!kd 73 (TMC, transition{metal carbides) 'Q73 (TMN, transition{metal nitrides) r| X b vi' 0 k Zyb j e'I (WT xsx Y BI V ^X0- 0k *1 d F * d9 E VX ] 'd @\ ** Z . .F n~ H* ; X3 7X^*N&jk|N X Zm ^ * k TiC . C 9 d
5A
23] 24] 25] 15 18] 15 18] 19] 20]
;
26]
MC coh
MC tot
freeM tot
freeC tot
MC coh
MC tot
freeM tot
freeC tot
;
21 22]
Table 1
L 1 K lE0 Y IVB ( VB "l?f 84 , Yj 9 , (_,4 Calculated and measured lattice constants a0 , bulk module B , and cohesive energies Ecoh of the bulk IVB and VB transtion metal carbides
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""`g {u8&^\o IVB ( VB "l?f 84 lE (Y_ (e: O' ! %$ 8 84 (F0Y7eo (e:~'K ( (4YuB 84Y_,4( (4Y 8 4 (F0Y $ (@55 Mu lE (4 ;_, 4 QY 8 D _,4( (F0>j +q $uB(vg IVB ( VB "l?f 84 (001) (4Y c _kQ `g &jy$ 84 _, 4 (4 H~w A Gb 0412;1961(2006)05;0554;07 Y]rb TG139
a0 ,
System TiC
ZrC
HfC
VC
NbC
TaC
GPa 250 252 242 1] 230 220.7 227.9 29] 272 243 { 305 304 27] 303 32] 307 333 302 1] 307 316 27] 317 33]
B,
14.62 14.60 14.31 0.14 5] 15.82 16.466 15.86 0.19 6] 16.00 16.53 16.22 0.16 7] 13.68 13.86 13.88 0.16 5] 15.94 15.91 16.52 0.19 6] 17.52 17.48 17.12 0.14 7]
Method This work GGA{PWPP 27] Experiment This work USPP{GGA 29] Experiment This work GGA{PW91 20] Experiment This work GGA{US 31] Experiment This work GGA{PW91 20] Experiment This work GGA{PW91 20] Experiment nm 0.432 0.433 0.433 28] 0.469 0.4731 0.4698 30] 0.453 0.4653 0.64 1] 0.415 0.4170 0.4172 31] 0.447 0.4514 0.4470 1] 0.456 0.4485 0.445 1]
jEcoh j, eV
556
c; ~ ;W;
'N&X6 R N gf(gM '3 '3 p .
19]
42t
. z /y
p(
2.2 Jz
J
L 2 @ 2 (Relax) (@ Table 2 Calculated (001) surface
Esurf
surf
= (E
n slab
; nE
bulk
)=2
2006 6 5
_ 42 t
554|560 d
_5A
ACTA METALLURGICA SINICA
Vol.42 No.5 May 2006 pp.554{560
IVB f VB aW
n^fU
(
o RS
h s
i}K{R p
#n $`+ |Y L "!_ ) |Y e; +
b
(
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FIRST{PRINCIPLES STUDY OF THE STRUCTURES AND ELECTRON STATES OF IVB AND VB TRANSITION METAL CARBIDES AND THEIR SURFACES
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016 Correspondent: ZHANG Huaizheng, Tel: (024)23971846, E-mail: hzzhang@ Supported by National Key Basic Research and Development Program of China (No.G2000067104) Manuscript received 2005{08{24, in revised form 2005{11{24
3 7] 8] 9] 10 11] 12] 13] 14]
9 Z : IVB ' VB !k>d 73DC ' X^ 'd9 X_f Zm 555 +5 ' E/X : h kD * : hr D X ' d9 t zt . d9Y< 3o x GGA{PW91 Z D t h o x Monkhorst{Pack zt WK }&X 7 b, =' " xX\m 3O . 350 eV. * -x * X '3}ktATp3 '7X!= Y 10 10 10] K b, ' KX0i. 9 1 1 ' L7 ' g 'd :'a '98 Z n~ 7 N PhN~ 1.5 nm, o xX v 10 10 1] K b, J 3 H* d a'XJ +5Zm * a'X^* ztX6RNjk Liu Z ; X B(gM T ' 73 H* X '3| '3 N L<a X/y *J X6RNv}k }X J +Kn 'i Xa ' ^* c N ; . h A Hugosson Z ' Vi~es Z n 73 H* X (001) ' g * 'N&XZmc v}{X n M Zm Hugosson ZZmX Q b v# |z ' E 2 MtdIyj /<E E/<E v !k> 73 (001) ' Xf ' 2.1 Nu C b E/X6dn 'H)'d9N&XtAh} . ^ BJ ztX6RN |:J H 2 Rv .F| 'E/n '3tA2 XZm 73Xi 8 + '^* 3 IVB ' VB d ._ pI z'X B v |mo' bX 73. NaCl ^ J ^*3 oxX p . 0J IVB ' VB !k>d 73; XN E = ;E + E +E (1) & # i 1b n IVB ' VB !k>d 73 (001) 'Xd9 ' '3 gM Zm J z ' XE p ( E vd 73 M C X^* 3 E .d /<E !IZm 'E/n '3' 'd%}&X 73X=3 E . d 9 M X=3 '3 73 ; tA '3 XZm( <*z E v C 9X= 3 * 9X X^*3' 'E/=iX 7 =^ '3X 7 v f 9| f :. 1 nm X z-9( Lt kD ~ '3 Xufp J 1 ( C H * XJ "'l^" J X 1 j ZX i 8 l ^" PX54hG~ 2.5%, * J X J zt-x@~ % ix# X =' "D 6RNv}k }X
ZHANG Huaizheng, LIU Limin, WANG Shaoqing
ABSTRACT The structures and electronic properties of IVB and VB transition metal carbides and their surfaces are systematically investigated by the rst{principles method. Some important questions are discussed, such as, the common characteristics and distinctions of the surface ripples on the (001) surfaces of the carbides, the e ects of the surface ripple on the surface energy and the sur cial charge distribution, the change trends of the cohesive energy and surface energy of the carbides and their surfaces, and the correlation between the surface energy and the cohesive energy. A new viewpoint is suggested that the cohesive energy of the bulk carbides and the ripple ratio of the (001) surface a ect and determine the surface energy of (001) surface of IVB and VB transition metal carbides together. KEY WORDS rst{principles, density functional theory, carbide, cohesive energy, surface energy