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The traditional methods for predicting the occurrence of deleterious topologically close-packed (TCP) phases in Ni-based superalloys have been based on the PHACOMP and newPHACOMP methodologies. These schemes use the average number of holes (N) over bar (h) or the centre of gravity of the elemental d-bands (M) over bard to predict whether or not a given multicomponent alloy will be prone to TCP formation. However, as both these one-dimensional methodologies are well-known to fail with respect to new generations of alloys, a novel two-dimensional structure map ((N) over bar, (Delta V/V) over bar) is introduced where N is the average electron concentration and (Delta V/V) over bar is a composition-dependent size-factor difference. This map is found to separate the experimental data on the TCP phases of binary A-B transition metal alloys into well-defined but sometimes overlapping regions corresponding to different structure types such as A15, sigma, chi, R, P, delta, mu, M and Laves. Detailed investigations of ternary phase diagrams and multicomponent systems show that TCP phases, regardless of the number of constituents, are located in the same regions of the structure map that are favoured by the binary compounds of the same structure type. The structure map is then used in conjunction with CALPHAD computations of sigma phase stability to show that the predictive power of newPHACOMP for the seven component Ni-Co-Cr-Ta-W-Re-Al system studied recently by Reed et al. [24] is indeed poor. This supports a growing consensus that robust methods of TCP phase prediction in multicomponent alloys will require the inclusion of reliable first-principles thermodynamic databases within the semi-empirical CALPHAD scheme.