# Help understanding and reading atomic positions of crystals

I am familiar with both Cartesian coordinates and fractional coordinates of crystals. However, I am having trouble reading the atomic positions that are listed in some research papers. For example, for orthorhombic CaTiO3 the atomic positions are listed as:

    Atom #      OX   SITE   X            Y            Z         SOF   H
Ca   1         2.0    4c   -0.00676(7)   0.03602(6)   0.25       1.   0
Ti   1         4.0    4b    0            0.5          0          1.   0
O    1        -2.0    4c    0.0714(3)    0.4838(2)    0.25       1.   0
O    2        -2.0    8d    0.7108(2)    0.2888(2)    0.0371(2)  1.   0


I assume that they are in Cartesian coordinates since they are labelled x, y, and z. However, when I use the coordinates to construct a unit cell, the atoms overlap.

In the drawing, red=oxygen, yellow=ca, gray=titanium. They are all bunched up at the origin (0,0,0). Furthermore, repeating the unit cell (such that it forms a lattice) does not yield me a correct structure. I also tried fractional coordinates, just to be sure. However, I obtain erroneous results. I think I am misunderstanding what these coordinates represents or how they are read. What am I doing wrong? Also why are there only 2 oxygens when the formula is CaTiO3? Any help would be appreciated

• could you perhaps post the reference? – bremsstrahlung Mar 7 '16 at 6:55
• icsd.kisti.re.kr/icsd/… – CoffeeIsLife Mar 7 '16 at 7:03
• the drawing I did it myself using Gaussview – CoffeeIsLife Mar 7 '16 at 7:04
• You would need to apply the appropriate symmetry operations to those points (using the 'site' type). It's ridiculously convoluted. You're best to look elsewhere (specifically, page 80-81 here). – lemon Mar 7 '16 at 9:57
• – CoffeeIsLife Mar 7 '16 at 11:30

## 1 Answer

The coordinates are known as Wyckoff Positions. These positions are dependent on the lattice constants a, b, and c AND the space group of the unit cell in question. As I posted on the comments, there is a link to the a post which gives advice on how to change Wyckoff Positions to Cartesian coordinates. One thing to note is that the use of Wyckoff Positions haven't been standardized. Some research papers will use fractional coordinates, some will use Cartesian, and some will use the term "atomistic coordinates." If the coordinates are listed using coordinates xyz and the magnitude of each of the coordinates is less than 1, they will be Wyckoff Positions (usually).