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An Introduction to Crystal Structures
Published in Elaine A. Moore, Lesley E. Smart, Solid State Chemistry, 2020
Elaine A. Moore, Lesley E. Smart
The screw axis combines translation with rotation. Screw axes have the general symbol ni, where n is the rotational order of the axis, that is, twofold, threefold, etc., and the translation distance is given by the ratio i/n.Figure 1.10 illustrates a 21 screw axis. In this example, the screw axis lies along the z direction and so the translation must also be in the z direction by c/2, where c is the repeat distance in the z direction. Notice that in this case, the molecule starts above the plane of the page (indicated by the + sign), but the effect of a twofold rotation is to take it below the plane of the page (– sign). Figure 1.11 probably illustrates this more clearly and also shows the different effects that the rotational and screw axes of the same order have on a repeating structure. Rotational and screw axes produce objects that are superimposable on the original. All other symmetry elements—glide plane, symmetry plane, inversion centre, and inversion axis—produce a mirror image of the original. Comparison of the effects of twofold and threefold rotation axes and screw axes.
Some physical properties of silicon
Published in O.A. Aktsipetrov, I.M. Baranova, K.N. Evtyukhov, Second Order Non-linear Optics of Silicon and Silicon Nanostructures, 2018
O.A. Aktsipetrov, I.M. Baranova, K.N. Evtyukhov
The space group of symmetry of silicon involves the operations of pure translation, rotation, combinations thereof, and the screw turns and glide reflection. Figure 1.5 shows the structure of a silicon crystal in consideration ‘against’ the axis OZ, i.e. the direction [001]. This picture shows one of the following locations of the screw axis 41. The presence of such a screw axis means that the crystal structure is reproduced in rotation around it by 2π/4, accompanied by a shift of the entire structure along the axis by a quarter of the lattice period a/4. For example, in Fig. 1.5 when rotating the structure counterclockwise by 2π/4 with respect to the shown axis the structure perpetuates itself when moving to a/4 ‘away from us’.
Introduction to Kinematics
Published in Kevin Russell, Qiong Shen, Raj S. Sodhi, Kinematics and Dynamics of Mechanical Systems Implementation in MATLAB® and Simmechanics®, 2018
Kevin Russell, Qiong Shen, Raj S. Sodhi
A mechanism link in 2D or 3D space can exhibit pure rotation, pure translation, complex motion, or screw motion. In pure rotation, a link rotates at a constant radius about a fixed axis. A link travels along a linear path in pure translation. Complex motion is a type of planar motion that includes simultaneous link rotations and translations. Screw motion is a type of spatial motion that includes simultaneous link rotations about and translations along a spatial axis called a screw axis.
Cesium immobilization from aqueous solution by struvite synthesis
Published in Journal of Nuclear Science and Technology, 2023
Takuhi Hara, Masahiko Nakase, Shinta Watanabe, Kenji Takeshita
Figure 13 shows the photographs of samples (a) uniaxially compressed at 10 MPa for 3 h and (b) heat-treated at 300°C, and then compressed at 20 MPa for 3 h. The Cs-struvite powder was solidified by compression treatment at room temperature. The sample structure before and after uniaxial compression treatment was measured by XRD (Figure 14–16). Compression caused the phase transition of Cs-struvite F to P63mc Cs-struvite (a, b = 6.88270 Å, c = 11.91880 Å, called Cs-struvite P) (Figure 14) [43]. Cs-struvite F is a cubic crystal with a four-fold rotatory inversion axis, three-fold rotation axes, and a mirror plane of symmetry, whereas Cs-struvite P is a hexagonal crystal with a structure with a six-fold screw axis, a mirror plane of balance, and a c-glide plane (Figure 15). The XRD patterns of the samples heat-treated at 100 and 300°C (CsMgPO4) after being compressed for 3 h showed no change in the structure (Figure 16).
Test-retest reliability of segment kinetic energy measures in the golf swing
Published in Sports Biomechanics, 2021
Segmental sequencing in the golf swing has predominantly been examined in terms of the summation of speed principle using analyses of segment angular velocities (Neal et al., 2007; Tinmark et al., 2010). However, numerous techniques of varying complexity have also been used; from the calculation of segment rotation velocity from the relative angle between two one-dimensional lines (Burden, Grimshaw, & Wallace, 2001; Horan & Kavanagh, 2012; Myers et al., 2008) to the calculation of segment angular velocity from a non-stationary instantaneous screw axis (Vena, Budney, Forest, & Carey, 2011b). Regardless of technique, the majority of analyses suggest that, for skilled performers, the magnitude of peak angular velocity increases sequentially from the most proximal to the most distal segments (Cheetham et al., 2008; Horan & Kavanagh, 2012; Neal et al., 2007; Tinmark et al., 2010; Vena et al., 2011a). Less conclusive evidence has been provided regarding the timing of peak segment angular velocity. Whilst timing conformed to a proximal-to-distal sequence in some studies (Neal et al., 2007; Tinmark et al., 2010), research has also suggested that the timing of peak angular velocities follows a participant-specific pattern (Cheetham et al., 2008; Vena et al., 2011b).