phase#

phase is a dictionary of arbitrarily labeled keys. Each phase entry requires a key lattice that specifies the lattice structure in Pearson notation. At least the type of the employed constitutive model for each active field (mechanical/elastic, mechanical/plastic, mechanical/eigen, thermal, or damage) is required; any further configuration details depend on the selected constitutive model. It is recommended to construct phase entries based on the Reference Examples (also included in config.tar.xz) rather than from scratch.

Detailed documentation of the configuration keywords is available for these constitutive models:

  • mechanical

    • plastic

      • Dislotungsten

      • Dislotwin

      • Isotropic

      • Kinehardening

      • Phenopowerlaw

The basic layout is sketched in the following:

phase:

 label_1:
   lattice: lattice_1
   mechanical:
     elastic:
       type: tbd
       ...:
     plastic:
       type: tbd
       ...:
     eigen:
       - type: tbd
         ...:
       - type: tbd
         ...:
   damage:
     type: tbd
     ...:
   thermal:
     source:
       - type: tbd
         ...:
       - type: tbd
         ...:

 label_2:
   lattice: lattice_2
   mechanical:
     elastic:
       type: tbd
       ...:
     plastic:
       type: tbd
       ...:
     eigen:
       - type: tbd
         ...:
       - type: tbd
         ...:
   damage:
     type: tbd
     ...:
   thermal:
     source:
       - type: tbd
         ...:
       - type: tbd
         ...:

 label_N:
   ...

Reference Examples#

Ag#

references:
  - https://en.wikipedia.org/wiki/Silver

lattice: cF
rho: 10490.0

Al#

references:
  - https://en.wikipedia.org/wiki/Aluminium

lattice: cF
rho: 2700.0

Au#

references:
  - https://en.wikipedia.org/wiki/Gold

lattice: cF
rho: 19300.0

Cu#

references:
  - https://en.wikipedia.org/wiki/Copper

lattice: cF
rho: 8960.0

Fe#

references:
  - https://en.wikipedia.org/wiki/Iron

lattice: cI
rho: 7874.0

Mg#

references:
  - D. Tromans,
    International Journal of Recent Research and Applied Studies 6(4):462-483, 2011,
    https://www.arpapress.com/Volumes/Vol6Issue4/IJRRAS_6_4_14.pdf

lattice: hP
c/a: 1.62350
rho: 1740.0

Ni#

references:
  - https://en.wikipedia.org/wiki/Nickel

lattice: cF
rho: 8908.0

Pt#

references:
  - https://en.wikipedia.org/wiki/Platinum

lattice: cF
rho: 21450.0

Si#

references:
  - https://en.wikipedia.org/wiki/Silicon

lattice: cF # face-centered diamond-cubic
rho: 2329.1

Sn-beta#

references:
  - J.A. Rayne and B.S. Chandrasekhar,
    Physical Review 120(5):1658-1663, 1960,
    https://doi.org/10.1103/PhysRev.120.1658
  - https://en.wikipedia.org/wiki/Tin

lattice: tI
c/a: 0.5458 # T=300K (c=31.83nm, a=5.832nm)
rho: 7265.0

Ti#

references:
  - https://www.totalmateria.com/page.aspx?ID=CheckArticle&site=ktn&NM=221
  - https://en.wikipedia.org/wiki/Titanium

lattice: hP
c/a: 1.587
rho: 4506.0

W#

references:
  - https://en.wikipedia.org/wiki/Tungsten

lattice: cI
rho: 19300.0

X2CrNi18-10#

references:
  - C.S. Kim,
    Thermophysical properties of stainless steels,
    Argonne National Laboratory, Argonne, Illinois, 1975,
    https://doi.org/10.2172/4152287,
    Eq. 16 (T=293.15K)

lattice: cF
rho: 7896.4

X2CrNiMo17-12-2#

references:
  - C.S. Kim,
    Thermophysical properties of stainless steels,
    Argonne National Laboratory, Argonne, Illinois, 1975,
    https://doi.org/10.2172/4152287,
    Eq. 18 (T=293.15K)

lattice: cF
rho: 7957.5

X5CrNi18-10#

references:
  - H.M. Ledbetter,
    physica status solidi (a) 85(1):89-96, 1984,
    https://doi.org/10.1002/pssa.2210850111

lattice: cF
rho: 7937.0

bcc#

lattice: cI

bct#

lattice: tI
c/a: 0.55

fcc#

lattice: cF

hcp#

lattice: hP
c/a: 1.6333

damage#

anisobrittle_cubic#

type: anisobrittle

output: [f_phi]

N_cl: [3]

g_crit: [0.5e+7]
s_crit: [0.006666]
dot_o_0: 1.e-3
p: 20

l_c: 1.0
mu: 0.001

isobrittle_generic#

type: isobrittle

output: [f_phi]

G_crit: 1400000.0
l_c: 1.0
mu: 0.001

mechanical#

eigen#

thermalexpansion_Al#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

Alpha_11: 23.1e-6
thermalexpansion_Au#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

Alpha_11: 14.e-6
thermalexpansion_C35E#
type: thermalexpansion

references:
  - https://commons.wikimedia.org/wiki/File:Coefficient_dilatation_lineique_aciers.svg,
    fit to image description (Scilab code)

Alpha_11: 10.2e-6
Alpha_11,T: 1.260e-8
Alpha_11,T^2: -1.000e-11

T_ref: 293.15
thermalexpansion_Cu#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

Alpha_11: 17.e-6
thermalexpansion_Fe#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

Alpha_11: 11.8e-6
thermalexpansion_Mg#
type: thermalexpansion

references:
  - P.D. Pathak and R.J. Desai,
    physica status solidi (a) 66:K179-K182, 1981,
    https://doi.org/10.1002/pssa.2210660271,
    fit to Fig. 1 (T_min=0°C, T_max=616°C)

Alpha_11: 26.2e-6
Alpha_11,T: 1.159e-8
Alpha_11,T^2: 1.382e-11

Alpha_33: 28.0e-6
Alpha_33,T: 9.564e-9
Alpha_33,T^2: 7.332e-12

T_ref: 293.15
thermalexpansion_Si#
type: thermalexpansion

references:
  - C. Bourgeois,
    Proceedings of International Frequency Control Symposium 791-799, 1997
    https://doi.org/10.1109/freq.1997.639192
    Table I

Alpha_11: 2.84e-6
Alpha_11,T: 8.5e-9
Alpha_11,T^2: -32.e-12

T_ref: 298.15
thermalexpansion_SiC-alpha#
type: thermalexpansion

references:
  - Z. Li and R.C. Bradt,
    Journal of the American Ceramic Society 69(12):863-866, 1986,
    https://doi.org/10.1111/j.1151-2916.1986.tb07385.x

