Research Article The Lattice Compatibility Theory LCT ...downloads.hindawi.com/journals/apc/2013/578686.pdf · Advances in Physical Chemistry BGO:Mn BSO:Mn BTO:Mn 30 25 20 15 10 5

Hindawi Publishing CorporationAdvances in Physical ChemistryVolume 2013 Article ID 578686 5 pageshttpdxdoiorg1011552013578686

Research ArticleThe Lattice Compatibility Theory LCTPhysical and Chemical Arguments fromthe Growth Behavior of Doped Compounds in terms ofBandgap Distortion and Magnetic Effects

K Boubaker

Ecole Superieure de Sciences et Techniques de Tunis (ESSTT) Universite de Tunis 63 Rue Sidi Jabeur Mahdia 5100 Tunisia

Correspondence should be addressed to K Boubaker mmbb11112000yahoofr

Received 21 January 2013 Revised 2 April 2013 Accepted 20 May 2013

Academic Editor Kenneth Ruud

Copyright copy 2013 K Boubaker This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Physical and chemical arguments for the recently discussed materials-related Lattice Compatibility Theory are presented Thediscussed arguments are based on some differences of Mn ions incorporation kinetics inside some compounds These differenceshave been evaluated and quantified in terms of alteration of bandgap edges magnetic patterns and Faraday effect

1 Introduction

Bismuth oxides are nanocrystalline fluorite-type materialswhich exhibit unexpected lattice expansion during dopingstagesThey are used in various domains such as transparentceramic glass microelectronics sensor technology opticalcoatings surface acoustic wave devices and gas sensing [1ndash9] Bismuth ternary oxides such as Bi

12SiO20 Bi4Ge3O12 and

Bi4Ti3O12 usually exhibit high oxide ionic conductivity and

hence can been used as high-efficiency electrolyte materialsfor several applications such as oxygen sensors and solidoxide fuel cells (SOFC) [7ndash10] Bi

4Ge3O12

(BGO Bismuthgermanate) is a high density scintillation inorganic oxidewithcubic eulytite structure It is used in detectors in particlephysics gamma pulse spectroscopy aerospace physics andnuclear medicine Bi

4Ti3O12

(BTO Bismuth titanate) is alayered Aurivillius phase perovskite ferroelectric compoundhaving a Curie temperature of about 675∘C In its monoclinicferroelectric state Bi

4Ti3O12

has been pointed at as a goodcandidate for use in nonvolatilememories thanks to its excel-lent fatigue resistance during repeated polarization reversalsunder electrical solicitation In some recent studies [11 12]manganese-doped bismuth oxides showed nearly 10 timesthe ionic conductivity of zirconia despite a low stability inreducing environments

In this study a support to the Lattice CompatibilityTheory LCT is presented in terms of alteration of bandgapedges magnetic patterns and Faraday effect The paper isorganized in the following way In Section 2 some relevantexperimental details along with main manganese-dopingfeatures are presented In Section 3 we present physicalparameters alteration analysis along with LCT principlesSection 4 is the conclusion

2 Samples Elaboration andMeasurement Techniques

Bi4Ti3O12

(BTO) Bi12SiO20

(BSO) and Bi4Ge3O12

(BGO)compounds have been prepared using the polymeric precur-sor and Czochralski [11ndash14] methods using titanium tetraiso-propoxide Bismuth acetate Bi

2O3 GeO

2and SiO

2as precur-

sors Complexation and pH adjustment were achieved usingwet ethylene glycol and ammonium hydroxide respectivelyMn-doping has been achieved using manganese carbonateMnCO

3and manganese oxide MnO

2in various proportions

Static magnetization and field dependence of magne-tization were measured at different applied fields in thetemperature range 2ndash350K with a SQUID magnetometer(QuantumDesign for 0ndash5 T field range) Measurements have

2 Advances in Physical Chemistry

been carried out as guides to determine zero field cooling(ZFC) molar susceptibility

Verdet coefficient 119881 measurement within the visiblespectral domain has been obtained using a Faraday rotatorwhich consists of a solenoid wrapped around a transparentdielectric material along with four symmetric coils whichproduce controlled AC magnetic fields The control unit wasequipped with a ldquoNew Focus Modelrdquo 8702 PCB mountablesingle-axis driver

