Free Essay

Physics

In: Science

Submitted By fanik
Words 5414
Pages 22
Computational Condensed Matter 4 (2015) 32e39

Contents lists available at ScienceDirect

Computational Condensed Matter journal homepage: http://ees.elsevier.com/cocom/default.asp

Regular article

Putting DFT to the trial: First principles pressure dependent analysis on optical properties of cubic perovskite SrZrO3
Ghazanfar Nazir a, b, *, Afaq Ahmad b, Muhammad Farooq Khan a, Saad Tariq b a b

Department of Physics and Graphene Research Institute, Sejong University, Seoul 143-747, South Korea
Centre of Excellence in Solid State Physics, University of the Punjab, Lahore, Pakistan

a r t i c l e i n f o

a b s t r a c t

Article history:
Received 8 July 2015
Received in revised form
21 July 2015
Accepted 27 July 2015
Available online 31 July 2015

Here we report optical properties for cubic phase Strontium Zirconate (SrZrO3) at different pressure values (0, 40, 100, 250 and 350) GPa under density functional theory (DFT) using Perdew-Becke-Johnson
(PBE-GGA) as exchange-correlation functional. In this article we first time report all the optical properties for SrZrO3. The real and imaginary dielectric functions has investigated along with reflectivity, energy loss function, optical absorption coefficient, optical conductivity, refractive index and extinction coefficient under hydrostatic pressure. We demonstrated the indirect and direct bandgap behavior of SrZrO3 at
(0) GPa and (40, 100, 250 and 350) GPa respectively. In addition, static dielectric constant, Optical bandgap, Plasma frequency and Static refractive index has also been reported. We verified the Penn's model and showed the inverse relation between static dielectric constant and optical bandgap. Further, we proved the direct relation between static dielectric constant and static refractive index. Both these constants increased by increasing the pressure. Our investigation explored that the material preserve its positive value of refractive index at all pressure values and thus is not a negative index metamaterial.
Also, we measured Plasma frequency for SrZrO3 which also increase by increasing the pressure which leads to a conclusion that material is going to be destabilize.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:
First principle
Cubic phase SrZrO3
High pressure phase
Density functional theory
Optical properties
Perovskite

1. Introduction
In recent days, researchers are busy in finding materials that have potential uses like hydrogen sensors, fuel cells and data storage devices such as random access memory, high intensity violet-blue light emission, optical wave-guides, high temperature oxygen sensors and capacitors in different functional devices [1e6].
Perovskite having general formula ABO3 are very fundamental materials to be used in various functional devices. These materials due to their wonderful properties of ferroelectricity and piezoelectricity have great attraction for the researchers to investigate them with provoking details. In the recent period, the focus of experimental research is the zirconate perovskite. A very few theoretical approach has been done on these perovskite. Among zirconate perovskite, strontium zirconate (SrZrO3) is very interesting material because of its high temperature protonic conductivity [7]. Besides this, SrZrO3 also has great potential for high voltage and high capacitor reliability applications. High dielectric

* Corresponding author.
E-mail address: zafarforall2004@gmail.com (G. Nazir).

constant, large value of breakdown strength and low leakage current are some of its fundamental characteristics [8,9].
Kennedy et al. used powder neutron diffraction and Rietveld method to investigate the phase transitions in SrZrO3 [10]. These people gave the solid evidence for the pathway of SrZrO3 and said this material is first orthorhombic (Pnma) changes to orthorhombic
(Cmcm) at about 970 K, then changes to tetragonal (14/mcm) at about 1100 K and then finally to cubic (Pm3m) at about 1400 K. It was also suggested that these materials have very high melting temperature of about 2920 K [11]. First principle method is used to study structural, electronic, optical and magnetic properties of materials [12e15]. Mete's group of researchers reported high temperature electronic properties of cubic phase SrZrO3 [16]. Terki et al. used full-potential linearized augmented plane wave (FPLAPW) method to investigate the structural, electronic and optical properties of BaTiO3 and SrZrO3 [17]. Evarestov et al. studied the density functional theory (DFT) LCAO and plane wave (PW) calculations for the known four phases of SrZrO3 [18,19].
It has been observed that previous studies on SrZrO3 mainly focused on its structural and electrical properties using experimental approach but few researchers also reported its optical

http://dx.doi.org/10.1016/j.cocom.2015.07.002
2352-2143/© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

G. Nazir et al. / Computational Condensed Matter 4 (2015) 32e39

ε2 ðuÞ ¼

Z e2 h0 X jMcv ðkÞj2 d½ucv ðkÞ À uŠd3 k pm2 u2 v;c
BZ

where the volume integral is limited to first Brillouin zone and dipole matrix element Mcv ðkÞ ¼ huck jeVjuvk i gives the information about direct transition between conduction band and valence band states. The relation ucv(k)¼EckÀEvk gives the account of the excitation energy used during the transition between conduction and valence band states, “e” represent polarization vector because of electric field and “uck” give detail about periodic portion of Bloch wave function in conduction band associated with wave vector k.
The real part of dielectric function ε(u) can be calculated from imaginary part using well known relation of Kramers-Kronig given by: Z∞
0

u0 ε2 ðu0 Þ du0 u02 À u2

The symbol P in the about relation tell us about principal value of integral. By knowing both the real and imaginary values of dielectric functions, different important optical properties can be determined. The refractive index of the material can be determined using the following relation:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi31 2
2
ε2 ðuÞ þ ε2 ðuÞ ε1 ðuÞ
1
2
5
þ nðuÞ ¼ 4
2
2
Whereas at low frequency i.e. at (u¼0), we have the following relation: 1

nð0Þ ¼ ε 2 ð0Þ
The above relation is called static refractive coefficient. The extinction coefficient can be computed by using following relation:

2
Àε ðuÞ þ kðuÞ ¼ 4 1
2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi31 2 ε2 ðuÞ þ ε2 ðuÞ
1
2
5
2
=

