Add palladium alloys

h_transport_materials/material.py

@@ -113,6 +113,8 @@ class MoltenSalt(Material):
 class FeCrAl(Steel):
     family = "fecral"
 
+class PalladiumAlloy(Alloy):
+    family = "palladium alloy"
 
 TUNGSTEN = Tungsten()
 BERYLLIUM = Beryllium()
@@ -146,7 +148,7 @@ class FeCrAl(Steel):
 FLINAK = MoltenSalt("flinak")
 LIPB = Alloy("lipb")
 LITHIUM = PureMetal("lithium", "Li")
-PDAG = Alloy("pdag")
+PDAG = PalladiumAlloy("pdag")
 ZIRCONIUM = PureMetal("zirconium", "Zr")
 YTTRIUM = PureMetal("yttrium", "Y")
 
@@ -161,4 +163,6 @@ class FeCrAl(Steel):
 FE22CR5AL = FeCrAl("fe22cr5al")
 OXIDIZED_1605 = FeCrAl("oxidized_1605")
 
-TZM = Alloy("tzm")
+TZM = Alloy("tzm")
+
+PD52CU = PalladiumAlloy("pd52cu")

h_transport_materials/property_database/__init__.py

@@ -68,3 +68,5 @@
 from . import yttrium
 
 from . import tzm
+
+from . import palladium_copper

h_transport_materials/property_database/palladium.py

@@ -1,5 +1,5 @@
 import h_transport_materials as htm
-from h_transport_materials import Diffusivity, Solubility
+from h_transport_materials import Diffusivity, Solubility, RecombinationCoeff
 import numpy as np
 
 u = htm.ureg
@@ -472,6 +472,14 @@
     source="powell_surface_1991",
 )
 
+takagi_recombination_d = RecombinationCoeff(
+    pre_exp=1.5e-27 * u.m**4 * u.s**-1 * u.particle**-1,
+    act_energy=0.48 * u.eV * u.particle**-1,
+    range=(398 * u.K, 571 * u.K),
+    isotope="D",
+    source="takagi_asymmetric_2003",
+    note="Equation 6",
+)
 
 properties = [
     volkl_diffusivity,
@@ -481,6 +489,7 @@
     solubility_powell_d,
     diffusivity_powell_h,
     diffusivity_powell_d,
+    takagi_recombination_d,
 ]
 
 for prop in properties:

h_transport_materials/property_database/palladium_copper.py

@@ -0,0 +1,59 @@
+import h_transport_materials as htm
+from h_transport_materials import (
+    Permeability,
+    Diffusivity,
+) 
+import numpy as np
+
+u = htm.ureg
+
+li_data_T = np.array(
+    [
+        350,
+        375,
+        400,
+        425,
+    ]
+) * u.degC
+
+li_data_y = (
+    np.array(
+        [
+            1.45e-8,
+            1.51e-8,
+            1.55e-8,
+            1.60e-8,
+        ]
+    )
+    * u.mol 
+    * u.m**-1 
+    * u.Pa**-0.5 
+    * u.s**-1
+)
+
+li_permeability_h = Permeability(
+    data_T=li_data_T,
+    data_y=li_data_y,
+    source="li_low_2023",
+    isotope="H",
+    note="SI Table 1 (supporting information)"
+)
+
+piper_diffusivity_h = Diffusivity(
+    D_0=3e-3 * u.cm**2 * u.s**-1,
+    E_D=2400 * u.cal * u.mol**-1,
+    range=(u.Quantity(50, u.degC), u.Quantity(600, u.degC)),
+    isotope="H",
+    source="piper_diffusion_2004",
+    note="Equation 6 - this Arrhenius fit holds for when the alloy is in the beta phase for 52.5 percent copper. These range values were found outside of the paper.",
+)
+
+properties = [
+    li_permeability_h,
+    piper_diffusivity_h,
+]
+
+for prop in properties:
+    prop.material = htm.PD52CU
+
+htm.database += properties

h_transport_materials/property_database/pdag/palladium_silver.py

@@ -114,6 +114,23 @@
     note="equation 17 + probably an error in the units of the activation energy in the original paper",
 )
 
+serra_permeability_h = Permeability(
+    pre_exp=5.58e-8 * u.mol * u.m**-1 * u.Pa**-0.5 * u.s**-1,
+    act_energy=6304 * u.J * u.mol**-1,
+    range=(373 * u.K, 773 * u.K),
+    isotope="H",
+    source="serra_hydrogen_1998-2",
+    note="Figure 2 or Equation 6",
+)
+
+serra_permeability_d = Permeability(
+    pre_exp=3.43e-8 * u.mol * u.m**-1 * u.Pa**-0.5 * u.s**-1,
+    act_energy=6156 * u.J * u.mol**-1,
+    range=(373 * u.K, 773 * u.K),
+    isotope="D",
+    source="serra_hydrogen_1998-2",
+    note="Figure 2 or Equation 7",
+)
 properties = [
     serra_diffusivity_h,
     serra_diffusivity_d,
@@ -127,6 +144,8 @@
     vadrucci_permeability_wt150,
     vadrucci_permeability_wt200,
     vadrucci_dissociation_h,
+    serra_permeability_h,
+    serra_permeability_d,
 ]
 
 for prop in properties:

