Dielectric MaterialsDielectric Materials

Chemistry 754Chemistry 754Solid State Chemistry Solid State Chemistry

Lecture #27Lecture #27June 4, 2002June 4, 2002

ReferencesReferencesA.R. WestA.R. West – “ – “Solid State Chemistry and it’s Solid State Chemistry and it’s

ApplicationsApplications”, Wiley (1984)”, Wiley (1984)

R.H. MitchellR.H. Mitchell – “Perovskites: Modern & Ancient ”, – “Perovskites: Modern & Ancient ”, Almaz Press, (www.almazpress.com) (2002)Almaz Press, (www.almazpress.com) (2002)

P. Shiv Halasyamani & K.R. PoeppelmeierP. Shiv Halasyamani & K.R. Poeppelmeier – – “Non-centrosymmetric Oxides”, “Non-centrosymmetric Oxides”, Chem. MaterChem. Mater. . 1010, 2753-2769 (1998)., 2753-2769 (1998).

M. Kunz & I.D. BrownM. Kunz & I.D. Brown – “Out-of-center Distortions – “Out-of-center Distortions around Octahedrally Coordinated daround Octahedrally Coordinated d00 Transition Transition Metals”, Metals”, J. Solid State Chem.J. Solid State Chem. 115115, 395-406 , 395-406 (1995).(1995).

A. Safari, R.K. Panda, V.F. Janas (Dept. of Ceramics, Rutgers University) http://www.rci.rutgers.edu/~ecerg/projects/ferroelectric.html

Dielectric ConstantDielectric ConstantIf you apply an electric field, E, across a material the charges in the If you apply an electric field, E, across a material the charges in the material will respond in such a way as to reduce (shield) the field material will respond in such a way as to reduce (shield) the field

experienced within the material, D (electric displacement)experienced within the material, D (electric displacement)

D = D = E = E = 00E + P = E + P = 00E + E + 00eeE = E = 00(1+(1+ee)E)E

where where 00 is the dielctric permitivity of free space (8.85 x 10is the dielctric permitivity of free space (8.85 x 101212 C C22/N-m/N-m22), P ), P is the polarization of the material, and is the polarization of the material, and ee is the electric susceptibility. is the electric susceptibility.

The relative permitivity or dielectric constant of a material is defined as:The relative permitivity or dielectric constant of a material is defined as:

rr = = 00 = 1+ = 1+ee

When evaluating the dielectric properties of materials it is this quantity When evaluating the dielectric properties of materials it is this quantity we will use to quantify the response of a material to an applied electric we will use to quantify the response of a material to an applied electric

field.field.

Contributions to Contributions to PolarizabilityPolarizability

= = ee + + ii + + dd + + ss

1. Electronic Polarizability (1. Electronic Polarizability (ee))Polarization of localized electronsPolarization of localized electrons

2. Ionic Polarizability (2. Ionic Polarizability (ii))Displacement of ionsDisplacement of ions

3. Dipolar Polarizability (3. Dipolar Polarizability (dd))Reorientation of polar moleculesReorientation of polar molecules

4. Space Charge Polarizability 4. Space Charge Polarizability ((ss))

Long range charge migrationLong range charge migration

Polarizability Polarizability (() increases) increases

Response Response Time Time

Increases Increases (slower (slower

response)response)

Frequency DependenceFrequency DependenceReorientation of the dipoles in response to an electric field is characterized by Reorientation of the dipoles in response to an electric field is characterized by a relaxation time, a relaxation time, . The relaxation time varies for each of the various . The relaxation time varies for each of the various contributions to the polarizability:contributions to the polarizability:

1. Electronic Polarizability (1. Electronic Polarizability (ee))Response is fast, Response is fast, is small is small

2. Ionic Polarizability (2. Ionic Polarizability (ii))Response is slowerResponse is slower

3. Dipolar Polarizability (3. Dipolar Polarizability (dd))Response is still slowerResponse is still slower

4. Space Charge Polarizability (4. Space Charge Polarizability (ss))Response is quite slow, Response is quite slow, is large is large

AudiofrequenciesAudiofrequencies (~ 10 (~ 1033 Hz) Hz) = = ee++ii++dd++ss

RadiofrequenciesRadiofrequencies (~ 10 (~ 1066 Hz) Hz) ( (ss 0) 0) = = ee++ii++dd

Microwave frequenciesMicrowave frequencies (~ 10 (~ 1099 Hz) Hz) ( (ss, , dd 0) 0) = = ee++ii

Visible/UV frequenciesVisible/UV frequencies (~ 10 (~ 101212 Hz) Hz) ( (ss, , dd, , ii 0) 0) = = ee

Dielectric LossDielectric Loss

When the relaxation time is much When the relaxation time is much fasterfaster than the than the frequency of the applied electric field, frequency of the applied electric field, polarization occurs instantaneouslypolarization occurs instantaneously..

