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Molecular System Organizations in the Solid State
239
P.J. Grobet et al. (Editors) / Innovation in Zeolite Materials Science © Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
MOLECULAR SYSTEM ORGANIZATIONS IN THE SOLID STATE V. GUTMANN and Go RESCH Institute of Inorganic Chemistry, Technical University of Vienna, Getreidemarkt 9, A-1060 Wien (Austria) ABSTRACT Application of the bond length variation rules of the extended donor-acceptor concept to real solids provides an understanding of the effects of "lattice defects" on local lattice structures and vice versa. Likewise, the changes at the interface due to adsorption and desorption are well illustrated. A metal surface appears to act as a "regulating. unit" for the redistribution of electrons, without being appreciably affected itself o It is concluded that each system must be subject to a system organization, which appears to be highly developed in zeolites. INTRODUCTION Quantum mechanics describe molecular interactions as due to charge transfer and to polarization effects. Chemists are used to account for charge transfer between two molecules by considering one of them as electron donor and the other one as electron acceptor. Despite the enormous varieties of changes, it has been possible to formulate rules which are (i) based on both qualitative and quantitative observations and (ii)
inde-
pendent of any model assumptions. THE BOND LENGTH VARIATION RULES According to the first of the "bond length variation rules" an intermolecular interaction leads to lengthening of those intramolecular bonds which are adjacent to the donor atom in the donor molecule and to the acceptor atom in the acceptor molecule respectively (ref. 1). This means that the charge density rearrangement occurs throughout the interacting system, and this involves (i) an overcompensation of the loss of negative net charge at the donor atom (pile-up effect of negative charge) due to an increase of positive net charge at the atoms adjacent to the donor atom in the donor molecule and (ii) an overcompensation of the gain in negative net charge at the acceptor atom (spill-over effect of
240
negative charge) due to an induced flow of negative charge to the adjacent atom(s)
in the acceptor component. As a result of
an intermolecular interaction the whole system becomes more polarized, more highly differentiated and more reactive (ref. 1). The positive charges are increased in the peripheric regions of the donor molecule, whereas the negative electric charges are increased in the peripheric regions of the acceptor molecule. Donormolecule
Acceptormolecule
i-
F
J+/ SB--F "<, sF
Induced intramolecular bond lengthening, pile~
effect
of negative charge at the N-atom
intermolecular interaction
Induced intramolecular bond lengthening, spillover effect of negative charge at the B-atom
The second rule concerns the changes in bond lengths in all other molecular areas. Bond lengthening occurs when negative charge is shifted from a more electropositive to a more electronegative atom (as it is usually the case with regard to the bonds adjacent to the donor- and acceptor atom respectively) • Bond shortening takes place when negative charge is shifted from a more electronegative atom to a more electropositive atom within the molecular system. In the first case the bond polarity is increased, whereas in the second case it is decreased. Because in most molecules atoms of higher and lower electronegativities are arranged in alternating positions, alternating bond lengthening and bond shortening is usually taking place (ref. 1). This is illustrated in fig. 1 for the interaction of the donor molecule tetrachloroethylenecarbonate and the acceptor molecule antimony(V)-chloride. Again, substantial amounts of negative charge are shifted from the donor atom towards the peripheric regions of the acceptor molecule (SbCl
thereby increasing the S)' negative net charges of the terminating (chlorine) atoms, whereas
241
the terminating atoms of the acceptor molecule (the chlorine atoms in tetrachloroethylene carbonate) are decreased in negative net charges. Distances after the interaction
Distances before the interaction
Intermolecular interaction (=0:
115 pm
122 pm
0-(:
133 pm
125 pm
(-0:
140 pm 153 pm 176 pm
147 pm 143 pm 174 pm
(-( : (-Cl:
. @ '-"
Sb
e
Cl
0
0
• (
Fig. 1. Changes in bond lengths due to coordination of SbCl to tetrachloroethylenecarbonate (ref. 2, by kind permission of S Barthel and Barthel Publishing). In large molecules the changes in bond lengths are found to decrease with increasing distance from the site of interaction, but they are found more pronounced in the regions terminating the molecular system under consideration. APPLICATIONS TO THE CRYSTALLINE STATE Studies on bond energies have revealed that such alternating changes appear to take place in crystals (ref. 3). For example, in the molecular lattice of crystalline iodine the intramolecular I-I-bonds are longer (272 pm) than in the gas phase (268 pm), because of the much stronger intermolecular interactions in the crystals (first rule). Likewise, the so-called pressure-distance paradox is readily explained (ref. 4)
as a consequence of the
Le Chatelier-Braun principle. Increase in pressure on a crystal leads to pronounced shortening of the greatest internuclear dis-
242
tances (which usually are not considered as chemical bonds). This leads - in accordance with the bond length variation rules to subsequent lengthening of the shortest internuclear bonds of the solid (denoted as chemical bonds)
(ref. 5). For example, when
coesite is converted into stishovite by pressure, both the Si-Sidistances and the O-O-distances are shortened, namely from 301 to 267 pm and from 263 to 251 pm respectively. These contractions of "intermolecular bonds" lead to the lengthening of the "intramolecular" Si-O-bonds from 161 to 178 pm. The model of the ideal crystal and hence the results of complete structure determinations do not allow to account for the properties of a real solid, such as hardness, color, index of refraction, vapor pressure, conductivity, tensile strength, elasticity, actions of cold work or temperature etc. For this reason Wagner and Schottky (ref. 6)
rightly deduced
the unavoidable existence of local "point defects" in any real crystal. Distinctions are made between (i) so-called impurities, (ii) building units at so-called "interstitial" positions and (iii) unoccupied positions (voids, vacancies) in the idealized lattice. Point defects are known to influence the local arrangements of the regular building units. An interstitial atom is always under strain, with rather short "internuclear" distances to its neighbours. This "intermolecular" interaction leads to lengthening of the adjacent distances. Due to alternating changes in internuclear distances a characteristic distortion is produced (refs. 1, 2 and 7), and this is illustrated in fig. 2A. Likewise, a vacancy is known to represent a centre of tension: in its neighbourhood the lattice is contracted, the internuclear distances around the vacancy are shorter than the mean values (refs. 2 and 7, illustrated in fig. 2B). This has been shown by the results of neutron diffraction experiments on TiC o , 85 crystals (ref. 8) and of X-ray investigations on understoichiometric vanadium carbide (ref. 9) and niobium carbide (ref. 10). The measurability of the effects depends also on the experimental technique used. For example, the effects of aluminium atoms in silicon dioxide have been found measurable through 20 layers of Si0
2
by means of the LEED-technique (ref. 11).
