Table 1 MINERALS WITH METALLIC TO SUBMETALLIC LUSTER
Name	H	Streak
Galena	2.5	gray
Chalcocite	2.5 – 3	black to lead gray
Bornite	3	grayish black

Galena

Galena Lead glance
Mohs scale hardness	2.5–2.75
Luster	Metallic on cleavage planes
Streak	Lead gray
Diaphaneity	Opaque

Fluorite and halite are two common minerals with a cubic shape.

Common minerals that have a cubic/isometric crystal form include halite, fluorite, galena, pyrite, magnetite. Gem minerals diamond, garnets, spinel, and gold.

They are cubic, tetragonal, hexagonal (trigonal), orthorhombic, monoclinic, and triclinic. Seven-crystal system under their respective names, Bravias lattice.

In total there are seven crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.

There are six basic crystal systems.

• Isometric system.
• Tetragonal system.
• Hexagonal system.
• Orthorhombic system.
• Monoclinic system.
• Triclinic system.

The 32 Crystal Classes

Crystal System	Crystal Class	Name of Class
Tetragonal	4/m2/m2/m	Ditetragonal-dipyramidal
Hexagonal	3	Trigonal-pyramidal
		Rhombohedral
	32	Trigonal-trapezohedral

5 Cubic System

The hexagonal crystal family consists of two crystal systems: trigonal and hexagonal. The hexagonal crystal system consists of the 7 point groups that have a single six-fold rotation axis. These 7 point groups have 27 space groups (168 to 194), all of which are assigned to the hexagonal lattice system.

Crystal Structure: Closest Packing

• The most efficient conformation atomic spheres can take within a unit cell is known as the closest packing configuration.
• Densely packed atomic spheres exist in two modes: hexagonal closest packing (HCP) and cubic closest packing (CCP).

The packing efficiency of both types of close packed structure is 74%, i.e. 74% of the space in hcp and ccp is filled. The hcp and ccp structure are equally efficient; in terms of packing. The packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.

Hexagonal close-packed lattice has the highest packing efficiency of 74%. The packing efficiencies of simple cubic and body-centred cubic lattices are 52.4% and 68% respectively.

The cubic closed packing is CCP, FCC is cubic structures entered for face. When we put the atoms in the octahedral void, the packing is of the form of ABCABC, so it is known as CCP, while the unit cell is FCC.

In numericals,we use Z values-1 for sc,2 for bcc and 4 for fcc, but in this given question: Potassium crystallises in a bcc lattice,hence the coordination number of potassium metal is 8.

As we know, number of tetrahedral voids in closed packed ccp or fcc and hcp is double the number of atoms (Z) forming the main lattice. So, the number of tetrahedral voids in the unit cell is equal to 2Z.

Caesium bromide

Names
Space group	Pm3m, No. 221
Lattice constant	a = 0.4291 nm
Lattice volume (V)	0.0790 nm3
Formula units (Z)	1

Z is the number of formula units in your unit cell. Z’ is the number of asymmetric units. This is Z divided by the lowest multiplicty in your list of Wyckoff positions. Sometimes, the formula unit is easy to see, as in salts or molecular compounds and many other simple structures with small unit cells.

Thus, the cubic unit cell with 4 atoms is face centred cubic.

The face-centered cubic (fcc) has a coordination number of 12 and contains 4 atoms per unit cell. The body-centered cubic (bcc) has a coordination number of 8 and contains 2 atoms per unit cell. The simple cubic has a coordination number of 6 and contains 1 atom per unit cell.

– Rank of face centered cubic structure is 4.

Primitive Cubic Unit Cell In the primitive cubic unit cell, the atoms are present only at the corners. Every atom at the corner is shared among 8 adjacent unit cells. There are 4 unit cells in the same layer and 4 in the upper (or lower) layer. Therefore, a particular unit cell has the only 1/8th of an atom.

What is the difference between Lattice and Crystal? Lattice describes the structure of crystals. When a group of molecules tends to arrange each unit repeatedly at a lattice point, a crystal is made. In a crystal structure, there is a pattern of arranging the atoms or units.

Answer: In a primitive unit cell, particles or points are present only at the corners while in a centred unit cell, the particles or points are also present at other positions in addition to the corner.

There are five types of the 2D Bravais lattices ( Fig. 2): oblique (a 1 = a 2 , ϕ = 90 • ), square (a 1 = a 2 , ϕ = 90 • ), hexagonal (a 1 = a 2 , ϕ = 120 • ), primitive rectangular (a 1 = a 2 , ϕ = 90 • ), centered rectangular (a 1 = a 2 , ϕ = 90 • ).

When a unit cell is repeatedly translated to fill all of 2D or 3D space, the vertices of all the unit cells in the filled space constitute a lattice. A lattice is an infinite array of regularly-spaced points.

There are 4 different symmetries of 2D lattice (oblique, square, hexagonal and rectangular). The symmetry of a lattice is referred to as CRYSTAL SYSTEM.

In 2 dimensions In two-dimensional space, there are 5 Bravais lattices, grouped into four crystal families.