h_transport_materials/references.bib

@@ -2561,3 +2561,48 @@ @article{ikeda_application_2011
 	doi = {10.13182/FST11-A12707},
 	url = {https://doi.org/10.13182/FST11-A12707},
 }
+
+@article{takagi_asymmetric_2003,
+title = {Asymmetric surface recombination of hydrogen on palladium exposed to plasma},
+journal = {Journal of Nuclear Materials},
+volume = {313-316},
+pages = {102-106},
+year = {2003},
+note = {Plasma-Surface Interactions in Controlled Fusion Devices 15},
+issn = {0022-3115},
+doi = {https://doi.org/10.1016/S0022-3115(02)01370-3},
+url = {https://www.sciencedirect.com/science/article/pii/S0022311502013703},
+author = {Ikuji Takagi and Kimikazu Moritani and Hirotake Moriyama},
+keywords = {Plasma–wall interactions, Palladium, Hydrogen, Recombination, Nuclear reaction analysis, Coverage},
+abstract = {Recombination coefficient of deuterium on either side of a palladium membrane was experimentally studied. Under conditions that one side of the membrane was continuously exposed to a deuterium plasma and the permeation flux was monitored on the other side, two experiments were conducted. One was to observe the transient behavior of the permeation when the incident flux from the plasma was quickly changed and the other was to observe the deuterium concentration by the nuclear reaction analysis. The permeation was limited by the second-order kinetics with respect to deuterium concentration, and the recombination coefficient ku on the plasma-facing side was expressed by ku=1.5×10−27exp(−0.48eV/kT) m4s−1, which is explained by the Pick’s model. The recombination coefficient kd on the downstream side was the same as ku at lower temperatures but showed different temperature dependence above 400 K. This can also be explained by the model but another process of the second-order kinetics may be present.}
+}
+
+@article{li_low_2023,
+title = {Low temperature hydrogen plasma permeation in palladium and its alloys for fuel recycling in fusion systems},
+journal = {Journal of Nuclear Materials},
+volume = {582},
+pages = {154484},
+year = {2023},
+issn = {0022-3115},
+doi = {https://doi.org/10.1016/j.jnucmat.2023.154484},
+url = {https://www.sciencedirect.com/science/article/pii/S0022311523002519},
+author = {Chao Li and Adam J. Job and Thomas F. Fuerst and Masashi Shimada and J. Douglas Way and Colin A. Wolden},
+keywords = {Palladium, Superpermeation, Hydrogen, Metal foil pump, Fusion fuel cycle},
+abstract = {Superpermeation of hydrogen isotopes through metal foils is a critical component for efficient fuel recycling in fusion power systems. In that context hydrogen permeation through foils of palladium and its alloys with silver and copper was studied at low temperature (60 - 200°C) under plasma exposure. These alloys differ significantly in both bulk and surface properties, and comparisons can provide mechanistic insights. Permeation was observed only during plasma operation, confirming the negligible contribution of molecular hydrogen to the observed flux. As-received foils required surface treatment to achieve top performance. For Pd and Pd75Ag25 an oxidation treatment increased permeation an order of magnitude, but proved unstable as this desirable surface was reduced under hydrogen plasma exposure. In contrast, an Ar plasma cleaning step provided both high and stable flux. As-received FCC phase Pd60Cu40 foils required annealing to transform it into the high permeability BCC phase that delivered top performance. All foils displayed similar temperature dependence with flux declining with temperature, suggesting that the primary rate-limiting step is absorption of superthermal hydrogen. Among these foils the hydrogen flux through PdCu was 3 - 5X greater than that of Pd or PdAg, which were similar. The superiority of BCC PdCu is attributed to its superior hydrogen desorption kinetics. Using PdCu 100% permeation of supplied hydrogen was achieved, and the flux saturated with increasing plasma power at values >10−2 mol H·m−2·s−1, and under these conditions permeation rates are equivalent with or without the membrane present. The fluxes achieved are the highest reported to date at these conditions, and the results highlight the important roles of both surface and bulk properties.}
+}
+
+@article{piper_diffusion_2004,
+    author = {Piper, John},
+    title = "{Diffusion of Hydrogen in Copper‐Palladium Alloys}",
+    journal = {Journal of Applied Physics},
+    volume = {37},
+    number = {2},
+    pages = {715-721},
+    year = {2004},
+    month = {06},
+    abstract = "{The diffusion of hydrogen in copper‐palladium alloys has been studied by utilizing the dependence of electrical resistivity upon hydrogen concentration—a technique both rapid and simple. At 25°C the diffusion coefficient in the range 0–58 at.\\% Cu is relatively insensitive to alloy composition but is extremely sensitive to the α‐β phase change: it increases two orders of magnitude to become 5×10−5 cm2/sec when the crystal structure of the alloy system changes from face‐centered cubic to ordered body‐centered cubic. Measurements at 130°C indicate that this large increase is due to a decrease by a factor of three in the activation energy for diffusion. The ratio of the diffusion coefficient for hydrogen to that for deuterium in the body‐centered cubic alloy was found to be approximately 1.5.}",
+    issn = {0021-8979},
+    doi = {10.1063/1.1708243},
+    url = {https://doi.org/10.1063/1.1708243},
+    eprint = {https://pubs.aip.org/aip/jap/article-pdf/37/2/715/7937414/715\_1\_online.pdf},
+}