982
ú{à®wï æ 68 ª æ 12 †(2004)977_
ÁWuvZóÔ}ÆÞ¿ÝvÖÌWJv
æ괝vZÉæé a_Fe †Ìu·^³fÆ
Nü^³f̊Ýìp
Vcp¾
ìãal
™R¹Í
Vú{»c”®ïÐæ[Zp¤†Š
J. Japan Inst. Metals, Vol. 68, No. 12 (2004), pp. 977_982
Special Issue on Computer Aided Phase Diagram Assessment and Its Extension to Materials Design
Ý 2004 The Japan Institute of Metals
Interaction between Substitutional and Interstitial Elements in a_Fe Studied
by First_Principles Calculation
Hideaki Sawada, Kazuto Kawakami and Masaaki Sugiyama
Advanced Technology Research Laboratories, Nippon Steel Corporation, Futtsu 293_
8511
Interaction energy values between substitutional 3d transition metal elements and interstitial carbon atom in a_
Fe is obtained
by the first_principles calculation method. Calculated values of interaction energy are in good agreement with experimental
values reported for those of Co, Ni and Cu elements, showing a repulsive interaction experimentally. On the other hand, the inter­
action energy for such elements as Ti, V, Cr and Mn is estimated to be a repulsive characteristics, although the attractive interac­
tion between them and a carbon atom is experimentally obtained. The cause for this contradiction is discussed based on a differ­
ent formation energy of carbide precipitation from the atomic pair interaction energy.
(Received June 21, 2004; Accepted August 6, 2004)
Keywords: first_
principles calculation, atomic pair interaction, precipitate, carbide, a_
Fe
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ìpGl‹M[ðˆèµ½Dµ©µC±êçÌÀ±†Ìsm
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Perdew çÉæÁÄñijêÄ¢é\®10,11)ðp¢½D
ȨCC ´q(Fig. 1 ̆ÅÍ X ÆLµ½)©ç©Äæ 1 ß
u·^³fÆNü^³f̊ÝìpGl‹M[ DE ͟®
Ú©çæ 5 ßÚÌ Fe ´qÌÊuð Fig. 1 ɦµ½DTable
1 ©çCC ´qªüé±ÆÉæÁÄæ 1 ßÚÌ Fe ´q͓
ðp¢Ä²×½D
DEE[Fen|1MX]{E[Fen ]|E[FenX]|E[Fen|1M]
´¯çêéªCæ 2 ßÚÈ“Ì Fe ´qÆ̗£ÉÍwÇÏ
±±ÅCE ͇ÊàÌPÊEÌSGl‹M[CM Íu·
»ªÈ¢±Æªª©éDXÉC±ÌlqÍ n54 Ìê‡Æ n
^³fCX ÍNü^³fÅ éDn ÍvZÉp¢½PÊEÉ
250 Ìê‡ÅwÇ·ªÈ¢D±êçÉæÁÄCn54 Èã
ÜÜêéNü^³f𜢽´q̔ŠéDÀÛÌvZÅ
Å êÎ C ´qÉæéiqÉaª×Ú·éZ‹†Ì´qÌ
ÍCüúI«Eððp¢ÄvZðsÁÄ¢é½ßCn ª¬
ÊuÉe¿ðyÚ·Â\«Íá¢Æ»fÅ«éDTable 2
³·¬éÆ×Ú·éPÊEÉÜÜêéu·^³fâNü^³
ÍCu·^³fÆµÄ Ti ´qª Fe ´qÌ 1 ÂÆu·µ½
fÌÔŊÝìpª­­±ÆÆÈèCŠÝìpGl‹M[ð
ê‡Ì Ti ´qÌüÍÌ Fe ´qÌiqÉaÌlq𦵽
³mÉ©Ïàé±ÆªÅ«È¢D»±ÅCPÊEÌ嫳ª
àÌÅ éDu·^³fÉæéiqÉaÌlqð©éÌÉ
n54(§û»ÌPÊE 3~3~3 Â)Æ n128(§û»ÌPÊ
Ti ðIðµ½ÌÍCTi ©ç Cu ÜÅÌ 3d JÚளf̆
E 4~4~4 Â)Æ n250(§û»ÌPÊE 5~5~5 Â)Ì 3
ÅÍ Ti ªÅà´q¼aªå«¢³f¾©çÅ éDȨC
ÂÌê‡É¢ÄCNü^³fÅ é C ´qª 1 ÂÜÜê
Table 2 †Ì Fe54 É¢ÄÍ Fe ´qԗ£ð¦µCTi ´
