.oct0
- 1.Oe-5 -2,Oe-5
!
I
I
I
I
0
100
200
3 00
4 00
500
Temperature (K)
Figure 2. Comparison of the predicted thermal expansion coefficient for certain siliceous and the same zeolites with A1 in the framework and charge-compensating cations (the Si:A1 ratios are LTL = 3; FAU = 1.52; CAN = 1; SOD = 1). cations would be purely a size effect, then we would expect sodalite and cancrinite to increase their expansivity. In an attempt to resolve the effect of the aluminum and cation content on the thermal contraction and the anisotropic nature of this effect on the unit cell parameters for siliceous and nonsiliceous zeolites, we considered zeolite L and cancrinite. The cell parameters for zeolite L at different temperatures are listed in Table 3 as an example. The contraction of zeolite L is anisotropic, with the a-axes approximately 70% (for siliceous zeolite L) and 40% (for nonsiliceous zeolite L; Si:Al = 3:l) more compressible than the c-axes for siliceous and nonsiliceous zeolite L, respectively. Similar results have been obtained for other zeolites which also show a contraction on heating. The anisotropy is also reflected by those zeolites which show a positive thermal expansion and is affected by the aluminum and cation content. For example, the a-axes of siliceous cancrinite are about 68% and of nonsiliceous cancrinite (Si:Al
18.051 18.048 18.041 18.034 18.026 18.020
7.547 7.545 7.540 1.534 7.529 7.524
18.199 18.200 18.194 18.190 18.187 18.184
7.607 7.607 7.605 7.604 7.602 7.601
TABLE 4: Unit Cell Parameters (A) for Siliceous and Nonsiliceous Cancrinite at Several Temperatures (the B:Al Ratio of Nonsiliceous Cancrinite Is 1:l) cancrinite Na-cancrinite temp (K) U C a C 50 100 200 300 400 500
12.3707 12.3720 12.3778 12.3838 12.3902 12.3948
5.1713 5.1722 5.1764 5.1806 5.1849 5.1878
12.7591 12.7587 12.7595 12.7616 12.7648 12.7686
5.2898 5.2897 5.2900 5.2908 5.2920 5.2934
= 1:l) about 40% more extensible than the c-axes. The cell parameters for siliceous and nonsiliceous cancrinite are listed in Table 4. We also calculated the thermal expansion coefficient of cancrinite with different Si:Al ratios, and the results are given in Figure 3. Again, it is shown that siliceous cancrinite has a much larger thermal expansion coefficient than nonsiliceous cancrinite. However, the complexity of the system becomes apparent as the thermal expansion behavior cannot be related linearly with the Si:Al ratios. The only feature the different Si:Al ratios have in common is a contraction of the cell dimensions at lower temperatures. In an attempt to resolve this outcome, the influence of the aluminum and cation positions within the framework on the thermal behavior was studied. Unlike using diffraction experiments which can assign partial occupancy, we have had to assign the cations and the aluminum to specific sites. In Figure 4a,b two examples are shown. In these two examples the thermal expansion coefficient at a Si:A1 ratio of 5:l and 11:l with different silicon, aluminum, and cation positions was calculated. As illustrated in the graphs, the positioning of the aluminum atoms and nonframework cations significantly modifies the expansion behavior. Hence, in the real material where all these configurations are accessible we can expect to observe a statistical average of expansions. The thermal expansion behavior was also calculated for sodalite with different Si:A1 ratios. However, it was observed that the simulated structure of pure siliceous sodalite displayed an incipient instability from 200 K onward. This is in contrast to nonsiliceous sodalite, which does not show this instability with increasing temperature and is independent of which Si:Al ratio is considered. This suggests that the presence of substituted aluminum or interframework cations confers thermal stability to the sodalite structure. Again, the siliceous form expands more than the nonsiliceous sodalite. In addition, there is also no recognizable correlation between the Si:Al ratio and the thermal expansion behavior, although for certain Si:& ratios the thermal expansion of sodalite is, as in cancrinite, dependent on the positioning of silicon, aluminum, and cations. Unfortunately there has been little detailed work on the thermal expansion behavior of framework silicates, apart from the silica minerals and feldspars. However, with hindsight a negative thermal expansion for silicas is not so surprising. For
10612 J. Phys. Chem., Vol. 99, No. 26, 1995
Tschaufeser and Parker TABLE 5: Calculated and Experimentalz1Lattice Parameters of Zeolite X calculated lattice parameters lattice parameter (A)
h
a. .
