Electric Polarization

Electric PolarizationUnderstanding Charge Dynamics

How a Charge Behave in an Electric field..?????????

Charge in a Electric fieldMovement of the charge based on its mass and charge

velocity and the kinetic energy of an electron or a negative ion increase as it travels toward a convergent field

Electron velocity decrease when it travels in divergent fieldCharge mechanics is influenced byProperty of the mediumMagnitude of the Electric fieldFrequency of the electric field Change in electric field in the spaceEverything boils down to finding the minimum energySo charges will move to reduce the system energyNeutral particle will polarize to reduce the energy

Dipole An OverviewTwo opposite polarity charges separated be a small distance (compare to observation point)

Dipole in an electric field try to align itself in the direction of electric fieldNeutral particle in the electric field creates dipoles, will feel force on the electric fieldForce on the particle in a electric field depends onFree charges in the particlePermittivity of the particle with respect to mediumGradient of electric field in spaceForce try to move the particle to the strong electric field to reduce the potential energy of the systemElectric field due to dipole vary wrt cube of the distance, so potential will vary squared

Electric Dipole momentElectric dipole momentMeasure of the separation of positive and negative electrical charges in a system of electric chargesElectric dipole moment at a point in the volume

If overall system is charge neutral, than dipole moment is independent of location

Potential of the dipole falls off faster with distance R than that of the point charge

Electron mobility-Case study

Charge carrier will move freely from x = 0 to x = d Charge carrier will be accelerated along the field direction without encountering any collisionSince constant force is acting on the charge, so it moves in a linearly increasing velocity, average velocity Mobility of the charge defined as the velocity per unit electric field strengthSolid have barrier for electron movement, it contains 10^23 atom /molecule per cubic cm (inertia of the electron due to interaction

Solid have lattice vibration (phonons), which disturb the electron Electron in solidAn electron (or a hole) will react with the lattice vibrations (phonons) and other imperfections in the materialInteraction within the material (atomic level), offers an inertia to electronThe term effective mass of the electron (mass of the electron in solid)Friction forces(inertia due to collision) oppose the electric force, it try to retard the motion

Mobility in solidAt steady state where dv/dt=0Collision time is depends on the temperatureElectron also have velocity due to temperature (thermal velocity)This collision time called relaxation time (time between a collision), periodicity of the lattice acts as an role (which have effect on temperature)So mobility of the electron decreases with increase in electronIons are much large in size, probability of ion movement depends on the probability of the creation of a vacancy next to the moving ionNo ionic conduction take place in the normal temperature

Electromechanical ForceElectrically stressed system exert a force to reduce the stored energyIf a material with permittivity is replaced by a material , so change in the stored energy of the system

Assume a object of permittivity is placed in a medium of permittivity and system is stressed by an uniform and constant electric field

Force on the Dielectric boundaryForce acting on the boundary with the tendency of expanding material 2 into material 1 to increase the volume of material-2Change in the energy is due to tangential field component

So tangential stress Normal Stress

Both pt and pn are normal to the boundary, dielectric material having a higher permittivity to move into the space occupied low permittivity mediumThis forces also creates compressive force in a dielectric placed between two metal platesThis is also changes shapes of the bubble in the liquid from normal spherical to spheroidDielectrophoretic forceElectrostriction force reason for electronic polarization( change in volume and density) for symmetrical object (charge)Non symmetric object reason for orientational polarization

Electrostatic induction-conductor

Here A is charged insulator(bounded source charge), no effect on A because of B, not the case with conductorElectrostatic inductionDepends on the free electron in the materialConductivity (type of the material)Molecular interaction in the multi atomic moleculeLattice structure of the materialCharged insulator with un-charge conductor (reduce the potential energy)

Concept of bound charge and free charge, so availability of free electrons is very important to reduce the electric field in the medium (rem- we are not maintaining voltage constant)Difference between isolated conductor and conductor near to charge sourceThe availability of free electron, makes conductor polarization is distinct from other materialsThe charge distribution is dependent solely on the geometric shape of the conductor B.

Electrostatic induction- InsulatorVery low availability of free electrons, so conductor like electro static induction doesnt occur (we are < critical field)If any, available charge carrier, it will try to move (like conductor), creates space charge polarizationElectric field will polarize the material by shifting slightly the normally symmetrical distribution of electron clouds of atomsDipoles (also) try to orient itself in the direction of fieldEach atom/molecule forms the dipole and orient to form big dipoleDielectric will go to the relaxation after removing from fieldRelaxationDepolarization of dipole happen due to thermal agitation (quantum mechanics)

Polarization(a tool for expressing material response to electric field..)

