Citation II S2/Bravo (C550)
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 90; Flight Crew Total 6000; Flight Crew Type 700
Communication Breakdown
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Runway
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Diverted
Aircraft; Chart Or Publication; Human Factors; Procedure
When our left generator appeared to have failed mechanically while enroute; we elected to divert to a nearby airport. We shot the ILS to Runway XX and everything went as planned; good CRM all the way to the ground. After landing we cleared the runway and ATC gave us taxi instructions to our selected FBO. As we approached Runway XX at Taxiway Delta we asked if we were cleared to cross. ATC's response was partially blocked but I thought I heard that we were cleared to cross Runway XX at Delta. I read back; '...cleared to cross Runway XX at Delta'.  There was no response from ATC. We cleared the runway left and right before proceeding across the runway. As we crossed ATC stated that we were not cleared to cross. At that point we were already across the runway.We were using NOS charts which were very difficult to use versus the commercially published charts which we are planning on using from now on.Although there seemed to be good communications going on I believe we must have been blocked by another aircraft. This possibility was increased because ATC was using the Tower frequency for both Ground and Tower operations.
After we cleared the runway; Tower asked us for our intentions. Because this was not part of the original plan; we were unsure of the location of the FBOs. They told us about the FBO options and we picked one....As we were rolling; Tower came back and told us to stop because he had told us to hold short. I immediately applied breaks and stopped the aircraft. As soon as we were stopped Tower told us that we were cleared to cross and then we proceeded with the taxi to the ramp.
After diverting to an enroute airport due to the failure of their left generator the flight crew of a C-550 began to cross a runway--believing they had been cleared to do so--but were stopped by Ground/Tower advising they had not been cleared. The pertinent transmission may have been partially blocked.