When the relaxation time is much When the relaxation time is much slowerslower than the than the frequency of the applied electric field, frequency of the applied electric field, no no polarization (of that type) occurspolarization (of that type) occurs..

When the relaxation time and the frequency of the When the relaxation time and the frequency of the applied field are similar, a phase lag occurs and applied field are similar, a phase lag occurs and energy is absorbed. This is called dielectric loss, it energy is absorbed. This is called dielectric loss, it is normally quantified by the relationshipis normally quantified by the relationship

tan tan = = rr”/”/rr’’

where where rr’ is the real part of the dielectric constant and ’ is the real part of the dielectric constant and rr” is ” is the imaginary part of the dielectric constant.the imaginary part of the dielectric constant.

Frequency DependenceFrequency Dependence()

0

log()

Microwave

s

I R

U V

die

ie

e only

tan (Loss)

r (Dielectric Const.)

Ionic Polarization and Ionic Polarization and FerroelectricityFerroelectricity

Most dielectric materials are insulating (no conductivity of Most dielectric materials are insulating (no conductivity of either electrons or ions) dense solids (no molecules that can either electrons or ions) dense solids (no molecules that can reorient). Therefore, the polarizability must come from either reorient). Therefore, the polarizability must come from either ionic and electronic polarizability. Of these two ionic ionic and electronic polarizability. Of these two ionic polarizability can make the largest contribution, particularly in polarizability can make the largest contribution, particularly in a class of solids called ferroelectrics. The ionic polarizability a class of solids called ferroelectrics. The ionic polarizability will be large, and a ferroelectric material will result, when the will be large, and a ferroelectric material will result, when the following two conditions are met:following two conditions are met:

1.1. Certain ions in the structure displace in response to Certain ions in the structure displace in response to the application of an external electric field. the application of an external electric field. Typically this requires the presence of certain types Typically this requires the presence of certain types of ions such as dof ions such as d00 or s or s22pp00 cations. cations.

2.2. The displacements line up in the same direction (or The displacements line up in the same direction (or at least they do not cancel out). This cannot happen at least they do not cancel out). This cannot happen if the crystal structure has an inversion center.if the crystal structure has an inversion center.

3.3. The displacements do not disappear when the The displacements do not disappear when the electric field is removed.electric field is removed.

What is a FerroelectricWhat is a FerroelectricA ferroelectric material develops a spontaneous polarization A ferroelectric material develops a spontaneous polarization (builds up a charge) in response to an external electric field. (builds up a charge) in response to an external electric field.

•The polarization does The polarization does not go away when the not go away when the external field is external field is removed.removed.

•The direction of the The direction of the polarization is polarization is reversible.reversible.

Applications of Ferroelectric MaterialsApplications of Ferroelectric Materials•Multilayer capacitorsMultilayer capacitors•Non-volatile FRAM (Ferroelectric Random Access Non-volatile FRAM (Ferroelectric Random Access Memory)Memory)

22ndnd Order Jahn-Teller Order Jahn-Teller DistortionsDistortions

Occurs when the HOMO-LUMO gap is small and there is a symmetry Occurs when the HOMO-LUMO gap is small and there is a symmetry allowed distortion which gives rise to mixing between the two. This allowed distortion which gives rise to mixing between the two. This distortion is favored because it stabilizes the HOMO, while destabilizing distortion is favored because it stabilizes the HOMO, while destabilizing the LUMO. Second order Jahn-Teller Distortions are typically observed the LUMO. Second order Jahn-Teller Distortions are typically observed for two classes of cations.for two classes of cations.

1.1. Octahedrally coordinated high valent dOctahedrally coordinated high valent d00 cations (i.e. Ti cations (i.e. Ti4+4+, , NbNb5+5+, W, W6+6+, Mo, Mo6+6+). ).

