mobilities it favors, because such tetrahedral structures are more tightly packed and usually have stiffer lattices than the rocksalt materials. They present high phonon frequencies and velocities giving rise to very high thermal conductivity. [9,10] Typical compound semiconductors in this class include the zincblende-, wurtzite-, and the chalcopyrite-type materials. [11][12][13][14] The AMQ 2 (A = Cu, Ag; M = Al, Ga, In, Tl; Q = S, Se, Te) ternary diamondoid compounds are a large family of relatively wide band gap (E g > 1 eV) semiconductors that possess various unique transport properties, and have many important applications in photovoltaic cells, [15] nonlinear optics, [16] and thermoelectricity. [11,13] Recently, a thermoelectric figure of merit (ZT) beyond 1.6 has been reported in Cu 1−x Ag x InTe 2 [17] and (Cu 1−x Ag x )(In 1−y Ga y ) Te 2 diamondoid compounds. [18,19] These performance advances have drawn intense interest in fundamental understanding of the electronic and heat transport properties of the diamondoid compounds in greater detail.The ternary diamondoid compounds (chalcopyrites) derived from the diamond structure can be considered as a double sphalerite cell (M'Q) stacked along the c-axis, where the divalent M' cation is replaced by monovalent A and trivalent M, see Figure 1a. Among compositions with the identical crystal structure, the Ag-based diamondoid compounds exhibit a much lower intrinsic lattice thermal conductivity than the Cu-based Typically, conventional structure transitions occur from a low symmetry state to a higher symmetry state upon warming. In this work, an unexpected local symmetry breaking in the tetragonal diamondoid compound AgGaTe 2 is reported, which, upon warming, evolves continuously from an undistorted ground state to a locally distorted state while retaining average crystallographic symmetry. This is a rare phenomenon previously referred to as emphanisis. This distorted state, caused by the weak sd 3 orbital hybridization of tetrahedral Ag atoms, causes their displacement off the tetrahedron center and promotes a global distortion of the crystal structure resulting in strong acoustic-optical phonon scattering and an ultralow lattice thermal conductivity of 0.26 W m −1 K −1 at 850 K in AgGaTe 2 . The findings explain the underlying reason for the unexpectedly low thermal conductivities of silver-based compounds compared to copper-based analogs and provide a guideline to suppressing heat transport in diamondoid and other materials.