pmutt.statmech.vib.EinsteinVib

class pmutt.statmech.vib.EinsteinVib(einstein_temperature, interaction_energy=0.0)

Bases: _ModelBase

Einstein model of a crystal. Equations used sourced from

Sandler, S. I. An Introduction to Applied Statistical Thermodynamics; John Wiley & Sons, 2010.

einstein_temperature

Einstein temperature (\(\Theta_E\)) in K

Type:: float

interaction_energy

Interaction energy (\(u\)) per atom in eV. Default is 0 eV

Type:: float, optional

__init__(einstein_temperature, interaction_energy=0.0)

Methods

`__init__`(einstein_temperature[, ...])
`from_dict`(json_obj)	Recreate an object from the JSON representation.
`get_Cp`(units, **kwargs)	Calculate the heat capacity (constant P)
`get_CpoR`(T)	Calculates the dimensionless heat capacity at constant pressure
`get_Cv`(units, **kwargs)	Calculate the heat capacity (constant V)
`get_CvoR`(T)	Calculates the dimensionless heat capacity at constant volume
`get_F`(units[, T])	Calculate the Helmholtz energy
`get_FoRT`(T)	Calculates the dimensionless Helmholtz energy
`get_G`(units[, T])	Calculate the Gibbs energy
`get_GoRT`(T)	Calculates the dimensionless Gibbs energy
`get_H`(units[, T])	Calculate the enthalpy
`get_HoRT`(T)	Calculates the dimensionless enthalpy
`get_S`(units, **kwargs)	Calculate the entropy
`get_SoR`(T)	Calculates the dimensionless entropy
`get_U`(units[, T])	Calculate the internal energy
`get_UoRT`(T)	Calculates the dimensionless internal energy
`get_ZPE`()	Calculates the zero point energy
`get_q`(T)	Calculates the partition function
`to_dict`()	Represents object as dictionary with JSON-accepted datatypes

classmethod from_dict(json_obj)

Recreate an object from the JSON representation.

Parameters:: json_obj (dict) – JSON representation
Returns:: Obj
Return type:: Appropriate object

get_Cp(units, **kwargs)

Calculate the heat capacity (constant P)

Parameters:

units (str) – Units as string. See R() for accepted units.
kwargs (keyword arguments) – Parameters needed by get_CpoR

Returns:

Cp – Heat capacity (constant P) in appropriate units

Return type:

float

get_CpoR(T)

Calculates the dimensionless heat capacity at constant pressure

\(\frac{C_P^{vib}}{R}=\frac{C_V^{vib}}{R}=3\bigg(\frac{ \Theta_E}{T}\bigg)^2\frac{\exp(-\frac{\Theta_E}{T})}{\big(1- \exp(\frac{-\Theta_E}{T})\big)^2}\)

Parameters:: T (float) – Temperature in K
Returns:: CpoR_vib – Vibrational dimensionless heat capacity at constant pressure
Return type:: float

get_Cv(units, **kwargs)

Calculate the heat capacity (constant V)

Parameters:

units (str) – Units as string. See R() for accepted units.
kwargs (keyword arguments) – Parameters needed by get_CvoR

Returns:

Cv – Heat capacity (constant V) in appropriate units

Return type:

float

get_CvoR(T)

Calculates the dimensionless heat capacity at constant volume

\(\frac{C_V^{vib}}{R}=3\bigg(\frac{\Theta_E}{T}\bigg)^2 \frac{\exp(-\frac{\Theta_E}{T})}{\big(1-\exp(\frac{- \Theta_E}{T})\big)^2}\)

Parameters:: T (float) – Temperature in K
Returns:: CvoR_vib – Vibrational dimensionless heat capacity at constant volume
Return type:: float

get_F(units, T=298.15, **kwargs)

Calculate the Helmholtz energy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_FoRT

Returns:

F – Hemholtz energy in appropriate units

Return type:

float

get_FoRT(T)

