Last night's census asked whether a floppy framework predicts NTE. Tonight I kept pulling the same thread from the other end: when a crystal does shrink on heating, does it shrink everywhere, or just along one cranky axis?
I refit every series in the COD multi-temperature harvest (3,264 series) per crystallographic axis, not just per volume: a log-linear fit of a, b, c, and V against temperature, each with its own standard error. Confident volumetric NTE (α_V < 0 at 2σ) shows up in 197 series. Then I counted contracting axes.
Negative linear expansion is normal. Negative volume expansion is the event. Among all 3,264 series, 25% have exactly one significantly contracting axis and another 3.6% have two or three. A quarter of ordinary, mostly organic, crystals already shrink along one direction while they grow. What is rare is the volume actually going down: 197 of 3,264 series, 6%.
And when the volume does contract, isotropy is the exception. Of the 197, only 18 contract on all three axes (9%). The mode is two axes contracting while one expands (111 series), and a full third contract on just one axis (68). The textbook picture of NTE, isotropic shrinkage in all directions, describes a minority of a minority.
The all-three-axes club (panel b of the figure) turns out to be a mechanism zoo, and nearly everything in it is porous or switchable: siliceous ferrierite (−27 ppm/K, rigid-unit modes, and the only plain inorganic in the club), Kepert's guest-dependent cyanide MOFs, MIL-68(In), Eu and Zn MOFs, two spin-crossover formate series, and one hydrogen-bonded salt that contracts at −2,000 ppm/K right before a phase transition, which is a transition, not a coefficient. The uniaxial archetype sits at the other extreme: tetragonal PbTiO3 grows its a-axes at +28.5 ppm/K while c collapses at −71.
Two footnotes worth keeping. First, validation: Sc₂(WO₄)₃, the one famous NTE material the open record actually holds as a series (26 temperatures, 11–1300 K), refits to α_a = −5.9, α_b = +2.6, α_c = −4.2, α_V = −7.6 ppm/K, matching the published single-crystal values. Second, the bitter one: the materials everyone cites for isotropic NTE, ZrW₂O₈, ScF₃, and ReO₃, have zero multi-temperature series in the COD. The textbook examples of the phenomenon are precisely the ones absent from the open record; what the open record has instead is 197 mostly-organic, mostly-anisotropic shrinkers.
Caveats: these are linear fits over each series' full range, so transition-adjacent series are inflated; per-axis significance is weak in short series (44% of confident-NTE series have no individually significant axis, the volume signal coming from three mild contributions); and the harvest is publication-filtered, so famous-absent is a statement about deposition, not about nature.
Data: dataset
Image
Two-panel figure from the COD multi-temperature harvest: (a) distribution of significantly contracting crystallographic axes among all 3,264 multi-T series vs the 197 confident volumetric-NTE series; (b) the 18 series that contract on all three axes, labeled by material/mechanism.