Axial relationships

The axes are labeled ai, aa, and as, which correspond to the x, y, z coordinates in the Cartesian coordinate system. The axis ai is assumed to extend toward the reader, as is perpendicular to ai but in the same plane, and as is the vertical axis. For a cubic unit cell the distance from the comer of the cell to each face of the cell is the same along each of the axes. Thus, ai, as, and as are equal in length in the cubic system (the lines representing the extension of the axes are drawn longer for convenience). The fact that the axes have the same length is emphasized in another name for the cubic system— isometric (jso means same or constant, metros means measure). 

These are the lengths of the bold lines along the inside edges of the unit cell. 

We must now add a slight complication. We have not discussed several other symmetry elements. These elements involve translation (movement) of the unit cell within the 

---

If the scale ratio is not the same along each axis, the relationship among the two bodies is of a distorted geometric similarity and the axial relationships are given by... 

Mercury fulminate consists of octahedral crystals, belonging to the orthorhombic system with the axial relationship a b c=0.712 1 1.353 (Miles [13]). The pure substance crystallizes into the form of white, silky needles. 

An additional feature of the protosteryl cation is that the C-10 methyl and H-5 also share an anti-axial relationship, and are also susceptible to Wagner-Meerwein rearrangements, so that the C-9 cation formed in the cycloartenol sequence may then initiate further migrations. This can be terminated by formation of a 5,6-double... 

For more conformationally-constrained chiral substrates, however, diastereoselectivity can be expected to be good to excellent. Lithium enolates derived from sterically unencumbered cyclohexanones undergo preferential axial acylation as illustrated by the reductive acylation of (R)-(-)-carvone 4 to afford a 3 1 mixture of esters 5 and 6. whereas equatorial acylation is favored in compounds that possess an alkyl substituent in a 1,3-syn-axial relationship to the reacting center, as in the conversion of tricyclic enone 7 to ester 8 (epimeric with the product from the more traditional sequence of acylation followed by alkylation). (In substrates of this kind it is assumed that the transition state structure is based on a twist-boat conformation which permits the reagent to approach along an axial-like trajectory on the less encumbered, lower face of the substrate.) ... 

The low tendency for formation of l,2 3,5-di-0-isopropylidene-a-D-glucofuranose may be explained in terms of the unfavorable interactions between the hydroxymethyl substituent on C-5 and one of the methyl groups of the 3,5-isopropylidene moiety, which would have a syn-axial relationship. One of the two most probable conformations12 is shown in formula 12. 

Crystal family Crystal system Axial relationships... 

Wenk H-R, Heidelbach F (1999) Crystal alignment of carbonated apatite in bone and calcified tendon results from quantitative texture analysis. Bone 24 361-369 White SW, Hulmes DJS, Miller A (1977) Collagen-mineral axial relationship in calcified turkey leg tendon by X-ray and neutron diffraction. Nature 266 421-425 Williams RAD, Elliott JC (1989) Basic and Applied Dental Biochemistry, 2nd edn. Churchill Livingstone, Edinburgh... 

The a-glucopyranose moiety was indicated by the chemical shifts in the and NMR spectra (Table 1). In the NMR spectrum, the small coupling constant (4.5 Hz) between the anomeric proton and H-2", due to an equatorial-axial relationship between both protons, established the a-configuration of glucose. 

In an isotope converter, a tank, a neutronic reactor in co-axial relationship with said tank and separated therefrom in spaced relationship thereto by a neutron-permeable wall, means for moving said tank, and... 

Keats TE, Teeslink R, Diamond AE, Williams JH (1966) Normal axial relationships of the major joints. Radiology 87 904-907... 

---