strain effects in thin films and progress in reference beam...

Shen / CHESS Aug.5, 2002

Strain Effects in Thin Films and Strain Effects in Thin Films and Progress in ReferenceProgress in Reference--Beam PhasingBeam Phasing

Qun ShenCornell High Energy Synchrotron Source (CHESS) and

Department of Materials Science & Engineering, Cornell University

Direct measurements of a large number of Bragg reflection phases in protein crystallography experiment

! Intro to reference beam diffraction ! Experimental setup & procedures ! Strategies on using measured phases ! Summary

Interplay between strain & physical properties in thin films=> semiconductor band gap=> exchange striction => magnetic anisotropy

! Ave. strain & strain gradients ! Magnetic thin-film Fe/GaAs ! Conclusions


Typical CrystallographyTypical Crystallography

F(H)=|F(H)|eiα(H)

α(H) = ??

Crystallization Expression Phasing Data collection |F(H)|

anomalous signal from heavy-

atoms

Incorporating heavy atoms into protein

structures

SeMetsubstitution

heavy-atom buffer

heavy-atom soak

Structure


Phasing Proteins w/o Heavy Atoms ?Phasing Proteins w/o Heavy Atoms ?

|F(H)| & α(H) Crystallization Expression Data collection

"" ReferenceReference--beam diffraction beam diffraction

Structure


(a) Conventional oscillation method

kH

k0

ψ

Reference Beam Diffraction TechniqueReference Beam Diffraction Technique

(b) Reference-beam diffraction

kH

k0

kGψ

θGkH-G

Phase difference: δ = αH-G + αG − αH # Triplet Phase


ReferenceReference--Beam Data CollectionBeam Data Collection

θ − θG 0 5 10 15 201600

1700

1800

1900

2000

∆ω (in 0.003o steps)

I (-3

0 1

)/(1

1 1)

δH= −142±10o

60000

70000

80000

90000

100000

I (2

2 -3

)/(1

1 1)

δH= 127±15o

2400

2600

2800

3000

I (0

2 -3

)/(1

1 1)

δH= −55±9o

θ − θG

RBD data set: RBD data set: II((hklhkl)) vs. vs. θθ−−θθGG

Analogy to MAD data set: Analogy to MAD data set: II((hklhkl)) vs. vs. λλ


Conventional 3Conventional 3--Beam DiffractionBeam Diffraction

Lipscomb (1949) Acta Cryst. "Relative phases of diffraction maxima by multiple reflection".

Weckert & Hummer (1997) Acta Cryst A53, 108-143

" Tetragonal lysozyme

" Time-consuming: ~10 min per profile

" Difficult for protein crystallography


Special Kappa Special Kappa DiffractometerDiffractometer

θ

2θ

κ

φ

ψ

x-rays

CCD

" Compact 50o κ-design" G-reflection alignment with κ-φ" Oscillation axis ψ with DC motor control" Easy incorporation into oscillation setup


RBD Experimental ProcedureRBD Experimental Procedure


PhasePhase--Sensitive XRD TheorySensitive XRD Theory

Kinematic theory

" single scattering" commonly used" no phase sensitivity

Approximate theories

" double scattering" triplet-phase sensitive" easy for curve-fitting

Dynamical theory

" all scattering terms" phase-sensitive" only numerical calc.

Second-order Born Approximation (2nd BA): Shen (1986) Acta Cryst. A.

)](cos[)(21)( GGH

G-HH θνδθθ ++= RF

FI

with RG(θ) = reflectivity and νG(θ) = phase shift of G.

L+++= )2()1()0( DDDD

Expanded Distorted-Wave Approach (EDWA): Shen (1999) PRL; Shen (2000) PRB.

−

++−=

G

G

GG2

G2

GH 2)2sin(

12

cos)(sin

sin1)(η

ηητδ

ητ

ηηδτη

AA

AA

IG

with τ = , A=πΓ |FG|t/(λcosθG) and AηG = π(θ−θG)t/d.HG-H FF

" takes into account phase-independent effect accurately.


