Immiscibility in the Fe3O4-FeCr2O4 Spinel Binary

Ziemniak, S.E. ; Castelli, R.A.

Lockheed Martin

关键词: Magnetic Moments;    42 Engineering;    Electrons;    Cations;    Spinels;   

DOI  :  10.2172/821371
RP-ID  :  LM-03K029
RP-ID  :  AC12-00SN39357
RP-ID  :  821371

美国|英语

来源: UNT Digital Library

【 摘 要 】

A recent thermodynamic model of mixing in spinel binaries, based on changes in cation disordering (x) between tetrahedral and octahedral sites, is investigated for applicability to the Fe{sub 3}O{sub 4}-FeCr{sub 2}O{sub 4} system under conditions where incomplete mixing occurs. Poor agreement with measured consolute solution temperature and solvus is attributed to neglect of: (1) ordering of magnetic moments of cations in the tetrahedral sublattice antiparallel to the moments of those in the octahedral sublattice and (2) pair-wise electron hopping between octahedral site Fe{sup 3+} and Fe{sup 2+} ions. Disordering free energies ({Delta}G{sub D}), from which free energies of mixing are calculated, are modeled by {Delta}G{sub D} = {alpha}{chi} + {beta}{chi}{sup 2} - T(S{sub c} + {chi}{sigma}{sub el} + {gamma}{chi}{sigma}{sup mag}) where the previously-neglected effects are accommodated by: (1) adding a non-configurational entropy term to provide coupling between cation disordering and magnetic ordering and (2) revising the configurational entropy (S{sub c}) analysis. Applying the constraint {alpha} = -(2/3){beta} and regressing the existing database for Fe{sup 2+} ion disorder in Fe{sub 3}O{sub 4} gives: {beta} = -31,020 {+-} 1050 J mol{sup -1}, {sigma}{sub el}/R = -0.730 {+-} 0.081 and {gamma}, the coupling parameter between cation disordering and magnetic ordering, = -0.664 {+-} 0.075. The revised mixing model predicts a consolute solution temperature (T{sub cs}) = 600 C and a solvus at 500 C of n = 0.05 and 0.70 for the Fe(Fe{sub 1-n}Cr{sub n}){sub 2}O{sub 4} spinel binary.