ionic conductors: characterisation of defect structure lectures 7-8 fast ion conduction in solids i...

Ionic Conductors: Characterisation of Defect

Structure

Lectures 7-8Fast ion conduction in solids I

crystalline materials

Dr. I. AbrahamsQueen Mary University of London

Lectures co-financed by the European Union in scope of the European Social Fund


Introduction to Solid Electrolytes

Solids that show high electrical conductivity wholly or mainly due to the conduction of ions, are collectively known as solid electrolytes, fast ion conductors or superionic conductors.

These materials can be crystalline or amorphous, organic or inorganic.

They are a very important class of materials particularly in battery and fuel cell technology.

Liquid electrolytes like 1 M KCl have conductivities in the range of 1 10–1 S cm–1.

Solid electrolytes such as Na--alumina, have similar conductivities in the solid state.

We shall examine both crystalline and amorphous solid electrolytes.


All ionic solids conduct due to the motion of defects,

e.g. in NaCl the Schottky defect is present and conductivity () 10–12 S cm–1.

If NaCl is dissolved in water (0.1 M), the conductivity rises because the Na+ ions are more mobile.

0.1M NaCl, 10–2 S cm–1

In solid electrolytes the conductivities are equally high.

Na--alumina, 10–1 S cm–1 at 300 C


Mobile sublattice can be cationic or anionic

Compound Mobile ion ConductivityLISICON Li+ 10-1 S cm-1 @ ca. 500C

Na -alumina Na+ 10-2 S cm-1 @ ca. 25C

RbAg4I5 Ag+ 10-1 S cm-1 @ ca. 25C

Hydr.-Ce1-xYxO3-x/2 H+ 10-1 S cm-1 @ ca. 400C

PbSnF4 F 10-2 S cm-1 @ ca. 390C

Zr1-xYxO2-x/2 O2 10-1 S cm-1 @ ca. 1000C


There are two basic requirements for fast ion conduction in solids.

(1) Partial occupancy of sites by mobile ions. Number of sites >> Number of ions

(2) Sites must be connected by continuous pathways of suitable energy.Pathways should have low activation energy.Bottleneck size ion size.

Specific conductivity () of a material is given by:

i

iiien

Where, ni is the number of charge carriers of type i, ei is the charge (the electronic charge for electrons and monovalent ions) and i is the mobility.

Requirements for Fast Ionic Conduction in Solids


In NaCl for example, the charge carrier is the Na+ vacancy. The concentration of these vacancies is very low at room temperature, therefore n is small and is low.

If we can introduce additional vacancies or interstitials into a system we can increase n and therefore increase .

When NaCl is heated, thermodynamics dictates that the number of Schottky vacancies increases. This is known as the intrinsic vacancy concentration. However only at very high temperatures is the intrinsic vacancy concentration and ion mobility high enough for NaCl to show high conductivity:

10–12 S cm–1 at 25 C 10–3 S cm–1 at 800 C

Ways of increasing charge carrier concentration n


We can increase the number of vacancies by adding an aliovalent impurity such as Mn2+. This can be achieved through solid solution formation with MnCl2.

Na1-2xMnxCl

2NaNa0 MnNa

+ VNa

These vacancies are described as extrinsic.

For all but the highest temperatures, the number of extrinsic Na+ vacancies is = x and is very much larger than the intrinsic vacancy concentration.

Thus at most temperatures the conductivity is dominated by extrinsic vacancies.


Doping with aliovalent ions through solid solution formation can be used to generate vacancies or interstitial ions.

