3.0 Theory of water electrolysis -...

Chapter 3 K. NAGA MAHESH Theory of water electrolysis

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CHAPTER – 3

THEORY OF WATER ELECTROLYSIS

3.0 Theory of water electrolysis

3.1 Thermodynamics and kinetics

Electrolysis of water is an electrochemical process, where water (H2O)

is split into hydrogen (H2) and oxygen (O2) at their respective

electrodes by passing electricity in a electrolysis cell. In this process

the water is supplied to anode, to decompose into oxygen, protons,

and electrons. The protons are transported through the proton

conductive membrane (PEM) to the cathode, The schematic of the

process has been given in Figure 3.1. The electrons are passed

through the external circuit, which supplies the driving force (i.e. cell

potential) for the reaction [P.Millet et al., 2010].

Anode : 2H2O → 4H+ + O2 + 4e- 3.1

Cathode : 4H+ + 4e- → 2H2 3.2

Overall cell : 2H2O → 2H2 + O2 3.3

The Gibbs free energy (∆G) for hydrogen and oxygen production

through water electrolysis is give below:

∆G = µH2(g) + ½ µO2(g) – µH2O 3.4

2 2

1

0 2ln( )G RT pH pO= ∆ + 3.5

Where ∆G is Gibbs free energy, µH2(g), µO2(g) and µH2O are chemical

potentials of hydrogen, oxygen and water, pH2 and p02 are partial


27

pressures of hydrogen and oxygen at conditions 1 atm and

temperature 25°C.

The reversible potential to split water electrochemically can be

explained using Nernst equation:

rev GE

nF

∆= − 3.6

( )O

2 2

G RTln pH pO

nF nF

∆= − − 3.7

( )O

2 2

RTE ln pH pO

nF= − 3.8

Where n is the number of electrons involved, R is the universal gas

constant, T is temperature (K), F is the Faraday constant, and EO is

the standard potential. At standard conditions (298 K, 1 atm) Erev =

1.23V which constitutes the lowest possible applied potential between

any two electrodes in order to split water.

½

½

Figure 3.1: Schematic of PEM water electrolysis [Aaron Marshall, 2007]


28

The energy balance for the cell reaction may also be written, with the

energy required to break and form molecular bonds and to bring the

reactants to their reference states being the enthalpy (∆H):

∆G = ∆H − T∆S 3.9

At standard conditions

Utn = H

nF

∆− 3.10

where Utn is the thermoneutral potential difference,

At the cell potential

Ecell < Utn (Cell absorbs heat from the environment)

whereas if

Ecell > Utn (Heat is lost from the cell)

Efficiencies for the overall reaction can also be written with the

thermal energy efficiency defined as:

tn

cell

UH

E

є ∆ = 3.11

and the energy efficiency based on Gibbs free energy defined as:

rev

cell

EG

E

є∆ = 3.12

Although thermodynamics gives the minimum potential required to

split water, due to the kinetics of electrochemical reactions there will

always be overpotentials decreasing the efficiency.

Ecell = Erev + η anode − η cathode + IR 3.13


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Where Ecell, η anode, η cathode, and IR represent actual cell potential,

anodic overpotential, cathodic overpotential and voltage gain due to

the cell ohmic resistance.

Both overpotentials and ohmic resistance vary with current density.

The resistance is given by Ohm’s law, whereas the overpotentials can

be given by the Tafel equation (which is a simplification of the Butler-

Volmer equation):

0

RTanode ln

a F

i

iη

αη = 3.14

0

C

RT | |cathode ln

F

i

iη

αη = − 3.15

The term RT/IηF is defined as the Tafel slope, which can be used to

determine the reaction mechanism. Both Tafel slope and exchange

current (i0) are material dependent, and are the principle measures of

specific electrocatalytic activity.

3.2 Faraday’s calculations for H2 production

The theoretical yield of hydrogen is calculated using faraday’s laws

equation (3.16) given below [Alshelyab M et al., 2008] at STP

conditions in cubic centimetre per minute (cc min-1).

Faraday’s laws equation (3.16):

2e

H

ItMW

FN= 3.16

Where W is the weight of the hydrogen produced at the cathode, I

applied current (A), t time (s), M the molecular weight of hydrogen (g


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mol-1), F the faraday’s constant (96485 C mol-1) and Ne the number of

electrons involved in the reaction.

