.. _Materials:
.. include:: ../shared.rst
Materials
=========
.. _Material:
Solid material specification
----------------------------
The material of the substrate and powder is defined in the ``Material`` section of the JSON file.
This should be a **string**.
The ``MaterialsLibrary`` section contains material specifications corresponding to the string defined in ``Material``.
``MaterialsLibrary`` consists of key-value pairs where:
- The **key** (a string) must match the value in ``Material`` field of the current JSON file.
- The **value** follows the format described on this page.
Example: User-Specified Material
--------------------------------
.. include:: ../json_desc/descUserMaterial.rst
Heat Capacity
^^^^^^^^^^^^^
The volumetric heat capacity is defined when:
- ``HeatCapacityIntervalsT`` = :math:`[T_1, T_2, ..., T_n]`
- ``HeatCapacityVolumeVals`` = :math:`[c_{vol,1}, c_{vol,2}, ..., c_{vol,n}]`
..
The expression for the volumetric heat capacity if ``HeatCapacityIntervalsT`` is :math:`[T_1, T_2, ..., T_n]` and ``HeatCapacityVolumeVals`` is :math:`[c_{vol,1}, c_{vol,2}, ..., c_{vol,n}]`,
.. math::
&T_1=0; \\
c_{vol}= & c_{vol,1}, \quad \text{if } T_1<T<T_2; \\
c_{vol}= & c_{vol,2}, \quad\text{if } T_2<T<T_3; \\
...\\
c_{vol}= & c_{vol,n}, \quad\text{if } T_n<T.
The expression for the heat capacity is :math:`c_{vol} = c_p\rho`
Evaporation
^^^^^^^^^^^
The ``Evaporation`` section includes 3 sections:
1. General Parameters
========================== ============================== ==========================================================
Key Value type Default value
========================== ============================== ==========================================================
``Tboiling`` value 0
``Tcritical`` value 0
:math:`T_{\text{boiling}}` and :math:`T_{\text{critical}}` (K) for the `ClausiusClapeyron` saturated pressure model
--------------------------------------------------------------------------------------------------------------------
``LatentHeatVaporization`` value 0
number — Latent heat of vaporization in J/kg used for `ClausiusClapeyron` saturated pressure model
--------------------------------------------------------------------------------------------------------------------
========================== ============================== ==========================================================
2. One-component evaporation. It is used if NULL is set in components field in the “main Materials section”.
In this case the material is considered to have one component, and the effective evaporation rate should be set:
========================== ============================== ==========================================================
Key Value type Default value
========================== ============================== ==========================================================
``name`` string Unknown
The name of the evaporation preset
--------------------------------------------------------------------------------------------------------------------
``SatPressureName`` string Antonie
The choice of the evaporation model. The possible types are ``Antonie``, ``AntonieExtended``, ``ClausiusClapeyron``
--------------------------------------------------------------------------------------------------------------------
``atomWeight`` value 58.6934
Atomic weight (amu)
--------------------------------------------------------------------------------------------------------------------
``gamma`` value 1.6666666666666667
Specific heat ratio
--------------------------------------------------------------------------------------------------------------------
``coeffA`` value 11.672
``coeffB`` value 20765.0
``coeffC`` value 0.0
``coeffD`` value 0
``coeffE`` value 0
``coeffF`` value 0
Coefficients for the `AntonieExtended` model
--------------------------------------------------------------------------------------------------------------------
========================== ============================== ==========================================================
For *Clausius-Clapeyron* model,
.. math::
&P_{sat}(T) \text{ [bars]} = \exp \left\{-m_a \cfrac{L_{vap0}}{k_B}
\left(
\cfrac{1}{T}\sqrt{1-\left(\cfrac{T}{T_{crit}}\right)^2} - \cfrac{1}{T_{boil}}\sqrt{1-\left(\cfrac{T_{boil}}{T_{crit}}\right)^2} +\right.\right.\\
&\qquad\qquad\qquad\qquad\qquad\qquad \left.\left.\cfrac{1}{T_{crit}}
\left( \arcsin\left(\cfrac{T}{T_{crit}}\right) - \arcsin\left(\cfrac{T_{boil}}{T_{crit}}\right)\right)
\right) \right\} ;\\
&L_{vap}(T) = L_{vap0}\sqrt{1-\left(\cfrac{T}{T_{crit}}\right)^2},\\
&L_{vap0}(T) = L_{vap_B}/\sqrt{1-\left(\cfrac{T_{boil}}{T_{crit}}\right)^2},\\
where :math:`L_{vap0}` is the specific heat of vaporization at absolute zero temperature (it can be derived from :math:`L_{vap_B}`, the heat of vaporization at boiling point which is known more often), :math:`T_{boil}` is the boiling temperature at standard atmosphere (1~bar) and :math:`T_{crit}` is the critical temperature.
