Structure of Olivine Group of Minerals

The video explains the basic structure of Olivine group of minerals.
In the nesosilicates the SiO4 tetrahedra are isolated and bound to each other only by ionic bonds from interstitial cations.
Mineralogists often call isolated tetrahedral silicates as island silicates because tetrahedra do not share oxygen.
In orthosilicates, all of the chemical formulas, the Z:O ratio is always 1:4, consistent with the ratio required by the structure.
Olivine, (Mg,Fe)2SiO4, and Garnet, (Ca,Mn,Fe,Mg)3Al2Si3O12 are examples.
The basic structure of the orthosilicates in most cases consists of isolated silicon tetrahedra bonded with other cations (Ca, Mg, Fe, Al, etc.) in octahedral or higher coordination with the oxygen anions of the silicon tetrahedra.
The atomic packing of the nesosilicate structure is generally dense, causing the minerals of this group to have relatively high specific gravity and hardness.
Have orthorhombic symmetry.
The structure of olivine has independent SiO4 tetrahedral cross linked with divalent octahedral cations.
It consists of a layered hexagonal close-packed array of oxygen atoms lying parallel to {100}.
The silicon ions (Si4+) occupying one- eighth of the tetrahedral voids, cross linked by divalent cations such as Ca2+, Ferous iron (Fe2+) and Mg cations occupying one-half of the octahedral sites.
The Si share oxygen with adjacent octahedral, not with other tetrahedral.
There are two symmetrically nonequivalent octahedral sites, M1 and M2.
In the (Mg,Fe)2SiO4 olivines, Mg and Fe2+ occupy the M1 and M2 sites without any specific preference for either site.
In the calcic olivines (e.g., monticellite, CaMgSiO4), larger site contains Ca2+ in the M2 site and Mg into M1.
Members of the olivine group are essentially rock forming minerals characterized by the presence of magnesium (Mg) in rocks poor in silica, or by iron (Fe) in rocks that are silica rich.
Mg-rich olivines are drawn from the upper reaches of the Upper Mantle at depths from the surface of approximately 550 km.
Olivines are also present in some metamorphic rocks and are an important constituent of meteorites.
References:
Introduction to Mineralogy, WD Nesse, Oxford University Press, 2000.
Mineralogy, Dexter Perkins (3rd Ed.), Pearson Education, 2014
Klein, C. and Hurlbut, C.S. 1993. Manual of Mineralogy, 2nd edn. New York.
Geology Today, The Geologists’ Association & The Geological Society of London, Vol. 25, No. 5, 2009, Blackwell Publishing Ltd.