3.3 Electrode reactions

3.3.1 Hydrogen evolution reaction (HER)

The standard potential of H2 is by definition zero, the electrochemical

activity of HER on different metals can be compared by using

“Vulcano-plot” shown in Figure 3.2 and it can be seen that the metals

of intermediate bond-strength energy is the most active towards the

HER represented by the noble metals [S.Trasatti et al., 1972]. On the

left side of the curve the metals with low bond-strength are seen, the

rate determining step shall be discharge of H atoms, whereas on the

right side metals with stronger bond length can be seen, the rate

determining step shall be the H desorption on the surface of the metal

[B.E.Conway et al., 2000]. The noble metals are more corrosion

resistant in acid solutions hence suitable for this kind of applications.

Attempts are being carried out worldwide to combine different metals

from the opposite branches of the “Vulcano-plot”, This means to

combine metals which have less than five d-electrons (hypo-electronic)

with metals which have more than five d-electrons (hyper-electronic)

in the outer shell to obtain better properties like intermediate bond

strengths. The choice of the metals are limited noble metals and its

oxides (Pt, Pd, RuO2, IrO2) and a few tungsten compounds (WO3, WC),

because of acidic environment of the membrane [S.Trasatti et al.,

1990].


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Hydrogen evolution on Palladium

Pd is considered as one of the most active catalyst for the HER

comparatively with Pt, even though the Pt is considered as one of the

best electrocatalyst commonly used in fuel cell for the catalysis (for

hydrogen oxidation and oxygen reduction). Pd, which is more

abundant than Pt, has been less extensively studied for such

applications despite interesting electrocatalytical properties [Grigoriev

S et al., 2006; Fenglei Li et al., 1997]. Reaction steps and Tafel slopes

of HER are given in table 3.1.

Figure 3.2: Vulcano-plot of HER on different metals [S.Trasatti, 1972]


32

Table 3.1: Reaction steps and Tafel slopes of HER [J.Fournier et

al., 1995]

ba

low η

ba

high η

3 2adsM H O e M H H O+ − →+ + − +← 120 120 Volmer

3 2( ) 2ads gM H H O e M H H O+ − →− + + + +← 40 120 Heyrovsky

2( )2 2ads gM H M H→− +← 30 α Tafel

3.3.2 Oxygen evolution reaction (OER)

The oxygen evolution reaction (known as the oxygen reduction

reaction in fuel cell) is one of the most studied electrochemical

processes. Even though the reaction and mechanism is still not widely

understood, and is difficult to interpret [S.Trasatti et al., 1990] due to

the following reasons.

The reaction is very sensitive to the electrode surface properties

due to its high energy reaction intermediates and complex

pathways of high activation energy

The electrode surface can go dramatic changes at the different

potential ranges

The kinetics may also be time dependent

Many theories have been proposed on OER mechanisms, but very few

take into consideration the nature of the electrode surface [S.Trasatti

et al., 1990], which is critical for understanding the real reaction

mechanism. Most of the cases only oxide covered electrodes are

discussed in any mechanism. The reaction will always occur on an


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oxide surface, as the metal-oxygen (M-O) bond is always stronger than

the O–O dissolution energy. The OER involves the formation and

breakage of bonds between the metal and oxygen species, indicating

that the electrocatalysis process includes some material

transformation processes as well. This complex combination of

reactions involving surface species and material transformations has

lead to the formation of a so-called Volcano plot (Figure 3.3). The

ability of the oxide to undergo solid state redox transitions is clearly

important in respect to the materials electrocatalytic activity. suggest

The strength of the M–O bond in the various intermediates is critical

in determining the rate of desorption and/or adsorption steps in the

oxygen evolution mechanism [Matsumoto and Sato, 1986]. They also

suggest that rate of electron transfer follows the Franck-Condon

principle, in which the electron transfer is controlled by the density of

electron states at the Fermi level and the degree of orbital overlapping

of the active sites and adsorbed intermediates.

