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Electronic structure near metal-metal interfaces
Surface Science 144 (1984) 220-223 North-Holland, Amsterdam
220
ELECTRONIC
STRUCTURE
J.W. DAVENPORT Deportment
Received
INTERFACES
*
and M. WEINERT
of Physics, Brookhaven
1 November
NEAR METAL-METAL
Natronal Laboratory,
1983; accepted
for publication
Upton, New York I1 973, USA
30 December
1983
A review will be given of recent calculations on metal films which give information about metal-metal interfaces. The systems discussed will include palladium on niobium, cesium on tungsten, and nickel on copper. In general it is found that the electronic structure closely resembles the bulk within one or two atomic layers of the interface. Using these methods it is possible to calculate directly the interface energy.
The purpose of this talk is to provide an overview of progress in the last few years in ab initio calculations on metal-metal interfaces. All of these calculations were performed with the density functional method so we begin with a brief discussion of its major tenets. We then mention what is required to accurately solve the density functional equations and finally consider several examples of metal on metal systems including palladium monolayers on niobium, cesium on tungsten, nickel on copper and silver on iron. None of these examples treats a grain boundary or a true interface. Rather they are idealizations of the true situations. They are examples of what could be done and we believe that the necessary extensions will be made in the next few years to treat systems of real interest to metallurgists. Density functional theory is reviewed by Schhiter and Sham [l] and more extensively in the book edited by Lundqvist and March [2]. It is based on a theorem by Hohenberg and Kohn that the exact ground state energy of an interacting electron system is a functional of the charge density. This is obviously true for the Coulomb energy which is given by: E cod
’
ptr>dr’)
J
(r -
d3r
djr’,
r’l
it is not so obvious that it is also true for the other parts of the total energy, kinetic and exchange-correlation. The problem is that the exact functional * The submitted
manuscript has been authored under contract DE-AC02-76CH00016 with the Division of Basic Energy Sciences, US Department of Energy. Accordingly, the US Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for US Government purposes.
0039-6028/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
221
J. W. Davenport, M. Weineri / Metal- metal interfaces
relationship adjusted
between density and energy is not known. In practice
to give the correct
total energy of a uniform
of the density. This does not mean that variations fact the charge density varies in a way consistent
electron
the theory is
gas for all values
in density are not treated, in with the atomic nature and
symmetry of the problem. Is this truly an “ab initio” theory? We would answer yes and no. It is not ab initio in the sense that it contains a parameterization (to the energy of the uniform gas). However, this parameterization is fixed once and for all. It is the same for atoms, molecules and solids. The same for ionic crystals, semiconductors and metals. The calculator has no parameter available to adjust results to a particular system. Nor is the parameter determined by experiments. It is determined by calculations on a specific system (the uniform electron gas) and can be improved as those calculations are improved. The density functional equations may be solved by varying the density to minimize the total energy. This leads to the solution of a one-electron Schrodinger equation
with an effective
potential.
be done with any of a large number
Solving
the Schrodinger
of techniques.
Accurate
equation solutions
can have
been obtained with linear combinations of atomic orbitals, pseudopotentials, augmented plane waves, augmented spherical waves, and multiple scattering methods.
(For
a description
of various
methods,
see the review by Koelling
[3].) The choice is largely a matter of preference. In addition, accurate solutions of Poisson’s equation are required. These are most easily obtained using pseudopotential
methods
other methods
as well [4].
We proceed
to describe
but accurate
solutions
several examples
have been obtained
of calculations
with the
which illustrate
the
power of the method. First, the Berkeley group metals using pseudopotential
has studied techniques.
a number of semiconductors and An example is their study of the
various crystallographic phases of germanium [S]. By direct calculation of the total energy as a function of volume they find that the diamond structure is the preferred one at zero pressure p-tin structure at a transition
and that Ge undergoes a phase transition to the pressure of 96 kbar compared with the experi-
mental value of 100 kbar. The calculated lattice constant for the diamond phase differs from experiment by 0.1% and the cohesive energy by 4.4%. As an example for bulk metals, the IBM group has calculated the cohesive energy, atomic
volume and bulk modulus
the periodic compounds.
