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On the electronic states of metalloid atoms in metal-metalloid systems
Physica B 168 (1991) North-Holland
278-284
On the electronic systems V.S. Stepanyuk’,
A.A.
states of metalloid Katsnelson”,
atoms in metal-metalloid
A. Szasz”, A.V. Kozlov”
“Department of Solid State Physics, Lomonosov State University. Lenin Hills, Moscow~ SU-117233. USSR hLaboratory of Surface and Interface Phyxcs, E?mG.s University, Museum krt.68. Budapest. H-1088. Hungcrr> Received 27 June lYY0 In final form received 10 October
1YYO
The electronic structure of the metalloids B and P in Ni and Fe metallic matrices is calculated by the LAPW method. The effect of different arrangements of nearest neighbourhood and the actual charge transfers arc also calculated.
1. Introduction Metal-metalloid type systems such as: Ni-P, Ni-B, Fe-P, Fe-B are now of great interest [l-5] because of their widespread applications. Nevertheless, numerous effects and processes related to their specific electronic structure remain mostly unclear or unexplained as yet. There are substantially contradictory data about charge transfer between metal and metalloid [S]. The effect of the local neighbourhood of the metalloid on the electronic band structure of the system is not established. there is no detailed analysis of possible types of hybridization of metal and metalloid states, the characteristic differences of the electronic structure of the various metalloids in the same matrix as well as of one metalloid in various matrices are not discussed thoroughly enough. In amorphous systems the electronic structure of the metalloid can be calculated considering only the arrangements of the nearest neighbourhood (short range order, SRO) or taking into account the interaction with more distant coordination spheres of atoms. To investigate the role OY21-4526/Y1/$03.50
0
1991 ~ Elsevier
Scicncc
Publishers
of nearest neighbourhood clustering such an approach is applicable, in which a simple metalloid atom is considered as an impurity in an infinite crystalline matrix. Here a unique SRO is given for clusters existing in the long range ordered (LRO) crystal. If one would change the crystal symmetry (different LROs) it would be possible to explain the effect of LRO on the actual electronic structure around the metalloid atom. So we made the relevant calculations in each case for one real and two hypothetical LROs. A procedure has been developed [6] for constructing the relevant Green function of the crystal with perturbations based on Dederichs’ method [7] on the basis of the linear augmented plane waves (LAPW) method [S], and a calculation was performed for impurities as well, [9]. In these approximations the Dyson equation of the system has been solved, and the Green function of the ideal crystal was determined by the LAPW method. Detailed discussion of this approach and its testing is given in refs. [6, 81. In our present work a calculation for the electronic structure of P and B metalloids in Ni and Fe metallic matrices is presented and discussed.
B.V. (North-Holland)
V.,Y. Stepanyuk
et al.
I
Electronic
states of metalloid
atoms
in metal-metalloid
systems
279
2. The method
The investigations on the electronic structure of defects in crystals have been started with Friedel’s classical work [lo]. The calculations nowadays are centered on the muffin tin Green function (MTGF) method, [6,11] used by us too. In the frame of this approach the Green function of the crystalline matrix with defects is expressed by the Dyson equation: G:;<(E)
= G:‘.‘(E)
+ ,;,, G;“,“.:‘(E) At;..(E) G;:;,(E)
(1)
,
(E) and G”,“;,(E) are Green functions of the ideal and perturbed crystal, At::’ is the change where GO,“,“,’ of the scattering matrix due to the effect of defects, n is the site-number, and L = {I, m} is a set of quantum numbers. In most of the cases the KKR-method has been applied to determined the Green functions, but this method has some problems, as the discontinuity of the basic wave functions and the requirement to use singular structure constants. In our present work an approximation has been developed to determined the Green function coefficients based on the self-consistent linear augmented plane wave (LAPW) method, [7], which needs much less computing time than other methods as in ref. (6791. To approximate the Green function of the ideal crystal a spectral presentation has been applied:
G(r, r’, E) = Q,/(~T)~ 2
j- ‘-&(r)
?Q(r’)(E - E,,)-’ dk ,
(2)
A BZ
where fl, is the volume of the Wigner-Seitz cell, r and r’ are the coordinate vectors, E is the energy, A the band index, and k the Bloch vector. Integration is carried out in the Brillouin zone (BZ), !Q(r) is the electron wave function in the crystal (calculated by the LAPW method [6]), corresponding to the energy-eigenvalue E,, . We present G(r, r’, E) in the form of a series expansion based on the solutions of the SchrGdinger equation in the muffin-tin (MT) sphere: G(r +
Rh,r’
+
R", E) = -i&,,K
2 R;(r<,
E)Y,(r)Hj’(r>,
E)Y,(r’)
L
+
L;,
R;(r, E)Y,(r)G”,“,R;.‘(r’,
E)Y,.(r’),
where r< = min(r, r’); r, = max(r, r’), R” and R”’ are the atomic positions,
H;(r, E) = R;(r, E) + iN;(r, E) .