Basic calculations of our research is done using full potential linearized augmented plane wave (FP-LAPW) based on density functional theory (DFT) as implemented in Wien2k. In addition to this, Kohn-Sham equations are calculated by applying full potential-linearized augmented plane wave (FP-LAPW) using selfconsistent method [23e28]. We performed pressure dependent characteristics instead of temperature dependent in order to study the optical response of the material under high pressure by using standard DFT at 0 K temperature. In this well-known FP-LAPW method, Slater's theory of Muffin-Tin radii has been used in order to divide this space into two regions. Close to the atoms, all interesting quantities are expanded in terms of spherical harmonics and as expansion of plane waves with wave vector having cut-off value of
KMAX in the interstitial region. The earlier kind of expansion is stated within a well-known muffin-tin sphere of radius RMT around every nucleus. The choice of sphere radii predicts the rate of convergence of these expansions, but this affects only the speed of the calculation. We choose RMT x KMAX ¼ 7 as convergence parameters for the matrix element that represent number of fundamental functions, in which KMAX is associated with plane wave cutoff in momentum space (k-space) and RMT represent the smallest radius of Muffin-Tin cube among all the atomic sphere radii. The value of Muffin-Tin radii for “Barium”, “Zirconium” and “Oxygen” are 2.5, 1.98 and 1.79 au respectively. Energy separation is considered to be À6 Ry. We used generalized gradient approximation
(GGA-PBE) given by Perdew et al.for the calculation of exchangeecorrelation potential [29,30]. We did our calculation without including spin-orbit effects. We choose maximum value of l to be lmax ¼ 10 for wave function expansion inside the atomic spheres.
Outside the muffin-tin spheres, the expansion of charge density is done by Fourier series. For reciprocal space integration under different pressure values in the irreducible Brillouin zone, 35 kpoints in grid of 10 Â 10 Â 10 meshes which is equal to 1000-k points in the complete Brillouin zone scheme has been used to achieve self-consistency. Optical characteristics for SrZrO3 are studied by dielectric function ε(u)¼ε1(u)þε2(u) consist of real and imaginary dielectric parameters. Following equations formulated by Ehrenreich and Cohen give brief description about the real and imaginary parts of dielectric function [29,31].

2
P
p

=

2. Computational details

ε1 ðuÞ ¼ 1 þ

=

properties. Ref. [17,20,21] reported the existence of large conductivity spectra at room temperature shown by SrZrO3. In many reports the calculation for band structure of cubic phase of SrZrO3
(which is stable above 1400 K) [16,20,22]. In this paper, we investigate all the possible optical properties of cubic phase SrZrO3 under different values of pressure (GPa).

33

Reflectivity of the mentioned material is calculated by:



ðn À 1Þ2 þ k2 ðn þ 1Þ2 þ k2

In the same way, energy loss function L(u), absorption coefficient a(u) and optical conductivity s(u) are determined using the following relation [32].

LðuÞ ¼ Imð À 1=e ðuÞÞ ε aðuÞ ¼ 4pkðuÞ=l sðuÞ ¼ ð2Wcv h0 uÞ=Eo
Where “Wcv” in the above relation represent transition probability per unit time.

3. Result and discussion
To discuss the internal structure of any material, the optical properties play a very supportive role. The Optical Properties of materials suggest the feasibility and suitability as industrial point of view especially in opto-electronics. Fig. 1 show theoretical cubic perovskite structure of compound SrZrO3. Atomic arrangements of
Sr, Zr and O atoms on different sites of cubic perovskite are: Sr at 8 corners, Zr at the center and O atoms on the 6 faces.
Figs. 2e10 show meaningful study of different optical parameters for cubic phase of SrZrO3 at different values of pressure at (0,
40, 100, 250 and 350) GPa calculated for energy range upto 45 eV.
We verified Penn's model by knowing the inverse relation between optical bandgap and static dielectric constant. Fig. 2 shows the variation of optical bandgap and static dielectric constant at different pressure values from (0, 40, 100, 250 and 350) GPa. We can say that optical bandgap and static dielectric constant satisfy Penn's model. This inverse relation between ε1(0) and bandgap can be explained by penn model mathematically given by [33,34].

34

G. Nazir et al. / Computational Condensed Matter 4 (2015) 32e39

Fig. 1. The compound SrZrO3 has an ideal cubic perovskite structure. The Strontium,
Oxygen and Zirconium atoms preferably reside at corners, on the faces and at the center respectively of single cubic unit cell.

À
 Á2 ε1 ð0Þz1 þ ħup Eg
The relation given by Penn's model can be used to determine Eg by knowing the values of ε1(0) and plasma energy “ħup ”. The measured values of static dielectric constant ε1(0) at different pressures (0, 40, 100, 250 and 350) GPa along with their bandgap values and plasma frequencies are given in Table 1.
The real and imaginary parts of dielectric function determined at different values of pressure are shown in Fig. 3. The real part of dielectric function ε1(u) gives information about how much a

Fig. 2. Static dielectric constant and optical bandgap for cubic phase SrZrO3 at (0, 40,
100, 250 and 350) GPa pressure values.

Fig. 3. Frequency dependent dielectric functions of cubic phase SrZrO3 at (0, 40, 100,
250 and 350) GPa pressure values (real part: black lines, imaginary part: red lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

material is polarized. It is observed from the Fig. 3 that the measured values of static dielectric constantε1(0), low energy limit ofε1(u), depends upon the bandgap of the material. It can be observe from the Fig. 3 that the real part of dielectric function start increasing from its static value ε1(0) given in Table 1 and reaches a highest peak at about 4.784 eV, 5.497 eV, 6.026 eV, 7.292 eV and
6.887 eV for cubic phase of SrZrO3 at different values of pressure from (0, 40, 100, 250 and 350) GPa. After reaching this peak value, real dielectric function start decreasing with some low peaks exist at different higher energy values and becomes zero at certain value of energy of about 9.740 eV, 11.117 eV, 12.150 eV, 13.110 eV and
13.270 eV at (0, 40, 100, 250 and 350) GPa respectively. On further increase in energy, it can be seen that dielectric function becomes negative which means that in these regions of energy, the medium will totally reflect all the incident electromagnetic waves and thus exhibiting metallic nature of the material. The graph also reveals that hump is shifted toward the higher energies by increasing the value of pressure upto 350 GPa.
It has been understood that imaginary part of dielectric function ε2(u) play very impressive role in the optical properties for any material. It has deep effect on the absorption of the medium. Absorption in the material is large for large value of imaginary part of dielectric function ε2(u) Fig. 3 also shows the behavior of imaginary part of dielectric function versus energy. It is clear that absorption starts at about 3.172 eV, 3.738 eV, 3.664 eV, 2.828 eV and 2.213 eV for cubic phase of SrZrO3 at (0, 40, 100, 250 and 350) GPa respectively. These points are related to minimum direct bandgap transition between maxima of the valence band to the minima of the conduction band. Fig. 3 also represents the strong absorbing nature of the material in these energy regions from 3.172 eV to 37.965 eV at