for all the metals in the 3d and 4d rows of
table. They are in the process of extending
these results to metallic
Recently, Delly, Freeman and Ellis [7] have studied the metal molecules Cr, and Mq. Again, they find good agreement with experiment for the bond energy and vibrational frequency. We believe this molecular case is important because if the density functional method works well for bulk metals and metal molecules it should also work well for systems of interest to metallurgists -
222
J. W. Dtmenpor~. M. Weinert / Metal-
metal rnterfaces
grain boundaries and interfaces which are in a sense intermediate cases. We turn now to several examples of model interfaces - metal on metal systems. First, is the palladium/niobium system [8]. It has been found that monolayers of palladium form commensurate structures on the (110) face of niobium. One way to understand this is to notice that the (110) face of a bee crystal (such as Nb) is the close packed face - it is a distorted version of the (111) face of an fee crystal (such as Pd). In the present case the area mismatch is about 18%. This system has been studied because it has very interesting interactions with hydrogen. The electronic states have been probed by photoelectron spectroscopy and by changes in work function. Also detailed calculations of both monolayers of palladium and five-layer niobium films with palladium adsorbed on each side have been performed [8]. There is excellent agreement with all the experimental results indicating again the power of density functional methods. Another system which has been studied recently is cesium on tungsten [9]. Cs is the classical metal used for lowering the work function of other metals. The classical model is that the cesium ionizes becoming Cs+ which produces a large dipole in the surface region through the image potential with a direction which reduces the energy required to remove electrons. The new calculation of this effect utilized a seven layer film, five tungsten and with a eesium layer on each side. The interesting thing is that charge density plots show only small “charge transfer” from Cs to W. Rather, the distributions are characterized by a build up of charge density between the atoms much as in a covalent bond plus a polarization of the metal monolayer. In addition, there is a substantial polarization of the outermost core orbitals. The closest calculation for an actual interface is the nickel-copper system which was studied for both one and two nickel overlayers on a five layer copper film [lo]. These calculations show that only the atoms immediately adjacent to the interface are perturbed. The charge density, and in the case of nickel, the spin density “heal” to their bulk values within one or two planes. Further, for the Ni/Cu system the magnetization is confined to the nickel layers. There is no induced magnetic moment on the copper. Simiiar results have been recently obtained for iron films with silver overlayers [ll]. In these calculations, the silver overlayers are found to “seal” the surface, i.e., the Fe at the interface already looks bulk-like. Moreover, these results are able to explain the previously not understood experimental Mossbauer data. There are several conclusions which follow from the examples cited above. First, it is now possible to calculate “ab initio” the structural and bonding properties of surfaces and interfaces. The accuracy for geometrical quantities is generally better than 1%. While the calculated cohesive energies are generally too large (due to non-cancelling errors in the local density atom [6]), differences in cohesive energies between different structures are accurate to the
order of 0.05 eV. This is accurate enough to provide an understanding of interface phenomena at zero temperature but probably not accurate enough for thermochemical or kinetic processes. We would expect applications soon to actual grain boundaries though the technology of treating such systems does require relatively extensive computation. This work was supported by The Division of Mate&& ment of Energy under contract DE-ACO2-~6CH~~~~
Sciences US Depart-
[I] M. SchJiiter and L.J. Sham, Phys. Today 35 (Feb. 1982) 36. [Z] S. Lundqvist and N.H. March, Eds., Theory of the Inhomogeneous Electron Gas (plenum, New York, 1983). [3] D.D. Koelling, Rept. Progr. Phys. 44 (1981) 140. [4] M. Weinert, J. Math. Fhys. 22 (1981) 2433. [S] MT. Yin and M.L. Cohen, Solid State Commun. 38 (1981) 625. [6] V.L. Moruzzi, J.F. Janak and A.R. Williams, Calculated Electronic Properties of Metals (Pergamon, New York, 1978). [7] B. Delley, A.J. Freeman and D.E. EIQ, Phys. Rev. Letters 50 (1983) 488. ]8] M. El-Batanouny. D.R. Hamann, S.R. Chubb and J.W. Davenport, Phys. Rev. B37 (1983) 2575. [9] E. Wimmer, A.J. Freeman, M. Weinert, H. Krakauer. J.R. Hiskes and A.M. Karo, phys. Rev. Letters 48 (1982) 1128. lo] D.S. Wang, A.J. Freeman and H. Krakauer, Phys. Rev. B26 (1982) 1340. 111 S. Dhnishi, M. Weinert and A.J. Freeman, Phys. Rev. B30 (1984) to be published.
