Partial phonon density of states

Fig. 11.5 (a) Observed INS spectrum (MARI, ISIS) of sillimanite at 15 K. The estimated one-phonon spectrum is shown by dashed lines, (b) Calculated spectrum broadened to an instrumental resolution of 16 cm", (c) Computed partial phonon density of states of the atoms in the asymmetric unit along x, y and z in sillimanite. Reproduced from [10] with permission from the American Physical Society. 

The nuclear resonant inelastic and quasi-elastic scattering method has distinct features favorable for studies concerning the microscopic dynamics (i.e., lattice vibration, diffusion, and molecular rotation) of materials. One advantageous feature is the ability to measure the element-specific dynamics of condensed matter. For example, in solids the partial phonon density of states can be measured. Furthermore, measurements under exotic conditions -such as high pressure, small samples, and thin films - are possible because of the high brilliance of synchrotron radiation. (For the definition of brilliance, see O Sect. 50.3.4.5 of Chap. 50, Vol. 5, on Particle Accelerators. ) This method is applicable not only to solids but also to liquids and gases, and there is no limitation concerning the sample temperature. 

A phonon density of states can be obtained from the measured phonon energy spectrum for compounds, the partial phonon density of states for the specific element can be obtained. It should be noted that since the direction of the conversion electron and the direction of the... 

The calculation reproduces the measured (O Fig. 26.6a) partial phonon density of states of Fe remarkably well. The characteristic vibrational modes of Fe in Al were found to be modes that vibrate resonantly with the host Al phonons. 

Nuclear forward scattering (NFS) allows to study hyperline interactions, as obtained with conventional Mossbauer spectroscopy nuclear inelastic scattering (NIS) allows to investigate local phonon spectra (partial density of states, PDOS) at the Mossbauer probe nucleus. Compared, for instance, to Raman spectroscopy, NIS can achieve a higher resolution without perturbation of surrounding vibrations. Both synchrotron radiation techniques, NFS and NIS, are certainly on then-way to a great future. 

A number of new results obtained with the "direct" ab initio methods include phonon frequencies, anharmonicities, predictions of displacement patterns, soft-mode phase transitions, effective charges, dielectric constant, local field variations, elements of inverse dielectric matrix, etc. they were all obtained from the same fundamental equations. The Density Functional method opens a way to unified description of ground state properties of solids static, dynamic and dielectric ones. Though all the partial results above are interesting by themselves, they are even more important by providing further tests of and support for the validity of the Density Functional theory. 

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