Inelastic neutron measurements of the high temperature lattice excitations in NaI show that in thermal equilibrium at 555 K an intrinsic mode, localized in three dimensions, occurs at a single frequency near the center of the spectral phonon gap, polarized along [111]. At higher temperatures the intrinsic localized mode gains intensity. Higher energy inelastic neutron and x-ray scattering measurements on a room temperature NaI crystal indicate that the creation energy of the ground state of the intrinsic localized mode is 299 meV.

The existence of anharmonic localization of lattice vibrations in a perfect 3-D diatomic ionic crystal is established for the rigid-ion model by molecular dynamics simulations. For a realistic set of NaI potential parameters, an intrinsic localized gap mode vibrating in the [111] direction is observed for fcc and zinc blende lattices. An axial elastic distortion is an integral feature of this mode which forms more readily for the zinc blende than for the fcc structure. Molecular dynamics simulations verify that in each structure this localized mode may be stable for at least 200 cycles.It has been proposed [1,2] and numerically demonstrated [3] that a large amplitude vibration in a perfect 1-D lattice can localize because of anharmonicity. More detailed analytical and numerical investigations of classical 1-D anharmonic chains made possible by simple eigenvalue generating recursion relations have revealed a variety of stable intrinsic localized modes with frequencies outside of the plane wave bands [3][4][5][6][7][8]. Recently quantum mechanical aspects of ILMs (Intrinsic Localized Modes) have been considered [9,10]. Some progress also has been reported for higher dimensional classical crystal lattices with simple nearest-neighbor model interactions [11,12]. Particularly important has been the recognition that diatomic crystal potentials like the Born-Mayer-Coulomb in 1-D produces an intrinsic gap mode (IGM) between the optic and acoustic branches instead of an ILM above the plane wave spectrum [13]. The possibility of IGMs in 3-D anharmonic lattices with realistic potentials has remained elusive. One approach has been to focus on crystal surfaces and edges where harmonic localization already plays an important role [14][15][16].In this Letter we demonstrate with molecular dynamics simulations that, for sufficiently large vibrational amplitude, anharmonicity can stabilize an IGM in a 3-D uniform diatomic crystal with rigid ion NaI potential arranged in either the fcc or zinc blende structure. By developing a self-consistent numerical technique for finding an intrinsic localized mode eigenvector, we have been able to show that for a given gap mode amplitude with the same potential that the localization is much stronger for a T d symmetry site when compared to an O h one.To construct the stationary localized mode eigenvector for the nonlinear 3-D diatomic lattice with long range interactions, we build on techniques which have been used successfully to identify 1-D anharmonic modes [13], one of which is the rotating wave approximation. A Fourier extension of that idea for vibration in a stationary periodic mode with fundamental frequency, ω, which includes the static and second harmonic for the i th particle displacement, r i (t), iswhere ri , is the distorted equilibrium position of the i th particle, and the r (n) i 's are the time-independent amplitudes of the different harmonics. The force acting on the i th particle can also be represented by a similar Fourier series. Substituting the coordinate and force Fou...

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