Alpha_11: 3.27e-6
Alpha_11,T: 3.25e-9
Alpha_11,T^2: -1.36e-12

Alpha_33: 3.18e-6
Alpha_33,T: 2.48e-9
Alpha_33,T^2: -8.51e-13

T_ref: 273.15
thermalexpansion_SiC-beta#
type: thermalexpansion

references:
  - Z. Li and R.C. Bradt,
    Journal of Materials Science 21:4366-4368, 1986,
    https://doi.org/10.1007/BF01106557

Alpha_11: 3.19e-6
Alpha_11,T: 3.60e-9
Alpha_11,T^2: -1.68e-12

T_ref: 273.15
thermalexpansion_Sn-beta#
type: thermalexpansion

references:
  - V.T. Deshpande and D.B. Sirdeshmukh,
    Acta Crystallographica 15:294-295, 1962,
    https://doi.org/10.1107/S0365110X62000742,
    fit to Tab. 2 (T_min=30ºC, T_max=210ºC)

Alpha_11: 16.4e-6
Alpha_11,T: 1.799e-8
Alpha_11,T^2: 1.734e-10

Alpha_33: 32.6e-6
Alpha_33,T: 1.387e-8
Alpha_33,T^2: 5.794e-10

T_ref: 293.15
thermalexpansion_W#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

Alpha_11: 4.5e-6
thermalexpansion_X20Cr13#
type: thermalexpansion

references:
  - https://commons.wikimedia.org/wiki/File:Coefficient_dilatation_lineique_aciers.svg,
    fit to Scilab code for generating the image (T_min=100ºC, T_max=400ºC)

Alpha_11: 10.1e-6
Alpha_11,T: 5.0e-9

T_ref: 293.15
thermalexpansion_X2CrNi18-10#
type: thermalexpansion

references:
  - C.S. Kim,
    Thermophysical properties of stainless steels,
    Argonne National Laboratory, Argonne, Illinois, 1975,
    https://doi.org/10.2172/4152287,
    Eq. 22 (T_min=300K, T_max=1600K)

Alpha_11: 14.1e-6
Alpha_11,T: 5.279e-9
Alpha_11,T^2: 7.238e-13

T_ref: 293.15
thermalexpansion_X2CrNiMo17-12-2#
type: thermalexpansion

references:
  - C.S. Kim,
    Thermophysical properties of stainless steels,
    Argonne National Laboratory, Argonne, Illinois, 1975,
    https://doi.org/10.2172/4152287,
    Eq. 24 (T_min=300K, T_max=1600K)

Alpha_11: 18.6e-6
Alpha_11,T: 2.589e-9
Alpha_11,T^2: 3.269e-13

T_ref: 293.15
thermalexpansion_X5CrNi18-10#
type: thermalexpansion

references:
  - R.H. Bogaard et al.,
    Thermochimica Acta 218:373-393, 1993,
    https://doi.org/10.1016/0040-6031(93)80437-F,
    fit to Fig. 6 (T_min=100K, T_max=1200K)

Alpha_11: 14.9e-6
Alpha_11,T: 1.838e-8
Alpha_11,T^2: -2.028e-11
Alpha_11,T^3: 9.173e-15

T_ref: 293.15

elastic#

Hooke_Ag#
type: Hooke

references:
  - J.R. Neighbours and G.A. Alers,
    Physical Review 111:707-712, 1958,
    https://doi.org/10.1103/PhysRev.111.707,
    fit to Tab. I (T_min=100K, T_max=300K)
  - Y.A. Chang and L. Himmel,
    Journal of Applied Physics 37:3567-3572, 1966,
    https://doi.org/10.1063/1.1708903,
    fit to Tab. II (T_min=300K, T_max=800K)

C_11: 124.1e+9
C_11,T: -3.148e+7
C_11,T^2: -6.594e+3

C_12: 93.7e+9
C_12,T: -1.657e+7
C_12,T^2: -4.220e+3

C_44: 46.4e+9
C_44,T: -1.775e+7
C_44,T^2: -1.973e+3

T_ref: 293.15
Hooke_Al#
type: Hooke

references:
  - G.N. Kamm and G.A. Alers,
    Journal of Applied Physics 35:327-330, 1964,
    https://doi.org/10.1063/1.1713309,
    fit to Tab. I (T_min=100K, T_max=300K)
  - D. Gerlich and E.S. Fisher,
    Journal of Physics and Chemistry of Solids 30:1197-1205, 1969,
    https://doi.org/10.1016/0022-3697(69)90377-1,
    fit to Tab. 2 (T_min=293K, T_max=900K)

C_11: 106.9e+9
C_11,T: -3.691e+7
C_11,T^2: -9.790e+3

C_12: 60.5e+9
C_12,T: -8.412e+6
C_12,T^2: -3.972e+3

C_44: 28.4e+9
C_44,T: -1.413e+7
C_44,T^2: -3.408e+3

T_ref: 293.15
Hooke_Au#
type: Hooke

references:
  - J.R. Neighbours and G.A. Alers,
    Physical Review 111:707-712, 1958,
    https://doi.org/10.1103/PhysRev.111.707,
    fit to Tab. II (T_min=100K, T_max=300K)
  - Y.A. Chang and L. Himmel,
    Journal of Applied Physics 37:3567-3572, 1966,
    https://doi.org/10.1063/1.1708903,
    fit to Tab. III (T_min=300K, T_max=800K)

C_11: 192.7e+9
C_11,T: -3.472e+7
C_11,T^2: 1.102e+3

C_12: 163.2e+9
C_12,T: -2.607e+7
C_12,T^2: 2.397e+3

C_44: 42.2e+9
C_44,T: -1.172e+7
C_44,T^2: -3.078e+3

T_ref: 293.15
Hooke_C50E-martensite#
type: Hooke

references:
  - S.A. Kim and W.L. Johnson,
    Materials Science & Engineering A 452-453:633-639, 2007,
    https://doi.org/10.1016/j.msea.2006.11.147,
    Tab. 1 (averaged for bcc)

C_11: 267.9e+9
C_12: 110.8e+9
C_44: 78.9e+9
Hooke_Cu#
type: Hooke

references:
  - W.C. Overton Jr. and J. Gaffney,
    Physical Review 98(4):969-977, 1955,
    https://doi.org/10.1103/PhysRev.98.969,
    fit to Tab. I (T_min=100K, T_max=300K)
  - Y.A. Chang and L. Himmel,
    Journal of Applied Physics 37:3567-3572, 1966,
    https://doi.org/10.1063/1.1708903,
    fit to Tab. II (T_min=300K, T_max=800K)