G. Nazir et al. / Computational Condensed Matter 4 (2015) 32e39

Fig. 4. Frequency dependent reflectivity of cubic phase SrZrO3 at (0, 40, 100, 250 and
350) GPa pressure values.

Fig. 5. Frequency dependent energy loss function of cubic phase SrZrO3 at different values at (0, 40, 100, 250 and 350) GPa pressure values.

35

Fig. 6. Frequency dependent Absorption coefficient of cubic phase SrZrO3 at (0, 40,
100, 250 and 350) GPa pressure values.

0 GPa, 3.738 eVe40.031 eV at 40 GPa, 3.664 eVe43.241 eV at
100 GPa, 2.828 eVe40.720 eV at 250 GPa and 2.123 eVe41.175 eV.
These regions consist of different peaks which exist as a result of interband transition between valence band and conduction band.
The width of the absorption region first increase upto 100 GPa and then decrease with the increase in pressure. Maximum absorption takes place in energy range of 3.664 eVe43.241 eV with energy width equal to 39.577 eV at 100 GPa and minimum at 0 GPa with energy width equal to 34.793 eV. We can also see that the absorption width shift toward the lower value of energy as the pressure exceeds 100 GPa.
To investigate deeply the surface behavior of the material, its reflectivity is measured which is equal to the ratio of incident power to reflected power. Fig. 4 represent reflectivity versus energy for cubic phase SrZrO3 at (0, 40, 100, 250 and 350) GPa. Fig. 4 shows that the zero frequency limit of reflectivity for cubic phase SrZrO3 is equal to 0.129, 0.127, 0.128, 0.130, 0.131 at (0, 40, 100, 250 and 350)
GPa respectively. It then increase from its zero limit as with the increase in pressure and reached at the highest peak of reflectivity for cubic phase SrZrO3 at 24.424 eV, 24.375 eV, 26.453 eV,
27.130 eV, 27.560 eV for (0, 40, 100, 250 and 350) GPa respectively.
These peaks produced as a result of interband transition between valence band and conduction band. On the other hand, the minimum value of reflectivity occurs in energy range from 10 eV to
40 eV as a result of collective plasma resonance. Imaginary part of dielectric function can be used to measure the depth of plasma resonance [34]. We can see very interesting behavior shown by the peak value of reflectivity. It shifts toward higher energy value as the pressure exceeds 40 GPa consistent with the imaginary part of dielectric function [35,36].
The energy loss function L(u) is an important parameter which describes the energy loss for electron moving in a material. Fig. 5

36

G. Nazir et al. / Computational Condensed Matter 4 (2015) 32e39

Fig. 7. Optical bandgap of cubic phase SrZrO3 at (0, 40, 100, 250 and 350) GPa pressure values.

show energy loss function L(u) versus at (0, 40, 100, 250 and 350)
GPa. The peaks in energy loss function L(u) gives us brief detail about characteristics related to plasma resonance and hence the associated frequency known as plasma frequency. No energy loss occur for photons having energy less than 6.186 eV, 7.096 eV,

7.637 eV, 8.449 eV, 8.670 eV at (0, 40, 100, 250 and 350) GPa respectively but as soon as the photons exceed these amount of energy, energy loss will start increasing and get the maximum peak at 26.035 eV, 32.246 eV, 35.124 eV, 36.969 eV, 37.571 eV for (0, 40,
100, 250 and 350) GPa respectively. It can be seen that highest peak

G. Nazir et al. / Computational Condensed Matter 4 (2015) 32e39

Fig. 8. Frequency dependent optical conductivity of cubic phase SrZrO3 at (0, 40, 100,
250 and 350) GPa pressure values (real part: black lines, imaginary part: red lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

shifts toward higher value of energy with the increase in pressure.
The highest peak has value 5.709 eV occur at 36.969 eV because of pressure value equal to 250 GPa. The observed peak in the energy loss function associated with the plasma frequency and can be treated as an interface between metallic and dielectric behavior.
Absorption coefficient is very important factor that gives information about the decay of light intensity per unit distance in medium. The frequency dependent absorption coefficient for cubic phase SrZrO3 at different pressure is shown in Fig. 6. The change in frequency is described in terms of energy with range from 0 upto
45 eV. The highest peaks occurred at 23.613 eV, 24.191 eV,
24.769 eV, 25.605 eV, 26.035 eV for (0, 40, 100, 250 and 350) GPa respectively. We can see largest value of peak equal to 382.809 eV exist at pressure value of 100 GPa. So we can say that by increasing pressure, the absorption peak shift toward higher value of energy upto 350 GPa. It has also been observed that there is no absorption for photon energy less than 4.033 eV, 4.525 eV, 5.288 eV, 5.755 eV,
5.989 eV for (0, 40, 100, 250 and 350) GPa respectively. However with photon energy greater than these values, absorption coefficient start increasing, which is associated with the direct bandgap values 3.307 eV, 3.175 eV, 3.023 eV, 2.605 eV, 2.156 eV calculated for cubic phase SrZrO3 at different high pressures, respectively.
We can see many peaks within the studied energy range, and the structures of these peaks can be understood from the interband transitions between valence band and conduction band. Fig. 7 shows optical bandgap values determined by measuring the direct and indirect behavior of the cubic phase SrZrO3 at different pressure values by using theoretical approach of square of absorption. The real and imaginary part of optical conductivity is also

37

Fig. 9. Frequency dependent refractive indices of cubic phase SrZrO3 at (0, 40, 100, 250 and 350) GPa pressure values (refractive index: black lines, extinction coefficient: red lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

studied for cubic phase SrZrO3 as shown in Fig. 8. It is observed that the real part of conductivity remained at zero and starts to originate from 3.66, 4.16, 4.31, 5.54 and 5.76 eV for different pressure values at (0, 40, 100, 250 and 350) GPa respectively. This is in good agreement with the bandgap of the material at different pressure.
When the photon energy exceed these particular values, the real

Fig. 10. Static Refractive indices for cubic phase SrZrO3 at (0, 40, 100, 250 and 350) GPa pressure values.

