Chapter 8: Physical Techniques in Inorganic Chemistry

Introduction to Physical Techniques

All the structures of molecules and materials covered in inorganic chemistry have been determined by applying physical techniques. These methods produce data that help determine a compound's structure, composition, or properties.

Key Principle Most physical techniques rely on the interaction of electromagnetic radiation with matter. Different regions of the EM spectrum probe different molecular properties.

The Electromagnetic Spectrum

📡 Electromagnetic Spectrum and Associated Techniques

Radio
NMR

μwave
EPR

IR
Vib

Vis
Elec

UV
PES

X-ray
XRD

γ
Möss

1 m 1 mm 1 μm 700 nm 400 nm 1 nm 1 pm

Timescales of Spectroscopic Techniques

Different techniques have different timescales, affecting the structural information obtained:

⏱️ Technique Timescales

X-ray diffraction

10⁻¹⁸ s

Mössbauer

10⁻¹⁸ s

UV-visible

10⁻¹⁵ s

IR/Raman

10⁻¹² s

EPR

10⁻⁶ s

NMR

10⁻³–10⁻⁶ s

Note: IR sees different states; NMR may see an average structure (fluxional molecules)

Overview of Techniques

Category	Techniques	Information Obtained
Diffraction	X-ray, Neutron	Crystal structure, bond lengths, atomic positions
Spectroscopy	UV-vis, IR, Raman	Electronic structure, vibrations, bonding
Resonance	NMR, EPR, Mössbauer	Local environment, oxidation state, dynamics
Ionization	PES, XAS, MS	Orbital energies, composition, mass
Analysis	AAS, CHN, TGA, XRF	Elemental composition, thermal behavior

8.1-8.2 Diffraction Methods

Key Points

X-ray diffraction is the most important method for structure determination
Scattering of ~100 pm radiation from crystals gives diffraction patterns
Neutron diffraction locates light atoms (H, Li) in presence of heavy atoms

Bragg's Equation

2d sin θ = nλ

where d = spacing between planes of atoms, θ = diffraction angle, λ = wavelength, n = integer

📐 Bragg Diffraction Visualization

X-ray Diffraction Techniques

Powder XRD

Single Crystal

Synchrotron

Neutron

Powder X-ray Diffraction

Used for polycrystalline samples with randomly oriented crystallites (0.1–10 μm).

Application	Information Obtained
Phase identification	Fingerprint comparison with JCPDS database (>50,000 patterns)
Sample purity	Monitor reaction progress in solid state
Lattice parameters	High-precision cell dimensions
Phase diagrams	Composition-structure mapping
Rietveld refinement	Atomic positions from powder data

Single-Crystal X-ray Diffraction

The most important method for complete molecular structure determination.

Requires crystals ≥50 × 50 × 50 μm
Determines bond lengths to ±0.1–0.5 pm precision
Modern diffractometers use area detectors (CCD, image plates)
Structure solution typically takes hours
ORTEP diagrams show thermal ellipsoids

Limitations

X-ray scattering ∝ number of electrons. Heavy atoms dominate scattering; H atoms difficult to locate, especially near heavy metals.

Synchrotron X-ray Sources

Synchrotron radiation is several orders of magnitude more intense than laboratory sources.

Can study crystals as small as 10 × 10 × 10 μm
Rapid data collection
Enables protein crystallography
National/international facilities

Neutron Diffraction

Neutrons are scattered by nuclei, not electrons—complementary to X-rays.

Advantages

Locates H, Li in presence of heavy atoms
Distinguishes isoelectronic species (O/N, Cl/S)
Magnetic structure determination

Limitations

Requires reactor or spallation source
Lower flux than X-rays
Larger samples needed

Example 8.1: TiO₂ Polymorphs by Powder XRD

TiO₂ exists as rutile, anatase, and brookite. Each has a unique diffraction pattern:

Polymorph	Strongest peaks (2θ/°)
Rutile	27.50, 36.15, 39.28, 41.32, 44.14, 54.44
Anatase	25.36, 37.01, 37.85, 38.64, 48.15, 53.97
Brookite	19.34, 25.36, 25.71, 30.83, 32.85, 34.90

8.3-8.5 Absorption and Emission Spectroscopies

Key Points Energies and intensities of electronic and vibrational transitions provide information on electronic structure, bonding, and chemical environment.

UV-Visible Spectroscopy

Observation of absorption in UV (200–400 nm) and visible (400–800 nm) regions. Excites electrons to higher energy levels.