Finally X-ray diffraction analysis of all prepared com-pounds was performed by a copper-source diffractometer(Analytical X Pert PROMPD) with the wavelength 120582 =

154056 A while optical absorption spectra were measuredon double-side polished parallel crystal plates using a SPM-2monochromator within accuracy of plusmn2 nm

3 Results and Discussion

31 Mn-Doping Patterns in terms of Bandgap Magnetizationand Faraday Effects In order to understand bandgap edgesalteration following doping agent insertion in host structuresUrbach energy 119864

119906has been determined for doped and

undoped samples through the equations

ln (120572 (ℎ])) = ln (1205720) +

ℎ]

119864119906

119864119906= 120572 (ℎ]) (

119889 [120572 (ℎ])]

119889 [ℎ]])

minus1

= ℎ[119889

119889](ln120572 (]))]

minus1

(1)

where 120572(ℎ]) represents for each sample the experimentallydeduced optical absorption profile

Urbach energy 119864119906is a measure of the inhomogenoeus

disorder and atomic scale dispersion inside structures as itindicates the width of the band tails of the localized statesin presence of defects (Figure 1) Its analytical formulation isdeduced by taking into account three components structuraldisorder carrier-phonon interaction and carrier-impurity

119864119906=

Structural disorder⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞1

2119896119861119880120579119863

+

Carrier-phonon interaction⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞

1198654120587211988521199024119898lowast1198713

119863

9radic31205762ℎ2

+

Carrier-impurity⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞

1198651015840 coth( 119865

10158401015840

2119896119861119879)

(2)

with Boltzmann constant 119880 lattice strain related with thestructural disorder 120579

119863 Debye temperature 119871

119863 Debye

length119898lowast Carrier effectivemass119885 impurity charge 119902 elec-tron charge 120576 static dielectric permittivity ℎ Planckrsquos con-stant and 119865 1198651015840 11986510158401015840 constants

The width of the localized states (band tail energy orUrbach energy 119864

119906) has been estimated from the slopes of the

plots of ln120572(]) versus energy ℎ] (Figure 2)Figure 3 reports the temperature-dependent zero field

cooling (ZFC)molar susceptibility 120594mol for BTO- BGO- andBSO- doped samples All the samples show clear transitionsfrom a paramagnetic (P) to a ferromagnetic (F) state For all

Density of states

Valence band

Intrinsiclevels

Conduction bandEner

gy

Ec

E

Defects

Wavevector

Figure 1 Urbach tailing and localized states in presence of defects

4

35

3

25

2

15

1

05

02 22 24 26 28 3

E (eV)

ln(120572)

BSO BTO BGOUndopedDoped

UndopedDoped

UndopedDoped

Figure 2 Plots of (ln120572(])) versus energy ℎ] (as guides for evaluat-ing 119864119906)

the considered samples saturation of the magnetisation wasreached by applying magnetic field up to 5 T The magneticmoment value per unit formula obtained frommagnetizationsaturation is in good agreement with the expected ones fromthe stoichiometric formula

Faraday effect (or Faraday rotation effect) is a magneto-optical phenomenon which was revealed in the beginningof the last century by Michael Faraday [15ndash18] and whichconsists of an interaction between light and a magnetic fieldinside a givenmedium [18 19] It causes a rotation of the planeof polarization which is linearly proportional to the compo-nent of themagnetic field in the direction of propagationTheFaraday effect is based on the notion of circular birefringencewhich causes a difference of propagation speed between leftand right circularly polarized waves

Advances in Physical Chemistry 3

BGOMn

BSOMnBTOMn

30

25

20

15

10

5

00 50 100 150 200 250 300

120594m

ol(e

mumiddot

mol

minus1)

T (K)

Figure 3 Zero field cooling (ZFC) molar susceptibility versus tem-perature for the doped samples

30 31 32

BGOMn BSOMn BTOMn

33 34 35 36 37 38 39 402120579 (∘)

Inte

nsity

(au

)

Figure 4 XRD diagrams of the prepared compounds

Faraday effect has been evaluated for the obtained sam-ples through the measurements of alterations of the Verdetcoefficient 119881 within the visible spectral domain This coeffi-cient [19] is deduced via the measurement of the polarisationrotating angle 120579 using the formula

119881 =1

119861119897120579 (3)

with 119861 applied magnetic field strength (in oersteds) and 119897light path length through the medium

