The bond lengths and bond angles of orthorhombic black phosphorus have been determined as a function of hydrostatic pressures to 26.6(5) kbar using time-of-flight neutron powder diffraction. We show that the markedly anisotropic compression reported previously results from a large pressure-induced shortening of the van der Waals bonds separating layers of atoms combined with a shear motion within the layers. Covalently bonded chains of atoms along the a direction remain very rigid. The average effective linear compressibility for van der Waals bonds is 1.48(9) ×10−3 kbar−1 while the average effective linear compressibility for covalent bonds is an order of magnitude smaller, 2.6(8) ×10−4 kbar−1.
In order to resolve reported differences in the compressibility of hexagonal selenium, lattice parameters have been measured at pressures up to 140 kbar. Independent measurements have been made by neutron time-of-flight and by x-ray diffraction. The results from these methods are in good agreement. The a axis is found to contract, but the c axis expands with increasing pressure. Values obtained for the average volume, a-axis, and c-axis zero-pressure compressibilities are 49.7±15, 31.9±7, and −14.3±4×10−4 kbar−1, respectively. These results compare favorably with a correlation of bulk modulus and cohesive energy. The expansion of the c axis under pressure is comparable to the contraction of the c axis with increase of temperature.
The lattice parameters, bond lengths and bond angles of Si2N2O have been determined at pressures up to 23 kbar by time‐of‐flight neutron diffraction. The average compressibility coefficients of the orthorhombic structure are Ka = 21 (2), Kb = 34 (2), Kc = 25 (2) and Kν = 79 (4) x 10−5 kbar−1, though the anisotropy is more pronounced at lower pressures with Ka (at zero pressure) estimated to be 10 (8) × 10–5 kbar−1. The major contribution to the compression is a cooperative rotation of adjacent SiN3O tetrahedra brought about by a decrease in the Si–O–Si bond angle. The shortening of one Si–N bond within each tetrahedron further enhances the compression, especially along the b direction.
The high-pressure behavior of a-quartz SiOz and GeO z , oxynitrides SizNzO and GezNzO and aandp-Si 3 N 4 depends markedly on the nature of the linking of the coordination polyhedra in their crystal structures. Where bond angles can vary between neighboring polyhedra linked at one corner, relative tilting or rotations can occur modifying the aspect of the three-dimensional framework. Such fine structural rearrangements can dominate the reponse of the crystal structure to applied stresses as induced by the application of high pressures or by temperature changes. Direct evidence for this is available from structural measurements at high pressure using time-offlight neutron diffraction with multicomponent profile refinement procedures, where atomic position changes have been determined up to pressures of -3 X 10 9 Pa. The crystal structures studied are the flexible a-quartz structures of SiOz and GeOz, the partially flexible structures SizN zO and GezN zO, and the rigid structures a-and P-Si 3 N 4 • The volume compressibility coefficients K" are greatest for a-quartz SiOz (274 X 10 -13Pa -I) and GeO z (256 X 10 -13 Pa -I) with the Si-O-Si and Ge-O-Ge angles varying the most; Kv is intermediate for SizNzO (79 X 10 "Pa I) and GezNzO (99 X 10 -13 Pa -I) where the Si-O-Si and Ge-O-Ge angles vary appreciably while the bond angles to the nitrogens change only slightly; K" is least for a-Si3N4 (35.5 X 10 -13 Pa -I) andp-Si 3 N 4 (27.5 X 10-13 Pa -I) where no bond angles vary appreciably. For all of the structures examined, bond length changes with pressure are very small in comparison to bond angle changes, which can be an order of magnitude greater. Each structural type behaves in a characteristic way. For example, SizNzO and GezNzO exhibit almost identical responses to pressure.The experimental data have been taken using time-offlight neutron diffraction with powder samples in a hydrostatic, supported piston-cylinder ce11. 7 • H The details of the individual studies of a-andp-Si 3 N 4 (Ref. 9-10), Si2N 20 (Ref. 11), Ge1NzO (Ref. 12), and the a-quartz forms ofSi01 and GeOz (Ref. 7) are published elsewhere.
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