C_11: 168.9e+9
C_11,T: -3.332e+7
C_11,T^2: -1.074e+4

C_12: 121.8e+9
C_12,T: -1.402e+7
C_12,T^2: -9.003e+3

C_44: 75.8e+9
C_44,T: -2.555e+7
C_44,T^2: -2.188e+3

T_ref: 293.15
Hooke_Fe#
type: Hooke

references:
  - D.J. Dever,
    Journal of Applied Physics 43(8):3293-3301, 1972,
    https://doi.org/10.1063/1.1661710,
    fit to Tab. II (T_min=25ºC, T_max=880ºC)

C_11: 232.2e+9
C_11,T: -4.683e+7
C_11,T^2: -5.988e+4

C_12: 136.4e+9
C_12,T: -1.970e+7
C_12,T^2: 3.760e+3

C_44: 117.0e+9
C_44,T: -2.015e+7
C_44,T^2: -7.485e+2

T_ref: 293.15
Hooke_IN625#
type: Hooke

references:
  - Z. Wang et al.,
    Materials Science and Engineering:A 674:406-412, 2016,
    https://doi.org/10.1016/j.msea.2016.08.010,
    fit to Tab. 2 (last 3 rows)

C_11: 243.9e+9
C_11,T: -5.410e+7

C_12: 157.0e+9
C_12,T: -9.352e+6

C_44: 117.9e+9
C_44,T: -2.798e+7

T_ref: 293.15
Hooke_Mg#
type: Hooke

references:
  - L.J. Slutsky and C.W. Garland,
    Physical Review 107(4):972-976, 1957,
    https://doi.org/10.1103/PhysRev.107.972,
    fit to Tab. I (T_min=100K, T_max=300K)

C_11: 59.5e+9
C_11,T: -1.930e+7
C_11,T^2: -1.215e+4

C_12: 25.6e+9
C_12,T: -2.216e+6
C_12,T^2: -4.138e+3

C_44: 16.5e+9
C_44,T: -1.006e+7
C_44,T^2: -7.692e+3

C_33: 61.7e+9
C_33,T: -2.175e+7
C_33,T^2: -5.624e+3

C_13: 21.5e+9
C_13,T: -1.921e+6
C_13,T^2: -4.283e+3

T_ref: 293.15
Hooke_Ni#
type: Hooke

references:
  - G.A. Alers,
    Journal of Physics and Chemistry of Solids 13(1-2):40-55, 1960,
    https://doi.org/10.1016/0022-3697(60)90125-6,
    fit to Tab. 2 (T_min=100K, T_max=700K)

C_11: 251.0e+9
C_11,T: -4.967e+7
C_11,T^2: -3.327e+4

C_12: 150.0e+9
C_12,T: -3.714e+6
C_12,T^2: -7.414e+3

C_44: 123.7e+9
C_44,T: -3.621e+7
C_44,T^2: -8.017e+3

T_ref: 293.15
Hooke_Pt#
type: Hooke

references:
  - S.M. Collard and R.B. McLellan,
    Acta Metallurgica et Materialia 40:699-702, 1992,
    https://doi.org/10.1016/0956-7151(92)90011-3

C_11: 373.42e+9
C_11,T: -8.929e+7
C_11,T^2: -1.298e+5
C_11,T^3: 1.2807e+2
C_11,T^4: -4.6114e-2

C_12: 241.74e+9
C_12,T: 5.705e+7
C_12,T^2: 0.4511e+5
C_12,T^3: -0.4860e+2
C_12,T^4: 1.446e-2

C_44: 77.65e+9
C_44,T: -1.342e+7
C_44,T^2: -0.1493e+5
C_44,T^3: 0.1260e+2
C_44,T^4: -0.6470e-2

T_ref: 0
Hooke_Si#
type: Hooke

references:
  - C. Bourgeois,
    Proceedings of International Frequency Control Symposium 791-799, 1997
    https://doi.org/10.1109/freq.1997.639192
    Table III and Table IV (p-type)

C_11: 165.64e+9
C_11,T: -73.25e-6
C_11,T^2: -49.26e-9

C_12: 63.94e+9
C_12,T: -91.59e-6
C_12,T^2: -32.70e-9

C_44: 79.51e+9
C_44,T: -60.14e-6
C_44,T^2: -51.28e-9

T_ref: 298.15
Hooke_Sn-beta#
type: Hooke

references:
  - J.A. Rayne and B.S. Chandrasekhar,
    Physical Review 120(5):1658-1663, 1960,
    https://doi.org/10.1103/PhysRev.120.1658,
    fit to Tab. IV (T_min=77K, T_max=300K)

C_11: 72.6e+9
C_11,T: -4.135e+7

C_12: 59.4e+9
C_12,T: 6.726e+6

C_44: 22.2e+9
C_44,T: -1.870e+7

C_33: 88.8e+9
C_33,T: -5.381e+7

C_13: 35.8e+9
C_13,T: -2.870e+6

C_66: 24.1e+9
C_66,T: -1.709e+7

T_ref: 293.15
Hooke_TWIP-steel#
type: Hooke

references:
  - D. Music et al.,
    Applied Physics Letters 99(19):191904, 2007,
    https://doi.org/10.1063/1.2807677
  - S.L. Wong et al.,
    Acta Materialia 118:140-151, 2016,
    https://doi.org/10.1016/j.actamat.2016.07.032

C_11: 175.0e+9
C_12: 115.0e+9
C_44: 135.0e+9
Hooke_Ta#
type: Hooke

references:
  - F.H. Featherston and J.R. Neighbours,
    Physical Review 130(4):1324-1333, 1963,
    https://doi.org/10.1103/PhysRev.130.1324,
    fit to Tab. II (T_min=100K, T_max=300K)

C_11: 523.6e+9
C_11,T: -7.704e+7
C_11,T^2: -1.562e+5

C_12: 204.6e+9
C_12,T: -2.485e+7
C_12,T^2: -1.182e+5

C_44: 160.7e+9
C_44,T: -1.028e+7
C_44,T^2: 1.291e+4

T_ref: 293.15
Hooke_Ti#
type: Hooke

references:
  - E.S. Fisher and C.J. Renken,
    Physical Review 135(2A):A482-A494, 1964,
    https://doi.org/10.1103/PhysRev.135.A482,
    fit to Tab. IV (T_min=77K, T_max=923K)

C_11: 162.5e+9
C_11,T: -5.915e+7
C_11,T^2: 1.156e+4

C_12: 91.8e+9
C_12,T: 2.192e+7
C_12,T^2: -1.621e+4

C_44: 46.8e+9
C_44,T: -1.857e+7
C_44,T^2: -3.745e+3

C_33: 180.6e+9
C_33,T: -4.110e+7
C_33,T^2: 7.330e+3

C_13: 68.9e+9
C_13,T: 2.965e+6
C_13,T^2: -5.767e+3

T_ref: 293.15
Hooke_W-10at.%Re#
type: Hooke

references:
  - R.A. Ayres et al.,
    Journal of Applied Physics 46:1526-1530, 1975,
    https://doi.org/10.1063/1.321804,
    fit to Table IV (T_min=100K, T_max=300K)