The Electrochemical Oxide path: [J.O.M.Bockris, 1956]

2 H eadsS H O S OH+ −→+ − + +← 3.17

H eadsS OH S O+ −→+ − + +← 3.18

( )22 2 gS O S O− → + 3.19

The Oxide path:

2 H eadsS H O S OH+ −→+ − + +← 3.20


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22 H OadsS OH S O S→− − + +← 3.21

( )22 2 gS O S O− → + 3.22

The Krasil’shchikov path:

2 H eadsS H O S OH+ −→+ − + +← 3.23

O + HadsS OH S− +→− −← 3.24

O O + eS S− −→− −← 3.25

( )22 2 gS O S O− → + 3.26

The reaction mechanism and rate determining step can be determined

from analysis of the Tafel slope found from steady state polarisation

measurements.

Figure 3.3 Electrocatalytic activities towards the oxygen evolution reaction

of various oxides as a function of the enthalpy of lower to higher oxide transition [S.Trasatti, 1984]


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3.4 The polymer electrolyte membrane

The polymer electrolyte membrane (PEM) is a solid polymer electrolyte

membrane used as electrolyte for fuel cells and water electrolysers.

These electrolyte membranes have high mechanical, chemical and

thermal stability, and shows high ionic conductivity and low

permeability to H2 and O2 gases. The perfluorosulfonated ionomer

(PFSI) membrane or PEM membrane consists of a

polytetrafluoroethylene backbone and perfluoronated pendant side

chains terminated by sulphonic groups. The perflouronated carbon

backbone chain is responsible for the mechanical and thermal

stability of these membranes and the sulphonic ionic groups are

responsible for the ionic conductivity. These membrane types are

developed for the chlor-alkali industry, several types of commercial

membranes are available and given in Table 3.2 below.

Table 3.2 Commercially available membranes

Commercial trade name

Manufacturer

Thickness (µm)

EW

(g.mol-1 3SO−)

Resistance (Ω.cm2)

Nafion 112 Dupont 50 1100 0.036

Nafion 115 Dupont 125 1100 0.168

Nafion 117 Dupont 175 1100 0.23

Flemion S Asahi Glass Co 80 1000 0.10

Aciplex –S Asahi Glass Co 120 1000 0.111

The Nafion membrane is today the most available type of membrane

and is commonly used in fuel cell and electrolysis research. The

polymer structures of the Nafion membrane from DuPont can be seen

in Figure 3.4. The different PFSI membranes typically differ in length


36

of repetitive units of the carbon backbone and in length of the side

groups.

T.D.Gierke (Gierke et al., 1981) have proposed a model of

microstructure of PFSI membranes as a series of ionic clusters or

inverted micelles of about 40˚A in diameter separated from

perfluorinated polymer bactbone (in the hydrated state). The clusters

are believed to be interconnected by narrow channels of about 10˚A,

upon hydration swelling of the membrane take place as water content

is increased, The primary hydration shell of the SO3H group consists

of six water molecules, and the ionic conductivity of the membrane

increases significantly when the average number of water molecules

per sulfonic acid group increases to more than six [C.Gavach et al.,

1989]. The membrane water content is defined by the number of mole

of water per moles of sulfonic group:

2

3

H O

SO

n

nλ

−

= 3.27

[ (C F 2 C F 2 )n (C F 2 C F )X ]

O C F 2 C F C F 3

O C F 2 C F 2 S O 3 H

n = 6 .6

Figure 3.4 Structure of Nafion (Perfluorosulfonated ionomer

membrane) [T. D. Gierke, 1981]


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Where n is number of moles. The ionic conductivity increases by

increasing the water content (λ) and reaches a value of 18 for 100%

relative humidity (RH) under fuel cell operation and approximately 22

when the membrane is swollen in water [T.A.Zawodzinski et al., 1995].

A certain number of water molecules are transferred per H+ ion by

electro-osmotic drag, during proton exchange. The drag coefficient, ξ,

has been found to be about 1 H2O/H+ and independent of current

density for less than 100% humidification and 2–3 H2O/H+ for a

Nafion membrane swollen in water [T.A.Zawodzinski et al., 1995]. The

equivalent weight (EW) is defined as weight of polymer per sulfonic

group and a lower EW represent more sulfonic groups and higher

specific ionic conductivity of the polymer. The membrane type must be

chosen according to the specific system. Gas permeation and risk of

membrane destruction must be taken into account.