– BaTiOBaTiO33, KNbO, KNbO33, WO, WO33

– Increasingly favored as the HOMO-LUMO splitting Increasingly favored as the HOMO-LUMO splitting decreases (covalency of the M-O bonds increases)decreases (covalency of the M-O bonds increases)

2.2. Cations containing filled valence s shells (SnCations containing filled valence s shells (Sn2+2+, Sb, Sb3+3+, Pb, Pb2+2+, Bi, Bi3+3+))

– Red PbO, TlI, SnO, BiRed PbO, TlI, SnO, Bi44TiTi33OO1212, Ba, Ba33BiBi22TeOTeO99

– SOJT Distortion leads to development of a stereoactive SOJT Distortion leads to development of a stereoactive electron-lone pair.electron-lone pair.

Octahedral dOctahedral d00 Cation Cation

point(kx=ky=0)

non-bonding

In the cubic perovskite structure In the cubic perovskite structure the bottom of the conduction band the bottom of the conduction band is non-bonding M tis non-bonding M t2g2g, and the top of , and the top of the valence band is non-bonding O the valence band is non-bonding O 2p. If the symmetry is lowered the 2p. If the symmetry is lowered the two states can mix, lowering the two states can mix, lowering the energy of the occupied VB states energy of the occupied VB states

and raising the energy of the and raising the energy of the empty CB states. This is a 2empty CB states. This is a 2ndnd

order JT dist.order JT dist.

22ndnd Order JT Distortion Order JT Distortion Band PictureBand Picture

M t2g(*)

EF

DOS

O 2p

M t2g(*)

EF

DOS

Overlap at Overlap at is non-is non-

bonding by bonding by symmetrysymmetry

Overlap at Overlap at is is slightly slightly

antibonding in antibonding in the CB & slightly the CB & slightly bonding in the bonding in the

VB.VB.

The 2The 2ndnd order JT distortion reduces the order JT distortion reduces the symmetry and widens the band gap. It is symmetry and widens the band gap. It is the driving force for stabilizing ionic shifts. the driving force for stabilizing ionic shifts. The stabilization disappears by the time The stabilization disappears by the time you get to a dyou get to a d11 TM ion. Hence, ReO TM ion. Hence, ReO33 is is

cubic.cubic.See Wheeler et al. J. Amer. Chem. Soc. 108, 2222 (1986), and/orT. Hughbanks, J. Am. Chem. Soc. 107, 6851-6859 (1985).

What Determines the What Determines the Orientation of the Cation Orientation of the Cation

Displacements?Displacements?

Tetragonal Tetragonal BaTiOBaTiO33

d=2.21d=2.21ÅÅs = s = 0.340.34

d=1.83d=1.83ÅÅs = s = 0.960.96

MoOMoO33

d=1.67d=1.67ÅÅs = s = 1.901.90

d=2.33d=2.33ÅÅs = s = 0.320.32d=1.95d=1.95

ÅÅs = s = 0.900.90The 2The 2ndnd Order JT effect at the Order JT effect at the

metal only dictates that a metal only dictates that a distortion should occur. It doesn’t distortion should occur. It doesn’t

tell how the displacements will tell how the displacements will order. That depends upon: order. That depends upon:

(i)(i) the valence the valence requirements at the anion requirements at the anion (i.e. 2 short or 2 long bonds to (i.e. 2 short or 2 long bonds to same anion is unfavorable),same anion is unfavorable),

(ii)(ii) cation-cation repulsions cation-cation repulsions (high oxidation state cations (high oxidation state cations

prefer to move away from each prefer to move away from each other)other)

See Kunz & Brown J. Solid State Chem.J. Solid State Chem. 115115, 395-406 (1995)., 395-406 (1995).

Why is BaTiOWhy is BaTiO33 Ferroelectric Ferroelectric

•BaBa2+2+ is larger than the vacancy in the is larger than the vacancy in the octahedral network tolerance factor > 1.octahedral network tolerance factor > 1.

•This expands the octahedron, which This expands the octahedron, which leads to a shift of Tileads to a shift of Ti4+4+ toward one of the toward one of the corners of the octahedron.corners of the octahedron.

•The direction of the shift can be altered The direction of the shift can be altered through application of an electric field.through application of an electric field.

