Prediction of concomitant structures in binary metallic systems from RG map: With MgCu2 structure type as an example

Charge transfer on the metallic atom-pair bond, and the crystal structures adopted by intermetallic compounds

“…Using the observed values of the mean atomic volume in the alloy, he then calculated the volumes of the ion pair in all the intermetallic compounds in the Ca Pb system, and found them to be nearly the same. Similar observations were reported by him (Pauling, 1987a) We note that the prediction of concomitant and mutually exclusive structure types in phase diagrams is possible from the Rajasekharan-Girgis ( ) maps (Rajasekharan & Girgis 1983a;1983b;Rajasekharan & Seshubai, 2010a;Kameswari et al, 2010;Kameswari, 2008) without any inputs regarding the compositions at which the structure types occur. The occurrence of lines and their ability to predict concomitant structures in metallic phase diagrams is puzzling since such predictions follow from just two parameters per element: and several competing energy contributions can be expected to decide such structures.…”

“…Rajasekharan and Girgis, ( ), (1983a;1983b), had observed that binary systems with intermetallic compounds of the same crystal structure occur on a straight line on a Δ , ∆N / map. It has been verified that their observation is true for all the structure types in which intermetallic compounds crystallize (Rajasekharan & Seshubai, 2010a;Kameswari et al, 2010;Kameswari, 2008), with all the straight lines having a slope ~ / 1/2 . The points on the map stand for binary systems; and the compositions at which the compounds occur do not have a role in deciding their coordinates.…”

“…In a binary system A-B, irrespective of whether we consider compounds occurring at AB, AB 2 , AB 3 or in general any A m B n , the structures of the concomitant phases are predicted by a knowledge of which RG lines or inverse RG lines pass through the point corresponding to that binary system on the ðÁ'; ÁN 1=3 Þ map (Rajasekharan & Seshubai, 2010a). This property can be used to predict concomitant and mutually exclusive structure types in binary metallic phase diagrams with excellent reliability (Rajasekharan & Girgis, 1983a,b;Rajasekharan & Seshubai, 2010a;Kameswari et al, 2010;Kameswari, 2008). These surprising observations were unexplained.…”

Charge transfer on the metallic atom-pair bond and the bond energy

“…Rajasekharan and Girgis (RG) 5,6 had observed that binary systems with intermetallic compounds of the same crystal structure occur along a straight line on a (D/,DN 1/3 ) map, referred to hereafter as the RG map. Considering 96 structure types with ;3000 compounds, [7][8][9] it has been demonstrated that D/ } DN 1/3 with a slope ; þ ffiffiffiffiffiffiffiffiffi Q=P p for all the structure types. Binary systems with compounds of 88 of the structure types formed single straight lines and six of them formed dual lines, whereas AuCu 3 and NaCl structure types formed multiple lines.…”

“…5,7,9 Another example is the prediction of 22 structure types including CaCu 5 (hP6), FeB (oP8), Er 2 Co 7 (hR18), Ce 2 Ni 7 (hP36), NbBe 3 (hR12), CFe 3 (oP16), and Si 3 Mn 5 (hP16) as possible concomitants to MgCu 2 type compounds in binary systems. 8 Since the choice of one crystal structure or another by intermetallic compounds is expected to be decided by small energy differences, the above observations are quite surprising.…”