C_11: 524.6e+9
C_11,T: -5.783e+7
C_11,T^2: -1.355e+5

C_12: 219.0e+9
C_12,T: 1.940e+7
C_12,T^2: 7.634e+4

C_44: 168.7e+9
C_44,T: -2.048e+7
C_44,T^2: -5.478e+4

T_ref: 293.15
Hooke_W-3at.%Re#
type: Hooke

references:
  - R.A. Ayres et al.,
    Journal of Applied Physics 46:1526-1530, 1975,
    https://doi.org/10.1063/1.321804,
    fit to Table IV (T_min=100K, T_max=300K)

C_11: 535.1e+9
C_11,T: -6.459e+7
C_11,T^2: -1.664e+5

C_12: 216.1e+9
C_12,T: 2.357e+7
C_12,T^2: 5.186e+4

C_44: 161.1e+9
C_44,T: -1.498e+7
C_44,T^2: -3.234e+4

T_ref: 293.15
Hooke_W#
type: Hooke

references:
  - F.H. Featherston and J.R. Neighbours,
    Physical Review 130(4):1324-1333, 1963,
    https://doi.org/10.1103/PhysRev.130.1324,
    fit to Tab. III (T_min=100K, T_max=300K)

C_11: 524.3e+9
C_11,T: -4.794e+7

C_12: 205.1e+9
C_12,T: -2.836e+6

C_44: 160.7e+9
C_44,T: -1.269e+7

T_ref: 293.15
Hooke_X2CrNiMo17-12-2#
type: Hooke

references:
  - J.-M. Scherer et al.,
    Materials Science & Engineering A 900:146471, 2024,
    https://doi.org/10.1016/j.msea.2024.146471,
    Eq. (6-8) adjusted to T_ref=293.15K (T_min=20°C, T_max=300°C)

C_11: 218.3e+9
C_11,T: -5.13e+7

C_12: 144.8e+9
C_12,T: -2.77e+7

C_44: 125.4e+9
C_44,T: -3.08e+7

T_ref: 293.15
Hooke_X5CrNi18-10#
type: Hooke

references:
  - H.M. Ledbetter,
    physica status solidi (a) 85(1):89-96, 1984,
    https://doi.org/10.1002/pssa.2210850111

C_11: 204.6e+9
C_12: 137.7e+9
C_44: 126.2e+9
Hooke_X6CrNiMo17-12-2#
type: Hooke

references:
  - M.R. Daymond and P.J. Bouchard,
    Metallurgical and Materials Transactions A 37:1863-1873, 2006,
    https://doi.org/10.1007/s11661-006-0129-4,
    fit to Fig. 6 (solid lines, T_min=0°C, T_max=600°C)

C_11: 118.6e+9
C_11,T: -5.491e+7

C_12: 154.2e+9
C_12,T: -6.059e+7

C_44: 229.0e+9
C_44,T: -1.058e+8

T_ref: 293.15
Hooke_vanishing-Poisson-ratio#
type: Hooke

references:
  - T. Maiti and P. Eisenlohr,
    Scripta Materialia 145:37-40, 2018,
    https://doi.org/10.1016/j.scriptamat.2017.09.047

C_11: 1.e+8
C_12: 1.e+6
C_44: 4.95e+7

plastic#

dislotungsten_W#
type: dislotungsten

references:
  - D. Cereceda et al.,
    International Journal of Plasticity 78:242-265, 2016,
    https://doi.org/10.1016/j.ijplas.2015.09.002
  - R. Gröger et al.,
    Acta Materialia 56(19):5412-5425, 2008,
    https://doi.org/10.1016/j.actamat.2008.07.037

output: [Lambda_sl]

N_sl: [12]

b_sl: [2.72e-10]
rho_mob_0: [1.0e+9]  # estimated from section 3.2
rho_dip_0: [1.0]     # not given
Q_s: [2.61154e-19]   # 1.63 eV, Delta_H0
B: [8.3e-5]
omega: [9.1e+11]     # nu_0
p_sl: [0.86]
q_sl: [1.69]
tau_Peierls: [2.03e+9]
h: [2.566e-10]
h_sl-sl: [0.009, 0.72, 0.009, 0.05, 0.05, 0.06, 0.09]
w: [2.992e-9] # 11b

# values in Cereceda et al. are high, using parameters from Gröger et al.
a_non-Schmid: [[0.0, 0.56, 0.75]] # Tab. 2

# (almost) no annhilation, adjustment needed for simulations beyond the yield point
i_sl: [1]  # c, eq. (25)
D: 1.0e+20 # d_g, eq. (25)
D_a: 1.0 # d_edge = D_a*b

# disable climb (not discussed in Cereceda et al.)
D_0: 0.0
f_at: 1
Q_cl: 1.0
dislotwin_IF-steel#
type: dislotwin

references:
  - K. Sedighiani et al.,
    International Journal of Plasticity 134:102779, 2020,
    https://doi.org/10.1016/j.ijplas.2020.102779
  - K. Sedighiani et al.,
    Mechanics of Materials, 164:104117, 2022,
    https://doi.org/10.1016/j.mechmat.2021.104117

output: [rho_dip, rho_mob]

N_sl: [12, 12]

f_edge: [1.0, 1.0]
b_sl: [2.49e-10, 2.49e-10]
rho_mob_0: [2.81e+12, 2.8e+12]
rho_dip_0: [1.0, 1.0] # not given
v_0: [1.4e+3, 1.4e+3]
Q_sl: [1.57e-19, 1.57e-19] # Delta_F
tau_0: [454.e+6, 454.e+6]
p_sl: [0.325, 0.325]
q_sl: [1.55, 1.55]
i_sl: [23.3, 23.3]
D_a: 7.4 # C_anni
B: [0.001, 0.001]
h_sl-sl: [0.1, 0.72, 0.1, 0.053, 0.053, 0.073, 0.137, 0.72, 0.72, 0.053, 0.053, 0.053, 0.053, 0.073, 0.073, 0.073, 0.073, 0.073, 0.073, 0.137, 0.073, 0.073, 0.137, 0.073]
Q_cl: 5.4e-19 # no recovery!
D: 40.e-6 # estimated
dislotwin_IN625#
type: dislotwin

references:
  - N. Prabhu and M. Diehl,
    Integrating Materials and Manufacturing Innovation 13:xx-yy, 2008,
    https://doi.org/10.1007/s40192-024-00359-1,
    Table 3(d)
  - R. Madec and L.P. Kubin,
    Acta Materialia 126:166-173, 2017,
    https://doi.org/10.1016/j.actamat.2016.12.040,
    Table 1 for Ni
  - L.P. Kubin et al.,
    Acta Materialia 56(20):6040-6049, 2008,
    https://doi.org/10.1016/j.actamat.2008.08.012,
    Table 1 (self and coplanar)

output: [rho_dip, rho_mob]