(3) K =
d!?,
and (4)
Ny(r, E) is the irregular solution of the radial SchrGdinger equation, GrL.(E) are the energydependent coefficients of the Green function. The first term in eq. (3) represents a Green function for the MT-sphere in vacuum and the second one characterizes the effect of the crystalline structure. On the boundary of the MT-sphere the solution Ry(r, E) fitted to the solution of the SchrGdinger equation for free space is given by Ry(r, E) = J,(kr) - ifi ff;(r,
E) =
h,(kr) ,
ty(E)h,(kr)
, (5)
280
V. S. Stepanyuk
et ul.
i Electronic
states of metalloid
atoms
in metal-metalloid
systems
where j,(kr) represents spherical Bessel function, t;(E) is the scattering matrix of the nth MT-sphere. and h,(kr) the first order spherical Hankel function. The Green function coefficients of a crystal with defects can be expressed by the coefficients of the Green function for the ideal crystal [5,6] (eq. (1)). If the perturbation is regarded as highly localized [12] and if angular momenta 1 g 2 are taken into account. eq. (1) in the case of cubic-site symmetry assumes the form of four scalar equations,
G’I’Z(E) =
G‘:‘;;(E) [1 -
’
G’:‘“I’(E) At;‘(E)]
(6)
Therefore the basic problem is to determine the coefficients of the Green function for the ideal crystal, G:,:(E). We will start from the representation of the crystal wave functions in the LAPW method:
[fl,p2 h,(r)
exp(ikr),
R, .
]rl>
=
(7) ~vRT[R,,]~“’
@i(b)
= a,,,Ur,
4,)
exp(ik,r,)
c
+ b,,,R,,(r,
Irl s R, ,
i@;(k,r)Y,,(r),
&,I
.
where the akh are solutions of the secular equation in the LAPW method, k, = k + G,, G, is a vector of the reciprocal lattice, and R,y is the radius of the MT-sphere for sth atom. a,, and b,, are coefficients. which can be determined from the condition of continuity of the wave functions at the’ boundary of the MT-sphere, and R,[(r, E,y,) is the solution of the radial Schrodinger equation in the MT-sphere (E,, is the reference energy). l?,,(r, E,,) its energy derivative. Contrary to the original KKR-method, the @f(k,, r) depend implicitly on energy through the vector k. Direct substitution of @“,~(k,, r) into (3) is not possible. Substituting (7) into (2) and multiplying (2) and (3) with the solution of the Schrodinger equation in the MT-sphere and integrating we get:
2RfRf.
c
J h HZ
KS X I
’ dk c aFA(aT*)” cxp[i(k,R” 1,
i’ ~“(E - EkA)
- k,R”]
R, @i(k,,
r)Ry(r,
E)r’dr
0
1 @I,(k,r)R;.‘(r. 0
E)r’
,
dr YL(k,)Y,,.(k,)
(8) where
the a;,“(E)-coefficients
a;;‘:‘(E)
= i R;‘(r, E)R;.‘(r,
Based on the LAPW-idea R;‘(r, E) in powers of energy
are determined
by the following
formula:
E)r’dr
we use for R;(r, E) a linear and stop it at the linear term,
(9)
representation
in energy
by expanding
V.S. Stepanyuk et al. I Electronic states of metalloid atoms in metal-metalloid
RY(r,E) = [R,,(r,4,) + (E - E.Jd,,(r,E,,)][(U;,“‘(E)(l
281
systems
(10)
+ (E - EF,)2NF,)-1]-1’Z )
where R,
IV,, =
I r*
dr
k:(r, Es,) .
