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Fixed and finalized implementation of the temperature-dependent shear modulus and thermal lattice expansion
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4 files changed

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‎contributed_definitions/NXmicrostructure_score_config.nxdl.xml‎

Lines changed: 49 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -158,23 +158,64 @@ exists: optional-->
158158
(Mechanical) properties of the material which scale the
159159
amount of stored (elastic) energy in the system and
160160
thus mainly affect recrystallization kinetics.
161+
162+
Temperature-dependent lattice softening of the shear modulus
163+
:math:`G(T)` is modeled according to `Nadal and Le Poac <https://dx.doi.org/10.1063/1.1539913>`_
164+
i.e., :math:`G(T) = \frac{1}{\mathfrak{J}(\frac{T}{T_m})} G_0 (1 - a \frac{T}{T_m})`
165+
with :math:`G_0` shear_modulus_zero, :math:`a` nadal_lepoac_a, :math:`\zeta` nadal_lepoac_zeta,
166+
and :math:`\mathfrak{J}(\frac{T}{T_m}) = 1 + exp(\frac{\frac{T}{T_m} - 1}{\zeta(1 - \frac{T}{T_m(1+\zeta)})})`.
167+
168+
The temperature-dependent Burgers vector :math:`b(T)` is
169+
modeled with a second order approximation :math:`b(T) = b_0 (1 + (a_2 T^2 + a_1 T + a_0))`
170+
with :math:`a_2` lattice_expansion_second, :math:`a_1` lattice_expansion_first,
171+
and :math:`a_0` lattice_expansion_null.
161172
</doc>
162-
<field name="shear_modulus" type="NX_FLOAT" units="NX_PRESSURE">
173+
<field name="melting_temperature" type="NX_FLOAT" units="NX_TEMPERATURE">
163174
<doc>
164-
Reference shear modulus at zero Kelvin.
175+
Empirical melting temperature measured at standard conditions.
165176
</doc>
166177
</field>
167-
<field name="burgers_vector" type="NX_FLOAT" units="NX_LENGTH">
178+
<field name="shear_modulus_zero" type="NX_FLOAT" units="NX_PRESSURE">
179+
<doc>
180+
Shear modulus at zero Kelvin.
181+
</doc>
182+
</field>
183+
<field name="nadal_lepoac_a" type="NX_FLOAT" units="NX_UNITLESS">
184+
<doc>
185+
Constant :math:`a` in the Nadal-Le Poac-based model of the temperature-dependent
186+
shear modulus.
187+
</doc>
188+
</field>
189+
<field name="nadal_lepoac_zeta" type="NX_FLOAT" units="NX_UNITLESS">
190+
<doc>
191+
Constant :math:`\zeta` in the Nadal-Le Poac-based model of the temperature-
192+
dependent shear modulus.
193+
</doc>
194+
</field>
195+
<field name="burgers_vector_zero" type="NX_FLOAT" units="NX_LENGTH">
168196
<doc>
169197
Magnitude of the Burgers vector at zero Kelvin.
170198
</doc>
171199
</field>
200+
<field name="lattice_expansion_second" type="NX_FLOAT" units="NX_ANY">
201+
<doc>
202+
Constant :math:`a_2` in the second-order model that is used
203+
for quantifying the temperature-dependent Burgers vector.
204+
</doc>
205+
</field>
206+
<field name="lattice_expansion_first" type="NX_FLOAT" units="NX_ANY">
207+
<doc>
208+
Constant :math:`a_1` in the second-order model that is used
209+
for quantifying the temperature-dependent Burgers vector.
210+
</doc>
211+
</field>
212+
<field name="lattice_expansion_null" type="NX_FLOAT" units="NX_LENGTH">
213+
<doc>
214+
Constant :math:`a_0` in the second-order model that is used
215+
for quantifying the temperature-dependent Burgers vector.
216+
</doc>
217+
</field>
172218
</group>
173-
<!--firstOrderedG0dT
174-
alloyConstantThermalExpCoeff
175-
FirstOrderThermalExpCoeff
176-
SecondOrderThermalExpCoeff
177-
melting_temperature(NX_FLOAT):-->
178219
<group name="deformation" type="NXparameters">
179220
<doc>
180221
Details about the geometry and properties of the polycrystal that represents the

