^{1}, D. Colognesi

^{2}, M. Catti

^{3}, A.-C. Nale

^{3}, M. A. Adams

^{4}, A. J. Ramirez-Cuesta

^{4}and J. Mayers

^{4}

### Abstract

In the present study we report neutron spectroscopic measurements on polycrystalline lithium imide, namely, incoherent inelastic neutron scattering at 20 K, and neutron Compton scattering from 10 K up to room temperature. From the former technique the H-projected density of phonon states up to 100 meV is derived, while the latter works out the spherically averaged single-particle (i.e., H, Li, and N) momentum distributions and, from this, the mean kinetic energies. Only for H at the lowest investigated temperature, non-Gaussian components of its momentum distribution are detected. However, these components do not seem directly connected to the system anharmonicity, being fully compatible with the simple N-H bond anisotropy. Neutron data are also complemented by *ab initio* lattice dynamics simulations, both harmonic and, at room temperature, carried out in the framework of the so-called “quantum colored noise thermostat” method. The single-particle mean kinetic energies in lithium imide as a function of temperature show a quite peculiar behavior at the moment not reproduced by *ab initio* lattice dynamics methods, at least as far as H and Li are concerned. As matter of fact, neither their low temperature values nor their temperature trends can be precisely explained in terms of standard phonon calculations.

This work has been in part supported by *Consiglio Nazionale delle Ricerche* (Italy) through the Cooperation Agreement No. 01/9001 with STFC (U.K.). One of the authors (A.P.) warmly thanks Professor Marco Bernasconi, Dr. Giacomo Miceli, and Dr. Michele Ceriotti for providing valuable unpublished *ab initio* calculation results.

I. INTRODUCTION

II. EXPERIMENTAL NEUTRON SCATTERING PROCEDURES

A. Incoherent inelastic neutron scattering on TOSCA-II

B. Neutron Compton scattering on VESUVIO

III. DATA ANALYSIS

A. TOSCA-II data analysis

B. VESUVIO data analysis

IV. DISCUSSION

A. H-projected density of phonon states

B. H single particle dynamics

C. Heavy-atoms single particle dynamics

V. CONCLUSIONS

### Key Topics

- Protons
- 28.0
- Lithium
- 25.0
- Neutrons
- 17.0
- Ab initio calculations
- 9.0
- Backscattering
- 8.0

## Figures

Measured raw spectra, *S* _{ s }(*Q* _{ B }, *E*), from sample “a” (lithium imide, dashed line), sample “b” (lithium amide, full line), and sample “c” (empty can, dotted-dashed line). All the spectra have been collected by the backscattering section of TOSCA-II at low temperature (*T* = 20 K). Plots have been vertically shifted for graphic reasons, namely, 0.055 arbitrary units for “b,” and 0.160 arbitrary units for “a.”

Measured raw spectra, *S* _{ s }(*Q* _{ B }, *E*), from sample “a” (lithium imide, dashed line), sample “b” (lithium amide, full line), and sample “c” (empty can, dotted-dashed line). All the spectra have been collected by the backscattering section of TOSCA-II at low temperature (*T* = 20 K). Plots have been vertically shifted for graphic reasons, namely, 0.055 arbitrary units for “b,” and 0.160 arbitrary units for “a.”

Backscattering time-of-flight spectrum obtained by focusing individual detector spectra in the angular range between 150° and 165°: the feature at about 290 μs is the Li recoil peak, while those at about 338 μs and 360 μs are the recoil peaks of N and Al, respectively.

Backscattering time-of-flight spectrum obtained by focusing individual detector spectra in the angular range between 150° and 165°: the feature at about 290 μs is the Li recoil peak, while those at about 338 μs and 360 μs are the recoil peaks of N and Al, respectively.

Estimates of the proton-projected density of phonon states extracted from TOSCA-II inelastic neutron scattering measurements on Li_{2}NH at *T* = 20 K: full line from the forward scattering detector banks, dashed line from the backscattering detector banks.

Estimates of the proton-projected density of phonon states extracted from TOSCA-II inelastic neutron scattering measurements on Li_{2}NH at *T* = 20 K: full line from the forward scattering detector banks, dashed line from the backscattering detector banks.

Estimates of the proton-projected density of phonon states extracted from TOSCA-II inelastic neutron scattering measurements on LiNH_{2} at *T* = 20 K: full line from the forward scattering detector banks, dashed line from the backscattering detector banks.