243
A
B
Fig. 2. Two-dimensional illustration of structure modifications of an idealized lattice region, due to the presence of an interstitial position (A) and a vacancy (B) (ref. 2, by kind permission of Barthel and Barthel Publishing). Not only is the lattice structure modified by the point defect, but also the point defect by the lattice. Each point defect is und~
stress and produces a strain pattern. It has therefore been
suggested to use the term "structure modified and modifying centre", or, abbreviated, SMM-centre (refs. 12 - 14). Point defects are known to exchange positions within the lattice. The driving forces for those "displacement"-reactions are gradients in chemical potentials, and they are structurally represented by structural inho~;ogeneities. When a building unit jumps from an interstitial into a vacant position, the surrounding lattice areas will be relaxed. When it jumps from a regular into an interstitial position, thus creating a vacancy, the surrounding lattice areas will be strained (refs. 12 - 14). The ordered sequences of displacement reactions are required for the existence of the system as to maintain its configuration under constant conditions and to exert its integral configuration in changing environments. In other words: the static structural aspects must be dynamically maintained. Such relaxations will not be confined to certain areas, but
244
may reach the surface areas, where well-pronounced changes may occur. It may be said that the three-dimensional structural information of the crystal appears to be contained in a reduced two-dimensional form at the interface. Hence, the structural differences between crystal structure and surface structure will be more pronounced the better developed the differentiation and the dynamic aspects in the system under consideration. THE ROLE OF INTERFACES Because the interactions between building units in the crystal are no longer continued at the phase boundary, the lattice parameters near and perpendicular to the crystal surface must be smaller than those within the crystal lattice. This prediction has been made by the quantum chemist Lennard Jones as early as in 1928 (ref. 15), but its confirmation had to await the development of the LEED-technique. By this method it has been established that the mean internuclear distances in silver(lll)-surface planes are by 6% smaller than within the crystal. Towards the interior of a crystal the contraction is followed by an expansion and this by a smaller contraction. What is generally called a "surface" is actually a selvedge of several layers (ref. 16). Accordingly, vibrations of surface constituents are higher both in frequency and in amplitude than their mean values derived for the constituents of the solid (ref. 17). Surface contractions may be overcompensated by strong adsorption, because such intermolecular interactions will lengthen the surface bonds. For example, Horill and Noller (ref. 18) have shown that the peripheric O-H-bonds of aerosile are lengthened to a greater extent, the greater the donor properties of the adsorbed molecules. Far-reaching effects due to adsorption may be seen, for example, from the results of investigations on metal surfaces. By adsorption of tungsten the C=O bonds of carbon monoxide are lengthened (first rule). The extent of bond lengthening is greater, the smaller the number of adsorbed CO-molecules (ref. 19). The mean values for c=o bond lengths of adsorbed molecules decreased with increasing adsorption, even though the adsorbed molecules are still separated from each other by a great number of tungsten atoms. This means that each electronic change due to adsorption at a given point of the surface must
245
be "reported" to other parts of the system, including the adsorbed molecules, which seem to have "informations" about each other. The same results are obtained from the so-called co-adsorption phenomena: the
c=o
bonds of adsorbed carbon monoxide are short-
ened by adsorption of oxygen, as negative charge attracted by adsorbed oxygen atoms is partly provided by adsorbed CO molecules.
