I want to design an iPhone case that will include a metal plate on the back of it. Is there any kind of metal that will not interfere with the phone's reception?
That depends on what you mean by interfere. If you mean as if there were nothing there but air, then no. But if you mean the cell phone still works, then yes.
By putting metal near the phone, this metal will intercept some of the electrical field emitted by the antenna. Consequently, there will be some RF currents in the metal. These currents will circulate around, and ultimately:
- be radiated again, or
- go into losses, making something warm
It's pretty hard to prevent the energy from being re-radiated. As the currents wave through the metal, it's likely they will hit the edge. When they do, the current can't continue flowing, so a voltage develops. You have current, you have voltage -- sounds like an antenna.
In fact if you cut a slot in a waveguide with the right dimensions, it makes a great antenna. It's called, unsurprisingly, a slot antenna.
Depending on the geometry and placement of your metal, it might re-radiate the energy it intercepts quite efficiently. Or, it might not radiate so efficiently, and instead a lot of the current will circulate in the metal and be absorbed by resistive losses. It's going to depend a lot on the specific geometry of the metal.
In addition to what's been previously stated, you will likely want to reduce the losses from induced currents. Using high-conductivity non-magnetic materials will be beneficial, eg. Gold, Copper, Aluminum. Metals to avoid would be those that interact with magnetic fields in a manner that makes their permeability factor much greater than 1, eg. nickel; such materials negatively impact the skin depth.