Automatic Curve FittingAutomatic Curve Fitting

" Curve-fit to experimental datausing EDWA, with 4 parameters

" Distorted-wave approximation(EDWA) is very accuratefor biological crystals

base I0

center θ0

amplitude p

phase δ

-80 -40 0 40 80

0.8

0.9

1.0

1.1

1.2A=0.12transparent crystal

δ=180o

δ=+90o

δ=0o

δ=-90o

Nor

mal

ized

Inte

nsity

Normalized Angle ηG

Comparison of EDWA with dynamical theory

" So far PC-based program ORIGINis used for automatic curve-fittingto obtain triplet-phase δ.


Experiment ExampleExperiment Example

Tetragonal Tetragonal lysozyme lysozyme P4P433221122 CHESS C1, CHESS C1, λλ = 1.097 = 1.097 ÅÅ, Q, Q--1 CCD1 CCD

•• Room temperature measurementsRoom temperature measurements•• Reference reflection G = (1,1,1) Reference reflection G = (1,1,1) •• Typical exposure ~15 sec for Typical exposure ~15 sec for ∆ψ∆ψ=2=2oo. . •• Number of Number of θθ--steps 15 to 21steps 15 to 21•• Typical Typical θθ range ~ 0.05range ~ 0.05oo to 0.1to 0.1oo•• 9090oo rotation rotation ## 86% completeness86% completeness•• Diffraction resolution to ~2.5 Diffraction resolution to ~2.5 ÅÅ

•• 14914 RBD profiles14914 RBD profiles•• Total time ~ 12 hrsTotal time ~ 12 hrs

"" 14914 triplet phases14914 triplet phases


MOSFLM Indexing and IntegrationMOSFLM Indexing and Integration

"" IndexingIndexing

"" IntegrationIntegration

"" Scale Scale (no merge)

"" Sort Sort => IH(θ)


Typical Interference ProfilesTypical Interference Profiles

P43212 lysozyme

All profiles shown from same oscillation series


Results: tripletResults: triplet--phase data setphase data set

• Whole data set:

14914 phases, 14914 phases, ∆δ∆δmm=61=61oo

•• With rejection criteria based With rejection criteria based on goodnesson goodness--ofof--fits parameters fits parameters ((σσ, , χχ22, , FFhghg): ):

7360 phases,7360 phases, ∆δ∆δmm=45=45oo

$ Error histogram for measuredtriplet-phase data set

• Whole data set:


Strategies on Using Measured PhasesStrategies on Using Measured Phases

RBD experiments # measured triplet-phases: δ = αH-G + αG − αH

" How to deduce individual structure-factor phases: αH = ??

0 10 20 30 40 50 60 70

0

5

10

15

20

with 1 ref-beam with 2 ref-beams with 3 ref-beams without phase info

SnB

Succ

ess

Rat

e (p

er 1

000)

Mean Triplet Phase Error (degrees)

•• Direct methodsDirect methods: :

replace guesses based on probability replace guesses based on probability with measured triplet phaseswith measured triplet phases

Weeks, et al. Weeks, et al. ActaActa CrystCryst. A (2000). . A (2000). ##

•• Other methods Other methods ?? ??


Unique Recurrence Pattern in RBDUnique Recurrence Pattern in RBD

G

H

H+GH+2GH+3G

ReferenceReference--beam method:beam method:δ0 = αG + αH-G − αHδ1 = αG + αH − αH+Gδ2 = αG + αH+G − αH+2G

……

N equationsN+2 unknowns

(hk0)

"" RBD geometry leads to a RBD geometry leads to a systematic recurrence pattern of systematic recurrence pattern of individual phases:individual phases:

a) all triplets contain a commona) all triplets contain a common ααGGb) b) ααHH appears in exactly 2 tripletsappears in exactly 2 tripletsc) the two c) the two ααHH--triplets are adjacenttriplets are adjacent

"" Different from conventional Different from conventional 33--beam measurementsbeam measurements

Conventional 3Conventional 3--beam:δ1 = αG1 + αH1-G1 − αH1δ2 = αG2 + αH2-G2 − αH2δ3 = αG3 + αH3-G3 − αH3

……

N equations~3N unknowns

beam:


Recursive RBD Phasing AlgorithmRecursive RBD Phasing Algorithm

Program: RBD_PhasingProgram: RBD_Phasing


RBD_phasing Using Measured PhasesRBD_phasing Using Measured Phases

• 191 unique (hk0) phases plus G=(111) phase from PDB 193L as starting phases• using measured data set of 7360 triplet phases with median phase error 45o

• obtained 1085 individual phases with mean phase error 66o

• calculated electron density map (z=0) of tetragonal lysozyme

Based on 7360 measured tripletBased on 7360 measured triplet--phasesphases Based on calculated tripletBased on calculated triplet--phasesphases


Reducing Number of Initial PhasesReducing Number of Initial Phases

"" LowLow--resolution phases from resolution phases from molecular envelope ?molecular envelope ?

"" Measurements of three RBD Measurements of three RBD datasets with nondatasets with non--coplanar G'scoplanar G's

"" Use of symmetry equivalent Use of symmetry equivalent indexing to effectively have indexing to effectively have three RBD datasets ?three RBD datasets ?

"" In principle, only 4 initial phasesIn principle, only 4 initial phasesare needed to solve a structureare needed to solve a structure


Inverse Beam MeasurementsInverse Beam Measurements

ReferenceReference--beam coupled beam coupled FriedelFriedel pairs:pairs:H H // G G // HH--G G %% H H // G G // GG--HH

0 5 10 15 20 25

0.98

0.99

1.00

1.01

1.02

∆θ (x0.003o)

(b)

Inte

nsity

(-3,2,-4)/(-2,-3,0) δfit=77

o

0.99

1.00

1.02

1.03 (a)

(3,-2,4)/(2,3,0) δfit=−116

o

Inte

nsity

Shen, et al. Shen, et al. ActaActa CrystCryst. A (2000).. A (2000).

1.01

(230)(230)


Summary onSummary onreferencereference--beam phasingbeam phasing

!! Where we are nowWhere we are now::

"" Experimental: Experimental: •• demonstrated RBD technique fordemonstrated RBD technique for

practical tripletpractical triplet--phase measurements phase measurements •• dedicated dedicated κκ--diffractometer diffractometer •• modified oscillation camera setupmodified oscillation camera setup

"" Theoretical: Theoretical: •• phasephase--sensitive diffraction theory sensitive diffraction theory •• automatic fits to obtain automatic fits to obtain δδ

"" Data reduction & usage: Data reduction & usage: •• tested existing tested existing crystallogrcrystallogr. software . software •• developed automatic fitting routinedeveloped automatic fitting routine•• started new phasing algorithmstarted new phasing algorithm

!! Where we are goingWhere we are going::

"" Further developments: Further developments: •• automated alignment control automated alignment control •• rejection criteria to selectrejection criteria to select

reliable measurementsreliable measurements•• dealing with simultaneous beams dealing with simultaneous beams

and mosaic spread and mosaic spread

"" Strategies for using phases: Strategies for using phases: •• use with direct methods use with direct methods •• recursive individual phasesrecursive individual phases•• ∆∆II±±HH =>=> analogy to SAD ?analogy to SAD ?

"" Goal:Goal:•• solve new protein structures solve new protein structures


AcknowledgmentsAcknowledgments

Andrew Stewart (CHESS)Dan PringleStefan KyciaJim LaIuppa

Rob Thorne (Cornell, Physics)Ivan Dobrianov Alexei KisselevCraig Caylor

Marian Szebenyi (MacCHESS) Chris Heaton Bill Miller

Jun Wang (BSRF)

Herbert Hauptman (HWI)Chuck WeeksHongliang Xu

NSF DMR 97NSF DMR 97--1342413424NIH GMNIH GM--46733 46733


Thin Films & NanostructuresThin Films & Nanostructures

InGaAs InGaAs / / GaAsGaAs Nanostructures: 1-100 nmsemiconductorsmagneticorganic polymers

Basic information:

sizeshape -- morphologystrain -- internal structure

Si Si (001)(001)Physical properties:

semiconductor band gapgrowth kineticsphase transitionsmagnetization……

Ge Ge / / SiSi


Measured PL energy shiftQuantum confinement

Quantum Wire Width (nm)