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Fig. 3. The donor-acceptor interpretation for co-adsorption of oxygen and carbon monoxide on nickel (ref. 17, by kind permission of Akademische Verlagsgesellschaft Wiesbaden) • Thus, the metal provides electronic charges quite freely when few CO molecules are adsorbed. As their number increases, the metal acts no longer as a source of electrons, but rather as a regulating unit that redistributes the electron densities between the adsorbed molecules but leaves its own electron density nearly unchanged. The regulating functions of the interface concern also the distribution of matter. Drop-like islands are observed in the electron micrographs taken in the course of vapor deposition of tin on a sodium chloride substrate (ref. 20). Nuclei grow to form islands, and ad-atoms deposited at other areas appear to be captured by the islands. As islands increase their size by further deposition, the larger ones appear to grow by coalescence of the smaller ones, which disappear in less than a fraction of a second. Agglomeration is even enhanced and the island density decreased, as the deposition rate is increased. Thus, the expectations for "random walk" or "statistical diffusion" are not fulfilled (ref. 21). The preferred sites for island formation may be the "craters",
246
which may be made visible as "etch pits", because they represent areas of greatest local surface energy and reactivity. The craters are the points of emergence of dislocations, through which matter and energy are distributed throughout the system. It appears therefore that the craters of a surface are of great significance for a solid system with regard to its maintenance of its chief characteristics under different conditions. SYSTEM ORGANIZATION We observe that a system responds to environmental changes without losing its basic characteristics, although each change provokes certain minor changes in it. In order to account for these observations, the following requirements appear inevitable:
(i) the parts of the system must
differ from each other, because a non-differentiated system could never respond to changes while maintaining its chief characteristics,
(ii) hence, each point must serve a certain different
purpose for the whole system, and therefore it must be under the influence of dominating forces of the whole system,
(iii) differ-
ences in domination among the various parts are required in order to allow for the specific influences on other parts, according to a kind of "guiding concept",
(iv) the whole system must have
its own organization, which is the cause of its existence in its own right, and to which we may refer to as system organization. Only a system organization allows a system to respond collectively towards changes in environment, as to counter the external changes in order to preserve its integrity in an optimal way, and this ability depends on the development of the "state" of the system organization. It allows not only to resist and to counteract the influences of the environment. The properties of both preserving and acting are the basis for its characteristic behaviour. In the absence of a system organization no characteristic system properties were possible, the system could not respond to environmental changes in a characteristic way, and hence knowledge about the system could not be obtained. In an attempt to study the different tasks of the different parts for the whole system, it must be borne in mind that such differences can exist only within the continuous matrix, and hence they can be perceived only to a limited extent. We may start their investigation from the wealth of qualitative ob-
247
servations and experimental data, and to pay full attention to all differences that can be noted in behaviour and properties under different conditions. We have even to consider carefully all results which appear anomalous or curious. Such results are of particular value, because they indicate the shortcomings of the present model assumptions rather than inadequacies of natural systems (ref. 6). One should even not ignore the results which are not strictly reproducible. Poor reproducibility is frequently a consequence of differences in system organization due to unknown factors. In order to learn about differences without observable discontinuities, one has to make use of abstractions and to introduce artificial discontinuities in intensities, which are arranged according to certain criteria, such as similarities and common features of different parts. In this way hierarchic levels are introduced. These, however, cannot be considered as clearly definable or independent entities of their own right, but rather as integrated within the whole. Because of their integration in the whole, the hierarchic levels cannot be considered separately, but they serve to illustrate certain aspects of the reality. Detailed studies on solid materials have led to results as illustrated in fig. 4 by means of a truncated pyramid (ref. 6). Fig. 4 shows that the different hierarchic levels parallel the dimensionalities of the so-called "imperfections" familiar to silid state scientists: a higher level corresponds to a higher dimensionality of the imperfections which, indeed, are of great significance for the system organization. It is very important to realize that each of the hierarchic levels is indispensable for the system. As the external conditions are changing, the highest level will "decide" in what way all the other parts have to contribute for the maintenance of the chief characteristics of the system (ref. 22). The highest level is dynamically active and responsible for the system properties (including the so-called "memory effects"), whereas the lowest level is more passive and provides the structural framework for the whole system. The results of various investigations referred to in ref. 7 lead to the conclusion that the lower levels are by no means "exploited" by the higher levels. Instead, the highest level appears to provide the most appropriate conditions for the per-
248 formance of all of the functions of the lower levels
Increasing.; hierarchic signiticance, energy per building unit Decreas!n't. nullber at building units per level
Flat arells ot Phase boundaries and Dislocation nodes fila-dimensional defeds
(ref. 2).
Not in thermal equilibrium ·Memory Eftects·
Dislocation lines one-dimensional defecfs
Regulation ot Number ot point detects ISMM-centre sl
Point detects (SMH-centrul Dissolved Holecules, Ions or Atoms, Vacancies, Interstitials zero-ditnensional def«fs
Indirectly interred
• Norml building units· lowest hierarchic level
Statistical Intorllation, Quantitative Characterization, ·Structural Fralllework" ·TherlllodyOOlllic Leve I •
Fig. 4. Illustration of system organization in a real solid (ref. 2, by kind permission of Barthel and Barthel Publishing). A system organization is improved by strengthening the highest levels, for example by increasing its outer and inner surface areas, by raising the temperature, by the actions of grinding, of fields, of radiation etc. A higher system organization may be retained at lower temperature by quenching. In other words: an amorphous body is considerably better organized than a single crystal. Differences in system organization for a solid of given composition may be illustrated by means of a truncated pyramid obtained in a plot of number of building units in each of the hierarchic levels descending from top to bottom vs. the mean energies per building unit in each level (fig. 5). Neglecting the steps in fig. 5, a broken line has been drawn from the upper edge to the lowest edge of the truncated pyramid. The greater the slope of this line, the better developed is the system organization.
