Unit Cell Parameter in Reference to End-member Spinels 75

faces of the spinel prism, and this shows the change in unit cell as a function of composition between end members. The smallest unit cells are associated with spinel (sensu stricto), MgAl2O4, having Mg2+ (0.585 Å) and Al3+ (0.53Å). The largest unit cells

are associated with magnesiochromite, MgFe2O4; this is due to Fe2+ (0.615 Å) and Cr3+

(0.615Å) being relatively large. The base of the prism is composed of normal spinel- group minerals: hercynite, chromite, magnesiochromite, and spinel. The first three are completely normal but spinel is 7% inverse (Hill and Roeder 1974). The top of the prism is defined by inverse spinel-group minerals, with ulvöspinel being 100% inverse and magnesioferrite being 90% inverse (Haggerty 1986).

4.4.4.1

Ternary Element Plots–Prism Faces

The trivalent prism, as seen in Figure 4-4(a) is defined by the Fe3+ on the vertical axis and the divalent prism is defined by the Ti4+, as seen in Figure 4-4(b). Considering the

ternary of the spinel prism enables a better understanding of how unit cell becomes affected by multiple substitutions at once. As a general measure of composition it is critical to understand how these relationships work in the natural environment and simultaneous to each other, as only through this understanding can we reduce ambiguity. Figure 4-12a shows the ternary projection of the elements controlling the prism of the oxidized trivalent prism. The most obvious driver of the unit cell parameter in this view is the Cr-Al relationship, but the unit cell parameter does increase slightly with increased Fe3+. Figure 4-12b shows the relationship between Cr-Al-Ti but due to the paucity of Ti in

Figure 4-12. Ternary projections. a) This plot shows the relationship between Cr, Al, Fe3+and unit cell. There is a clear increase in unit cell size with increasing Cr (and decreasing Al); a slight increase in unit cell can be observed toward Fe3+. b) This plot shows the relationship between Cr, Al, Ti and unit cell. There is minimal Ti in our data set. Plotting software adapted from (Sandrock. 2002).

4.4.4.2

Trivalent Plot Sides / Divalent Plot Sides

Some data did spread upwards toward the magnesioferrite and magnetite end members, as can be seen on the side view of the prism in Figure 4-13. A slight spread toward the ulvöspinel (Fe2TiO4) may exist, but there was only a small amount of Ti. It is worth

noting Fe3+ and Ti often are linked since Ti has a greater ability to partition in magnetite (Barnes and Roeder 2001). It is important that there be minimal Fe3+ and Ti4+ in the samples, when deciding on populations to attempt using the unit cell parameter as a compositional proxy, because order-disorder relationships will lead to scattering. When greater proportions of end-member inverse spinels are included in the system, the data become more scattered. This could be due to cation order-disorder (O'Neill and Navrotsky 1983).

Figure 4-13: Side view of spinel prism that emphasizes the importance of a constrained system when using unit cell as a proxy for composition. (Note: Fe2+ and Fe3+ are calculated values.)

4.4.4.3 Prism Base

The base of the prism, Figure 4-14, shows the clear spread from spinel through to

chromite, with increasing unit cell size toward the chromite. A limitation of unit cell as a chemical proxy in spinel group minerals is illustrated by the Matsitami/Tutume series where the more Fe-rich end members provide similar unit cells to a subset of Cr-rich grains with lower Fe. The spinel gap described by Barnes and Roeder (2001) will limit the number of possible overlaps but will not eliminate the issue entirely. This can be most easily seen in the base of the spinel prism which is common to both the divalent and trivalent prisms as seen below. The utility of using unit cell as a proxy is caused by the substitution of Cr3+ (0.615Å) for Al3+ (0.53Å) and, as the larger ionic radius atom is

Figure 4-14: Spinel prism base, showing the clear use of unit cell in binary systems. The Cr substitution for Al is clearly demarcated by an increase in unit cell size.

Fe

/(Fe

+Mg)

substituted in the unit cell, it swells. We also see a similar increase in unit cell from chromite to magnesiochromite, with the substitution of Fe2+(0.615 Å) for Mg2+ (0.585 Å). The multiple substitutions lead to ambiguity, because any of these larger ions can cause a swelling or shrinking of the unit cell parameter. Again, some scatter is also caused by order-disorder relationships, but these effects should be small compared with chemical substitutions, because the crystallization and subsequent annealing histories of most of the studied grains should be reasonably similar. A double substitution reaction occurs between hercynite and chromite, where Cr3+ (0.615 Å) substitutes for Al3+ (0.53 Å) simultaneous with Mg2+(0.585 Å) substituting for Fe2+(0.615 Å). The Cr3+ for Al3+

substitution has the greater net effect, because the radii difference is greater and there are twice as many Cr3+ substitutions occurring as Fe2+, but as mentioned previously, in the Matsitami/Tutume series there is some ambiguity because the system is not constrained to a binary solid solution. There is some spread in the divalent pyramid due to

magnesioferrite and magnetite components, but it is minimal due to the low amount of Fe3+ in the system. The spread can be seen in the largest unit cells with a high Cr number (Cr/Cr+Al). The unit cell parameter of the compositions around Cr # 90 increases more rapidly with increasing Fe2+ than the unit cells with a Cr number of 70. This is because as the spinel composition evolves toward magnetite or magnesioferrite with greater than ~40 mol% according to Raman observations of Lenz et al. (2013), the Fe2+ or Mg2+ instead of being in the tetrahedral site is in the octahedral site and has a larger atomic radii (0.74 and 0.71 Å, respectively). The Ti substitution would produce a similar increase in unit cell size but due to the limited extent of Ti substitution and the greater amount of Fe3+, as seen in Figure 12a/b, it is most likely due to the Fe3+.