N_sl: [12]

b_sl: [2.48e-10]
rho_mob_0: [2.8e+12]
rho_dip_0: [1.0]
v_0: [1400.0]
Q_sl: [2.34e-19]
tau_0: [600.0e+6]
p_sl: [0.42]
q_sl: [1.55]
i_sl: [7.5]
D_a: 4.0
B: [0.001]
Q_cl: 5.4e-19
D: 1.08e-5

h_sl-sl: [0.122, 0.122, 0.672, 0.044, 0.102, 0.09, 0.168]
dislotwin_TWIP-TRIP#
type: dislotwin

references:
  - S.L. Wong et al.,
    Acta Materialia 118:140-151, 2016,
    https://doi.org/10.1016/j.actamat.2016.07.032
  - K. Sedighiani et al.,
    Mechanics of Materials, 164:104117, 2022,
    https://doi.org/10.1016/j.mechmat.2021.104117
  - L.P. Kubin et al.,
    Acta Materialia 56:6040-6049,
    https://doi.org/10.1016/j.actamat.2008.08.012

output: [rho_mob, rho_dip, gamma_sl, Lambda_sl, tau_pass, f_tw, Lambda_tw, f_tr]

# Glide
N_sl: [12]

f_edge: [1.0]
b_sl: [2.56e-10] # a/sqrt(2)
Q_sl: [3.5e-19]
p_sl: [0.325]
q_sl: [1.55]
B: [0.001]
i_sl: [30.0]
v_0: [1.4e+3]
tau_0: [5.5e+8] # adjusted
D_a: 2.0
Q_cl: 3.0e-19

rho_mob_0: [5.0e+10]
rho_dip_0: [5.0e+10]

h_sl-sl: [0.122, 0.122, 0.625, 0.07, 0.137, 0.137, 0.122]

# Twin
N_tw: [12]
b_tw: [1.47e-10] # a_cF/sqrt(6)
L_tw: 1.91e-7 # 1300 *b_tw
i_tw: 10.0
t_tw: [5.0e-8]
p_tw: [7] # A, adjusted

h_tw-tw: [1.0, 1.0]
h_sl-tw: [1.0, 1.0, 1.0]

# Transformation
N_tr: [12]
b_tr: [1.47e-10] # a_cF/sqrt(6)
L_tr: 2.21e-7 # 1500 *b_tr
i_tr: 10.0 # adjusted
t_tr: [1.0e-7]
p_tr: [4] # B, adjusted
V_mol: 7.09e-6
c/a_hP: 1.633

Delta_G: 1.2055e+2
Delta_G,T: 2.5515
Delta_G,T^2: 1.4952e-3

h_tr-tr: [1.0, 1.0]
h_sl-tr: [1.5, 1.5, 1.5]

# Twin & Transformation
T_ref: 293.15
Gamma_sf: 2.833e-2
Gamma_sf,T: 1.214e-4
Gamma_sf,T^2: 1.473e-7

x_c: 1.0e-9
V_cs: 1.67e-29

# Slip & Twin & Transformation
D: 5.0e-5
dislotwin_alpha-Brass-shearbanding#
type: dislotwin

references:
  - N. Jia et al.,
    Acta Materialia 60(3):1099-1115, 2012,
    https://doi.org/10.1016/j.actamat.2011.10.047
  - N. Jia et al.,
    Acta Materialia 60:3415-3434, 2012,
    https://doi.org/10.1016/j.actamat.2012.03.005

gamma_0_sb: 0.0001
tau_sb: 180.0e6 # tau_hat_sb
Q_sb: 4.0e-19 # Q_0
p_sb: 1.15
q_sb: 1.0
isotropic_free-surface#
type: isotropic

references:
  - T. Maiti and P. Eisenlohr,
    Scripta Materialia 145:37-40, 2018,
    https://doi.org/10.1016/j.scriptamat.2017.09.047

output: [xi]

dot_gamma_0: 0.001
n: 20.
xi_0: 0.3e+6
xi_inf: 0.6e+6
a: 2.
h_0: 1.e+6
M: 1.
h: 1.
dilatation: True
kinehardening_X2CrNiMo18-15-4#
type: kinehardening

references:
  - J.A. Wollmershauser et al.,
    International Journal of Fatigue 36(1):181-193, 2012,
    https://doi.org/10.1016/j.ijfatigue.2011.07.008

output: [xi, chi, chi_flip, gamma_flip, gamma, sgn(gamma)]

N_sl: [12]

xi_0:     [0.070e+9] # τ_0,for
xi_inf:   [0.015e+9] # τ_1,for
h_0_xi:   [0.065e+9] # θ_0,for
h_inf_xi: [0.045e+9] # θ_1,for

chi_inf:  [0.027e+9] # τ_1,bs
h_0_chi:     [55e+9] # θ_0,bs
h_inf_chi:  [1.3e+9] # θ_1,bs

n: [20]                # not mentioned in the reference
dot_gamma_0: [1e-4]    # not mentioned in the reference
h_sl-sl: [1, 1, 1, 1, 1, 1, 1]
nonlocal_Al#
type: nonlocal

references:
  - C. Kords,
    On the role of dislocation transport in the constitutive description of crystal plasticity,
    RWTH Aachen 2013,
    http://publications.rwth-aachen.de/record/229993/files/4862.pdf

output: [rho_u_ed_pos, rho_b_ed_pos, rho_u_ed_neg, rho_b_ed_neg, rho_u_sc_pos, rho_b_sc_pos, rho_u_sc_neg, rho_b_sc_neg, rho_d_ed, rho_d_sc]

N_sl: [12]

b_sl: [2.86e-10]
V_at: 0.017e-27 # Omega
d_ed: [1.6e-9]
d_sc: [10.e-9]
i_sl: [60]      # k_2 (lambda_0 in Tab. 7.1)
f_ed_mult: 0.1  # k_1

rho_u_ed_neg_0: [1.25e9] # 6e10 / (12*4)
rho_u_ed_pos_0: [1.25e9] # 6e10 / (12*4)
rho_u_sc_neg_0: [1.25e9] # 6e10 / (12*4)
rho_u_sc_pos_0: [1.25e9] # 6e10 / (12*4)
rho_d_ed_0: [0]
rho_d_sc_0: [0]