BaTiOBaTiO33 Phase Phase TransitionsTransitions

Cubic (Pm3m)Cubic (Pm3m)T > 393 KT > 393 K

Ti-O Distances Ti-O Distances (Å)(Å)

662.002.00Tetragonal (P4mm)Tetragonal (P4mm)273 K < T < 393 K273 K < T < 393 KTi-O Distances (Å)Ti-O Distances (Å) 1.83, 41.83, 42.00, 2.212.00, 2.21

Toward a cornerToward a corner

Orthorhombic Orthorhombic (Amm2)(Amm2)

183 K < T < 273 K183 K < T < 273 KTi-O Distances (Å)Ti-O Distances (Å)

221.87, 21.87, 22.00, 2.00, 222.172.17

Toward an edgeToward an edgeRhombohedral Rhombohedral (R3m)(R3m)

183 K < T < 273 K183 K < T < 273 KTi-O Distances (Å)Ti-O Distances (Å)

331.88, 31.88, 32.132.13Toward a faceToward a face

In the cubic structure BaTiOIn the cubic structure BaTiO33 is is paraelectric. That is to say that paraelectric. That is to say that

the orientations of the ionic the orientations of the ionic displacements are not ordered displacements are not ordered

and dynamic.and dynamic.

Below 393 K BaTiOBelow 393 K BaTiO33 becomes becomes ferroelectric and the ferroelectric and the

displacement of the Tidisplacement of the Ti4+4+ ions ions progressively displace upon progressively displace upon

cooling.cooling.

See Kwei et al. J. Phys. Chem. 97, 2368 (1993),

Structure, Bonding and PropertiesStructure, Bonding and PropertiesGiven what you know about 2Given what you know about 2ndnd order JT distortions and order JT distortions and ferroelectric distortions can you explain the following physical ferroelectric distortions can you explain the following physical properties.properties.

BaTiOBaTiO33 : : Ferroelectric (TFerroelectric (TCC ~ 130°C, ~ 130°C, rr > 1000) > 1000)–

SrTiOSrTiO33 : : Insulator, Normal dielectric (Insulator, Normal dielectric (rr ~ x) ~ x)–

PbTiOPbTiO33 : : Ferroelectric (TFerroelectric (TCC ~ 490°C) ~ 490°C)–

BaSnOBaSnO3 3 :: Insulator, Normal dielectric (Insulator, Normal dielectric (rr ~ x) ~ x)–

KNbOKNbO33 : : Ferroelectric (TFerroelectric (TCC ~ x) ~ x)–

KTaOKTaO33 : : Insulator, Normal dielectric (Insulator, Normal dielectric (rr ~ x) ~ x)–

Structure, Bonding and PropertiesStructure, Bonding and PropertiesBaTiOBaTiO33 : : Ferroelectric (TFerroelectric (TCC ~ 130°C, ~ 130°C, rr > 1000) > 1000)

– BaBa2+2+ ion stretches the octahedra (Ti-O dist. ~ 2.00Å), this lowers energy of ion stretches the octahedra (Ti-O dist. ~ 2.00Å), this lowers energy of CB (LUMO) and stabilizes SOJT dist.CB (LUMO) and stabilizes SOJT dist.

SrTiOSrTiO33 : : Insulator, Normal dielectric (Insulator, Normal dielectric (rr ~ x) ~ x)– SrSr2+2+ ion is a good fit (Ti-O dist. ~ 1.95Å), this compound is close to a ion is a good fit (Ti-O dist. ~ 1.95Å), this compound is close to a

ferroelectric instability and is called a quantum paraelectric.ferroelectric instability and is called a quantum paraelectric.

PbTiOPbTiO33 : : Ferroelectric (TFerroelectric (TCC ~ 490°C) ~ 490°C)– Displacements of both TiDisplacements of both Ti4+4+ and Pb and Pb2+2+ (6s (6s226p6p00 cation) stabilize ferroelectricity cation) stabilize ferroelectricity

BaSnOBaSnO3 3 :: Insulator, Normal dielectric (Insulator, Normal dielectric (rr ~ x) ~ x)– Main group SnMain group Sn4+4+ has no low lying t has no low lying t2g2g orbitals and no tendency toward SOJT orbitals and no tendency toward SOJT

dist.dist.

KNbOKNbO33 : : Ferroelectric (TFerroelectric (TCC ~ x) ~ x)– Behavior is very similar to BaTiOBehavior is very similar to BaTiO33

KTaOKTaO33 : : Insulator, Normal dielectric (Insulator, Normal dielectric (rr ~ x) ~ x)– Ta 5d orbitals are more electropositive and have a larger spatial extent Ta 5d orbitals are more electropositive and have a larger spatial extent

than Nb 4d orbitals (greater spatial overlap with O 2p), both effects raise the than Nb 4d orbitals (greater spatial overlap with O 2p), both effects raise the energy of the tenergy of the t2g2g LUMO, diminishing the driving force for a SOJT dist. LUMO, diminishing the driving force for a SOJT dist.

