Why was quartz not a major product of the Lunar Magma Ocean?

Question

Fractional crystallisation generally makes magma more silicic. Why was a substantial quartz layer not a product of the stratification of the Lunar mantle?

Answer 1

Fractional crystallization indeed makes magmas more silicic. However, you'll never reach a magma composition with 100 % silica, which could then cool and crystallize as quartz. The starting material (i.e., mantle rocks like peridotite) is just too mafic. For this part, see answers to Why aren't there ultra acid igneous rocks?

If you are thinking of the crystals left over by the fractional crystallization process, generally referred to as "extract", "cumulate", or "residue", they are always less silicic than the starting material. It has to be, if you want to make the magma more silicic while keeping the mass-balance. The process can be graphically represented like this (redrawn after Cox et al., 1979):

The three diagrams represent the fractional crystallization process of a parental magma (PM), yielding a diffentiated magma (DM), more silicic, and a less silicic residue (R) consisting of one (top) to three (bottom) minerals. The mass balance, for an element $\alpha$, can then be written as:

$C_0^{\alpha} = FC_L^{\alpha} + (1 - F)\displaystyle\sum_{i=1}^n (m_i c_i^{\alpha})$

where $C_0^{\alpha}$ is the concentration of said element in the parental magma, $C_L^{\alpha}$ the concentration of the element in the differentiated magma, $F$ the fraction of liquid remaining, $m_i$ is the mass fraction of each of the $n$ minerals in the cumulate, and $c_i^{\alpha}$ is the concentration of element $\alpha$ in mineral $i$. You see that even if somehow the diffentiated magma had a 100 wt% SiO2 composition, the crystals left in the residue would be less silicic, hence not quartz.