Scattering Contrast

Dr. Hongzhou Zhang hozhang@tcd.ie

SNIAM 1.06 896 4655

Lecture 5

• Dynamical contrast: Characteristic Images of Perfect Crystals (perfect crystal, annealed, single phase)

• Thickness fringes

• Bend contours

TEM Contrast

• Scattering/Amplitude Contrast – BF/DF: thickness, tilt – Low-medium magnification – Applications

• Crystal defects: dislocations, stacking faults, phase boundaries, precipitates, defect clusters

• Contrast: g, type of the fault, its depth in the crystal

• Quantitative determination of b • Resolution: strongly excited: 10 nm; weak beam:

1nm

• Phase Contrast: – High magnification – Highly coherent beam – Large defocusing – Resolution: 0.1-0.2 nm – Reliable interpretation: Simulation

What is contrast?

11

12

I

I

I

IIC

Difference in intensity between two adjacent areas

•Eyes: < 5% - can’t detect <10% - difficult

•Enhance digital image electronically

Mass-thickness Contrast • The diaphragm

– the focal plane of the objective lens – Limiting angle : Transmission T()

• Absorbs scattered electrons > 0

• T() – The objective aperture 0

– The electron energy E – The mass thickness x=t – The material composition:

» Atomic weight, A » Atomic number Z

• The illumination aperture < 0 (TEM)

• Samples – Amorphous

• Incoherent scattering? Diffuse maxima

– Surface replica – Biological sections – Polycrystalline films with very small

crystals xfZh

mef

2

2

2

0 sin24

1

Mass-Thickness: an Example Latex particles on a carbon support film

Thickness-contrast

Diffraction Contrast

• Dominant mechanism

- Delineating object details >~ 1.5 nm

• BF and DF imaging

BF

Atomic Model of Dislocations

An Edge dislocation

A screw dislocation

Burgers Vectors

Dislocation line

Strain field ~ distortion of the lattice

Low Angle Grain Boundry

•A low angle tilt boundary in Ge. •Spacing of dislocations in the boundary is inversely proportional to the angle of mis-orientation. •D=b/

Relevance of Diffraction Theory to Studies of Crystal Defects

• Equivalent form of the dynamical diffraction theory – Plane waves: Darwin-Howie-Whelan equations – Block waves – Modified Block waves – slowly varying strain field – Scattering Matrix – Planar defect/precipitates

• Defects – Locally varying strain field (dislocation, misfitting precipitates, etc. ) – Planar defect(stacking faults, interfaces) – Void/gas bubbles

• Important parameters – The reflecting plane vector: g – The deviation from the Bragg position: s – The extinction distance: g ~ (g ) – Deviation from the Bragg position: w = gs – The anomalous absorption coefficient (ANO= g / ’g )

• Depends on g • Stacking faults sensitive to ANO … determine ANO

Bright Field and Dark Field Images

•Maps of the intensity distribution across the T/D beams •Point-to-point efficiency of diffraction process •The atomic planes near a dislocation core are strained and hence the diffraction conditions surrounding a dislocation are different. •Resolution of DF images are usually better than BF images.

Bright Field Images

• Thin film BF images showing two parallel rows of edge dislocations.

• Thickness of the film is ≈ 200 nm.

• The photograph above is a projected image of the dislocation lines which are illustrated in the line image.

Kinematical Theory

The contribution from layers parallel to the surface: n

g

rkiai

exp

Imperfect crystal: nnn Rrr

The displacement of the unit cell

from its proper position rn

sgk

iszRgi expexp

Neglecting s.Rn

Assume R does not change too rapidly in directions normal to the column

The amplitude of the scattered beam: t

g

g dziszRgii

0expexp

- The imperfection: additional phase factor: Rgi

The local reciprocal lattice vector: g’= g +g grgr nn

grgRgrgrggRrgr nnnnn

0 gRgrn

griRgi n

- R and g depend on z

Evaluate the integral

Find the dependence

- If R g : no contrast Basis of Burgers vector determinations

- If R //g : maximum contrast

Single Screw Dislocation: Elastically isotropic

• Elastically isotropic material: – W, Al, Zn, Mg, Ti, MC –

• Dislocation image: g.b – A perfect dislocation g.b = 0 or N – A partial dislocation g.b = 0, fraction, or N

