Hagg limit

The carbon-metal atomic radius ratio for the room temperature form of iron, a-Fe, is 0.60, just in excess of the Hagg limit. Consequently, the ability of a-Fe to accept interstitial C is marginal only 0.022 weight % or 0.06 atom % C can be accommodated in the random solid solution known... 

Hagg found that metals can accommodate interstitial nonmetal atoms of radius up to 59% of that of the metal atoms. Show that, in this limiting case, accommodation of the nonmetal atoms in the octahedral holes of a face-centered cubic metal lattice should result in an expansion of the unit cell dimension by 12.4%. [Hint Review the radius ratio rules in Section 4.5.]... 

Several octahedral crystals were ground to powder and studied by the Guinier-Hagg technique (Cu radiation). All diffraction lines could be indexed on the basis of a cubic cell with a = 4.560 0.001 A., which is within experimental error of that reported previously for MnSi, 4.558 0.001 A.2 In view of the similarity of the cell constants of the ground crystals to those of previous preparations, significant replacement of manganese by copper is not indicated. This was checked on a few crystals by emission spectrographic analysis which indicated an upper limit of ca. 1% of copper. 

Podgurski, Kummer, DeWitt, and Emmett (14) carburized reduced fused catalysts with propane, butane, and pentane at 325°C. Although x-ray patterns of Hagg carbide were found, the carbon content of these preparations approached 7.5 weight-% as a limit rather than 9.1% which was obtained upon carburization with carbon monoxide. Hall (15) found that during carburization of a reduced fused catalyst (Bureau of Mines number D3001) in n-butane at 300°C., C increased only to 0.22, and the carbide phase was cementite rather than Hagg carbide. Methane is too stable thermodynamically to carburize iron rapidly at low temperatures however, at 500°C. relatively pure cementite may be prepared with methane (15). 

Hagg carbide was the final phase up to 500°C., whereas cementite was formed at 700°C. Hagg carbide appeared when N had been decreased below 0.18, i.e., when about 64% of the nitrogen corresponding to the upper limit of the e-phase (Fe N) had been replaced by carbon. According to Jack s phase diagram (Fig. 2), the upper limit of the ("-carbonitride phase may be as high as C + N = 0.56. 

Hagg mapped out a phase diagram for the Mn-N system [324]. Juza adjusted the phase limits slightly [325]. 

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