# XPS for Beginners

Fundamentals 1

#### Doublet Peaks in XPS

Doublets are commonly observed in XPS analysis

In fact only S-orbitals produce single peaks!

#### Spin-Orbit Coupling

The origin of these peaks is doublets is what’s called ‘Spin-orbit coupling’

SOC describes the interaction between an unpaired electron (of spin ‘S’) and the angular momentum of it’s parent orbital (L)

These may combine to give us our total angular momentum (J) (J = | L + S |)

Electrons may therefore come from the same orbital, but have different total angular momentum (i.e. from spin up & spin down electrons)

Differing total angular momentums will result in slightly different peak energies

This is what gives us our doublet peaks

S-orbital effectively have NO orbital angular momentum (quantum number L = 0)

This is because the spherical symmetry means that the probability of finding an electron at a given position is NOT dependant on angle

More specifically, the wavefunction has no angular dependency and so the S-orbital eigenvalue for angular momentum = 0

Example – O 1s

Quantum numbers:
Principal (n) = 1
Azimuthal (l) = 0
Magnetic (m) = 0
Spin (s) = + ½ or – ½

What do you think J is?

## J = + ½

• Using J = | L + S |
• J = | 0 + ½ | or J = | 0 – ½ |
• J = | + ½ | or | – ½ |
• J = + ½

#### Peak Naming

Using the same process, we can determine the total angular momentums of all of our orbitals

We use the total angular momentum to refer to the individual peaks in the following format:

Element OrbitalAngular Momentum

For example – Au 4f

How would we label the two peaks?

## 7/2 and 5/2

Low binding energy peak = Au 4f7/2

High binding energy peak = Au 4f5/2

#### Area Ratios

2J + 1 describes the degeneracy of the states at their respective total angular momentum (sum of all m(j) states)

Individual m(j) states described as J, J-1, … , -J

m(j) = 2J + 1

J = 7/2 and 5/2

2*7/2+1 and 2*5/2+1 = 8 and 6

Area ratio = 8/6 or 4/3 (1.333r)

Measured area ratio = 57/43 (1.3336)

Therefore we have fixed ratios for each orbital type:

P-orbitals – Peak A = Peak B*2

D-orbitals – Peak A = Peak B*3/2

F-orbitals – Peak A = Peak B*4/3

These ratios are fixed – so we can use them to model spectra with overlapping doublets

Example – Pt 4f + Al 2p overlap

• Pt 4f5/2 peak directly overlaps with Al 2p
• Can use properties of Pt 4f7/2 to model the overlap
• Obtain additional information from peak modelling

#### FWHM Ratios

In most cases the FWHM of doublet peaks is a constant 1:1

Very exceptions (e.g. Ti 2p), will not be touched on in this course

#### Doublet Separation

Doublet separation proportional to atomic number, principle quantum number and orbital angular momentum

When atomic mass increases, separation increases

When principle quantum number increases, separation decreases

When orbital angular momentum increases, separation decreases

Values for doublet separation may be found readily online

And of course, HarwellXPS.guru!