Equilibrium defect properties of sodium in the high temperature range

Adlhart, W.; Fritsch, Gerhard; Lüscher, E.

doi:10.1016/0022-3697(75)90224-3

Cited by 37 publications

(2 citation statements)

References 21 publications

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“…This equation, when using T = 370.2 K (which is close to the melting point T = 370.9 K), the values = 40.069 × 10 −24 cm 3 , B = 5.744 GPa (see table 9.12 of [12]) and the concentration n/N ≈ 7 × 10 −14 reported in [29] at the melting point, gives the value c f = 0.159. This value, when inserted into the relation υ f = c f ( dB dP | T − 1)-similar to equation (3) but applied here to the formation process-leads to (after using the aforementioned value ( dB dP ) 0 = 3.886, see equation ( 8))…”

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confidence: 87%

Self-diffusion in sodium under pressure revisited

Varotsos

2007

J. Phys.: Condens. Matter

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The pressure-volume relation in sodium has been measured up to 100 GPa using high-resolution angle-dispersive synchrotron x-ray diffraction (Hanfland et al 2002 Phys. Rev. B 65 184109). In the light of these data, we show that a model suggested long ago (e.g., Varotsos et al 1978 J. Phys. C: Solid State Phys. 11 L305-15) can satisfactorily answer the long-standing question of the variation of the diffusion coefficient D under pressure P, which resulted in a curved lnD versus P plot, in the frame of a single operating mechanism (monovacancies). This is achieved without using any adjustable parameters.

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confidence: 87%

Self-diffusion in sodium under pressure revisited

Varotsos

2007

J. Phys.: Condens. Matter

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“…In these equations φ i = dφ/dr and φ i = d 2 φ/dr 2 evaluated at r i , where r i is the equilibrium distance to the ith shell of neighbors. In addition to the vacancy formation energy E UF 1v , b Vacancy formation energies from [14] (Li), [15] (Na), [16] (K), [17] (Rb, Cs). c Lattice constants from [18] (Li), [19,20] (Na), [21] (K), [20] (Rb), [18] (Cs).…”

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confidence: 99%

An embedded-atom-method model for alkali-metal vibrations

Wilson¹,

Riffe²

2012

J. Phys.: Condens. Matter

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We present an embedded-atom-method (EAM) model that accurately describes vibrational dynamics in the alkali metals Li, Na, K, Rb, and Cs. Bulk dispersion curves, frequency-moment Debye temperatures, and temperature-dependent entropy Debye temperatures are all in excellent agreement with experimental results. The model is also well suited for studying surface vibrational dynamics in these materials, as illustrated by calculations for the Na(110) surface.

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On the Relaxation Energy of Vacancy Formation and the Jellium Model for the Alkali Metals

Maganta

Vázquez

1993

Physica Status Solidi (b)

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Within the jellium model we write the vacancy formation energy E' as the sum of several terms:E' = AT + AExc + BE, + E,, where AT is the change in kinetic energy of the electrons, AExc is the change in exchange and correlation energy, AEc is the change in electrostatic energy, and E , is thc contribution because of lattice relaxation. Each term in this equation, except E,, is calculated using the density functional formalism for Li, Na, K, Rb, and Cs, respectively. To obtain E, we used the corresponding experimental values of E' and subtracted from each of them the corresponding calculated values of the other terms. The resulting values for E , are all positive and relatively large, varying from about 0.1 to 0.23 eV. lntroductionThe formation energy for a vacancy E' is obtained by subtracting the energy of a metal with a perfect lattice consisting of N ions in a volume Q from the total ground state energy of a similar system in which one atomic cell has been removed from the bulk and placed on the surface. The vacancy formation energy can be written as the sum of several terms [l, 21,where AT is the change in kinetic energy of the electrons, AExc is the change in exchange and correlation energy, AEc is the change in electrostatic energy, and E, is the relaxation energy.Within the density functional formalism and the local density approximation, the vacancy formation energy can be expressed for a monovalent metal [l, 21 aswhere BEcigcn is the change in the energy eigenvalues of the electrons when the vacancy is formed and it is given by (see, for example, [l, 3, 41)where k , is the Fermi wave vector, ?il(k) is the corresponding phase shift of wave vector k and angular momentum 1 produced by the vacancy. The term U , , is the electrostatic energy,. ~-' ) Apartado Postal 20-364, Codigo Postal 01000, Mexico D.F., Mexico.

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Equilibrium defect properties of sodium in the high temperature range

Cited by 37 publications

References 21 publications

Self-diffusion in sodium under pressure revisited

Self-diffusion in sodium under pressure revisited

An embedded-atom-method model for alkali-metal vibrations

On the Relaxation Energy of Vacancy Formation and the Jellium Model for the Alkali Metals

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