The research staff of the Cambridge Polymer Labs were contracted by the military to create a new polymer, which could then be incorporated into existing suits of Power Armor. When the bombs fell, their supervisor locked them in the laboratory, knowing that they would likely flee, otherwise; he was still in contact with the military, and believed that, should they manage to complete their project, they'd be deemed important enough to evacuate. His plan almost worked, but the reactor sustained damage during the initial bombardment, and one of the researchers began devoting all of his energy to subverting the security system; as a result, all staff-members either died from gunshot wounds or radiation poisoning, or became ghouls. When the Sole Survivor discovered the lab, 210 years later, they were able to complete the project, but due to the extremely limited supply of materials, they were only able to produce this one piece of power armor at the time.
Due to the item and NPC spawn level for Cambridge Polymer Labs being capped at 14, the piezonucleic power armor can only spawn as a T-51 or T-45 variant.
Note that completing the manufacturing process at a high level is in no way guaranteed to spawn the T-51 version. Even at level 100 and above, the T-45 torso can spawn instead of its more advanced counterpart. The mechanism behind this choice is not entirely clear at the moment.
This piece of power armor cannot be made twice, even though the reagents stay in one's inventory, and the computer stating that it is running the fabrication.