Optics and Photonics Journal, 2011, 1, 1-4
doi:10.4236/ opj.2011.11001 Published Online March 2011 (http://www.SciRP.org/journal/opj)
Copyright © 2011 SciRes. OPJ
Investigation of the Optical Properties of CdBr2
Hamdollah Salehi, Nastaran Asareh
Department of Physics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
E-mail: salehi_h@sua.ac.ir
Received Feburary 13, 2011; revised Feburary 28, 2011; accepted March 7, 2011
The optical properties of CdBr2 were studied by first principle using the density functional theory. The di-
electric functions and optical constants are calculated using the full potential-linearized augmented plane
wave (FP-LAPW) method with the generalized gradient approximation (GGA). The theoretical calculated
optical properties and energy Loss (EEL) spectrum yield a static refractive index of 2.1 and a plasmon ener-
gy of 13eV for hexagonal phase. The results, in comparison with the published data, are in good agreement
with the experimental and previous theoretical results.
Keywords: Optical Properties, CdBr2, WIEN2k, FP-LAPW, DFT, GGA
1. Introduction
Cadmium halogenides are widely uses as radiations. The
lattice of these complicated crystals are strongly anisotropic.
The CdBr2 structure is of the CdCl2 type, namely, the
rhombic lattice with 5
D symmetry [1]. Cadmium
bromide Crystallise with layer structures in which band-
ing within the layer is strong with a large ionic contribu-
tion, while bonding between the layers is weak. The ba-
sic structure of these materials is an infinite hexagonal
sheet of Cd atoms sandwiched between two similar
sheets of halogen atoms, the Cd atoms being Octahe-
drally coordinated. These three-sheet sandwiches (or
layers) are then stacked to form the three-dimensional
compound. Because of the weak binding between the
layers, different stacking sequences represent only slight
differences in total energy and so several such sequences
are possible. There is relatively little information availa-
ble about the electronic and optical properties of the
cadmium halides as a whole. Band structure calculations
have recently been made for CdI, (McCanny et al 1977,
Bordas et al 1978, Robertson 1979). Optical experiments
in the main have been concerned with the strong excitons
exhibited by all three materials [2]. Cadmium bromide is
known as a photochromic crystal and is widely used as
window for Infrared applications [3].
In the present work the optical properties of CdBr2 have
been studied using the full potential linearized augmented
plane wave method (FP-LAPW). The results, in compari-
son with the published data, are in good agreement with
the experimental and previous theoretical results.
2. Method of Calculation
Calculation of the optical properties, of CdBr2 were car-
ried out with a self-consistent scheme by solving the
Kohn-Sham equation using a FP-LAPW method in the
framework of the DFT along with the GGA method [4,5]
by WIEN2k package [6]. In the FP-LAPW method,
space is divided into two regions, a spherical “muf-
fin-tin” around the nuclei in which radial solutions of
Schrödinger Equation and their energy derivatives are
used as basis functions, and an “interstitial” region be-
tween the muffin tins (MT) in which the basis set con-
sists of plane waves. There is no pseudopotential ap-
proximation and core states are calculated selfconsis-
tently in the crystal potential. Also, core states are treated
fully relativistically while valence and semi-core states
are treated semi-relativistically (i.e. ignoring the spin
orbit coupling). The cut-off energy, which defines the
separation of the core and valance states, was chosen as
–6 Ryd.
The complex dielectric tensor was calculated, in this
program, according to the well-known relations [7].
Imdkc|p|vv|p |cδεεω
 
 
Re πPd
 
 
and the optical conductivity is given by:
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 
Re Im
 
In Equation (1), ck and vk are the crystal wave funtions
corresponding to the conduction and the valance bands
with crystal wave vector k. In Equation (3) the conduc-
tivity tensor relating the inter band current density j
the direction
which flows upon application of an elec-
tric field E in direction
in which the sum in Equation
(1) is over all valence and conduction band states labeled
by v and c. Moreover, the complex dielectric constant of
a solid is given as:
 
 (4)
Here, real and imaginary parts are related to optical
constants n(
) and k(
) as:
 
