Biomedical subjects

Hans Grimmer

Publications and source records attributed to Hans Grimmer.

4 recordsLinked to original sources

PubMed2006

Spectral decomposition of the linear elastic tensor for trigonal symmetry; classification of symmetry restrictions for arbitrary point groups.

The linear compliance tensor for trigonal symmetry has four different eigenvalues, two of which have multiplicity 1, the others multiplicity 2. They and the corresponding eigenvectors have been calculated in terms of the seven parameters of the corresponding Voigt matrix. Necessary and sufficient conditions have been derived for these components to guarantee positive eigenvalues and thus a positive strain energy. The hierarchy of restrictions on the linear elastic tensors that follow from Neumann's principle for arbitrary point groups in three dimensions has been established for the standard choice of the Cartesian coordinate system, as well as in coordinate-independent form.

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PubMed2006

Quartz aggregates revisited.

Quartz aggregates that formed by coalescence of quartz crystals in the magma or in hydrothermal solution are considered. If the individuals have rhombohedral faces in contact, there will be two special cases: parallel intergrowths and intergrowths that agree in orientation and contact plane with Esterel twins grown from a twinned nucleus. For all other known cases, i.e. when the relative orientation satisfies the Japan, Sardinian, Tiflis, Zyndel-A or Samshvildo law, both individuals have exactly coinciding short symmetry translations in only one direction in the contact plane (monoperiodic twins). If a rhombohedral face is in contact with a prism face, monoperiodic twins will occur if the relative orientation satisfies the Zinnwald, Disentis or a proposed hypothetic law. The orientation of the two lattices can be expressed by a 180 degrees rotation about an axis with low indices independent of c/a in the case of the Esterel, Japan and Sardinian laws. The same is true for the Tiflis and Zyndel-A laws only if they are redefined, and not at all in the case of the Samshvildo, Zinnwald, Disentis and hypothetic laws. When the two individuals have rhombohedral faces in contact, there will even be exact two-dimensional coincidence (multiplicity sigma) in the contact plane and exact three-dimensional coincidence (multiplicity Sigma) in space if the square of the axial ratio c/a is rational. Indications are found that (despite their high values) these multiplicities may be related to the frequency of occurrence of intergrowths in low- and high-quartz.

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PubMed2004

Twinning by reticular pseudo-merohedry in trigonal, tetragonal and hexagonal crystals.

Twin laws for trigonal, tetragonal and hexagonal crystals describing twins with principal axes inclined by an angle Phi > 0 are analysed. Twins by reticular merohedry (i.e. obliquity delta = 0) are possible only for certain values s of the axial ratio c/a. For any other axial ratio r, the laws describe twinning by reticular pseudo-merohedry, i.e. with obliquity delta > 0. It is shown that (a) tandelta is a product of two factors, one of which is sinPhi, the other depends only on the relative deviation of r from s; (b) tandelta approximately epsilon, where epsilon denotes the deformation parameter introduced by Bonnet & Durand [Philos. Mag. (1975), 32, 997-1006]. The angle Phi is listed for all cases of reticular merohedry of trigonal, tetragonal and hexagonal (i.e. optically uniaxial) crystals with twin index Sigma </= 5. Mallard's criterion requires that twin laws by (reticular) pseudo-merohedry have Sigma </= 5 and delta </= 6 degrees. Le Page [J. Appl. Cryst. (2002), 35, 175-181] has written a program determining laws with twin index Sigma </= Sigma(max) and obliquity delta </= delta(max) for any given lattice geometry. Here those solutions are analysed and completed for optically uniaxial crystals. Their lattices are characterized by the Bravais class (tP, tI, hP or hR) and the axial ratio c/a = r. For small delta(max), most solutions are related to (reticular) merohedry for an appropriate value s approximately r of the axial ratio. It is argued that other solutions, which are not related to (reticular) merohedry, are not needed to explain observed laws of growth twinning but may be important to interpret observed laws of deformation twinning.

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PubMed2003

Determination of all misorientations of tetragonal lattices with low multiplicity; connection with Mallard's rule of twinning.

Two congruent lattices are considered, which are misoriented in such a way that they have a fraction 1/Sigma of symmetry translations in common. Whereas for cubic lattices body or face centring does not affect the 'multiplicity' or 'twin index' Sigma, this is not generally true for tetragonal lattices. Consider a fixed misorientation and let Sigma(P) and Sigma(I) be the multiplicities for tP and tI lattices with the same axial ratio c/a. Grimmer [Mater. Sci. Forum (1993), 126-128, 269-272] has given an explicit formula for Sigma(P) (depending on the misorientation and the axial ratio) and showed that Sigma(I) = Sigma(P)/2, Sigma(P) or 2Sigma(P). Here stronger results on the occurrence of the three possibilities are presented. Lists of all axial ratios c/a of tP and tI lattices admitting misorientations with Sigma < or = 5 are given. For each of these misorientations, the twin mirror planes and their normals are listed, so that a synopsis of all possible twin laws of tetragonal crystals by reticular merohedry with Sigma < or = 5 is obtained. It is shown that the two twin laws observed in beta-Sn can be described by reticular pseudomerohedry with Sigma(I) = 2 and obliquity delta = 2.6134 degrees.

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