According to Pauling's rules for crystal structures, the allowed size of the cation for a given structure is determined by the critical radius ratio.
12.
If the radius of the insulated cylinder is smaller than the critical radius for insulation, the addition of any amount of insulation will increase heat transfer.
13.
A cluster of nanotubes is kept afloat by having a lower density than water, provided by a thin film of air trapped between nanotubes closer than the critical radius by surface tension.
14.
Hence, at a critical radius of about 5 nm, dislocations will preferably cut across the obstacle, while for a radius of 30 nm, the dislocations will readily bow or loop to overcome the obstacle.
15.
Bubbles with semipermeable surfaces will either stabilise at a specific radius depending on the pressure, the composition of the surface layer, and the supersaturation, or continue to grow indefinitely, if larger than the critical radius.
16.
"' Jeans'length "'is the critical radius of a cloud ( typically a cloud of interstellar dust ) where thermal energy, which causes the cloud to expand, is counteracted by gravity, which causes the cloud to collapse.
17.
This theorem states the existence of a critical radius r _ c \, \ ! such that the state of lowest free energy is one of uniform magnetization if r ( i . e . the existence of a critical size under which spherical ferromagnetic particles stay uniformly magnetized in zero applied field ).
18.
The third proposed theory for ion suppression in ESI relates to the presence of non-volatile species which can either cause co-precipitation of analyte in the droplet ( thus preventing ionisation ) or prevent the contraction of droplet size to the critical radius required for the ion evaporation and / or charge residue mechanisms to form gas phase ions efficiently.
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