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7
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84926799934
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Essentially, the majority and minority charge densities undergo long-wavelength fluctuations of comparable magnitude through Poisson's equation. This leads to constructive (destructive) interference in the sum (difference) of the two. Thus, the magnetization, which is the difference of the two, is less affected locally. Another way to see this is to note that within the local-density approximation the magnetization density at a given point in space is dependent on a local exchange-correlation functional, which is less affected by long-wavelength changes in the density.
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11
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0001008029
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An efficient method for finding the minimum of a function of several variables without calculating derivatives
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(1964)
The Computer Journal
, vol.7
, pp. 155
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Powell, M.J.D.1
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12
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84926843666
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For a nonmagnetic, binary, disordered alloy ( Ac B1-c ) calculation using the KKR-CPA, there are two charge densities in the vector | n(m) > = | nA ( r1 ) ,..., nA ( rn ) , nB ( rn+1 ) ,..., nB ( r2n ) > . Defining a vector transpose < f ( ri ) | == < c1 ,..., cn , ( 1 - c )n+1 ,..., ( 1 - c )2n | , charge neutrality is established if c ZA + ( 1 - c ) ZB = < f ( ri ) | n(m+1) ( ri ) > , where c [ ( 1 - c ) ] and ZA^[B ] are the concentration and the atomic numbers of the A [ B ] atoms, respectively. As long as < f | is independent of iteration and the initial guess of the charge densities is charge conserving, it is easily shown that all of Broyden's methods are charge conserving. For a given definition of the vector n, an appropriate definition of the vector f can be chosen.
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19
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84926843665
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The KKR method is a multiple-scattering Green's-function method developed by Korringa, Kohn, and Rostoker to calculate accurate electronic structure of ordered systems. When formulated within the KKR method, the coherent-potential approximation (CPA) developed by Soven and Taylor can describe the electronic structure of disordered alloys, see papers in Ref. 16 and in references therein.
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20
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84926799932
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The variational nature of the total energy is true for ordinary band-structure calculations and has been shown to be true in disordered alloy calculations using the Korringa-Kohn-Rostoker multiple-scattering approach within the coherent-potential approximation;
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