Cement chemist notation

Before this page

Chemical Formula Manipulation.

Cement chemistry writes its phases in a shorthand that is opaque on first sight and indispensable once learned: alite is C3S, portlandite is CH, ettringite is C6AS̄3H32. This page is the key to it, and to how ChemistryLab reads it.

The idea is simple. A cement phase is an assembly of oxides, so each oxide gets a one-letter symbol and a phase is written as the oxides it contains, with their molar multiplicities. C3S is three parts lime to one of silica —    — which is written the way a cement chemist thinks about it: not as an arbitrary silicate, but as this much lime combined with that much silica.

The alphabet

using ChemistryLab
using DynamicQuantities
using Markdown, Printf

# The names are this page's. The formulas are the parser's own mapping,
# CEMENT_TO_MENDELEEV, and the molar masses are computed from them.
oxide_names = [
    :C => "lime", :S => "silica", :A => "alumina", :F => "ferric oxide",
    :M => "magnesia", :K => "potassium oxide", :N => "sodium oxide",
    :T => "titania", :P => "phosphorus pentoxide", :H => "water",
    :C̄ => "carbon dioxide", :S̄ => "sulfur trioxide", :N̄ => "nitrate",
]
mapping = Dict(CEMENT_TO_MENDELEEV)
@assert Set(first.(oxide_names)) == Set(keys(mapping))   # every letter, and no other

rows = ["| Symbol | Oxide | Name | Molar mass |", "|:------:|:------|:-----|-----------:|"]
for (letter, oxide_name) in oxide_names
    formula = join(string(el, n == 1 ? "" : n) for (el, n) in mapping[letter])
    M = ustrip(us"g/mol", Species(formula).M)
    push!(rows, @sprintf("| `%s` | %s | %s | %.2f g/mol |",
                         letter, phreeqc_to_unicode(formula), oxide_name, M))
end
Markdown.parse(join(rows, "\n"))

Symbol	Oxide	Name	Molar mass
C	CaO	lime	56.08 g/mol
S	SiO₂	silica	60.08 g/mol
A	Al₂O₃	alumina	101.96 g/mol
F	Fe₂O₃	ferric oxide	159.69 g/mol
M	MgO	magnesia	40.30 g/mol
K	K₂O	potassium oxide	94.20 g/mol
N	Na₂O	sodium oxide	61.98 g/mol
T	TiO₂	titania	79.86 g/mol
P	P₂O₅	phosphorus pentoxide	141.94 g/mol
H	H₂O	water	18.01 g/mol
C̄	CO₂	carbon dioxide	44.01 g/mol
S̄	SO₃	sulfur trioxide	80.06 g/mol
N̄	NO₃	nitrate	62.00 g/mol

The table is produced from the mapping the parser itself uses, CEMENT_TO_MENDELEEV, and its molar masses are computed from the formulas, so it cannot drift from what ChemistryLab accepts.

The first four are the oxides a clinker is made of, and the four a datasheet always reports; the next five are the minor oxides; the last three are the acidic ones that take a bar.

Two conventions decide everything, and they are where a newcomer stumbles:

• A letter stands for an oxide, not an element. C is lime , not carbon; S is silica , not sulfur; N is , not nitrogen.

• The bar marks the acidic oxides whose letter is already taken. Carbon dioxide is C̄ because C is lime, and sulfur trioxide is S̄ because S is silica. The bar is a combining macron (U+0304): type the letter, then that character.

H is water, which is why hydrates carry a large H count: C4AH13 is     .

Reading and building a phase

CemSpecies parses the shorthand. Ordinary ASCII digits and Unicode subscripts are both accepted, and non-integer multiplicities are allowed — which matters for C-S-H, whose lime-to-silica ratio is a composition, not a constant:

for name in ["C3S", "C2S", "C3A", "C4AF", "CH", "C₄AH₁₃", "C1.7SH4"]
    sp = CemSpecies(name)
    println(rpad(name, 9), " -> ", rpad(unicode(sp), 12),
            "  M = ", round(ustrip(us"g/mol", sp.M), digits = 2), " g/mol")
end

C3S       -> C₃S           M = 228.31 g/mol
C2S       -> C₂S           M = 172.24 g/mol
C3A       -> C₃A           M = 270.19 g/mol
C4AF      -> C₄AF          M = 485.96 g/mol
CH        -> CH            M = 74.09 g/mol
C₄AH₁₃    -> C₄AH₁₃        M = 560.46 g/mol
C1.7SH4   -> C₁.₇SH₄       M = 227.47 g/mol