Doping with supervalent cations

Cation Vacanciese.g. 3Li+ Al3+ in Li4-3xAlxSiO4

Anion Interstitialse.g. Ca2+ Y3+ + F–

in Ca1-xYxF2+x

Doping with subvalent cations

Cation Interstitialse.g. P5+ Si4+ + Na+ in Na1+xZr2P3-xSixO12

Anion Vacanciese.g. 2Zr4+ + O2– 2Y3+ in Zr1-2xY2xO2-x


Cation Vacancies: An+ substituted by Bm+ where (m > n)

mAA0 BA

(m - n) + (m - n)VA

Anion Interstitials: An+ substituted by Bm+ and interstitial anion Zk- where (m > n)

AA0 BA

(m - n) + [(m - n)/k]Zik

Cation Interstitials: An+ substituted by Bm+ and interstitial cation Ck+ where (m < n)

AA0 BA

(n - m) + [(n - m)/k]Cik

Anion Vacancies: An+ substituted by Bm+ where (m < n) vacancy introduced on Zk-

AA0 + [(m - n)/k]ZZ

0 BA(m - n) + [(m - n)/k]VZ

k

General Equations for Defect Formation in Cation Substitutional

Solid Solutions


Ionic Mobility Increasing results in an increase in . Ionic conduction mechanism rely on ions squeezing past ions of opposite charge. These are known as bottle necks.

Consider ionic conduction in NaCl.

In order for the Na+ ion to enter the interstitial tetrahedral site, it must first squeeze through the bottleneck formed by the three Cl– ions.


The size of the bottleneck is small. Similarly the size of the interstitial site is small. The resulting energy profile might look something like:

In order to lower the migration energy and hence increase mobility it helps if the mobile ion is small and the stationary ion is polarisable.


Factors affecting Em.

(1) Bottleneck sizeShould be ion size

(2) Rigid framework should be polarisable

(3) Charge on mobile ionsHighly charge ions are less mobile (they become trapped).


Ionic mobility is related to the ionic self-diffusion coefficient D (Einstein relationship):

(1)kT

qD

where q is the is the charge, k is the Boltzman constant and T is the absolute temperature. The value of D can be obtained through consideration of random walk theory.

where z is number of equivalent sites in the 3D lattice, a0 is the distance between equivalent sites, c is the fraction of occupied sites, f is a correlation factor representing the deviation from randomness of atomic jumps (ca. 0.65 in a simple cubic system). 0 is the phonon frequency for the specific lattice and Gm is the free energy of migration.

(2)

kT

Gacf

zD mexp1

6 020


where:mmm STHG

We can define a term as:

k

Sf

z mexp6

The mobility can therefore be defined as:

(3)

kT

Hac

kT

q mexp1 020

Which can be abbreviated to:

kT

Hmexp0


Ionic conductivity can be defined as:

The value of n is the product of N and c where N is the number of equivalent partially occupied sites per unit volume. Therefore:

(1)

(2)

Which can be expressed as an Arrhenius type form:

nq

kT

Hacn

kT

q mexp1 020

2

kT

E

Taexp0

Where Ea is the activation energy for conductivity


Taking logs and plotting gives an Arrhenius plot of conductivity, the slope of which gives the activation energy.


Ionic Conduction Mechanisms in Solids

Ionic conduction in solids arises through ions hopping from one site to a vacant site in the crystal lattice.

Three basic types of mechanisms:

(1) Vacancy mechanism Where an ion hops onto an intrinsic or extrinsic vacancy (2) Interstitial mechanism Where an interstitial ions hops onto a neighbouring vacant interstitial site.

(3) Interstitialcy mechanism Where an interstitial ion pushes a neighbouring ion in a normal lattice site into an interstitial vacancy and then takes its place on the normal lattice site (cooperative motion).


Mechanism of Proton Conductivity

The mechanism of proton conduction in solids have been the subject of some debate. One of the most accepted theories is the Grothuss mechanism. Grothuss (1806)

This involves protons moving through the solid via a hydrogen bond network.


Applications of Solid Electrolytes

(1) Portable electric power sources for electric vehicle, mobile phones, digital watches, calculators, heart pacemakers etc.

(2) Fuel cells (electric vehicles and space programme).

(3) Gas sensors (emission control)

(4) Electrolysers (gas separation)

(5) Electrochromic displays


e.g. The Sodium-Sulfur Cell

Batteries can be primary (used once then disposed of) or secondary (rechargeable). Conventional secondary batteries use solid electrodes and liquid electrolytes (e.g. lead-acid car battery). The sodium-sulfur cell has a solid electrolyte and liquid electrodes.


