ARTCC D-Side Controller described a loss of separation event when both he and the R-Side when distracted by required emergency actions; suggesting training regarding emergency's actions and responses would be helpful.

Narrative

I moved over to work the D-Side as the R-Side had an emergency flight of F16s that were trying to get back to their home base. There was a high workload with the emergency as the flight wouldn't take the frequency change; and kept coming back to us. This caused quite a distraction to the sector; and at that time the R-Side was trying to sequence two airplanes to the same landing airport. Air Carrier X was at FL300 and turned 15 left to go behind Air Carrier Y at FL320; inbound. Another Air Carrier was eastbound at FL310; but wasn't traffic because of the route of flight. I went offline a couple of times while the R-Side was working the two arrivals; and didn't catch all of the instructions he gave to the aircraft. However; I thought that the 15 left was going to work; and that the Air Carrier X was going to fall behind Air Carrier Y. The R-Side put a halo up on the Air Carrier X and we were watching the altitudes; as they both descended. I didn't hear the R-Side tell the Air Carrier Y to expedite and when I looked at the altitudes the Air Carrier Y was catching up to the Air Carrier X 's altitude. The R-Side told Air Carrier Y to stop at FL290; and at the time I didn't think the altitude would work; but I thought the heading was good enough. During some of the instructions I had called Sector 91; because they were stopping departure traffic at FL310; which provided more of a distraction and a higher workload. I didn't understand why they had stopped 2 aircraft at FL310; when they could have climbed and gone to Sector 80. This didn't help the situation on Sector 90. Recommendation; I would recommend training for controllers to relax and try to calm down when they are finished working an emergency. I think the R-Side was hyped up and thinking he didn't have time; when he did. I also was distracted with the emergency and the calls I had to make based on that emergency. When dealing with a critical situation; when it's over controllers just need to go back to basics and focus.