Miller Indices Homework

Miller Indices Homework

Lab 2: External Geometry Lab Name______

In a box in the classroom are some wooden models of crystals. Do them in order. Turn in your work at the next class.

1. Block 1 is a rectangular solid
Orient the block so that the long axis is vertical and three faces are visible. Then carefully sketch the model in perspective view.After you determine the crystal system, draw an axis for each face, with a set of labels that is correct for that system. The Appendix at the end of this document will help.

  1. Examine the model. The three sides are (choose: about the same lengths / one is very different / all are very different ).
  2. Measure the angles between the faces. The three angles are (choose: about the same / one is very different / all are very different )
  3. The angles are approximately ______.
  1. What crystal system is this? ______
  1. Can you find any 2-fold rotation axes? Y/N .

Markall 2-fold rotation axes with a 2-fold symbol on the drawing.

Are there any mirror planes? Y/N

Draw all mirror planes in, using a line for each.

  1. Are any of the mirror planes perpendicular to a rotation axis? Y/N
  2. What is the Hermann-Mauguin symbol for each 2-fold rotation axis with a mirror plane perpendicular to it? Choose one: (2-m , 2/m , 2*m)
  3. Write the Hermann-Mauguin class symbol for this crystal class, one for each axis ______
  4. Label the (100), (010) and (001) faces.
  1. Block 2 is a parallelepiped.
  2. Orient the block so that the long axis is vertical and three faces are visible. Then carefully sketch the model in perspective view.
  1. Examine the model. The three sides are (choose: about the same lengths / one is very different / all are very different )
  2. Measure the angles between the faces. The three angles are (choose: about the same / one is very different / all are very different )
  3. The angles are approximately ______,______,______.
  4. What crystal system is this? ______
  5. Can you find any 2-fold rotation axes? Y/N .
  6. Mark any 2-fold rotation axis/axes with a 2-fold symbol.
  7. Are there any mirror planes? Y/N
  8. How many mirror planes? ______
  9. Draw (the/all) mirror plane(s) in, using a line.
  10. Are there any mirror planes perpendicular to a rotation axis? Y/N
  11. What is the Hermann-Mauguin symbol for a 2-fold rotation axis with a mirror plane perpendicular to it? Choose one: (2-m , 2/m , 2*m)
  12. Are there any more? Y/N
  13. Write the Hermann-Mauguin symbol for this shape:______

3. Block 3 is a rectangular solid

Orient the block so that the long axis is vertical and three faces are visible. Then carefully sketch the model in perspective view. Draw an axis sticking out of the center of each face.

  1. Examine the model. The three sides are (choose: about the same lengths / one is very different / all are very different ).
  2. Measure the angles between the faces. The three angles are (choose: about the same / one is very different / all are very different )
  3. The angles are approximately ______.
  1. What crystal system is this? ______
  1. Can you find any 4-fold rotation axes? Y/N .

Mark all 4-fold rotation axes with a 4-fold symbol.

Are there any mirror planes? Y/N

  1. Are any of the mirror planes perpendicular to a rotation axis? Y/N

Draw in any mirror plane perpendicular to a 4-fold axis on your sketch.

  1. What is the Hermann-Mauguin symbol for a4-fold rotation axis with a mirror plane perpendicular to it? Choose one: (4-m , 4/m , 4*m)
  2. Label the (100), (010) and (001) faces.
  3. Notice we skipped many 2-fold rotation axes and many mirrors. How many 2-fold rotation axes can you find? ______

Choose: all 2-fold axes pass through the centers of faces/ some pass through edges

  1. Block 4 is a cube.

Orient the block so that all three front faces are visible. Then carefully sketch the model in perspective view. Draw an axis sticking out of the center of each face. Label them once you have determined the crystal system below.

  1. Examine the model. The three sides are (choose: about the same lengths / one is very different / all are very different ).
  2. Measure the angles between the faces. The three angles are (choose: about the same / one is very different / all are very different )
  3. The angles are approximately ______.
  4. What crystal system is this? ______

Correctly label the crystal axes on your sketch, using the convention for this crystal system.

  1. Can you find any 4-fold rotation axes? Y/N . How many? ____

Mark ONE 4-fold rotation axes with a 4-fold symbol.

Can you find any 3-fold rotation axes? Y/N . How many? ____

Mark ONE 3-fold rotation axes with a 3-fold symbol.

Choose: 3-fold axes pass through faces / edges / corners /all of these

  1. How many 2-fold rotation axes can you find? ______

Choose: some 2-fold axes pass through the corners/ some pass through edges

Mark ONE 2-fold rotation axes with a 2-fold symbol.

  1. Label the (100), (010) and (001) faces.

Turn in your work at the next class.

  1. Appendix: Here are the Crystal System definitions from your Lecture 1 slides. You should memorize the axes, the axis lengths, and the angles for each system.

Top View