e .L! u
1,Oe-5
Eu 8
experimental lattice parameters
temp
zeolite
Na-zeolite
temp
(K)
X"
Xb
( K)
lattice parameter (A) Na-zeolite Xc
50 100 200 300 400
24.2946 24.2908 24.2804 24.2695 24.2593 24.2494
24.9409 24.9337 24.9261 24.9189 24.9125 24.9067
24.9(5) 43.3(5) 54.6(5) 84.7(5) 109.9(5) 145.5(5) 179.2(5) 2 17.2(5) 293.0(5)
24.8047 (5) 24.8059(5) 24.8062(7) 24.8042(6) 24.802 1( 1) 24.8005(7) 24.8006( 1) 24.7988(8) 24.7998(8)
500
Purely siliceous faujasite. Na-zeolite X, %:A1 = 1.525. "azeolite X, Si:A1 = 1.54.
VIVO
- 1,Oe-5 4
1
0
100
300
200
400
1,000
500
Temperature (K) Figure 3. Calculated thermal expansion coefficient of cancrinite with different Si:AI ratios.
0,999 0,998
'
1
1
1
* * *
8 * :
1 Na-Zeolite X (calc) Na-Zeolite X (exp)
0,996 0,995
0
50
100
150
200
250
300
350
Temperature (K) Figure 5. Experimental and calculated unit cell volume normalized P
0
100
200
300 400 Temperature (K)
500
to the ambient unit cell volume for the thermal expansion studies of Na-zeolite X.
TABLE 6: Calculated and Experimentalz1Lattice Parameters of Sodalite ~
calculated lattice parameters
~~~
experimental lattice parameters
lattice parameter (A) sodalite"
temp
(K)
(K)
lattice parameter (A) gallosodalite
50 100
8.8046 8.8267
15.4 35.2 62.5 92.5 125.9
8.8190(3) 8.8 190(2) 8.8212(5) 8.8230(4) 8.8270(3)
temp
Purely siliceous sodalite. 0
100
200
300
400
500
Temperalure (K)
Figure 4. (a, top) Calculated thermal expansion coefficient of cancrinite with a Si:A1 ratio of 5 : 1 and different Al, Si, and Na positions (the Na and A1 positions are presented simplified on the right-hand side). (b, bottom) Calculated thermal expansion coefficient of cancrinite with a Si:A1 ratio of 11:l and different Al, Si, and Na positions (the Na and A1 positions are presented simplified on the right-hand side).
example a-quartz shows a negative thermal expansion below 50 K, and above the transition temperature of quartz, @-quartz shows a slight but measurable contraction in the cell volume, which was observed and calculated.I0 This apparently anomalous behavior of @-quartz is interpreted as being due to an increase in the amplitude of the anisotropic motion of the oxygen atoms on increasing the temperature, resulting in a further shortening of the Si-0 bond distances.18
Apart from silicates and AlP04s several other systems show negative thermal expansion. For example, InBi, a semimetal with a layered tetragonal structure. It has, in contrast to most anisotropic crystals, a negative thermal expansion in the c-dire~tion.'~Another example is crystalline polyethylene. Theoretical studies undertaken by Barron and Rogersz0 show that the thermal expansion is negative in all directions. This result was also in good agreement with experiment. However, the results of the negative thermal expansion behavior have now been observed by high-resolution powder diffraction studies of dehydrated Na-zeolite X by Couves et al.*' The experimental results indicate that the qualitative predictions of the simulations are correct, although the calculations underestimate the magnitude of the negative coefficient of expansion. The calculated and experimental results are shown in Table 5 and in Figure 5 . The experimental results indicate that Na-
J. Phys. Chem., Vol. 99,No. 26, 1995 10613
Thermal Expansion Behavior of Zeolites and AlP04s 6.0e-5
4,0e-5
2,Oe-5
O,Oe+O
-2,Oe-5
-4,Oe-5
I
1
I
I
1
I
1
0
100
2 00
3 00
400
500
Temperature (K) Figure 6. Predicted thermal expansion coefficient for several A1PO4-s~ctures. TABLE 7: Unit Cell Parameters (A) for VPI-5, A1P04-52, and AIP04-8 at Several Temperatures VPI-5
AlP04-8
A1PO4-52
temp (K)
a
C
U
C
a
b
c
50 100 200 300 400 500
19.0981 19.0858 18.9275 18.9313 18.9371 18.9438
8.6618 8.6592 8.1912 8.4940 8.4984 8.5035
