Dipolar energy

The higher the WF of the metal, the larger the shift of the dipolar energy. 

We will consider dipolar interaction in zero field so that the total Hamiltonian is given by the sum of the anisotropy and dipolar energies = E -TEi. By restricting the calculation of thermal equilibrium properties to the case 1. we can use thermodynamical perturbation theory [27,28] to expand the Boltzmann distribution in powers of This leads to an expression of the form [23]... 

We are now almost in a position to calculate the zero-field spin-rotation and spin spin dipolar energies of the N, J levels, but we have first to discuss the parity restrictions on the levels for para- and ortho-H2(see also chapter 6). 

Values of the magnetic dipolar energy reported to one MnFe6 unit in Ba7MnFe6F34, as calculated over a sphere of radius 75 A for various possible structures... 

Fig. 3. Definition and numbering of the magnetic symmetries whose magnetic dipolar energies are given in Table 1.

We evaluate the system s total dipolar energy for the following situations ... 

For both situations, we calculate the (dimensionless) dipolar energy per particle, a Ux)/fj, N, via the slab-adapted three-dimensional Ewald sum [see Eq. (6.44)] and with the rigorous Ewald method for dipolar slab systems... 

Similar expressions are obteiined for case 1. Data plotted in Figs. 6.2 have been obtained by truncating the sums over Z and ly at 5000, which yields convergent results as long as n, < 4. Comparing these results with those from the two Ewald methods, we conclude that not only the rigorous Ewald summation, but also the slab-adapted three-dimensional version provide quasi-exact results for th( dipolar energy. 

To get some insight into these questions we have performed various lattice calculations similar in spirit to those de.scribod in Section 6.3.3. Specifically, we have considered (infinitely extended) slabs composed of dipolar particles located at the sites of a face-centered cubic (fee) lattice with (reduced) density pfee = 10. We have then employed the Ewald sum for dipolar systems between metallic walls [see Eq. (6.69)] to calculate the total dipolar energy f/o for various configurations characterized by perfect orientational order. Numerical results for Uq as a function of the number of lattice layers are... 

We now derive an expression for the self-contribution to the dipolar energy in Ewald formulation given in Eq. (6.32) by recalling that the corresponding... 

For dipolar particles, all for( e contributions within the slab-adapted three-dimensional Ewald sum coincide with those for truly three-dimensional systems discussed in Appendix F.2.2. This result arises because the correction term to the total dipolar energy [see Eqs. (6.44) and (6.43)] is independent of particle positions. There is, however, a contribution to the total torque that we need to consider separately. The total torque can be cast as... 

Van Steenwinkel R (1969) The spin lattice relaxation of the nuclear dipolar energy in some organic crystals with slow molecular motions. Z. Naturforsch. 24a 1526... 

The self-assembly process possesses an intrinsic limit with respect to the colunm spacing. Explicitly, the array must be sufficiently concentrated so that the repulsive energy between the different columns is strong enough to enforce the hexagonal structure. The repulsive dipolar energy scales... 

Monolayers of dipolar particles are relevant for many experimental systems of molecules with 3D dipoles located on planar surfaces and at interfaces. The Ewald expression of the dipolar energy [45] of such a system is easily derived by taking the limit z = 0 in Eqs. 25 and 26... 

The determination of the properties of the 1-g interface of a dipolar fluid has been performed for a Stockmayer system and a system of diatomic particles which, in addition to the point dipole interaction, interact by site-site LJ potentials in [202]. The estimates of the surface tension are shown to be in reasonable agreement with experimental results for 1,1-difluoroethane when state variables are reduced by the critical temperature and density. The preferential orientation of the dipoles is parallel to the interface. This work also contains methodological aspects of the simulation of thin liquid films in equilibrium with their vapour. In particular, a comparison is made between the results obtained for the true (Eq. 25) and slab-adapted Ewald potentials. The agreement between the two numerical determinations of the dipolar energy is quite satisfactory asserting the validity of the use of the 3D Ewald approach for the simulation in a slab geometry. 

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