The composition in ordinary elements is always available, so the shorthand is a way of writing a species and never a different kind of object:

atoms(CemSpecies("C3S"))

OrderedCollections.OrderedDict{Symbol, Int64} with 3 entries:
  :Ca => 3
  :O  => 5
  :Si => 1

The trap: Species and CemSpecies read the same string differently

This is the single most expensive mistake to make, and it is silent:

cem = CemSpecies("C3S")
ord = Species("C3S")

println("CemSpecies(\"C3S\") = ", unicode(cem), "   M = ",
        round(ustrip(us"g/mol", cem.M), digits = 2), " g/mol   (3 CaO + SiO2)")
println("Species(\"C3S\")    = ", unicode(ord), "   M = ",
        round(ustrip(us"g/mol", ord.M), digits = 2), " g/mol   (3 carbons + 1 sulfur)")

CemSpecies("C3S") = C₃S   M = 228.31 g/mol   (3 CaO + SiO2)
Species("C3S")    = C₃S   M = 68.09 g/mol   (3 carbons + 1 sulfur)

Both display as C₃S, and they differ by more than a factor of three in molar mass. Species applies the ordinary rules of chemical formulas, in which C is carbon and S is sulfur; CemSpecies applies the cement convention. Neither is wrong — they answer different questions — but a recipe that reaches for the wrong one is wrong everywhere downstream and raises no error.

Read a database phase by name, never by re-parsing its symbol

A phase read from a thermodynamic database already carries its composition and its molar mass. Look it up by name — byname["C3S"] — rather than rebuilding it from its symbol with Species, which would read C3S as three carbons and a sulfur. This is the reason the worked examples in this documentation never write a molar mass by hand.

The common phases, and what they weigh

Nothing below is typed from a table: each mass is computed from the formula and the element data.

phases = [
    ("C3S",       "alite"),
    ("C2S",       "belite"),
    ("C3A",       "aluminate"),
    ("C4AF",      "ferrite"),
    ("CS̄H2",      "gypsum"),
    ("CH",        "portlandite"),
    ("CC̄",        "calcite"),
    ("C6AS̄3H32",  "ettringite (AFt)"),
    ("C4AS̄H12",   "monosulfoaluminate (AFm)"),
    ("C4AH13",    "hydroxy-AFm"),
    ("C2ASH8",    "strätlingite"),
    ("C3AH6",     "hydrogarnet"),
    ("M5AH13",    "hydrotalcite"),
]

for (name, english) in phases
    sp = CemSpecies(name)
    println(rpad(unicode(sp), 13), rpad(english, 28),
            lpad(round(ustrip(us"g/mol", sp.M), digits = 2), 8), " g/mol")
end

C₃S          alite                         228.31 g/mol
C₂S          belite                        172.24 g/mol
C₃A          aluminate                     270.19 g/mol
C₄AF         ferrite                       485.96 g/mol
CS̄H₂         gypsum                        172.16 g/mol
CH           portlandite                    74.09 g/mol
CC̄           calcite                       100.09 g/mol
C₆AS̄₃H₃₂     ettringite (AFt)             1255.07 g/mol
C₄AS̄H₁₂      monosulfoaluminate (AFm)      622.51 g/mol
C₄AH₁₃       hydroxy-AFm                   560.46 g/mol
C₂ASH₈       strätlingite                  418.32 g/mol
C₃AH₆        hydrogarnet                   378.28 g/mol
M₅AH₁₃       hydrotalcite                  537.68 g/mol

Ettringite carries alumina, and the shorthand must say so

Ettringite is — six lime, one alumina, three sulfate, thirty-two water — at 1255 g/mol. Dropping the A gives C6S̄3H32, which parses without complaint, weighs 1153 g/mol and is not a cement phase. The shorthand is compact enough that an omission looks like a typo and behaves like a different substance.

Where the notation is used

• CemSpecies for the species themselves;

• the oxide components of a stoichiometric decomposition — see Stoichiometric matrices, where a clinker phase is expressed over C, S, A, F;

• the Bogue Calculation, which is that decomposition inverted and converted to mass.

Where to go next

The notation is attached to species in Cement Species, and its inversion from an oxide analysis to phase masses is Bogue Calculation.