D_0: 7.e-29
Q_cl: 0.0 # no temperature dependency
Q_sol: 2.00272e-19 # 1.25 eV
c_sol: 1.5e-6       # correct unit?
f_sol: 2.0          # d_obst in multiples of b
tau_Peierls_ed: [.1e6]
tau_Peierls_sc: [.1e6]
w: 10              # w_k in multiple of b

p_sl: 1
q_sl: 1

nu_a: 50.e+9
B: 1.e-2
f_ed: 1.0  # k_3

h_sl-sl: [0, 0, 0.625, 0.07, 0.137, 0.137, 0.122] # Tab. 3.4

chi_GB: 0.0      # full blocking at GB
chi_surface: 1.0 # no blocking at surface

f_F: 0.0         # no line tension correction
sigma_rho_u: 0   # no random distribution


short_range_stress_correction: false
rho_significant: 1.e6
nonlocal_Ni#
type: nonlocal

references:
  - C. Kords,
    On the role of dislocation transport in the constitutive description of crystal plasticity,
    RWTH Aachen 2013,
    http://publications.rwth-aachen.de/record/229993/files/4862.pdf

output: [rho_u_ed_pos, rho_b_ed_pos, rho_u_ed_neg, rho_b_ed_neg, rho_u_sc_pos, rho_b_sc_pos, rho_u_sc_neg, rho_b_sc_neg, rho_d_ed, rho_d_sc]

N_sl: [12]

b_sl: [2.48e-10]
V_at: 0.012e-27 # Omega
d_ed: [2.6e-9]
d_sc: [12.e-9]
i_sl: [45]      # k_2
f_ed_mult: 0.1  # k_1

rho_u_ed_neg_0: [6.e+10] # 2.88e12 / (12*4)
rho_u_ed_pos_0: [6.e+10] # 2.88e12 / (12*4)
rho_u_sc_neg_0: [6.e+10] # 2.88e12 / (12*4)
rho_u_sc_pos_0: [6.e+10] # 2.88e12 / (12*4)
rho_d_ed_0: [0]
rho_d_sc_0: [0]

D_0: 3.e-53
Q_cl: 0.0 # no temperature dependency
Q_sol: 1.79444e-19 # 1.12 eV
c_sol: 5.e-7       # correct unit?
f_sol: 1.          # d_obst
tau_Peierls_ed: [.1e6]
tau_Peierls_sc: [.1e6]
w: 10              # w_k

p_sl: 1
q_sl: 1

nu_a: 50.e+9
B: 1.e-3
f_ed: 0.01  # k_3

h_sl-sl: [0, 0, 0.625, 0.07, 0.137, 0.137, 0.122] # Tab. 3.4

chi_GB: 0.0      # full blocking at GB
chi_surface: 1.0 # no blocking at surface

f_F: 0.0         # no line tension correction
sigma_rho_u: 0   # no random distribution


short_range_stress_correction: false
rho_significant: 1.e6
phenopowerlaw_AA6022-T4#
type: phenopowerlaw

references:
  - T.J. Barrett and M. Knezevic,
    Computer Methods in Applied Mechanics and Engineering 354:245-270, 2019,
    https://doi.org/10.1016/j.cma.2019.05.035,
    fitted to data shown in Fig 1 and Fig. 2a

output: [xi_sl, gamma_sl]

N_sl: [12]

dot_gamma_0_sl: [0.001]
n_sl: [20]
a_sl: [3.7]
xi_0_sl: [76.e+6]
xi_inf_sl: [266.e+6]
h_0_sl-sl: [1.02e+9]
h_sl-sl: [1, 1, 5.123, 0.574, 1.123, 1.123, 1]
phenopowerlaw_Al#
type: phenopowerlaw

references:
  - W.F. Hosford et al.,
    Acta Metallurgica 8(3):187-199, 1960,
    https://doi.org/10.1016/0001-6160(60)90127-9,
    fitted to Fig. 5 ([111] and [001])

output: [xi_sl, gamma_sl]

N_sl: [12]

dot_gamma_0_sl: [7.5e-5]
n_sl: [20]
a_sl: [5.4]
xi_0_sl: [2.69e+6]
xi_inf_sl: [67.5e+6]
h_0_sl-sl: [0.2815e+9]
h_sl-sl: [1, 1, 5.123, 0.574, 1.123, 1.123, 1]
phenopowerlaw_Au#
type: phenopowerlaw

references:
  - D. Ma et al.,
    Acta Materialia 103:796-808, 2016,
    https://doi.org/10.1016/j.actamat.2015.11.016
  - I. Kovács and G.Vörös,
    International Journal of Plasticity 12:35-43, 1996,
    https://doi.org/10.1016/S0749-6419(95)00043-7
  - U.F. Kocks,
    Metallurgical and Materials Transactions B 1:1121–1143, 1970,
    https://doi.org/10.1007/BF02900224

output: [xi_sl, gamma_sl]

N_sl: [12]

dot_gamma_0_sl: [0.001]
n_sl: [83.3]
a_sl: [1.0]
xi_0_sl: [26.25e+6]
xi_inf_sl: [53.0e+6]
h_0_sl-sl: [75.0e+6]
h_sl-sl: [1, 1, 1.4, 1.4, 1.4, 1.4, 1.4]
phenopowerlaw_Cu#
type: phenopowerlaw

references:
  - T. Takeuchi,
    Transactions of the Japan Institute of Metals 16(10):629-640, 1975,
    https://doi.org/10.2320/matertrans1960.16.629,
    fitted to Fig. 3b ([111] and [001])

output: [xi_sl, gamma_sl]

N_sl: [12]

dot_gamma_0_sl: [3.e-3]
n_sl: [20]
a_sl: [0.6]
xi_0_sl: [1.6e+6]
xi_inf_sl: [96.4e+6]
h_0_sl-sl: [0.35e+9]
h_sl-sl: [1, 1, 5.123, 0.574, 1.123, 1.123, 1]
phenopowerlaw_DP-steel-ferrite#
type: phenopowerlaw

references:
  - C.C. Tasan et al.,
    Acta Materialia 81:386-400, 2014,
    https://doi.org/10.1016/j.actamat.2014.07.071,
    Table 1
  - U.F. Kocks,
    Metallurgical and Materials Transactions B 1:1121–1143, 1970,
    https://doi.org/10.1007/BF02900224

output: [xi_sl, gamma_sl]

