Crystal paradox

In principle, the force necessary to cause a brittle break F = E jL can be calculated from the energy E required to separate chemical and physical bonds by an interbond-partner distance L. To break extended-chain poly-(ethylene) crystals perpendicular to the chain direction (i.e., breaking covalent bonds), a force of about 20 000 MPa is necessary, whereas to cause a break parallel to the chain direction (i.e., working only against dispersion forces), only 200 MPa is required. Experimentally, however, a maximum tensile strength of 20 MPa is observed (the so-called crystal paradox). Consequently, the break must occur at inhomogeneities, since these lead to an inhomogeneous distribution of the tensile stress onto disruption points and thus lead to stress concentrations. 

The commonest form of phosphorus, and the one which is usually formed by condensation from the gaseous or liquid states, is the waxy, cubic, white form o -P4 (d 1.8232 gcm at 20°C). This, paradoxically, is also the most volatile and reactive solid form and thermodynamically the least stable. It is the slow phosphorescent oxidation of the vapour above these crystals that gives white phosphorus its most characteristic property. Indeed, the emission of yellow-green light from the oxidation of P4 is one of the earliest recorded examples of chemiluminescence, though the details of the reaction... 

In conclusion, nucleosome cleavage periodicity data, together with direct measurements of a defined nucleosome crystal structure, suggest that wrapped DNA may be overtwisted to different extents, but in no case do these overtwistings appear sufficient to explain the paradox ( 0.5 bp/turn overtwisting required, against 0.2 bp/turn observed at the most). 

Calcium fluoride does not form a hydrate, yet the surface easily acquires a layer of water this, however, is not formed on crystals which form hydrates. This at first sight appears to be somewhat paradoxical, but the explanation is quite simple. The water molecules are held very strongly by the calcium fluoride, due to the strong field of the ions which also holds the crystal together and at the same time prevents the penetration of water. Water can only penetrate those compounds which have weaker ionic fields, but it will then no longer be held so strongly and certainly not on the surfaces of the crystal. 

Single-crystal cesium electride" is almost entirely diamagnetic. Reconcile this with the formulation [Cs(ligand)) e. Is there a paradox here ... 

It is worthwhile to discuss why the mass-action law on concentration basis (moles/litre) is plausible. It is beyond doubt that it is not always valid. The concentration 5.5 M of saturated aqueous sodium chloride indicates the solubility product 30 moles2/litre2. If an equal amount of such a solution is added to 12 M hydrochloric acid, the concentration of Na+ is 2.75 M and of Cl- (12 + 5.5)/2 = 8.75 M. Their product 24.06 M2 is distinctly below the solubility product, but nevertheless, more than 80 percent of the NaCl present crystallizes out. It would be to short-circuit this paradox to speak about the mass-action law on activity basis. The introduction of activity a as the product a =/Cof the activity coefficient/and the concentration is a tautological trick to keep the mass-action law valid, and it is more fruitful to try to explain why/varies more dramatically in some cases than in others. 

Apart from subtle exceptions, an isolated molecule differs from a molecule in a crystal in that the isolated molecule has no shape, whereas in a crystal it acquires shape, but loses its identity as an independent entity. This paradoxical situation is best understood through the famous Goldstone theorem, which for the present purpose is interpreted to state that any phase transition, or symmetry broken, is induced by a special interaction. When a molecule is introduced into an environment of other molecules of its own kind, a phase transition occurs as the molecule changes its ideal (gas) behaviour to suit the non-ideal conditions, created by the van der Waals interaction with its neighbours. An applied electric or magnetic field may induce another type of transformation due to polarization of the molecular charge density, which may cause alignment of the nuclei. When the field is switched off the inverse transformation happens and the structure disappears. The Faraday effect (6.2.3) is one example. 

Freeze-tolerant insects and plants have been found to contain substantial concentrations of AFP s, a phenomenon that may appear paradoxical. However, THPs present in the extracellular fluids may contribute importantly to freeze-tolerance by inhibiting recrystallization, thus keeping the ice crystals that do form in the extracellular space small enough to prevent... 

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