sphinxcontrib.bibtex and Arrhenius law

docs/source/bibliography/references.bib

@@ -0,0 +1,61 @@
+@article{McNabb1963,
+	title        = {{A New Analysis of the Diffusion of Hydrogen in Iron and Ferritic Steels}},
+	author       = {McNabb, A. and Foster, P. K.},
+	year         = 1963,
+	journal      = {Trans. Metall. Soc. AIME},
+	volume       = 227,
+	number       = {June},
+	pages        = 618,
+	abstract     = {A consideration of the literature shows the inadequacy of Fick's Laws to describe the diffusion of hydrogen in steels below 400°C. These laws are modified an the assumption that hydrogen is delayed at fixed sites in the lattice. Approximate and exact solutions of the resulting nonlinear system are derived for simple geometrical shapes. The results qualitatively account for the observed anomalous behavior. Experimental methods for verifying the theory are suggested. 1 HIS paper presents a new analysis of the diffusion behavior of hydrogen in steel based on a physical model which supposes that hydrogen atoms wander in a random manner through the crystal lattice, but tend to get trapped or delayed at certain fixed sites uniformly distributed throughout the metal. These sites, which will be called traps, are regarded merely as potential wells of significantly greater depth than those encountered in regular regions of the crystal lattices and no assumptions are made concerning their nature or origin. The results of experimental studies of the diffusion of hydrogen in iron and steel have usually been reported in the literature in terms of a diffusion constant D derived under the assumptions that the hydrogen concentration C is governed by Fick's laws.1 Fig. I is a composite of published graphs of the man. ner in which the values of D, so derived, vary with temperature. It is convenient to consider this material in two categories; the high temperature results above 400°C, and the results at lower temperatures. The graphs 2, 3, 4, 5 in the first class lie within a factor of three of each other and are relatively consistent compared with the low-temperature values. There is an increasing divergence in values of D with decreasing temperature till at room temperature they are spread over three orders of magnitude. Small values of D have been obtained for work-hardened specimens.' It is evident that D is a function of other variables besides temperature in this range and that these neglected variables are in some way connected with the work hardening experienced by the specimen. In view of evidence for an interaction between hydrogen in solution and dislocations9'10 and adsorption on crack surfaces,' some doubts must be entertained about the validity of Fick's laws and their associated physical model of noninteracting particles in random motion through the medium. More direct evidence of their inapplicability to the diffusion of hydrogen in steel was first produced by Darken and smith." Consider the permeation of hydrogen through a plate of thickness a under a boundary concentration Co at the ingoing, and zero at the outgoing, face. If Fick's first law1 is valid, the steady state flux P, through unit area is DCo/a. In addition, the concentration C varies linearly throughout and Qo, the mean quantity of hydrogen in the medium, is co/2. Compare Qo with Q1 the mean quantity required to saturate the same specimen to a uniform concentration G. In this case Ql = Co and hence the ratio}
+}
+@article{Longhurst1985,
+	title        = {{The soret effect and its implications for fusion reactors}},
+	author       = {Longhurst, G. R.},
+	year         = 1985,
+	journal      = {J. Nucl. Mater.},
+	volume       = 131,
+	number       = 1,
+	pages        = {61--69},
+	issn         = {00223115},
+	url          = {https://linkinghub.elsevier.com/retrieve/pii/0022311585904258}
+}
+@techreport{Pendergrass1976,
+	title        = {{Temperature-dependent ordinary and thermal diffusion of hydrogen isotopes through thermonuclear reactor components}},
+	author       = {Pendergrass, J. H.},
+	year         = 1976,
+	url          = {http://www.osti.gov/servlets/purl/7333557/},
