72-hour free Transit at Xi'an airport

Thanks for the response to my previous question. We have a different question now. We have valid US passports. On our way to India from USA, we intend to take a stopover for 72 hours or less at Xi'an airport so that we can visit the nearby Terracotta Warriors excavation site. Ww will fly to Xi'an from Bangkok, Thailand and leave Xi'an on a flight to either Kualalumpur, Malaysia or Hong Kong, China. Can we take advantage of the 72-hour free transit at Xi'an? Also, is the Terracotta Warrior tourist attraction site (about one hour drive?) in the same municipality as Xi'an or same administrative area? Because there may be some limitation on the travel area where we must stay while with a transit visa.