# Lattice modes in molecular crystals measured with nuclear inelastic scattering

## Abstract

We reveal an important property of nuclear inelastic scattering in a molecular crystal with well-separated lattice and molecular modes: The presence of the molecular modes does not change the shape but merely rescales the lattice part of the energy dependence of nuclear inelastic scattering. Therefore, the density of states (DOS) of the lattice vibrations can be properly derived even from the lattice part of nuclear inelastic scattering alone. In this case, one has to substitute the mean recoil energy of a nucleus by the effective recoil energy of the molecule. In first approximation, the ratio of the recoil energies is close to the ratio of the nuclear and molecular masses. More precisely, it is given by the relative area of the lattice part in the entire DOS. The theoretical analysis is verified with numerical calculations for a model DOS and with the experimental data for the decamethyl ferrocene molecular crystal. More generally, the analysis is valid for any region of nuclear inelastic scattering around the central elastic peak with sufficiently narrow lines beyond it. Therefore, the demonstrated property of nuclear inelastic scattering allows for a much shorter measuring time in studies of lattice modes in molecular crystals, low-energy molecular modesmore »

- Authors:

- Russian Research Center 'Kurchatov Institute', 123182, Moscow (Russian Federation)
- Russian Research Center ''Kurchatov Institute'', 123182, Moscow (Russian Federation)
- (France)
- European Synchrotron Radiation Facility BP220, F-38043 Grenoble (France)

- Publication Date:

- OSTI Identifier:
- 20787959

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 73; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevB.73.094306; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; APPROXIMATIONS; ENERGY DEPENDENCE; ENERGY-LEVEL DENSITY; FERROCENE; INELASTIC SCATTERING; LATTICE VIBRATIONS; MOLECULAR CRYSTALS; MOLECULES; PROTEINS; RECOILS

### Citation Formats

```
Kohn, V. G., Chumakov, A. I., European Synchrotron Radiation Facility BP220, F-38043 Grenoble, and Rueffer, R..
```*Lattice modes in molecular crystals measured with nuclear inelastic scattering*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVB.73.0.

```
Kohn, V. G., Chumakov, A. I., European Synchrotron Radiation Facility BP220, F-38043 Grenoble, & Rueffer, R..
```*Lattice modes in molecular crystals measured with nuclear inelastic scattering*. United States. doi:10.1103/PHYSREVB.73.0.

```
Kohn, V. G., Chumakov, A. I., European Synchrotron Radiation Facility BP220, F-38043 Grenoble, and Rueffer, R.. Wed .
"Lattice modes in molecular crystals measured with nuclear inelastic scattering". United States.
doi:10.1103/PHYSREVB.73.0.
```

```
@article{osti_20787959,
```

title = {Lattice modes in molecular crystals measured with nuclear inelastic scattering},

author = {Kohn, V. G. and Chumakov, A. I. and European Synchrotron Radiation Facility BP220, F-38043 Grenoble and Rueffer, R.},

abstractNote = {We reveal an important property of nuclear inelastic scattering in a molecular crystal with well-separated lattice and molecular modes: The presence of the molecular modes does not change the shape but merely rescales the lattice part of the energy dependence of nuclear inelastic scattering. Therefore, the density of states (DOS) of the lattice vibrations can be properly derived even from the lattice part of nuclear inelastic scattering alone. In this case, one has to substitute the mean recoil energy of a nucleus by the effective recoil energy of the molecule. In first approximation, the ratio of the recoil energies is close to the ratio of the nuclear and molecular masses. More precisely, it is given by the relative area of the lattice part in the entire DOS. The theoretical analysis is verified with numerical calculations for a model DOS and with the experimental data for the decamethyl ferrocene molecular crystal. More generally, the analysis is valid for any region of nuclear inelastic scattering around the central elastic peak with sufficiently narrow lines beyond it. Therefore, the demonstrated property of nuclear inelastic scattering allows for a much shorter measuring time in studies of lattice modes in molecular crystals, low-energy molecular modes in proteins, and in investigations of glass dynamics with molecular probes.},

doi = {10.1103/PHYSREVB.73.0},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 9,

volume = 73,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2006},

month = {Wed Mar 01 00:00:00 EST 2006}

}