3.5 Electrocatalysis and electrocatalysts

As mentioned in section 3.1 at standard conditions,

thermodynamically only 1.23V, are required to split water.

Unfortunately due to the kinetics of the reactions, some extra energy

(i.e. the overpotentials) is required in order to have the reaction

proceed at a reasonable rate. The overpotentials are strongly

dependent on the material used for the electrodes (i.e. the

electrocatalysts). Therefore the electrocatalysts are chosen in order to

decrease the overpotentials as well as to improve other important

aspects of the process.


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Requirements of electrocatalysts

High surface area

High electrical conduction

Good electrocatalytic properties

Long-term mechanical and chemical stability

Minimised gas bubble problems

Enhanced selectivity

Availability and low cost

Health safety

Factors influencing electrocatalysis

Chemical nature of the catalyst

Morphology (dispersion, crystal size, crystallinity, lattice

distortion etc.)

Non-stoichiometry (ionic defects, electronic defects, solid-state

redox etc.)

Magnetic properties

Band structure of the oxide

Bond strength of M–O

Number of d-electrons

Effective Bohr magneton

Surface electronic structure

Geometric factors

Crystal-field stabilization energy

Synergetic effects (mixed and doped oxides)


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The catalyst structure (particle size) is an important aspect, when

used as a catalytic layer consisting of catalytic particles (e.g. fuel cell

or PEM water electrolysis). These particle structures will influence the

dispersion or utilization of active material, the total available surface

area, layer morphology, product and reactant transport phenomena,

layer and particle electronic conductivity, and layer mechanical

stability. The particles with nano-sized structure also influence atomic

behavior and properties of the materials [D.D.Macdonald et al., 1991],

and different catalytic properties can be exhibited by metal-support

interactions [S.Trasatti et al., 1972].

3.6 Experimental and characterization methods

3.6.1 Polarization methods

By polarizing the electrode under equilibrium conditions, the steady

state polarization behaviour of the electrode reaction can be

measured. The measurement can be performed either by controlling

the current (galvanostatic control) or the potential (potentiostatic

control) and the response in potential or current is measured. The

steps are performed in small increments and the response is

measured typically after 10 minutes where equilibrium conditions of

the electrode reactions can be assumed. Steady state polarization

measurements include all polarization effects including the

thermodynamic potential, the overpotential due to the surface

reactions, ohmic losses and diffusion terms.


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To drive the reaction 3.1 at a practical rate, additional energy must be

applied to overcome the kinetic hindrance of the reaction and the

ohmic resistance. The potential which must be applied at a given rate

is given by:

Ucell = Erev + η + i · RΩ 3.28

Where RΩ is the ohmic resistance of electrolyte, cable connections and

wires. η can be divided into cathodic and anodic parts:

η = ηc − ηa 3.29

and are given by the Tafel equations above. By polarization of an

electrode, e.g. in anodic direction, and measuring the potential versus

a reference electrode the cathodic term can be neglected and equation

3.17 is written:

reva

0

E E b . log .i

i Ri

Ω = + + 3.30

a E' b . log .i i RΩ= + + 3.31

where

E’ = Erev + ba . log i0 3.32

At low current density (cd) where RΩ can be neglected, ba and E’ can

be found from the slope of the curve. For high cd the data must first

be corrected from iR-drop or, if proper knowledge about the reaction

exists, it can be found by fitting equation 3.19 to the measured data.

Figure 3.5 illustrates the efficiency of the electrolyser in a

characteristic I-V curve.


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3.6.2 Cyclic voltammetry

Cyclic voltammetry (CV) is a surface sensitive technique where each

material gives rise to a unique spectrum in a given medium. The

method is often applied for determination of the physio-chemical state

of an electrode surface. CV is useful to study the behaviour of

adsorbed species, participating as reaction intermediates in a given

reaction or as impurities, as well as redox couples in the solution and

at the electrode surface. Cycling the potential at different scan rates

can be performed to find diffusion coefficients of electroactive species

and the capacitance of an electrode (active surface area). Additionally,

CV can give information about the reversibility of the

charging/discharging process. In CV the potential is swept at a

Figure 3.5 Schematic of Current–voltage performances of a PEM water electrolyser [P.Millet, 2010]


42

certain rate, ν, within the potential range of interest and the current

response is measured. The potential at a given time can be written

[A.J. Bard, 1980]:

Et = Et=0 ± ν · t 3.33

Where t is the time, Et is the controlled potential, Et=0 is the starting

potential, plus and minus indicates anodic and cathodic direction of

the sweep respectively. Table 3.3 shows some diagnostic criteria to

determine the reversibility of a charge transfer reaction without

diffusion or activation limitations where p indicate a point of interest

in the voltammogram, usually a peak or a point at fixed potential.

