Edit on GitHub

Collections

The current EquationOfStates contain

EquationOfState
├─ AntonSchmidt
├─ BreenanStacey
├─ FiniteStrainEOS
│  ├─ BirchMurnaghan2nd
│  ├─ BirchMurnaghan3rd
│  ├─ BirchMurnaghan4th
│  ├─ BirchMurnaghan5th
│  ├─ PoirierTarantola2nd
│  ├─ PoirierTarantola3rd
│  ├─ PoirierTarantola4th
│  └─ PoirierTarantola5th
├─ Murnaghan
├─ PolynomialEOS
├─ Shanker
└─ Vinet

Usage

Construct an EquationOfState

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 = Murnaghan(1, 2, 3.0)
Murnaghan{Float64}(1.0, 2.0, 3.0, 0.0)

julia> @set! eos.v0 = 4
Murnaghan{Float64}(4.0, 2.0, 3.0, 0.0)

julia> eos
Murnaghan{Float64}(4.0, 2.0, 3.0, 0.0)

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)
BirchMurnaghan4th{Float64}(1.0, 2.0, 3.0, 4.0, 0.0)

julia> set(eos, lens, (5, 6, 7, 8))
BirchMurnaghan4th{Float64}(5.0, 2.0, 6.0, 7.0, 8.0)

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

julia> eos = BirchMurnaghan3rd(1, 2, 3, 4.0)
4-element BirchMurnaghan3rd{Float64}:
 1.0
 2.0
 3.0
 4.0

julia> eos.v0
1.0

Calculate energy on an EquationOfState

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

  1. Murnaghan:

    \[E(V) = E_{0}+K_{0} V_{0}\left[\frac{1}{K_{0}^{\prime}\left(K_{0}^{\prime}-1\right)}\left(\frac{V}{V_{0}}\right)^{1-K_{0}^{\prime}}+\frac{1}{K_{0}^{\prime}} \frac{V}{V_{0}}-\frac{1}{K_{0}^{\prime}-1}\right].\]

  2. BirchMurnaghan2nd:

    \[E(V) = E_{0} + \frac{9}{8} B_{0} V_{0} \left(\left( V / V_0 \right)^{-2 / 3}-1\right)^{2}.\]

  3. 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].

  4. 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.

  5. PoirierTarantola2nd:

    \[E(V) = E_{0}+\frac{1}{2} B_{0} V_{0} \ln ^{2} x.\]

  6. PoirierTarantola3rd:

    \[E(V) = E_{0}+\frac{1}{6} B_{0} V_{0} \ln ^{2} x\left[\left(B_{0}^{\prime}+2\right) \ln x+3\right].\]

  7. 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.

  8. Vinet:

    \[E(V) = E_{0}+\frac{9}{16} V_{0} B_{0} \frac{\left(x^{2 / 3}-1\right)^{2}}{x^{7 / 3}}\left\{x^{1 / 3}\left(B_{0}^{\prime}-4\right)-x\left(B_{0}^{\prime}-6\right)\right\}.\]

  9. AntonSchmidt:

    \[E(V)=\frac{\beta V_{0}}{n+1}\left(\frac{V}{V_{0}}\right)^{n+1}\left[\ln \left(\frac{V}{V_{0}}\right)-\frac{1}{n+1}\right]+E_{\infty}.\]

Calculate pressure on an EquationOfState

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

  1. Murnaghan:

    \[P(V) = \frac{B_{0}}{B_{0}^{\prime}}\left[\left(\frac{V_{0}}{V}\right)^{B_{0}^{\prime}}-1\right].\]

  2. BirchMurnaghan2nd:

    \[P(V) = \frac{3}{2} B_{0}\left(x^{-7 / 3}-x^{-5 / 3}\right).\]

  3. BirchMurnaghan3rd:

    \[P(V) = \frac{3}{8} B_{0} \frac{x^{2 / 3}-1}{x^{10 / 3}}\left\{3 B_{0}^{\prime} x-16 x-3 x^{1 / 3}\left(B_{0}^{\prime}-4\right)\right\}.\]

  4. BirchMurnaghan4th:

    \[P(V) = \frac{1}{2} B_{0}(2 f+1)^{5 / 2}\left\{\left(9 H-63 B_{0}^{\prime}+143\right) f^{2}\right.\left.+9\left(B_{0}^{\prime}-4\right) f+6\right\}.\]

  5. PoirierTarantola2nd:

    \[P(V) = -\frac{B_{0}}{x} \ln x.\]

