Raman Spectroscopy

When I first read about Raman spectroscopy, it seemed like an abstract and difficult technique to understand. I kept encountering arcane terms such as lattice vibrations and phonons, which never made much sense to me, and I couldn’t form an intuitive picture of how the technique worked. But now I think I do understand it, thanks to a wonderful explanation by my senior lab mates, Nithin Abraham and Andres Allcca. Looking back, I feel it need not have been so hard to grasp. So here, I’ll try to break down those intimidating terms and give a simple explanation of the technique using some analogies.

This is a brief introduction to Raman spectroscopy, and anyone who has studied physics at the high-school level should find it easy to understand. Raman spectroscopy is a vast topic—an entire book could be written about it—but this post focuses on building an intuitive understanding.

A brief disclaimer: Although I have made every effort to avoid mistakes, some may still remain. Any feedback or criticism is welcome.

Lattice vibrations and phonon modes

Let’s first understand what lattice vibrations mean. They refer to the vibrations of the atoms that make up a crystal lattice. To connect this to something familiar, think of the vibrations of macroscopic objects—after all, macroscopic vibrations are simply the collective result of microscopic lattice vibrations.

Consider the example of a bell. When the clapper strikes the bell, its kinetic energy is transferred to the atoms in the bell’s material. Upon absorbing this energy, the atoms begin to vibrate about their equilibrium positions in a collective and coherent manner. This atomic motion gives rise to the macroscopic vibration of the bell that we can see and hear.

(You can check out this link to see how atoms vibrate—it almost looks like they’re dancing, doesn’t it?) Hopefully, this gives you some intuition for how atoms vibrate, which will be useful when we move on to understanding lattice vibrations and eventually Raman spectroscopy.

Picture of a bell labeling its different parts. — Picture of a bell. (Image source: Wikipedia)

Atoms can vibrate randomly, or—if arranged in an orderly structure—they can vibrate in well-defined ways. Let’s go back to the example of the bell. Bells are typically made of bronze, an alloy of copper and tin. Most metals, including copper and tin, are crystalline, meaning their atoms are arranged in a definite pattern that extends over long range. This periodic arrangement restricts how the atoms can move, allowing only certain specific patterns of vibration called vibrational modes. In short, lattice vibrations are the collective vibrations of atoms in a crystal lattice, and Raman spectroscopy is the study of these vibrations.

Two Analogies for Vibrational Modes

Example 1: Imagine yourself standing in a human chain, holding hands with others. The ways you can move are limited—you can’t move freely without breaking the chain. Similarly, an atom bonded to other atoms can only move or vibrate in certain ways known as modes.

Example 2: Think of a guitar string. A string can only vibrate in specific modes—it cannot produce arbitrary frequencies. For example, an E string will only sustain the mode corresponding to an E note (in this example, you are not allowed to press any fret). The allowed modes depend on the string’s length, mass per unit length, tension, and material.

The frequency of the nth harmonic is given by:

$f_n = \frac{n}{2L}\sqrt{\frac{T}{\mu}}$

where $f_n$ is the frequency of the nth harmonic, $n$ is harmonic number, $L$ is the length of the string, $T$ is tension, $\mu$ is mass per unit length.

Just like a guitar string, atoms in a crystal lattice can only vibrate in specific allowed modes. These are called phonon modes, and the quantized vibrations themselves are known as phonons. Each material has its own unique set of phonon modes—its vibrational fingerprint—which Raman spectroscopy can identify.

Raman scattering

In the bell example, energy from the clapper was transferred mechanically. In Raman spectroscopy, however, we use a laser to excite the atoms. When laser light strikes the sample, the photons interact with the material in several ways—through Rayleigh scattering, Mie scattering, and Raman scattering.

Rayleigh and Mie scattering are elastic processes, meaning the scattered photons have the same energy (and wavelength) as the incident photons. Raman scattering, however, is inelastic—the scattered photons have different energies than the incident photons.

Schematic showing energy transitions for different scattering mechanisms. For Rayleigh scattering, the scattered photon has the same energy as the incident photon. For Stokes scattering, the scattered photon has lower energy; for anti-Stokes scattering, it has higher energy. (Image source: Wikipedia)

In Raman scattering, the incident photons transfer part of their energy to the atoms, causing them to vibrate. Each phonon mode has a specific energy, so the amount of energy lost (or gained) by the photon is fixed. By measuring the energy difference between the incident and scattered photons, we can determine the phonon energies and thus identify the vibrational modes of the material.

Stokes scattering and Anti-Stokes scattering:

In Stokes Raman scattering, the incident photon loses energy to excite lattice vibrations. However, if the atoms are already vibrating before the photon arrives, the photon can gain energy from them—this is anti-Stokes Raman scattering.

In fact, Stokes and anti-Stokes scattering always occur simultaneously. For a given phonon mode, the energy shifts for both processes are equal in magnitude but opposite in direction relative to the incident photon energy.

This energy shift, measured in terms of wavenumber, is called the Raman shift. It can be calculated using the formula:

$\Delta\nu=\frac{1}{\lambda_{incident}}-\frac{1}{\lambda_{scattered}}$

For Stokes scattering $\lambda_{incident}$ is the wavelength of the laser and $\lambda_{scattered}$ is that of the scattered photon. For anti-Stokes scattering, the terms are reversed.

Raman Shift is usually calculated in cm^-1 units.

An example Raman spectrum of Silicon is shown below.

Key Takeaways

Lattice vibrations are the collective oscillations of atoms about their equilibrium positions in a crystal lattice.
The periodic arrangement of atoms restricts their motion to specific vibrational (phonon) modes.
Raman spectroscopy is a non-destructive optical technique that probes these vibrational modes.
The allowed vibrational modes depend on the crystal structure, bond type, and atomic masses, acting as a fingerprint of the material.
Raman scattering is an inelastic process involving energy transfer between incident photons and phonons.
Each phonon mode has a characteristic energy, so by analyzing the scattered photon energies, we can extract detailed information about a material’s structure and composition.

AKSHAY AGRAWAL