énÌvZðs¢CC ´qÌüÍÌiqÉaÉ¢IJ׽D
q(Fig. 2 ̆ÅÍ M ÆLµ½)©ç©Äæ 1 ßÚ©çæ 5
Table 1 ÉÍCC ´qªÜÜêĢȢnCn54 ÌPÊE
ßÚÌ Fe ´qÌÊuÍ Fig. 2 ɦµ½DiFig. 2 ÉÍ M ´
É 1  C ´qªÜÜêÄ¢énCn128 ÌPÊEÉ 1  C
q©ç©½æ 1 ßÚ©çæ 5 ßÚÜÅÌiqÔ´qÌÊu
´qªÜÜêÄ¢énCn250 ÌPÊEÉ 1  C ´qªÜ
঵½DjNü^³fÅ é C ´qÌê‡ÉÍCæ 1 ßÚ
ÜêÄ¢énCÌ 4 ÂÌê‡É¢ÄCC ´q©ç©½æ 1
Table 1 Distance (in nm) between C atom and Fe atoms locat­
ed at 1st to 5th nearest neighbor sites from C atom. Brillouin_
zone integrations have been performed on a grid of (a~b~c) k
points. The a, b and c are written as abc in the 2nd row.
Fe54
k_
mesh
Fe54C
111
444
Fe128C
222
333
Fe250C
111
222
1st nn
0.143
0.175
0.177
0.178
0.178
0.178
0.178
2nd nn
0.202
0.198
0.198
0.198
0.198
0.199
0.198
3rd nn
0.320
0.321
0.321
0.321
0.321
0.322
0.322
4th nn
0.350
0.356
0.356
0.358
0.358
0.359
0.359
5th nn
0.429
0.428
0.428
0.428
0.428
0.429
0.429
Fig. 1 1st to 5th nearest neighbor Fe atom sites from intersti­
tial atom (X).
Table 2 Distance (in nm) between Ti atom and Fe atoms lo­
cated at 1st to 5th nearest neighbor sites from Ti atom. Number
of grid points for the Brillouin_
zone integrations are given as in
Table 1.
Fe54
k_mesh
1st nn
0.248
Fe53Ti
Fe127Ti
Fe249Ti
111
444
222
333
111
222
0.250
0.252
0.252
0.252
0.253
0.252
2nd nn
0.286
0.287
0.287
0.286
0.287
0.288
0.287
3rd nn
0.404
0.404
0.404
0.405
0.405
0.407
0.405
4th nn
0.474
0.474
0.474
0.474
0.475
0.476
0.475
5th nn
0.495
0.495
0.496
0.497
0.497
0.499
0.497
Fig. 2 1st to 5th nearest neighbor Fe atom sites (open circle)
and 1st to 5th nearest neighbor interstitial sites (closed circle)
from substitutional atom (M).
æ
12
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Fe †Ìu·^³fÆNü^³f̊Ýìp
æ괝vZÉæé a_
ÊuÌ Fe ´qªå«­Éa·élqð Table 1 É©é±Æ
979
´qâ Ti ´qÌüÍÌiqÉaÉÖ·éÀèCvZÉp¢
ªÅ«½ªCu·^³fÅ é Ti ´qÌê‡ÉÍCæ 1 ß
éPÊEÍ n54 Å\ªÅ éÆl¦çêéDܽCvZ
ÚÊuÌ Fe ´qų¦CiqÉaÍÍ©Å é±Æªª©
ÍæêuŠ‹A“][“†Ì¡”Ìtiq_É¢Äs¢C
éDXÉCu·^³fÌ Ti ´q 1 ÂÆNü^³fÌ C ´q
vZ³ê½SÄÌtiq_ÅÌg®Ö”ðp¢ÄCdq§x
1 ÂðPÊEÉü꽞̼´qÔ̗£ð Table 3 ɦµ
ªzâSGl‹M[ð¾é±ÆªÅ«éDTable 1`3 ɦ
½D±Ì\Ìæ n ßÚÍCC ´q©çæ n ßÚÉ é Fe ´
µ½‹ÊÍCPÊEÌ嫳˶«¾¯ÅÈ­Ctiq_Ì
qÌ 1 Âð Ti ´qÆu·µ½±ÆðÓ¡µÄ¢éD±Ìv
”Éηé˶«É¢Äà²×½àÌÅ èCC ´qÆ
Z‹ÊàCTi ´qÆ C ´qÔ̗£ªPÊEÌ嫳Éw
Ti ´qÌüèÌiqÉaÍtiq_̔ÉàwÇ˶µÈ
Ç˶µÈ¢±Æð¦µÄ¢éD±êçÌvZ‹Ê©çCC
¢±Æªª©éD
ŸÉCPÊEÌ嫳˶«Ætiq_”˶«É¢
Table 3 Distance (in nm) between C atom and Ti atoms locat­
ed at 1st to 5th nearest neighbor sites from C atom. Number of
grid points for the Brillouin_zone integrations are given as in
Table 1.