220
ELECTRONIC
STRUCTURE
J.W. DAVENPORT Deportment
Received
INTERFACES
*
and M. WEINERT
of Physics, Brookhaven
1 November
NEAR METAL-METAL
Natronal Laboratory,
1983; accepted
for publication
Upton, New York I1 973, USA
30 December
1983
A review will be given of recent calculations on metal films which give information about metal-metal interfaces. The systems discussed will include palladium on niobium, cesium on tungsten, and nickel on copper. In general it is found that the electronic structure closely resembles the bulk within one or two atomic layers of the interface. Using these methods it is possible to calculate directly the interface energy.
The purpose of this talk is to provide an overview of progress in the last few years in ab initio calculations on metal-metal interfaces. All of these calculations were performed with the density functional method so we begin with a brief discussion of its major tenets. We then mention what is required to accurately solve the density functional equations and finally consider several examples of metal on metal systems including palladium monolayers on niobium, cesium on tungsten, nickel on copper and silver on iron. None of these examples treats a grain boundary or a true interface. Rather they are idealizations of the true situations. They are examples of what could be done and we believe that the necessary extensions will be made in the next few years to treat systems of real interest to metallurgists. Density functional theory is reviewed by Schhiter and Sham [l] and more extensively in the book edited by Lundqvist and March [2]. It is based on a theorem by Hohenberg and Kohn that the exact ground state energy of an interacting electron system is a functional of the charge density. This is obviously true for the Coulomb energy which is given by: E cod
’
ptr>dr’)
J
(r -
d3r
djr’,
r’l
it is not so obvious that it is also true for the other parts of the total energy, kinetic and exchange-correlation. The problem is that the exact functional * The submitted
manuscript has been authored under contract DE-AC02-76CH00016 with the Division of Basic Energy Sciences, US Department of Energy. Accordingly, the US Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for US Government purposes.
0039-6028/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
221
J. W. Davenport, M. Weineri / Metal- metal interfaces
relationship adjusted
between density and energy is not known. In practice
to give the correct
total energy of a uniform
of the density. This does not mean that variations fact the charge density varies in a way consistent
electron
the theory is
gas for all values
in density are not treated, in with the atomic nature and
symmetry of the problem. Is this truly an “ab initio” theory? We would answer yes and no. It is not ab initio in the sense that it contains a parameterization (to the energy of the uniform gas). However, this parameterization is fixed once and for all. It is the same for atoms, molecules and solids. The same for ionic crystals, semiconductors and metals. The calculator has no parameter available to adjust results to a particular system. Nor is the parameter determined by experiments. It is determined by calculations on a specific system (the uniform electron gas) and can be improved as those calculations are improved. The density functional equations may be solved by varying the density to minimize the total energy. This leads to the solution of a one-electron Schrodinger equation
with an effective
potential.
be done with any of a large number
Solving
the Schrodinger
of techniques.
Accurate
equation solutions
can have
been obtained with linear combinations of atomic orbitals, pseudopotentials, augmented plane waves, augmented spherical waves, and multiple scattering methods.
(For
a description
of various
methods,
see the review by Koelling
[3].) The choice is largely a matter of preference. In addition, accurate solutions of Poisson’s equation are required. These are most easily obtained using pseudopotential
methods
other methods
as well [4].
We proceed
to describe
but accurate
solutions
several examples
have been obtained
of calculations
with the
which illustrate
the
power of the method. First, the Berkeley group metals using pseudopotential
has studied techniques.
a number of semiconductors and An example is their study of the
various crystallographic phases of germanium [S]. By direct calculation of the total energy as a function of volume they find that the diamond structure is the preferred one at zero pressure p-tin structure at a transition
and that Ge undergoes a phase transition to the pressure of 96 kbar compared with the experi-
mental value of 100 kbar. The calculated lattice constant for the diamond phase differs from experiment by 0.1% and the cohesive energy by 4.4%. As an example for bulk metals, the IBM group has calculated the cohesive energy, atomic
volume and bulk modulus
the periodic compounds.