  6. PoirierTarantola3rd:

    \[P(V) = -\frac{B_{0} \ln x}{2 x}\left[\left(B_{0}^{\prime}+2\right) \ln x+2\right].\]

  7. PoirierTarantola4th:

    \[P(V) = -\frac{B_{0} \ln x}{6 x}\left\{\left(H+3 B_{0}^{\prime}+3\right) \ln ^{2} x+3\left(B_{0}^{\prime}+6\right) \ln x+6\right\}.\]

  8. Vinet:

    \[P(V) = 3 B_{0} \frac{1-\eta}{\eta^{2}} \exp \left\{-\frac{3}{2}\left(B_{0}^{\prime}-1\right)(\eta-1)\right\}.\]

  9. AntonSchmidt:

    \[P(V) = -\beta\left(\frac{V}{V_{0}}\right)^{n} \ln \left(\frac{V}{V_{0}}\right).\]

Calculate bulk modulus on an EquationOfState

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

  1. BirchMurnaghan2nd:

    \[B(V) = B_{0}(7 f+1)(2 f+1)^{5 / 2}.\]

  2. BirchMurnaghan3rd:

    \[B(V) = \frac{B_{0}}{8 x^{10 / 3}}\left\{x^{5 / 3}\left(15 B_{0}^{\prime}-80\right)-x\left(42 B_{0}^{\prime}-196\right)\right.\left.+27 x^{1 / 3}\left(B_{0}^{\prime}-4\right)\right\}.\]

  3. BirchMurnaghan4th:

    \[B(V) = \frac{1}{6} B_{0}(2 f+1)^{5 / 2}\left\{\left(99 H-693 B_{0}^{\prime}+1573\right) f^{3}\right.\left.+\left(27 H-108 B_{0}^{\prime}+105\right) f^{2}+6\left(3 B_{0}^{\prime}-5\right) f+6\right\}.\]

  4. PoirierTarantola2nd:

    \[B(V) = \frac{B_{0}}{x}(1-\ln x).\]

  5. PoirierTarantola3rd:

    \[B(V) = -\frac{B_{0}}{2 x}\left[\left(B_{0}^{\prime}+2\right) \ln x(\ln x-1)-2\right].\]

  6. PoirierTarantola4th:

    \[B(V) = -\frac{B_{0}}{6 x}\left\{\left(H+3 B_{0}^{\prime}+3\right) \ln ^{3} x-3\left(H+2 B_{0}^{\prime}+1\right) \ln ^{2} x\right.\left.-6\left(B_{0}^{\prime}+1\right) \ln x-6\right\}.\]

  7. Vinet:

    \[B(V) = -\frac{B_{0}}{2 \eta^{2}}\left[3 \eta(\eta-1)\left(B_{0}^{\prime}-1\right)+2(\eta-2)\right]\times \exp \left\{-\frac{3}{2}\left(B_{0}^{\prime}-1\right)(\eta-1)\right\}.\]

  8. AntonSchmidt:

    \[B(V) = \beta\left(\frac{V}{V_{0}}\right)^{n}\left[1+n \ln \frac{V}{V_{0}}\right].\]

Public interfaces

Missing docstring.

Missing docstring for Energy. Check Documenter's build log for details.

Missing docstring.

Missing docstring for Pressure. Check Documenter's build log for details.

Missing docstring.

Missing docstring for BulkModulus. Check Documenter's build log for details.

Missing docstring.

Missing docstring for EquationOfState. Check Documenter's build log for details.

EquationsOfState.Collections.Murnaghan — Type
Murnaghan(v0, b0, b′0, e0)

Create a Murnaghan equation of state.

This equation of state can have units. The units are specified in Unitful.jl's @u_str style.

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. Its default value is 0u"eV" (0), if other parameters have (no) units.

Examples

julia> Murnaghan(1, 2, 3.0)
Murnaghan{Float64}(1.0, 2.0, 3.0, 0.0)

julia> Murnaghan(Int8(1), 2//1, 3.0, 4)
Murnaghan{Float64}(1.0, 2.0, 3.0, 4.0)

julia> Murnaghan(1u"nm^3", 2u"GPa", 3, 3.0u"eV")
Murnaghan{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 3.0, 3.0 eV)
source
EquationsOfState.Collections.BirchMurnaghan2nd — Type
BirchMurnaghan2nd(v0, b0, e0)

Create a Birch–Murnaghan 2nd order equation of state.

Arguments

  • v0: the volume of solid at zero pressure.
  • b0: the bulk modulus of solid at zero pressure.
  • e0: the energy of solid at zero pressure. Its default value is 0u"eV" (0), if other parameters have (no) units.