Calculates the dimensionless Helmholtz energy

\(\frac{A^{vib}}{RT}=\frac{U^{vib}}{RT}-\frac{S^{vib}}{R}\)

Parameters:: T (float) – Temperature in K
Returns:: FoRT_vib – Vibrational dimensionless Helmholtz energy
Return type:: float

get_G(units, T=298.15, **kwargs)

Calculate the Gibbs energy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_GoRT

Returns:

G – Gibbs energy in appropriate units

Return type:

float

get_GoRT(T)

Calculates the dimensionless Gibbs energy

\(\frac{G^{vib}}{RT}=\frac{H^{vib}}{RT}-\frac{S^{vib}}{R}\)

Parameters:: T (float) – Temperature in K
Returns:: GoRT_vib – Vibrational dimensionless Gibbs energy
Return type:: float

get_H(units, T=298.15, **kwargs)

Calculate the enthalpy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_HoRT

Returns:

H – Enthalpy in appropriate units

Return type:

float

get_HoRT(T)

Calculates the dimensionless enthalpy

\(\frac{H^{vib}}{RT}=\frac{U^{vib}}{RT}=\frac{N_A u^0_E}{k_BT} +3\frac{\Theta_E}{T}\bigg(\frac{\exp(-\frac{\Theta_E}{T})}{1- \exp(-\frac{\Theta_E}{T})}\bigg)\)

Parameters:: T (float) – Temperature in K
Returns:: HoRT_vib – Vibrational dimensionless enthalpy
Return type:: float

get_S(units, **kwargs)

Calculate the entropy

Parameters:

units (str) – Units as string. See R() for accepted units.
kwargs (keyword arguments) – Parameters needed by get_SoR

Returns:

S – Entropy in appropriate units

Return type:

float

get_SoR(T)

Calculates the dimensionless entropy

\(\frac{S^{vib}}{R}=3\bigg(\frac{\Theta_E}{T}\frac{\exp\big( \frac{-\Theta_E}{T}\big)}{1-\exp\big(-\frac{\Theta_E}{T}\big)} \bigg)-\ln\bigg(1-\exp\big(\frac{-\Theta_E}{T}\big)\bigg)\)

Parameters:: T (float) – Temperature in K
Returns:: SoR_vib – Vibrational dimensionless entropy
Return type:: float

get_U(units, T=298.15, **kwargs)

Calculate the internal energy

Parameters:

units (str) – Units as string. See R() for accepted units but omit the ‘/K’ (e.g. J/mol).
T (float, optional) – Temperature in K. Default is 298.15 K
kwargs (keyword arguments) – Parameters needed by get_UoRT

Returns:

U – Internal energy in appropriate units

Return type:

float

get_UoRT(T)

Calculates the dimensionless internal energy

\(\frac{U^{vib}}{RT}=\frac{u^0_E}{k_BT}+3\frac{\Theta_E}{T} \bigg(\frac{\exp(-\frac{\Theta_E}{T})}{1-\exp(-\frac{\Theta_E} {T})}\bigg)\)

Parameters:: T (float) – Temperature in K
Returns:: UoRT_vib – Vibrational dimensionless internal energy
Return type:: float

get_ZPE()

Calculates the zero point energy

\(u^0_E=u+\frac{3}{2}\Theta_E k_B\)

Returns:: zpe – Zero point energy in eV
Return type:: float

get_q(T)

Calculates the partition function

\(q^{vib}=\exp\bigg({\frac{-u}{k_BT}}\bigg)\bigg(\frac{ \exp(-\frac{\Theta_E}{2T})}{1-\exp(\frac{-\Theta_E}{T})}\bigg)\)

Parameters:: T (float) – Temperature in K
Returns:: q_vib – Vibrational partition function
Return type:: float

to_dict()

Represents object as dictionary with JSON-accepted datatypes

Returns:: obj_dict
Return type:: dict