249
B
A \
Craters on Phase boundw'ies 'Flat' areas of Phase bound
[\
Craters on Phose boundaries
,,
\
\
Dislocations 'SMH"- centres
·Normal building ooits·
,
\
'Flat' areas of Phase boundaries
\
1\, 1'\ , t
\
Dislocations ., SMM"- centres
·Normal building units· \
log n
\
\
\
\
\
\
\
\
\
\
(\
\
I' \
log n
\
Fig. 5. Illustration of the system organization in a crystal (A) and in an amorphous body (B). (From ref. 2, by kind permission of Barthel and Barthel Publishing) • Another important discovery is that an optimal system organization is developing in the course of a phase transformation in the solid state. The highly developed dynamic aspects of order are evidenced by the high values in specific heat, in entropy changes and in chemical reactivity (Headvall effect). The well-balanced static and dynamic aspects of order allow the system to acquire different properties by appropriate changes in environment. These are more readily retained by the system the faster it is removed from the transition range (ref. 23). SYSTEM ORGANIZATION IN ZEOLITES The open framework structures of zeolites consist of rings of aluminates and silicate tetrahedra, that provide interconnected networks of holes and channels of various diameters. The wellpronounced amphoteric properties of these inner surface areas resemble those of water and account for the ability to "activate" solutes, whereby the structural framework is but slightly modified and essentially maintained. This means that the inner surface
250
areas function as a kind of "regulating" areas for the redistribution of matter and energy. These activities are subject to the admission of solutes into the channel network. For example, molecular sieve properties depend on the size of the apertures that connect the channels with the outer surface. Their size may be changed by the presence of cations near them. They appear hierarchically higher than the large inner surface areas of the channel-network, as they regulate the admission of water and ions into the latter. The framework of the inner surface area is by no means totally rigid. For example, in chabazite shrinkage is observed in the course of dehydration. Minor framework changes have been reported with ca++, but major changes occur for the ca++ ions. Thus, the properties of the ions appear to be influenced by the more static boundary conditions of the structural framework, and this is modified itself by the actions of the former. Ions and water molecules are not fixed to certain positions, but have a considerable freedom of movement. The reversibilities of the interactions suggest a fair "balance" between dynamic and static features, maintained over a wide range of changes in environmental conditions. This resembles the situation found for
(gradual) phase transformations
in the solid state (ref. 23). Indeed, synthetic zeolites are frequently metastable and liable to phase transformations. The investigation of such transformations may offer possibilities for the manufacture of zeolites with hitherto unknown properties and particularly well-developed system organizations. REFERENCES 2 3 4 5 6 7 8
V. Gutmann, The Donor-Acceptor Approach to Molecular Interactions, Plenum Press, New York, 1978. G. Resch and V. Gutmann, Scientific Foundations of Homoeopathy, Barthel and Barthel Publishing, Berg near Mlinchen, 1987. G.M. Bliznakov and Sv.P. Delineshev, Kristall und Technik, 7 (1972) 793-802 V. Gutmann and H. Mayer, Structure and Bonding, 31 (1976) 49-66. T. Zoltai and M.J. Buerger, Z. Kristallographie, 111 (1959) 129-141. G. Wagner and W. Schottky, Z. physik. Chern. (B), 11 (1930) 163-210. V. Gutmann and G. Resch, Zeitschr. f. Chem., 19 (1979) 406-412. H. Goretzki, Phys. Status Solidi, 20, K (1967) 141-144.
251
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
D.Kordes, Phys. Status Solidi, 24, K (1968) 103-108. C. Froidevaux and D. Rossier, J. Phys. Chern. of Solids, 28 (1967) 1197-1209. A. Weiss, Hauptversammlung Deutscher Chemiker, Kaln, 1975 G. Resch and V. Gutmann, Z. physik. Chern. (Frankfurt), 121 ( 1 980) 211 - 23 5. V. Gutmann and G. Resch, Acta Chim. Acad. Sci. Hung., 106 (1981) 115-129. V. Gutmann and G. Resch, Revs. Inorg. Chern. 2 (1980) 93-138. E.J. Lennard-Jones and B.M. Dent, Proc. Roy. Soc. London, A, 121 (1928) 247-259. K. Mliller, Ber. Bunsenges. Phys. Chern., 90 (1986) 184-190. G. Resch and V. Gutmann, Z. physik. Chern. (Frankfurt), 126 (1981) 223-241 P. Horill and H. Noller, Z. physik. Chern. (Frankfurt), 100 (1976) 155-163 J.T. Yates and D.A. King, Surface Science, 30 (1972) 601-616. L.E. Murr, Interface Phenomena in Metals and Alloys, AddisonWeseley, Reading/Mass., 1975. K.L. Chopra, Thin Film Phenomena, McGraw Hill Co., New York, 1969. V. Gutmann and G. Resch, Comments Inorg. Chern., 1 (1982) 265-278. V. Gutmann and G. Resch, Inorg. Chim. Acta, 72 (1983) 269-275.