• BF: – A dark line: g.b = 1,2, … etc. – Complicated: g.b = fractions – g.b = 0 Invisibility criterion:

• To get b • Diffracting planes contain b – not distorted

– g.b 0 • Undistorted: +; s>0 → BF brighter • Distorted: s = 0 → strongly diffracted, BF darker

g

g

g

g

g

iRgiisz

i

dz

d

Rgiiszii

dz

d

exp

exp

0

0

0

0

0

2

bR

Quantitative analysis: Dislocations

• Quantitative analysis: Crystal defects – Image characteristics of crystal

defects – Procedures for

indentifying/obtaining quantitative information • Determine the direction of b • Computer matching:

the magnitude and sense of b • Solve equations:

– Dislocation line direction: u – The Burgers vector: b – Orientation within the thin foil – The elastic anisotropy of the material

– Dynamical conditions

`The same region of an aluminium foil with different operative reflections

(020) (200)

(11-1)

Dark Field Contrast of Dislocations

• Screw Dislocations in Si.

• The first figure has g {220} vector parallel one set of dislocations and perpendicular to the other.

• Second figure is a similar situation.

• Third figure has g{400} which reveals both sets of dislocations.

• Note the ability to view dislocations with improved contrast

Complex Dislocation Tangles

• A crack in Si (Dark line) emits a number of dislocations on thermal cycling.

• The dislocations were formed to relieve thermal stresses.

Imaging Techniques (TEM)

• First set is a comparison of DF image and a Weak Beam Image.

• Second set is a comparison between a Weak beam image and a BF image.

• The WB technique is a higher resolution form of DF imaging and is primarily used for imaging closely spaced defect structures on the nanometer scale

• Note that in the WB image the contrast and resolution is better than corresponding BF or DF images.

Experimental Conditions for Quantitative Analysis

• Two-beam conditions • BF

– s>0 and small (bright Kikuchi line just outside diffraction spot) – w=gs ~ 0.1-1.0

• DF: w ~ ±1.0

• Avoid thin areas (< 2-3g): rearrangement of defects • Avoid regions of rapidly changing thickness: thickness

fringes • Suitable thickness: 5-8*g

• Penetration depends on reflection – Hcp: {2-200} better than {1-100} – Poor penetration:

• Systematically absent reflections appear due to double diffraction • Ordered materials, superlattice reflections

Determination of the Burgers Vector Perfect dislocation/Elastically isotropic

• g.b = 0 – a series of 2-beam images (w~1) showing the same area

– b = the zone of any two sets of the reflecting planes of the g.b=0 images

– Image computation

– 3 cases of invisible must be obtained • W<1.0

• Kikuchi lines close to the spot

• Use Low-index spots

• g.b=1 confused with g.b=0 – If w >~1.5: g.b =2 sharp; g.b=1 invisible

– High index spots used

Determination of the Burgers Vector Perfect dislocation/Elastically anisotropic

• g.b = 0 inappliable – g.b=0, considerable contrast occurs – Image matching must be used

• Computer simulation: – different operative diffractions – Guess a b

• Enables: magnitude + direction

• Calculation shows – considerably modification of the previous discussion – Different form of displacement field – distort the diffracting planes – Impossible to obtain well-defined invisibility – Complicates the determination of b

• Pseudo-isotropically – Cubic (pure edge or screw {110} or{100}) – Hexagonal (basal and planes basal)

Mixed/edge dislocation: Elastically isotropic

• The displacement – be:the edge component of the Burgers vector – u: a unit vector along the dislocation line

• Image contrast: – Complete invisible (g.b =0, g.be =0, g.b x u =0) – Effective invisibility (three cases with w<1.0, low index reflection)

• Faint residual contrast (g.b =0, g.be 0, g.b x u 0) • Simple to use and complete self-consistent • BF: A black line slightly displaced from the core (shift g.bXs changes signs) • BF and DF not necessarily complimentary at the top of the foil (anomalous

absorption) • Zig-zag contrast near the surface / steeply inclined, w ~ 0.1-10 • Double (w~ 0.1) or single (w~0.1-10) images for g.b =2 • Double images if two-beam not adhered • b is not guaranteed (almost certain)

• Edge dislocation: b = be

14

2cosln

)1(2

21

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2sin

2

1rub

bbR e

Lecture 6

• Phase contrast and HRTEM