(11)
0
Eventually
we obtain:
x
C
d*(u;kh)*
exp[i(k,R” - k,R”‘)](a,,, + (E - E,y,)b,,,N,,)
11 x [l + (E - Es,)ZN~,]-“2(a, ‘,‘, + (E - E,.,.)b.@ x [l + (E - E ,‘,’)2N,.,.]~1i?Y~(k;)Y,.(k,)
.
,‘,.) (12)
The formula obtained has been applied to find the imaginary part of the Green function. The self-consistent potential of the matrix was determined by the LAPW-method. For the exchange potential Vosko’s parametrization procedure [13] has been adopted. Using the coefficients of the Green function defined in this way for the crystals with defects it is easy to obtain the local density of states in the MT-sphere,
n(E) = -2/lT
Im G(r, r, E) dr ,
I
(13)
“MT
and the electronic
n(r) = -~/IT
density
Im G(r, r, E) dE .
(14)
3. Case of phosphorus Considering the metalloid atoms as an impurity in an infinite crystalline matrix the density of states is calculated. The results on the density of states (DOS) of P in Fe and Ni are given in figs. 1 and 2. In the energy. range approximately 5-7 eV below the Fermi energy (EF) a p-state of phosphorus, while at still lower energies a bonded s-state (not shown in the figures) is found.
The calculated s-state energy positions and charges are given in table 1. Both s- and p-states of P are lying slightly lower in Fe than in Ni. The general characteristics of the electronic structure of P is similar in Fe and Ni matrices: - hybridization of the s- and p-states of P with the d-states of the metal is increasing from
V.S.
Stepanyuk
et al.
I
Electronic
states of metalloid
energy-positions
E(eV) IQ1
and charges
for various
systems. Fe
FCC
BCC
SC
FCC
BCC
SC
-12.2 1.33
~11.6 1.35
~ 10.2 1.40
- 12.8 0.92
-11.9 1.40
- 10.4 1.41
FCC to SC through BCC, - p-states appear, _ anti-bonding p-states appear, which is well indicated by a peak above the Fermi level.
Ni-P Fe-P
systems
I Ni
Table 2 Charge transfer
in metal-metalloid
Fig. 2. The partial density of electronic states (PDOS) of P in Ni matrices of various crystalline symmetries. The curves a. b and c give the s. s + p and s + p + d PDOS. respectively.
Fig. 1. The partial density of electronic states (PDOS) of P in Fe matrices of various crystalline symmetries. The curves a. b and c give the s, s + p and s + p + d PDOS. respectively. Table s-state
atoms
The charge transfer takes place in the direction from the phosphorus atom towards the metal, by values collected in table 2.
4. Case of boron for P impurity. FCC
BCC
SC
0.32 0.28
0.31 0.17
0.24 0.10
The DOS of B in metallic matrices of Ni and Fe are shown in figs. 3 and 4. For all symmetry types an s-state of B is observable for which the energy position is heavily depending on local
V.S. Stepanyuk et al. I Electronic states of metalloid atoms in metal-metalloid
,,W,:i
systems
283
SK I
T------
-1
Fig. 3. The partial density of electronic states (PDOS) of B in Fe matrices of various crystalline symmetries. The curves a, b and c give the s, s + p and s + p + d PDOS, respectively. Table 3 Charge transfer
Ni-B Fe-B
Fig. 4. The partial density of electronic states (PDOS) of B in Ni matrices of various crystalline symmetries. The curves a, b and c give the s, s + p and s + p + d PDOS, respectively.
of B impurity. FCC
BCC
SC
0.18 0.31
0.17 0.30
0.23 0.35
environment. In the energy range from 0 to -4 eV under the Fermi level the d-states of the metal are heavily hybridized by the p-states of B, and similarly for Fe and Ni. Over the Fermi level anti-bonding p-states are situated, which for FeB lie slightly higher than for Ni-B. Charge transfer is taking place in both systems from the metal atom towards B and has the values collected in table 3.
