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mode analysis of any ferroic structure. As input only the ferroic distorted structure and the (real or virtual) non-distorted one of higher symmetry is required. With this information the program AMPLIMODES identifies the displacive distortion present in the structure and decomposes it in terms of modes of different symmetries associated with irreducible representations of the highsymmetry space group. The decomposition of the structure in collective symmetry-adapted distortion modes is given in terms of global amplitudes and normalized polarization vectors for each of the modes present. The importance and character of each of the allowed symmetry modes can be extracted from a comparison of their amplitudes and the internal structure of their polarization vectors. The polarization vector of each frozen mode is presented in a crystallographic way, as a list of relative atomic displacements within an asymmetric unit. This allows a straightforward construction of virtual structures corresponding to the sole presence with arbitrary amplitudes of any of the relevant modes. This type of analysis allows to distinguish and isolate the correlated atomic displacements that correspond to the structural instabilities at the origin of the ferroic distortion, i.e. the so-called primary modes. In this way, secondary weaker induced distortions of marginal relevance are separated. The Bilbao Crystallographic Server, where this tool can be used on-line, is a free web site with many other crystallographic databases and programs [1,2]. [1] M. I. Aroyo et al., Acta Cryst. (2006). A62, 115-128 [2] M. I. Aroyo et al., Z. Krist. (2006), 221, 1, 15-27.

Phase and glass-forming diagrams in the gallium borate and ternary barium gallium borate systems