Ener

gy S

hift

(meV

) 2520

15

10

5

0

Measured PL energy shiftQuantum confinementMeasured PL energy shiftQuantum confinement

Quantum Wire Width (nm)

Ener

gy S

hift

(meV

) 2520

15

10

5

0

25

20

15

10

5

0InGaAs QWR: t = 10nmInGaAs QWR: t = 10nm

Reed, Tentarelli, Eastman et al. (1995)

Size, Shape & Strain Effects Size, Shape & Strain Effects on Physical Propertieson Physical Properties

Example: band gap in semiconductors

hνhν'

hνhν'

??


Intrinsic and External StrainIntrinsic and External Strain

Elastic StrainElastic Strain:: {{σσ} = {C} {} = {C} {εε} Hook’s Law} Hook’s Law

⇒ ⇒ External: external pressurelattice mismatch

⇒ ⇒ Intrinsic: microscopic natureexchange striction

In general, strain information is not easily available from manysurface probe (AFM, SEM, STM) measurements


Structural CharacterizationStructural Characterization

Experimental Methods: TEMXRD

Technical challenges:

Signal to background ?Particle size broadening ?Strain variation ?1-10nm

nondestructive


Basic Concepts in XRDBasic Concepts in XRD

Size EffectSize Effect:

Real spaceReal space Reciprocal spaceReciprocal space

L∆Q ~ 1 / L

∆Q = independent of |Q|

Q(220) (440)

Strain EffectStrain Effect:

∆a

∆Q ∝ |Q|

Q(220) (440)

∆Q = −|Q| ∆a/a

∆θ

∆Q = |Q| ∆θ


Advanced XRD TechniquesAdvanced XRD Techniques

4.005

4

3.995

-0.015 0 0.015Qx [2π/a]

Qz

[2π

/a]⇒ ⇒ Reciprocal space mapping⇒ ⇒ Grazing-incidence diffraction⇒ ⇒ Coherent Grating diffraction⇒ ⇒ Crystal truncation rod (CTR)


Examples of Grating DiffractionExamples of Grating Diffraction

InGaAs InGaAs QWR QWR / / GaAsGaAs (001)(001) Si Si (001) (001)

needlesneedles


Average StrainAverage Strain

tt = 10 nm= 10 nm

Sample:multiple regionsw/ different QWRs

~0.5mm2

(h, h, 0)


Strain Effects on Strain Effects on Band Gap

Deformation potentials:

a = −9.016 eVb = −1.96 eV

Band-gap change w.r.t. quantum well:

( ) ( )2/xxzzzzxx baE εεεε −++=∆

Band Gap

Size-dependent strain in QWRs

Shen et al. (1996) PRB 54, 16381.


Average Strain vs. Strain GradientAverage Strain vs. Strain Gradient


Strain Gradient ExampleStrain Gradient Example

Shen & Kycia (1997)PRB 55, 15791.


Longitudinal vs. Longitudinal vs. Transverse GradientsTransverse Gradients

xa

GradientalLongitudin

x∂

∂:Longitudinal wave

Transverse wave

xa

GradientTransverse

z∂

∂:

Shen & Kycia (1997)PRB 55, 15791.


Transverse Strain GradientsTransverse Strain Gradients


Simulations Compared with ExperimentsSimulations Compared with Experiments


Information that can be obtainedInformation that can be obtainedfrom crystal gratingsfrom crystal gratings

=>=> Size and shape information:width, height, period,side-wall slope, ...

=> => Imperfections: inhomogeneities, defects, ...

=> => Time-resolved changes e.g. during oxidation, …

=> => Superlattice registry w.r.t. substrate lattice

=> => Strain in nanostructures:average strainstrain variation (gradient)

=> longitudinal ∂ax/∂x=> transverse ∂az/∂x


AntiAnti--ferromagnetic Thin Film ferromagnetic Thin Film ZnZn0.070.07MnMn0.930.93Te / Te / ZnTeZnTe

ZnTe

ZnMnTe: fcc1 µm


Three Orthorhombic DomainsThree Orthorhombic Domains

Interfacial stress => Prefered c-type domainpopulation 3:1:1


Spatial Dependence ofSpatial Dependence ofExchange Constant Exchange Constant JJnn(r)(r)

Shen, Luo & Furdyna, PRL 75, 2590 (1995).


