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The present contribution introduces theoretical studies of photonic crystals. On the basis of Maxwell's equations and a `plane wave expansion' band structures and densities of states are computed for triangular and square 2D lattices of air columns in silicon. The main topic of the paper are investigations of band gap modifications (TM-and TE-polarization) for pores of deteriorating roundness, approximated by ellipses of varying eccentricity. The presented computations include the consideration of background structures in the form of stripes (SiO 2 ) in the model. The results are compared with calculations for circular air columns of varying filling factors.Im vorliegenden Beitrag werden theoretische Untersuchungen zu photonischen Kristallen vorgestellt. Auf der Grundlage der Maxwellschen Gleichungen und einer `ebenen Wellen Entwicklung' werden fu È r triangulare und quadratische 2D Gitter Bandstrukturen und Zustandsdichten berechnet. Schwerpunkt der Publikation bilden Untersuchungen zu Vera È nderungen der Bandlu È cken (TM-und TE-Polarisation), wenn die Poren in Silizium nicht mehr exakt rund sind, sondern durch Ellipsen mit variabler Exzentrizita È t gena È hert werden. Die vorgestellten Berechnungen erlauben zusa È tzlich, streifenfo È rmige Hintergrundstrukturen (SiO 2 ) in den Modellen zu beru È cksichtigen. Die Ergebnisse werden mit Rechnungen fu È r kreisfo È rmige Luftsa È ulen bei variablem Fu È llfaktor verglichen.

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CaAg – SrAg – BaAg: Between CrB and FeB Structure Type Depending on both electronic (valence electron numbers) and geometric (atom size ratios) characteristics of the contributing elements, the 1:1 compounds AIIM of the heavier alkaline earth elements A and electron‐rich transition metals M form the well known CrB or FeB structure types. Both structure types exhibit M zig‐zag chains, which are stacked in different orientations against each other. In systematic studies of the pseudo‐binary sections CaxSr1−xAg and SrxBa1−xAg three new ternary phases with different stacking variants between the CrB (cubic stacking, c) and the FeB (hexagonal stacking, h2) structure type have been prepared and determined on the basis of single crystal x‐ray data. Starting from CaAg (CrB type, stacking c), up to 25 percent of Sr (i.e. in Ca0.75(2)Sr0.25(2)Ag: orthorhombic, space group Cmcm, a = 413.4(1), b = 1157.8(3), c = 467.4(2) pm, Z = 4, R1 = 0.0453) can be substituted without a change in the structure type. At a 1:1 ratio of Ca and Sr, a new structure type with stacking sequence (hc5)2 is formed (Ca0.48(3)Sr0.52(3)Ag: space group Pnma, a = 4800.1(1), b = 471.8(12), c = 624.11(9) pm, Z = 24, R1 = 0.0881). Further reduced cubic stacking ((hc2)2) is observed in the Sr rich region with Ca proportions between 39 and 25(2) % (space group Pnma, x = 0.39(1)/0.25(2): a = 2412.2(3)/2434.67(4), b = 472.75(5)/473.97(8), c = 626.17(7)/629.2(3) pm, Z = 12, R1 = 0.0430/0.0489) where the HT‐TbNi structure type is formed. The stability range of the SrAg structure type ((hc)2) starts at a Ca content of 5 % (Ca0.05Sr0.95Ag: space group Pnma, a = 1643.1(2), b = 476.79(7), c = 636.27(9) pm, Z = 8, R1 = 0.0318). From a new second modification of SrAg (space group Pnma, a = 4131.5(4), b = 478.79(6), c = 638.81(6) pm, Z = 20, R1 = 0.0394) up to a Ba proportion of 8 percent, the α‐CaCu structure type with sequence (hch2c)2 is formed. The stability range of the FeB structure with purely hexagonal stacking extends from Sr0.84(1)Ba0.16(1)Ag (a = 830.78(12), b = 479.35(8), c = 644.93(11) pm, Z = 4, R1 = 0.0413) to the border phase BaAg. In an accompanying computational study, the chemical bonding in the binary compounds CaAg, SrAg and BaAg is analyzed using FP‐LAPW band structure methods. Together with geometrical criteria, the results are used to compare and discuss the stability of the different stacking variants of the polar intermetallic 1:1 phases inbetween the CrB and the FeB structure type.

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