A solution and solid state study of niobium complexes University of ...

3.5.4 Least-squares refinement
Chapter 3
The least square refinement is a way of comparing the calculated diffraction pattern
with the observed diffraction pattern. If the atoms of the model structure are in the
approximate correct positions, then there should be a degree of resemblance
between the calculated diffraction pattern and the observed one. The calculated
structure factor (Fc) is compared to the experimental data (F0) and described in terms
of residual index or R-factor.
R = | || |
| |
51
(3.12)
The value of the R-factor for a correct and complete crystal structure as determined
from well measured experimental data is around 0.02-0.07. 17
3.6 Chemical Kinetics
Chemical kinetics involves the study of the rate of chemical reactions and the
mechanism by which they occur. Chemistry is concerned with the study of molecular
structures, equilibria between these structures and the rates at which these
structures are transformed into others. Spectrophotometry is often used to follow
reaction kinetics as every molecule displays a different and unique absorption
spectrum. From the Beer-Lambert law, the relationship of concentration to
absorption can be found. 18
Log10 =
= εcl = A (3.13)
with I0 the intensity of the incident monochromatic light, Itrs the transmitted intensity, ε
the extinction coefficient, c the concentration, l the pathlength and A the
absorbance. The total absorbance of a solution is calculated by adding the individual
absorbances of each species:
17
J. P. Gluster, M. Lewis, M. Rossi, Crystal Structure Analysis for Chemist and Biologists, Wiley and Sons, New
York, 389, 1994.
18
E. T. Denisov, O. M. Sarkisov, G. I. Likhtenshtein, Chemical Kinetics: Fundamentals and New Developments,
Elsevier, Amsterdam, 1, 2003.