The results of an extensive investigation of structure, surface morphology, composition and the superconducting-normal phase diagram of a new unconventional superconductor LaAg1-cMnc with nominal composition c = 0.0, 0.025, 0.05, 0.1, 0.2 and 0.3, reveal the following. The alloys with c = 0, 0.025 and 0.05 are essentially single phase alloys with the actual Mn concentration, x, same as the nominal one, i.e., c = x, whereas in the alloys with c = 0.1, 0.2 and 0.3, the actual Mn concentration of the majority phase (crystalline grains) is x = 0.050(1), 0.080(1) and 0.100(1), respectively. The ternary Mn addition does not alter the CsCl structure of the parent compound LaAg. Neither a structural phase transition occurs nor a long-range antiferromagnetic order exists at any temperature within the range 1.8K < = T < = 50K in any of the Mn containing alloys. Mn has exclusive La (Ag) site preference in the alloy (alloys) with x = c = 0.025 (x < = 0.05 or c < = 0.1) whereas in the alloy with x = c = 0.05, Mn has essentially no site preference in that all the Mn atoms either occupy the La sites or the Ag sites. In the alloys (alloy) with x < = 0.05 (x = c = 0.025), substitution of Ag (La) by Mn at the Ag (La) sub-lattice sites in LaAg host gives rise to unconventional superconductivity (destroys the conventional phonon-mediated superconductivity prevalent in the parent LaAg compound).
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