py_utils.loop_energetics.LoopEnergetics Class Reference

Collaboration diagram for py_utils.loop_energetics.LoopEnergetics:

Public Member Functions
None	__post_init__ (self)
	area (self, n, int char)
	R_star (self, n, int char)
	perimeter (self, n, int char)
	E_l_111 (self, n)
	E_l_100_core (self, n)
	E_l_100_pre (self, n)
	Fhat_100 (self, T_K)
	E_l_100 (self, n, T_K)
	delta_F (self, n, T_K)
float	calibrate (self, float|None T_star_C=None, float|None n_ref=None)
	crossover_temperature (self, n)
np.ndarray	conversion_mask (self, T_K, int n_max)
np.ndarray	driving_force_array (self, T_K, int n_max)

Public Attributes
	b_111
	b_100
	T_star_C
	n_ref
	delta
	Fc_111
	Fc_100
	Fhat_100_0

Static Public Attributes
float	a = 2.8665
float	Omega = 11.78
float	delta = 4.0
float	Tc = 1185.0
float	Fhat_111 = 0.28
float	Fhat_100_0 = None
float	Fdelta_111 = 0.345
float	Fc_111 = 0.46
float	Fdelta_100 = 0.387
float	Fc_100 = 0.33
float	T_star_C = 450.0
float	n_ref = 30.0

Protected Member Functions
float	_b (self, int char)
	_Lln (self, n, int char)
	_softening (self, T_K)

Detailed Description

½⟨111⟩ / ⟨100⟩ loop energies and the unary-conversion driving force.

Lengths are in ångström and energies in eV.  Defaults are bcc-Fe values
consistent with :mod:`binding_energies`.

Definition at line 61 of file loop_energetics.py.

Member Function Documentation

__post_init__()

None py_utils.loop_energetics.LoopEnergetics.__post_init__

(

self

)

Definition at line 93 of file loop_energetics.py.

_b()

float py_utils.loop_energetics.LoopEnergetics._b (   self, int  char  )

protected

Definition at line 100 of file loop_energetics.py.

_Lln()

py_utils.loop_energetics.LoopEnergetics._Lln (   self,   n, int  char  )

protected

Definition at line 118 of file loop_energetics.py.

_softening()

py_utils.loop_energetics.LoopEnergetics._softening (   self,   T_K  )

protected

(1 − T/T_c)^{1/4}, clipped to ≥ 0 above T_c (Dudarev Eq. 4).

Definition at line 136 of file loop_energetics.py.

area()

py_utils.loop_energetics.LoopEnergetics.area	(		self,
			n,
		int	char
	)

Platelet area A = n·Ω/b_X  [Ų].

Definition at line 103 of file loop_energetics.py.

calibrate()

float py_utils.loop_energetics.LoopEnergetics.calibrate	(		self,
		float | None	T_star_C = None,
		float | None	n_ref = None
	)

Set F̂_100^0 so that ΔF(n_ref, T*) = 0; return F̂_100^0.

Guarantees ΔF(n_ref, T) < 0 for T < T* and > 0 for T > T* (the
softening is monotonic), i.e. ½⟨111⟩ stable below the crossover and
⟨100⟩ above it.  Requires E_l^111(n_ref) > E_l^100_core(n_ref) (the
⟨100⟩ core alone lies below the ½⟨111⟩ energy), which holds for the
defaults.

Definition at line 153 of file loop_energetics.py.

conversion_mask()

np.ndarray py_utils.loop_energetics.LoopEnergetics.conversion_mask	(		self,
			T_K,
		int	n_max
	)

Boolean array over sizes 1..n_max where ΔF(n,T) > 0 (⟨100⟩ favoured).

The unary-conversion kernel Γ_uni(n,T) is nonzero only on this support
(and is further gated by the [1 − exp(−ΔF/k_BT)] factor in
``reaction_rates``).  Independent of the ⟨100⟩ population's admissible
size floor, which is the loop-onset size, not this thermodynamic set.

Definition at line 194 of file loop_energetics.py.

crossover_temperature()

py_utils.loop_energetics.LoopEnergetics.crossover_temperature	(		self,
			n
	)

Temperature [°C] where ΔF(n,T)=0, or NaN if none in (0, T_c).

Solves F̂_100^0·(1−T/T_c)^{1/4}·E_pre = E_l^111 − E_l^100_core.

Definition at line 179 of file loop_energetics.py.

delta_F()

py_utils.loop_energetics.LoopEnergetics.delta_F	(		self,
			n,
			T_K
	)

Unary-conversion driving force ΔF(n,T) [eV]; > 0 favours ⟨100⟩.

Definition at line 149 of file loop_energetics.py.

driving_force_array()

np.ndarray py_utils.loop_energetics.LoopEnergetics.driving_force_array	(		self,
			T_K,
		int	n_max
	)

ΔF(n,T) over sizes n = 1..n_max  [eV] (0-indexed by size−1).

Definition at line 205 of file loop_energetics.py.