Fe Thin Film on Fe Thin Film on GaAs GaAs (001)(001)

Misfit = -1.4% aGaAs= 0.56537 nm

aFe=0.28664 nmCube on cube epitaxy

Olivier ThomasU. Marceille

In-plane uniaxial magnetic anisotropy below 5 nm

J. Krebs, B. Jonker, G. Prinz, JAP 61 (1987) 2596

-40-20 0 20 40

-1,0

-0,5

0,0

0,5

1,0

M /

Ms

H (Oe )-40-20 0 20 40 -500 0 500

-1,0

-0,5

0,0

0,5

1,0

[110] [100] ]011[

-500 0 500

-1,0

-0,5

0,0

0,5

1,0

M /

Ms

H (Oe )-40-20 0 20 40 -500 0 500

-1,0

-0,5

0,0

0,5

1,0

[110] [100] ]011[[010]

[100]

Mφ

tf = 1.7 nm: [110] easytf = 80 nm: easy


Magnetic AnisotropyMagnetic Anisotropy

Domain shape anisotropy

σ σMagnetoelastic coupling

Magnetocrystalline anisotropy

Interface-induced effect


Fe / Fe / GaAs GaAs (001) Samples(001) Samples

Fe thickness from 1.5 to 13 nm

MBE: GaAs 500 nm bufferAs rich (2x4) surface 1.5 ×10-10 TorrFe: 1 nm/min at RT3 nm Al capping layer

[110]: defined as unit-cell doubling direction


XX--ray Diffraction Studyray Diffraction Study

CHESS F3: 8 keVGaAsFe

⇒ ⇒ Out-of-plane reflections:(004) and (224)film thicknessout-of-plane lattice const.separate Fe and GaAs peaks

⇒ ⇒ In-plane reflections:(220), (400), …in-plane lattice strainin-plane domain size & shapein-plane correlations

(000) (220)

(004) (224)

(002) (222)


Out of Plane ScansOut of Plane Scans

3.4 3.6 3.8 4.0 4.2 4.41

10

102

103

104

105Data: s389_JModel: Lor2AsymSinc Equation: y=y0+A0/(1+((x-x0)/w0)^2)/(1+((x-x0)/w0)^2)+Ac*exp(-((x-xc)/w2)^3-((x-xc)/w1)^2)*(sin((x-xc)/wc)/((x-xc)/wc))^2 y0 3 ±--A0 600000 ±--x0 3.9988 ±--w0 0.0065 ±--Ac 12000 ±--xc 3.8885 ±--wc 0.047 ±--w1 0.36 ±--w2 0.37 ±--

Inte

nsity

(cts

/1.5

sec)

(2, 2, L)1.98 1.99 2.00 2.01 2.02

3.6

3.8

4.0

4.2

(H,H)

L

(224)(224)

3.9 nm Fe on GaAs (001)1.5 nm Fe on GaAs (001)

Thomas, Shen, et al. (2002).


InIn--plane Map for plane Map for tt =1.5 nm

-2.010 -2.005 -2.000 -1.995 -1.990-2.010

-2.005

-2.000

-1.995

-1.990

1.990 1.995 2.000 2.005 2.010-2.010

-2.005

-2.000

-1.995

-1.990

-2.010 -2.005 -2.000 -1.995 -1.9901.990

1.995

2.000

2.005

2.010

1.990 1.995 2.000 2.005 2.0101.990

1.995

2.000

2.005

2.0101.000

1.641

2.692

4.417

7.248

11.89

19.51

32.02

52.53

86.19

141.4

232.0

380.7

624.7

1025

1682

2759

4528

7429

1.219E4

2.000E4

-0.010 -0.005 0.000 0.005 0.010-4.010

-4.005

-4.000

-3.995

-3.990

-0.010 -0.005 0.000 0.005 0.0103.990

3.995

4.000

4.005

4.010

3.990 3.995 4.000 4.005 4.010-0.010

-0.005

0.000

0.005

0.0101.000

1.585

2.512

3.981

6.310

10.00

15.85

25.12

39.81

63.10

100.0

158.5

251.2

398.1

631.0

1000

1585

2512

3981

6310

10000

-4.010 -4.005 -4.000 -3.995 -3.990-0.010

-0.005

0.000

0.005

0.010

MBE95: 1.5 nmFe/GaAs (001)