See also: BirchMurnaghan3rd, BirchMurnaghan4th, BirchMurnaghan5th

Examples

julia> BirchMurnaghan2nd(1, 2.0)
BirchMurnaghan2nd{Float64}(1.0, 2.0, 0.0)

julia> BirchMurnaghan2nd(Int8(1), 2//1, 0.0)
BirchMurnaghan2nd{Float64}(1.0, 2.0, 0.0)

julia> BirchMurnaghan2nd(1u"nm^3", 2u"GPa", 3.0u"eV")
BirchMurnaghan2nd{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 3.0 eV)
source
EquationsOfState.Collections.BirchMurnaghan3rd — Type
BirchMurnaghan3rd(v0, b0, b′0, e0)

Create a Birch–Murnaghan 3rd order equation of state.

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. Its default value is 0u"eV" (0), if other parameters have (no) units.

See also: BirchMurnaghan2nd, BirchMurnaghan4th, BirchMurnaghan5th

Examples

julia> BirchMurnaghan3rd(1, 2.0, 3)
BirchMurnaghan3rd{Float64}(1.0, 2.0, 3.0, 0.0)

julia> BirchMurnaghan3rd(Int8(1), 2//1, 4, 0.0)
BirchMurnaghan3rd{Float64}(1.0, 2.0, 4.0, 0.0)

julia> BirchMurnaghan3rd(1u"nm^3", 2u"GPa", 4.0, 3u"eV")
BirchMurnaghan3rd{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 4.0, 3.0 eV)
source
EquationsOfState.Collections.BirchMurnaghan4th — Type
BirchMurnaghan4th(v0, b0, b′0, b′′0, e0)

Create a Birch–Murnaghan 4th order equation of state.

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.
  • b′′0: the second-order pressure-derivative bulk modulus of solid at zero pressure.
  • e0: the energy of solid at zero pressure. Its default value is 0u"eV" (0), if other parameters have (no) units.

See also: BirchMurnaghan2nd, BirchMurnaghan4th, BirchMurnaghan5th

Examples

julia> BirchMurnaghan4th(1, 2.0, 3, 4)
BirchMurnaghan4th{Float64}(1.0, 2.0, 3.0, 4.0, 0.0)

julia> BirchMurnaghan4th(Int8(1), 2//1, 4, 5.0, Float16(6))
BirchMurnaghan4th{Float64}(1.0, 2.0, 4.0, 5.0, 6.0)

julia> BirchMurnaghan4th(1u"nm^3", 2u"GPa", 3.0, 4u"1/GPa", 5u"eV")
BirchMurnaghan4th{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 3.0, 4.0 GPa⁻¹, 5.0 eV)
source
EquationsOfState.Collections.BirchMurnaghan5th — Type
BirchMurnaghan5th(v0, b0, b′0, b′′0, b′′′0, e0)

Create a Birch–Murnaghan 5th order equation of state.

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.
  • b′′0: the second-order pressure-derivative bulk modulus of solid at zero pressure.
  • b′′′0: the third-order pressure-derivative bulk modulus of solid at zero pressure.
  • e0: the energy of solid at zero pressure. Its default value is 0u"eV" (0), if other parameters have (no) units.

See also: BirchMurnaghan2nd, BirchMurnaghan3rd, BirchMurnaghan4th

Examples

julia> BirchMurnaghan5th(1, 2.0, 3, 4, 5 // 1)
BirchMurnaghan5th{Float64}(1.0, 2.0, 3.0, 4.0, 5.0, 0.0)

julia> BirchMurnaghan5th(Int8(1), 2//1, 3.0, Float16(4), 5)
BirchMurnaghan5th{Float64}(1.0, 2.0, 3.0, 4.0, 5.0, 0.0)

julia> BirchMurnaghan5th(1u"nm^3", 2u"GPa", 3, 4u"1/GPa", 5u"1/GPa^2", 6.0u"eV")
BirchMurnaghan5th{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 3.0, 4.0 GPa⁻¹, 5.0 GPa⁻², 6.0 eV)
source
EquationsOfState.Collections.PoirierTarantola2nd — Type
PoirierTarantola2nd(v0, b0, e0)

Create a Poirier–Tarantola order equation of state.

Arguments

  • v0: the volume of solid at zero pressure.
  • b0: the bulk modulus of solid at zero pressure.
  • e0: the energy of solid at zero pressure. Its default value is 0u"eV" (0), if other parameters have (no) units.

