The negative thermal expansion material potassium cadmium dicyanoargentate, KCd[Ag(CN) 2 ] 3 , is studied at high pressure using a combination of X-ray single-crystal diffraction, X-ray powder diffraction, infrared and Raman spectroscopy, and density functional theory calculations. In common with the isostructural manganese analogue, KMn[Ag(CN) 2 ] 3 , this material is shown to exhibit very strong negative linear compressibility (NLC) in the crystallographic c direction due to structure hinging. We find increased structural flexibility results in enhanced NLC and NTE properties, but this also leads to two pressure-induced phase transitionsto very large unit cells involving octahedral tilting and shearing of the structurebelow 2 GPa. The presence of potassium cations has an important effect on the mechanical and thermodynamic properties of this family, while the chemical versatility demonstrated here is of considerable interest to tune unusual mechanical properties for application. ■ INTRODUCTION Materials where external stimuli induces an anomalous response, such as expansion upon cooling (negative thermal expansion, NTE 1−3) or on application of hydrostatic pressure (negative linear compressibility, NLC 4,5), have recently received considerable attention. These materials that "break the rules"as a result of specific, and therefore rare, elastic anomalies 6−8 are curious from a fundamental point of view but might also be revolutionary for a range of technologies including interferometric pressure sensors, pressure-controlled or pressure-sensitive electronic devices, and smart actua-tion. 2,4,9−11 The ability to design materials with unusual properties is therefore a key focus of the field: can we understand these elastic anomalies so that we can tune the magnitude and/or range of negative responses? Negative thermal expansion may occur in one, two, or all principal directions without violating thermodynamics. 12,13 Thus, for example, the volume coefficient of thermal expansion (CTE), () V V V T p 1 α = ∂ ∂ , takes large negative values in zirconium tungstate ZrW 2 O 8 and zinc(II) cyanide Zn(CN) 2 over large temperature ranges. 14 Under hydrostatic pressure, however, volume must always reduce and so the volume compressibility (() K V V V p T 1 = − ∂ ∂ , conventionally formulated as the bulk modulus, B = (K V) −1), must be definite and positive. 15 Expansion under pressure can occur in one or two directions, as long as this is coupled to volume reduction. 5,12,16 Therefore, negative linear compressibility (NLC)the expansion in one principal direction of a material under hydrostatic pressureis conceptually and empirically related to linear-NTE. In both cases, anomalous response relies on mechanical anisotropy. The so-called "wine-rack" model is often invoked where mechanical hinging allows linear expansion coupled to volume reduction on increasing pressure or decreasing temperature. 5,8 Attention in this field has focused on a class of materials known as coordination polymers (CPs), in particular due to the very large magnitude of responses found in comparison to conventional oxide-based materials. 7 Examples that show large NTE and NLC include cyanide frameworks such as Ag 3 [Co-(CN) 6 ] (refs 17 and 18), KMn[Ag(CN) 2 ] 3 (refs 19 and 20), Zn[Au(CN) 2 ] 2 (refs 21 and 22), and metal−organic frameworks 23 (MOFs) such as MIL-53 (ref 24), UTSA-16 (ref 25), ZAG-4 (ref 26), and [NH 4 ][Zn(HCOO) 3 ] (ref 27). In many cases, mechanical response can be predicted in these systems by considering the framework as a set of rigid connectors and hinges, sodepending on geometry and topologyNTE or