P.J. Grobet et al. (Editors) / Innovation in Zeolite Materials Science © Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
MOLECULAR SYSTEM ORGANIZATIONS IN THE SOLID STATE V. GUTMANN and Go RESCH Institute of Inorganic Chemistry, Technical University of Vienna, Getreidemarkt 9, A-1060 Wien (Austria) ABSTRACT Application of the bond length variation rules of the extended donor-acceptor concept to real solids provides an understanding of the effects of "lattice defects" on local lattice structures and vice versa. Likewise, the changes at the interface due to adsorption and desorption are well illustrated. A metal surface appears to act as a "regulating. unit" for the redistribution of electrons, without being appreciably affected itself o It is concluded that each system must be subject to a system organization, which appears to be highly developed in zeolites. INTRODUCTION Quantum mechanics describe molecular interactions as due to charge transfer and to polarization effects. Chemists are used to account for charge transfer between two molecules by considering one of them as electron donor and the other one as electron acceptor. Despite the enormous varieties of changes, it has been possible to formulate rules which are (i) based on both qualitative and quantitative observations and (ii)
inde-
pendent of any model assumptions. THE BOND LENGTH VARIATION RULES According to the first of the "bond length variation rules" an intermolecular interaction leads to lengthening of those intramolecular bonds which are adjacent to the donor atom in the donor molecule and to the acceptor atom in the acceptor molecule respectively (ref. 1). This means that the charge density rearrangement occurs throughout the interacting system, and this involves (i) an overcompensation of the loss of negative net charge at the donor atom (pile-up effect of negative charge) due to an increase of positive net charge at the atoms adjacent to the donor atom in the donor molecule and (ii) an overcompensation of the gain in negative net charge at the acceptor atom (spill-over effect of
240
negative charge) due to an induced flow of negative charge to the adjacent atom(s)
in the acceptor component. As a result of
an intermolecular interaction the whole system becomes more polarized, more highly differentiated and more reactive (ref. 1). The positive charges are increased in the peripheric regions of the donor molecule, whereas the negative electric charges are increased in the peripheric regions of the acceptor molecule. Donormolecule
Acceptormolecule
i-
F
J+/ SB--F "<, sF
Induced intramolecular bond lengthening, pile~
effect
of negative charge at the N-atom
intermolecular interaction
Induced intramolecular bond lengthening, spillover effect of negative charge at the B-atom
The second rule concerns the changes in bond lengths in all other molecular areas. Bond lengthening occurs when negative charge is shifted from a more electropositive to a more electronegative atom (as it is usually the case with regard to the bonds adjacent to the donor- and acceptor atom respectively) • Bond shortening takes place when negative charge is shifted from a more electronegative atom to a more electropositive atom within the molecular system. In the first case the bond polarity is increased, whereas in the second case it is decreased. Because in most molecules atoms of higher and lower electronegativities are arranged in alternating positions, alternating bond lengthening and bond shortening is usually taking place (ref. 1). This is illustrated in fig. 1 for the interaction of the donor molecule tetrachloroethylenecarbonate and the acceptor molecule antimony(V)-chloride. Again, substantial amounts of negative charge are shifted from the donor atom towards the peripheric regions of the acceptor molecule (SbCl
thereby increasing the S)' negative net charges of the terminating (chlorine) atoms, whereas
241
the terminating atoms of the acceptor molecule (the chlorine atoms in tetrachloroethylene carbonate) are decreased in negative net charges. Distances after the interaction
Distances before the interaction
Intermolecular interaction (=0:
115 pm
122 pm
0-(:
133 pm
125 pm
(-0:
140 pm 153 pm 176 pm
147 pm 143 pm 174 pm
(-( : (-Cl:
. @ '-"
Sb
e
Cl
0
0
• (
Fig. 1. Changes in bond lengths due to coordination of SbCl to tetrachloroethylenecarbonate (ref. 2, by kind permission of S Barthel and Barthel Publishing). In large molecules the changes in bond lengths are found to decrease with increasing distance from the site of interaction, but they are found more pronounced in the regions terminating the molecular system under consideration. APPLICATIONS TO THE CRYSTALLINE STATE Studies on bond energies have revealed that such alternating changes appear to take place in crystals (ref. 3). For example, in the molecular lattice of crystalline iodine the intramolecular I-I-bonds are longer (272 pm) than in the gas phase (268 pm), because of the much stronger intermolecular interactions in the crystals (first rule). Likewise, the so-called pressure-distance paradox is readily explained (ref. 4)
as a consequence of the
Le Chatelier-Braun principle. Increase in pressure on a crystal leads to pronounced shortening of the greatest internuclear dis-
242
tances (which usually are not considered as chemical bonds). This leads - in accordance with the bond length variation rules to subsequent lengthening of the shortest internuclear bonds of the solid (denoted as chemical bonds)
(ref. 5). For example, when
coesite is converted into stishovite by pressure, both the Si-Sidistances and the O-O-distances are shortened, namely from 301 to 267 pm and from 263 to 251 pm respectively. These contractions of "intermolecular bonds" lead to the lengthening of the "intramolecular" Si-O-bonds from 161 to 178 pm. The model of the ideal crystal and hence the results of complete structure determinations do not allow to account for the properties of a real solid, such as hardness, color, index of refraction, vapor pressure, conductivity, tensile strength, elasticity, actions of cold work or temperature etc. For this reason Wagner and Schottky (ref. 6)
rightly deduced
the unavoidable existence of local "point defects" in any real crystal. Distinctions are made between (i) so-called impurities, (ii) building units at so-called "interstitial" positions and (iii) unoccupied positions (voids, vacancies) in the idealized lattice. Point defects are known to influence the local arrangements of the regular building units. An interstitial atom is always under strain, with rather short "internuclear" distances to its neighbours. This "intermolecular" interaction leads to lengthening of the adjacent distances. Due to alternating changes in internuclear distances a characteristic distortion is produced (refs. 1, 2 and 7), and this is illustrated in fig. 2A. Likewise, a vacancy is known to represent a centre of tension: in its neighbourhood the lattice is contracted, the internuclear distances around the vacancy are shorter than the mean values (refs. 2 and 7, illustrated in fig. 2B). This has been shown by the results of neutron diffraction experiments on TiC o , 85 crystals (ref. 8) and of X-ray investigations on understoichiometric vanadium carbide (ref. 9) and niobium carbide (ref. 10). The measurability of the effects depends also on the experimental technique used. For example, the effects of aluminium atoms in silicon dioxide have been found measurable through 20 layers of Si0
2
by means of the LEED-technique (ref. 11).