5. Conclusion
The overall characteristics of all the investigated systems are: (1) new states in the energy
range from -10 to -4 eV under E,, (2) definite anti-bonding p-states above the E, in range O4 eV, manifested itself in a peak in the region, (3) E, is lying near the minimum density of the metalloid states, in accordance with the stability criteria introduced by Nagel and Taut, [14]. This is at the same time one of the proofs for the idea [15] that the electronic structure stabilizes the amorphous state of these metal-metalloid alloys. Some conclusions can be drawn also concerning differences in the electronic structure of P and B impurities. (1) The s-state of B is lower than the p-state of P, (2) the half-width (HW) of B s-states, measured for individual peaks corresponding to the state, is considerably less (by 5-8 times) than the HW of the p-state of a P atom, (3) the phosphorus atom appears to be a weak donor while boron a weak acceptor.
2x4
V.S. Stepanyuk
et al.
i Electronic
state.\ of meialloid
The basic characteristics of the metalloid in all the above discussed lattice types remain the same which indicates that substantial changes in the electronic states could be related to the MRO order.
References [l]
A. Szasz, J. Kojnok and E. Belin, Solid State Commun. 64 (1987) 77s. 121 A. Szasz, X-D. Pan, J. Kojnok and D.J. Fabian, J. Non-Cryst. Solids 108 (1989) 304. 131 K. Tanaka, T. Saito, K. Suzuki and P. Hasegawa, Phys. Rev. B 32 (1985) 6853. [4] T. Tanaka, M. Yoshino and K. Suzuki. J. Phys. Sot. Jpn. 51 (1982) 3882. [S] J. Kojnok. A. Szasz. E. Nagy, G. Mark. V.S. Stepanyuk. A.A. Katsnelson and W. Krasser. to he published.
atoms i/t meta-metalloid
161V.S.
sy.stern.\
Stcpanyuk. A.V. Kozlov. A.A. Katsnelson, O.V. Farberovich, A. Szasz and J.J. Kojnok. Fiz. Tvcrd. Tela 32 (1989) I46 (in Russian). Phys. Rev. Lett. 32 I71 R. Zeller and P.H. Dederichs. (lY7Y) 1713 R. Podlosky. R. Zeller and P.H. Dedericha, Phys. Kc\. B 22 (IWO) 5777. B.M. Klein, W.E. Pickctt. L.L. Boyer and R. Zeller. Phys. Rev. B 35 (IY87) 5802. J. Friedel. Nuovo Cimento Suppl. 7 (1956) 2X7. D.D. Koelling and G.O. Arhman. J. Phys. F 5 (lY75) 204 I V.S. Stepanyuk. A. Szasz. A.A. Katsnclson. A.V. Kozlov and O.V. Farberovich, 2. Phys. B 81 (1YYO) 3Yl. S.H. Vosko. L. Wilk and M. Nusair. Cana. J. Phys. 58 (1YXO) 1200. S.R. Nagel and J. Taut, Solid State Commun. 22 179 (1077). A. Szasz, Xiao-Dan Pan, J. Kojnok and D.J. Fabian. J. Non-Cryst. Sol. 108 304 (IYXY).
278-284
On the electronic systems V.S. Stepanyuk’,
A.A.
states of metalloid Katsnelson”,
atoms in metal-metalloid
A. Szasz”, A.V. Kozlov”
“Department of Solid State Physics, Lomonosov State University. Lenin Hills, Moscow~ SU-117233. USSR hLaboratory of Surface and Interface Phyxcs, E?mG.s University, Museum krt.68. Budapest. H-1088. Hungcrr> Received 27 June lYY0 In final form received 10 October
1YYO
The electronic structure of the metalloids B and P in Ni and Fe metallic matrices is calculated by the LAPW method. The effect of different arrangements of nearest neighbourhood and the actual charge transfers arc also calculated.