E_l_100()

py_utils.loop_energetics.LoopEnergetics.E_l_100	(		self,
			n,
			T_K
	)

⟨100⟩ loop free energy E_l^100(n,T)  [eV].

Definition at line 144 of file loop_energetics.py.

E_l_100_core()

py_utils.loop_energetics.LoopEnergetics.E_l_100_core	(		self,
			n
	)

T-independent core part of the ⟨100⟩ loop energy  [eV].

Definition at line 128 of file loop_energetics.py.

E_l_100_pre()

py_utils.loop_energetics.LoopEnergetics.E_l_100_pre	(		self,
			n
	)

⟨100⟩ prelog part *without* the F̂_100(T) factor  [eV·Å/(eV/Å)].

Definition at line 132 of file loop_energetics.py.

E_l_111()

py_utils.loop_energetics.LoopEnergetics.E_l_111	(		self,
			n
	)

½⟨111⟩ loop free energy E_l^111(n)  [eV]  (T-independent here).

Definition at line 122 of file loop_energetics.py.

Fhat_100()

py_utils.loop_energetics.LoopEnergetics.Fhat_100	(		self,
			T_K
	)

⟨100⟩ prelogarithmic factor F̂_100(T)  [eV/Å].

Definition at line 140 of file loop_energetics.py.

perimeter()

py_utils.loop_energetics.LoopEnergetics.perimeter	(		self,
			n,
		int	char
	)

Loop perimeter: hexagon (½⟨111⟩) or square (⟨100⟩)  [Å].

Definition at line 111 of file loop_energetics.py.

R_star()

py_utils.loop_energetics.LoopEnergetics.R_star	(		self,
			n,
		int	char
	)

Equivalent-circle radius R*_X = √(A/π)  [Å].

Definition at line 107 of file loop_energetics.py.

Member Data Documentation

a

float py_utils.loop_energetics.LoopEnergetics.a = 2.8665

static

Definition at line 69 of file loop_energetics.py.

b_100

py_utils.loop_energetics.LoopEnergetics.b_100

Definition at line 95 of file loop_energetics.py.

b_111

py_utils.loop_energetics.LoopEnergetics.b_111

Definition at line 94 of file loop_energetics.py.

delta [1/2]

float py_utils.loop_energetics.LoopEnergetics.delta = 4.0

static

Definition at line 71 of file loop_energetics.py.

delta [2/2]

py_utils.loop_energetics.LoopEnergetics.delta

Definition at line 119 of file loop_energetics.py.

Fc_100 [1/2]

float py_utils.loop_energetics.LoopEnergetics.Fc_100 = 0.33

static

Definition at line 82 of file loop_energetics.py.

Fc_100 [2/2]

py_utils.loop_energetics.LoopEnergetics.Fc_100

Definition at line 130 of file loop_energetics.py.

Fc_111 [1/2]

float py_utils.loop_energetics.LoopEnergetics.Fc_111 = 0.46

static

Definition at line 80 of file loop_energetics.py.

Fc_111 [2/2]

py_utils.loop_energetics.LoopEnergetics.Fc_111

Definition at line 126 of file loop_energetics.py.

Fdelta_100

float py_utils.loop_energetics.LoopEnergetics.Fdelta_100 = 0.387

static

Definition at line 81 of file loop_energetics.py.

Fdelta_111

float py_utils.loop_energetics.LoopEnergetics.Fdelta_111 = 0.345

static

Definition at line 79 of file loop_energetics.py.

Fhat_100_0 [1/2]

float py_utils.loop_energetics.LoopEnergetics.Fhat_100_0 = None

static

Definition at line 76 of file loop_energetics.py.

Fhat_100_0 [2/2]

py_utils.loop_energetics.LoopEnergetics.Fhat_100_0

Definition at line 176 of file loop_energetics.py.

Fhat_111

float py_utils.loop_energetics.LoopEnergetics.Fhat_111 = 0.28

static

Definition at line 75 of file loop_energetics.py.

n_ref [1/2]

float py_utils.loop_energetics.LoopEnergetics.n_ref = 30.0

static

Definition at line 91 of file loop_energetics.py.

n_ref [2/2]

py_utils.loop_energetics.LoopEnergetics.n_ref

Definition at line 97 of file loop_energetics.py.

Omega

float py_utils.loop_energetics.LoopEnergetics.Omega = 11.78

static

Definition at line 70 of file loop_energetics.py.

T_star_C [1/2]

float py_utils.loop_energetics.LoopEnergetics.T_star_C = 450.0

static

Definition at line 85 of file loop_energetics.py.

T_star_C [2/2]

py_utils.loop_energetics.LoopEnergetics.T_star_C

Definition at line 97 of file loop_energetics.py.

Tc

float py_utils.loop_energetics.LoopEnergetics.Tc = 1185.0

static

Definition at line 72 of file loop_energetics.py.

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The documentation for this class was generated from the following file:

• radcluster_code/py_utils/loop_energetics.py