For the *Antonie* model:
.. math::
& P_{sat}(T) \text{ [Pascal]} = 10^{\mathcal{A}-\mathcal{B}/\left(\mathcal{C}+T\right)}, \\
& L_{vap}(T) = \cfrac{\mathcal{B}\ln{10}}{(\mathcal{C}+T)^2}\cdot \cfrac{k_BT^2}{m_a};\\
and for *Antonie Extended* model:
.. math::
& P_{sat}(T) \text{ [Pascal]} = 10^{\mathcal{A}-\mathcal{B}/\left(\mathcal{C}+T\right)
+\mathcal{D}T + \mathcal{E}T^2 + F\log_{10}(T) },\\
& L_{vap}(T) = \cfrac{k_BT^2}{m_a} \cdot \left(\cfrac{\mathcal{B}}{(\mathcal{C}+T)^2} + \mathcal{D} + 2\mathcal{E}+\cfrac{\mathcal{F}}{T\ln{10}}\right)\ln{10}. \\
The coefficients :math:`\mathcal{A}`, :math:`\mathcal{B}`, :math:`\mathcal{C}` can usually be found from any reference book with saturated vapor data
(for example, see `Wikipedia article on vapor pressure <https://en.wikipedia.org/wiki/Vapor_pressures_of_the_elements_\%28data_page\%29>`_).
The additional coefficients :math:`\mathcal{D}`, :math:`\mathcal{E}`, :math:`\mathcal{F}` can be used for more precise fitting of saturated vapor curves.
The recommended model in |kissam| is the *Antonie* model.
3. Several component evaporation. It is used if something is set in the components field in the “main Materials section”, for example, ``{“Al”: 0.05, “Ti”: “balanced”}``.
In this case the material is considered to be an alloy, and the evaporation rates for each component should be set in the components section.
For examples of the section, refer to the alloy materials (such as :ref:`Ti6Al4V`) below.
========================== ============================== ==========================================================
Key Value type Contents
========================== ============================== ==========================================================
``components`` JSON data Description for each component
--------------------------------------------------------------------------------------------------------------------
``ActivityMixingCoeffs`` JSON data Acitivity mixing coefficients
========================== ============================== ==========================================================
The ``components`` section has mandratory fields:
========================== ============================== ==========================================================
Key Value type Sample value
========================== ============================== ==========================================================
``name`` string `'name1'`
The name of the component
--------------------------------------------------------------------------------------------------------------------
``atomWeight`` value 58.6934
Atomic weight (amu)
--------------------------------------------------------------------------------------------------------------------
``coeffsABCDEF`` list [11.672, 20765.0, 0.0, 0, 0, 0]
Coefficients for the Antonie and AntonieExtended evaporation expressions.
--------------------------------------------------------------------------------------------------------------------
========================== ============================== ==========================================================
The ``ActivityMixingCoeffs`` are the :math:`L1`, :math:`L2`, :math:`L3` coefficients specified as linear dependencies on temperature:
========================== ============================== ==========================================================
Key Value type Sample value
========================== ============================== ==========================================================
``L1`` list of 2 values [-153707 , 34.8594]
``L2`` list of 2 values [-153707 , 34.8594]
``L3`` list of 2 values [-153707 , 34.8594]
The two values, e.g. :math:`[a,b]` , are used as in :math:`L1=a+bT`.