Estimates of the proton-projected density of phonon states extracted from TOSCA-II inelastic neutron scattering measurements on LiNH_{2} at *T* = 20 K: full line from the forward scattering detector banks, dashed line from the backscattering detector banks.

(a) *n* _{H}(*p*) at *T* = 10 K, 150 K, 220 K, and 300 K reconstructed from the Gauss-Laguerre expansion with the coefficient listed in Table II; (b) *n* _{H}(*p*) at the two extreme temperatures and their difference, with error bars.

(a) *n* _{H}(*p*) at *T* = 10 K, 150 K, 220 K, and 300 K reconstructed from the Gauss-Laguerre expansion with the coefficient listed in Table II; (b) *n* _{H}(*p*) at the two extreme temperatures and their difference, with error bars.

(a) *n* _{H}(*p*) at all the investigated temperatures in a logarithmic scale enhancing the differences in the tails above *p* = 15 Å^{−1}; (b) the same as in (a), but only for the two extreme temperatures, with error bars.

(a) *n* _{H}(*p*) at all the investigated temperatures in a logarithmic scale enhancing the differences in the tails above *p* = 15 Å^{−1}; (b) the same as in (a), but only for the two extreme temperatures, with error bars.

Proton mean kinetic energy in lithium imide as a function of temperature obtained from: deep inelastic neutron scattering measurements (open black circles); H-projected density of phonon states measured at *T* = 20 K, via Eq. (4) (full blue lozenges); *ab initio* lattice dynamics simulations (full red squares). Red line is a guide for the eyes.

Proton mean kinetic energy in lithium imide as a function of temperature obtained from: deep inelastic neutron scattering measurements (open black circles); H-projected density of phonon states measured at *T* = 20 K, via Eq. (4) (full blue lozenges); *ab initio* lattice dynamics simulations (full red squares). Red line is a guide for the eyes.

Li and N mean kinetic energies in lithium imide as a function of temperature obtained from: deep inelastic neutron scattering measurements (Li: open black circles, N: open black squares); *ab initio* lattice dynamics simulations (Li: full red circles, N: full blue squares). Lines are guides for the eyes. Errors on N neutron data are smaller than symbols.

Li and N mean kinetic energies in lithium imide as a function of temperature obtained from: deep inelastic neutron scattering measurements (Li: open black circles, N: open black squares); *ab initio* lattice dynamics simulations (Li: full red circles, N: full blue squares). Lines are guides for the eyes. Errors on N neutron data are smaller than symbols.

## Tables

Experimental conditions of the IINS (*a, b, c*) and NCS (*i, ii, iii, iv*) measurements, where IPC stands for the integrated proton current of the ISIS neutron source.

Experimental conditions of the IINS (*a, b, c*) and NCS (*i, ii, iii, iv*) measurements, where IPC stands for the integrated proton current of the ISIS neutron source.

Standard deviation, σ, of the longitudinal momentum distribution *J*(*y*) for H, and its mean kinetic energy, in Li_{2}NH at the different temperatures investigated. The last two columns lists the expansion coefficient *c* _{2} and *c* _{3} related to the 4th-order and the 6th-order Hermite polynomials, respectively.

Standard deviation, σ, of the longitudinal momentum distribution *J*(*y*) for H, and its mean kinetic energy, in Li_{2}NH at the different temperatures investigated. The last two columns lists the expansion coefficient *c* _{2} and *c* _{3} related to the 4th-order and the 6th-order Hermite polynomials, respectively.

Standard deviations of the longitudinal momentum distribution *J*(*y*), for lithium and nitrogen and corresponding mean kinetic energies at the different temperatures investigated (see main text for details).

Standard deviations of the longitudinal momentum distribution *J*(*y*), for lithium and nitrogen and corresponding mean kinetic energies at the different temperatures investigated (see main text for details).

Momentum standard deviations and mean kinetic energies for Li, N, and H as obtained from harmonic lattice dynamics (HLD) calculations, and from quantum molecular dynamics simulations (only at *T* = 300 K) relying on the use of the so-called “quantum colored noise thermostat” (QCNT) technique (see Refs. 21,33 for details).

Momentum standard deviations and mean kinetic energies for Li, N, and H as obtained from harmonic lattice dynamics (HLD) calculations, and from quantum molecular dynamics simulations (only at *T* = 300 K) relying on the use of the so-called “quantum colored noise thermostat” (QCNT) technique (see Refs. 21,33 for details).

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