1. Introduction Metal-metalloid type systems such as: Ni-P, Ni-B, Fe-P, Fe-B are now of great interest [l-5] because of their widespread applications. Nevertheless, numerous effects and processes related to their specific electronic structure remain mostly unclear or unexplained as yet. There are substantially contradictory data about charge transfer between metal and metalloid [S]. The effect of the local neighbourhood of the metalloid on the electronic band structure of the system is not established. there is no detailed analysis of possible types of hybridization of metal and metalloid states, the characteristic differences of the electronic structure of the various metalloids in the same matrix as well as of one metalloid in various matrices are not discussed thoroughly enough. In amorphous systems the electronic structure of the metalloid can be calculated considering only the arrangements of the nearest neighbourhood (short range order, SRO) or taking into account the interaction with more distant coordination spheres of atoms. To investigate the role OY21-4526/Y1/$03.50
0
1991 ~ Elsevier
Scicncc
Publishers
of nearest neighbourhood clustering such an approach is applicable, in which a simple metalloid atom is considered as an impurity in an infinite crystalline matrix. Here a unique SRO is given for clusters existing in the long range ordered (LRO) crystal. If one would change the crystal symmetry (different LROs) it would be possible to explain the effect of LRO on the actual electronic structure around the metalloid atom. So we made the relevant calculations in each case for one real and two hypothetical LROs. A procedure has been developed [6] for constructing the relevant Green function of the crystal with perturbations based on Dederichs’ method [7] on the basis of the linear augmented plane waves (LAPW) method [S], and a calculation was performed for impurities as well, [9]. In these approximations the Dyson equation of the system has been solved, and the Green function of the ideal crystal was determined by the LAPW method. Detailed discussion of this approach and its testing is given in refs. [6, 81. In our present work a calculation for the electronic structure of P and B metalloids in Ni and Fe metallic matrices is presented and discussed.
B.V. (North-Holland)
V.,Y. Stepanyuk
et al.
I
Electronic
states of metalloid
atoms
in metal-metalloid
systems
279
2. The method
The investigations on the electronic structure of defects in crystals have been started with Friedel’s classical work [lo]. The calculations nowadays are centered on the muffin tin Green function (MTGF) method, [6,11] used by us too. In the frame of this approach the Green function of the crystalline matrix with defects is expressed by the Dyson equation: G:;<(E)
= G:‘.‘(E)
+ ,;,, G;“,“.:‘(E) At;..(E) G;:;,(E)
(1)
,
(E) and G”,“;,(E) are Green functions of the ideal and perturbed crystal, At::’ is the change where GO,“,“,’ of the scattering matrix due to the effect of defects, n is the site-number, and L = {I, m} is a set of quantum numbers. In most of the cases the KKR-method has been applied to determined the Green functions, but this method has some problems, as the discontinuity of the basic wave functions and the requirement to use singular structure constants. In our present work an approximation has been developed to determined the Green function coefficients based on the self-consistent linear augmented plane wave (LAPW) method, [7], which needs much less computing time than other methods as in ref. (6791. To approximate the Green function of the ideal crystal a spectral presentation has been applied:
G(r, r’, E) = Q,/(~T)~ 2
j- ‘-&(r)
?Q(r’)(E - E,,)-’ dk ,
(2)
A BZ
where fl, is the volume of the Wigner-Seitz cell, r and r’ are the coordinate vectors, E is the energy, A the band index, and k the Bloch vector. Integration is carried out in the Brillouin zone (BZ), !Q(r) is the electron wave function in the crystal (calculated by the LAPW method [6]), corresponding to the energy-eigenvalue E,, . We present G(r, r’, E) in the form of a series expansion based on the solutions of the SchrGdinger equation in the muffin-tin (MT) sphere: G(r +
Rh,r’
+
R", E) = -i&,,K
2 R;(r<,
E)Y,(r)Hj’(r>,
E)Y,(r’)
L
+
L;,
R;(r, E)Y,(r)G”,“,R;.‘(r’,
E)Y,.(r’),
where r< = min(r, r’); r, = max(r, r’), R” and R”’ are the atomic positions,
H;(r, E) = R;(r, E) + iN;(r, E) .
