Solid-State displacement reactions between selected metals and sulfides
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RESULTS AND DISCUSSION S e v e r a l features distinguish the displacement r e a c tions of metals with sulfides from the previous studies with oxides. 1) All sulfide displacement reactions studied produced the a g g r e g a t e morphology. This indicates that the rate controlling step in a tentatively a s s u m e d layered arrangement would be the diffusion of atomic sulfur through the product m e t a l . 2) In all but one c a s e , the a g g r e g a t e structure was completely interwoven. 3) The detailed analysis of the sulfide displacement reactions was not possible b e c a u s e of the lack of available thermodynamic and diffusivity data for the sulfide systems with the exception of the Fe-NiaS2 reaction couple. Morphological Prediction for the Fe-Ni3S2 Reaction at 700°C According to the criterion developed by Rapp et a l1 a comparison of the calculated rational rate constants for the growth of the product m e t a l and the product compounds in an a s s u m e d layered arrangement can be used t o predict the resultant morphology. The relevant reaction is : 2Fe + Ni~S2 ~ 3Ni + 2FeS.
Tentatively a wavy interface between the product layers is assumed. L o c a l equilibrium is a s s u m e d at the reaction interfaces and the reaction rate is limited only by diffusion of the r e a c t i n g species in the product phase. If the e n t i r e Gibbs e n e r g y change is assumed to d r i v e cation diffusion a c r o s s the product sulfide, then the rate of reaction should be described by Wagn e r ' s4 parabolic oxidation rate theory according t o the parabolic rate constant: t!
Zcat k~peS = 1/2 fPS2, [Zan [ DFe* (FeS) dlnPs2.
[2]
PS2 At 700°C, t h e / ~ 2 for the F e - F e S coexistence equals 5 10 -7.2 Pc, P~' for the Ni-N%Sz coexistence equals v 10 -a's Pc, an~ D~e (FeS) is 10.5 × 10-8 cm2/s.6 Bec a u s e FeS is a m e t a l l i c conductor,7,8 the self-diffusion coefficient of F e in FeS is essentially independent of
ISSN 0360-2133/79/0511-0591500.75/0 AMERICAN SOCIETYFOR METALS AND THE METALLURGICAL SOCIETY OF AIME
© 1979
[1]
VOLUME 10A, MAY 1979-59 1
PS2 and can therefore be r e m o v e d from the integral. Upon evaluation, kpFes = 4.5 × 10-7 c m 2 / s . This product thickening rate constant can be converted to a rational rate constant k r = k p . (ZFe/VFes ), where VFes = 18.5 c c / m o l is the m o l a r volume of FeS, to give k Fes = 4.9 × 10"~ e q u i v / c m - s . If one alternatively a s s u m e s that the e n t i r e Gibbs e n e r g y change is used to d r i v e sulfur diffusion through the product Ni layer, then for two mol of sulfur t r a n s ported, t h r e e mol of Ni would be added t o the Ni layer. The use of Sieverts' law, a l i n e a r sulfur concentration profile a c r o s s the nickel layer, and a concentration independent diffusion coefficient are assumed. T hen: dy 3 VNi J~Si 3 dt - 2 = -~ VNi
Ni A C s Ds Y
[3]
w h e r e y is the thickness of the nickel layer, V'Ni is the m o l a r volume of nickel, jNi is the flux of sulfur a t o m s through the n i c k e l layer (~nol//cm2-s), and A
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