Lecture one and two Flashcards
What is a lattice?
A Lattice is a pattern of repeating points along which crystal unit cells can be arranged
What is the word to describe a set of repeating points along which a Crystal unit cell is placed
A lattice
What is a primitive unit cell
The unit cell which Only has lattice points in each corner
What is a Unit cell that only has lattice points in each corner called
A primitive unit cell
What is the atomic arrangement associated with a unit cell called
A motif
What is a motif?
The atomic arrangement associated with a unit cell
What components are required to describe the structure of an atomic arrangement
A lattice and a motif
What happens when you add a motif to a lattice
You get the whole atomic structure
How many arrangements of lattice points are possible?
Only five
What are the five possible arrangements of lattice points called
The primitive square lattice, the regular primitive lattice, The oblique P lattice, The rectangular centred lattice, and the hexagonal P lattice
What is a primitive square lattice
The sides are of equal length and the angle between the sides is 90°
What is a regular Primitive lattice
Besides can be of any length but the angle between the sides must always be 90°
What is an oblique p lattice
The sides can be of any length and it can have any angle between the sides except 90°
What is a rectangular centred lattice
It is the same as a regular primitive lattice except that it also has a lattice point in its centre
What is a hexagonal P lattice
A special form of the oblique P lattice with an angle between the sides of 60°
What is a symmetry element in a lattice
An element that when applied to a point on a lattice will restore the lattice to it’s original position
What fold of rotation symmetry can a lattice not have and why
Five-fold symmetry because a planar space cannot be filled with regular pentagons
What are the 4 symmetry elements of a lattice
Translation symmetry, mirror plane symmetry, glide Plane symmetry, and rotation symmetry
What is translation symmetry
Symmetry such that a point can be moved in a straight direction along the lattice maintaining its structure
What is mirror plane symmetry
Symmetry such that an element can be reflected over the line and maintain its structure
What is glide plane symmetry
Mirror Symmetry and translation symmetry in half steps form glide plane symmetry
What is rotation symmetry
Symmetry such that an object can be rotated around an axis a regular number of times maintaining its structure
What is a triclinic system
A system where the three axes are not equal in length and the angles between the axes are not equal to each other
What is a monoclinic system
A system where the axes are not equal in length and two of the angles between the axes are 90° while the third angle is greater than 90°
What is an orthorhombic system
A system where the three axes are not equal in length but all of the angles between the axes are equal to 90°
What is a Tetragonal system
A system Where two of the axes are equal in length and all of the angles between the axes are 90°
What is a hexagonal system
A system with four axes such that three of the axes are of equal length and are spaced at 120° angles, Perpendicular to the fourth irregular axis
What is an isometric system
A system such that the three axes are of equal length and at 90° to each other
What are the three rules which assist in choosing the best definition of a unit cell
One the edges of the unit cell should coincide with the symmetry of the lattice. Two the edges of the unit cell should be related by the symmetry of the lattice. Three the smallest possible cell which contains all the elements should be chosen
What are Vectorial properties
Properties of a crystal which depend on direction within the crystal
Which coordinate axis does axis “a” Correspond with
The x axis
Which coordinate axis does axis “b” Correspond with
The Y axis
Which coordinate axis does axis “c” Correspond with
The Z axis
Which two axes does angle alpha define
B and c
Which two axes does angle beta define
A and c
Which two axes does angle gamma define
A and B
How many crystal systems are there
There are six crystal systems
What are the six Crystal systems
Cubic or isometric system, tetragonal system, orthorhombic system, monoclinic system, triclinic system, and the trigonal or hexagonal system
Do the 6 Crystal systems describe All of the variations of 3-D crystal arrangements?
No the six systems can also be primitive, face centred, or body centred, Such that the arrangement of lattice points upholds the rules of symmetry
How many possible 3-D arrangements of lattices are there And what is this set called
14 Called the bravais lattices
What are the two types of spaces between neighbouring spheres in stacked sheets called
Tetrahedral sites and octahedral sites
What is a tetrahedral site
A space bound by four spheres where the centre of each of these spheres is joined to form a tetrahedron
What is an octahedral site
A Space bound by six spheres where the centre of the spheres are joined to form an octahedron
What is hexagonal close packing
An arrangement whereby the layers are repeated in an A.B. A.B. A.B. pattern
What is cubic close packing
An arrangement where the layers I repeated in an A.B.C.A.B.C pattern
What is body centred cubic packing
A way of stacking spheres such that the atoms only have eight neighbours
What are the three types of Crystal symmetry
Planar symmetry, Axial symmetry, centres of symmetry
What is planar symmetry
A plane of symmetry that divides a crystal into two similar halves such that one half is the mirror image of the other
What is axial symmetry
A type of symmetry where a Crystal can be rotated around an axis in intervals where the original crystal shape and orientation is repeated
What are the four types of Axial symmetry
A diad axis (two-fold) a triad axis (thee-fold) a tetrad axis (four-fold) and a hexad axis (six-fold)
What are crystal centres of symmetry
An element of symmetry that is recognized when all like faces or edges of a crystal are arranged in pairs on opposite sides of a central point
What are Miller indices
A system of defining Crystal faces, Developed by WH Miller in the 19th century which uses the unit cell of the Crystal and three points which cut the axes of that cell into ratios. Only the denominator of the ratios are displayed in a set enclosed by brackets.
What Is a vector
A line which has both magnitude and direction
