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This study focuses on the refinement and interpretation of anharmonic atomic displacement parameters (ADPs) in the chemical compound Ag3SbS3, commonly known as pyrargyrite. It examines the structural units linked by short S–Ag–S bonds, describing the intricate spiraling systems along the c-axis. Using the Gram-Charlier expansion in Jana2006, the study details the calculation of anharmonic displacement tensors. The program CONTOUR is employed to plot and analyze the probability density function, providing insights into the shape of selected atoms, further visualized using VESTA.
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Example 10.1: AgSbS Refinement and interpretation of anharmonic ADPs Chemical formula: Ag3SbS3 pyrargyrite
SbS3 pyramids • these units are linked together via shortS–Ag–S bonds (2.444 Å and 2.448 Å). • short Ag—S bonds form two spiralling systems running parallel to the caxis
Anharmonic ADP used in Jana2006 are based on the Gram-Charlier expansion of the structure factor: The tensors C, D, E and F are the symmetrical tensors of order 3,4,5 and 6, respectively. More details concerning theory of ADP can be found in Kuhs, W.F. (1992). Acta Cryst. A48, 80-98
anharmonic ADP parameters in M40 Ag1 1 3 1.000000 0.361444 0.086636 0.073547 0.052123 0.098578 0.067890 0.037878-0.031247-0.002105 0111111111 -0.006237-0.004404 0.006951 0.000056 0.007124-0.006336 111111 0.012222 0.005992-0.009893 0.005870 1111
. . . . where are Hermite polynomials, C,D,E,F are anharmonic displacement tensors The program CONTOUR allows to plot and analyse the probability density function (p.d.f.) , which makes visualization of the refined “shape” of the selected atom. For more complex picture of the density the individual p.d.f.’s have to be combined. The resulting function is called joinedprobability density function (j.p.d.f)