N_sl: [12, 12]

dot_gamma_0_sl: [0.001, 0.001]
n_sl: [20, 20]
a_sl: [2.25, 2.25]
xi_0_sl: [95.e+6, 96.e+6]
xi_inf_sl: [222.e+6, 412.e+6]
h_0_sl-sl: [1.0e+9, 1.0e+9]
h_sl-sl: [1, 1.4, 1, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4]
phenopowerlaw_IN625#
type: phenopowerlaw

references:
  - N. Prabhu and M. Diehl,
    Integrating Materials and Manufacturing Innovation 13:xx-yy, 2008,
    https://doi.org/10.1007/zzz,
    Table 3(d)
  - L.P. Kubin et al.,
    Acta Materialia 56(20):6040-6049, 2008,
    https://doi.org/10.1016/j.actamat.2008.08.012,
    Table 1

output: [xi_sl, gamma_sl]

N_sl: [12]

dot_gamma_0_sl: 2.e-4
xi_0_sl: [143.5e+6]
xi_inf_sl: [470.e+6]
h_0_sl-sl: 1.12e+9
a_sl: 1
n_sl: 40

h_sl-sl: [1, 1, 5.123, 0.574, 1.123, 1.123, 1]
phenopowerlaw_Mg#
type: phenopowerlaw

references:
  - F. Wang et al.,
    Acta Materialia 80:77-93, 2014,
    https://doi.org/10.1016/j.actamat.2014.07.048

output: [xi_sl, xi_tw]

N_sl: [3, 3, 6, 0, 6]  # basal, prism, 1. pyr<a>, -, 2. pyr<c+a>
N_tw: [6, 0, 6]        # tension, -, compression

xi_0_sl:   [10.e+6,  55.e+6,  60.e+6, 0.,  60.e+6]
xi_inf_sl: [40.e+6, 135.e+6, 150.e+6, 0., 150.e+6]
xi_0_tw:   [40.e+6, 0., 60.e+6]

a_sl: [2.25, 2.25, 2.25, 1, 2.25]
dot_gamma_0_sl: [0.001, 0.001, 0.001, 0, 0.001]
dot_gamma_0_tw: [0.001, 0, 0.001]
n_sl: [20, 20, 20, 1, 20]
n_tw: [20, 1, 20]
f_sat_sl-tw: [10.0, 10.0, 10.0, 0, 10.0]

h_0_sl-sl: [0.5e+9, 0.5e+9, 0.5e+9, 0, 0.5e+9]
h_0_tw-tw: [50.0e+6, 0, 50.0e+6]
h_0_tw-sl: [0.15e+9, 0, 0.15e+9]
h_sl-sl: [+1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0, -1.0, -1.0, -1.0, -1.0,  1.0,  1.0,  1.0, -1.0,
          -1.0, -1.0, -1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0]  # unused entries are indicated by -1.0
h_tw-tw: [+1.0,  1.0, -1.0, -1.0, -1.0, -1.0,  1.0, -1.0,  1.0,  1.0,
          -1.0,  1.0]  # unused entries are indicated by -1.0
h_tw-sl:  [1.0, -1.0,  1.0, -1.0,  1.0, -1.0,  1.0, -1.0,  1.0, -1.0,
           1.0, -1.0, -1.0, -1.0, -1.0, -1.0, +1.0, -1.0,  1.0, -1.0]  # unused entries are indicated by -1.0
h_sl-tw:  [1.0, -1.0,  1.0, -1.0,  1.0, -1.0,  1.0, -1.0,  1.0, -1.0,
           1.0, -1.0, -1.0, -1.0, -1.0, -1.0, +1.0, -1.0,  1.0]  # unused entries are indicated by -1.0
phenopowerlaw_Pt-5%Cu#
type: phenopowerlaw

references:
  - K.M. Jackson and C. Lang,
    Platinum Metals Review 50:15-19, 2006,
    https://doi.org/10.1595/147106705X93359,
    fitted to Fig. 5 (Pt-5% Cu recrystallised)

output: [xi_sl, gamma_sl]

N_sl: [12]

dot_gamma_0_sl: [0.001]
n_sl: [20]
a_sl: [0.9]
xi_0_sl: [0.114e+9]
xi_inf_sl: [0.207e+9]
h_0_sl-sl: [0.7812e+9]
h_sl-sl: [1, 1, 5.123, 0.574, 1.123, 1.123, 1]
phenopowerlaw_Sn-beta#
type: phenopowerlaw

references:
  - A. Chakraborty and P. Eisenlohr,
    Journal of Applied Physics 124:025302, 2018,
    https://doi.org/10.1063/1.5029933

output: [xi_sl, gamma_sl]

N_sl: [2, 2, 2, 4, 2, 4, 2, 2, 4, 0, 0, 8]

n_sl: [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 1, 1, 6.0]
a_sl: [2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 1.0, 1.0, 2.0]
h_0_sl-sl: [20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 0.0, 0.0, 20e+6]
xi_0_sl:   [8.5e+6,  4.3e+6, 10.4e+6, 4.5e+6,  5.6e+6,  5.1e+6,  7.4e+6, 15.0e+6, 6.6e+6, 0.0, 0.0, 12.0e+6]
xi_inf_sl: [11.0e+6, 9.0e+6, 11.0e+6, 9.0e+6, 10.0e+6, 10.0e+6, 10.0e+6, 10.0e+6, 9.0e+6, 0.0, 0.0, 13.0e+6]
h_sl-sl: [+1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0, # 50
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, # 100
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0, -1.0, -1.0,  1.0,  1.0, -1.0, -1.0,  1.0,  1.0,  1.0, # 150
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0]  # unused entries are indicated by -1.0
dot_gamma_0_sl: [2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 1.0, 1.0, 2.6e-8]
phenopowerlaw_Ti#
type: phenopowerlaw

references:
  - C. Zambaldi et al.,
    Journal of Materials Research 27(1):356-367, 2021,
    https://doi.org/10.1557/jmr.2011.334
  - L. Wang et al.,
    Acta Materialia 132:598-610, 2017,
    https://doi.org/10.1016/j.actamat.2017.05.015

output: [gamma_sl]

N_sl: [3, 3, 0, 12]   # basal, prism, -, 1. pyr<c+a>

dot_gamma_0_sl: [0.001, 0.001, 0.0, 0.001]
n_sl: [20, 20, 1, 20]
a_sl: [2.0, 2.0, 1.0, 2.0]

# C. Zambaldi et al.:
xi_0_sl:   [0.349e+9, 0.15e+9, 0.0, 1.107e+9]
xi_inf_sl: [0.568e+9, 1.50e+9, 0.0, 3.420e+9]
# L. Wang et al. :
# xi_0_sl:   [127.e+6, 96.e+6, 0.0, 240.e+6]

h_0_sl-sl: [0.2e+9, 0.2e+9, 0.0, 0.2e+9]
h_sl-sl: [+1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0] # unused entries are indicated by -1.0
phenopowerlaw_bcc-martensite#
type: phenopowerlaw

references:
  - C.C. Tasan et al.,
    Acta Materialia 81:386-400, 2014,
    https://doi.org/10.1016/j.actamat.2014.07.071,
    Table 1
  - U.F. Kocks,
    Metallurgical and Materials Transactions B 1:1121–1143, 1970,
    https://doi.org/10.1007/BF02900224