[100]

[010]

=1.5 nmL

1-10


InIn--plane Map for plane Map for tt =13 nm=13 nm

-4.02 -4.00 -3.98 -3.96 -3.94-0.04

-0.02

0.00

0.02

0.04

4.000

6.533

10.67

17.42

28.46

46.48

75.90

124.0

202.5

330.6

540.0

-0.04 -0.02 0.00 0.02 0.043.94

3.96

3.98

4.00

4.02

4.000

6.533

10.67

17.42

28.46

46.48

75.90

124.0

202.5

330.6

540.0

-2.02 -2.01 -2.00 -1.99 -1.98 -1.97 -1.96-2.02

-2.01

-2.00

-1.99

-1.98

-1.97

-1.96

4.000

7.483

14.00

26.19

48.99

91.65

171.5

320.8

600.0

1123

2100

-2.02 -2.01 -2.00 -1.99 -1.98 -1.97 -1.961.96

1.97

1.98

1.99

2.00

2.01

2.02

4.000

7.875

15.50

30.53

60.10

118.3

233.0

458.6

903.0

1778

3500

-0.04 -0.02 0.00 0.02 0.04-4.02

-4.00

-3.98

-3.96

-3.94

4.000

6.602

10.90

17.98

29.68

48.99

80.86

133.5

220.3

363.5

600.0

3.94 3.96 3.98 4.00 4.02-0.04

-0.02

0.00

0.02

0.04

4.000

6.602

10.90

17.98

29.68

48.99

80.86

133.5

220.3

363.5

600.0

1.96 1.97 1.98 1.99 2.00 2.01 2.021.96

1.97

1.98

1.99

2.00

2.01

2.02

4.000

7.483

14.00

26.19

48.99

91.65

171.5

320.8

600.0

1123

2100

1.96 1.97 1.98 1.99 2.00 2.01 2.02-2.02

-2.01

-2.00

-1.99

-1.98

-1.97

-1.96

4.000

7.875

15.50

30.53

60.10

118.3

233.0

458.6

903.0

1778

3500

MBE241: 13 nmFe/GaAs (001)

L 110

[100]

[010]


In In- -plane plane θ θ- -scans

scans

23.423.5

23.623.7

23.823.9

24.024.1

1 10

102

103

104

105

Data: s2203_K

Model: G

auLor2 Equation: y=y0+A0*exp(-(0.5*((x-x0)/w

0)^2))+Ac/(1+((x-xc)/w

c)^2)/(1+((x-xc)/wc)^2)

y05.61822

±0.13778A0

105671.65136±296.8045

x023.7534

±0w

00.00111

±2.8769E-6Ac

31508.56867±58.37348

xc23.7534

±0w

c0.01935

±0.00002

Intensity (cts/1.5sec)

θ (degrees)

23.423.5

23.623.7

23.823.9

24.024.1

1 10

102

103

104

105

106

Data: s2230_K

Model: G


0)^2))+Ac/(1+((x-xc)/w

c)^2)/(1+((x-xc)/wc)^2)

y07

±0A0

195136.1448±438.86x0

23.75699±0

w0

0.00103±2.3244E-6

Ac68598.327±182.35018

xc23.75699

±0w

c0.00866

±0.00001


θ (deg)

23.023.2

23.423.6

23.824.0

24.224.4

10

102

103

Data: s479_K

Model: G

aussAmp

Equation: y=y0+A*exp(-0.5*((x-xc)/w

)^2) y0

10±0

xc23.66996±0.00037

w0.09096±0.00035

A3204.40878±17.98515


θ (deg)