Table 3.3: Diagnostic criteria for reversible reactions

1. ip I ν

2. | / | 1

a ci ip p

=

3. Ep independent of ν

4. 59 a c

Ep E E mVp p n

∆ = − <

Capacitance

The double-layer capacitance, Cdl, arises from the potential

dependence of electrostatic charging of the electrode surface balanced

by dipole orientation of ions and water molecules in the solution near

the surface. Electrosorption of species at the surface of an electrode

give rise to a so-called pseudocapacitance, Cφ, where an intermediate

is formed that stores charge at the surface. In contrast to double layer


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charging, psuedocapacitance is a Faradaic process where the

electrons cross the double layer region. The total capacitance of an

electrode can be derived from CV by performing multiple scans at

different scan rates, ν [B.E.Conway et al., 1999]:

.dV

i C C vdt

= = 3.34

iC

v= 3.35

For a reversible process controlled by electrode kinetics, a plot of i

versus ν will give a straight line with slope equal to C.

Porous electrodes can give raise to a non-uniformity of

charging/discharging down the pores, due to ohmic effects which

makes potential penetration into the pores more difficult and may

result in a locally smaller potential range [B.E.Conway, 2001].

Integrated charge

The voltammetric charge of an electrode can be found from equation

3.35:

2

1*

E

E

iq dV

v∆ = ∫ 3.36

by integration between E1 and E2. q* is independent of ν in the

absence of ohmic drop, diffusion and/or kinetic limitations of the

charging process.


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A typical cyclic voltammogram of polished Palladium disk in N2

saturated 0.1 M H2SO4 solution at a sweep rate of 50 mV sec-1 has

been shown in Figure 3.6. The corresponding peaks observed shows

electrochemical activity of the Pd sample, a positive sweep started

from lower voltage values and moving right, the first peak at -0.1 V

(vs. SCE) is the hydrogen desorption peak. If the surface of the

catalyst is a thin film or very smooth and pure, multiple peaks could

be distinguished for desorption of monolayers of various strengths.

The reaction corresponding with the hydrogen desorption peak is:

adsH H e+ −→ + 3.37

Sweeping to higher voltages, formation of PdO takes place and

represented by the following chemical reaction:

Figure 3.6 CV of polished palladium disk in N2 saturated

0.1 M H2SO4 at a sweep rate 50 mVsec-1 [R.W.Reeve, 1998]


45

2 2 2adsH O O H e+ −→ + + 3.38

The oxide formation region could be divided into two peaks that are

often distinguishable. At around 0.5 V SCE, the following reaction

occurred:

2Pd H O PdOH H e+ −+ → + + 3.39

A second small bump is seen around 0.8 V SCE. The second peak in

the oxide formation region corresponded to the following reaction:

PdOH PdO H e+ −→ + + 3.40

The voltage sweep then reached its set maximum of 1.0V and reversed

direction. At around 0.45 V SCE in Figure 3.6, the oxide reduction

region is reached. Here, PdO is reduced and the following general

reaction occurred:

22 2adsO H e H O+ −+ + → 3.41

At oxide 0.45 V SCE where the reduction peak occurred, both

reactions in Equations (3.39) and (3.40) occurred in reverse.

Finally, the cathodic hydrogen region peaks occurred at the same

potential as the hydrogen desorption peaks from the reaction in

Equation (3.37). The hydrogen adsorption reaction is:

adsH e H+ −+ → 3.42

The gap between the values for the positive sweep and the negative

sweep are the result of the electrical double-layer capacitance on the

surface of the catalyst.


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Figure 3.7 and 3.8 shows the typical CV of Pd/C and RuO2

respectively.