38

G. Nazir et al. / Computational Condensed Matter 4 (2015) 32e39

Table 1
Static Dielectric Constant ε1(0), Optical Band-gap(Eg), Plasma Frequency up and Static Refractive Index n0 at (0, 40, 100, 250 and 350) GPa pressure values.
Pressure (GPa)

Static dielectric constant ε1(0)

Band-gap(Eg)

Plasma frequency (up)

Static refractive Index (n0)

0
40
100
250
350

4.526
4.452
4.496
4.555
4.570

3.307
3.157
3.023
2.605
2.156

0.2714
0.3188
1.0127
1.0514
1.0386

2.122
2.113
2.122
2.132
2.136

part of conductivity start increasing and attains the maximum peak values at 23.231 eV, 23.539 eV, 23.797 eV, 12.618 eV, 13.011 eV for pressure at (0, 40, 100, 250 and 350) GPa respectively. It is observed that as the pressure is increased, the maximum real conductivity peak shifted toward higher value of energy for (0, 40 and 100) GPa.
With the further increase in pressure, the highest peak shift toward the lower value. of energy as seen for 250 GPa and then again it goes toward higher value of energy for 350 GPa. After reaching at highest peak, it starts decreasing with the further increase in photon energy
(eV).
The refractive index and the extinction coefficient for cubic phase SrZrO3 can be determined by the relation:

n2 À k2 ¼ ε1 And 2nk ¼ ε2
Fig. 9 shows the broad spectrum of refractive index and extinction coefficient over wide range of energy. The Figure shows that the spectrum of n(u) nearly follow ε1(u) pattern [37]. It can be seen from the Figure that static refractive index n0 values are 2.122,
2.113, 2.122, 2.132, 2.136 for cubic phase SrZrO3 at (0, 40, 100, 250 and 350) GPa values of pressure which is in good agreement with static dielectric function values with the formula (n2 ¼ ε1 ð0Þ). We
0
can see that the peak in the refractive index shift toward higher value of energy as the pressure increase from (0, 40, 100, 250 and
350) GPa. In the middle of the graph, we can see different humps which vanish at higher values of photon energy. It is due to the fact that beyond certain value of energy, the material will no longer remain transparent and start absorbing high energy photons. At certain value of energy, the value of refractive index becomes less than unity as can be seen from Fig. 9.
Refractive index with value less than unity (vg ¼ c/n) describes that group velocity of the falling radiation becomes greater than speed of light. This means that group velocity move toward the negative domain and nature of the medium will no longer remain linear. In other words, we can say that the material converts to superluminal medium for high energy photons [38,39]. The extinction coefficient is also shown in the Fig. 9. The extinction coefficient gives information about the absorption of light, and at the same time, absorption characteristics at the band edges. The peaks in refractive index as well as in the extinction coefficient are due to the interband transition of electrons from valence band to conduction band. The response of k(u) is closely related with the response of ε2(u) at different values of pressure [40e42]. Fig. 10 shows the behavior of static refractive index with different values of pressure (GPa) which increased as the value of pressure is increased from 0 GPa to 350 GPa. To the best of our knowledge, there is lack of data available on pressure dependent optical properties of cubic phase SrZrO3. We therefore hope that our work will motivate researcher to do theoretical studies in this direction using different exchange-correlation functional, so we can compare our results with them to get better understanding about the material. 4. Conclusion
In summary, we performed first principle computational analysis on cubic phase SrZrO3 to measure the optical properties. We have seen that at 0 GPa, the SrZrO3 has indirect nature and become direct as the pressure equals to 40 GPa, after that it remained direct with further increase in pressure upto 350 GPa as confirmed by the optical bandgap measurements. Further, static dielectric constant, plasma frequency, static refractive indices are also measured which increase as the pressure is increased. However, the optical bandgap is decreased with the increased in pressure consistent with Penn's model. Also material showed positive refractive index value at all pressure which leads to conclusion that our material did not change into negative index metamaterial under pressure measurement.
Plasma frequency is also increased with pressure increase exhibiting de-stability of the material which is confirmed by increment in the optical bandgap values. We try our best to discuss all the optical properties in detail and show path to the researcher to do experimental study for comparison.
Acknowledgment
We have no financial support for this work.
References
[1] R. Davies, M. Islam, J. Gale, Dopant and proton incorporation in perovskitetype zirconates, Solid State Ionics 126 (1999) 323e335.
[2] Z. Wu, et al., Effect of BaO-Al2O3-B2O3-SiO2 glass additive on densification and dielectric properties of Ba0. 3Sr0. 7TiO3 ceramics, J. Ceram. Soc. Jpn. 116
(2008) 345e349.
[3] R.V. Shende, D.S. Krueger, G.A. Rossetti, S.J. Lombardo, Strontium zirconate and strontium titanate ceramics for high-voltage applications: synthesis, processing, and dielectric properties, J. Am. Ceram. Soc. 84 (2001) 1648e1650.
[4] N. Fukatsu, N. Kurita, T. Yajima, K. Koide, T. Ohashi, Proton conductors of oxide and their application to research into metal-hydrogen systems, J. Alloys
Compd. 231 (1995) 706e712.
[5] T. Yajima, H. Suzuki, T. Yogo, H. Iwahara, Protonic conduction in SrZrO3-based oxides, Solid State Ionics 51 (1992) 101e107.
[6] H. Iwahara, T. Yajima, T. Hibino, H. Ushida, Performance of solid oxide fuel cell using proton and oxide ion mixed conductors based on BaCe1À x Sm x O3À a,
J. Electrochem. Soc. 140 (1993) 1687e1691.
[7] P. Colomban, Proton Conductors: Solids, Membranes and Gels-materials and
Devices, vol. 2, Cambridge University Press, 1992.
[8] T. Yu, W. Zhu, C. Chen, X. Chen, R.G. Krishnan, Preparation and characterization of solegel derived CaZrO3 dielectric thin films for high-k applications,
Phys. B Condens. Matter 348 (2004) 440e445.
[9] C.-Y. Lin, M.-H. Lin, M.-C. Wu, C.-H. Lin, T.-Y. Tseng, Improvement of resistive switching characteristics in thin films with embedded Cr layer, Electron Device Lett. IEEE 29 (2008) 1108e1111.
[10] B.J. Kennedy, C.J. Howard, B.C. Chakoumakos, High-temperature phase transitions in SrZrO3, Phys. Rev. B 59 (1999) 4023.
[11] D. Souptel, G. Behr, A. Balbashov, SrZrO3 single crystal growth by floating zone technique with radiation heating, J. Cryst. Growth 236 (2002) 583e588.
[12] J. Muscat, A. Wander, N. Harrison, On the prediction of band gaps from hybrid functional theory, Chem. Phys. Lett. 342 (2001) 397e401.
[13] J. Sambrano, J. Martins, J. Andres, E. Longo, Theoretical analysis on TiO2(110)/V surface, Int. J. Quantum Chem. 85 (2001) 44e51.
[14] J. Sambrano, G. Nobrega, C. Taft, J. Andres, A. Beltran, A theoretical analysis of the TiO2/Sn doped (110) surface properties, Surf. Sci. 580 (2005) 71e79.
[15] J. Sambrano, et al., Theoretical analysis of the structural deformation in Mndoped BaTiO3, Chem. Phys. Lett. 402 (2005) 491e496.