--------------------------------------------------------------------------------------------------------------------
========================== ============================== ==========================================================
Grains
^^^^^^
======================================= ============================== ==========================================================
Key Value type Contents
======================================= ============================== ==========================================================
``GrowthCoeffs`` list of 3 values Grain growth coefficients :math:`[K_1,K_2,K_3]`
``Nucleation`` JSON data Nucleation model parameters section
======================================= ============================== ==========================================================
The ``Nucleation`` section has two subsections: ``Bulk``, and ``Surface``.
Both sections contain ``Density`` and ``CriticalTdiff`` fields.
======================================= ============================== ==========================================================
Key Value type Contents
======================================= ============================== ==========================================================
``Nucleation.Bulk`` JSON data Bulk parameters section
``Nucleation.Surface`` JSON data Surface model parameters section
``Nucleation.Bulk.Density`` value Nucleation density (concentration) in 1/m³ (for example, `1e15`)
``Nucleation.Bulk.CriticalTdiff`` list of 2 values Critical temperature difference :math:`(T_\text{liquidus}-T_\text{critical})` Gaussian distribution parameters when the nuclei can grow (mean in K and standard deviation in K) (for example, `[9.5, 0.5]`)
``Nucleation.Surface.Density`` value Nucleation density (concentration) in :math:`1/m^2` (for example, `2e8`)
``Nucleation.Surface.CriticalTdiff`` list of 2 values Critical temperature difference :math:`(T_\text{liquidus}-T_\text{critical})` Gaussian distribution parameters when the nuclei can grow (mean in K and standard deviation in K) (for example, `[2, 0.1]` )
======================================= ============================== ==========================================================
The grain growth velocity (m/s) is :math:`v = K_1 \Delta T + K_2\Delta T^2 + K_3\Delta T^3` , where the coefficients :math:`K_1` is in m/s/K, :math:`K_2` is in m/s/K :math:`{}^2`, :math:`K_3` is in m/s/K³ and
the temperature difference :math:`\Delta T = \max(T_{liquidus} - T, 0)` is in K.
Add New Material
----------------
To use another material, add the ``MaterialsLibrary`` to your JSON file, and, in it, specify a gas in the same format. Then, specify the name of your material in the ``Material`` section of the JSON file.
All default values for every built-in material can be changed. If you want to adjust the properties of a built-in material, you can specify only the field you need to adjust in the JSON file.
For example, to use the AA5182 material with custom density:
.. code:: json
{
...
"Material": "AA5182",
...
"MaterialsLibrary": {
"AA5182": {
"density" : 2700.0,
}
}
Gas material specification
--------------------------
The properties of the gas in the gas chamber influence the evaporation process.
Here is the explanation of the material settings on the example of the built-in argon gas.
The entry is in the ``MaterialsLibrary`` section of the JSON file.
To use another gas, add the ``MaterialsLibrary`` to your JSON file, and, in it, specify a gas in the following format.
.. include:: ../json_desc/descAr.rst
To use the specified gas, its name should be in the ``Camera.AmbientGas`` field of the JSON file.
Built-in Materials
------------------
Some materials are already specified in the :file:`default.json` file.
These materials are verified for the use in KiSSAM.
Some materials have additional parameters for microstructure modeling and multicomponent evaporation.
The table below shows which models were verified.
If the material properties for the multicomponent evaporation are missing, users can input custom properties.
.. table::
:widths: 20 20 20
:align: left
========= ================================== ===================================
Material Verified Verified
Microstructure Multicomponent
Parameters Evaporation
========= ================================== ===================================
AA5182_
CoCr_
In625_ yes
Ti6Al4V_ yes
SS316L_
NiTi_ yes
AlSi10Mg_
Mo_
========= ================================== ===================================
.. include:: ../json_desc/desc_material.rst