243
A
B
Fig. 2. Two-dimensional illustration of structure modifications of an idealized lattice region, due to the presence of an interstitial position (A) and a vacancy (B) (ref. 2, by kind permission of Barthel and Barthel Publishing). Not only is the lattice structure modified by the point defect, but also the point defect by the lattice. Each point defect is und~
stress and produces a strain pattern. It has therefore been
suggested to use the term "structure modified and modifying centre", or, abbreviated, SMM-centre (refs. 12 - 14). Point defects are known to exchange positions within the lattice. The driving forces for those "displacement"-reactions are gradients in chemical potentials, and they are structurally represented by structural inho~;ogeneities. When a building unit jumps from an interstitial into a vacant position, the surrounding lattice areas will be relaxed. When it jumps from a regular into an interstitial position, thus creating a vacancy, the surrounding lattice areas will be strained (refs. 12 - 14). The ordered sequences of displacement reactions are required for the existence of the system as to maintain its configuration under constant conditions and to exert its integral configuration in changing environments. In other words: the static structural aspects must be dynamically maintained. Such relaxations will not be confined to certain areas, but
244
may reach the surface areas, where well-pronounced changes may occur. It may be said that the three-dimensional structural information of the crystal appears to be contained in a reduced two-dimensional form at the interface. Hence, the structural differences between crystal structure and surface structure will be more pronounced the better developed the differentiation and the dynamic aspects in the system under consideration. THE ROLE OF INTERFACES Because the interactions between building units in the crystal are no longer continued at the phase boundary, the lattice parameters near and perpendicular to the crystal surface must be smaller than those within the crystal lattice. This prediction has been made by the quantum chemist Lennard Jones as early as in 1928 (ref. 15), but its confirmation had to await the development of the LEED-technique. By this method it has been established that the mean internuclear distances in silver(lll)-surface planes are by 6% smaller than within the crystal. Towards the interior of a crystal the contraction is followed by an expansion and this by a smaller contraction. What is generally called a "surface" is actually a selvedge of several layers (ref. 16). Accordingly, vibrations of surface constituents are higher both in frequency and in amplitude than their mean values derived for the constituents of the solid (ref. 17). Surface contractions may be overcompensated by strong adsorption, because such intermolecular interactions will lengthen the surface bonds. For example, Horill and Noller (ref. 18) have shown that the peripheric O-H-bonds of aerosile are lengthened to a greater extent, the greater the donor properties of the adsorbed molecules. Far-reaching effects due to adsorption may be seen, for example, from the results of investigations on metal surfaces. By adsorption of tungsten the C=O bonds of carbon monoxide are lengthened (first rule). The extent of bond lengthening is greater, the smaller the number of adsorbed CO-molecules (ref. 19). The mean values for c=o bond lengths of adsorbed molecules decreased with increasing adsorption, even though the adsorbed molecules are still separated from each other by a great number of tungsten atoms. This means that each electronic change due to adsorption at a given point of the surface must
245
be "reported" to other parts of the system, including the adsorbed molecules, which seem to have "informations" about each other. The same results are obtained from the so-called co-adsorption phenomena: the
c=o
bonds of adsorbed carbon monoxide are short-
ened by adsorption of oxygen, as negative charge attracted by adsorbed oxygen atoms is partly provided by adsorbed CO molecules.