[16] E. Mete, R. Shaltaf, S. Ellialtıoglu, Electronic and structural properties of a 4
¸

G. Nazir et al. / Computational Condensed Matter 4 (2015) 32e39 d perovskite: cubic phase of SrZrO3, Phys. Rev. B 68 (2003) 035119.
[17] R. Terki, H. Feraoun, G. Bertrand, H. Aourag, Full potential calculation of structural, elastic and electronic properties of BaZrO3 and SrZrO3, Phys. Status
Solidi (b) 242 (2005) 1054e1062.
[18] R. Evarestov, A. Bandura, V. Aleksandrov, Calculations of the electronic structure of crystalline SrZrO3 in the framework of the density-functional theory in the LCAO approximation, Phys. Solid State 47 (2005) 2248e2256.
[19] R. Evarestov, A. Bandura, V. Alexandrov, E. Kotomin, DFT LCAO and plane wave calculations of SrZrO3, Phys. Status Solidi (b) 242 (2005) R11eR13.
[20] R. Vali, Band structure and dielectric properties of orthorhombic SrZrO3, Solid
State Commun. 145 (2008) 497e501.
[21] K. Galicka-Fau, et al., Thickness determination of SrZrO3 thin films using both
X-ray reflectometry and SIMS techniques, Thin Solid Films 516 (2008)
7967e7973.
[22] Y. Lee, et al., Systematic trends in the electronic structure parameters of the 4 d transition-metal oxides SrMO3 (M ¼ Zr, Mo, Ru, and Rh), Phys. Rev. B 67
(2003) 113101.
[23] Z. Feng, H. Hu, S. Cui, C. Bai, First-principles study of optical properties of
SrZrO3 in cubic phase, Solid state Commun. 148 (2008) 472e475.
[24] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964)
B864.
[25] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965) A1133.
[26] K. Schwarz, P. Blaha, G. Madsen, Electronic structure calculations of solids using the WIEN2k package for material sciences, Comput. Phys. Commun. 147
(2002) 71e76.
[27] H. Eschrig, The Fundamentals of DFT, Teubner, Stuttgart, 1996.
[28] I. Levin, et al., Phase equilibria, crystal structures, and dielectric anomaly in the BaZrO3eCaZrO3 system, J. Solid State Chem. 175 (2003) 170e181.
[29] S. Cottenier, Density Functional Theory and the Family of (L) APW-methods: a
Step-by-step Introduction, vol. 4, Instituut voor Kern-en Stralingsfysica, KU
Leuven, Belgium, 2002, p. 41.
[30] J.P. Perdew, et al., Atoms, molecules, solids, and surfaces: applications of the

[31]

[32]
[33]
[34]
[35]

[36]

[37]

[38]
[39]
[40]
[41]

[42]

39

generalized gradient approximation for exchange and correlation, Phys. Rev. B
46 (1992) 6671.
S. Kurth, J.P. Perdew, P. Blaha, Molecular and solid-state tests of density functional approximations: LSD, GGAs, and meta-GGAs, Int. J. Quantum Chem.
75 (1999) 889e909.
H. Ehrenreich, M.H. Cohen, Self-consistent field approach to the manyelectron problem, Phys. Rev. 115 (1959) 786.
D. Groh, et al., First-principles study of the optical properties of BeO in its ambient and high-pressure phases, J. Phys. Chem. Solids 70 (2009) 789e795.
D.R. Penn, Wave-number-dependent dielectric function of semiconductors,
Phys. Rev. 128 (1962) 2093.
A.H. Reshak, Z. Charifi, H. Baaziz, First-principles study of the optical properties of PbFX (X ¼ Cl, Br, I) compounds in its matlockite-type structure, Eur.
Phys. J. B 60 (2007) 463e468.
B. Amin, I. Ahmad, M. Maqbool, Conversion of direct to indirect bandgap and optical response of B substituted InN for novel optical devices applications,
Light. Technol. J. 28 (2010) 223e227.
R. Khenata, et al., First-principle calculations of structural, electronic and optical properties of BaTiO 3 and BaZrO 3 under hydrostatic pressure, Solid
State Commun. 136 (2005) 120e125.
A.M. Fox, Optical Properties of Solids, vol. 3, Oxford university press, 2001.
L.J. Wang, A. Kuzmich, A. Dogariu, Gain-assisted superluminal light propagation, Nature 406 (2000) 277e279.
D. Mugnai, A. Ranfagni, R. Ruggeri, Observation of superluminal behaviors in wave propagation, Phys. Rev. Lett. 84 (2000) 4830.
R. Eglitis, M. Rohlfing, First-principles calculations of the atomic and electronic structure of SrZrO3 and PbZrO3(001) and (011) surfaces, J. Phys. Condens.
Matter 22 (2010) 415901.
R. Eglitis, Ab initio calculations of SrTiO3, BaTiO3, PbTiO3, CaTiO3, SrZrO3,
PbZrO3 and BaZrO3(001),(011) and (111) surfaces as well as F centers, polarons, KTN solid solutions and Nb impurities therein, Int. J. Mod. Phys. B 28
(2014) 1430009.

