Grain boundary segregation of sulfur and nitrogen in sintered molybdenum
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(1 + k c )
[1]
a n d a, b a r e c o n s t a n t s f o r t h e f i e l d c o n t r i b u t i o n s f r o m NN and NNN atoms, respectively, m, n are the respect i v e n u m b e r of s o l u t e a t o m s , a n d k, c r e p r e s e n t t h e bulk contribution. The above assumptions then give t h r e e e q u a t i o n s i n f o u r u n k n o w n s , u s i n g H.r + kc v a l u e s a t v a r i o u s t i m e s :is 1 . 1 3 1 1 2 = 1 + 3 a + 1.Sb (1 h) 1.12766 = 1 + ma + (11.12298= 1 +ma+nb
m)b
[2] (8 h)
[3]
(100h).
[4]
work was performed at the Science Center, Rockwell International, Thousand Oaks, CA, under the auspices of the Independent Research and Development Program. 1. A. W. Thompson: Scr. Met., 1974, vol. 8, pp. 1167-70. 2. A. W. Thompson and R. G. Baggerly:MetalSci., 1975, vol. 9, pp. 280-82. 3. T. J. Bureh, J. I. Budnick, and S. Skalski:J. Phys. Soe. Japan, 1970, vol. 28, pp. 1180-81. 4. A. Wolfenden,W. H. Robinson, and A. W. Thompson: Scr. Met., 1977, vol. ll,pp. 71-76. 5. H. Hnili~aand L. Karmazin: Scr. Met., 1974, vol. 8, pp. 1029-32. 6. A. Ci~ek, F. Pa~izek,J. Adam, I. Ya. Dekhtyar, and V. S. Mikhalenkov: Czech. J. Phys. B, 1969, vol. B19, pp. 629-33. 7. F. Pa~izekand A. Ci~ek: Czech. J. Phys. B, 1969, vol. BI9, pp. 276-78. 8. H. Thomas: Z. Phys., 1951, vol. 129, pp. 219-32. 9. U. Dehlinger: Z. Metallk., 1962, vol. 53, pp. 577-79. 10. E. A. Starke, V. Gerold, and A. G. Guy: ActaMet., 1965, vol. 13, pp. 95764. 11. For example, R. L. Cohen: Science, 1972, vol. 178, pp. 828-35. 12. G. P. Huffman and G. R. Dunmyre: J. Appl. Phys., 1970, vol. 41, pp. 132324. 13. J. C. Love, F. E. Obenshain, and G. Czjzek: Phys. Rev. B, 1971, vol. 3, pp. 2827-40. 14. T. Zem~ik and J. V~e~{al:Czech. J. Phys. B, 1971, vol. B21, pp. 104-05. 15. T. Zem~ikand J. V~e~al:Proc. Conf. on MOssbauer Spectroscopy (Dresden}, pp. 294-97, Deutsche Akad. Wissenschaften(DDR), Berlin, 1971. 16. T. Zem~ikand J. V~e~tal:Proc. Conf. on MOssbauer Spectroscopy (Bratislava), pp. 305-08, Czech. Acad. Sci., Bmo, 1973. 17. J. M. Cowley:Phys. Rev., 1950, vol. 77, pp. 669-75; 1960, vol. 120, pp. 1648-57. 18. G. K. Wertheim,V. Jaccarino, J. H. Wernick,and D. N. E. Buchanan: Phys. Rev. Lett., 1964, vol. 12, pp. 24-27. 19. M. B. Stearns: Phys. Rev., 1966, vol. 147, pp. 439-53. 20. T. Zem~ik: CzechoslovakAcademy of Sciences, Brno, Czechoslovakia, personal communication, 1976. 21. S. C. Moss:J. Appl. Phys., 1964, vol. 35, pp. 3547-53. 22. S. Mader: Electron Microscopy and Strength of Crystals, pp. 183-228, Interscience, New York, 1963. 23. F. H. Hayes, F. Mfiller,and O. Kubaschewski:J. Inst. Metals, 1970, vol. 98, pp. 20-22.
These result in a quadratic equation in m, g m 2 + (gn + j ) m + 2 ( h -
ni) = O,
[5]
where g = 0.087413, h = 0.12298, i = 0.12766, and j =i-g-3h. A l l o w i n g n t o t a k e o n v a l u e s f r o m 0 t o 6, i t i s f o u n d t h a t m o n l y v a r i e s o v e r a n a r r o w r a n g e of p o s i t i v e values and moreover varies linearly between n = 0.5 a n d 3 (it i s n e g a t i v e f o r n > 3). T h i s l i n e a r r a n g e
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