Electric polarization- DefinitionElectric polarizationPhenomenon of the relative displacement of the negative and positive charges of atoms or moleculesThe orientation of existing dipoles toward the direction of the fieldSeparation of mobile charge carriers at the interfaces of impurities or defect boundaryElectric polarizationCharge redistribution in a material caused by an external electric fieldThe work done for the charge re-distribution and energy loss need a energy sourceThe potential energy released from the process, utilized for polarization

Permittivity related charge density and field produced by it . It is independent of the dimension

Permittivity in materialsVacuum spaceDensity of the atomInteraction between atomsSo gases (in a P & T) equals itConducting material

This holds only for low frequency and static field, not for very high frequencies (>microwave), gamma rays just pass through the metal (charge can't instantaneously respond)

Remember, we are not having constant external supply source, only potential energy of the charge are considered

Dielectric Material permittivityPermittivity also called dielectric constantMost materials(linear), the dielectric constant is independent of the electric field strength below critical fieldDielectric constant depends onFrequency of the electric fieldMolecular and atomic structureTemperatureMechanical and physicochemical property of mixtureElectric conductivityThe ratio of the electric field in free space Fo to that filled with the dielectric material FF is the so-called dielectric constant

Dielectric material, try to arrange its neutral atom such that to reduce potential energy--So Birth of dipole inside the dialectic material

Polarization Basics- Simple case studyCharge on the plateBound charge (compensate the Dipole)Free charge

Polarization

Polarization is depends on number of dipole moment per unit volumeAverage dipole moment PolarizabilityMaterial with permanent dipole, dipole moment wont lie inline with applied field ( become tensor)Direction is Depends on symmetry of the molecule(particle) in the materialPolarizabilityIt is the scalar quantityPolarizability a of a particle in a dielectric material is induced by the local field

How to include polarization into Maxwell EquationMaterial placed in a E-field creates dipolesNeed to include this in Maxwell equation Need a relationship between polarization and dipole momentPotential can be separated into Bound charge Free charge potential

Divergence of polarization density gives bound charge density

How a dipole moment is related to displacement charge density (to add it in maxwell equation)

Polarization Vs Dipole MomentDipole moment (without higher order moments) is the cause for polarization (try to equal it and analyze)

Potential due to both charges (and surface and volume dipole moment)

Maxwell equation inclusion of dipole moment (considering only volume dipole moment)

Higher order modes also contribute to polarization (high freq)Surface dipole moments and its effectPotential due to dipole moment contains both surface and volume integration

Effects due to volume dipole moment is neglected for constant dipole moment densitySurface charge density

For a spherical object (at the center considering surface charge)

Dipole moment in boundary (interface) assumed to be a smooth functionBoundary/interface charge density (dipole moment densityat interface step change ) will give the surface charge

Time Vs PolarizationPolarizationElastic displacement of electron clouds of the particles (atoms and molecules) need less time (0.01ps to 0.1ps)Movement of the particlesOrientation of permanent dipolesThe migration of charge carriers (electrons or ions)Dielectric lossTransition from some energy consumed to overcome the inertia resistance (friction)

DepolarizationElastic polarization will regain its original (depolarize) position, due to its elastic actionRefer the first order approximation of polarization

Relaxation time ,time required for the originally induced charge to decay to 36.7% of its original value.

Polarizability Average dipole moment densityPolarizabilityAverage dipole moment per unit field strength of the local field FlocalDepends only on the mechanism of polarizationEffective PolarizabilityDepends on Material with high field concentration of conducting chargesTotal Polarizability

Polarization p=NFlocalFerro electric material Spontaneous polarization mechanismSusceptibility , relates electric field with Polarization/unit volume

Mechanism of polarizationCharge in an electric field may re-distribute in many ways/mechanismIntra molecular polarization mechanism Self restoringElectronics PolarizationIt is elasticIndependent of temperatureAtomic/Ionic polarizationIt is lattice vibrationPolyatomic materialInter Molecular thermal vibration restoringOrientation polarizationMovement of dipole (orientation)Friction and loss, depends on lattice vibrationIn elasticPolar materialPermanent dipole materialLossyDepends on temperatureMaterial with conductivity (Mobile charge carrier)Space Charge PolarizationFerroelectric materialSpontaneous polarization

