They are the minerals that possess the Brucite layer, and magnesium occupies the three crystalline sites of the octahydra layer such as serpentine (1: 1), saponite(2:1), chlorite(2:2) and others.
Dioctahedral two-layer silicates in which 2/3 of the octahedral gaps are covered with Al3 + ions are called kaolinite minerals. Relevant examples here are the minerals kaolinite and disordered kaolinite-D, where the crystal lattice is arbitrarily shifted in the b direction.
Ideal structural formula for Kaolinite is: Al4 [(OH)8ISi4O10]
Ideal total formula for Kaolinite is: Al2Si2O5(OH)4
In contrast, two-layer silicates with full occupancy by Mg2 + ions in the octahedron are called serpentine minerals. Examples are the minerals chrysotile and antigorite with the ideal structural formula
chrysotile Mg6 [(OH)8ISi4O10]
antigorite (Mg,Fe2+)6 [(OH)8ISi4O10]
For further details please search in https://www.mindat.org
Dioctahedral and trioctahedral clay minerals are described in the most simple way by the difference in the charge balance of dioctahedral and trioctahedral clay minerals and can easily be documented by the two important clay mineral groups of the mica and smectite groups.
Muscovite is dioctahedral showing the chemical composition KAl₂[(OH, F)₂|AlSi₃O₁₀], biotite is trioctahedral with the chemical composition K(Mg,Fe2+,Mn2+)3[(OH,F)2|(Al,Fe3+,Ti3+)Si3O10].
The dioctahedral phyllosilicate muscovite needs to accommodate a monovalent cation K + and two trivalent cations of Al +++ in its lattice to achieve charge balance, whereas biotite needs three bivalent cations (Mg++, Fe++, Mn++) and one monovalent cation (K+). For trivalent Al also trivalent Fe can substitute.
The same approach can be taken for another more complex clay mineral group called smectites. Saponite has the chemical formula (Ca/2,Na)0.3(Mg,Fe2+)3(Si,Al)4O10(OH)2.4(H2O). It is as far as the crystallographic structure is concerned similar to biotite (trioctahedral), whereas another Fe-bearing smectite , called nontronite is dioctahedral Na0.3Fe3+2 Si3AlO10(OH)2.4(H2O). The latter clay mineral couple can be used as a geo-redox marker. Nontronite is common to environments of oxidizing regimes due to the trivalent Fe , whereas bivalent Fe-bearing saponite is typical of reducing environments.
Please refer to a book on clay minerals. One such book is ''Minerals in soil environments'' by Dixon, J.B., Weed, S.B. (Eds.), Second Edition. : Soil Science Society of America Book Series (Number 1), Wisconsin, USA,
The term is not directly related to charge balance, as suggested above. It's simply referring to the occupancy of the octahedral layer/sheet. It might be fully occupied (mostly by a divalent cation), and then it's a brucite or trioctahedral layer, or occupied in a proportion of 2/3 (mostly by a trivalent cation), and then it's a gibbsite or dioctahedral layer. However, there are trioctehadral layers containing trivalent cations, and here comes charge balance into play.
the crystallographic structure and charge balance go hand in hand and to visualize the differences between the two common structures (see attached file in my fits post) charge balance is the best choice as long as you try and avoid crystallographic lattice cartoons of saponite, nontronite or kaolinite and serpentine group models.
It depends on the name of the layer The second structural unite in clay mineral structure is the octahedral sheet, in which the hydroxyl atoms (OH) in the corners and cations in the centre. . When aluminium with positive valence of three (Al +3) is present in the octahedral sheet, only two-thirds of the possible positions are filled in order to balance the charges. When only two octahedral sites filled with trivalent cations is a dioctahedral sheet. When magnesium with a positive charge of two (Mg+2) is present, all three positions are filled by divalent cations is a trioctahedral sheet .
In dioctahedral minerals two of the crystalline sites are filled with trivalent cations like Al+3, Fe+3 Like the muscovite mineral with the chemical composition KAl2(AlSi3O10)(FOH)2, As for the trioctahedral all crystalline sites are filled with a divalent cation like Mg+2, Fe+2 Like the biotite mineral with the chemical composition
@ Awatif Hameed Alshamare, u have made it simpler, but in addition, Octahedral layer of silicate clay has 6 chrystalline site which requires to be filled with positively charged ions, if this sites are filled with divalent cation like Mg2+ or Fe2+ etc, then the site will require 3 of any of the divalent cation to be stable, filling up the charge space thereby it's called tri-octahedral e.g biotite., on the other hand if the charge space is filled with trivalent cation e.g Al3+ or Fe3+ etc, the charge space will only require 2 of the trivalent cation to be stable, this is called Di-octahedral, e.g muscovite mineral.
In the case of smectite group minerals, the octahedral layer in which all three octahedral positions are filled is called trioctahedral and when two-thirds of the possible positions are filled is called dioctahedral. As an example of smectite mineral, beidellite is dioctahedral smectite when Al 3+ fills only two out of three octahedral positions.