N_sl: [12, 12]

dot_gamma_0_sl: [0.001, 0.001]
xi_0_sl: [405.8e+6, 456.7e+6]
xi_inf_sl: [872.9e+6, 971.2e+6]

h_0_sl-sl: [563.0e+9, 563.0e+9]

n_sl: [20, 20]
a_sl: [2.0, 2.0]

h_sl-sl: [1, 1.4, 1, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4]
phenopowerlaw_polygonal-ferrite#
type: phenopowerlaw

references:
  - F.-J. Gallardo-Basile et al.,
    Materials Science & Engineering A 881:145373, 2023,
    https://doi.org/10.1016/j.msea.2023.145373,
    Table 2, Fig. 19 indent II with contraints

N_sl: [12, 12, 24]

h_0_sl-sl: [1.0e+9, 1.0e+9, 1.0e+9]
dot_gamma_0_sl: [4.e-2, 4.e-2, 4.e-2]
n_sl: [20., 20., 20.]

xi_0_sl: [61.e+6, 54.e+6, 52.e+6]
xi_inf_sl: [277.e+6, 248.e+6, 237.e+6]
a_sl: [2.1, 2.1, 2.1]

h_sl-sl: [1.0, 1.4, 1.0, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4,
          1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4,
          1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4]

thermal#

Al#

references:
  - J.G. Hust and A.B. Lankford,
    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
    US Department of Commerce, Boulder, Colorado, 1984,
    fit to Tab. 3.4.1 (RRR=1000, T_min=200K, T_max=900K)
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

output: [T]

K_11: 237.36
K_11,T: 8.952e-3
K_11,T^2: 2.650e-5
K_11,T^3: -5.687e-7
K_11,T^4: 6.407e-10

T_ref: 293.15

C_p: 910.0

Au#

references:
  - https://de.wikipedia.org/wiki/Gold

K_11: 320.0
C_p: 128.0

Cu#

references:
  - J.G. Hust and A.B. Lankford,
    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
    US Department of Commerce, Boulder, Colorado, 1984,
    fit to Tab. 2.4.1 (RRR=300, T_min=150K, T_max=1000K)
  - https://www.mit.edu/~6.777/matprops/copper.htm

output: [T]

K_11: 4.005e+2
K_11,T: -1.075e-1
K_11,T^2: 3.293e-4
K_11,T^3: -7.533e-7
K_11,T^4: 5.223e-10

T_ref: 293.15

C_p: 385.0

Fe#

references:
  - J.G. Hust and A.B. Lankford,
    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
    US Department of Commerce, Boulder, Colorado, 1984,
    fit to Tab. 4.4.1 (RRR=300, T_min=150K, T_max=1000K)
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

output: [T]

K_11: 80.34
K_11,T: -1.216e-1
K_11,T^2: 1.327e-4
K_11,T^3: -7.993e-8

T_ref: 293.15

C_p: 450.0

Ni#

references:
  - Y.S. Touloukian et al.,
    TPRC Data Series Volume 1. Thermal conductivity - metallic elements and alloys,
    IFI/Plenum, 1970,
    fit to Tab. 35R (T_min=80K, T_max=500K)
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

output: [T]

K_11: 93.11
K_11,T: -8.719e-2
K_11,T^2: -3.793e-4
K_11,T^3: -4.003e-6
K_11,T^4: 2.676e-8

T_ref: 293.15

C_p: 440.0

Si#

references:
  - https://periodictable.com/Elements/014/data.html

output: [T]

K_11: 150.0
C_p: 710.0

Sn-beta#

references:
  - Y.S. Touloukian et al.,
    TPRC Data Series Volume 1. Thermal conductivity - metallic elements and alloys,
    IFI/Plenum, 1970,
    fit to Tab. 61R (T_min=80K, T_max=500K)
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

output: [T]

K_11: 74.95
K_11,T: -5.646e-2
K_11,T^2: 1.420e-5
K_11,T^3: -5.390e-7
K_11,T^4: 4.012e-9

K_33: 52.04
K_33,T: -3.940e-2
K_33,T^2: 7.037e-6
K_33,T^3: -3.738e-7
K_33,T^4: 2.873e-9

T_ref: 293.15

C_p: 210.0

W#

references:
  - J.G. Hust and A.B. Lankford,
    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
    US Department of Commerce, Boulder, Colorado, 1984,
    fit to Tab. 5.4.1 (RRR=300, T_min=100K, T_max=2000K)
  - https://www.mit.edu/~6.777/matprops/tungsten.htm

output: [T]

K_11: 175.0
K_11,T: -1.809e-1
K_11,T^2: 2.257e-4
K_11,T^3: -1.395e-7
K_11,T^4: 3.192e-11

T_ref: 293.15

C_p: 132.51

X2CrNi18-10#

references:
  - C.S. Kim,
    Thermophysical properties of stainless steels,
    Argonne National Laboratory, Argonne, Illinois, 1975,
    https://doi.org/10.2172/4152287,
    Eq. 5 and Eq. 28 (T_min=300K, T_max=1600K)

K_11: 12.86
K_11,T: 1.618e-2

C_p: 508.7
C_p,T: 1.347e-1 # not implemented

T_ref: 293.15

X2CrNiMo17-12-2#

references:
  - C.S. Kim,
    Thermophysical properties of stainless steels,
    Argonne National Laboratory, Argonne, Illinois, 1975,
    https://doi.org/10.2172/4152287,
    Eq. 7 and Eq. 30 (T_min=300K, T_max=1600K)

K_11: 13.85
K_11,T: 1.571e-2

C_p: 497.7
C_p,T: 1.327e-1 # not implemented

T_ref: 293.15

X5CrNi18-10#

references:
  - B.F. Blackwell et al.,
    Proceedings of 34th National Heat Transfer Conference 2000,
    https://www.osti.gov/servlets/purl/760791
  - R.H. Bogaard et al.,
    Thermochimica Acta 218:373-393, 1993,
    https://doi.org/10.1016/0040-6031(93)80437-F

K_11: 14.34
C_p: 470.0

adiabatic#

K_11: 0
K_33: 0
C_p: 1

fast-convection#

K_11: 1.e+30
K_33: 1.e+30
C_p: 1

steel-0.5C#

references:
  - https://www.engineeringtoolbox.com/thermal-conductivity-metals-d_858.html
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

K_11: 54.0
C_p: 490.0

source#

dissipation_generic#
type: dissipation

kappa: .9
externalheat_ramp-and-hold#
type: externalheat

f: [1, 1, 0, 0]
t: [0, 500, 500.001, 1000]