‎contributed_definitions/NXmicrostructure_score_results.nxdl.xml‎

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -446,7 +446,7 @@ the typically storage-costlier snapshot data-->
446446
<dim index="1" value="n_grains"/>
447447
</dimensions>
448448
</field>
449-
<field name="volume" type="NX_FLOAT" units="NX_UNITLESS">
449+
<field name="volume" type="NX_FLOAT" units="NX_VOLUME">
450450
<doc>
451451
Volume of each grain (partially transformed cells are accounted for).
452452

@@ -564,7 +564,7 @@ the typically storage-costlier snapshot data-->
564564
<dim index="1" value="n_front"/>
565565
</dimensions>
566566
</field>
567-
<field name="recrystallized_fraction" type="NX_FLOAT" optional="true" units="NX_DIMENSIONLESS">
567+
<field name="recrystallized_fraction" type="NX_FLOAT" recommended="true" units="NX_DIMENSIONLESS">
568568
<doc>
569569
The fraction to which the cell is assumed transformed.
570570
</doc>

‎contributed_definitions/nyaml/NXmicrostructure_score_config.yaml‎

Lines changed: 93 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -89,20 +89,54 @@ NXmicrostructure_score_config(NXobject):
8989
(Mechanical) properties of the material which scale the
9090
amount of stored (elastic) energy in the system and
9191
thus mainly affect recrystallization kinetics.
92-
shear_modulus(NX_FLOAT):
92+
93+
Temperature-dependent lattice softening of the shear modulus
94+
:math:`G(T)` is modeled according to `Nadal and Le Poac <https://dx.doi.org/10.1063/1.1539913>`_
95+
i.e., :math:`G(T) = \frac{1}{\mathfrak{J}(\frac{T}{T_m})} G_0 (1 - a \frac{T}{T_m})`
96+
with :math:`G_0` shear_modulus_zero, :math:`a` nadal_lepoac_a, :math:`\zeta` nadal_lepoac_zeta,
97+
and :math:`\mathfrak{J}(\frac{T}{T_m}) = 1 + exp(\frac{\frac{T}{T_m} - 1}{\zeta(1 - \frac{T}{T_m(1+\zeta)})})`.
98+
99+
The temperature-dependent Burgers vector :math:`b(T)` is
100+
modeled with a second order approximation :math:`b(T) = b_0 (1 + (a_2 T^2 + a_1 T + a_0))`
101+
with :math:`a_2` lattice_expansion_second, :math:`a_1` lattice_expansion_first,
102+
and :math:`a_0` lattice_expansion_null.
103+
melting_temperature(NX_FLOAT):
104+
unit: NX_TEMPERATURE
105+
doc: |
106+
Empirical melting temperature measured at standard conditions.
107+
shear_modulus_zero(NX_FLOAT):
93108
unit: NX_PRESSURE
94109
doc: |
95-
Reference shear modulus at zero Kelvin.
96-
burgers_vector(NX_FLOAT):
110+
Shear modulus at zero Kelvin.
111+
nadal_lepoac_a(NX_FLOAT):
112+
unit: NX_UNITLESS
113+
doc: |
114+
Constant :math:`a` in the Nadal-Le Poac-based model of the temperature-dependent
115+
shear modulus.
116+
nadal_lepoac_zeta(NX_FLOAT):
117+
unit: NX_UNITLESS
118+
doc: |
119+
Constant :math:`\zeta` in the Nadal-Le Poac-based model of the temperature-
120+
dependent shear modulus.
121+
burgers_vector_zero(NX_FLOAT):
97122
unit: NX_LENGTH
98123
doc: |
99124
Magnitude of the Burgers vector at zero Kelvin.
100-
101-
# firstOrderedG0dT
102-
# alloyConstantThermalExpCoeff
103-
# FirstOrderThermalExpCoeff
104-
# SecondOrderThermalExpCoeff
105-
# melting_temperature(NX_FLOAT):
125+
lattice_expansion_second(NX_FLOAT):
126+
unit: NX_ANY
127+
doc: |
128+
Constant :math:`a_2` in the second-order model that is used
129+
for quantifying the temperature-dependent Burgers vector.
130+
lattice_expansion_first(NX_FLOAT):
131+
unit: NX_ANY
132+
doc: |
133+
Constant :math:`a_1` in the second-order model that is used
134+
for quantifying the temperature-dependent Burgers vector.
135+
lattice_expansion_null(NX_FLOAT):
136+
unit: NX_LENGTH
137+
doc: |
138+
Constant :math:`a_0` in the second-order model that is used
139+
for quantifying the temperature-dependent Burgers vector.
106140
deformation(NXparameters):
107141
doc: |
108142
Details about the geometry and properties of the polycrystal that represents the
@@ -541,7 +575,7 @@ NXmicrostructure_score_config(NXobject):
