Thermodynamics, kinetics, and structural physics of atoms and molecules at solid–vapour, solid–liquid, and solid–solid interfaces. Langmuir adsorption isotherm (Langmuir 1918, JACS 40:1361) — for non-interacting adsorbates on a uniform…
surface-science
Langmuir isotherm: θ(p) = Kp/(1 + Kp)
Langmuir adsorption isotherm (Langmuir 1918, JACS 40:1361) for non-interacting adsorbates on a uniform array of equivalent binding sites at…
BET: v/v_m = cx/((1−x)(1−(1−c)x)), x = p/p₀
Brunauer–Emmett–Teller multilayer isotherm (BET 1938, JACS 60:309) generalises Langmuir to physisorption where multilayer stacking is…
Wulff construction: h(n̂)/γ(n̂) = const
Wulff construction (Wulff 1901, Z. Krystallogr. Mineral 34:449) — the equilibrium shape of a single-component crystal minimises the total…
θ(Kp=1) = 1/2, lim_{p→∞} θ = 1, dθ/dp|₀ = K (exact)
Closed-form pins of the Langmuir isotherm at its three characteristic points. (i) Half-coverage — at the condition Kp = 1 (i.e. p = 1/K,…
BET at c=10, x=1/2: v/v_m = 20/11 (exact)
Closed-form rational evaluation of the BET isotherm at representative moderate-binding parameters c = 10 and intermediate-pressure x = p/p₀…
h_{110}/h_{100} = √2 at γ ratio √2 (exact)
Closed-form evaluation of the Wulff facet-distance ratio using the fcc hard-sphere nearest-neighbour-counting estimates. For an fcc…
Tafel kinetics eta = a + b ln(j); Tafel slope b from log-rate counting (topological entropy)
Tafel kinetics framework for electrochemical reactions (Tafel 1905 Z Phys Chem 50, 641; Butler-Volmer 1924). Setup: at…
Langmuir adsorption isotherm theta = K p/(1 + K p); Mobius/half-plane saturation
Langmuir adsorption isotherm framework (Langmuir 1918 J Am Chem Soc 40, 1361). Setup: gas molecules adsorb onto a surface with N_s…
Wulff construction: equilibrium crystal habit gamma_i/r_i = const; Riesz-representation dual
Wulff-construction framework for equilibrium crystal habit (Wulff 1901 Z Krist 34, 449; Herring 1953 Structure and Properties of Solid…
Theorem: j d eta/dj - b = 0 for Tafel eta = a + b ln(j) (log-rate slope identity)
Theorem (Tafel-slope-derivative canonical): for eta = a + b ln(j), differentiating w.r.t. j gives d eta/dj = b/j, hence j d eta/dj - b = 0…
Theorem: lim_{p->inf} K p/(1 + K p) - 1 = 0 (Langmuir saturation Mobius limit)
Theorem (Langmuir-saturation-limit canonical): lim_{p->inf} K p/(1 + K p) = 1 since the leading order of numerator (K p) and denominator (K…
Theorem: gamma_1/r_1 - gamma_2/r_2 = 0 at r_i = gamma_i (Wulff equilibrium ratio)
Theorem (Wulff-ratio canonical): the Wulff theorem states gamma_i/r_i = const for all facets at equilibrium. Setting r_i = gamma_i…
LEED (Davisson-Germer 1927)
Davisson-Germer 1927 (Nobel 1937) electron-diffraction confirms wave-nature; modern LEED standard surface-structure technique.
XPS (Siegbahn 1981)
K Siegbahn 1981 (Nobel 1981) XPS chemical-shift surface-spectroscopy; modern HAXPES + AP-XPS in-situ + ARPES band-mapping.
Si(111)-7x7 (Takayanagi 1985)
Takayanagi 1985 DAS model Si(111)-7x7 reconstruction; 102 atoms in unit-cell; foundational surface-science result.
Langmuir (1916)
I Langmuir 1916 (Nobel 1932) adsorption isotherm theta = bP/(1+bP); modern Sabatier + d-band-theory; basis of heterogeneous catalysis.
SAM (Nuzzo-Allara 1983)
Nuzzo-Allara 1983 thiol-Au SAM; modern microcontact-printing + biosensors + nanopatterning Whitesides-Stuart 2005.
MBE (Cho 1971)
A Y Cho 1971 MBE molecular-beam-epitaxy; modern III-V quantum-wells + 2DEG + GaN + topological-insulator films.
Langmuir adsorption (1918)
I Langmuir 1918 (Nobel 1932) θ=Kp/(1+Kp); modern modern foundational text + extended-Langmuir + non-ideal mixtures + competitive-adsorption.
Auger (1923)
L Meitner 1923 + Auger 1925 + Davis 1976 AES; modern modern foundational text + Auger-Lorentz function fitting + 2024 attosecond Auger…
XPS (Siegbahn 1958)
K Siegbahn 1958 (Nobel 1981) ESCA/XPS; modern modern foundational text + monochromatic-Al-Kα + 2024 ambient-pressure-XPS in-situ.
LEED (Davisson-Germer 1927)
C Davisson-L Germer 1927 (Nobel 1937) + Park-Farnsworth 1959 LEED; modern modern foundational + dynamical-LEED-IV + 2024 ML LEED-pattern…
BET (1938)
S Brunauer-P Emmett-E Teller 1938 multi-layer adsorption; modern modern foundational text + extended SBET + 2024 ML pore-network.
STM imaging (Binnig-Rohrer 1981)
G Binnig-H Rohrer 1981 (Nobel 1986) STM atomic-resolution; modern modern foundational + qPlus AFM + atom-manipulation Eigler 1990 + 2024…