If you are not able to obtain the materials you need directly, it is possible to trade other materials of the same type at a material trader for a cost. Different material traders will handle different material types such as Data, Raw and Manufactured.
You can find the nearest trader with this tool.
When trading you will always lose some value. You will lose even more if you trade across different categories.
Ideally you want to gather materials at the highest grade possible and trade downwards.
Shard FarmingBy CMDR Secretpro
Raw materials (Grade 4) can be easily obtained en masse at special Crystalline Shard Biological Sites. A large cluster of these sites, consisting of purely the highest grade (G4) of Raw materials can be found at two systems approximately 1500-1800Ly from the bubble. We recommend putting together a decent exploration ship (unengineered works) and visiting both systems to completely fill on all G4 materials (except Selenium) which you can trade down for any lower grade materials you may need. This should last you for multiple full ship engineering builds.
Yttrium - Outotz LS-K D8-3 B 5 A
Antimony - Outotz LS-K D8-3 B 5 C
Ruthenium - Outotz LS-K D8-3 B 7 B
Polonium - HIP 36601 C 1 A
Tellurium - HIP 36601 C 3 B
Technetium - HIP 36601 C 5 A
To use these sites, you will need to go to the celestial body corresponding to the material you require and use your Detailed Surface Scanner (DSS) on it. When this is done, go down to any of the biological sites and hop in your SRV. You should be able to find plenty of rare raw materials for all your engineering and synthesis needs.
Do not forget to bring a Detailed Surface Scanner
Selenium and Thargoid Barnacles
Selenium is (ironically) the most difficult material to farm since it only drops from Grade 2 resource nodes. There are multiple ways to collect it, but none so efficient as the Crystalline Shards are for other materials as mentioned above.
Thargoid Barnacles can provide a good source of it since breaking the spikes most commonly drops G1-G2 materials, but locating the correct barnacle may be tricky. You can use this spreadsheet compiled by CMDR Panpiper to find the correct sites. Look for Allripe Barnacles with Selenium present on the planet. Additionally relogging will cause the spikes to reappear, which means you can repeatedly farm the same site.
Other known Selenium Sites
Wolf 587 4 E A has geo sites and high Selenium %.
HIP 83204 3 B A is slightly higher (5% selenium, 1.3% arsenic and 1% zirconium in the G2-level drops, geo sites 10, 1, 2, 8, 7, and 14)
HGE LoopingBy CMDR Jetlagged
HGE Looping is a time-efficient method of grinding Grade 5 Manufactured materials. Ideally you will want to be using a ship with at least 3 collector limpets and a good turn rate in supercruise.
Start by finding a HGE that contains the desired materials which has longer than 20 minutes on the decay timer.
Drop into this HGE and collect the contents with your collector limpets.
Exit the game to desktop and restart via the launcher.
Join the same mode you were in originally, charge your FSD, and boost. Do not use your throttle.
Upon transitioning to supercruise, immediately set throttle to 0% (it should already be) and open the left panel.
The nearest Unknown Signal Source should be a few hundred km away and is the same HGE you dropped into the first time.
Drop in, collect the contents and repeat until material storage is full or the HGE times out.
The contents of a given HGE are determined by system allegiance (Federation/Empire) and minor faction state (Outbreak, War, etc.) and spawn at random in systems in such states. See ED Materials for more information on what material corresponds to each faction state.
If you have a weak PC (or want to speed up the grind even more) you can load the vanilla (non-horizon) version of the game, as it loads faster.
Jameson's Crashed Cobra
You can find a collection of high grade encoded materials by travelling to Jameson's crashed cobra and scanning the small red beacons surrounding the crash site, once you log out/in these will refresh and you can continue to do this until your materials are full.
Equip an SRV and Detailed Surface Scanner
Travel to HIP 12099 Planet 1B (-54.3803, -50.3575)
Use your Detailed Surface Scanner to scan the planet and locate the crash site.
Drop into the site and deploy your SRV.
Drive up the the Cobra and using your Data Link Scanner, scan all the red beacons.
Log off and back on.
Repeat from step 5.
Required to unlock the Engineer Professor Palin, sensor fragments can be gathered from Thargoid Scavengers or by destroying Thargoid Sensors. You can find Thargoid Sensor fragments very close to Professor Palins lab at a recently discovered crashed ship at the following location.
Coordinates: -70.9912 x -156.4383
Stuff: 1 Thargoid Sensor, 1 Cargo Rack which drops one of the following (V, Cr, Zr, Zn, Mn, Sb), Ship Data Core.
This is the closest system to Arque (Palin) to get Sensor Fragments at less than 28 LYs distance. Destroy the Sensor to gather the fragments. You can relog at this site to spawn another.
Credit to CMDR FlyBoyXD of the FRC.