Encyclopedie de la recherche sur l'aluminium au Quebec - Edition 2014 | Page 53
TRANSFORMATION ET mechanical//pressure
Effect of high APPLICATIONS TRANSFORMATION AND APPLICATIONS
and temperature on the plasmon
L'EFFET DE LA PRESSION MÉCANIQUE
energy of aluminum L'ÉNERGIE DE PLASMON DE ÉLEVÉE ET DE
LA TEMPÉRATURE SUR
L'ALUMINIUM
L’effet de la pression mécanique
EFFECT OF HIGH MECHANICAL PRESSURE AND
élevée et de la température sur
TEMPERATURE ON THE PLASMON ENERGY OF ALUMINUM
l'énergie de plasmon de l'aluminium
51
M. Attarian Shandiz and R. Gauvin
Department of Materials Engineering, McGill University, Montreal, Quebec, Canada, H3A 0C5.
Introduction
Model
DFT calculations
Plasmon excitations, originating from the
collective oscillations of the valence electrons
in reply to an applied electric field, are the key
characteristic of low-loss electron energy loss
spectroscopy (EELS) [1]. Plasmon energy is
associated with the density of valence
electrons and so it can be used to monitor
electronic structure of material. There are
many studies connecting the plasmon energy
to the measurement of other physical and
mechanical properties [2]. The mechanical
properties such as Young modules have been
measured in a clear relationship with plasmon
energy [2]. Hence, understanding the effect of
physical and thermodynamical parameters on
the plasmon energy can be helpful for the
investigation of many other electronic
structure-related properties of materials.
By combination of the free electron model and
the equation of state (EOS) based on the
pseudo-spinodal theory by Banzona et al [],
the pressure and temperature dependency of
the plasmon energy was modeled. The EOS
suggested by Banoza et al [3] based on
pseudo-spinodal method offers a precise EOS
for a vast range of temperature and pressure
for the solids. The temperature and pressure
dependency of plasmon energy can be
explained according to our model [4] as:
The volume change of crystal is the main
reason responsible for the change of valence
electron density and plasmon energy in the
free electron model. So, to introduce the effect
of temperature and pressure for the density
functional theory (DFT) calculations of
plasmon energy, the temperature and
pressure dependency of lattice parameter was
employed.
In this study, DFT calculations were performed
with full potential linear augmented plane
wave (FLAPW) method using WIEN2k code
[5]. Optical properties and energy loss function
(ELF) were computed by the code via random
phase approximation (RPA) based on the work
of Ambrosch-Draxl and Sofo [6].
Al
15
20
10
5
14
15
16
Energy Loss (eV)
25
0.2
10 K
223 K
473 K
773 K
a)
0
13
'
' G
B0 P 3B0 0 N t k B E
B0 B0V0 (eE /T 1)
17
The change in energy loss function of
Al by variation of temperature
0
-0.2
-0.4
0
b)
Im(-1/)
ELF
20
Q(T , P )
1
Ep(eV)
Results
1 Q(T2 , P2 )1 Q1 (T1, P1 )1
exp
'
2
E p (T1, P )
B0 ( 1 1)
1
E p (T2 , P2 )
Abe et al
Moorthy and Howe
DFT calculations
200
400
T (K)
15
10
5
600
0
0
800
The comparison between the results of
difference in the plasmon energy from
DFT calculations and experiments for Al.
Results
Al
c)
0 GPa
10.7 GPa
30.8 GPa
69.6 GPa
147.5 GPa
10
20
Energy Loss (eV)
30
The change in energy loss function of
Al by variation of pressure
Conclusion
Temperature and pressure dependency of
plasmon energy of aluminum can successfully
explained based on the results of free electron
model and pseudo-spinodal equation of
states. DFT calculations based on the lattice
parameters variation can also predict the
variation of plasmon energy accurately.
M. Attarian Shandiz
Raynald Gauvin
Département de génie des
matériaux,
Université McGill
References
Contour plots of difference in valence
electron density (Δn) in (1 0 0) plane of Al for
a) V/V0=1, b) V/V0=0.8 c) V/V0=0.7 and d)
V/V0=0.6
Plasmon energy variation by temperature
and pressure according to the results of
developed model.
[1] R.F. Egerton, Electron Energy-Loss Spectroscopy in the Electron
Microscope, third ed. (Springer, New York, 2011).
[2] V. P. Oleshko, M. Murayama, J. M. Howe, Microsc. Microanal. 8,
350 (2002).
[3] V. G. Baonza, M. Cáceres , J. Núñez, Phys. Rev. B 51, 28 (1995).
[4] M. Attarian Shandiz , R. Gauvin, J. Appl. Phys. 116, 163501 (2014)
[5] P. Blaha,et al, WIEN2K: An Augmented Plane Wave Plus Local
Orbitals Program for Calculating Crystal Properties (2001).
[6] C. Ambrosch-Draxl, J. O. Sofo, Comp. Phys. Comm. 175, 1 (2006).
Journée des étudiants – REGAL of the free electron model and the equation of state based on the
By combination
En combinant le modèle des électrons libres et l'équation d'état basée sur
la théorie pseudo-spinodale, l’effet de la pression et de la température sur la
18 novembre 2014
dépendance énergétique des plasmons de l'aluminium a été modélisé. P