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The title pretty much says it all. I cannot find a satisfactory definition of "lattice bound", just a number of examples of it being used in literature. For example, in this paper about removing lattice bound trace elements from quartz, I understand how germanium or titanium is quite literally a part of the lattice and not interstitial and the charge compensators are not, but quartz has a very simple unit cell.

In illite or, more importantly for me, in glauconite is iron bound in the octahedral sites considered "lattice bound" and why? Is this an octahedral void they are occupying or not? As a bonus I would love to know how both oxidation states of iron (2+ and 3+) can be bound in glauconite simultaneously. Are they both occupying octahedral sites or are they bound in different structural sites depending on oxidation number?

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We definitely have +2 and +3 ions bonded within the same type of site. And it's not just iron; magnesium can become involved among the +2 ions and aluminum among the +3 ions. As for whether they are "lattice bound" or not, I would say that those multiply charged ions are tighly bound into a lattice structure that covers their part of the overall layered mineral structure, and only some weakly bound alkali metal ions elsewhere, between the layers, "look" interstitial.

Glauconite has a mica-group phyllosilicate structure and the (nominal) chemical formula

$\ce{(K,Na)\color{blue}{(Fe,Al,Mg)2}\color{brown}{(Si,Al)4O10}\color{blue}{(OH)2}}.$

where I mark parts of the formula is different colors for the purpose of understanding this structure.

Mica, as readers of this question thread probably know, consists of layers that are weakly bound by interlayer ions. The black ions noted above, which are akali metals carrying one positive charge per ion ($\ce{Na^+,K^+}$), are the interlayer ions. It is these interlayer iins, which are only weakly bound and give micas their sheetlike structure and low Mohs hardness, that most qualify as "interstitail"; the more strongly bound rest of the structure is more arguably "lattice-bound".

The brown part of the formula is the silicate sheets that form the outer parts of the layers, like buns of a burger. These are polymrized tetrahedral silicate networks in which some of the silicon ($\ce{Si^{4+}}$) may be replaced by aluminum ($\ce{Al^{3+}}$), All of these are bound tetrahedrally to oxygen ($\ce{O^{2-}}$), with three of the oxygen atoms bonded to each silicon serving as bridges within the "bun" and the fourth oxygen open for bonding to the "meat" inside.

Which brings us to the meat of the burger, indicated in blue. The open oxygen valences from the silicate layers are bonded to the multiply charged ions indicated in blue, which are additionally bonded to hydroxide ions ($\ce{OH^-}$) also shown in blue. The metals ions are octahedrally coordinated and may be any combination of those indicated in the formula: $\ce{Fe^{2+},Fe^{3+},Al^{3+},Mg^{2+}}$. The mixed charges come from the fact that the two positive ions have to balance out with the net negative charge in the rest of the structure, and that charge balance can't be done wuth one type of ion charge.

Let's look at the charge balance, recalling the chemical formula above:

$\ce{(K,Na)\color{blue}{(Fe,Al,Mg)2}\color{brown}{(Si,Al)4O10}\color{blue}{(OH)2}}$

The "black", interlayer alkali metal iobs contribute one positive charge per site. The "brown" or "bun" layer can contribute anywhere from four to eight negative charges per $\ce{(Si,Al)4O10}$ unit, with four corresponding to all silicon and eight to all aluminum; in practice the tetrahedrally bound atoms are mostly silicon and thus this figure is really between four ($\ce{Si4O10^{4-}}$) and five (($\ce{AlSi3O10^{5-}}$)). The hydroxide ions within the "meat" add two more negative charges per formula unit. Adding all this up we find that the two metal ion sites per formula unit in the "meat" must add up to between five and six positive charges. Thus the mixture of +2 and +3 ions, with the latter becoming more predominant if the "buns" are relatively rich in aluminum. Given the ion size constraints to fit in the mica structure and which metallic ions are most common in the crust, we will end up with some combination of primarily iron, aluminum and magnesium satisfying this mixed charge requirement.

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