3. Symmetry Table of contents 3.1 Definitions 3.2 Bravais lattice 3.3 Point groups 3.4 Space groups 3.5 Crystal systems 3.5.1 Cubic crystals 3.5.2 Hexagonal and trigonal crystals 3.1 Definitions Questions & answers What is symmetry in crystal physics? What is the difference between a unit cell and a lattice point? What are the symmetries in crystal structure? How many lattice points are there in one unit cell, and why? Is crystal lattice and crystal structure the same? What is the term crystal and unit cell? How do you determine the axis of x, y, and z of crystallography? 3.2 Bravais lattice Questions & answers How do crystals lattices form? What are crystal latice? Crystal: What type of closed packing leads to all 14 Bravais lattices? What are the differences between Bravais lattice and non-Bravais lattice? What are ‘lattice points’? Can crystal with a lattice that is not a Bravais lattice exist? For example, is there crystal that has a honeycomb structure? What is crystal lattice in metals? What is an explanation for an electrical engineering student? Which type of crystals contain only one Bravais lattice? How many lattice types are associated with crystal lattice? What is the Bravais lattice and structure? What are the 14 Bravais types of crystal? 3.3 Point groups Questions & answers What are symmetric letters? What is point symmetry? Do parallelograms have rotational symmetry? Why or why not? What is an easy way to understand the symmetry elements and those associated with certain molecules? What is the symmetry point group of propyne? What is the principal axis of a planar oxalate anion molecule and its symmetry elements and point groups? What kind of symmetry does the number 8 have? What is the formula to find the axis of symmetry? 3.4 Space groups Questions & answers What does it mean that atoms are arranged spirally around an axis in quartz and tridymite? How does a tetrahedron contain 6 planes of symmetry? What are the main effects of the space group in crystal structures? What is a common symmetry element between acetylene (C2H2) and XeF4 (do not include inversion centre)? 3.5 Crystal systems Questions & answers Which solid crystal structure is the most asymmetrical? How could I draw the monoclinic crystal? What is meant by the term, “Minimum symmetry of a crystal system”? Which of the crystal system body centered unit cell does not exist? What is the difference between crystal structure and crystal system? Why are there only 7 types of unit cells and 14 types of Bravais lattices? How do I know that a crystal is either cubic or tetragonal if it possesses two types of 14 phases? Why do we have only 7 classes in a crystal system and not more? What is the difference between hexagonal and monoclinic unit cells? 3.5.1 Cubic crystals Questions & answers What are the examples of simple cubic crystal structure? Why is there no ECC in the cubic crystal class? For cubic crystal structures, which configuration has the most symmetry: simple cubic, body-centered cubic, or face-centered cubic, and why? Why can't a face-centered cubic lattice be considered as a body-centered tetragonal lattice? Why are CCP and FCC the names of the same lattice? What is a cubic crystal system? For a simple cubic lattice, is the lattice constant the same as the distance between lattice points? 3.5.2 Hexagonal and trigonal crystals Questions & answers How are the trigonal and hexagonal crystal systems different? Why are they "symmetrically" equivalent? Why does a dolomite have a lower symmetry than calcite? How does a primitive unit cell of a hexagonal closed pack can have 2 lattice points, since according to the definition of the primitive cell, it can contain only one lattice point? Why is a face-centered trigonal not possible? Why is a trigonal crystal structure called by its name? Is one of the unit cell angles of hexagonal crystal 120°?