A = log₁₀(I₀/I) = εcL (Beer-Lambert Law)

where A = absorbance, ε = molar absorption coefficient, c = concentration, L = path length

Transition Type	ε (dm³ mol⁻¹ cm⁻¹)	Selection Rule
Fully allowed (Δl = ±1)	>10⁵	Allowed
Charge transfer	10³–10⁴	Usually allowed
d-d (spin allowed)	10–100	Laporte forbidden
d-d (spin forbidden)	<1	Spin + Laporte forbidden

Infrared and Raman Spectroscopy

IR Spectroscopy

Measures absorption of IR radiation (4000–400 cm⁻¹).

Selection rule: Change in dipole moment required

Sample types: Gas, liquid, solid (KBr pellet, ATR)

Raman Spectroscopy

Measures inelastic scattering of visible light.

Selection rule: Change in polarizability required

Advantage: Water-compatible; symmetric vibrations intense

Mutual Exclusion Rule In centrosymmetric molecules, vibrations active in IR are inactive in Raman, and vice versa. No vibration is both IR and Raman active.

Important IR Frequencies

Group	ν̃ (cm⁻¹)	Notes
O–H (free)	3600–3650	Sharp
O–H (H-bonded)	3200–3500	Broad
N–H	3300–3500	Medium
C≡N	2100–2250	Strong, diagnostic
C≡O (terminal)	1850–2125	Very strong
C≡O (bridging)	1700–1850	Lower than terminal
M–H	1700–2200	Metal hydrides

8.6-8.8 Resonance Techniques

Nuclear Magnetic Resonance (NMR)

Key Points NMR detects nuclear spin transitions in a magnetic field. Chemical shifts and coupling constants reveal molecular structure and dynamics.

NMR is sensitive to nuclei with non-zero spin (I ≠ 0). Common nuclei:

Nucleus	I	Natural Abundance (%)	Sensitivity
¹H	½	99.98	High (reference)
¹³C	½	1.1	Low
¹⁹F	½	100	High
³¹P	½	100	Medium
¹¹B	³⁄₂	80.4	Medium
²⁷Al	⁵⁄₂	100	Medium
¹⁹⁵Pt	½	33.8	Low

NMR Information Content

Chemical shift (δ): Electronic environment of nucleus
Integration: Number of equivalent nuclei
Coupling constants (J): Connectivity, geometry
Relaxation times: Dynamics, molecular motion

Electron Paramagnetic Resonance (EPR)

EPR / ESR

Detects species with unpaired electrons: radicals, d-block ions, f-block ions.

The g-value provides information on the electronic environment (g_e = 2.0023 for free electron).

Hyperfine coupling to nuclei with I ≠ 0 gives information on electron distribution.

Mössbauer Spectroscopy

Measures recoilless nuclear γ-ray absorption. Most common: ⁵⁷Fe, ¹¹⁹Sn.

Parameter	Information
Isomer shift (δ)	Oxidation state, electron density at nucleus
Quadrupole splitting (Δ)	Symmetry of environment
Magnetic splitting	Magnetic ordering

8.9-8.11 Ionization-Based Techniques

Photoelectron Spectroscopy (PES)

E_k = hν − E_i

Kinetic energy of ejected electron = photon energy − ionization energy

XPS (X-ray PES)

Source: Mg Kα (1254 eV) or Al Kα (1486 eV)
Probes core electrons
Surface-sensitive (~1 nm depth)
Elemental analysis (ESCA)

UPS (UV PES)

Source: He(I) (21.22 eV), He(II) (40.8 eV)
Probes valence electrons
Higher resolution than XPS
Vibrational fine structure

X-ray Absorption Spectroscopy (XAS)

Regions of an X-ray Absorption Spectrum

Region	Energy Range	Information
Pre-edge	< E_i	Excited states, local symmetry
XANES	E_i to E_i+10 eV	Oxidation state, coordination
NEXAFS	E_i+10 to +50 eV	Surface adsorbate orientation
EXAFS	> E_i+50 eV	Bond lengths, coordination number

Mass Spectrometry

Key Point Mass spectrometry measures mass-to-charge ratio (m/z) of gaseous ions. Provides molecular mass and fragmentation patterns.

Ionization Methods

Method	Abbreviation	Application
Electron impact	EI	Volatile compounds; causes fragmentation
Fast atom bombardment	FAB	Less fragmentation than EI
Matrix-assisted laser desorption	MALDI	Polymers, large molecules
Electrospray ionization	ESI	Ionic compounds in solution

Example 8.9: Interpreting Mass Spectra

For [Mo(η⁶-C₆H₆)(CO)₂PMe₃] (M = 306):

M⁺ appears as ~10 peaks due to Mo isotopes (most abundant: ⁹⁸Mo)
M⁺ − 28: loss of one CO
M⁺ − 56: loss of two CO
M⁺ − 76: loss of PMe₃

8.12-8.15 Chemical Analysis

Atomic Absorption Spectroscopy (AAS)

AAS

Free atoms absorb radiation characteristic of the element. Used for quantitative elemental analysis.