Types of Electric Polarization

(What drives, material response to a electric field..)Types of polarizationA dielectric material is made up of atoms or molecules that possess one or more of five basic types of electric polarizationElectronic polarizationAtomic or ionic polarizationDipolar polarizationSpontaneous polarizationInterface or space chage polarizationEach type of polarization requires time to perform (have its own inertia) frequency dependentPerfect Dielectric material material with no mobile chargesElectronic Polarization - OpticalThe electric field causes deformation or translation of the originally symmetrical distribution of the electron clouds of atoms or molecules.Displacement of the outer electron clouds with respect to the inner positive atomic cores creates small dipoleElectronic Polarizability Depends onNumber of atom per cubic meterNumber of electronics in the outer most cellMaterial with Completely filled outer cell has low PolarizabilityGroup-I elements H,Li,Na,K,Rb & Cs with one electron in outer cell has high PolarizabilityGases have spare density, so interaction between atoms are negligibleIt is elastic, so self restoringInteraction between dipoles increases the applied electric field seen by an atomIntra molecular, so independent of temperatureVery high response time, and negligible lossPolarization is effective upto optical frequencies (300nm/700nm)

Electronic Polarizability Classical approachColumbic force is exerted on electrons, not surrounding nucleus

Elastic restoring force

Displacement force by applied electric fieldElectron cloud move till the force equality

Dipole moment (of an atom)

Polarizability due to Electronic polarizationDepends on volume of the atom

We are discussing only mono atom, neglecting interaction between dipoles, refer clausis-mosutti equation

Electronic polarization _ HydrogenHydrogen has Atomic radius of 0.5APolarizability For displacement is very smallSusceptibility =1.57 *10^-24 NFor gas number of atoms per unit volume N=2.687*10^18 cm^-3 (Loschmidt number)Susceptibility =4.22 *10^-5Relative Permittivity of hydrogen =1+susceptibility =1

Electronic polarization for spheroidMany material/gas e.g H & O has diatomic molecule, gases are formed by molecule H2, O2 .Molecules are not spherical in shape, so it can be assumed as spheroidHere molecule geometry and orientation of the play an important roleWhen both field and molecular axis is parallel (Polarizability is two times higher than single atomic gas)

When field and molecular axis is perpendicular, it has less Polarizability than parallel oneSo orientation of molecule is very important

Atomic/Ionic polarizationDielectric material consisting of polyatomic molecules (dissimilar)Poly atomic moleculeWithout permanent dipole (NaCl Na+, Cl- ionic bond)Dipole of each Ion pairs cancels out due to lattice symmetry and charge neutralityWith permanent dipole (HCl H+, Cl-)Crystal lattice is less symmetricalInternal field in +ve ion and ve ion may be different\Predominantly material with ionic bondElectro-negativity of both ions are differentSo even though , it posses an permanent dipole, it wont align due to the fieldNo much contribution of permanent dipole due to electric fieldIntra atomic/molecule polarizationEffective upto infrared regionLess lossInsensitive to temperature

Mechanism-Atomic polarization NaClA (Na) is more electropositive (give away its lone outer most electron), B (Cl) is electronegativeFirst electronic polarization happens (time =10^-15s), than ionic polarization happens due to +ve and Ve ions (10^-13s)Molecules always vibrate due to temperatureElastic restoring force is proportional to the difference between displacements of neighbouring ionsHarmonic oscillation

Atomic polarizationAssuming harmonic oscillation

For static frequency =0

Ionic and electronic polarizations are related to each otherIonic polarization happens upto infrared frequency, wont be observed in optical frequency, because of their high mass moleculeResonance of the both ionic and electronic polarization occurs at different frequency

Orientation PolarizationOrientation of permanent dipoles in the direction of applied fieldPermanent dipole why & How..?One molecule lends its electron to anotherDipole moment is product of transferred electrons and its distanceSome ions (NaCl) lattice structured arranged such that dipole moment always cancels each other (so no use of orienting it)CO2, which contains three atoms, bonding structure is symmetrical and cancroids of both positive and negative ions are at a same point , so dipole moment is zeroWater constrains permanent dipole moment due to its bonding angle