14.0893 14.0521 14.0601 14.0670 14.0718 14.0758
29.9871 29.9467 29.8548 29.7823 29.7331 29.6935
34.1682 34.1708 34.1782 34.1878 34.1987 34.2 105
18.6027 18.0457 18.6099 18.6168 18.6248 18.6333
8.4042 8.4065 8.4131 8.4217 8.4316 8.4424
Zeolite X expands at temperatures above 200 K, whereas the calculations predict continuous contraction. The discrepancies may be due to uncertainties concerning the samples (e.g. the presence of significant quantities of water and other sorbents or the amount and positioning of aluminum and cations) or due to the importance of intrinsic anharmonicity. Moreover, the positive thermal expansion behavior of sodalite is also verified. Thermal expansion data for synthetic aluminosilicate sodalites were determined by powder X-ray diffraction from Henderson and Taylor.22 The calculated thermal expansion curves show the same trend as the experimental with increasing temperature. Some variations of the cell parameters may bee related to the expansion characteristics of the bond between the cavity cations, the positioning of the cations, and the amount of cations present in the different sodalite structures. Couves et aL2' also measured the thermal expansion behavior of dehydrated gallosodalite using a high-resolution powder diffractometer. A comparison of the cell parameters between the calculated siliceous sodalite and the experimental gallosodalite shows the same features. The results are reported in Table 6. B. The Structure and the Thermal Expansion Behavior of AlP04s. The calculations of the thermal expansion coefficient of zeolites have shown, surprisingly, that most of the zeolite structures show a contraction of their cell dimensions on heating. This is a major characteristic of zeolite structures, as it has not been observed yet for any other framework structure, except for silicas. Therefore, it was of great in-
terest to calculate the thermal expansion behavior of aluminophosphates, as many of them are structurally related to zeolites. In Figure 6 the thermal expansion coefficient at elevated temperatures of some aluminophosphate structures and a-berlinite is illustrated. The results show that a-berlinite, AlP048, and A1P04-5 have a positive thermal expansion, whereas A1P04-17 and AlPo4-52 show a negative thermal expansion, which means again a contraction of their cell dimensions on heating. Interestingly, VPI-5, which has very large channel systems with approximately 11.2 8, free aperture diameters, shows a contraction of the cell dimensions at lower temperatures, and from 200 K onward, an expansion. It was also demonstrated that the nature of the expansion or contraction of zeolites is anisotropic. This feature was also observed for the aluminophosphate structures considered in this study. In Table 7 the unit cell parameters of some aluminophosphate structures are listed to show that the structural changes of aluminophosphates are also anisotropic. V. Discussion of the Results
Although the negative thermal expansion behavior of most zeolites and AlP04s is of great academic significance, it is also of potential industrial importance. The adsorption and diffusion of molecules in zeolite and Alp04 catalysts are partly dependent on the pore and channel geometry. Blockages such as a contraction of the pores and channels may alter the rate of diffusion and the total sorption, as some channels or cages are either totally or partially blocked by this unusual behavior.
10614 J. Phys. Chem., Vol. 99, No. 26, 1995
A13 C-GTYPE
Tschaufeser and Parker
VPI
-5
AIPO,
-8
Figure 7. Structures of an ABC-6 type, VPI-5 type, and ALP04-8 along their a- and b-axis.
M
M
AUC-GTYPE
-
VPI 5
AIX’O,,
-8
Figure 8. Structures of an ABC-6 type, VPI-5 type, and ALPO4-8 along their c-axis.
