Separating Silica from silicates
Mechanically speaking, it is not possible to separate $\ce{SiO_2}$ from these minerals. The only way to do it is carrying out a chemical transformation. Here is an example of such a treatment.
Mix a sample of one of these minerals with $\ce{Na_2CO_3}$ in excess, and heat it in a platinum crucible with a Bunsen burner. When the substance is liquid, wait $10$ minutes. Let it cool down. The mineral is now transformed into sodium silicate $\ce{Na2SiO3}$ plus some oxides and carbonates. If I choose the specially simple olivine $\ce{MgFeSiO_4}$ as an example, the following reaction may happen : $$\ce{MgFeSiO_4  +  Na_2CO_3 -&gt; Na_2SiO_3 + MgCO_3 + FeO}$$ The reaction is somewhat more complicated, because usually $\ce{FeO}$ is oxidized in air into $\ce{Fe_2O_3}$, and $\ce{MgCO_3}$ is partially decomposed into $\ce{MgO}$ and $\ce{CO_2}$. Furthermore, the sodium silicate $\ce{Na2SiO3}$is partly transformed into $\ce{Na4SiO4}$. Fortunately this side reactions do not really modify the rest of the process.
Anyway, put the crucible in a small beaker. Add $20$ mL water. Let it boil for a couple of minutes. When the substance is pulverized, add an excess of diluted $\ce{HCl}$. Heat on a water bath until the substance is dry. Add $2$ mL concentrated $\ce{HCl}$. The following reactions happen : $$\ce{Na_2SiO_3  +  2 HCl -&gt;  H_2SiO_3 + 2 NaCl}$$ $$\ce{MgCO_3 + 2 HCl-&gt; MgCl_2 + CO_2 + H_2O}$$ $$\ce{Fe_2O_3 + 6 HCl-&gt; 2 FeCl_3 + 3 H_2O}$$ After $10$ minutes, add some hot water and filtrate. $\ce{H_2SiO_3}$ remains on the filter. Calcium, magnesium and iron chlorides are soluble into water and are eliminated.  Then $\ce{H_2SiO_3}$ can later be heated to obtain $\ce{SiO2}$ $$\ce{H2SiO3 -&gt; SiO2 + H2O}$$  This is one way for obtaining $\ce{SiO2}$ from the proposed silicates. Other processes are known, using for example fluorhydric acid $\ce{HF}$. But, of course, using this acid is not recommended, because of its toxicity.