Electrolyte = Na--alumina

Electrodes = molten sodium (anode) molten sulfur (cathode)

The cell operates at around 300 C. But the reactions are exothermic and once heated can be self sustaining if adequately insulated.

Anode: At the interface between the molten sodium and the electrolyte Na is ionised to Na+. Na+ migrates through the electrolyte e– passes into the external circuit.

Na Na+ + e–


Cathode:Molten sulfur is reduced to the sulfide ion, where it can form sodium sulfide with the Na+ ions entering from the electrolyte.

S + 2e– S2–

The reactions are reversed on charging.

The overall cell reaction may be written as

2Na + 5S Na2S5 2.08 V

The cell voltage varies from 2.08 to 1.8 V depending on the state of charge and is very similar to that of the lead acid cell. The main advantage is that it is much lighter.


The Oxygen Concentration Sensor

The oxygen concentration sensor utilises an oxide ion conducting solid electrolytes such as calcium stabilised zirconia.

Zr1-xCaxO2-x

The cell consists of a solid electrolyte tube coated with porous electrodes on its inner and outer surfaces. There are different oxygen pressures inside and outside the tube.


If PO2’’ > PO2’ oxygen ionises on the inner electrode (which becomes the cathode).

O2 2O·2O· + 2e– O2–

The O2– migrates through the solid electrolyte to the outside chamber where it is oxidised (anode).

O2– O· + 2e–

2O· O2

At equilibrium, the EMF of the cell (E) is given by the Nernst equation.

'

O

''O

2

2ln4 P

P

F

RTE

Therefore if we keep PO2’ constant we can obtain PO2’’ by measuring E and hence obtain the oxygen concentration.


Similar cells used as fuel cells, for example using air in the inner chamber and H2 in outer.

Inner chamber reactionO2 2O·2O· + 2e– O2–

Outer chamber reactionO2– O· + 2e–

O·+ H2 H2O

Therefore uses H2 and air or O2 as fuels and produces water.

Very clean and efficient (ca. 90%).


Important Structures adopted by Solid Electrolytes

The structures adopted by solid electrolytes are often massively defective. They are all characterised by pathways for ionic conduction. Here we will examine a few of the important structural types.

Apatites: A10 (MO4)6X2 (A = alkaline earth, rare earth, Pb; M = Si, Ge, P, V; X = O, OH, halides)

The apatites are an important group of structures, particularly in biomaterials where minerals such as hydroxylapatite Ca10(PO4)6(OH)2 form the main component of bone mineral.

Their structure consists of a framework of isolated MO4 tetrahedra, which corner share with A atom polyhedra to give a hexagonal channel structure with channels running parallel to the c-axis.


Emma Kendrick, Alodia Orera and Peter R. Slater

J. Mater. Chem., 2009, 19, 7955-7958

e.g. La8Y2Ge6O27.

The mechanism of conductivity has been the subject of debate.

Recent Neutron and modelling studies have confirmed a mechanism involving the GeO4 tetrahedra. Conduction can also occur via this mechanism between channels.


Na--alumina is a Na+ ion conductor. It is formed as a solid solution between Al2O3 and Na2O. The general formula is:

Na1+2xAl11O17+x

(note that there is some argument as to the true solid solution formula).

In the stoichiometric end member, NaAl11O17, is low

However in the solid solutions

= 10–3 S cm–1 at 25 C = 10–1 S cm–1 at 300 C

Structure consists of thick layers of alumina (Al2O3) separated by oxygen deficient layers in which the Na+ ions reside.

Na--alumina:


The Na+ ions are mobile within the oxygen deficient layer but cannot penetrate the thick alumina layers. Hence Na+ conduction is 2-D.


NASICON:

Na3Zr2PSi2O12

NASICON is an important sodium ion conductor that is commercially used in batteries. The structure consists of corner sharing ZrO6 octahedra and P/SiO4 tetrahedra.

This results in 3 dimensional tunnels in which the Na+ ions reside. Similar structure adopted by fast lithium ion conductors such as Al doped Li1+xTi2-

xAlx(PO4)3 (LATP)

NASICON based battery

Ceramatec

http://www.iitg.ernet.in/physics/fac/padmakumarp/nasicon.htm


Fluorite based structures:

The fluorite structure is an important host for ionic conduction of anions, such as O2- and F-.