Another factor affecting sorption and catalysis is the size of the pores, which restricts the entrance of a molecule and the formation of reaction products. Hence, the negative thermal expansion of several zeolites and AlP04s may have, in fact, an opposite effect by decreasing framework dimensions, for example, on attempts to enhance guest molecule diffusivities in framework structures with increasing temperature, which has to be considered in future experimental investigations. However, the reasons for this behavior are not yet fully understood, but a possible explanation may be found by considering the zeolite and Alp04 structures themselves. For the zeolites, both sodalite and cancrinite are more stable and dense structures than the other zeolites.’0 They also have only a one-dimensional channel system, which seems to allow no reduction of their cell dimensions on heating. All other zeolites studied have a highly porous framework and a two- or three-dimensional channel system, which seems to allow a structural “expansion” into the pores and channels on heating, leading to the observation of the zeolites showing a negative thermal expansion. Similarly to the zeolite studies, it is demonstrated that the most stable and dense Alp04 structures (AlPO4-8, AlP04-5, and VPI-5) expand with increasing temperature, whereas the less stable and dense structures (AlPO4-17 and AlP04-52) show a contraction of their cell dimensions on heating. Additionally, AlP04-8, A1P04-5, and VPI-5 have only a one-dimensional channel system, which may not allow a reduction of their cell dimensions. Indeed, viewing the VPI-5 or APO4-8 structure at right angles to the main pores demonstrates the high density in that direction. This is in contrast to those aluminophosphate structures which are structural analogues of the zeolites (for example, AlP04-17 is a structural analogue of erionite) and show a contraction of the cell dimensions on heating. In Figure 7 the structures of an ABC-6 type (e.g. AlPo4-17, A1P04-52), VPIJ, and AlP04-8 are shown along their a- or b-axis to illustrate the dense packed structures of V P I J and AlP04-8 compared to the more porous framework structures of A1P04-17 or A1P04-52. These observations are in conformity with the observations made for the expansion behavior of zeolites.
An additional explanation of the different thermal expansion behavior of aluminophosphates may be found by considering the crystal structures. In Figure 8 the structures of an ABC-6 type aluminophosphate, VPI-5, and AlP04-8 are shown along their c-axis or channel system. The ABC-6 type (AlP04-17 or U 0 4 - 5 2 ) has one 4-ring and one 6-ring, VPI-5 has two 4-rings and one 6-ring, and AlPO4-8 has two 4-rings and two 6-rings altemately surrounding the channel. With an increasing number of 4- and 6-rings surrounding the channel, the structure may become more “stiff” and therefore does not allow any contraction toward the channels. This view is also supported by the bulk modulus, which has been calculated for these Alp04 structures at elevated temperatures. The ABC-6 type aluminophosphates show a much higher bulk modulus than the AlP04-8, AlP04-5, and VPI-5 structures. A major contribution in this field has been made by T. H. K. Barron. He has discussed the thermal expansion behavior of several different systems (for example, see refs 19, 20, 23, and 24). For a-quartz he postulates that the contraction is related to the oxygen atoms vibrating at right angles to the two silicon atoms to which it is bonded. The frequency of such vibrations decreases as the structure shrinks, and this decrease results in negative thermal expansion. The empirical correlation between the observation of negative thermal expansion and the existence of two- and threedimensional channel systems strongly suggests that the expansion behavior is dependent on the nature of the channel system. Mechanistic studies, using computer graphics techniques, are now planned to attempt to elucidate the underlying reasons for the contraction on heating of aluminophosphates and zeolites with two- and three-dimensional channels. This work will focus on the difference in behavior of the one-dimensional and the two- and three-dimensional systems, because, as noted above, this difference could well hold the key to understand this fascinating behavior. Further, it will be necessary to consider the anharmonic lattice dynamics of the atomic vibrations. Therefore, future development in the simulation methods must include anharmonic effects, which play an important role in the calculation.
J. Phys. Chem., Vol. 99, No. 26, 1995 10615
Thermal Expansion Behavior of Zeolites and AlP04s Acknowledgment. We would like to thank A. Wall for her help with the program PARAPOCS. This work was supported in part by the Bundesministerium fur Wissenschaft und Forschung (Austria). References and Notes (1) Thomas, J. M.; Vaughan, D. E. W. J . Phys. Chem. Solids 1989, 50, 449.
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