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Fig. 3. The donor-acceptor interpretation for co-adsorption of oxygen and carbon monoxide on nickel (ref. 17, by kind permission of Akademische Verlagsgesellschaft Wiesbaden) • Thus, the metal provides electronic charges quite freely when few CO molecules are adsorbed. As their number increases, the metal acts no longer as a source of electrons, but rather as a regulating unit that redistributes the electron densities between the adsorbed molecules but leaves its own electron density nearly unchanged. The regulating functions of the interface concern also the distribution of matter. Drop-like islands are observed in the electron micrographs taken in the course of vapor deposition of tin on a sodium chloride substrate (ref. 20). Nuclei grow to form islands, and ad-atoms deposited at other areas appear to be captured by the islands. As islands increase their size by further deposition, the larger ones appear to grow by coalescence of the smaller ones, which disappear in less than a fraction of a second. Agglomeration is even enhanced and the island density decreased, as the deposition rate is increased. Thus, the expectations for "random walk" or "statistical diffusion" are not fulfilled (ref. 21). The preferred sites for island formation may be the "craters",
246
which may be made visible as "etch pits", because they represent areas of greatest local surface energy and reactivity. The craters are the points of emergence of dislocations, through which matter and energy are distributed throughout the system. It appears therefore that the craters of a surface are of great significance for a solid system with regard to its maintenance of its chief characteristics under different conditions. SYSTEM ORGANIZATION We observe that a system responds to environmental changes without losing its basic characteristics, although each change provokes certain minor changes in it. In order to account for these observations, the following requirements appear inevitable:
(i) the parts of the system must
differ from each other, because a non-differentiated system could never respond to changes while maintaining its chief characteristics,
(ii) hence, each point must serve a certain different
purpose for the whole system, and therefore it must be under the influence of dominating forces of the whole system,
(iii) differ-
ences in domination among the various parts are required in order to allow for the specific influences on other parts, according to a kind of "guiding concept",
(iv) the whole system must have
its own organization, which is the cause of its existence in its own right, and to which we may refer to as system organization. Only a system organization allows a system to respond collectively towards changes in environment, as to counter the external changes in order to preserve its integrity in an optimal way, and this ability depends on the development of the "state" of the system organization. It allows not only to resist and to counteract the influences of the environment. The properties of both preserving and acting are the basis for its characteristic behaviour. In the absence of a system organization no characteristic system properties were possible, the system could not respond to environmental changes in a characteristic way, and hence knowledge about the system could not be obtained. In an attempt to study the different tasks of the different parts for the whole system, it must be borne in mind that such differences can exist only within the continuous matrix, and hence they can be perceived only to a limited extent. We may start their investigation from the wealth of qualitative ob-
247
servations and experimental data, and to pay full attention to all differences that can be noted in behaviour and properties under different conditions. We have even to consider carefully all results which appear anomalous or curious. Such results are of particular value, because they indicate the shortcomings of the present model assumptions rather than inadequacies of natural systems (ref. 6). One should even not ignore the results which are not strictly reproducible. Poor reproducibility is frequently a consequence of differences in system organization due to unknown factors. In order to learn about differences without observable discontinuities, one has to make use of abstractions and to introduce artificial discontinuities in intensities, which are arranged according to certain criteria, such as similarities and common features of different parts. In this way hierarchic levels are introduced. These, however, cannot be considered as clearly definable or independent entities of their own right, but rather as integrated within the whole. Because of their integration in the whole, the hierarchic levels cannot be considered separately, but they serve to illustrate certain aspects of the reality. Detailed studies on solid materials have led to results as illustrated in fig. 4 by means of a truncated pyramid (ref. 6). Fig. 4 shows that the different hierarchic levels parallel the dimensionalities of the so-called "imperfections" familiar to silid state scientists: a higher level corresponds to a higher dimensionality of the imperfections which, indeed, are of great significance for the system organization. It is very important to realize that each of the hierarchic levels is indispensable for the system. As the external conditions are changing, the highest level will "decide" in what way all the other parts have to contribute for the maintenance of the chief characteristics of the system (ref. 22). The highest level is dynamically active and responsible for the system properties (including the so-called "memory effects"), whereas the lowest level is more passive and provides the structural framework for the whole system. The results of various investigations referred to in ref. 7 lead to the conclusion that the lower levels are by no means "exploited" by the higher levels. Instead, the highest level appears to provide the most appropriate conditions for the per-
248 formance of all of the functions of the lower levels
Increasing.; hierarchic signiticance, energy per building unit Decreas!n't. nullber at building units per level
Flat arells ot Phase boundaries and Dislocation nodes fila-dimensional defeds
(ref. 2).
Not in thermal equilibrium ·Memory Eftects·
Dislocation lines one-dimensional defecfs
Regulation ot Number ot point detects ISMM-centre sl
Point detects (SMH-centrul Dissolved Holecules, Ions or Atoms, Vacancies, Interstitials zero-ditnensional def«fs
Indirectly interred
• Norml building units· lowest hierarchic level
Statistical Intorllation, Quantitative Characterization, ·Structural Fralllework" ·TherlllodyOOlllic Leve I •
Fig. 4. Illustration of system organization in a real solid (ref. 2, by kind permission of Barthel and Barthel Publishing). A system organization is improved by strengthening the highest levels, for example by increasing its outer and inner surface areas, by raising the temperature, by the actions of grinding, of fields, of radiation etc. A higher system organization may be retained at lower temperature by quenching. In other words: an amorphous body is considerably better organized than a single crystal. Differences in system organization for a solid of given composition may be illustrated by means of a truncated pyramid obtained in a plot of number of building units in each of the hierarchic levels descending from top to bottom vs. the mean energies per building unit in each level (fig. 5). Neglecting the steps in fig. 5, a broken line has been drawn from the upper edge to the lowest edge of the truncated pyramid. The greater the slope of this line, the better developed is the system organization.