Orientation PolarizationOrientation of a molecule involves the energy required to overcome the resistance of the surrounding moleculesStrongly temperature dependent, decreases with increasing temperatureMolecules having a permanent dipole moment experience a torque in an electric field, tending to orient themselves to the field directionThermal agitation act as an restoring forceEvery point (angle with respect to field direction) in the material have its ownActivation energyThermal energyNormally dipoles are aligned in the different direction to reduce the potential energy it is depend on the temperatureProbabilistic approach is used to find how dipole react to the fieldorientation Polarizability is much larger than electronic and atomic polarizabilities at normal conditions

Orientation polarizationEquilibrium state for a dipole between thermal energy and electric fieldDipole moment is affected by applied field and temperature in solid and liquid not for gasesSo each dipole faces a crystalline field which is influenced by neighboring dipole and thermal energy vibrations

With applied field and temperature

Potential energy Multiatomic molecule uo is depends on temperature

Dipole momentAverage dipole moment in the field direction

L Langevin function, it reaches unity in very temperature with high fieldWhen ration of F/T increase than all dipole moment try to align toward applied field

Orientation in solidsDipoles do not rotate freely as do dipoles in liquids or gasesRotation is constrained to a few discrete orientationsDetermined by interaction of the dipole with neighbouring onescrystal structure of solid act as an important rolethe potential energy is directly related to the crystalline field acting on the dipoleFrozen and critical temperatureMany material for T0.002mm to 0.05mmClay smaller than silt and feels sticky and platic when wet , it is customary to use the name that favors the finer fraction.

Moisture content & Water Holding CapacityWater is held in the pore spaces in the form of films adhering to the soil particlesPoresMacroporesMacropores do not hold water well because the water films become too thick to adhere well to the surrounding soil particlesWater is lost downward as it drains below the root zone by gravityMicroporesFilms of micropore water, resist being drained away by gravity and are responsible for the water-holding capacity of soils (root tap this water)Sands have a lot of macro pores due to their large grain size but few micro pores. Thus, their water-holding capacity is low although their drainage is good.Heavy clay soils that have a lot of micro pores may have a higher water-holding capacity, but because they have fewer macrospores', their drainage is poor

Soil dielectric permittivity modelSoil mixture modelingRelate the complex dielectric constant of heterogeneous mixtures to the complex dielectric constant of the constituents.Soil particles are suspended in the water and air-mixturesRandom arrangement of soil particle in random granule shapeAdsorption of water in the soil surface (colloids)Depends on surface areaMultiphase (Gas, Liquid, Solid)So Double charged boundary layer - difficult to modelMain Constituents in soilAirParent materialWaterOrganic materialInput to the ModelDielectric properties of the constituentDeposition and shape of the constituentVolume of the each constituents

Difficulties in Multiphase modelingRandom shape and distribution of solid particleDielectric properties of water in soil and bulk is differentFrequency , temperature dependence of the water in soil differ greatly from its bulk propertiesVery difficult to model boundary layer

The Semi disperse Model - Darold Wobschell, 1977Based on Hanai/Bruggelman/Wagner theory of mixturesConsider Water as partly partly dispersed and partly the dispersing mediumsemi disperse describes the behaviour of soils containing moisture in the high-frequency range (1 MHz-1 GHz)Equivalent series and parallel RC model is given

This Paper try to showApproximate normal curve is predictable from extension of existing dielectric theories of mixturesRelates variation dielectric permittivity to the ionic conductivity of the water also try to explain degree of dispersion in water in the soil

Hanai/Bruggelman/Wagner theory of MixturesComplex dielectric constant in a two phase heterogeneous object.Wagner TheoryDerived for spheres widely dispersed in a medium , both or conducting dielectricsCalculate E-field in both the material using boundary conditionSoils assumed a spherical averageWorks in the diluted mixture but this is not the case in soilBruggelmanTry to find permittivity (real) by infinitesimal addition of disperse phase by reducing the dispersing mediumWorks to calculate real permittivityHanaiImplemented Bruggelman for complex permittivity with two phase mixture

Hanai Method for Two Phase mixtureFor two phase mixture (d-disperse phase, m-medium)

Real value of the above third order equation

Imaginary Part

Find the correct root from the three roots obtained in the above solution based on high frequency limitKnow which phase is disperse and which dispersingDerivation was done assuming volume of disperse phase is very very less than dispersing , but found aprox valid for 0.7 upto 0.95

Variation of dielectric constant with frequency occurs only when1. L is conducting2. very high dielectric constant at low freq, if L is disperse and conducting3.Predicts different results for H disperse4. Relaxation time of conductor-dielectric must be less than the E field time harmonic period 5. Water assume pure dielectric with conductivity=06. Many C between solid