Fe54
k_
mesh
1st nn
0.143
Fe53TiC
Fe127TiC
Fe249TiC
ÄCiqcÌÉa¾¯ÅÈ­C¥CIȊÝìpâ±Ì¤†
̆ÅÅàdvȊÝìpGl‹M[É¢IJ׽DFig.
3 ÉÍ Ti ´qÆ C ´qÌ¥C‚[“gÌPÊEÌ嫳
˶«Ætiq_”˶«ð¦µ½DȨCTi ´qÆ C ´
qÌÊuÖWÉ¢ÄÍCFig. 1 ɦµ½æ 1 ßÚ©çæ 5
111
444
222
333
111
222
ßÚÌê‡É¢IJ×C»êÉÁ¦ÄCTi ´qÌÝC½
0.196
0.196
0.198
0.198
0.200
0.199
¢Í C ´qÌݪ a_Fe †É éê‡É¢IJ׽DFig.
3 ©çª©éæ¤ÉCTi ´qÌ¥C‚[“gÉ¢ÄÍ
2nd nn
0.202
0.217
0.217
0.218
0.218
0.219
0.218
3rd nn
0.320
0.318
0.319
0.319
0.319
0.319
0.319
n54, k1~1~1 Æ n128, k2~2~2 ̋ÊðCC ´q
4th nn
0.350
0.354
0.356
0.358
0.358
0.359
0.359
É¢ÄÍ n54, k1~1~1 Æ n250, k1~1~1 ̋
5th nn
0.429
0.431
0.431
0.431
0.431
0.432
0.432
Êðœ¢Äwǯ¶lð¦·DXÉCæ 1 ßÚ©çæ 5 ß
ÚÖÆ Ti ´qÆ C ´q̗£ª£êéÉÂêÄCTi ´q
Æ C ´qÌ¥C‚[“gÍCTi ´qÌÝCC ´qÌݪ
a_Fe †É éÆ«ÌlÉßâĢ«Cæ 5 ßÚÅÍwÇ
¯¶ÉÈÁÄ¢é±Æªª©éD±Ì±ÆÍCæ 5 ßÚÅ
Í Ti ´qÆ C ´qÌ¥CIŠÝìpªñíɬ³¢±Æð
¦µÄ¢éDiqÉaÉ¢ÄÍCSÄÌvZ‹ÊÅLÓÆ
l¦çêéë·Í¶¶È©Á½ªC¥C‚[“gÉ¢Ä
ÍÁÉtiq_ª­È¢ê‡É뷪嫭Èé±Æªª©
Á½D±êÍCtiq_ª­È¢ê‡ÉÍÁÙÈtiq_Ì
ݪp¢çêC»ê窼ÚIÉe¿·é¥C‚[“gÅ
Íå«Èë·ð¶¶CÔÚIÉe¿·éiqÉaÉ¢ÄÍ
ë·ªÚ§½È¢ÆðßÅ«éDSGl‹M[É¢ÄÍ¥
Fig. 3 Magnetic moment of (a) Ti atom and (b) C atom for
different unit cell sizes and number of grid points for the
Brillouin_zone integrations. Magnetic moments of C atom for n
128, k2~2~2 are the same as those for n128, k3~3~
3.
Fig. 4 Interaction energy between Ti atom and C atom for
different unit cell sizes and number of grid points for the
Brillouin_
zone integrations.