Verdet coefficient119881 changes for doped andundoped sam-ples have been gathered in Table 1 XRD diagrams are alsogathered in Figure 4

32 Lattice CompatibilityTheory LCT Fundaments and Analy-sis Stability of Mn ions within host matrix does not occur in

Table 1 Values of Verdet coefficient for doped and undoped sam-ples

Sample Verdet coefficient (a u)

BSO Undoped 0052Mn-doped 0039

BTO Undoped 0041Mn-doped 0038

BGO Undoped 0053Mn-doped 0047

Bi

Bi

O

O

TiGe

Si

203 pm

890 pm

768 p

m

Figure 5 BTO and BGO lattices structure

the same way inside the three studied lattice structures (BSOBGO and BTO) The Lattice Compatibility Theory [20ndash23]tries to give a plausible understanding of this disparity start-ing from intrinsic doping-element lattice properties in com-parison to those of the host In the studied materials changesin the studied parameters have been associated to a Mn-doping-induced disorder in BSO matrices against a relativeunaltered stability of both BGO and BTO For explanationpurposes main lattice constants of Mn intrinsic lattice havebeen compared to those of BSO BGO and BTO (Figure 5)Consecutively a thorough study of BSO structures revealed a


Mn atom

Host

(a)

Mn atom

Host

(b)

Figure 6 Mn-element incorporation within host matrix (a) inter-stitial position (b) substitutional position

strong incompatibility with the Mn cubic lattice in terms ofboth bond length and incorporation kinetics (Figure 6)

Finally a possible explanation for the paradox of disparityof incorporation behaviors of doping agent is formulated asfollows

ldquothe stability of doping agents inside host struc-tures is favorized trough geometrical compati-bility expressed in terms of matching patterns

between doping agent intrinsic lattice and those ofthe hostrdquo

The many principles of this theory have been judged ingood agreement with results published in the recent literature[17ndash23]

4 Conclusion

The present study tries to give new arguments and fun-daments to the Lattice Compatibility Theory (LCT) Maininvestigations have carried out comparative studies of thebehavior of titanates (BTO) germanates (BGO) and sillenites(BSO) under transient-metal-doping Urbach tailing andFaraday effect along with lattice constants alterations havebeen compared and discussed Recoded results were in goodagreement with this theory A possible statement has beenformulated

ldquothe stability of doping agents inside host struc-tures is favorized trough geometrical compati-bility expressed in terms of matching patternsbetween doping agent intrinsic lattice and those ofthe hostrdquo

Nevertheless some additional investigationmay be need-ed in order to confirm validity and universality

References

[1] P C Joshi S B Krupanidhi andAMansingh ldquoRapid thermallyprocessed ferroelectric Bi

4Ti3O12thin filmsrdquo Journal of Applied

Physics vol 72 no 11 pp 5517ndash5519 1992[2] S E Cummins andL ECross ldquoElectrical and optical properties

of ferroelectric Bi4Ti3O12

single crystalsrdquo Journal of AppliedPhysics vol 39 no 5 7 pages 1968

[3] N F Mott Nobel Prize Lecture 1977[4] WW Li J J Zhu J DWu et al ldquoComposition and temperature

dependence of electronic and optical properties in manganesedoped tin dioxide films on quartz substrates prepared by pulsedlaser depositionrdquo ACS Applied Materials and Interfaces vol 2no 8 pp 2325ndash2332 2010

[5] H Kimura T Fukumura M Kawasaki K Inaba T HasegawaandHKoinuma ldquoRutile-type oxide-dilutedmagnetic semicon-ductor Mn-doped SnO

2rdquo Applied Physics Letters vol 80 no 1

pp 94ndash96 2002[6] S J Liu C Y Liu J Y Juang and H W Fang ldquoRoom-tem-

perature ferromagnetism in Zn and Mn codoped SnO2filmsrdquo

Journal of Applied Physics vol 105 no 1 4 pages 2009[7] B Liu C W Cheng R Chen Z X Shen H J Fan and H D

Sun ldquoFine structure of ultraviolet photoluminescence of tinoxide nanowiresrdquo Journal of Physical Chemistry C vol 114 no8 pp 3407ndash3410 2010

[8] G Sanon R Rup and A Mansingh ldquoBand-gap narrowing andband structure in degenerate tin oxide (SnO

