Date: 201512
Local time of day: 1201-1800
Location: ZME.ARTCC, TN
Flight conditions: VMC
Weather elements / visibility: Thunderstorm; 100
Light: Daylight
Aircraft: Challenger 300
Operator: Corporate
Operating under: Part 91
Flight plan: IFR
Mission: Passenger
Flight phase: Cruise
Airspace: Class A ZME
ATC / advisory: Center ZME
Reporter organization: Corporate
Reporter function: Pilot Not Flying; First Officer
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Confusion
Second reporter function: Pilot Flying; Captain
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Detector: Automation Aircraft TA; Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance; Flight Crew Became Reoriented
Contributing factors: Human Factors; Procedure; Weather; Airspace Structure
Primary problem: Ambiguous

Narrative: During cruise we began deviations for thunderstorms off of our clearance. We requested MEM DCT SGF DCT ZZZ [Destination] for routing through the weather. As we moved closer to our route the weather shifted north and we needed to begin deviations to find our way around a severe line of weather. Our deviation took us right of course and we had been getting any deviation right of course we needed to cross the weather with Memphis center. As we crossed the tops of a line running southwest to northeast Memphis cleared us FAM DCT SLVER DCT ZZZ 'when able'. We crossed the top of the weather and rounding to top of a large cell we began a 10 degree turn to the south back towards our previously cleared route; I announced (Pilot Monitoring) our intentions to ATC and was alerted to traffic at our same altitude moving inside our 12.5 mile TCAS ring. He told us to stop the turn; turn back right and comply with the clearance which we were still unable due to the west edge of severe weather laying over our new routing. We immediately turned back to the right and the traffic passed off our left approximately 10 miles to the left according to the TCAS display. The controller then questioned our turn to the left asking why we turned left if our clearance was routing north. I stated that we had been given deviations as necessary right of course and then FAM SLVER ZZZ 'when able' and we were not able that clearance. He requested we begin a descent and 'handed' us off to ZKC. ZKC then proceeded to continue to force us back towards the weather over our new routing. We requested alternate routing over DELMA to give us time to descend to which we were denied because we were 'too high'. We eventually were able to make a turn back towards our routing and landed with no further event. ATC in my opinion was very vague in their clearances based on our deviations. We were making our turns based on deviating 'right of course' with the intention that we could work our way back to our course between MEM and SGF. Our new Clearance of FAM SLVER was not accepted as we were not 'ABLE' and had not proceeded on that clearance. If ATC needs us to not turn in a certain direction because of traffic; we need more specific clearance.I think there was some confusion between deviations 'right of course' or 'to the right'. We were under the impression we could deviate anywhere on the right side of our course. We had not accepted our new clearance yet since it was issued 'when able'. Factors to the event were severe weather including a convective SIGMET in our area. We were very aware of our surroundings and saw the traffic prior to ATC notifying us of it. We appreciate the ability to 'stay high' over the weather prior to descending after it. We would prefer to take further routing west then be forced back into weather to facilitate a descent. ZKC's ability to manage traffic descending into the area with weather around is always an issue and they are very unwilling to help. This includes their desire to force us back towards severe weather in order to get us onto their preferred arrival routes and descents. We would have gladly stayed over our requested routing over SGF and will state that next time. We planned to have extra fuel for weather deviations anyways.


Second narrative: While in route to ZZZ we encountered weather in the form of thunderstorms along our route while south of Memphis and in Memphis center. We made the request to turn right of course; we were given 'cleared right of course as needed; cleared to SGF ZZZ when able' and acknowledged. Shortly after passing Memphis; and verifying with on board weather radar; made the decision to make the turn back left slowly to our cleared fix SGF. At that time we were handed off to another controller and advised we would still be continuing north (right of course) and that it would be another 75 miles before fully turning west for SGF. This was a decision we made and requested so as to descend on the back side of the weather. About the time of our westerly turn the controller issued another clearance for us to proceed to 'FAM; SLVR; then destination when able' at this point; a direct to; FAM VOR would have been directly into the WX we were trying to avoid in the first place. The safest option for our flight was to continue as we had planned earlier and make a turn west to make a perpendicular track to the weather and cross. As we made a turn further west (while still right of original course) we got a TCAS advisory on our CAS (Crew Alerting System) about a conflict at our altitude. I immediately changed course back to the north. At this point the PNF (Pilot Not Flying) made a call to center and advised that we just got a TCAS alert. That communication was followed by our current controller saying 'don't turn left!' and issued a heading command to avoid traffic. We never heard the controller issue a turn to the other airplane involved in the potential conflict. A conversation commenced about why we turned left with the controller. We were under the impression that our course was still deviations for weather and the position of our aircraft was still right of course and maneuvering as necessary for the safety of our flight. It should be noted that during this event that we never saw the other aircraft break our 10 mile ring on our TCAS display; separation was never in doubt. This event could have been avoided had several things been handled differently. First our communication with the second controller should have been more thoroughly interrogated from our end to better understand his instructions. The second item is the controller could have given a traffic advisory; considering we were on deviations; we were never issued a traffic advisory or told not to turn left. Lastly it is my absolute firm belief this all could have been avoided if it wasn't for center agreements if this controller had the freedom to do his job and control as opposed to making sure he hands us off to the next sector at the right altitude and fix per agreements.


Synopsis: CL30 Flight Crew reported misunderstanding a clearance to deviate right of course around weather at FL450. A TCAS TA is generated and ATC is advised. ATC orders a right turn to avoid the traffic and indicates the crew was not cleared to turn left even though they were still right of their original course.