23.023.2

23.423.6

23.824.0

24.224.4

10

102

103

Data: s486_K

Model: G


0)^2))+Ac/(1+((x-xc)/w

c)^2)/(1+((x-xc)/wc)^2)

y023.87539

±0.89751A0

1885.8887 ±10.801x0

23.62667±0.00064

w0

0.13935±0.00057

Ac0

±0


θ (deg)

t=13 nm

23.423.5

23.623.7

23.823.9

24.024.1

10

102

103

104

105

Data: s3159_K

Model: G


0)^2))+Ac/(1+((x-xc)/w

c)^2)/(1+((x-xc)/wc)^2)

y011.60655±0.34096

A0202459.67 ±260.568

x023.75092±3.1039E-6

w0

0.00171±1.235E-6

Ac378.60334±2.7471

xc23.75085

±0w

c0.0946

±0.00067


θ (deg)

23.423.5

23.623.7

23.823.9

24.024.1

10

102

103

104

105

Data: s3187_K

Model: G


0)^2))+Ac/(1+((x-xc)/w

c)^2)/(1+((x-xc)/wc)^2)

y08.44063

±0.21856A0

228182.445 ±273.82x0

23.75053 ±1.9045E-6w

00.00173

±1.1586E-6Ac

646.88472 ±5.3003xc

23.75085±0

wc

0.05205±0.00032


θ (deg)

t=3.9 nmt=1.5 nm

(220)

(220)


InIn--plane plane θθ--22θθ scansscans

(220)

(220)

47.3 47.4 47.5 47.6 47.710

102

103

104

105

106 Data: s2229_LModel: GauLor2 Equation: y=y0+A0*exp(-(0.5*((x-x0)/w0)^2))+Ac/(1+((x-xc)/wc)^2)/(1+((x-xc)/wc)^2) y0 7 ±0A0 459449.89±1024409475.7x0 47.50531±529.59952w0 0.00617±4.59E-6Ac 68598.32722±0xc 47.5112±0.00022wc 0.02642±0.00002

Inte

nsity

(cts

/1.5

sec)

2θ (deg)

47.0 47.2 47.4 47.6 47.8 48.01

10

102

103

104

105Data: s2204_LModel: GauLor2 Equation: y=y0+A0*exp(-(0.5*((x-x0)/w0)^2))+Ac/(1+((x-xc)/wc)^2)/(1+((x-xc)/wc)^2) y0 3.59184 ±0.15614A0 111477 ±304.x0 47.50427 ±4.5607E-6w0 0.00465 ±9.4459E-6Ac 31509 ±0xc 47.50986 ±0.00002wc 0.01125 ±0.00003

Inte

nsity

(cts

/1.5

sec)

2θ (degrees)

47.2 47.3 47.4 47.5 47.6 47.7 47.81

10

102

103

104

105Data: s3161_LModel: GauLor2 Equation: y=y0+A0*exp(-(0.5*((x-x0)/w0)^2))+Ac/(1+((x-xc)/wc)^2)/(1+((x-xc)/wc)^2) y0 4.13499±0A0 230000 ±0x0 47.496 ±0w0 0.00628±0Ac 891.84698±7.24xc 47.43448±0.00017wc 0.07069±0.00047

Inte

nsity

(cts

/1.5

sec)

2θ (deg)

23.5 23.6 23.7 23.8 23.9 24.01

10

102

103

104

105Data: s3186_LModel: GauLor2 Equation: y=y0+A0*exp(-(0.5*((x-x0)/w0)^2))+Ac/(1+((x-xc)/wc)^2)/(1+((x-xc)/wc)^2) y0 8 ±0A0 226359.939 ±259.69236x0 23.75124 ±9.7241E-7w0 0.00355 ±2.0367E-6Ac 414.44966 ±6.81267xc 23.73112 ±0.00023wc 0.03332 ±0.00042

Inte

nsity

(cts

/1.5

sec)

θ−2θ (deg)

23.3 23.4 23.5 23.6 23.7 23.8 23.9 24.01

10

102

103

Data: s485_LModel: GauLor2 Equation: y=y0+A0*exp(-(0.5*((x-x0)/w0)^2))+Ac/(1+((x-xc)/wc)^2)/(1+((x-xc)/wc)^2)

y0 3.40615 ±0.2869A0 3821.005 ±57.92237x0 23.74339 ±0.00007w0 0.00139 ±0.00001Ac 1985.57358 ±10.09136xc 23.61601 ±0.0001wc 0.05731 ±0.00024