It is essentially made up of a ccp array of large cations with anions in the tetrahedral sites.

http://electronicstructure.wikidot.com/predicting-the-ionic-conductivity-of-ysz-from-ab-initio-calc


e.g. YSZ

The cubic phase of zirconia can be stabilised through solid solution formation with a variety of oxides. Most commonly yttria stabilised zirconia Zr1-xYxO2-x is used commercially in fuel cells.

YSZ shows a maximum in conductivity at around x = 0.10

The mechanism of conductivity has been widely studied and modelled using a variety of methods. Most studies agree that diffusion occurs via the edge shared between two neighbouring OZr4 tetrahedra.


e.g. PbSnF4

Cordered ccp array of Pb and Sn resulting in a lyared tetragonal fluorite structure.

In -PbSnF4, ¾ of the fluoride ions located in two crystallographic sites F2 and F3 corresponding to those in the ideal fluorite structure and the remaining fluoride ions located in an octahedral site F4 between the Sn and Pb layers. Ions located in the F4 site. The remaining tetrahedral site, F1 between adjacent Sn layers is vacant.


The mechanism of conductivity was studied by NMR and neutron diffraction.


Pyrochlores

Pyrochlores are fluorite based phases that show cation ordering and have 1/8 of the anion sites vacant.

e.g. Gd2-xCaxTi2O7-x/2

These materials show good ionic conductivity at around 1000C. Vacancies are introduced through subvalent substitution of Gd3+

https://web.chemistry.ohio-state.edu/~woodward/ch754/lect2003/solid_electro_lect27.pdf


Brownmillerite

In the brownmillerite structure 1/6 of the perovskite oxygen sites are vacant. These are ordered in layers giving a perovskite like octahedral layers separated by tetrahedral layers.

e.g. Ba2In2O5

There is high oxide ion conductivity in the tetrahedral layers at ca. 10-1 S cm-1 at 800C


Perovskite based structures:

e.g. KCaF3

This is a classic perovskite structure that shows high fluoride ion conductivity at intermediate temperatures.

Neutron diffraction studies using an anharmonic model for thermal vibration reveal details of the F- ion conduction pathway.


Ruddlesden Popper Phases

e.g. Lan+1NinO3n+1

Ruddlesden-Popper phases are tetragonal layered perovskite materials with a general formula of AO(ABO3)n . A typical Ruddlesden-Popper structure is made of alternating perovskite blocks, with the perovskite blocks increasing as the n value increases.

n = 1 n = 2 n = 3


In La2NiO4+δ there are excess oxide ions located in interstitial sites. This gives high ionic conductivity up to a value of δ = 0.2.

Doping also alows the improvement of ionic/electronic conductivity in these systems.

Doping can be either for A site (La) or B site (Ni) cations. Successful doping occurs with Sr, Nd, and Sm on the A-site of the perovskite layer, and Cu, Fe, and Co in the B-site.

Experimental results suggest that doping at the A-site of the RP phase have resulted in improvements in electronic conductivity of nickelate material, while on the B-site, it has improved ionic and decreased electronic conductivities respectively.

e.g. La2Ni1-xCoxO4+δ and La4Ni3-xCoxO10±δ


Aurivillius Structures:[Bi2O2][An-1BnO3n+1] (A = large cation, B = small cation)

These are layered structures based on stacking of layers of [Bi2O2]n

2n+ or equivalent lead oxide layers and perovskite like layers of metal octahedra such as [WO4]n

2- (in Bi2WO6).

The structure of Bi4V2O11 is that of an n = 1 Aurivillius phase with vacancies concentrated in the vanadate layer. [VO3.5V0.5]n

2n-

The BIMEVOXes are derived by substitution of V/Bi by a variety of cations and show exceptionally high conductivity at low and intermediate temperatures.e.g. Bi2V1-xCuxO5.5-3x/2

ionic conductors: characterisation of defect structure lectures 7-8 fast ion conduction in solids i...

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