I am working at some lab in xyz, I have been granted access to solid state NMR,SEM,TEM. I have recently collaborated with researchers who don't have these facilities. They want me to collaborate by using characterizing their samples and then interpreting the results accordingly.Should I take permission from my supervisor or should I use it on my own.
The correct way of handling this is, especially as you have an existing collaboration, to get your supervisor to approve the use of the instruments as part of this work. Collaborations where different groups undertake different tasks are very common, but they are regulated by contracts/MOUs/other legal frameworks imposed by the funding agencies/the universities and there is no shortcut to this. Once your project is approved you might get a lot of leeway when it comes to the details (how many samples to analyse etc), but you need to get the overall approval first.
Using the instruments without approval might be a career ending move. The fact that you are asking here precludes any claims to a "misunderstanding". Remember that your supervisor might be reading StackExchange as well - I am just going to assume that your username is the equivalent of "John Smith" in Urdu, otherwise you might want to change it.
No and yes.
If the lab tests involve expensive instruments - and since you mention SEM, TEM and NMR, this is the case - then you cannot do work on your university's facilities without the permission of the heads of those laboratories.
For sure, you will not be allowed daytime access to these kind of facilities for work to the benefit of external researchers. They may allow you to so so in late evening or night.
In my own time I did a share of non-permission lab work and observed some other PhDs and lab staff do so too. But the type of work observed was simple quick work and not using EMs or spectrometry.
One thing you have to keep in mind is that, if you apply for any kind of IP protection for developments made using university facilities, the university will claim ownership of the lion's share of that IP should they become aware of your free use of their labs to develop it.
In all cases, I would advise that the request for work done be made by the benefitting parties and you be involved only as someone who is willing to do the microscopy/spectroscopy. Keep things above board and that way you avoid your labs' managers and your supervisor accusing you of running a business with the department and getting restrictive with you.