Stoichiometric Matrix

From the definition of species, it is possible to construct a stoichiometric matrix that establishes the relationship between species and chemical elements for species or oxides for cement species. This is called canonical decomposition.

Stoichiometric matrix for species

Any species can be described as a linear combination of chemical elements. A species vector can be expressed as a function of the chemical elements on which they depend. This dependence leads to the creation of a stoichiometric matrix.

H2O = Species("H₂O")
HSO4 = Species("HSO₄⁻")
CO2 = Species(Dict(:C => 1, :O => 2); symbol="CO₂")
species = [H2O, HSO4, CO2]
CSM = CanonicalStoichMatrix(species)

Stoichiometric matrix for cement species

A cement species vector can also be expressed in terms of other species on which they depend. Here, the cement species are expressed in terms of the oxides from which they are composed.

C3S = CemSpecies("C3S")
C2S = CemSpecies("C2S")
C3A = CemSpecies("C3A")
C4AF = CemSpecies(Dict(:C=>4, :A=>1, :F=>1); name="C4AF")
cemspecies = [C3S, C2S, C3A, C4AF]
CSM = CanonicalStoichMatrix(cemspecies)

Define stoichiometric matrix from primary species

The decomposition of a set of species can also be done according to a base of primary species.

H2O = Species("H₂O")
HSO4 = Species("HSO₄⁻")
CO2 = Species(Dict(:C => 1, :O => 2); symbol="CO₂")
species = [H2O, HSO4, CO2]
H⁺ = Species("H⁺")
SO₄²⁻ = Species("SO₄²⁻")
CO₃²⁻ = Species("CO₃²⁻")
primary_species = [H⁺, SO₄²⁻, CO₃²⁻, H2O]
SM = StoichMatrix(species, primary_species)

Display of the stoichiometric matrix

The stoichiometric matrix can be pretty-printed with different column and row labels using pprint. Simply add the keyword row_label, col_label or label for both, which can take the following values: :name, :symbol, :formula

SM = StoichMatrix(species)
pprint(SM; label=:name)

Construct stoichiometric matrix from database

In chemistryLab, it is possible to construct a stoichiometric matrix of species as a function of primary species given a database. Primary species candidates can be found in a database. Those from Cemdata18 can be listed with the following command:

using ChemistryLab
df_elements, df_substances, df_reactions = read_thermofun("../../../data/cemdata18-merged.json")
df_primaries = extract_primary_species("../../../data/CEMDATA18-31-03-2022-phaseVol.dat")
dict_species = Dict(zip(df_substances.symbol, df_substances.species))
candidate_primaries = [s == "Zz" ? Species("Zz") : dict_species[s] for s in df_primaries.symbol]

For a given number of species (eg. Portlandite and water), all ionic species which could appear during chemical reactions have to be identified:

given_species = filter(row -> row.symbol ∈ split("Portlandite H2O@"), df_substances)
secondaries = filter(row->row.aggregate_state == "AS_AQUEOUS" 
                          && all(k->first(k) ∈ union_atoms(atoms.(given_species.species)), atoms(row.species))
                          && row.symbol ∉ split("H2@ O2@"),
                          df_substances)

Primary species concerning by the reactions can then be deduced.

species = unique(vcat(given_species, secondaries), :symbol).species
candidate_primaries = [s == "Zz" ? Species("Zz") : dict_species[s] for s in df_primaries.symbol]

Finally, the stoichiometric matrix can be calculated:

SM = StoichMatrix(species, candidate_primaries)