541575
during post-processing the results with the solitary unit modeling approach.
542576
543577
# ++++++++++++++++++++++++++++++++++ SHA HASH ++++++++++++++++++++++++++++++++++
544-
# 2dbb3e82d6536c45ed97fb3e8f35c1f680d1da4b8c58369c09b85959fdb0fabe
578+
# f2395e1f8b2a98c71102f1332cb6e122b2a04e378ad1e80944d1294628acedc9
545579
# <?xml version="1.0" encoding="UTF-8"?>
546580
# <?xml-stylesheet type="text/xsl" href="nxdlformat.xsl"?>
547581
# <!--
@@ -702,23 +736,64 @@ NXmicrostructure_score_config(NXobject):
702736
# (Mechanical) properties of the material which scale the
703737
# amount of stored (elastic) energy in the system and
704738
# thus mainly affect recrystallization kinetics.
739+
#
740+
# Temperature-dependent lattice softening of the shear modulus
741+
# :math:`G(T)` is modeled according to `Nadal and Le Poac &lt;https://dx.doi.org/10.1063/1.1539913&gt;`_
742+
# i.e., :math:`G(T) = \frac{1}{\mathfrak{J}(\frac{T}{T_m})} G_0 (1 - a \frac{T}{T_m})`
743+
# with :math:`G_0` shear_modulus_zero, :math:`a` nadal_lepoac_a, :math:`\zeta` nadal_lepoac_zeta,
744+
# and :math:`\mathfrak{J}(\frac{T}{T_m}) = 1 + exp(\frac{\frac{T}{T_m} - 1}{\zeta(1 - \frac{T}{T_m(1+\zeta)})})`.
745+
#
746+
# The temperature-dependent Burgers vector :math:`b(T)` is
747+
# modeled with a second order approximation :math:`b(T) = b_0 (1 + (a_2 T^2 + a_1 T + a_0))`
748+
# with :math:`a_2` lattice_expansion_second, :math:`a_1` lattice_expansion_first,
749+
# and :math:`a_0` lattice_expansion_null.
705750
# </doc>
706-
# <field name="shear_modulus" type="NX_FLOAT" units="NX_PRESSURE">
751+
# <field name="melting_temperature" type="NX_FLOAT" units="NX_TEMPERATURE">
752+
# <doc>
753+
# Empirical melting temperature measured at standard conditions.
754+
# </doc>
755+
# </field>
756+
# <field name="shear_modulus_zero" type="NX_FLOAT" units="NX_PRESSURE">
707757
# <doc>
708-
# Reference shear modulus at zero Kelvin.
758+
# Shear modulus at zero Kelvin.
709759
# </doc>
710760
# </field>
711-
# <field name="burgers_vector" type="NX_FLOAT" units="NX_LENGTH">
761+
# <field name="nadal_lepoac_a" type="NX_FLOAT" units="NX_UNITLESS">
762+
# <doc>
763+
# Constant :math:`a` in the Nadal-Le Poac-based model of the temperature-dependent
764+
# shear modulus.
765+
# </doc>
766+
# </field>
767+
# <field name="nadal_lepoac_zeta" type="NX_FLOAT" units="NX_UNITLESS">
768+
# <doc>
769+
# Constant :math:`\zeta` in the Nadal-Le Poac-based model of the temperature-
770+
# dependent shear modulus.
771+
# </doc>
772+
# </field>
773+
# <field name="burgers_vector_zero" type="NX_FLOAT" units="NX_LENGTH">
712774
# <doc>
713775
# Magnitude of the Burgers vector at zero Kelvin.
714776
# </doc>
715777
# </field>
778+
# <field name="lattice_expansion_second" type="NX_FLOAT" units="NX_ANY">
779+
# <doc>
780+
# Constant :math:`a_2` in the second-order model that is used
781+
# for quantifying the temperature-dependent Burgers vector.
782+
# </doc>
783+
# </field>
784+
# <field name="lattice_expansion_first" type="NX_FLOAT" units="NX_ANY">
785+
# <doc>
786+
# Constant :math:`a_1` in the second-order model that is used
787+
# for quantifying the temperature-dependent Burgers vector.
788+
# </doc>
789+
# </field>
790+
# <field name="lattice_expansion_null" type="NX_FLOAT" units="NX_LENGTH">
791+
# <doc>
792+
# Constant :math:`a_0` in the second-order model that is used
793+
# for quantifying the temperature-dependent Burgers vector.
794+
# </doc>
795+
# </field>
716796
# </group>
717-
# <!--firstOrderedG0dT
718-
# alloyConstantThermalExpCoeff
719-
# FirstOrderThermalExpCoeff
720-
# SecondOrderThermalExpCoeff
721-
# melting_temperature(NX_FLOAT):-->
722797
# <group name="deformation" type="NXparameters">
723798
# <doc>
724799
# Details about the geometry and properties of the polycrystal that represents the