Hollow cathode lamp specific to each element
Flame atomization (2500–3000 K) or graphite furnace
Detection limits: ppb (flame) to 10⁻¹⁵ (furnace)

CHN Analysis

Automated determination of C, H, N (and O, S) content by combustion.

Sample heated to 900°C in O₂
Products: CO₂, H₂O, N₂, NOₓ
Reduction over Cu at 750°C
Sequential trapping and thermal conductivity detection

🧮 CHN Analysis Calculator

Carbon (%)

Hydrogen (%)

Nitrogen (%)

Other element (optional)

X-ray Fluorescence (XRF)

XRF / EDAX

Core electron ejection followed by X-ray emission. Characteristic X-rays identify elements.

Qualitative and quantitative analysis
Elements with Z > 8 (oxygen)
Non-destructive
EDAX: used in electron microscopes

Thermal Analysis

⚖️

TGA

Thermogravimetric Analysis

Mass change vs temperature. Dehydration, decomposition, oxidation.

🌡️

DTA

Differential Thermal Analysis

Temperature difference vs reference. Phase transitions.

🔥

DSC

Differential Scanning Calorimetry

Heat flow vs temperature. Quantitative enthalpy data.

Example 8.12: TGA of CuSO₄·5H₂O

Heating CuSO₄·5H₂O shows three stepwise mass losses:

CuSO₄·5H₂O → CuSO₄·3H₂O + 2H₂O
CuSO₄·3H₂O → CuSO₄·H₂O + 2H₂O
CuSO₄·H₂O → CuSO₄ + H₂O

Magnetometry and Magnetic Susceptibility

Key Point Magnetic susceptibility measurements determine the number of unpaired electrons in a complex, distinguishing high-spin from low-spin configurations.

Types of Magnetic Behavior

Type	χ	Origin
Diamagnetic	Negative, small	All paired electrons
Paramagnetic	Positive	Unpaired electrons
Ferromagnetic	Large positive	Aligned unpaired electrons
Antiferromagnetic	Small positive	Opposed unpaired electrons

Magnetic Moment

μ_eff = √[n(n+2)] μ_B (spin-only formula)

where n = number of unpaired electrons, μ_B = Bohr magneton

n	μ_eff/μ_B	Example
1	1.73	Cu²⁺ (d⁹)
2	2.83	Ni²⁺ (d⁸)
3	3.87	Co²⁺ (d⁷ HS)
4	4.90	Fe²⁺ (d⁶ HS)
5	5.92	Mn²⁺, Fe³⁺ (d⁵ HS)

Measurement Techniques

Gouy balance: Measures force on sample in inhomogeneous field
Faraday balance: Higher precision than Gouy
SQUID magnetometer: Superconducting quantum interference device; highest sensitivity
Evans method: NMR-based; convenient for solutions

8.16-8.17 Microscopy

Scanning Probe Microscopy

STM (Scanning Tunneling Microscopy)

Sharp tip scans surface
Quantum tunneling current measured
Atomic resolution on conducting surfaces
Can manipulate individual atoms

AFM (Atomic Force Microscopy)

Tip on cantilever deflected by surface forces
Works on insulators and conductors
Contact, non-contact, and tapping modes
Surface topography at nm resolution

Electron Microscopy

🔬

SEM

Scanning Electron Microscopy

Surface imaging
Secondary electrons detected
Resolution ~1 nm
Combined with EDAX for analysis

🔍

TEM

Transmission Electron Microscopy

Electrons pass through thin sample
Internal structure
Resolution ~0.1 nm (atomic)
Electron diffraction possible

Chapter Summary

Structure Determination

X-ray diffraction: primary method
Neutron diffraction: H positions
NMR: solution structure
EXAFS: local structure

Electronic Structure

UV-vis: d-d transitions, CT
PES: orbital energies
EPR: unpaired electrons
Mössbauer: oxidation state

Bonding & Vibrations

IR: polar vibrations
Raman: symmetric vibrations
Mutual exclusion rule
Group frequencies

Composition & Properties

Mass spectrometry: molecular mass
CHN/AAS/XRF: elemental analysis
TGA/DSC: thermal behavior
Magnetometry: unpaired electrons

Choosing a Technique

Information Needed	Primary Technique	Complementary
Complete molecular structure	Single-crystal XRD	NMR
Phase identification	Powder XRD	IR
H atom positions	Neutron diffraction	NMR
Oxidation state	Mössbauer / XANES	UV-vis, EPR
Bonding information	IR / Raman	NMR, UV-vis
Molecular mass	Mass spectrometry	CHN
Elemental analysis	CHN / XRF / AAS	EDAX
Spin state	Magnetic susceptibility	EPR