Melilite Natural melilite from San Venanzo, Umbria, Italy Formula: (Ca 1.89 Sr 0.01 Na 0.08 K 0.02 )(Mg 0.92 Al 0.08 )(Si 1.98 Al 0.02 )O 7 Superspace group: P-42 1 m(αα0, α-α0) + translation part Cell parameters: a=7.860 (1), c=5.024 (1) Å q vectors : (3)(a*+b*), (3)(-a*+b*) l=1

Reflection (“h”)

Point detector measurement at various Ψ of reflection – 1 3 – 2 – 1 – 1 ( “ h ” )

Symmetry in SBN Formula: Sr 0.61 Ba 0.39 Nb 2 O 6 Superspace group: P4bm(αα½, α-α½) + translation part Cell parameters: a= (9), c= (6) Å q vectors : q 1 =(α,α,½), q 2 =(α,-α,½), α=0.3075(6)

Cell parameters: a=12.482, c=3.943 Å P4bm(αα½, α-α½) The rational part of q-vector must be removed by doubling c. Transformation matrix on indices (row): Resulting indices: (h, k, 2l+m+n, m, n) New super space group: X4bm(αα0, α-α0) Centring: (0,0,0,1/2,1/2,1/2)

Example: Five dimensional incommensurate structure of fresnoite Acta Cryst. (2006). B62, 1031–1037 The sample from Museo di Storia Naturale, Sezione di Mineralogia e Litologia, Universita di Firenze, Italy, catalogue number 44362/G originates from the sanbornite deposits of eastern Fresno County, California. Fresnoite, Ba 2 TiS i2 O 8, is structurally related to the melilite group minerals. Composition from electron microprobe: (Ba Ca ) = Ti Si O Unit cell (3) (3) (5) (4) (3) (3) (6) q(1): (3) (3) 0 q(2): (3) (3) 0 PEAK TABLE 5865 main refl.; 6745 q1 ; 6668 q2 satellites; 1298 cross q1/q2 Instead of (a a ½) we use doubled c and X centering (0 0 ½ ½ ½ )

Reconstruction of reciprocal space, scaling factor 1000 Plane hk1 Plane hk0 Only first order satellites q 1, q 2 Main reflections and satellites q 1 +q 2, q 1 -q 2

Jana indexing tool We see both combined satellites and lambda/2 reflections

Verification in by typing symmetry operators to finding toolhttp://stokes.byu.edu/ssg.html