Hanai Model with low dielectric solid

Semi-Dispersive Soil ModelSoils contain irregular particle containing crevices and pores (gradulay filled by water)No single dispersive Phase obvious over the entire range of moisture contentWater and particles are mutually interdispersedTry to apply two-phase HBW method to multi phase system (soil) Hypothetical intermediate phase (based on pearce et all)Hypothetical Phase Moist-particle phasesolid particle within which water-filled crevices or micro pores are dispersed and around which is water coating.Here water is disperse phaseMoist-particle and air disperse is assume to be dispersed in the water dispersing mediumHere water is the dispersing mediumEffective fraction of water dispersed is an important parameter

Semi-dispersive techniqueCalculation have four stage with different dispersive and dispersing medium, Soil particle have crevices and pores in itFind the permittivity of a hypothetical conducting particle phase Consisting of a non conducting solid with crevices containing waterHere soil particle is dispersed in the small amount of waterThe water is having a ionic conductivityCalculate permittivity of moist soil phaseConducting water is dispersed in pores within the conducting particleMoist-particle phase is now dispersed in the ordinary water (less conductivity) without airVoids containing air is dispersed in the above air-free phase

Semi-dispersive model ImplementationAt very high frequency, change in permittivity assumed negligiblePermittivity of solid particle assumed 3.5 irrespective of soil type with no frequency dependent dispersionPore water has conductivity due to dissolved saltEach step we have one disperse phase and dispersing medium with its volumetric content and dielectric constantVarious volume fraction has to be taken care with respect to over all soil volume fraction of disperse phase in the two phase system - Volume fraction soil as a wholeVolume fraction of non conducting soil Void volume fraction, soil porosityVolume fraction of Air volume fraction of water in the crevices depends on volume fraction of crevices in the soil particle

Semi-dispersive model Volume fractionFor high water

For low water

Assumption made -> water first fill the crevices capillary actionVolume fraction of conducting solid phase (soil particle +water in crevices)

Since soil is not fully saturated, so only part of the void is considered dispersed also Third stage, non dispersed water , which act like dispersing medium

First & second stageFirst StageSolid particle is dispersed in the small amount of crevice water

Permittivity of non conducting soil particle with conducting water particle medium

Distinction between micro-crevice conductivity and pore conductivitySecond stageWater is considered dispersive in the pore

Third and Fourth stageThird StageMoist-particle disperse phase is water dispersing medium (in the air-free phase)

Fourth StageAir is considered dispersed in the third stage hypothetical mixture phase

Over all permittivity of the soil is

Three step processIn this step 1 & 2 is merged by assuming a particle conductivity as a parameter, considers the micro-crevices conductivityIt is depends on frequency dependence of the Since in the first step disperse phase is low conductivity and low dielectric constant, so effect of elimination of first step is less

Input parametersThis method have many parameters, some can be kept fixed by varying the otherNormally volume fraction of water and frequency is varied to obtain the final valueHere soil permittivity is assumed 3.5Water permittivity is assumed 80For most soil void fraction vary between 0. 3 to 0.6, here 0.5 is takenWater conductivities chosen between 0.01 to 50 mmho/mHigher water content will have less conductivity due to dis-solved salts dilutionHypothetical Volume fraction of void water and micro crevice is used as a parameter to fine tune the value as per with observed data

Parameter variation study for different &

High and low frequency permittivity limit indexHigh-to-low-frequency limit index

As we know, high frequency limit is independent of the water conductivity and strongly depend on volume fraction of the soilConductivity index

Break frequency fxBreak frequency for dielectric constant and conductivityFrequency at which permittivity is equal to average of both low and high frequency permittivity

Low-high frequency index and break frequency index are matching with the experimental results

Theoretical Dielectric constant LimitLow frequency limitIt is mainly depends on water dispersion and its conductivityHigh frequency limitsIt can't be more than the volume fraction weighted average of individual constituents permittivityMainly depends on volume fraction of water and its dispersionAt zero volume water content act as a full soilWater conductivity also act as an important\Role in low frequency

In very optical frequency only soil particleDominate the permittivity

Polynomial interpolationHigh frequency limit of soil found by using an approximate expression, which relate volume fraction of soil, with its dispersion parametersUse polynomial interpolationThe High frequency permittivity Limit

High frequency conductivity limit

Approximation is accurate for +/- 5% for

Equivalent circuitApproximate frequency dependent of permittivity can be found using D and Fx

