The assignment is clearly stated on the attached file. I have also attached the models you need to finish the assignment.
GEO3020
Laboratory Exercise 4
CRYSTAL FORMS AND MILLER INDICES
In this exercise, you will learn to: (1) orient crystals with respect to hypothetical
crystallographic axes; (2) describe the orientation of crystal faces and directions; (3) recognize
common crystal forms.
Material: You will use the 7 plastic models of perfect crystals. Please refer to the description of
your kits in the lab folder for the model numbers. The 3D-models are also available on Canvas
and can be downloaded and view with a 3D viewer.
For this lab, you need to submit your Lab4_report (Table). 2 sections – 120 points
Previously, in Lectures 4 and 5β¦
Crystallographic Axes
Reference axes used to describe crystals are called crystallographic axes and, by convention, are
labeled a, b, and c with interaxial angles Ξ± (angle between b & c), Ξ² (angle between a & c), and
Ξ³ (angle between a & b). Each crystal system is also identified by its diagnostic symmetry.
None or i
One π¨π
Three π¨π
One π¨π
One π¨π
One π¨π
Three π¨π
In order that unit volumes have the maximum symmetry of each crystal system, symmetry
considerations require the following restrictions on the unit lengths and interaxial angles (the β
should be read “is not restricted to be equal”):
β’
β’
β’
β’
β’
β’
β’
Triclinic – Since this system has such low symmetry there are no constraints on the
axes, but the most pronounced face should be taken as parallel to the c-axis.
Monoclinic – The A2 is the b-axis, or if only a mirror plane is present, the b-axis is
perpendicular to the mirror plane.
Orthorhombic – The crystallographic axes coincide with the 2-fold axes. For the
purpose of this lab we will use the old convention: c has the longest axis and a as
the shortest axis. If the crystal shows 1A2 and 2mirrors, the A2 is parallel to the caxis.
Tetragonal – The c-axis is parallel to the A4 (or Μ
Μ
Μ
π΄4 )
Μ
Μ
Μ
Hexagonal – The c-axis is parallel to the A6 (or π΄6 )
Trigonal- The c-axis is parallel to the A3 (or Μ
Μ
Μ
π΄3 )
Isometric The crystallographic axes are parallel with the three A4, or, in cases where
no 4-fold axis present, with the three A2.
Miller indices
A system of notation known as Miller indices is used almost universally to describe the
orientation of planes in or on the face of a crystal.
Procedure:
1. Determine the intercept of the plane on each crystallographic axis;
2. Invert;
3. Clear fractions;
4. Enclose within parentheses the three whole numbers representing the a,b, and c axes, in
that order (four in the case of the hexagonal system: a,a,a,c).
Miller indices have the general form, (hkl) [and (hkil) for the hexagonal system]. The indices are
simply interpreted: (hkl) indicates a set of parallel planes that divides the unit on a into h parts;
the unit on b into k parts and the unit on c into l parts.
For example, the plane (111) intersects each axis at unit length and represents the so-called
unit face of a crystal. The Miller index (210) indicates a plane that intersects at 1/2 the unit
distance on a, the unit distance on b, and is parallel to c. The symbol also indicates the
orientation of a set of planes parallel to the (210) face that divides the unit on a into two
parts; the unit on b into one part; and the unit on c into zero parts. (in other works, parallel
plans have the same Miller indices).
While we did not discuss the hexagonal system in details in the lecture material, the system is
the same: h, k and i are the intercept reciprocals for the three a-axes and with i=-(h+k), and l is
the intercept reciprocal on the c-axis.
2
Crystal Forms
A form is a set of equivalent crystal faces that are related by symmetry. A number of crystal
faces are regarded as equivalent if all faces in the group can be found by operating on a single
face with all the symmetry elements in the crystal. Therefore, the number of faces in a form is
controlled by the symmetry of the crystal. Altogether there are 48 distinct crystal forms, some
of which are found only in one crystal class. Therefore, in the absence of perfect crystals, it is
sometimes possible to determine the crystal class of a compound or mineral if a diagnostic
form is present. For example, if a cube is present as one of the crystal form, this is not very
useful, because it is found in all five isometric crystal classes, but the hexoctahedron is only
found in the class 4/m 3 2/m.
Instructions:
Using your seven plastic models:
Table 1: For each model identify all the forms present. Also report the crystal system with its
diagnostic symmetry. Refer to your Lecture5-Part I for a full list of the crystal forms. (10 points
per model)
Table 2: For the five listed models, determine the Miller indices of the faces in each form. If the
same type of form is present several times in the crystal, give the Miller indices for each. (10
points per model)
Example 1:
Example 2 (see example in L5-P1):
3
Table 1: For each model, identify all the forms present and report the crystal system with its diagnostic
symmetry (DS).
Model #
Forms present (number and names)
Crystal system (DS)
Example #1
Example #2
Model #1
Model #2
Model #3
Model #4
Model #5
Model #6
Model #7
1 Octahedron
1 rhombic pyramid
2 pinacoids
1 dome
1 pedion
Isometric (3A3)
Orthorhombic (1A2, 2m)
Table 2: For the following 5 models: determine the Miller indices of the faces in each form present.
(models 2 and 5 are not requested)
Model #
Name of the form
Miller indices of the faces of each form
Example #1
octahedron
(111), (1-11), (-111), (-1-11), (11-1), (1-1-1), (-11-1), (-1-1-1)
Example #2
rhombic pyramid
(111), (1-11), (-111) (-1-11)
pinacoid #1
(010) (0-10)
pinacoid #2
(100) (-100)
dome
(103) (-103)
pedion
(00-1)
Model #1
Model #3
Model #4
(tip: each face is parallel to one of the crystallographic axes)
Model #6
Model #7