Michael Wiescher

Physics Methods in Art and Archaeology

PHYS 178

Archaeologist in the 1920ties

Somewhere in South America

80 years later ---

in the Valley of the Kings, Egypt

Physics Tools & Technology

Danger & Adventure is gone …Physics tools and modern technology dominatethe analysis of art and archaeological artifacts!

and worse (?): biological & medical techniques are at the horizon!

Be prepared!

Goal of course:• Present a comprehensive overview of physics techniques• Present examples for application of these techniques

1. The Physics Principles

1. Principles of physics tools and monitors• Must provide unique signature • Must be non-destructive or must require only limited sample size

2. General summary of toolsa. Atomic and nuclear spectroscopy• Origin and nature of the electromagnetic spectrum• Atomic line spectroscopy in IR, optical, and UV• x-ray signatures• γ-ray signatures

b. Radiation Origin and Radiation Laws• Nature of radiation• Production of radiation• Radiation decay laws

1.1. Goals and Purpose of Archaeometry

“Within archaeological artifacts there is arecord to which an archaeologist is blindbut which a physicists can hope to read”

(M.J. Aitken, Physics Report 1978)

To be able to “read” and analyze archaeological or historical artifacts, you need to probe the micro-structure of the matter to determine it’s consistency and age. This requires non-destructive methods for

material analysis and material dating which areprovided by the tools developed for

atomic and nuclear spectroscopy!

Purpose of Material Analysis TechniquesArtifact Purpose of Material Analysis

Material Identification Technology Analysis Location Analysis

Stone mineral contenttracer elements

Obsidian tracer elementsO, Sr isotopes

Marble O isotopes

Ceramics hardness, element tracer elementscontent, texture C profile

Glas chem. componentsSilicat structure

analysis of material element contentcharacteristics, chem.

Metal components, molecular hardness, alloy structurestructure, elemental isotope distribution

or isotope componentsPaint, Tinctures and distribution, texture chem. structure, element

content, crystal phase

Purpose of Material Dating TechniquesDetermine age of artifact or material

Physics Methods in Material Analysis

Atomic Spectroscopy Techniques include:• atomic absorption and emission

spectroscopy, • X-ray fluorescence analysis (XRF), • proton-induced X-ray emission (PIXE).

Nuclear Spectroscopy Methods range from:• neutron activation techniques, • nuclear resonance analysis, • mass separation techniques• natural decay measurements.

Physics Methods in Material Dating

Dating methods rely on natural radioactivity:

• radio-carbon dating,• potassium/argon dating,• uranium/thorium dating,• analysis of radiation damage,• thermoluminiscence

critical parameter, time-scale of radioactive clock!

1.2. Basic Principles of Atomic PhysicsExtremely simplified quantum mechanical model of the atom is the Bohr model based on Rutherford scattering experiments.Negative electrons are ‘bound’ by electric (Coulomb) attraction to positive nucleus

The atomic nucleus:• positive charge: +1.6 ·10-19 C • atomic mass: ~ A · 1.66 · 10-24 g• miniscule size: ~ 5 · 10-13 cm

The electron orbits:• negative charge: -1.6 · 10-19 C • negligible mass: ~ 9 · 10-28 g• fair size: ~ 1-5 · 10-10 cm

excitation de-excitation

K

ML

N

Only certain orbits for electrons are allowed: quantum states are characterized by certain radius and energy stateonly limited number of electrons allowed per quantum state

The Hydrogen Atom

E ZEn

E eV

EZ Z

n = − =2 02 0

0

136.

is energy necessary to ionize atom is charge of nucleus, = 1

http://www.walter-fendt.de/ph14e/bohrh.htmhttp://www.falstad.com/qmatom/

n=1ℓ=0

n=2ℓ=0

n=2ℓ=1

n = main quantum numberℓ = n-1 orbital momentum quantum number

Mathematics of Quantum TransitionsHydrogen atom: single proton in nucleus, single electron in orbit

r n m

En

eV

n

n

= ⋅ ⋅

= −

−2 9

2

0529 10

13606

. [ ]

.[ ]

n = 1 2 3 4, , , .....

