In addition to the congruent reactions mentioned above, there are a number of different types of chemical reactions in which one or more materials react to produce products with different compositions. Reactions in which the reactants and products have different compositions arenon-congruent.
In some cases the result of the reaction is a change in the chemical composition of one or more of the phases present by the addition of another species to it, or deletion of a species from it. Such reactions are called by the general labelinsertion reactions.
There are also a number of important chemical reactions in which some phases grow or shrink, or new phases form and others disappear. The result is that the microstructure of the material gets significantly changed, or reconstituted. Such reactions, of which there are several types, are calledreconstitution reactions.
In order to see how to make use of them for energy storage, it is important to understand the major types ofreaction mechanisms, as well as thedriving forces that tend to cause such reactions to occur.
4.2.1 Insertion Reactions
Changes in the chemical composition of materials can be the result of theinsertion of guest species into normally unoccupied crystallographic sites in the crystal structure of an existing stable host material. The opposite can also occur, in which atoms aredeletedfrom crystallographic sites within the host material.
Such reactions, in which the composition of an existing phase is changed by the incorporation of guest species, can also be thought of as asolutionof the guest into the host material. Therefore, such processes are also sometimes calledsolid solu- tion reactions. In the particular case of the insertion of species into materials with layer-type crystal structures, insertion reactions are sometimes calledintercalation reactions.
Although the chemical composition of the host phase initially present can be changed substantially, this type of reaction does not result in a change in the identity, the basic crystal structure, or amounts of the phases in the microstructure.
However, in most cases the addition of interstitial species into previously unoccupied locations in the structure, or their deletion, causes a change in volume.
This involves mechanical stresses, and absorbs or emits mechanical energy. The mechanical energy related to the insertion and extraction of interstitial species plays a significant role in thehysteresis, and thus energy loss, observed in a number of reversible battery electrode reactions.
Generally, the incorporation of such guest species occurstopotactically. This means that the guest species tend to be present at specific (low energy) locations inside the crystal structure of the host species.
30 4 Reversible Chemical Reactions
A simple reaction of this type might be the reaction of an amount x of speciesA with a phaseBX to produce thesolid solutionproductAxBX. This can be written as
xAþBX¼AxBX ð4:1Þ
4.2.2 Formation Reactions
A different type of reaction results in the formation of a new phase, rather than the modification of an existing one. A simple example can be the reaction of species A with species B to form a new phase AB. This is aformation reaction, and can be represented simply by the equation
AþB¼AB ð4:2Þ
Since this modifies the microstructure, this is an example of one type ofreconsti- tution reaction.
There are many examples of this type of formation reaction. There can also be subsequent additional formation reactions whereby other phases can be formed by further reaction of the products of an original reaction.
The driving force for the simple reaction in Eq. (4.2) is the difference in the values of the standard Gibbs free energy of formationof the products, only ABin this case, and the standard Gibbs free energies of formation of the reactants, AandB:
ΔG0r ¼X
ΔG0fðproductsÞ X
ΔG0fðreactantsÞ ð4:3Þ The standard Gibbs free energy of formation of all elements is zero, so ifA and Bare simple elements, the value of the standard Gibbs free energy change,ΔGr0, that results per mol of this reaction is simply the standard Gibbs free energy of formation per mol ofAB,ΔGf0
(AB). That is
ΔG0r ¼ΔG0fð ÞAB ð4:4Þ Values of the standard Gibbs free energy of formation for many materials can be found in a number of sources, for example, [1]. These values change with the temperature, due to the change in the product of the temperature and the entropy related to the reaction, as was discussed in Chap.2.
In addition to the change in Gibbs free energy, there is a change in enthalpy, and thus the stored heat, related to such reactions. This is the difference between the enthalpies of the products and the reactants:
ΔH0r ¼X
ΔH0fðproductsÞ X
ΔH0fðreactantsÞ ð4:5Þ
4.2 Types of Non-congruent Chemical Reactions 31
Values of the enthalpy of most materials are relatively temperature-insensitive, except when phase changes take place that involve structural changes, and therefore changes in the entropy.
4.2.3 Decomposition Reactions
A number of materials can undergodecomposition reactionsin which one phase is converted into two related phases. This is the reverse offormation reactions, and can be represented simply as
AB¼AþB ð4:6Þ
There are two general types of these reactions. In one case, one phase decomposes into two other phases when it is cooled, and in the other, a single phase decomposes into two other phases when it is heated. There are specific names for these reactions.
If a single liquid phase is converted into two solid phases upon cooling, it is called a eutectic reaction. On the other hand, if the high temperature single phase is also solid, rather than being a liquid, this is aeutectoid reaction.
In the case of a single solid phase decomposing into a solid phase and a liquid phase when it is heated, the mechanism is called aperitectic reaction. Likewise, if all phases are solids, what happens is called aperitectoid reaction.
These types of reactions will be discussed in more detail later.
4.2.4 Displacement Reactions
Another type ofreconstitution reactioninvolves adisplacementprocess that can be simply represented as
AþBX¼AXþB ð4:7Þ
in which speciesAdisplaces speciesBin the simple binary phaseBX, to formAX instead. A new phase, consisting of elementalB, will be formed in addition. This will tend to occur if phaseAXhas a greater stability, i.e., has a more negative value ofΔGf
0, than the phaseBX. An example of this type is
LiþCu2O¼Li2OþCu ð4:8Þ in which the reaction of lithium withCu2O results in the formation of two new phases,Li2Oand elemental copper. In this case
ΔG0r ¼ΔG0fðLi2OÞ ΔG0fðCu2OÞ ð4:9Þ since the standard Gibbs free energy of formation of all elements is zero.
32 4 Reversible Chemical Reactions
The thermal effect of such a reaction is therefore
ΔH0r ¼ΔH0fðLi2OÞ ΔH0fðCu2OÞ ð4:10Þ It is also possible to have adisplacement reactionoccur by the replacement of one interstitial species by another inside a stable host material. In this case, only one additional phase is formed, the material that is displaced. The term extrusionis sometimes used in the technical literature to describe this type of process.
In some cases, the new element or phase that is formed by such aninterstitial displacement processiscrystalline, whereas in other cases, it can beamorphous.