Jensen symbol

Table 1.1 gives the structures of the elements at zero temperature and pressure. Each structure type is characterized by its common name (when assigned), its Pearson symbol (relating to the Bravais lattice and number of atoms in the cell), and its Jensen symbol (specifying the local coordination polyhedron about each non-equiyalent site). We will discuss the Pearson and Jensen symbols later in the following two sections. We should note,... 

Fig. 1.4 The local coordination polyhedra and associated Jensen symbols that characterize the elemental ground-state structure types. After Villars and Daams (1993).

The ten most commonly occurring structure types in order of frequency are NaCl, CsCl, CrB, FeB, NiAs, CuAu, cubic ZnS, MnP, hexagonal ZnS, and FeSi respectively. Structures cF8 (NaCl) and cP2 (CsCl) are ordered with respect to underlying simple cubic and body-centred cubic lattices respectively, as is clear from Figs 1.10(a) and 1.11(a). The Na, G sites and Cs, Cl sites are, therefore, six-fold octahedrally coordinated and fourteen-fold rhombic dodecahedrally coordinated, respectively, as indicated by the Jensen symbols 6/6 and 14/14. 

Structure tP4 (CuAu) is ordered with respect to an underlying face-centred cubic lattice, so that it takes the Jensen symbol 12/12. The CuAu lattice does show, however, a small tetragonal distortion since the ordering of the copper and gold atoms on alternate (100) layers breaks the cubic symmetry. Zinc blende (cF8(ZnS)) and wurtzite (hP4(ZnS)) are ordered structures with respect to underlying cubic and hexagonal diamond lattices respectively. Since both lattices are four-fold tetrahedrally coordinated, differing only in... 

The Jensen symbols are very important in helping to unravel the relationship between the different structure types in neighbouring domains. For example, it is not fortuitous that the NaCl and NiAs domains adjoin each other. Their Jensen symbols 6/6 and 8IV/6 tell us immediately that in NaCl the Na and Cl sites are octahedrally coordinated, whereas in NiAs the Ni site is octahedrally coordinated (but with two extra capping atoms), and the As site is trigonally coordinated. It is also not surprising that at the boundary between cF8 (NaCl) 6/6 and hP4(NiAs) IV/6 we find the two much smaller domains of hP8(TiAs) 7/6, 6 and tI8(NbAs) 6 /6. Nor is it unexpected to find the two islands of oP8(MnP) 10 78 " stability in the hP4(NiAs) 8rv/6 domain. A distorted NiAs structure type, MnP leads to the bicapping of the trigonal prismatic coordination about the As site, that is 6 - 8W (cf Fig. 1.9). Further, we see that the cP8(FeSi) 13713 domain adjoins a cP2(CsCl) 14/14 domain they are related structure types as mentioned earlier. 

The symbols suggested by Jensen, based on Niggli s proposals, describe the local coordination by means of coordination number ratios. For instance, a formula AEm/n will indicate a binary compound where m is the coordination number (defined as the nearest-neighbour number (NNN)) of atoms E around A and n is the similarly defined coordination number of A around E. 

According to Jensen, the dimensionality of a structure (or of a substructure of the same) is indicated by enclosing its compositional formula in square brackets and prefixing an appropriate symbol. ... 

We will not deal here with the subject of EPR spectroscopy of the solid state. In this field of investigation a kind of delta-like approach such as that recently proposed to deal with molecular dynamics in the liquid state has developed naturally. According to the European Molecular Liquid Group (EMLG), the symbol A symbolizes the cooperative efforts of computer simulation, experiment, and theory. Knak Jensen and Hansen, for instance, carried out a computer simulation of the dynamics of N identical spins placed in a rigid simple cubic lattice subject to an external magnetic field Bq. a further example of numerical study is the paper of Sur and Lowe. Free-induction decay measurements,on the other hand, represent the experimental comer of this ideal triangle, the theoretical comer of which is, of course, expressed by the theoretical papers mentioned above. 

Sign, Symbol and Script an Account of Man s Efforts to Write. B. Jensen, 1970. 

Fig. 5 Methane-water phase diagram. The solid line is the experimental [47] three-phase equilibrium curve of methane hydrate. The snowflakes show the result of Jensen et al. [33] for TlP4P/lce model. The filled blue, green, and red symbols show the three-phase coexistence points of Conde and Vega [31], and open symbols show our results Yellow triangles are for SPC/E, green diamonds and red squares for T1P4P/2005 with x = 1 07 and 1.00 in (1), respectively, and blue circles for TlP4P/lce. Our symbols correspond to 5510 unit cell systems. The statistical errors are within the symbols...

Gutmann proposed that acid-base characteristics could be represented by a donor number, generally designated as DN (a single symbol, not a product) and an acceptor number AN. DN represents the base properties of the molecule and is essentially a molar heat of reaction with a reference acid, under standardized conditions. AN represents the acid properties of the molecule. The asterisk in AN indicates that the original Gutmann values have been corrected for dispersion force interactions and are expressed as molar enthalpies. Jensen has discussed limitations of the Gutmann DN/AN theory. ... 

Fig. 16. The ordering wave vector in Ho as a function of temperature below 50 K. The calculated results are shown by the horizontal solid lines, which are connected with vertical thin solid or thin dashed lines corresponding respectively to the results obtained at zero field, or at a field of lOkOe applied along the c-axis. The symbols show the neutron scattering results of Cowley et al. (1991) at various values of the c-axis field as defined in the figure. The thick dashed line, between 35 and 48K, indicates the variation of r derived by Tindall et al. (1993) from the position of the primary magnetic peak in a c-axis filed of 30kOe. The smooth curve shown by the thin solid line is the temperature dependent position of the maximum in (From Jensen...

Fig. 3. Ion parameters from literature, (a) anions, (b) cations. Shown are the parameter sets of Roux, Jensen,Dang (summarised by Rajamani et a/. ) and Joung. Different symbols represent different ions. The numbers inside every symbol indicate the parameter set to which the parameters belong. Taken from previous work. ...

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