 
The other optical parameters, such as energy-loss
spectrum and oscillator strength sum rule are imme-
diately calculated in terms of the components of the
complex dielectric function [8].
3. Results and Discussion
The calculations first were carried out using the experi-
mental data for lattice constants, a = 3.954 A0, c = 18.672
A0 in the hexagonal phase. Then by minimizing the ratio
of the total energy of the crystal to its volume (volume
optimizing) the theoretical lattice constants were ob-
tained = 4.039 and c = 19.328 A0.
In order to reduce the time of the calculations we used
the symmetries of the crystal structure and some other
approximations for simplicity. The calculation was per-
formed with 6000 k-points in the hexagonal phase.
The self-consistent process, for both phases, after 11
cycles had convergence of about 0.0001 in the eigenvalues
in which for the hexagonal phase 1612 plane waves were
produced. Under these conditions the values of the other
parameters were Gmax = 14, RMT(Cd) = 2.5 au, RMT(Br) =
2.4 a.u. The iteration halted when the total charge ad-
justment was less than 0.0001 between steps.
3.1. Dielectric Function
We calculated optical properties of CdBr2 in the hex-
agonal phase, but here we only present the optical prop-
erties. The real and the imaginary parts of the dielectric
functions are shown in Figure 1 for CdBr2 in the hex-
agonal phase. The value of the main peak of 1(
) curve
is 8.6 at energy of 5.5 eV and for 2(
) is 8.2 at the
energy equal 7.6 eV.
The real and the imaginary parts of optical conductivity
are shown in Figure 1 for CdBr2 in hexagonal phase.
In Figure 2 the optical constant n() and Extinction
coefficient k() is shown for CdBr2 in hexagonal phase.
The static refractive index value for CdBr2in the hex-
agonal phase calculated in this work, and the values ob-
tained by other methods are summarized in Table 1.
Referring to Table 1 , it can be seen that the calculated
refractive index in this work is equal with the values
measured experimentally.
3.2. Electron Energy Loss Spectroscopy
EELS is a valuable tool for investigating various aspects
of materials [8]. It has the advantage of covering the
complete energy range including non-scattered and elas-
tically scattered electrons (Zero Loss).At intermediate
energies (typically 1 to 50 eV) the energy losses are due
primarily to a complicated mixture of single electron
excitations and collective excitations (plasmons). The
positions of the single electron excitation peaks are re-
lated to the joint density of states between the conduction
and valence bands, whereas the energy required for the
Figure 1. Real and imaginary part of the dielectric function
for CdBr2 in hexagonal phase.
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Figure 2. The optical constant n () and k () is CdBr2 in
hexagonal phase.
excitation of bulk plasmons depends mainly on the elec-
tron density in the solid. Here electrons,which excite the
atoms electrons of the outer shell is called Valence Loss
or valence interaband transitions (Figure 3). At higher
energies, typically a few hundred eV, edges can be seen
in the spectrum, indicating the onset of excitations from
the various inner atomic shells to the conduction band. In
this case the fast electrons excite the inner shell electrons
(Core Loss) or induce core level excitation of Near Edge
Structure (ELNES) and XANES. The edges are charac-
teristic of particular elements and their energy and height
can be used for elemental analysis.
Table 1. The CdBr2 static refractive index in hexagonal
phase calculated by various methods.
Method FP-LAPW
(GGA96) Experimental Theoretical
n 5.5 5.17,5.68[1] -
Difference with
experimental (%) 6,-3.27 - -
ε (0) 4.2 4.1[1],4[2] -
Difference with
experimental (%) 2.38 - -
In the case of interband transitions, which consist mostly
of plasmon excitations, the scattering probability for vo-
lume losses is directly connected to the energy loss func-
tion. One can then calculate the EEL spectrum from the
following relations.
and EELSpectrumIm[1/()]
 
 
In Figure 3 the energy loss function is plotted for
CdBr2 in hexagonal phase. These peaks can, however,
have different origins such as charge carrier plasmons
and interband or intraband excitations. The energy of the
maximum peak of Im [--1(E)] at 13 eV is assigned to the
energy of the volume plasmon
. The first peak at 8
eV and second peak at 10 eV originates from orbitals d
atom Br. The value of p
obtained in this work and
for free electron is given in Table 2.
For free electrons the plasmon energy is calculated
according to the following model:
 (7)
Figure 3. Electron energy loss spectrum Im[--1(E)] for
CdBr2 in hexagonal phase.
Table 2. The CdBr2 plasmon energy p
of the energy
loss function in hexagonal phase calculated by this method
and free electron.
Methods Plasmon energy p
FP-LAPW (GGA96) (this work)13
Free electron (ignoring Cd-4p
andBr-3d states) 18.7
Free electron 15.8
Copyright © 2011 SciRes. OPJ
If we use this model, then what should be the number
of valance electrons per CdBr2 molecule,N,used to cal-
culate the density of valance electrons, n, and thus the
plasmon energy in Equation (7).
4. Conclusions
We have calculated the optical properties of (PT) in hex-
agonal and tetragonal phases using the full poten-
tial-linearized augmented plane wave (FP-LAPW) method
with the generalized gradient approximation (GGA). The
calculations show a static refractive index of 2.1 and an
EEL spectrum of 13eV for the hexagonal phase.
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