In my code I define a new MPI user-defined data type. I was wondering if the MPI_Barrier function must follow the MPI_Commit or must be placed at some point where the first use of the new data type appears so that all the processes acknowledge and agree on the defintion of the new data type.
Thanks.
No - there's no communication within the MPI_Type commands, they're completely local. In particular, processes don't necessarily have to agree on the definition of a new type.
If rank 1 sends a new data type to rank 0, all they have to agree on is the amount of data, not the layout of the type. For instance, imagine rank 1 was sending all of it's (say, 2d) local array to rank 0 - it might just choose to send an MPI_Type_contiguous of NX*NY floats. But rank 0 might be receiving this into a larger global array; it might choose to receive it into a Subarray type of the global type. Even if those data types had the same names, they can describe different final layouts in memory, as long as the total amount of data is the same.