for all the metals in the 3d and 4d rows of
table. They are in the process of extending
these results to metallic
Recently, Delly, Freeman and Ellis [7] have studied the metal molecules Cr, and Mq. Again, they find good agreement with experiment for the bond energy and vibrational frequency. We believe this molecular case is important because if the density functional method works well for bulk metals and metal molecules it should also work well for systems of interest to metallurgists -
222
J. W. Dtmenpor~. M. Weinert / Metal-
metal rnterfaces
grain boundaries and interfaces which are in a sense intermediate cases. We turn now to several examples of model interfaces - metal on metal systems. First, is the palladium/niobium system [8]. It has been found that monolayers of palladium form commensurate structures on the (110) face of niobium. One way to understand this is to notice that the (110) face of a bee crystal (such as Nb) is the close packed face - it is a distorted version of the (111) face of an fee crystal (such as Pd). In the present case the area mismatch is about 18%. This system has been studied because it has very interesting interactions with hydrogen. The electronic states have been probed by photoelectron spectroscopy and by changes in work function. Also detailed calculations of both monolayers of palladium and five-layer niobium films with palladium adsorbed on each side have been performed [8]. There is excellent agreement with all the experimental results indicating again the power of density functional methods. Another system which has been studied recently is cesium on tungsten [9]. Cs is the classical metal used for lowering the work function of other metals. The classical model is that the cesium ionizes becoming Cs+ which produces a large dipole in the surface region through the image potential with a direction which reduces the energy required to remove electrons. The new calculation of this effect utilized a seven layer film, five tungsten and with a eesium layer on each side. The interesting thing is that charge density plots show only small “charge transfer” from Cs to W. Rather, the distributions are characterized by a build up of charge density between the atoms much as in a covalent bond plus a polarization of the metal monolayer. In addition, there is a substantial polarization of the outermost core orbitals. The closest calculation for an actual interface is the nickel-copper system which was studied for both one and two nickel overlayers on a five layer copper film [lo]. These calculations show that only the atoms immediately adjacent to the interface are perturbed. The charge density, and in the case of nickel, the spin density “heal” to their bulk values within one or two planes. Further, for the Ni/Cu system the magnetization is confined to the nickel layers. There is no induced magnetic moment on the copper. Simiiar results have been recently obtained for iron films with silver overlayers [ll]. In these calculations, the silver overlayers are found to “seal” the surface, i.e., the Fe at the interface already looks bulk-like. Moreover, these results are able to explain the previously not understood experimental Mossbauer data. There are several conclusions which follow from the examples cited above. First, it is now possible to calculate “ab initio” the structural and bonding properties of surfaces and interfaces. The accuracy for geometrical quantities is generally better than 1%. While the calculated cohesive energies are generally too large (due to non-cancelling errors in the local density atom [6]), differences in cohesive energies between different structures are accurate to the
order of 0.05 eV. This is accurate enough to provide an understanding of interface phenomena at zero temperature but probably not accurate enough for thermochemical or kinetic processes. We would expect applications soon to actual grain boundaries though the technology of treating such systems does require relatively extensive computation. This work was supported by The Division of Mate&& ment of Energy under contract DE-ACO2-~6CH~~~~
Sciences US Depart-
[I] M. SchJiiter and L.J. Sham, Phys. Today 35 (Feb. 1982) 36. [Z] S. Lundqvist and N.H. March, Eds., Theory of the Inhomogeneous Electron Gas (plenum, New York, 1983). [3] D.D. Koelling, Rept. Progr. Phys. 44 (1981) 140. [4] M. Weinert, J. Math. Fhys. 22 (1981) 2433. [S] MT. Yin and M.L. Cohen, Solid State Commun. 38 (1981) 625. [6] V.L. Moruzzi, J.F. Janak and A.R. Williams, Calculated Electronic Properties of Metals (Pergamon, New York, 1978). [7] B. Delley, A.J. Freeman and D.E. EIQ, Phys. Rev. Letters 50 (1983) 488. ]8] M. El-Batanouny. D.R. Hamann, S.R. Chubb and J.W. Davenport, Phys. Rev. B37 (1983) 2575. [9] E. Wimmer, A.J. Freeman, M. Weinert, H. Krakauer. J.R. Hiskes and A.M. Karo, phys. Rev. Letters 48 (1982) 1128. lo] D.S. Wang, A.J. Freeman and H. Krakauer, Phys. Rev. B26 (1982) 1340. 111 S. Dhnishi, M. Weinert and A.J. Freeman, Phys. Rev. B30 (1984) to be published.