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The contribution of ionic polarization takes account of the fact that when in a molecule some of the atoms have an excess positive or negative charge (resulting from the ionic character of the bonds),an electric field tend to shift positive ions relative to negative ones. This leads to an induced moment of other origin from the moment induced by electron clouds shifting relative to nuclei. In this case a solid material should have some ionic character. It then automatically has internal dipoles, exactly cancels each other and is unable to rotate. The external field them induces net dipoles by slightly displacing the ions from their rest position. The paradigmatic materials are simple ionic crystal like NaCl. The polarization of a given volume, though, is exactly zero as for every dipole moment there is a neighbouring one with exactly the same magnitude, but with opposite sign. Note that the dipoles cannot dipoles, their direction is permanent. In electric field, the ions feel forces in opposite directions. The Na+ ions moved a bit to the right, the Chlorine ions to the lift. The dipoles moments between adjacent NaCl pairs in field direction are now different and there is a net dipole moment in a finite volume now. It can be observed that it is enough to take one dipole in field direction.
Invoke the boundary condition Φ '(0)=0 to obtain a power series where the powers of x are multiples of 3.
The points where amplitude is minimized are called as nodes.
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what is the unit of hardness?
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