Space groups derivation (Schoenflies)

In summary, the conversation is about a search for a complete derivation of space groups similar to the one done by A. Schoenflies in 1891. The person is looking for resources in English or German, specifically mentioning the book "Die Bewegungsgruppen der Kristallographie" by J.J. Burckardt. They also mention that their German is not as good as their English.
  • #1
physicsworks
Gold Member
83
63
Hi! I'm looking for a complete derivation of space groups as Schoenflies did over 100 years ago... Does anybody know where I can find this paper (in English or in German at least):
A. Schoenflies Kristallsysteme und Kristallstruktur, Leipzig, 1891
or maybe a book where the whole process of derivation (as Scnhoenflies did) is described. Thanks!
 
Physics news on Phys.org
  • #2
I have on my shelf "J. J. Burckardt, "Die Bewegungsgruppen der Kristallographie" from 1948.
Also in German but seems to be very a very clear derivation of the groups, also I haven't studied it in detail.
 
  • #3
Thank you, DrDu!
Any books or articles in English? My German is worse than my English :rolleyes:
 
Last edited:

1. What is the purpose of deriving space groups?

Deriving space groups allows us to categorize and classify the different ways in which atoms and molecules can be arranged in a unit cell. This helps us understand the physical and chemical properties of different materials and predict their behavior.

2. How are space groups derived using Schoenflies notation?

Schoenflies notation is a method of describing the symmetry of a crystal structure. It involves identifying the types of rotations and reflections that can be applied to a unit cell to recreate the entire crystal. By systematically applying these symmetry operations, we can derive the space group for a particular crystal lattice.

3. What are the different types of symmetry operations in Schoenflies notation?

There are four types of symmetry operations in Schoenflies notation: identity (E), rotations (C), reflections (σ), and improper rotations (S). These operations are defined based on the number of times a unit cell needs to be rotated or reflected to recreate the entire crystal.

4. How many space groups can be derived using Schoenflies notation?

There are 230 unique space groups that can be derived using Schoenflies notation. These are organized into seven crystal systems (triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic) and 14 Bravais lattices.

5. What is the importance of knowing the space group of a crystal structure?

Knowing the space group of a crystal structure is essential in understanding its symmetry and physical properties. It also helps in identifying the possible direction of growth for crystals and predicting the behavior of materials under different conditions, such as temperature and pressure. Additionally, it aids in the analysis and interpretation of experimental data, such as X-ray diffraction patterns.

Similar threads

  • Atomic and Condensed Matter
Replies
1
Views
984
  • Special and General Relativity
2
Replies
41
Views
2K
  • Quantum Physics
Replies
1
Views
597
Replies
6
Views
879
  • Beyond the Standard Models
Replies
0
Views
904
  • Quantum Physics
3
Replies
87
Views
5K
  • STEM Educators and Teaching
Replies
4
Views
2K
  • STEM Academic Advising
Replies
25
Views
2K
  • Beyond the Standard Models
Replies
0
Views
412
  • Electromagnetism
Replies
3
Views
94
Back
Top