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íÉå«È³ÌŠÝìpGl‹M[(Ë͊Ýìp)ð^¦
¥C‚[“gÉä×êÎÔÚIÉtiq_ÌIðÌe¿ð
éDêûCæ 3 ßÚȓÌê‡ÉͳfÉæéá¢Íå«
ó¯éÆl¦çêéDFig. 4 ÉÍCu·^³fÆNü^³f
­È­Cµ©àC»ÌlÍ 0.3~10|19 J ȺƬ³¢DÂ
̊ÝìpGl‹M[É¢ÄCPÊEÌ嫳˶«Æt
ÜèCu·^³fªßTɶݷé C ´qÉå«­e¿ð
iq_”˶«ð²×½‹Ê𦵽D½¾µCu·^³f
yÚ·ÌÍæ 2 ßÚÜÅÅ èC»êȓÍÍ©Å éÆ
ÆNü^³fÌÊuÖWÉ¢ÄÍCFig. 1 ɦµ½æ 1 ß
l¦çêéD
Ú©çæ 5 ßÚÌê‡ðÎÛƵ½DŠÝìpGl‹M[
ŠÝìpGl‹M[̳f˶«ª½ÉNö·é©ð²×
ÍCn54 Å k1~1~1 ÌvZ‹Êðœ¢ÄSÄÌvZ‹
é½ßÉCu·^³fÆNü^³fÌÔ̗£ð²×½Ìª
ʪwÇdÈÁĨèCn54 Å k4~4~4 ÌvZ‹ÊÆ
Fig. 6 Å éD±Ì}ÅÍCu·^³f M ´qÆ C ´qÆ
ÅàPÊEÌå«¢ n250 Å k2~2~2 ÌvZ‹ÊÆÌ
̗£(M_C)Ì M ´qªÈ¢Æ«Ì Fe ´qÆ C ´qÆÌ
J ȺŠé±Æªª©Á½DȨCã
—£(Fe_C)©ç̸êðp[Z“gÅ\¦µ½DFig. 6 Æ
qÌSÄÌê‡É¨¢ÄCiqè”ƵÄÍÀ±Å¾çêÄ
Fig. 5 ðär·éÆCæ 1 ßÚÌê‡ÉC(M_C)̗£Æ
¢él 0.286 nm ðp¢½D½¾µCFe54 É墀 k4~4
ŠÝìpGl‹M[Ɋ֪ éæ¤É©¦éDXÉCæ 1
~4 ÌvZÅÅK»³ê½iqè”ÌlÍ 0.285 nm Å ßÚÌ(M_C)̗£ÍCu·^³fÌ´q¼aƯ¶Xü
èCvZë·Í\ªÉ 1÷ȺŠé±ÆðmFµ½DXÉC
ðÂDàµCS†Éu·³ê½ 3d JÚபCüèÌ
ë·ª
0.2~10|19
n54, k4~4~4 Ìê‡ÉCFe54, Fe54C, Fe53Ti, Fe53TiC
Fe ´qƤL‹‡Iȋ‡ð‹ÔÆ·êÎCdq”ÈÇÉ
(æ 1 ßÚ©çæ 5 ßÚÌSÄ)É¢Äiqè”ðÅK»
ž¶½}ƒÈÏ»ª\z³êéªCu·^³fªà®IÈó
µCŠÝìpGl‹M[ÌÏ»ð²×½‹ÊCŠÝìpGl
‹M[Ìë·Íæ 1 ßÚ©çæ 5 ßÚÜÅÌ¢¸êÉ¢
Äà 0.2~10|19 J ȺŠÁ½DÅK»Éæéiqè”Ì
Ï»ÍCPÊEª n128 â n250 Å éê‡Éä×ÄC
sƒ¨ZxÌÅà‚¢ n54 Ìê‡ÉÅåÅ é½ßCn
128 Æ n250 Ìê‡ðÜßÄCiqè”ÌÅK»ÉæéŠ
ÝìpGl‹M[Ìë·Í 0.2~10|19 J ȺŠéÆl¦
çêéD
3.
u·^³fÆNü^³fÔ̊ÝìpGl‹M[
ãqµ½æ¤ÉCŠÝìpGl‹M[Í n54 ÌPÊE
Å k4~4~4 Ìtiq_bV…ðp¢ÄvZ·êÎ\ª
ÈvZ¸xª¾çêé±Æªª©Á½D»±ÅC±ÌvZð
ÌºÅ 3d JÚளfÆ C ´q̊ÝìpGl‹M[ð
ß½(Fig. 5)D}©çª©éæ¤ÉCu·^³fÆNü^
Fig. 6 Normalized distance between substitutional 3d transi­
tion metal atom and interstitial C atom.
