Quick google search shows that China has its own Quartz mines, so I'm not sure if those are unsuitable for certain semiconductors or if the use of "world" here just means 
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i am like baby when it comes to tech manufacturing but i do happen to be aware that quartz is an exceedingly common rock, so what on earth is this about
like do semiconductors need literal tons of quartz? very specific kinds of quartz? this is genuinely baffling
Quartz is pretty common as a digital oscillator but it's possible to use other methods. Certain iPhones used a different oscillator that are sensitive to atmospheric Helium.
Not sure where else in the supply chain it's needed, and how easily it is to swap quartz oscillators for other components in existing designs.
i have no idea what an oscillator gizmo entails
Your computer's chips all have a clock rate, which controls how fast these circuits switches from positive to negative voltages. These clock rates are synchronised using an oscillator, often made of quartz.
By driving the clock rates from a single oscillator, multiple components can have different speeds but can stay in sync with each other, which is how we can transfer data from different components seamlessly.