Five-component B-phase may be readily formed through the nucleation and crystallisation heat treatment of nitrogen-rich parent glasses with composition (e/o) 35R:45Si:20Al:83O:17N. This paper is focussed on the B-phase structure where R stands for ytterbium, erbium or yttrium. Fine probe EDX analysis in the TEM has shown that the lenticular B-phase crystals take up a substantial range of composition and that the element R is always clearly anti-correlated with silicon. A larger R3+ cation radius moves the B-phase composition range to lower R contents, and as a consequence of the anti-correlation with silicon, the silicon solid solution range goes to higher values. The EDX results lend support to a B-phase structure consisting of two-dimensional network of randomly linked (Si,Al)(O,N)4 tetrahedra between layers of R3+ cations. It is suggested that, in addition to the random substitution of silicon by aluminium in the (Si,Al)(O,N)4 tetrahedra, a locally increased density in the bi-dimensional network of randomly oriented tetrahedra is associated with an increased density of vacancies in the R3+ cation lattice.