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