Similar Documents

Free Essay

Physics

...Assignment in Physics... 1. Definition of Science, Major branches of science 2. Scientific Method 3. Definition of Physics and its major branches 4. Notable Physicist and their contribution 5. Importance of Physics in our everyday life and in our society. (Write the references) Short bond paper, written or computerized (font: Times New Roman/font size: 12) Reading assign. Measurement Diff. system of measurement fundamentals and derive quantities scientific notation rules in significant figures conversion of units http://www.hep.man.ac.uk/babarph/babarphysics/physicists.html ) I.1 Science The intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment. I.2 The Branches of Science The Physical Sciences * Physics: The study of matter and energy and the interactions between them. Physicists study such subjects as gravity, light, and time. Albert Einstein, a famous physicist, developed the Theory of Relativity. * Chemistry: The science that deals with the composition, properties, reactions, and the structure of matter. The chemist Louis Pasteur, for example, discovered pasteurization, which is the process of heating liquids such as milk and orange juice to kill harmful germs. * Astronomy: The study of the universe beyond the Earth's atmosphere. The Earth Sciences * Geology: The science of the origin, history, and structure...

Words: 1431 - Pages: 6

Free Essay

Physics

...Aristotle was perhaps the first in the Western tradition to look at mechanics in any sort of structured way. A philosopher, rather than physicist, Aristotle thought about the way objects interact with each other, particularly their motions. One of the ideas to come from Aristotle’s work is that objects “like” to remain at rest. This seems rather reasonable put a book on a table and it remains still, push it gently and it will move until you stop. This begs the question, though what happens when we throw ad object? Our hand stops pushing, but the object continues to move. Likewise when we roll a ball we release the ball and it continues to move. Aristotle’s answer was impetus. When an object is moved by another (your hand, for example, throwing a ball), it accrues impetus. When the mover stops acting upon the movee, the impetus it accrued whilst being acted upon is used to continue the motion. Under this model, we would expect objects to exhibit straight-line trajectories rather than the parabolic trajectories we see when we throw an object A second idea of Aristotle’s is that heavier objects fall faster than lighter objects. It does, at first glance, seem rather reasonable but it is, like the idea of impetus, quite easily shown incorrect. The Aristotleans didn’t bother to take observations or do experiments to support their beliefs and most of those that came after them were content to trust Aristotle. Thus for more than 100 years, our understanding of mechanics was......

Words: 667 - Pages: 3

Free Essay

Physics

...1. (5) famous physicist in their invention. Denis Papin (22 August 1647 - c. 1712) was a French physicist, mathematician andinventor, best known for his pioneering invention of the steam digester, the forerunner of the steam engine and of the pressure cooker. Thomas Alva Edison (February 11, 1847 – October 18, 1931) was an American inventorand businessman. He developed many devices that greatly influenced life around the world, including the phonograph, the motion picture camera, and a long-lasting, practical electriclight bulb. Dubbed "The Wizard of Menlo Park" by a newspaper reporter, he was one of the first inventors to apply the principles of mass production and large-scale teamwork to the process of invention, and because of that, he is often credited with the creation of the first industrial research laboratory Alexander Graham Bell (March 3, 1847 – August 2, 1922) was an eminent scientist, inventor, engineer and innovator who is credited with inventing the first practical telephone. Many other inventions marked Bell's later life, including groundbreaking work in optical telecommunications, hydrofoils and aeronautics. In 1888, Bell became one of the founding members of the National Geographic Society.[8] He has been described as one of the most influential figures in human history. John Logie Baird FRSE (13 August 1888 – 14 June 1946) was a Scottish engineer and inventor of the world's first practical, publicly demonstrated television system, and also the world's......

Words: 508 - Pages: 3

Free Essay

Physics

...Statics of Rigid Bodies STATICS OF RIGID BODIES Chapter 1: Introduction Department of Engineering Sciences enter 〉〉 Statics of Rigid Bodies DEFINITION Mechanics • the study of the relationship among forces and their effects on bodies. • the science which describes and predicts the conditions for rest and motion of bodies under the action of forces. • a physical science (for it deals with physical phenomena) Prev Department of Engineering Sciences Jump to… Stop Show Next Statics of Rigid Bodies MECHANICS MECHANICS RIGID BODIES STATICS bodies at rest DYNAMICS bodies in motion DEFORMABLE BODIES INCOMPRESSIBLE FLUIDS COMPRESSIBLE Prev Department of Engineering Sciences Jump to… Stop Show Next Statics of Rigid Bodies What is a FORCE? represents the action of one body on another that tends to change the state or state of motion of a body. may be exerted by actual contact or at a distance (e.g. gravitational and magnetic forces). characterized by its point of application, magnitude and direction. represented by a vector. Prev Department of Engineering Sciences Jump to… Stop Show Next Statics of Rigid Bodies Effects of a FORCE • development of other forces (reactions or internal forces) • deformation of the body • acceleration of the body Applied Force Prev Department of Engineering Sciences Jump to… Stop Show Next Statics of Rigid Bodies Development of other......