Inte

nsity

(cts

/1.5

sec)

θ−2θ (deg)

23.3 23.4 23.5 23.6 23.7 23.8 23.9 24.01

10

102

103

Data: s478_LModel: GauLor2 Equation: y=y0+A0*exp(-(0.5*((x-x0)/w0)^2))+Ac/(1+((x-xc)/wc)^2)/(1+((x-xc)/wc)^2)

y0 0 ±0A0 3388.50902 ±0x0 23.7455 ±0w0 0.00141 ±0Ac 3450 ±14.24131xc 23.669 ±0.00004wc 0.055 ±0.00015

Inte

nsity

(cts

/1.5

sec)

θ−2θ (deg)

t =13 nmt =3.9 nmt =1.5 nm


AnisotropicAnisotropicDomain & Strain RelaxationDomain & Strain Relaxation


Magnetic Free EnergyMagnetic Free Energy

[010]

[100]

M

φ-40-20 0 20 40

-1,0

-0,5

0,0

0,5

1,0

M /

Ms

H (Oe )-40-20 0 20 40 -500 0 500

-1,0

-0,5

0,0

0,5

1,0

∫=SM

m dMHf0

Magnetic free energy density:

φ = angle between magnetization and [100] K1= 48 kJ m-3 is the cubic anisotropy energy of Fe B2 = 7620 kJ m-3 is the magneto-elastic coupling coefficient of Feε6 = shear strain measured in x-ray diffraction experiment

φεπφφ 2sin2

)4

(sin2sin4

62221 Bt

KKf um +−+=

=> additional Ku/t term that favors [110] easy: Ku = 1 10-4 J m-2


(MOKE data from André Guivarch, Université de Rennes) Comparison with MOKEComparison with MOKE

t =3.9 nmt =1.5 nm t =13 nm


Conclusions on Fe / Conclusions on Fe / GaAsGaAs

⇒⇒ Considerable strain and shape anisotropies do exist Considerable strain and shape anisotropies do exist in these Fe thin filmsin these Fe thin films

⇒⇒ The interfacial effect, The interfacial effect, KKuu / / tt term, is the principal term, is the principal contributor to the observed UMA for thin Fe filmscontributor to the observed UMA for thin Fe films

⇒⇒ The strain anisotropy is the main factor responsible The strain anisotropy is the main factor responsible for the reversal of UMA at thicker Fe filmsfor the reversal of UMA at thicker Fe films


AcknowledgmentsAcknowledgments

CollaboratorsCollaboratorsin Thinin Thin--film & Nanostructure Researchfilm & Nanostructure Research

Stefan Kycia (CHESS / LNLS) Kit Umbach, So Tanaka, Jack Blakely (MSE, Cornell)

Jason Reed, Eric Tentarelli, Lester Eastman (EE, Cornell)

Hong Luo, Jacek Furdyna (U. Notre Dame)

Richard Mirin (NIST, Boulder)

Ulli Pietsch, Nora Darowski (U. Potsdam, Germany)

Olivier Thomas (U. Aix-Marseille III, France)André Guivarch (U. de Rennes, France)

Strain Effects in Thin Films and Progress in Reference-Beam PhasingTypical CrystallographyPhasing Proteins w/o Heavy Atoms ?Reference Beam Diffraction TechniqueReference-Beam Data CollectionConventional 3-Beam DiffractionSpecial Kappa DiffractometerRBD Experimental ProcedurePhase-Sensitive XRD TheoryAutomatic Curve FittingExperiment ExampleMOSFLM Indexing and IntegrationTypical Interference ProfilesResults: triplet-phase data setStrategies on Using Measured PhasesUnique Recurrence Pattern in RBDRecursive RBD Phasing AlgorithmRBD_phasing Using Measured PhasesReducing Number of Initial PhasesInverse Beam MeasurementsSummary onreference-beam phasingAcknowledgments

strain effects in thin films and progress in reference beam...

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