Whenever the N = (2, 2) supersymmetry algebra of non-linear σ-models in two dimensions does not close off-shell, a holomorphic two-form can be defined. The only known superfields providing candidate auxiliary fields to achieve an off-shell formulation are semi-chiral fields. Such a semi-chiral description is only possible when the two-form is constant. Using an explicit example, hyperKähler manifolds, we show that this is not always the case. Finally, we give a concrete construction of semi-chiral potentials for a class of hyper-Kähler manifolds using the duality exchanging a pair consisting of a chiral and a twistedchiral superfield for one semi-chiral multiplet.

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Steel is used for many applications, yet little research has centred on the optical properties of steel and its oxides compared to low-density materials such as aluminium and titanium.In this paper, the optical properties of iron oxides on interstitial free steel substrates are studied. The oxide layers were thermally grown under an oxygen atmosphere at 250°C. Two iron oxide types were present, i.e. a-Fe 2 O 3 (hematite) and Fe 3 O 4 (magnetite). The optical constants of the oxide layer are determined by visual spectroscopic ellipsometry (VISSE). VISSE allows a fast and non-destructive determination of both layer thickness and optical constants. An optical model was constructed to allow for the extraction of the layer thickness from the ellipsometric data. From this model, the total reflection, and therefore also the colour of the sample were calculated. The model is a good predictor of the system's colour, which proves that the colour originates from both interference and absorption effects.

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