Electron orbit radius

Electron orbit energy

Electron transition between orbits requires or releases energy:

Energy comes quantized as light particles: photons

1 eV = 1.6·10-19 J

Transition between energy orbitals

Possible emission or absorptionof light with fixed wavelengthsby transitions of electrons betweenorbits! Wavelength depends on energy difference between orbits!

Hydrogen emission spectrum

Balmer Series

n=1

n=2

En = -13.6/n2

Energy and wavelength of emitted or absorbed light photons

2 2

−⋅=

⋅=⋅= 22

111

ifH nn

RchhEλλ

νν

E E ERh c n n

. m . J s. m s

n nH

f ii fν = − ∝

⋅−

≡ ⋅

≡ ⋅

≡ ⋅

−

−

1 1

1097 106 626 102 987 10

2 2

7 1

34

8

R Rydberg Constant: h Planck Constant: ]c Speed of Light:

H [ ][

[ / ]

[ ]eVnn

E

nnRchEEE

if

ifHnn fi

−⋅=

−⋅⋅⋅=−=

22

22

116.13

11

ν

ν

ExamplesCalculate the wavelength of a photon emitted by an electron transition in the hydrogen atom from the L-shell (n = 2) to the K-shell (n = 1) (Lyman-series Lα)!

[ ]

wavelength:5.121105.121

75.0/110097.121

11111

9

72222

nmm

mRnn

R Hif

H

=⋅=

⋅⋅=

−⋅=

−⋅=

−λ

λ

In interstellar space you find highly excited hydrogen atoms which emit radio waves. The wavelength corresponds transition from n = 273 to n = 272. Calculate the wavelength!

[ ]

h wavelengtradio:923.0

1088.9/110097.1273

1272

1111 872222

m

mRnn

R Hif

H

=

⋅⋅⋅=

−⋅=

−⋅= −

λ

λ

Wavelength range in the electromagnetic spectrum

The wavelength range extends from 10-15 m (γ-radiation)or 10-9 m (X-ray radiation) through 10-6 m (visible light)to radio wave lengths 1 m.

Each element has its own characteristic transitions depending on the orbit quantum numbers and thecharge Z (number of electrons, protons). These transitions can be analyzed by so-called spectroscopyof light to determine the elemental abundance!

Characteristic spectrum of elements

Solar Spectrum

ultraviolet visible infrared

Multi-Electron AtomsMore than one electron, Z is the charge and determines the chemical characteristics of the element, e.g. Z=1(Hydrogen) Z=47 (Silver). Electron transitions and photon emission is more complex and depends on Z and the shielding Sn by inner electron shells.

( ) ( )

( ) ( )

( )

1

22

22

22

1

22

22

116.131

16.1316.131

6.1316.13

EEhc

Ehc

hcn

ZE

Zn

ZEEE

nZ

nSZE

nK

KK

nK

nn

−==

=

−⋅⋅−=

⋅−+⋅−−=−=

⋅−−≈⋅−−=

γ

λ

λ

K-transitionsto n=1

X-ray transitions in high Z atoms

Ag anlysis

Example: Calculate the K and L x-ray lines for Ag

( ) [ ]

[ ] [ ]

[ ] [ ]

( ) [ ]

( ) [ ] [ ]eVeVE

neVZE

eVeVE

eVeVE

ZAgn

eVZE

L

iL

K

K

iK

399791

416.1346

1216.131

255809116.1346

215834116.1346

47:

116.131

2

222

2

2

22

=

−⋅⋅=

−⋅⋅−=

=

−⋅⋅=

=

−⋅⋅=

=

−⋅⋅−=

α

β

α

n=3

Kβ Lα

n=2Kα

n=1

transition scheme with orbital momentum quantum number

Level splittingdue to ellipticorbitals

higher accuracy x-ray energiesZ Element Kα1 Kα2 Kβ1 Lα1 Lα2 Lβ1 Lβ247 Ag 22.163 21.990 24.942 2.984 2.978 3.151 3.348

Easy to obtain: http://xray.uu.se/hypertext/XREmission.htmlhttp://www.csrri.iit.edu/mucal.htmlhttp://ie.lbl.gov/xray/

Typical spectra: http://ie.lbl.gov/xray/ag.htm

!Summary!

To use atomic spectroscopy methodsyou need to excite the atoms of the

material that you want to analyze. The decay back to the atomic ground state configuration causes the emission of photons with characteristic energies!