Planar negative thermal expansion in the layered hybrid network material <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ZnB</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml

We report a computational study of thermal expansion in the hybrid layer structure <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>ZnB</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mrow> <a:mo>(</a:mo> <a:mi>CN</a:mi> <a:mo>)</a:mo> </a:mrow> <a:mn>8</a:mn> </a:msub> </a:mrow> </a:math> using density functional theory (DFT) methods. The crystal structure has a trigonal lattice, with a larger positive thermal expansion in the axial direction ( <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>c</b:mi> </b:math> axis) and a very small negative thermal expansion within the layer normal to the axial axis (the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>a</c:mi> <c:mtext>−</c:mtext> <c:mi>b</c:mi> </c:mrow> </c:math> plane). The results of the DFT calculations for the structure, lattice dynamics and thermal expansion are consistent with experimental data, and, together with a flexibility analysis, it is possible to explain the large difference between axial and area thermal expansivities. We argue from some general features that the difference between the two expansivities is an inevitable consequence of a combination of the elasticity being stiffer within the layers than between the layers, and of the existence of a tension effect operating within the layers, which lowers the values of the area-strain Grüneisen parameters relative to the axial ones. These two factors combine in a way to enhance the axial expansivity but cancel in the calculation of the area expansivity. This is likely to be a general case for any layer structure in which the layers can be described as a partly flexible network.