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Pseudomorphic and relaxed    $$\alpha$$  α -(Al   $$_x$$  x Ga   $$_{1-x}$$  1 - x )   $$_2$$  2 O   $$_3$$  3 thin films are grown by combinatorial pulsed laser deposition in the entire composition range on prismatic a- and m-plane    $$\alpha$$  α -Al   $$_2$$  2 O   $$_3$$  3 substrates. Pseudomorphic growth on m-plane sapphire has been achieved for    $$x \ge 0.45$$  x ≥ 0.45 . A distinct difference between the a- and m-epitaxial plane is observed in reciprocal space map measurements being in agreement with continuum elasticity theory for rhombohedral heterostructures. While pseudomorphic layers on m-plane sapphire show a pronounced shear strain    $$e'_5$$  e 5 ′ along the  c -axis direction, relaxed layers exhibit a global lattice tilt in the same direction. Both effects are not present on the a-epitaxial plane. Out-of-plane lattice constants as well as    $$e'_5$$  e 5 ′ are modeled as function of  x  employing elasticity theory, confirming theoretical values of the elastic stiffness tensor for    $$\alpha$$  α -Ga   $$_2$$  2 O   $$_3$$  3 , especially the non-zero value of the    $$C_{14}$$  C 14 component. Possible pyramidal slip systems for strain relaxation in  c -axis direction are examined to explain and numerically model the difference in lattice tilt for the two substrate orientations. Graphic abstract

journal of materials research/pratt's guide to venture capital sources

Strain states and relaxation for $$\alpha$$-(Al$$_x$$Ga$$_{1-x}$$)$$_2$$O$$_3$$ thin films on prismatic planes of $$\alpha$$-Al$$_2$$O$$_3$$ in the full composition range: Fundamental difference of a- and m-epitaxial planes in the manifestation of shear strain and lattice tilt