2) filmsrdquo Physical

Review B vol 44 no 11 pp 5672ndash5680 1991[9] L F Jiang W Z Shen and Q X Guo ldquoTemperature depen-

dence of the optical properties of AlInNrdquo Journal of AppliedPhysics vol 106 no 1 8 pages 2009

[10] D Davazoglou ldquoDetermination of optical dispersion and filmthickness of semiconducting disordered layers by transmission


measurements application for chemically vapor deposited Siand SnO

2filmrdquo Applied Physics Letters vol 70 no 2 3 pages

1997[11] S P S Badwal andK Foger ldquoMaterials for solid oxide fuel cellsrdquo

Materials Forum vol 21 pp 187ndash224 1997[12] W Schafer A Koch U Herold-Schmidt and D Stolten ldquoMate-

rials interfaces and production techniques for planar solidoxide fuel cellsrdquo Solid State Ionics vol 86ndash88 no 2 pp 1235ndash1239 1996

[13] W Wardzynski H Szymczak K Pataj T Lukasiewicz and JZmija ldquoLight induced charge transfer processes in Cr dopedBi12GeO20and Bi

12SiO20single crystalsrdquo Journal of Physics and

Chemistry of Solids vol 43 no 8 pp 767ndash769 1982[14] H Chen W Zhu E Kaxiras and Z Zhang ldquoOptimization of

Mn doping in group-IV-based dilute magnetic semiconductorsby electronic codopantsrdquo Physical Review B vol 79 no 23 13pages 2009

[15] M Bass Handbook of Optics vol 2 McGraw-Hill 2nd edition1995

[16] D A VanBaak ldquoResonant Faraday rotation as a probe of atomicdispersionrdquo American Journal of Physics vol 64 no 6 p 7241996

[17] C D Hodgman Handbook of Chemistry and Physics vol 2Chemical Rubber Publishing 35th edition 1953

[18] J H van der Merwe ldquoStrain relaxation in epitaxial overlayersrdquoJournal of Electronic Materials vol 20 no 10 pp 793ndash803 1991

[19] M Ichimura and J Narayan ldquoAtomistic study of dislocationnucleation in Ge(001)Si heterostructusesrdquo Philosophical Mag-azine A vol 72 no 2 pp 281ndash295 1995

[20] P Petkova and K Boubaker ldquoThe Lattice Compatibility Theory(LCT) an attempt to explain Urbach tailing patterns in copper-doped bismuth sillenites (BSO) and germanates (BGO)rdquo Jour-nal of Alloys and Compounds vol 546 pp 176ndash179 2013

[21] K Boubaker ldquoPreludes to the lattice compatibility theory LCTurbach tailing controversial behavior in some nanocom-poundsrdquo ISRN Nanomaterials vol 2012 Article ID 173198 4pages 2012

[22] K Boubaker ldquoThe lattice compatibility theory arguments forrecorded I-III-O

2ternary oxide ceramics instability at low

temperatures beside ternary telluride and sulphide ceramicsrdquoJournal of Ceramics vol 2013 Article ID 734015 6 pages 2013

[23] K BoubakerM Amlouk Y Louartassi andH Labiadh ldquoAboutunexpected crystallization behaviors of some ternary oxideand sulfide ceramics within lattice compatibility theory LCTframeworkrdquo Journal of the Australian Ceramics Society vol 49no 1 pp 115ndash117 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


been carried out as guides to determine zero field cooling(ZFC) molar susceptibility

Verdet coefficient 119881 measurement within the visiblespectral domain has been obtained using a Faraday rotatorwhich consists of a solenoid wrapped around a transparentdielectric material along with four symmetric coils whichproduce controlled AC magnetic fields The control unit wasequipped with a ldquoNew Focus Modelrdquo 8702 PCB mountablesingle-axis driver

Finally X-ray diffraction analysis of all prepared com-pounds was performed by a copper-source diffractometer(Analytical X Pert PROMPD) with the wavelength 120582 =

154056 A while optical absorption spectra were measuredon double-side polished parallel crystal plates using a SPM-2monochromator within accuracy of plusmn2 nm

3 Results and Discussion

31 Mn-Doping Patterns in terms of Bandgap Magnetizationand Faraday Effects In order to understand bandgap edgesalteration following doping agent insertion in host structuresUrbach energy 119864

119906has been determined for doped and

undoped samples through the equations

ln (120572 (ℎ])) = ln (1205720) +

ℎ]