The above model contains same break frequency for both dielectric constant and conductivity (possible only for high value of )Alternative circuit based method1. arulananandan 4 capacitor and 4 resistorSachs and Spiegler simplified method

ConclusionThe given value better accurate for sand than clay soilSand is match with spherical low dielectric solidClay also matches at high frequencies (0.3-3GHz) Adequate fit in the high frequency is obtain at =0.9 and =0.7Values are experimentally matching with the tuning of parameters

ConclusionIncrease in Dielectric constant of the soil with different water content independent of soil type at High Frequencies

Observation of author from old literatureLack of all inclusive successful model to explain the observed anomalous dispersionInfluence of the factors have been studied as a isolated causeThe primary cause of the dielectric and conductivity dispersion is the dispersion of electric potential field due to heterogeneities in the electrical properties of different phases in the media to make energy is minimum

FREQUENCY-DOMAIN ANALYSIS OF ELECTRICAL DISPERSION OF SOILS-Theivanayagam (1995)Concentrate on A theoretical frequency-domain general solution for the electric dispersion of soilsTakes in to accountParticle shapeFrequencyMineralogyPore fluid typeSoil fluid interactionPorosityAnisotropyElectrical dispersion of the soil is affected byRatio of effective permittivity and conductivity of solid particle and fluidSolid fluid interaction is depends onVolumetric content of particle, water, voidSurface area of the soil particle (clay)Engineering property of porous media (multiphase)Mechanical behavior of mixturePhysciochemistry interaction

83Debye ModelBhagat and kadaba, Univ of kentuckyIn general Complex curve fitting based on experimental data (used)Bhagat..at el study suggestBergmann modification of the Debye equation -fit experimental data on 12% moisture content soilBelow 1 GHz -need to consider Residual surface effectsIntermediate forms of bound water.Work well for 12% moisture content, for all value of frequency (but to account for all soil-texture and moisture content need to limit the applicable frequency to 1GHz and above)No parameter to account a moisture content of the soilBaghat and Kadaba using DebyeRelaxation models based on a modification of the Debye equationMaterial with permanent dipole moments can be described by a modification of the Debye equation due to Cole and ColeFor soils at lower microwave frequencies , the ionic conductivity is very important

Static Dielectric constant for pure water

Soil contain many relaxation process, modeled in terms of super position of two debye processes (Bergmann et al) (based on weight factor)

First Soil Permittivity modelExperimental results were matched with the relaxation models for a spectrum of freq

Require to find the unknown values of model (5 to 8) with defined upper and lower boundarySteepest descendent method or Newton Raphson methods were usedThe values are based on starting parameter biasStarting vector defines the local minima of the convergence of the least square

ResultsThe experimental results obtained for 12% (g H20/g soil) soil sampleRelaxation time obtained is longer than pure free water

Comparison between the experimental and theoretical values of the attenuation constant, a, in nepers/m for 30% volumetric water content at 24 C (o = 3 10 -2 mho/m)

ConclusionsFor 1GHz and above the relaxation process is predominantly due to water than the nature of the soilion exchange characteristics of soil material are negligible above 500 MHz.Static permittivity of 5 has been used for as a compromise between dry soil and the high frequency limit for pure waterDistribution factor shown as 0.3Value of conductivity 6.6 mho/m assumed for the theoretical calculations, gives very good agreement.below 1 GHz, the influence of the soil definitely needs to be taken into account in describing the relaxation process.A mixture relation such as the one described by Deloor [10] can be usedThe effect of this mixture relation is to shift the relaxation frequency from that of pure water.For spherical particles, the shifts are the least and increase for other shapes.Another effect which might become important below 1 GHz and is probably more plausible, is the phenomenon of two dimensional surface conductivity, so shape and size of the soil particle will change the relaxation frequency (for surface charge polarization)At high frequencies, the mobility of these charge carriers becomes too low to follow the alternations of the e-m field and the granules behave as a dielectric inclusion without surface effectsIntermediate form of the Bound water also play a roleExperimental Technique

Suitable Experimental techniqueBased on water content(conductivity) dielectric constant of the materialFrequency of interestSample preparationExperimental TechniqueStatic measurementTime domainFrequency DomainSlotted line waveguide (shorted waveguide)Waveguide dimension and sample dimension is depends on frequencyE.g. rect.wave guide of 4.755/2.215cm with sample size of 1.67cm thick for freq G Band (4-8GHz)Redheffer & WestphallSuitable for dielectric constant of