³fÌÊuÖWªæ 1 ßÚCæ 2 ßÚÌê‡É͊Ýìp
Fig. 5 Interaction energy between substitutional 3d transition
metal atom and interstitial C atom.
Fig. 7 Magnetic moment of Fe atom located at 1st to 5th
nearest neighbor sites from the substitutional 3d transition
metal atom.
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Fe †Ìu·^³fÆNü^³f̊Ýìp
æ괝vZÉæé a_
ÔðÛÁÄ¢é½ßÉCu·^³fÆ C ´q̊ÝìpG
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ªdvÅ éƦ´³êéD
³fÆ C ´qÆ̗£É¢ÄÍCŠÝìpGl‹M[Æ
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XÉCŠÝìpGl‹M[̳f˶«ðð·é½ß
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ÉCu·^³fÌüèÌ Fe ´qÌ¥C‚[“gÉ¢Ä
‹M[ð½Ï·é±ÆÅCÀ±‹ÊÆvZ‹Êðär·é±
à²×½DFig. 7 ɦµ½ÌÍCa_Fe †Ì Fe ´qÌ 1 Â
Æðl¦½D½ÏÉÛµÄÍCPƒÉŠÝìpGl‹M[Ì
ðu·^³f M Åu·µ½žÌCM ´q©ç©½æ 1 ßÚ
lð½Ï·éÌÅÍÈ­CŠÝìpGl‹M[Ìá¢Æ±ë
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ÙÇ´q̶Ým¦ª‚­CÀ±IÉÏ@³êélÉߢÍ
lÍCn54, k4~4~4 ÅÌvZ‹Ê©çß½àÌÅ ¸ÈÌÅCŠÝìpGl‹M[É{‹c}“öqð|¯Ä½
éDêûCªÊÌÊuɶݷé C ´qÌ¥C‚[“g
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é C ´qªCM ´q©ç©ÄÇÌÊuÉ é Fe ´qɲ
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»±ÅCFig. 7 ðp¢ÄCTable 4 ɦµ½æ 2 ßÚ©çæ
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5
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5
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i1
“g̽Ïlðß½Ìª Fig. 8 Å éDu·^³fÉ
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æéæ 2 ßÚ©çæ 5 ßÚÜÅÌ¥C‚[“gÌÏ»
‹M[ͼVÌñ1)ÆÇ­êvµÄ¢éDêûCTi, V, Cr,
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Table 4 Position of C atom from the substituional 3d transition
metal atom is shown in the first column. There are two Fe atoms
next to the C atom, since the C atoms are located at the octa­
hedral site. In the 2nd and 3rd column position of the two Fe
atoms from the substitutional 3d transition metal atom is given.
C
Fe
1
M
2
2
1
1
3
2
3
4
1
4
5
3
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nearest neighbor sites from C atom. Substitutional 3d transition
metal atom is located at 2nd and 5th nearest neighbor sites from
C atom.
Fig. 9 Interaction energies between substitutional 3d transi­
tion metal atom and interstitial C atom are averaged for 1st to
5th nearest neighbors.
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1) T. Nishizawa: Bull. Inst. Metals 12(1973) 401.
2) H. Numakura, G. Yotsui and M. Koiwa: Acta Metall. Mater.
43(1995) 705.
3) T. Hoshino, M. Asato and T. Mizuno: Meeting Abstracts of the
Physical Society of Japan, vol. 55, issue. 2 (2000) p. 853.
4) D. Vanderbilt: Phys. Rev. B41(1990) 7892.
5) K. Laasonen, A. Pasquarello, R. Car, C. Lee and D. Vanderbilt:
Phys. Rev. B47(1993) 10142.
6) G. Kresse and J. Hafner: Phys. Rev. B47(1993) 558.
7) G. Kresse and J. Hafner: Phys. Rev. B49(1994) 14251.
8) G. Kresse and J. Furthmuller: Comput. Mat. Sci. 6(1996) 15.
9) G. Kresse and J. Furthmuller: Phys. Rev. B54(1996) 11169.
10) J. P. Perdew and Y. Wang: Phys. Rev. B45(1992) 13244.
11) J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R.
Pederson, D. J. Smith and C. Fiolhais: Phys. Rev. B46(1992)
6671.
12) T. Ohnuma and N. Soneda: Meeting Abstracts of the Physical
Society of Japan, vol. 55, issue. 1 (2000) p. 868.