In feldspars, mean tetrahedral T–O bond lengths (T = Al,Si) are the standard measure of the tetrahedral Al content. However, for a sophisticated assessment of the Al,Si distribution, factors have to be accounted for (1) that cause individual T–O bond lengths to deviate from their tetrahedral means and (2) that cause mean tetrahedral lengths to deviate from values specified by the Al content. We investigated low albite, Na[AlSi3O8], from six X-ray crystal structure refinements available in the literature. The Al,Si distribution of low albite is fully ordered so that Al,Si–O bond length variations result only from bond perturbing factors. For the intra-tetrahedral variation ΔT–O≡T–O−⟨T–O⟩, only two factors turned out to be effective: (1) the sum of bond critical point electron densities in the Na–O and T–O bonds neighbouring the T–O bond under consideration and (2) the fractional s-bond character of the bridging oxygen atom. This model resulted in a root mean square (rms) value for ΔT–O of only 0.002 Å, comparable to the estimated standard deviations (esd's) routinely quoted in X-ray and neutron structure refinements. In the second step, the inter-tetrahedral differences Δ⟨T–O⟩≡⟨T–O⟩−⟨⟨T–O⟩⟩ were considered. ... mehrHere, apart from the tetrahedral Al content, the only size-perturbing factor is the difference between the tetrahedral and the grand mean fractional s-characters. The resulting rms value was as small as 0.0003 Å.
From this analysis, Al site occupancies, t, can be derived from observed mean tetrahedral distances, 〈T–O〉$_{obs}$, as
t =0.25(1+n$_{An}$)+(⟨T–O⟩$_{adj}$−⟨⟨T–O⟩⟩)/0.12466(17),
with the observed distance 〈T–O〉$_{obs}$ adjusted for the influence of the fractional s-character, ⟨T–O⟩$_{adj}$=⟨T–O⟩$_{obs}$+0.1907(51)[⟨f$_{s}$(O)⟩−⟨⟨fs(O)⟩⟩]. This equation served to determine the site occupancies of 16 intermediate to high albites and one analbite from their mean tetrahedral distances. It was found that the individual site occupancies t$_{1}$0, t$_{1}$m and t$_{2}$0= t$_{2}$m all vary linearly with the difference Δt$_{1}$= t$_{1}$0− t$_{1}$m. Δt$_{1}$, in turn, varies linearly with the length difference, Δtr[110], between the unit cell repeat distances [1∕2a, 1∕2b, 0] and [1∕2a, −1/2b, 0]. Then, from the Δtr[110] indicator, values of t were obtained as
t$_{1}$0=(1−b$_{0}$)+b$_{0}$(b$_{1}$+b$_{2}$Δtr[110])
t$_{1}$m =(1−b$_{0}$)−(1−b$_{0}$)(b$_{1}$+b$_{2}$Δtr[110])
t$_{2}$0 = t$_{2}$m=(b$_{0}$−0.5)−(b$_{0}$−0.5)(b$_{1}$+b$_{2}$Δtr[110]),
with b$_{0}$=0.7288(16), b$_{1}$=0.1103(59) and b$_{2}$=3.234(32) Å$^{-1}$.
Finally, from an expression that converts the Δ2θ(131) measure of order into Δtr[110] and thus into site occupancies, it was possible to obtain from the unique suite of bracketed high-pressure experiments performed on albites by Goldsmith and Jenkins (1985) the evolution with equilibrium temperature of the thermodynamic order parameter Qod and of the individual Al site occupancies t at a pressure of 1 bar. For that purpose, since the Goldsmith and Jenkins experiments were performed at ≈18 kbar, a procedure was devised that accounts for the effect of pressure on the state of order. At 1 bar, low albite is stable up to 590 ∘C, where it begins to disorder, turning into high albite above 720 ∘C. The highly though not fully disordered monoclinic state (monalbite) is reached at 980 ∘C, 1 bar, and 1055 ∘C, 18 kbar, respectively. Eventually, when applying the determinative equations given above to low microcline, full order is predicted as in low albite.
