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Thispaper presents a systematic and comparative study of the composition and volumedependence of the cohesive properties for a large group of Me-X intermetallicphases (IPs) with Me=Cu,Ni and X=In,Sn, which are of interest in relation withthe design of lead-free soldering (LFS) alloys. The work relies upon a databasewith total-energy versus volumeinformation developed by using projected augmented waves (PAW) calculations. Inprevious papers by the current authors it was shown that these results accountsatisfactorily for the direct and indirect experimental data available. In thepresent work, the database is further expanded to investigate the compositiondependence of the volume (Vo), and the composition and volumedependence of the bulk modulus (Bo) and cohesive energy (Ecoh).On these bases, ananalysis is performed of the systematic effects of replacing Cu by Ni inseveral Me-X phases (Me=Cu,Ni and X=In,Sn) reported as stable and metastable,as well as various hypothetical compounds involved in the thermodynamicmodeling of IPs using the Compound-Energy Formalism. Moreover, it is shown thatthe cohesion-related quantities (Bo/Vo)½ and(Ecoh½/Vo) can be correlated with a parameterexpressing the number of valence electrons per unit volume. These findings arecompared in detail with related relations based on the Miedema empiricalelectron density at the boundary of the Wigner-Seitz cell. In view of theco-variation of the cohesive properties, Ecoh is selected as a keyproperty and its composition and structure dependence is examined in terms of atheoretical view of the bonding which involves the hybridization of the d-states of Cu or Ni with the s and p-states of In or Sn, for this class of compounds. In particular, acomparative analysis is performed of the DOS of various representative,iso-structural Me-X compounds. Various effects of relevance to understand theconsequences of replacing Cu by Ni in LFS alloys are highlighted and explainedmicroscopically for the first time.