Figure 2 | MRS Communications

Figure 2

From: Integrating lattice materials science into the traditional processing-structure-properties paradigm

Figure 2

Contrasting elements of structure and defects in traditional materials science and in lattice materials science. (a–d) Pertinent length scales in traditional materials science are well established: grains are typically 10–100 µm in size, precipitates 10–100 nm, dislocation spacings 10–100 nm, and solute atoms and vacancies at the sub-nm level. (e–o) Lattice structures and lattice defects are distinctly different from those in traditional materials science. Examples of low-order lattice topologies include (e) elementary cubic, (f) compound cubic, (g) super compound cubic, (h) the Kagome lattice, and (i) the diamond lattice. The Kagome structure, denoted \(\left\{ {R\left\lfloor {0\,0\,0} \right\rfloor \left\lfloor {{1 \mathord{\left/ {\vphantom {1 {2\,0\,0}}} \right. \kern-\nulldelimiterspace} {2\,0\,0}}} \right\rfloor \left\lfloor {{{0\,1} \mathord{\left/ {\vphantom {{0\,1} {2\,0}}} \right. \kern-\nulldelimiterspace} {2\,0}}} \right\rfloor \left\lfloor {{{0\,0\,0\,1} \mathord{\left/ {\vphantom {{0\,0\,0\,1} 2}} \right. \kern-\nulldelimiterspace} 2}} \right\rfloor } \right\}\) is based on a rhombohedral space lattice in which the three interaxis angles are 60°; four nodes are assigned to each lattice point, at \(\left\lfloor {0\,0\,0} \right\rfloor ,\left\lfloor {{1 \mathord{\left/ {\vphantom {1 {2\,0\,0}}} \right. \kern-\nulldelimiterspace} {2\,0\,0}}} \right\rfloor ,\left\lfloor {{{0\,1} \mathord{\left/ {\vphantom {{0\,1} {2\,0}}} \right. \kern-\nulldelimiterspace} {2\,0}}} \right\rfloor \) and \(\left\lfloor {{{0\,0\,1} \mathord{\left/ {\vphantom {{0\,0\,1} {2\,}}} \right. \kern-\nulldelimiterspace} {2\,}}} \right\rfloor \), and struts are placed between nearest-neighbor nodes. High-order lattices, based on (j) graded, (k) hierarchical, (l) and poly-topological designs, may provide access to property combinations notattainable with a single topology. (m) Defects include missing struts, shown here in the {FCC}structure and distinguished by their orientation relative to the loading direction. Type I struts are oriented perpendicular to the load axis, while types II and III are at 45° to the load axis. (n) Nodes and (o) external surfaces also constitute potential defects. Developments in node design and surface engineering will be required to mitigate effects ofthese features on lattice properties. (Features in (j–l) are represented by 2D schematics although they could be readily extended into 3D. Images in (e–i) reprinted from Ref. [18] and images in (m) reprinted from Ref. [19], with permission from Elsevier.)

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