See also: PoirierTarantola3rd, PoirierTarantola4th, PoirierTarantola5th

Examples

julia> PoirierTarantola2nd(1, 2.0)
PoirierTarantola2nd{Float64}(1.0, 2.0, 0.0)

julia> PoirierTarantola2nd(Int8(1), 2//1, 3.0)
PoirierTarantola2nd{Float64}(1.0, 2.0, 3.0)

julia> PoirierTarantola2nd(1u"nm^3", 2u"GPa", 3.0u"eV")
PoirierTarantola2nd{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 3.0 eV)
source
EquationsOfState.Collections.PoirierTarantola3rd — Type
PoirierTarantola3rd(v0, b0, b′0, e0)

Create a Poirier–Tarantola 3rd order equation of state.

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. Its default value is 0u"eV" (0), if other parameters have (no) units.

See also: PoirierTarantola2nd, PoirierTarantola4th, PoirierTarantola5th

Examples

julia> PoirierTarantola3rd(1, 2.0, 3)
PoirierTarantola3rd{Float64}(1.0, 2.0, 3.0, 0.0)

julia> PoirierTarantola3rd(Int8(1), 2//1, 3.0, Float16(4))
PoirierTarantola3rd{Float64}(1.0, 2.0, 3.0, 4.0)

julia> PoirierTarantola3rd(1u"nm^3", 2u"GPa", 3, 4.0u"eV")
PoirierTarantola3rd{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 3.0, 4.0 eV)
source
EquationsOfState.Collections.PoirierTarantola4th — Type
PoirierTarantola4th(v0, b0, b′0, b′′0, e0)

Create a Poirier–Tarantola 4th order equation of state.

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.
  • b′′0: the second-order pressure-derivative bulk modulus of solid at zero pressure.
  • e0: the energy of solid at zero pressure. Its default value is 0u"eV" (0), if other parameters have (no) units.

See also: PoirierTarantola2nd, PoirierTarantola3rd, PoirierTarantola5th

Examples

julia> PoirierTarantola4th(1, 2.0, 3, 4)
PoirierTarantola4th{Float64}(1.0, 2.0, 3.0, 4.0, 0.0)

julia> PoirierTarantola4th(Int8(1), 2//1, 3.0, Float16(4), 5)
PoirierTarantola4th{Float64}(1.0, 2.0, 3.0, 4.0, 5.0)

julia> PoirierTarantola4th(1u"nm^3", 2u"GPa", 3, 4u"1/GPa", 5.0u"eV")
PoirierTarantola4th{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 3.0, 4.0 GPa⁻¹, 5.0 eV)
source
EquationsOfState.Collections.PoirierTarantola5th — Type
PoirierTarantola5th(v0, b0, b′0, b′′0, b′′′0, e0)

Create a Poirier–Tarantola 5th order equation of state.

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.
  • b′′0: the second-order pressure-derivative bulk modulus of solid at zero pressure.
  • b′′′0: the third-order pressure-derivative bulk modulus of solid at zero pressure.
  • e0: the energy of solid at zero pressure. Its default value is 0u"eV" (0), if other parameters have (no) units.

See also: PoirierTarantola2nd, PoirierTarantola3rd, PoirierTarantola4th

Examples

julia> PoirierTarantola5th(1, 2.0, 3, 4, 5 // 1)
PoirierTarantola5th{Float64}(1.0, 2.0, 3.0, 4.0, 5.0, 0.0)

julia> PoirierTarantola5th(Int8(1), 2//1, 3.0, Float16(4), 5)
PoirierTarantola5th{Float64}(1.0, 2.0, 3.0, 4.0, 5.0, 0.0)

julia> PoirierTarantola5th(1u"nm^3", 2u"GPa", 3, 4u"1/GPa", 5u"1/GPa^2", 6.0u"eV")
PoirierTarantola5th{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 3.0, 4.0 GPa⁻¹, 5.0 GPa⁻², 6.0 eV)
source
EquationsOfState.Collections.Vinet — Type
Vinet(v0, b0, b′0, e0)

Create a Vinet equation of state.

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. Its default value is 0u"eV" (0), if other parameters have (no) units.

Examples

julia> Vinet(1, 2.0, 3)
Vinet{Float64}(1.0, 2.0, 3.0, 0.0)

julia> Vinet(Int8(1), 2//1, 3.0, Float16(4))
Vinet{Float64}(1.0, 2.0, 3.0, 4.0)

julia> Vinet(1u"nm^3", 2u"GPa", 3, 4.0u"eV")
Vinet{Quantity{Float64,D,U} where U where D}(1.0 nm³, 2.0 GPa, 3.0, 4.0 eV)
source