22ndnd Order Jahn-Teller Order Jahn-Teller Distortions with sDistortions with s22pp00 Main Main

Group CationsGroup CationsFactFact: : Main group cations that retain 2 valence electrons (i.e. TlMain group cations that retain 2 valence electrons (i.e. Tl++, Pb, Pb2+2+, ,

BiBi3+3+, Sn, Sn2+2+, Sb, Sb3+3+, Te, Te4+4+, Ge, Ge2+2+, As, As3+3+, Se, Se4+4+, ect.) tend to prefer distorted , ect.) tend to prefer distorted environments. environments.

M-X Bonding:M-X Bonding: The occupied cation s orbitals have an antibonding The occupied cation s orbitals have an antibonding interaction with the surrounding ligands. interaction with the surrounding ligands.

Symmetric CoordinationSymmetric Coordination: The occupied M s and empty M p orbitals : The occupied M s and empty M p orbitals are not allowed by symmetry to mix.are not allowed by symmetry to mix.

Distorted CoordinationDistorted Coordination: : The lower symmetry allows mixing of s The lower symmetry allows mixing of s and at least one p orbital on the metal. This lowers the energy of the and at least one p orbital on the metal. This lowers the energy of the occupied orbital, which now forms an orbital which is largely non-occupied orbital, which now forms an orbital which is largely non-bonding and has strong mixed sp character. It is generally referred to bonding and has strong mixed sp character. It is generally referred to as a stereoactive electron lone pair (for example as seen in NHas a stereoactive electron lone pair (for example as seen in NH33).).

Tetrahedral CoordinationTetrahedral Coordination (T (Tdd): s-orbital = ): s-orbital = aa11, p-orbitals = , p-orbitals = tt22

Trigonal Pyramidal Coord.Trigonal Pyramidal Coord. (C (C3v3v): s-orbital = ): s-orbital = aa11, p-orbitals = , p-orbitals =

e,e,aa11

Octahedral CoordinationOctahedral Coordination (O (Ohh): s-orbital = ): s-orbital = aa1g1g, p-orbitals = , p-orbitals = tt1u1u

Square Pyramidal Coord.Square Pyramidal Coord. (C (C4v4v): s-orbital = ): s-orbital = aa11, p-orbitals = , p-orbitals =

e,e,aa11

Some Examples sSome Examples s22pp00 SOJT SOJT

Red PbORed PbODistorted Distorted

CsClCsCl

CsGeBrCsGeBr33

Distorted Distorted PerovskitePerovskite

SbClSbCl33

Trig. Trig. Pyramidal Pyramidal

SbSb3+3+

Cooperative SOJT DistortionsCooperative SOJT Distortions

Tetragonal PbTiOTetragonal PbTiO33

TTCC = 490°C = 490°C

Ti displacement = 0.323 Ti displacement = 0.323 ÅÅ

Ti-O short = 1.77 ÅTi-O short = 1.77 ÅTi-O long = 2.39 ÅTi-O long = 2.39 Å

PbPb2+2+ displacement = displacement = 0.48 Å0.48 Å

Tetragonal BaTiOTetragonal BaTiO33

TTCC = 120°C = 120°C

Ti displacement = 0.125 Ti displacement = 0.125 ÅÅ

Ti-O short = 1.83 ÅTi-O short = 1.83 ÅTi-O long = 2.21 ÅTi-O long = 2.21 Å

BaBa2+2+ displacement = displacement = 0.067 Å0.067 Å

Related Dielectric Related Dielectric PhenomenaPhenomena

PyroelectricityPyroelectricity – Similar to ferroelectricity, but the – Similar to ferroelectricity, but the ionic shifts which give rise to spontaneous ionic shifts which give rise to spontaneous polarization cannot be reversed by an external field polarization cannot be reversed by an external field (i.e. ZnO). Called a pyroelectric because the (i.e. ZnO). Called a pyroelectric because the polarization changes gradually as you increase the polarization changes gradually as you increase the temperature.temperature.

