What are "Periodic" weapons?

There's an item in-game called "Periodic Weapon Select Ticket". This lets you choose an item that you can rent for a specified period of time and use it on your character.

One way to can get this from the blessing of Ceres if you purchase it for 200 rubies, it's part of a 7 day log in reward. You can check this on the upper left area just below your Troop Leader's Icon. Others can be obtained through the battle mode.

When you use the ticket, you can choose a weapon based on the selection provided. Once you've equipped it on your character, you can view the time duration by clicking on the item.

If you want the weapon to be permanent, you need to get a Periodic Weapon Unlock Ticket, you can purchase this through the Shop, under the Special Tab.

There are Myth and Legend versions of this. Period Weapons provide high stats, and they can serve as temporary weapons just in case you don't have any strong ones yet.