Words: 534 - Pages: 3

Premium Essay

Physics: The Physics Of Roller Coasters

...In any amusement park, the roller coaster is usually the most popular ride. It was first built in Russia during the 16th century, ever since then, the roller coaster has been a hit. With the car slowly moving up the everlasting height of the hill, high enough to touch the clouds, and then rushing downwards through many loops and twists, is enough to keep one’s adrenaline pumping. But what is the secret of the roller coaster? How is it possible for it to work this way? The answer is science. Many may not know, but science, specifically physics, has a lot to do with roller coasters. The roller coaster is actually powered by many types of energy: mechanical, potential, and kinetic. Mechanical energy is ‘the energy acquired by the objects upon which work is done.’ (Definition of Mechanical Energy). Potential energy is ‘energy possessed by an object because of its height above the ground’ (Definition of Potential Energy). Kinetic energy is ‘the energy of motion’ (Definition of Kinetic Energy)....

Words: 444 - Pages: 2

Free Essay

Physics

...Discussion #3 For this experiment we measured gravitational acceleration and velocity of a cart getting pushed up a ramp. First we had to make a prediction of how a velocity and acceleration graph would look like with a cart going up the ramp. After that we actually started to do the experiment. We then went to the computer which would help us graph our measurements of each time we did the experiment. It measured velocity, acceleration, and position of the cart each time. We did the experiment about a couple times until we got a good looking graph, then we recorded it on our lab reports and used it for the rest of our remaining results. Before using that, we took a measurement of the angle of the ramp which turned out to be 4.04 degrees. After that, we then took the graphs we did that were on the computer and we used different tools to find out the acceleration and slope of each specific time in the reading the lab report told us to do. From there after we were done, we then waited till the whole class was done and we all wrote down what our readings were for each measurement. Our measurements were; 4.04 degrees for angle A, .63 kg for the mass of the cart, .582 with an uncertainty of .009 for our acceleration from the average slope, .58 with an uncertainty of .009 for th average acceleration from STATS , 1.13 for mass of the cart with added mass, .569 with an uncertainty of .032 for acceleration from average slope with the doubled mass, and finally 8.199 with an......

Words: 285 - Pages: 2

Premium Essay

Physics Research

...Galileo was born in Pisa (then part of the Duchy of Florence), Italy in 1564, the first of six children of Vincenzo Galilei, a famous lutenist, composer, and music theorist; and Giulia Ammannati. Galileo was named after an ancestor, Galileo Bonaiuti, a physician, university teacher and politician who lived in Florence from 1370 to 1450. Galileo Galilei  was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the scientific revolution. Galileo has been called the "father of modern physics Galileo's theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and René Descartes, was a precursor of the classical mechanics developed by Sir Isaac Newton. Galileo conducted several experiments with pendulums. It is popularly believed that these began by watching the swings of the bronze chandelier in the cathedral of Pisa, using his pulse as a timer. Later experiments are described in his Two New Sciences. Galileo claimed that a simple pendulum is isochronous, i.e. that its swings always take the same amount of time, independently of the amplitude. In fact, this is only approximately true. Galileo also found that the square of the period varies directly with the length of the pendulum. It is said that at the age of 19, in the cathedral of Pisa, he timed the oscillations of a swinging lamp by means of his pulse beats and found the time for each swing to be the same, no matter what the amplitude...

Words: 734 - Pages: 3

Premium Essay

Math and Physics

...MOST DIFFICULT SUBJECTS FOR HIGHSCHOOL STUDENTS: MATH AND PHYSICS A Term Paper Presented to the Faculty of Saint Joseph's School In Partial Fulfillment of the Requirement in English IV Submitted to: Gemalyn Cantes Submitted by: Jovilyn Bumohya Date of submission: January 5, 2009 iii CONTENTS TITLE PAGE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii CONTENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii ACKNOWLEDGEMENT. . . . . . . . . . . . . . . . . . . . . . . . . xii CHAPTER I: THE PROBLEM AND ITS BACKGROUND A. Statement of the Problem. . . . . . . . . . . . . . . . 1 B. Objectives of the Study. . . . . . . . . . . . . . . . . 1 C. Hypothesis. . . . . . . . . . . . . . . . . . . . . . . . . . . 1 D. Significance of the Study. . . . . . . . . . . . . . . . 1 E. Scope and Delimitation. . . . . . . . . . . . . . . . . 2 F. Definition of Terms. . . . . . . . . . . . . . . . . . . . 2 CHAPTER II: MOST DIFFICULT SUBJECTS FOR HIGHSCHOOLSTUDENTS: MATH AND PHYSICS A. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . 3 B. Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . 3 CHPATER III: SUMMARY, CONCLUSION AND RECOMMENDATION A. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 B. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . 5 C.......

Words: 1424 - Pages: 6

Free Essay

Real World Physics

...REAL WORLD PHYSICS Did you know that Physics and Sports cannot be separated? In sports, athletes need to apply the concepts of Physics. But the application of Physics is not just limited to the machineries but also on how people should move the parts of their body. If successfully applied, well it can increase an athlete’s performance. But there are far more reasons why I believe Physics is a spectator of sports: firstly the physics of ice skating or figure skating which was shown in the movie Ice Princes that I recently watched; second, the physics of playing basketball and lastly, the physics of archery. To start off, the movie Ice Princess is the perfect example wherein Physics was applied into sports. Remember Isaac Newton’s first law of motion? Which states: An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. (Mckinley, 2000) It is also known as inertia, and the very main reason why ice skaters glide smoothly on ice with the help of friction simply because there is less friction on ice. It is truly amazing on how the girl in the movie successfully applied Physics in figure skating. Another argument I have is, when your playing basketball. Physics is applied and can be seen when basketball players shoot the ball into the ring. As seen in the viral game angry birds, it basically shows and applies the concept of projectile motion wherein before the bird flies, a...

