Magnetic potential parameters

Relevant Magnetic Potential Parameters Calculation of the Static Magnetization Inclusion of Thermal Agitation A. Langevin s Treatment of Brownian Motion ... 

The xenon atom can therefore be used as a delicate probe to determine the number of surrounding water molecules and their orientations. These results demonstrate the sensitivity of the easily polarizable xenon electronic structure to the electrostatic properties of its surrounding and the great potential for achieving accurate interpretations of magnetic resonance parameters from imaging experiments with hyperpolarized xenon. 

More difficult to calculate are the properties which depend on the response of the solid to an outside influence (stress, electric field, magnetic field, radiation). Elastic constants are obtained by considering the response of the crystal to deformation. Interatomic potential methods often provide good values for these and indeed experimental elastic constants are often used in fitting the potential parameters. Force constants for lattice vibrations (phonons) can be calculated from the energy as a function of atomic coordinates. In the frozen phonon approach, the energy is obtained explicitly as a function of the atom coordinates. Alternatively the deriva-tive, 5 - can be calculated at the equilibrium geometry. 

As an example of a set of standard parameters, Table 4.1 lists all the potential-dependent information needed to perform an energy-band calculation for (non-magnetic) chromium metal. In the following, chromium is used as an example when we discuss the physical significance of each of the four potential parameters (4.1). At the end of the chapter we derive free-electron potential parameters, give expressions for the volume derivatives of some se-... 

Table 4.1. Standard potential parameters for non-magnetic chromium at S = 2.684 a.u., from [4.1]. Here Ev is relative to the Coulomb potential at S. This is a natural choice since for a monoatomic material in the ASA the spheres are neutral and their charge density is spherically symmetric. Relative to this energy zero, v(S) = -0.8181 Ry... 

Fig.4.1. Estimates of the extent (bottom B, top A) and position (centre C) of the s, p, and d bands of non-magnetic chromium obtained by the third-order expression (3.50), definitions (2.22), and the potential parameters in Table 4.1. Expression (3.50) spans only the square-well pseudopotentials V for the s and p bands, i.e. Vd is outside the energy window...

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