(3) K =
d!?,
and (4)
Ny(r, E) is the irregular solution of the radial SchrGdinger equation, GrL.(E) are the energydependent coefficients of the Green function. The first term in eq. (3) represents a Green function for the MT-sphere in vacuum and the second one characterizes the effect of the crystalline structure. On the boundary of the MT-sphere the solution Ry(r, E) fitted to the solution of the SchrGdinger equation for free space is given by Ry(r, E) = J,(kr) - ifi ff;(r,
E) =
h,(kr) ,
ty(E)h,(kr)
, (5)
280
V. S. Stepanyuk
et ul.
i Electronic
states of metalloid
atoms
in metal-metalloid
systems
where j,(kr) represents spherical Bessel function, t;(E) is the scattering matrix of the nth MT-sphere. and h,(kr) the first order spherical Hankel function. The Green function coefficients of a crystal with defects can be expressed by the coefficients of the Green function for the ideal crystal [5,6] (eq. (1)). If the perturbation is regarded as highly localized [12] and if angular momenta 1 g 2 are taken into account. eq. (1) in the case of cubic-site symmetry assumes the form of four scalar equations,
G’I’Z(E) =
G‘:‘;;(E) [1 -
’
G’:‘“I’(E) At;‘(E)]
(6)
Therefore the basic problem is to determine the coefficients of the Green function for the ideal crystal, G:,:(E). We will start from the representation of the crystal wave functions in the LAPW method:
[fl,p2 h,(r)
exp(ikr),
R, .
]rl>
=
(7) ~vRT[R,,]~“’
@i(b)
= a,,,Ur,
4,)
exp(ik,r,)
c
+ b,,,R,,(r,
Irl s R, ,
i@;(k,r)Y,,(r),
&,I
.
where the akh are solutions of the secular equation in the LAPW method, k, = k + G,, G, is a vector of the reciprocal lattice, and R,y is the radius of the MT-sphere for sth atom. a,, and b,, are coefficients. which can be determined from the condition of continuity of the wave functions at the’ boundary of the MT-sphere, and R,[(r, E,y,) is the solution of the radial Schrodinger equation in the MT-sphere (E,, is the reference energy). l?,,(r, E,,) its energy derivative. Contrary to the original KKR-method, the @f(k,, r) depend implicitly on energy through the vector k. Direct substitution of @“,~(k,, r) into (3) is not possible. Substituting (7) into (2) and multiplying (2) and (3) with the solution of the Schrodinger equation in the MT-sphere and integrating we get:
2RfRf.
c
J h HZ
KS X I
’ dk c aFA(aT*)” cxp[i(k,R” 1,
i’ ~“(E - EkA)
- k,R”]
R, @i(k,,
r)Ry(r,
E)r’dr
0
1 @I,(k,r)R;.‘(r. 0
E)r’
,
dr YL(k,)Y,,.(k,)
(8) where
the a;,“(E)-coefficients
a;;‘:‘(E)
= i R;‘(r, E)R;.‘(r,
Based on the LAPW-idea R;‘(r, E) in powers of energy
are determined
by the following
formula:
E)r’dr
we use for R;(r, E) a linear and stop it at the linear term,
(9)
representation
in energy
by expanding
V.S. Stepanyuk et al. I Electronic states of metalloid atoms in metal-metalloid
RY(r,E) = [R,,(r,4,) + (E - E.Jd,,(r,E,,)][(U;,“‘(E)(l
281
systems
(10)
+ (E - EF,)2NF,)-1]-1’Z )
where R,
IV,, =
I r*
dr
k:(r, Es,) .
(11)
0
Eventually
we obtain:
x
C
d*(u;kh)*
exp[i(k,R” - k,R”‘)](a,,, + (E - E,y,)b,,,N,,)
11 x [l + (E - Es,)ZN~,]-“2(a, ‘,‘, + (E - E,.,.)b.@ x [l + (E - E ,‘,’)2N,.,.]~1i?Y~(k;)Y,.(k,)
.
,‘,.) (12)
The formula obtained has been applied to find the imaginary part of the Green function. The self-consistent potential of the matrix was determined by the LAPW-method. For the exchange potential Vosko’s parametrization procedure [13] has been adopted. Using the coefficients of the Green function defined in this way for the crystals with defects it is easy to obtain the local density of states in the MT-sphere,
n(E) = -2/lT
Im G(r, r, E) dr ,
I
(13)
“MT
and the electronic
n(r) = -~/IT
density
Im G(r, r, E) dE .