‎contributed_definitions/nyaml/NXmicrostructure_score_results.yaml‎

Lines changed: 5 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -335,7 +335,7 @@ NXmicrostructure_score_results(NXobject):
335335
rank: 1
336336
dim: (n_grains,)
337337
volume(NX_FLOAT):
338-
unit: NX_UNITLESS
338+
unit: NX_VOLUME
339339
doc: |
340340
Volume of each grain (partially transformed cells are accounted for).
341341
@@ -447,15 +447,15 @@ NXmicrostructure_score_results(NXobject):
447447
rank: 1
448448
dim: (n_front,)
449449
recrystallized_fraction(NX_FLOAT):
450-
exists: optional
450+
exists: recommended
451451
unit: NX_DIMENSIONLESS
452452
doc: |
453453
The fraction to which the cell is assumed transformed.
454454
dimensions:
455455
rank: 1
456456

457457
# ++++++++++++++++++++++++++++++++++ SHA HASH ++++++++++++++++++++++++++++++++++
458-
# ab78c3fa746db4836c7be5fea696c9e16395eb7a3cb6acfd5f1c07445dadeadf
458+
# 3c5dbf746e80543c1b3d28330df4717e72745f61610e8be581a9e54d24b84370
459459
# <?xml version="1.0" encoding="UTF-8"?>
460460
# <?xml-stylesheet type="text/xsl" href="nxdlformat.xsl"?>
461461
# <!--
@@ -904,7 +904,7 @@ NXmicrostructure_score_results(NXobject):
904904
# <dim index="1" value="n_grains"/>
905905
# </dimensions>
906906
# </field>
907-
# <field name="volume" type="NX_FLOAT" units="NX_UNITLESS">
907+
# <field name="volume" type="NX_FLOAT" units="NX_VOLUME">
908908
# <doc>
909909
# Volume of each grain (partially transformed cells are accounted for).
910910
#
@@ -1022,7 +1022,7 @@ NXmicrostructure_score_results(NXobject):
10221022
# <dim index="1" value="n_front"/>
10231023
# </dimensions>
10241024
# </field>
1025-
# <field name="recrystallized_fraction" type="NX_FLOAT" optional="true" units="NX_DIMENSIONLESS">
1025+
# <field name="recrystallized_fraction" type="NX_FLOAT" recommended="true" units="NX_DIMENSIONLESS">
10261026
# <doc>
10271027
# The fraction to which the cell is assumed transformed.
10281028
# </doc>

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