AntiferroelectrictyAntiferroelectricty – Each ion which shifts in a – Each ion which shifts in a given direction is accompanied by a shift of an ion of given direction is accompanied by a shift of an ion of the same type in the opposite direction (i.e. PbZrOthe same type in the opposite direction (i.e. PbZrO33))

Piezoelectricity Piezoelectricity – A spontaneous polarization – A spontaneous polarization develops under the application of a mechanical develops under the application of a mechanical stress, and vice-versa (i.e. quartz)stress, and vice-versa (i.e. quartz)

PZT Phase DiagramPZT Phase DiagramPb(ZrPb(Zr1-x1-xTiTixx)O)O33 (PZT) is probably the most important piezoelectric (PZT) is probably the most important piezoelectric material. The piezoelectric properties are optimal near x = 0.5, material. The piezoelectric properties are optimal near x = 0.5, This composition is near the morphotropic phase boundary, This composition is near the morphotropic phase boundary, which separates the tetragonal and rhombohedral phases.which separates the tetragonal and rhombohedral phases.

Hysteresis Loops in PbZrHysteresis Loops in PbZr1-1-

xxTiTixxOO33

PbTiOPbTiO33

FerroelectriFerroelectricc

TetragonalTetragonal

PbZrPbZr1-x1-xTiTixxOO33

x ~ 0.3x ~ 0.3FerroelectriFerroelectri

ccRhombohedRhombohed

ralral

PbZrOPbZrO33

AntiferroelectAntiferroelectricric

MonoclinicMonoclinic

PbZrPbZr1-x1-xTiTixxOO33

ParaelectricParaelectricCubicCubic

An antiferroelectic material does not polarize much for low applied fields, An antiferroelectic material does not polarize much for low applied fields, but higher applied fields can lead to a polarization loop reminiscent of a but higher applied fields can lead to a polarization loop reminiscent of a ferroelectric. The combination gives split hysteresis loops as shown above. ferroelectric. The combination gives split hysteresis loops as shown above.

What is PiezoelectricityWhat is Piezoelectricity

A piezoelectric material converts mechanical (strain) A piezoelectric material converts mechanical (strain) energy to electrical energy and vice-versa. energy to electrical energy and vice-versa.

Voltage InVoltage In

Mechanical Signal Mechanical Signal OutOut

i.e. Speakeri.e. Speaker

Mechanical Mechanical Signal InSignal In

Voltage OutVoltage Out

i.e. Microphonei.e. Microphone

Applications of Applications of PiezoelectricsPiezoelectrics

Piezo-ignition systemsPiezo-ignition systems Pressure gauges and transducersPressure gauges and transducers Ultrasonic imaging Ceramic Ultrasonic imaging Ceramic

phonographic cartridgephonographic cartridge Small, sensitive microphonesSmall, sensitive microphones Piezoelectric actuators for precisely Piezoelectric actuators for precisely

controlling movements (as in an AFM)controlling movements (as in an AFM) Powerful sonarPowerful sonar

Symmetry Constraints and Symmetry Constraints and Dielectric PropertiesDielectric Properties

Dielectric properties can only be found with certain crystal Dielectric properties can only be found with certain crystal symmetries symmetries

PiezoelectricPiezoelectricDo not posses an inversion center (noncentrosymmetric)Do not posses an inversion center (noncentrosymmetric)

Ferroelectric/PyroelectricFerroelectric/PyroelectricDo not posses an inversion center (noncentrosymmetric)Do not posses an inversion center (noncentrosymmetric)Posses a Unique Polar AxisPosses a Unique Polar Axis

The 32 point groups can be divided up in the following manner The 32 point groups can be divided up in the following manner (color coded according to crystal system: triclinic, monoclinic, etc.). (color coded according to crystal system: triclinic, monoclinic, etc.). PiezoelectricPiezoelectric

1, 1, 2, m,2, m, 222, mm2,222, mm2, 4, -4, 422, 4mm, 42m, 4, -4, 422, 4mm, 42m, 3, 32, 3m,3, 32, 3m, 6, -6, 6, -6, 622, 6mm, 6m2, 622, 6mm, 6m2, 23, 43m23, 43m

Ferroelectric/PyroelectricFerroelectric/Pyroelectric 1, 1, 2, m,2, m, mm2,mm2, 4, 4mm, 4, 4mm, 3, 3m,3, 3m, 6, 6mm6, 6mm

