Pressure-coordination rule

Generally, the following rules apply for pressure-induced phase transitions Pressure-coordination rule by A. Neuhaus with increasing pressure an increase of the coordination number takes place. 

In 1985 McMahan and LeSar predicted that the triple bond in molecular nitrogen should be breakable under very high pressures and a solid should be formed which consists of trivalent (i.e. three-coordinate) nitrogen atoms (pressure-coordination rule). Such structures already exist at normal pressures for the other group 15 elements phosphorus, arsenic, antimony and bismuth. The transformation pressure for nitrogen should lie in a range between 500 and 940 kbar. An estimation... 

The most useful rule in describing the effect of pressure on solids is the so-called Pressure-Coordination Rule (i, 2) according to which the coordination number is increased with pressure. In Table 1 and 2 examples are listed for various crystal structure transformations which follow this qualitative mle at different pressures and temperatures. An exception to this mle is known, however, for ytterbium (2) the cubic face-centered modification (coordination number = 12) of the metal is transformed at 40 kbar into a cubic space-centered stmcture (coordination number = 8). 

Although this simple cubic phase is unknown for Te, the structurally closely related rhombohedral Te(lV) phase with the [jS-Po] structure (stable between 11 and 27 GPa) exhibits just such an octahedral Te coordination where all six nearest-neighbor distances are equal [276]. This finding may be looked upon as a reminiscence of the pressure-homologue rule of crystal chemistry [5], namely that, under pressure, an element tends to adopt the structure of its higher homologues. 

This expression describes the variation of the pressure-temperature coordinates of a first-order transition in terms of the changes in S and V which occur there. The Clapeyron equation cannot be applied to a second-order transition (subscript 2), because ASj and AVj are zero and their ratio is undefined for the second-order case. However, we may apply L Hopital s rule to both the numerator and denominator of the right-hand side of Eq. (4.47) to establish the limiting value of dp/dTj. In this procedure we may differentiate either with respect to p. 

For any specific BW application, the boiler design, pressure-temperature, operation, and heat-flux rate are all contributing factors these chemistries generally function at substoichiometric levels (the coordinating and complexing polycarboxylic component of polymers aside), so that the use of reliable, directly measurable relationships is not always possible. Nevertheless, some rules and recommendations do exist, a few of which are discussed later. 

A chart which correlates experimental P - V - T data for all gases is included as Figure 2.1 and this is known as the generalised compressibility-factor chart.(1) Use is made of reduced coordinates where the reduced temperature Tr, the reduced pressure Pr, and the reduced volume Vr are defined as the ratio of the actual temperature, pressure, and volume of the gas to the corresponding values of these properties at the critical state. It is found that, at a given value of Tr and Pr, nearly all gases have the same molar volume, compressibility factor, and other thermodynamic properties. This empirical relationship applies to within about 2 per cent for most gases the most important exception to the rule is ammonia. 

In the case of a unary or one-component system, only temperature and pressure may be varied, so the coordinates of unary phase diagrams are pressure and temperature. In a typical unary diagram, as shown in Figure 3.11, the temperature is chosen as the horizontal axis by convention, although in binary diagrams temperature is chosen as the vertical axis. However, for a one-component system, the phase rule becomes F=l-P+2 = 3-P. This means that the maximum number of phases in equilibrium is three when F equals zero. This is illustrated in Figure 3.11 which has three areas, i.e., solid, liquid, and vapour In any... 

Pressure-distance paradox by W. Kleber When the coordination number increases according to the previous rule, the interatomic distances also increase. 

Further examples where these rules are observed are as follows. Under pressure, some compounds with zinc blende structure, such as AlSb and GaSb, transform to modifications that correspond to the J3-Sn structure. Others, such as InAs, CdS, and CdSe, adopt the NaCl structure when compressed, and their atoms thus also attain coordination number 6. Graphite (c.n. 3, C-C distance 141.5 pm, density 2.26 gem-3) pr Te diamond (c.n. 4, C-C 154 pm, 3.51 gem-3). 

Accdg to remarks of Dunkle (Ref 8), an ideal detonation can be visualized as a steady-state process, in a frame of reference in which the detonation zone is stationary and time-invariant, with the undetonated explosive being "fed into the front at the detonation velocity D and with laminar flow of the products away from the C-J plane the rear boundary of the reaction zone is at velocity (D-u), where u is the particle velocity of the products in stationary coordinates. By the Chapman-Jouguet rule, D-u = c, the local sonic velocity at the C-J plane. That is, the velocity of the products with respect to the detonation front is sonic at the C-J temperature and pressure. Thus, even if the products were expanding into a vacuum, the rarefaction wave would never overtake the detonation front as long as any undetonated explosive remains... 

High-temperature modifications generally have lower coordination numbers, just as low-pressure modifications do. Structures of certain metals such as Zn, Cd and Hg do not conform to this pattern. Mercury has a rhombohedral structure in which each atom is six-coordinated following the (8 — N) rule indicating the presence of the covalent... 

Propane as a degradation product of polyethylene (a byproduct in the reaction) was ruled out because ethylene alone under the same conditions does not give any propane. Under similar conditions but under hydrogen pressure, polyethylene reacts quantitatively to form C3 to C6 alkanes, 85% of which are isobutane and isopentane. These results further substantiate the direct alkane alkylation reaction and the intermediacy of the pentacoordinate carbonium ion. Siskin also found that when ethylene was allowed to react with ethane in a flow system, n-butane was obtained as the sole product, indicating that the ethyl cation is alkylating the primary C—H bond through a five-coordinate carbonium ion [Eq. (5.66)]. 

The alkali metals react with many other elements directly to make binary solids. The alkali halides are often regarded as the most typical ionic solids. Their lattice energies agree closely with calculations although their structures do not all conform to the simple radius ratio rules, as all have the rock salt (NaCl) structure at normal temperature and pressure, except CsCl, CsBr and Csl, which have the eight-coordinate CsCl structure. The alkali halides are all moderately soluble in water, LiF being the least so. 

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