(14)
3. Case of phosphorus Considering the metalloid atoms as an impurity in an infinite crystalline matrix the density of states is calculated. The results on the density of states (DOS) of P in Fe and Ni are given in figs. 1 and 2. In the energy. range approximately 5-7 eV below the Fermi energy (EF) a p-state of phosphorus, while at still lower energies a bonded s-state (not shown in the figures) is found.
The calculated s-state energy positions and charges are given in table 1. Both s- and p-states of P are lying slightly lower in Fe than in Ni. The general characteristics of the electronic structure of P is similar in Fe and Ni matrices: - hybridization of the s- and p-states of P with the d-states of the metal is increasing from
V.S.
Stepanyuk
et al.
I
Electronic
states of metalloid
energy-positions
E(eV) IQ1
and charges
for various
systems. Fe
FCC
BCC
SC
FCC
BCC
SC
-12.2 1.33
~11.6 1.35
~ 10.2 1.40
- 12.8 0.92
-11.9 1.40
- 10.4 1.41
FCC to SC through BCC, - p-states appear, _ anti-bonding p-states appear, which is well indicated by a peak above the Fermi level.
Ni-P Fe-P
systems
I Ni
Table 2 Charge transfer
in metal-metalloid
Fig. 2. The partial density of electronic states (PDOS) of P in Ni matrices of various crystalline symmetries. The curves a. b and c give the s. s + p and s + p + d PDOS. respectively.
Fig. 1. The partial density of electronic states (PDOS) of P in Fe matrices of various crystalline symmetries. The curves a. b and c give the s, s + p and s + p + d PDOS. respectively. Table s-state
atoms
The charge transfer takes place in the direction from the phosphorus atom towards the metal, by values collected in table 2.
4. Case of boron for P impurity. FCC
BCC
SC
0.32 0.28
0.31 0.17
0.24 0.10
The DOS of B in metallic matrices of Ni and Fe are shown in figs. 3 and 4. For all symmetry types an s-state of B is observable for which the energy position is heavily depending on local
V.S. Stepanyuk et al. I Electronic states of metalloid atoms in metal-metalloid
,,W,:i
systems
283
SK I
T------
-1
Fig. 3. The partial density of electronic states (PDOS) of B in Fe matrices of various crystalline symmetries. The curves a, b and c give the s, s + p and s + p + d PDOS, respectively. Table 3 Charge transfer
Ni-B Fe-B
Fig. 4. The partial density of electronic states (PDOS) of B in Ni matrices of various crystalline symmetries. The curves a, b and c give the s, s + p and s + p + d PDOS, respectively.
of B impurity. FCC
BCC
SC
0.18 0.31
0.17 0.30
0.23 0.35
environment. In the energy range from 0 to -4 eV under the Fermi level the d-states of the metal are heavily hybridized by the p-states of B, and similarly for Fe and Ni. Over the Fermi level anti-bonding p-states are situated, which for FeB lie slightly higher than for Ni-B. Charge transfer is taking place in both systems from the metal atom towards B and has the values collected in table 3.
5. Conclusion
The overall characteristics of all the investigated systems are: (1) new states in the energy
range from -10 to -4 eV under E,, (2) definite anti-bonding p-states above the E, in range O4 eV, manifested itself in a peak in the region, (3) E, is lying near the minimum density of the metalloid states, in accordance with the stability criteria introduced by Nagel and Taut, [14]. This is at the same time one of the proofs for the idea [15] that the electronic structure stabilizes the amorphous state of these metal-metalloid alloys. Some conclusions can be drawn also concerning differences in the electronic structure of P and B impurities. (1) The s-state of B is lower than the p-state of P, (2) the half-width (HW) of B s-states, measured for individual peaks corresponding to the state, is considerably less (by 5-8 times) than the HW of the p-state of a P atom, (3) the phosphorus atom appears to be a weak donor while boron a weak acceptor.
2x4
V.S. Stepanyuk
et al.
i Electronic
state.\ of meialloid
The basic characteristics of the metalloid in all the above discussed lattice types remain the same which indicates that substantial changes in the electronic states could be related to the MRO order.
References [l]
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atoms i/t meta-metalloid
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