Figure 3.7 Cyclic voltammtery of (1) Pt40/Vulcan XC72 (2) PtPt0.5Pd0.540/Vulcan

XC72 and (3) Pd40/Vulcan XC72, v = 20 mVs-1 [S.A. Grigoriev, 2008]

Figure 3.8 Voltammogram of a RuO2 DSA electrode in 0.5 M H2SO4 [S. Ardizzone, 1990]


47

The electrochemical surface area (ECSA) of the Pd/C catalysts can be

calculated using equation 3.43. It has been reported that Pd is entirely

oxidized to Pd oxide at potentials above 0.50V vs SCE. On the other

hand, Pd oxide is completely reduced to Pd below 0.30 V vs SCE

[S.I.Pyun et al., 1996]. Assuming that Pd oxide is composed of PdO or

Pd(OH)2, the amount of charge necessary for reduction of a monolayer

of Pd oxide on a smooth Pd electrode was reported to be

0.255 mC.cm-2. The hydrogen desorption and oxygen chemisorptions

peaks are shown in figure 3.6 (R.W.Reeve et al., 1998). ECSA of the

catalyst can be calculated using the following equation 3.43.

ECSA (m2 g-1) = 0.1 × Qr/m·c 3.43

Where

Qr = Area of Pd oxide reduction peak (C)

m = quantity of Pd loading (mg)

c = 0.255 mC cm-2

3.6.3 Inductive coupled plasma spectroscopy

Inductive coupled plasma (ICP) spectroscopy method is commonly

employed to determine the composition of the metal present in

sample. In the present work ICP technique has been used to

determine the weight percentage of Pd loaded on carbon support. A

known concentration of standard sample is introduced into the

plasma and the absorption frequency of the sample is recorded and

compared with prepared sample. Based on the absorption frequencies

the weight percentage of the sample has been calculated.


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3.6.4 Surface area measurement

The Surface area of the catalysts is determined by BET and Langmuir

isotherms, multilayer adsorption can be determined using BET

method. In the BET and Langmuir methods the adsorbed N2 gas is

measured, the adsorption process occurs by the formation of chemical

bonds (chemisorption), or by a weak vander Waals forces

(physisorption). The enthalpy for formation of the first monolayer is

assumed to be different and greater in magnitude than that of the

second and higher layers.

BET equation

( 1)1

1

oo

m m

o

C Cm

PP cPP

P V VV

P

−

= +

−

3.44

Where P is the equilibrium pressure, P0 is the vapour pressure of the

adsorbate at standard conditions, Vm is the volume required to cover

the adsorbent surface with a monolayer of adsorbate and c is a

temperature-dependent constant related to the enthalpies of

adsorption of the first and higher layers.

3.6.5 X-ray diffraction method

X-ray diffraction is a powerful technique that is commonly used to

determine the structures of new materials such as crystalline or

amorphous. However, the technique is limited by the ability to grow

nearly perfect crystals that are suitable for diffraction. For routine

structural characterization of materials, X-ray powder diffraction is far


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more common. The samples for powder diffraction may be large

crystals, or they may be in the form of a powder composed of

microcrystals that are too small to be seen by the human eye.

XRD is a non-destructive tool to characterize the electrode by

determining the material's crystal structure and the various phases.

XRD patterns of scattered x-ray photons showed peaks as specific

angles for crystalline materials. Peak patterns are specific to

individual materials. Peaks could be analyzed to determine average

crystal size using the Scherrer equation (3.46).

0.9

cost

B

λ

θ= 3.46

Where t is Average particle (crystalline) size of particle, B is the full

width half max (FWHM) of the diffraction peak, θ is the diffraction

angle, and λ is the wavelength of the x-rays, in all experiments fixed at

1.5406 A for CuK [S.L.Gojkovic et al., 2003].

The lattice parameter (α) has been calculated using the equation given

below.

αfcc = 2½ λ/sinθ 3.47

In the present study the prepared Pd/C electrocatalyst has been

characterized for its crystalline and structure orientation. The

schematic of the powder XRD has been represented in figure 3.9.


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sample

liq N2

detectorX-ray source

θ θ

Geometry of XDS 2000

sample

liq N2

detectorX-ray source

θ θ

Geometry of XDS 2000

Figure 3.9 Schematic of X-ray diffractometer with sample, X-ray

source, and detector

3.0 Theory of water electrolysis -...

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