153 lines
4.5 KiB
Fortran
153 lines
4.5 KiB
Fortran
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!=======================================================================
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!
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MODULE DIFFUSION_COEFFICIENT
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!
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USE ACCURACY_REAL
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!
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!
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CONTAINS
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!=======================================================================
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!
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SUBROUTINE DIFFUSION_COEF(DC)
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!
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! This subroutine computes the diffusion coefficient
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!
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 23 Oct 2020
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!
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!
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USE MATERIAL_PROP, ONLY : DMN,RS
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USE EXT_FIELDS, ONLY : T
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!
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USE DAMPING_VALUES, ONLY : DC_TYPE
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!
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USE EL_ELE_INTER, ONLY : S,EPS
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!
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USE REAL_NUMBERS, ONLY : ZERO
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(OUT) :: DC
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!
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IF(DMN == '3D') THEN !
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CALL DIFFUSION_COEFFICIENT_3D(T,S,EPS,RS,DC_TYPE,DC)
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ELSE IF(DMN == '2D') THEN !
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DC = ZERO ! not yet implemented
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ELSE IF(DMN == '1D') THEN !
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DC = ZERO ! not yet implemented
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END IF !
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!
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END SUBROUTINE DIFFUSION_COEF
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!
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!=======================================================================
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!
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SUBROUTINE DIFFUSION_COEFFICIENT_3D(T,S,EPS,RS,DC_TYPE,DC)
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!
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! This subroutine computes the diffusion coefficient for 3D systems
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!
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! Input parameters:
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!
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! * T : temperature (SI)
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! * S : \
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! * EPS : / parameters of the soft-sphere potential
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * DC_TYPE : diffusion coefficient in 3D
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! DC_TYPE = 'ASHO' --> Ashurst-Hoover
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!
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!
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! Output parameters:
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!
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! * DC : diffusion coefficient
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 11 Jun 2020
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 4) :: DC_TYPE
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!
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REAL (WP) :: T,S,EPS,RS
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REAL (WP) :: DC
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!
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IF(DC_TYPE == 'ASHO') THEN !
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DC = ASHO_DC_3D(T,S,EPS,RS) !
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END IF !
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!
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END SUBROUTINE DIFFUSION_COEFFICIENT_3D
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!
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!=======================================================================
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!
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FUNCTION ASHO_DC_3D(T,S,EPS,RS)
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!
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! This function computes the Ashurst-Hoover diffusion coefficient
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! for 3D hard-sphere fluid at a given value of the temperature T
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!
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! References: (1) W. T. Ashusrt and W. G. Hoover, Phys. Rev. A 11,
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! 658 (1975)
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!
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! Note: the model uses a soft-sphere interaction potential given by
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!
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! V_SS(R) = EPS * ( S/R )**12
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!
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! Warning: the result is valid for reduced densities XX > 0.6
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!
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! with XX = N0 * (EPS / K_B*T)**0.25
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!
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!
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! Input parameters:
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!
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! * T : temperature (SI)
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! * S : \
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! * EPS : / parameters of the soft-sphere potential
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! * RS : Wigner-Seitz radius (in units of a_0)
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!
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!
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! Output parameters:
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!
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! * ASHO_DC_3D
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!
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! Author : D. Sébilleau
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!
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! Last modified : 11 Jun 2020
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!
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!
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USE REAL_NUMBERS, ONLY : TWO,FOURTH
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USE CONSTANTS_P1, ONLY : H_BAR,M_E,K_B
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USE PI_ETC, ONLY : PI
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USE UTILITIES_1, ONLY : RS_TO_N0
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!
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IMPLICIT NONE
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!
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REAL (WP) :: T,S,EPS,RS
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REAL (WP) :: ASHO_DC_3D
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REAL (WP) :: N0
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REAL (WP) :: D0,CC,XX,KK,S3
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!
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REAL (WP) :: SQRT,EXP
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!
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KK = 0.416666666666666666666666666666666667E0_WP ! 5/12
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!
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S3 = S * S * S !
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!
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! Computing the electron density
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!
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N0 = RS_TO_N0('3D',RS) !
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!
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D0 = 4.9E0_WP !
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CC = 6.3E0_WP !
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XX = N0 * S3 * (EPS / (K_B*T))**FOURTH / SQRT(TWO) ! reduced density p. 663
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!
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ASHO_DC_3D = S * SQRT(EPS / M_E) * (K_B * T / EPS)**KK * & !
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D0 * EXP(- CC * XX) ! ref. 1 p. 666
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!
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END FUNCTION ASHO_DC_3D
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!
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END MODULE DIFFUSION_COEFFICIENT
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