Chemistry is the same, no matter where you go, so the idea of "new planets = new minerals" doesn't really pan out. However, even without inventing "unobtainium" you can make the scenario work:
On a low-tech world without electricity, extracting aluminum from bauxite is extremely difficult, so aluminum would be unobtanium locally, even if it's common elsewhere.
On a desert world that never had ocean life, you probably don't have sedimentary rock, or shellfish, and so would find it difficult to make concrete because there's no source of cement.
A world without trees proabably won't have anything resembling amber.
Rare earth elements such as lanthanum are rare even on Earth, and are just as likely to be rare elsewhere.
A geologically inactive world, with only one tectonic plate and no molten cose, probably doesn't have quartz crystals. Or diamonds. Or any other crystals that form as a result of both heat and pressure.
As an aside…
In the Classic Traveller adventure "Leviathan" zuchai crystals were introduced. The concept was ported over to MegaTraveller and zuchai crystals were stated to be vital components of the jump drive. If they're vital to jump drives, then zuchai crystals would have had to exist on Earth, since the Solomani were one of the races that invented jump drive. But, we don't have anything with that name. So, what are Zuchai crystals? In my Traveller universe, Zuchai was the name of the Vilani scientist who invented jump drive, and the crystals ended up bearing his name, as "Zuchai's crystals" but over time the possessive form was lost, leaving just "Zuchai crystals." On Earth, they're called Galena, the same crystals once used in early-twentieth century crystal radio sets.