119864119906

119864119906= 120572 (ℎ]) (

119889 [120572 (ℎ])]

119889 [ℎ]])

minus1

= ℎ[119889

119889](ln120572 (]))]

minus1

(1)

where 120572(ℎ]) represents for each sample the experimentallydeduced optical absorption profile

Urbach energy 119864119906is a measure of the inhomogenoeus

disorder and atomic scale dispersion inside structures as itindicates the width of the band tails of the localized statesin presence of defects (Figure 1) Its analytical formulation isdeduced by taking into account three components structuraldisorder carrier-phonon interaction and carrier-impurity

119864119906=

Structural disorder⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞1

2119896119861119880120579119863

+

Carrier-phonon interaction⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞

1198654120587211988521199024119898lowast1198713

119863

9radic31205762ℎ2

+

Carrier-impurity⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞

1198651015840 coth( 119865

10158401015840

2119896119861119879)

(2)

with Boltzmann constant 119880 lattice strain related with thestructural disorder 120579

119863 Debye temperature 119871

119863 Debye

length119898lowast Carrier effectivemass119885 impurity charge 119902 elec-tron charge 120576 static dielectric permittivity ℎ Planckrsquos con-stant and 119865 1198651015840 11986510158401015840 constants

The width of the localized states (band tail energy orUrbach energy 119864

119906) has been estimated from the slopes of the

plots of ln120572(]) versus energy ℎ] (Figure 2)Figure 3 reports the temperature-dependent zero field

cooling (ZFC)molar susceptibility 120594mol for BTO- BGO- andBSO- doped samples All the samples show clear transitionsfrom a paramagnetic (P) to a ferromagnetic (F) state For all

Density of states

Valence band

Intrinsiclevels

Conduction bandEner

gy

Ec

E

Defects

Wavevector

Figure 1 Urbach tailing and localized states in presence of defects

4

35

3

25

2

15

1

05

02 22 24 26 28 3

E (eV)

ln(120572)

BSO BTO BGOUndopedDoped

UndopedDoped

UndopedDoped

Figure 2 Plots of (ln120572(])) versus energy ℎ] (as guides for evaluat-ing 119864119906)

the considered samples saturation of the magnetisation wasreached by applying magnetic field up to 5 T The magneticmoment value per unit formula obtained frommagnetizationsaturation is in good agreement with the expected ones fromthe stoichiometric formula

Faraday effect (or Faraday rotation effect) is a magneto-optical phenomenon which was revealed in the beginningof the last century by Michael Faraday [15ndash18] and whichconsists of an interaction between light and a magnetic fieldinside a givenmedium [18 19] It causes a rotation of the planeof polarization which is linearly proportional to the compo-nent of themagnetic field in the direction of propagationTheFaraday effect is based on the notion of circular birefringencewhich causes a difference of propagation speed between leftand right circularly polarized waves


BGOMn

BSOMnBTOMn

30

25

20

15

10

5

00 50 100 150 200 250 300

120594m

ol(e

mumiddot

mol

minus1)

T (K)


30 31 32

BGOMn BSOMn BTOMn

33 34 35 36 37 38 39 402120579 (∘)

Inte

nsity

(au

)



119881 =1

119861119897120579 (3)









Bi

Bi

O

O

TiGe

Si

203 pm

890 pm

768 p

m




Mn atom

Host

(a)

Mn atom

Host

(b)







4 Conclusion




References

















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


BGOMn

BSOMnBTOMn

30

25

20

15

10

5

00 50 100 150 200 250 300

120594m

ol(e

mumiddot

mol

minus1)

T (K)


30 31 32

BGOMn BSOMn BTOMn

33 34 35 36 37 38 39 402120579 (∘)

Inte

nsity

(au

)



119881 =1

119861119897120579 (3)









Bi

Bi

O

O

TiGe

Si

203 pm

890 pm

768 p

m




Mn atom

Host

(a)

Mn atom

Host

(b)







4 Conclusion




References

















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Mn atom

Host

(a)

Mn atom

Host

(b)







4 Conclusion




References

















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Documents

Research Article The Lattice Compatibility Theory LCT ...downloads.hindawi.com/journals/apc/2013/578686.pdf · Advances in Physical Chemistry BGO:Mn BSO:Mn BTO:Mn 30 25 20 15 10 5