249
B
A \
Craters on Phase boundw'ies 'Flat' areas of Phase bound
[\
Craters on Phose boundaries
,,
\
\
Dislocations 'SMH"- centres
·Normal building ooits·
,
\
'Flat' areas of Phase boundaries
\
1\, 1'\ , t
\
Dislocations ., SMM"- centres
·Normal building units· \
log n
\
\
\
\
\
\
\
\
\
\
(\
\
I' \
log n
\
Fig. 5. Illustration of the system organization in a crystal (A) and in an amorphous body (B). (From ref. 2, by kind permission of Barthel and Barthel Publishing) • Another important discovery is that an optimal system organization is developing in the course of a phase transformation in the solid state. The highly developed dynamic aspects of order are evidenced by the high values in specific heat, in entropy changes and in chemical reactivity (Headvall effect). The well-balanced static and dynamic aspects of order allow the system to acquire different properties by appropriate changes in environment. These are more readily retained by the system the faster it is removed from the transition range (ref. 23). SYSTEM ORGANIZATION IN ZEOLITES The open framework structures of zeolites consist of rings of aluminates and silicate tetrahedra, that provide interconnected networks of holes and channels of various diameters. The wellpronounced amphoteric properties of these inner surface areas resemble those of water and account for the ability to "activate" solutes, whereby the structural framework is but slightly modified and essentially maintained. This means that the inner surface
250
areas function as a kind of "regulating" areas for the redistribution of matter and energy. These activities are subject to the admission of solutes into the channel network. For example, molecular sieve properties depend on the size of the apertures that connect the channels with the outer surface. Their size may be changed by the presence of cations near them. They appear hierarchically higher than the large inner surface areas of the channel-network, as they regulate the admission of water and ions into the latter. The framework of the inner surface area is by no means totally rigid. For example, in chabazite shrinkage is observed in the course of dehydration. Minor framework changes have been reported with ca++, but major changes occur for the ca++ ions. Thus, the properties of the ions appear to be influenced by the more static boundary conditions of the structural framework, and this is modified itself by the actions of the former. Ions and water molecules are not fixed to certain positions, but have a considerable freedom of movement. The reversibilities of the interactions suggest a fair "balance" between dynamic and static features, maintained over a wide range of changes in environmental conditions. This resembles the situation found for
(gradual) phase transformations
in the solid state (ref. 23). Indeed, synthetic zeolites are frequently metastable and liable to phase transformations. The investigation of such transformations may offer possibilities for the manufacture of zeolites with hitherto unknown properties and particularly well-developed system organizations. REFERENCES 2 3 4 5 6 7 8
V. Gutmann, The Donor-Acceptor Approach to Molecular Interactions, Plenum Press, New York, 1978. G. Resch and V. Gutmann, Scientific Foundations of Homoeopathy, Barthel and Barthel Publishing, Berg near Mlinchen, 1987. G.M. Bliznakov and Sv.P. Delineshev, Kristall und Technik, 7 (1972) 793-802 V. Gutmann and H. Mayer, Structure and Bonding, 31 (1976) 49-66. T. Zoltai and M.J. Buerger, Z. Kristallographie, 111 (1959) 129-141. G. Wagner and W. Schottky, Z. physik. Chern. (B), 11 (1930) 163-210. V. Gutmann and G. Resch, Zeitschr. f. Chem., 19 (1979) 406-412. H. Goretzki, Phys. Status Solidi, 20, K (1967) 141-144.
251
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
D.Kordes, Phys. Status Solidi, 24, K (1968) 103-108. C. Froidevaux and D. Rossier, J. Phys. Chern. of Solids, 28 (1967) 1197-1209. A. Weiss, Hauptversammlung Deutscher Chemiker, Kaln, 1975 G. Resch and V. Gutmann, Z. physik. Chern. (Frankfurt), 121 ( 1 980) 211 - 23 5. V. Gutmann and G. Resch, Acta Chim. Acad. Sci. Hung., 106 (1981) 115-129. V. Gutmann and G. Resch, Revs. Inorg. Chern. 2 (1980) 93-138. E.J. Lennard-Jones and B.M. Dent, Proc. Roy. Soc. London, A, 121 (1928) 247-259. K. Mliller, Ber. Bunsenges. Phys. Chern., 90 (1986) 184-190. G. Resch and V. Gutmann, Z. physik. Chern. (Frankfurt), 126 (1981) 223-241 P. Horill and H. Noller, Z. physik. Chern. (Frankfurt), 100 (1976) 155-163 J.T. Yates and D.A. King, Surface Science, 30 (1972) 601-616. L.E. Murr, Interface Phenomena in Metals and Alloys, AddisonWeseley, Reading/Mass., 1975. K.L. Chopra, Thin Film Phenomena, McGraw Hill Co., New York, 1969. V. Gutmann and G. Resch, Comments Inorg. Chern., 1 (1982) 265-278. V. Gutmann and G. Resch, Inorg. Chim. Acta, 72 (1983) 269-275.