Words: 570 - Pages: 3

Free Essay

Understanding the World of Physics

...UNDERSTANDING PHYSICS – Part 1 MOTION, SOUND & HEAT Isaac Asimov Motion, Sound, and Heat From the ancient Greeks through the Age of Newton, the problems of motion, sound, and heat preoccupied the scientific imagination. These centuries gave birth to the basic concepts from which modern physics has evolved. In this first volume of his celebrated UNDERSTANDING PHYSICS, Isaac Asimov deals with this fascinating, momentous stage of scientific development with an authority and clarity that add further lustre to an eminent reputation. Demanding the minimum of specialised knowledge from his audience, he has produced a work that is the perfect supplement to the student’s formal textbook, as well se offering invaluable illumination to the general reader. ABOUT THE AUTHOR: ISAAC ASIMOV is generally regarded as one of this country's leading writers of science and science fiction. He obtained his Ph.D. in chemistry from Columbia University and was Associate Professor of Bio-chemistry at Boston University School of Medicine. He is the author of over two hundred books, including The Chemicals of Life, The Genetic Code, The Human Body, The Human Brain, and The Wellsprings of Life. The Search for Knowledge From Philosophy to Physics The scholars of ancient Greece were the first we know of to attempt a thoroughgoing investigation of the universe--a systematic gathering of knowledge through the activity of human reason alone. Those who attempted this rationalistic search for......

Words: 259 - Pages: 2

Free Essay

Physics Test Paper

...[pic] |Level 1 Science | |90940 (1.1): Demonstrate understanding of aspects | |of mechanics | Credits: Four You should answer ALL parts of ALL questions in this booklet. If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly number the question. Check that this booklet has pages 2–13 in the correct order and that none of these pages is blank. YOU MUST HAND THIS BOOKLET TO YOUR TEACHER AT THE END OF THE ALLOTTED TIME. |For Assessor’s |Achievement Criteria | | |use only | | | |Achievement |Achievement |Achievement | | |with Merit |with Excellence ......

Words: 976 - Pages: 4

Free Essay

Physics

...Roger Truong Week 4 Physics Notes Experiment 1 * Rise and fall is pressure in the sound wave makes the flame move * The rise and fall in pressure makes the click sound * The rise and fall in the disturbance to what brings the sound to your ear * The square waves to what makes the flame move and bring the sound to your ear * The air molecules don’t move the disturbance does * For a 0.5 Hz your hear a click and the flame moves and resets * For 100 Hz the flame remains displaced and doesn’t recover * The transition from a click to a tone is between 20 and 50 Hz Reflection * Change in direction of a wave at an interference between two media wave returns into media from which it originated form. Wave Refraction * Change in direction of a wave when it passes from one medium to another caused by the different speeds of a wave * When water moves into different depths Wave Diffraction * Bending waves when they encounter an obstacle Absorption of waves * Reduction of energy in wave consumed by medium which it travels. * The main cause of absorption is Viscosity Interference * Two or more waves form coming together to make up a new wave Resonance * Tendency of a system to oscillate at a large amplitude at certain frequencies * Tendency to magnify a sound * The difference between an acoustic and electric guitar Wave Motion in Space and Time * Wave Motion in Space * Horizontal......

Words: 323 - Pages: 2

Free Essay

Physics Collisions

...Throughout our previous unit, we described the constant velocity of objects in motion. That laid the basis for this next unit, where we will be studying why and how the object moves the way it does, specifically the "push" or "pull" of force. The heavier cart in a same-direction elastic collision seems to push the lighter cart, which causes an increase in speed for the lighter cart. Although we may have brushed on the surface of movement, this unit will pave the path for further investigation on velocity as well as momentum. According to today's lab, it is possible to measure the mass of the carts and then multiple the mass by the velocity to determine momentum. These two things will be related to almost everything that we will be doing in physics, as how can we study how things move if we don't know how they're...

Words: 279 - Pages: 2

Free Essay

The Physics of Bull Riding

...Rodeo is a sport that came about by everyday work being made into competition. Every event in rodeo has a practical purpose; all but one that is. There is no practical reason to get on a bull; only the thrills, chills, and rush of excitement. It¡¦s more than a challenge between riders. It¡¦s a challenge between man and beast. Legendary cowboy Larry Mahan had an even different way of looking at it. He said, ¡§It¡¦s not a challenge with the animal but with the weakness in one¡¦s self¡¨. At any rate, it¡¦s all about the challenge. The challenge is simple; stay on the bull¡¦s back for eight seconds while keeping one hand fee from contact with the bull or your own body. Well it sounds simple anyways. Bull riding is a difficult challenge that involves overcoming many forces. Bulls will try just about anything to get a rider off their back. This includes raring, kicking, spinning, jumping, belly rolls, and some unintended moves such as stumbling and falling down. All the moves produce some sort of force the rider has to overcome. Fortunately ... in great shape. Much energy is spent in the course of a bull ride. The energy is equal to the force applied times the distance traveled. The forces are great and as fast as a bull can move they can cover a lot of ground in eight seconds. This adds up to a lot of energy being expended. Bull riding can be loads of fun. But it is definitely no...

Words: 261 - Pages: 2

Free Essay

Atomic Physics

...Constant and the Bohr Magneton 9/21/2015 Abstract In this lab, the Rydberg constant is found by observing the Balmer Series. With the experiment below, a Rydberg Constant was found to be 10116000 meters-1 with a 7.82% error. The Bohr Magneton is also found, and a value of 6.03*10-24 JT was obtained with a large error. The error can arise from each optical equipment having some fundamental error in its creation. Introduction With the help of atomic physics, quantum mechanics, and optics, the Rydberg constant and the Bohr magneton will be calculated in this experiment. The Rydberg constant is one of the most important constants in atomic physics because of its relation to other fundamental constants in atomic physics, such as the speed of light or Planck’s constant [1]. The Bohr Magneton tells us the magnetic moment of an electron by its angular momentum [2]. Attempting to calculate the Rydberg constant and the Bohr Magneton will inadvertently teach the basis of quantum mechanics, optics, and atomic physics. Atomic spectra of hydrogen, mercury, and helium will be studied in detail along with the Zeeman Effect. Theory In quantum mechanics, labeling often times helps discern descriptions of certain events. To describe the movement and trajectories of an electron in an atom, scientists use quantum numbers to label what is going on. The principal quantum number n, tells the energy level of the electron and the distance from the nucleus. The angular momentum......

Words: 4148 - Pages: 17