+	abstract     = {To permit more accurate calculations of tritium permeation for design purposes, theoretical expressions for quasiunidirectional ordinary diffusion of hydrogen isotopes through nonisothermal plane, cylindrical shell, and spherical shell barriers are presented. Arrhenium-type dependence of mass diffusivity on temperature and steady-state constant-thermal-conductivity temperature gradients through the barriers are considered. Analyses that consider thermal diffusion with both constant and temperature-dependent heat of transport are also presented. Other topics discussed are amounts of dissolved hydrogen, variable-thermal-conductivity temperature profiles, hydrogen isotope trapping by chemical impurities, crystal lattice imperfections, and grain boundaries, and mixing rules for dilute dissolution of hydrogen isotope mixtures in metals. Numerical results are given which reveal that neglect of thermal diffusion can lead to errors of up to several hundred percent in calculations of hydrogen isotope transfer through reactor components having large temperature gradients through them. Calculations of combined ordinary and thermal diffusion that rigorously treat the temperature dependences of thermophysical properties typically yield results that differ by only a few percent from results based on physical property evaluations at the arithmetic average of barrier face temperatures.},
+	institution  = {Los Alamos National Laboratory (LANL)}
+}
+@article{Delaporte-Mathurin2021,
+	title        = {{Influence of interface conditions on hydrogen transport studies}},
+	author       = {Delaporte-Mathurin, R. and Hodille, E. A. and Mougenot, J. and Charles, Y. and {De Temmerman}, G. and Leblond, F. and Grisolia, C.},
+	year         = 2021,
+	journal      = {Nucl. Fusion},
+	volume       = 61,
+	number       = 3,
+	pages        = {036038},
+	issn         = {0029-5515},
+	url          = {https://iopscience.iop.org/article/10.1088/1741-4326/abd95f},
+	abstract     = {This work investigates the influence of hydrogen chemical potential continuity across solid material interfaces. The implementation of the mathematical model in FESTIM is verified using the method of exact solutions (MES) and the method of manufactured solutions (MMS) in 1D, 2D, with complex material properties and inhomogeneous temperature fields. A comparison test between FESTIM, TMAP7 and Abaqus codes is also performed and the codes show good agreement. The chemical potential continuity condition has an impact up to 40{\%} on the outgassing particle flux on 4 mm composite slabs (W/Cu and Cu/EUROFER) compared to mobile concentration continuity. A method for rapid identification of materials properties from outgassing flux measurements is given. The influence of chemical potential conservation on monoblock inventory is then studied. It is shown that, for the 1D and 2D ITER divertor monobolocks cases, discrepancies only start to appear after approximately 5 × 10 6 s of full power.}
+}
+@phdthesis{Delaporte-Mathurin2022,
+	title        = {{Hydrogen transport in tokamaks : Estimation of the ITER divertor tritium inventory and influence of helium exposure}},
+	author       = {Delaporte-Mathurin, R.},
+	year         = 2022,
+	number       = {2022PA131054},
+	url          = {https://theses.hal.science/tel-04004369},
+	school       = {{Universit{\'e} Paris-Nord - Paris XIII}},
+	keywords     = {Hydrogen ; Finite elements ; Numerical modelling ; Hydrog{\`e}ne ; El{\'e}ments finis ; Mod{\'e}lisation num{\'e}rique},
+	type         = {Theses}
+}
+@article{Schmid2016,
+	title        = {{Diffusion-trapping modelling of hydrogen recycling in tungsten under ELM-like heat loads}},
+	author       = {Schmid, K.},
+	year         = 2016,
+	journal      = {Phys. Scr.},
+	volume       = {T167},
+	pages        = {014025},
+	issn         = {0031-8949},
+	url          = {https://iopscience.iop.org/article/10.1088/0031-8949/T167/1/014025}
+}

docs/source/conf.py

@@ -38,6 +38,7 @@
     "sphinx.ext.napoleon",
     "sphinx.ext.viewcode",
     "sphinx_design",
+    "sphinxcontrib.bibtex",
     "matplotlib.sphinxext.plot_directive",
 ]
 
@@ -62,6 +63,9 @@
 # shorten module names in readme
 add_module_names = False
 
+# bibliography file
+bibtex_bibfiles = ['bibliography/references.bib']
+
 # -- Options for HTML output -------------------------------------------------
 
 # The theme to use for HTML and HTML Help pages.  See the documentation for