Cross-polarised light images of three HED achondrite meteorites. The different colours represent different minerals. Grey crystals are feldspar, beige ones are orthopyroxene, and brightly coloured ones are clinopyroxene.
Source: NASA/University of Tennessee
Achondrites are igneous meteorites that are largely made of crystalline olivine, pyroxene, and feldspar. Importantly for researchers, some achondrites record the first stages of melting and have compositions that are very similar to chondrites. We call these "primitive achondrites". Achondrites that have experienced longer periods of heating and underwent igneous processes like fractional crystallisation are called "evolved achondrites". Scientists can use the chemical and isotopic signatures of these rocks to work out which parent body they came from.
We can also include stony-iron and iron meteorites in the achondrite group because they are the result of extensive melting on their parent bodies.
As their name would suggest, stony achondrites are made out of rock. These achondrites represent the crusts and mantles of rocky bodies in the Solar System including Mars and the Moon.
Primitive achondrites are mostly made from olivine and pyroxene, but there are a few unusual types of primitive achondrite. The most famous are ureilites. These are carbon-rich olivine-pyroxene achondrites, and that carbon is often converted into tiny diamonds which makes them very hard rocks to cut open for analysis.
Evolved achondrites are much more common than the primitive ones and include Martian, Lunar, and Vestan (HED) meteorites. These meteorites are often basaltic in composition and display a wide range of igneous and metamorphic textures, hinting at the complexities of geological activity that happened billions of years ago. A large amount of these rocks are breccias - a mixture of several different rocks types that have been broken apart and stuck back together through impact processes. Impacts were very common in the early Solar System, and you can see the remains of this violent period by the sheer amount of craters on the Moon, other planets, and asteroids. Earth is geologically active so a lot of the craters we'd see here have been erased, but you can still find a lot of impact structures around the world if you know where to look!
Stony-Irons & Iron Meteorites
Stony-iron and iron meteorites are exactly what they sound like - meteorites made out of silicate minerals and/or nickel-iron!
Stony-iron meteorites (mesosiderites and pallasites) might not be made out of very many minerals, but they are one of the most mysterious meteorite groups. Mesosiderites are around 50:50 silicate and nickel-iron alloy, and are usually breccias. The silicates are similar in composition to those in HED meteorites which is an ongoing mystery. The largest mesosiderite is called Bondoc, which was found in the Philippines and weighs in at over 880kg! Pallasites have cm-sized crystals of olivine suspended in a network of nickel-iron metal, and could either represent the core-mantle boundary of an asteroid that got completely destroyed in the early Solar System - we call this "catastrophic dirsuption" - or they might have formed by mixing core and mantle material during a big impact event. Either way, pallasites are arguably the most beautiful type of meteorite.
Iron meteorites are made of large crystals of two iron-nickel alloys called kamacite and taenite and scientists can use certain acid etching techniques the unique interlocking texture that these crystals grow in, called the Widmanstätten pattern. Iron meteorites are rare and represent that cores of asteroids and protoplanetary bodies that were catastrophically disrupted in the early Solar System. One interesting fact about iron meteorites is that they were one of the earliest sources of metal that humans had before smelting was developed in the Iron Age!
For some meteorites, scientists can be pretty confident about what class they belong to and which body they've come from. For others, we really can't tell. Meteorites only record a small portion of their parent body so a lot is still unknown, and a lot of parent bodies no longer exist as whole pieces in the modern Solar System.
We call meteorites that don't fit into an established group "ungrouped". This is based on chemistry, rather than appearance - a meteorite can look perfectly normal but turn out to be completely different! Ungrouped meteorites aren't very common, but we can learn a lot from them.