Centrosymmetric (Neither)Centrosymmetric (Neither)-1-1, , 2/m2/m, mmm, , mmm, 4/m, 4/mmm4/m, 4/mmm, , -3, 3/m-3, 3/m, 6/m, 6/mmm, , 6/m, 6/mmm, m3, m3mm3, m3m

Electronic PolarizabilityElectronic PolarizabilityLet’s limit our discussion to insulating extended solids. In the Let’s limit our discussion to insulating extended solids. In the absence of charge carriers (ions or electrons) or molecules, we absence of charge carriers (ions or electrons) or molecules, we only need to consider the electronic and ionic polarizabilities.only need to consider the electronic and ionic polarizabilities.

The presence of an electric field polarizes the electron The presence of an electric field polarizes the electron distribution about an atom creating a dipole moment, distribution about an atom creating a dipole moment,

=qx=qxThe dipole moment per unit volume, P, is then given byThe dipole moment per unit volume, P, is then given by

P = nP = nmmwhere nwhere nmm is the number of atoms per unit volume. is the number of atoms per unit volume.

- qq

+ qq

EEwithout without fieldfield

with with fieldfield xx

Microwave DielectricsMicrowave Dielectrics

Were not talking microwave ovens here, rather Were not talking microwave ovens here, rather communication systems which operate in the communication systems which operate in the

microwave region:microwave region:

– Ultra high frequency TV (470-870 MHz)Ultra high frequency TV (470-870 MHz)– Satellite TV (4 GHz)Satellite TV (4 GHz)– Mobile (Cellular) Phones (900-1800 MHz)Mobile (Cellular) Phones (900-1800 MHz)

All such systems depend upon a bandpass filter All such systems depend upon a bandpass filter that selects a narrow frequency range and blocks that selects a narrow frequency range and blocks

all others. These filters are constructed from all others. These filters are constructed from ceramics with desirable dielectric properties.ceramics with desirable dielectric properties.

Microwave Dielectrics-Microwave Dielectrics-PropertiesProperties

The following dielectric properties are intimately related to The following dielectric properties are intimately related to it’s performanceit’s performance

Dielectric Constant (Permitivity)Dielectric Constant (Permitivity)– A high dielectric constant allows components A high dielectric constant allows components

to be miniaturizedto be miniaturized

Dielectric LossDielectric Loss – A low dielectric loss is needed to prevent A low dielectric loss is needed to prevent

energy dissipation and minimize the bandpass energy dissipation and minimize the bandpass of the filterof the filter

Temperature CoefficientTemperature Coefficient– For device stability the dielectric properties For device stability the dielectric properties

should be relatively insensitive to temperatureshould be relatively insensitive to temperature

Microwave DielectricsMicrowave DielectricsMaterials by DesignMaterials by Design

The the required properties it is possible to apply some concepts The the required properties it is possible to apply some concepts of rational design to the search for materials. of rational design to the search for materials.

High Dielectric ConstantHigh Dielectric Constant– High electron density (dense structure type, polarizable cations, High electron density (dense structure type, polarizable cations,

i.e. Tai.e. Ta5+5+).).

Low Dielectric LossLow Dielectric Loss – Ionic polarizability comes with large losses in the microwave Ionic polarizability comes with large losses in the microwave

region. Therefore, one needs to avoid ferroelectrics, disorder and region. Therefore, one needs to avoid ferroelectrics, disorder and impurities. Ions should not be able to rattle around too much.impurities. Ions should not be able to rattle around too much.

Temperature CoefficientTemperature Coefficient– Very sensitive to rotations of polyhedra, vibrations of atoms, as Very sensitive to rotations of polyhedra, vibrations of atoms, as

well as thermal expansion. In perovskites the temperature well as thermal expansion. In perovskites the temperature coefficient is linked to octahedral tilting distortions. Tolerance coefficient is linked to octahedral tilting distortions. Tolerance factors just below 1 tend to have very low temperature factors just below 1 tend to have very low temperature coefficientscoefficients..

Commercial Microwave Commercial Microwave DielectricsDielectrics

See Dr. Rick Ubic’s (University of Sheffield) site for a more See Dr. Rick Ubic’s (University of Sheffield) site for a more detailed treatment of microwave dielectrics.detailed treatment of microwave dielectrics.

http://www.qmul.ac.uk/~ugez644/index.html#microwavehttp://www.qmul.ac.uk/~ugez644/index.html#microwave