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The current EquationOfStateOfSolidsParameters are

julia> using TypeTree
julia> tt(EquationsOfStateOfSolids.EquationOfStateOfSolidsParameters)ERROR: UndefVarError: EquationsOfStateOfSolids not defined

Here the leaves of the type tree are concrete types and can be constructed.

Usage

Construct a `EquationOfStateOfSolidsParameters` instance

We will use BirchMurnaghan3rd as an example.

A BirchMurnaghan3rd can be constructed from scratch, as shown above. It can also be constructed from an existing BirchMurnaghan3rd, with Setfield.jl @set! macro:

julia> using Setfield
julia> eos = Murnaghan1st(1, 2, 3.0)ERROR: UndefVarError: Murnaghan1st not defined
julia> @set! eos.v0 = 4ERROR: UndefVarError: eos not defined
julia> eosERROR: UndefVarError: eos not defined

To modify multiple fields (say, :v0, :b′0, :b″0, :e0) at a time, use @batchlens from Kaleido.jl:

julia> using Setfield, Kaleido
julia> lens = @batchlens(begin
                  _.v0
                  _.b′0
                  _.b″0
                  _.e0
              end)IndexBatchLens(:v0, :b′0, :b″0, :e0)
julia> eos = BirchMurnaghan4th(1, 2.0, 3, 4)ERROR: UndefVarError: BirchMurnaghan4th not defined
julia> set(eos, lens, (5, 6, 7, 8))ERROR: UndefVarError: eos not defined

Users can access BirchMurnaghan3rd's elements by "dot notation":

julia> eos = BirchMurnaghan3rd(1, 2, 3, 4.0)ERROR: UndefVarError: BirchMurnaghan3rd not defined
julia> eos.v0ERROR: UndefVarError: eos not defined

Evaluate energy

The $E(V)$ relation of equations of state are listed as below:

Murnaghan:
BirchMurnaghan2nd:
\[\]
BirchMurnaghan3rd:
\[E(V) = E_{0}+\frac{9}{16} V_{0} B_{0} \frac{\left(x^{2 / 3}-1\right)^{2}}{x^{7 / 3}}\left\{x^{1 / 3}\left(B_{0}^{\prime}-4\right)-x\left(B_{0}^{\prime}-6\right)\right\}.\]
where $x = V / V_0$, and $f = \frac{ 1 }{ 2 } \bigg[ \bigg( \frac{ V_0 }{ V } \bigg)^{2/3} - 1 \bigg]$.
BirchMurnaghan4th:
\[E(V) = E_{0}+\frac{3}{8} V_{0} B_{0} f^{2}\left[\left(9 H-63 B_{0}^{\prime}+143\right) f^{2}+12\left(B_{0}^{\prime}-4\right) f+12\right].\]
where $H = B_0 B_0'' + (B_0')^2$.
PoirierTarantola2nd:
\[E(V) = E_{0}+\frac{1}{2} B_{0} V_{0} \ln ^{2} x.\]
PoirierTarantola3rd:
\[E(V) = E_{0}+\frac{1}{6} B_{0} V_{0} \ln ^{2} x\left[\left(B_{0}^{\prime}+2\right) \ln x+3\right].\]
PoirierTarantola4th:
\[E(V) = E_{0}+\frac{1}{24} B_{0} V_{0} \ln ^{2} x\left\{\left(H+3 B_{0}^{\prime}+3\right) \ln ^{2} x\right. \left.+4\left(B_{0}^{\prime}+2\right) \ln x+12\right\}.\]
where $H = B_0 B_0'' + (B_0')^2$.
Vinet:
\[E(V) = E_{0}+\frac{9}{16} V_{0} B_{0} \frac{\left(x^{2 / 3}-1\right)^{2}}{x^{7 / 3}}\left\{x^{1 / 3}\left(B_{0}^{\prime}-4\right)-x\left(B_{0}^{\prime}-6\right)\right\}.\]
AntonSchmidt:
\[E(V)=\frac{\beta V_{0}}{n+1}\left(\frac{V}{V_{0}}\right)^{n+1}\left[\ln \left(\frac{V}{V_{0}}\right)-\frac{1}{n+1}\right]+E_{\infty}.\]

Evaluate pressure

The $P(V)$ relation of equations of state are listed as below:

Murnaghan:
\[1\]
BirchMurnaghan2nd:
\[P(V) = \frac{3}{2} B_{0}\left(x^{-7 / 3}-x^{-5 / 3}\right).\]
BirchMurnaghan3rd:
\[P(V) = \frac{3}{8} B_{0} \frac{x^{2 / 3}-1}{x^{10 / 3}}\left\{3 B_{0}^{\prime} x-16 x-3 x^{1 / 3}\left(B_{0}^{\prime}-4\right)\right\}.\]
BirchMurnaghan4th:
\[P(V) = \frac{1}{2} B_{0}(2 f+1)^{5 / 2}\left\{\left(9 H-63 B_{0}^{\prime}+143\right) f^{2}\right.\left.+9\left(B_{0}^{\prime}-4\right) f+6\right\}.\]
PoirierTarantola2nd:
\[P(V) = -\frac{B_{0}}{x} \ln x.\]
PoirierTarantola3rd:
\[P(V) = -\frac{B_{0} \ln x}{2 x}\left[\left(B_{0}^{\prime}+2\right) \ln x+2\right].\]
PoirierTarantola4th:
\[P(V) = -\frac{B_{0} \ln x}{6 x}\left\{\left(H+3 B_{0}^{\prime}+3\right) \ln ^{2} x+3\left(B_{0}^{\prime}+6\right) \ln x+6\right\}.\]
Vinet:
\[P(V) = 3 B_{0} \frac{1-\eta}{\eta^{2}} \exp \left\{-\frac{3}{2}\left(B_{0}^{\prime}-1\right)(\eta-1)\right\}.\]
AntonSchmidt:
\[P(V) = -\beta\left(\frac{V}{V_{0}}\right)^{n} \ln \left(\frac{V}{V_{0}}\right).\]

Evaluate bulk modulus

The $B(V)$ relation of equations of state are listed as below:

BirchMurnaghan2nd:
\[B(V) = B_{0}(7 f+1)(2 f+1)^{5 / 2}.\]
BirchMurnaghan3rd:
\[B(V) = B_{0}(2 f+1)^{5 / 2} \left\{ 1 + (3B_{0}^{\prime} - 5) f + \frac{ 27 }{ 2 }(B_{0}^{\prime} - 4) f^2 \right\}\]
BirchMurnaghan4th:
\[B(V) = \frac{1}{6} B_{0}(2 f+1)^{5 / 2}\left\{\left(99 H-693 B_{0}^{\prime}+1573\right) f^{3}\right.\left.+\left(27 H-108 B_{0}^{\prime}+105\right) f^{2}+6\left(3 B_{0}^{\prime}-5\right) f+6\right\}.\]
PoirierTarantola2nd:
\[B(V) = \frac{B_{0}}{x}(1-\ln x).\]
PoirierTarantola3rd:
\[B(V) = -\frac{B_{0}}{2 x}\left[\left(B_{0}^{\prime}+2\right) \ln x(\ln x-1)-2\right].\]
PoirierTarantola4th:
\[B(V) = -\frac{B_{0}}{6 x}\left\{\left(H+3 B_{0}^{\prime}+3\right) \ln ^{3} x-3\left(H+2 B_{0}^{\prime}+1\right) \ln ^{2} x\right.\left.-6\left(B_{0}^{\prime}+1\right) \ln x-6\right\}.\]
Vinet:
\[B(V) = -\frac{B_{0}}{2 \eta^{2}}\left[3 \eta(\eta-1)\left(B_{0}^{\prime}-1\right)+2(\eta-2)\right]\times \exp \left\{-\frac{3}{2}\left(B_{0}^{\prime}-1\right)(\eta-1)\right\}.\]
AntonSchmidt:
\[B(V) = \beta\left(\frac{V}{V_{0}}\right)^{n}\left[1+n \ln \frac{V}{V_{0}}\right].\]

Public interfaces

EquationsOfStateOfSolids.Murnaghan1st — Type

Murnaghan1st(v0, b0, b′0, e0=zero(v0 * b0))

Create a Murnaghan first order equation of state.

The energy and pressure equations are:

\[\begin{align*} E(V) &= E_0+B_0 V_0\left[\frac{1}{B_0'\left(B_0'-1\right)}\left(\frac{V}{V_0}\right)^{1-B_0'}+\frac{V}{B_0' V_0}-\frac{1}{B_0'-1}\right]\\ P(V) &= \frac{B_0}{B_0'}\left[\left(\frac{V_0}{V}\right)^{B_0'}-1\right] \end{align*}\]

Arguments

v0: the volume of solid at zero pressure.
b0: the bulk modulus of solid at zero pressure.
b′0: the first-order pressure-derivative bulk modulus of solid at zero pressure.
e0: the energy of solid at zero pressure.