structure of materials- the key to its properties

8/11/2019 STRUCTURE of MATERIALS- The Key to Its Properties

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STRUCTURE OF MATERIALSSTRUCTURE OF MATERIALS

The Key to its PropertiesAAMultiscaleMultiscale PerspectivePerspective

Anandh Subramaniam

Materials and Metallurgical Engineering

INDIAN INSTITUTE OF TECHNOLOGY KANPURINDIAN INSTITUTE OF TECHNOLOGY KANPUR

Kanpur-

208016

Email: [email protected]

http://home.iitk.ac.in/~anandh

Jan 2009


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Properties of Materials

The Scale of Microstructures

Crystal Structures

+ Defects

Microstructure

With Examples from the Materials World

OUTLINEOUTLINE


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PROPERTIES

Structure sensitive Structure Insensitive

E.g. Yield stress, Fracture toughness E.g. Density, Elastic Modulus

Structure Microstructure


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What determines the properties?

Cannot just be the composition!

Few 10s of ppm

of Oxygen in Cu can degrade its conductivity

Cannot just be the amount of phases present!

A small amount of cementite

along grain boundaries can cause thematerial to have poor impact toughness

Cannot just be the distribution of phases!

Dislocations can severely weaken a crystal

Cannot just be the defect structure in the phases present!

The presence of surface compressive stress toughens glass

Composition

Phases &

TheirDistribution

Defect Structure

Residual Stress

[1]

[1] Metals Handbook, Vol.8, 8thEdition, ASM, 1973


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Nucleus Atom Crystal Microstructure Component

Defects

Length Scales Involved

Unit Cell* Crystalline Defects Microstructure Component

*Simple Unit Cells

Angstroms

Dislocation Stress fields

Nanometers Microns Centimeters

Grain Size


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Atom Structure

Crystal

Electro-magnetic

Microstructure Component

Thermo-mechanicalTreatments

Phases Defects+

Casting Metal Forming Welding Powder Processing Machining

Vacancies Dislocations Twins

Stacking Faults Grain Boundaries Voids Cracks

+

Residual

Stress

Processing determines shape and microstructure of a component

Crystalline Quasicrystalline

Amorphous

Ferromagnetic Ferroelectric

Superconducting

Property

based

Structure

based

Avoid Stress Concentrators Good Surface Finish


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Atom Structure

Crystal

Electro-magnetic


Thermo-mechanicalTreatments

Phases Defects+

Casting Metal Forming Welding Powder Processing Machining



+

Residual

Stress

Processing determines shape and microstructure of a component

Crystalline Quasicrystalline

Amorphous

Ferromagnetic Ferroelectric

Superconducting

Property

based

Structure

based

Avoid Stress Concentrators Good Surface Finish

& their distribution


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METALSEMI-METAL

SEMI-CONDUCTORINSULATOR

GAS

BAND STRUCTURE

AMORPHOUS

ATOMIC

STATE / VISCOSITY

SOLID LIQUID LIQUIDCRYSTALS

QUASICRYSTALS CRYSTALSRATIONALAPPROXIMANTS

STRUCTURE

NANO-QUASICRYSTALS NANOCRYSTALS

SIZE


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Atom Structure

Crystal

Electro-

magnetic


Why is BCC Iron the stable form of Iron at room temperature and not the FCCform of Iron?

1 Atm

G vs

T showing regions of stability of FCC andBCC Iron(Computed using thermo-calc software and database developed at

the Royal Institute of Technology, Stockholm)The Structure of Materials, S.M. Allen & E.L. Thomas, John Wiley & Sons, Inc. New York, 1999.


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Microstructure

Phases Defects+



+

Residual

Stress

This functional definitionof microstructure

includes all lengthscales


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Microstructure

Phases Defects+



+Residual

Stress


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Microstructure

Phases Defects+

Vacancies Dislocations

Twins Stacking Faults Grain Boundaries Voids Cracks

+

Residual

Stress

Microstructural

Defects (Crystalline)

Component

Vacancies Dislocations

Phase Transformation Voids

Cracks

Stress corrosion cracking

+ Residual SurfaceCompressive Stress


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CRYSTAL STRUCTURESCRYSTAL STRUCTURES


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Crystal =

Lattice (Where to repeat)+Motif (What to repeat)

Crystal =Space group

(how to repeat)

+Asymmetric unit (Motif: what to repeat)

+ =

Unit cell of BCC lattice


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Cubic

Tetragonal

Triclinic

Monoclinic

Orthorhombic

Progressive lowering of symmetry amongst the 7 crystal systems

Hexagonal

Trigonal

I

ncreasing

symmetry

Arrow marks lead from supergroups to subgroups


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1.

Cubic Crystals

a = b= c

=

=

= 90

Simple Cubic (P)

Body Centred

Cubic (I)

BCC

Face Centred

Cubic (F) -

FCC

FluoriteOctahedron

PyriteCube

m23

m4432,,3m3m,423,groupsPoint

[1] http://www.yourgemologist.com/crystalsystems.html

[2] L.E. Muir, Interfacial Phenomenon in Metals, Addison-Wesley Publ. co.

[1] [1]Garnet

Dodecahedron

[1]

Vapor grown NiO crystal

[2]

Tetrakaidecahedron(Truncated Octahedron)


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(The symmetry of) Any physical property of a crystal has at least thesymmetry of the crystal

Crystals are anisotropic with respect to most properties

The growth shape of a (well grown) crystal has the internal symmetry ofthe crystal

Polycrystalline materials or aggregates of crystals may have isotropicproperties (due to averaging of may randomly oriented grains)

The properties of a crystal can be drastically altered in the presence ofdefects (starting with crystal defects)

Crystals and Properties


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0D(Point defects)

CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY

1D(Line defects)

2D(Surface / Interface)

3D(Volume defects)

Vacancy

Impurity

Frenkel

defect

Schottky

defect

Dislocation SurfaceInterphase

boundary

Grain

boundary

Twin

boundary

Twins

Precipitate

Faulted

region

Voids /

Cracks

Stacking

faults

Disclination

Dispiration

Thermal

vibration

Anti-phase

boundaries


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0D

(Point defects)


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0D

(Point defects)

Vacancy

Impurity

Frenkel

defect

Schottky

defect

Non-ionic

crystals

Ionic

crystals

Imperfect point-like regions in the crystal about the size of 1-2 atomic

diameters

Interstitial

Substitutional

Other ~


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Vacancy

Missing atom from an atomic site Atoms around the vacancy displaced

Tensile stress field produced in the vicinity

Tensile Stress

Fields

R l ti


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Impurity

Interstitial

Substitutional

SUBSTITUTIONAL IMPURITY

Foreign atom replacing the parent atom in the crystal

E.g. Cu sitting in the lattice site of FCC-Ni

INTERSTITIAL IMPURITY

Foreign atom sitting in the void of a crystal

E.g. C sitting in the octahedral void in HT FCC-Fe

Compressive stress

fields

Tensile StressFields

CompressiveStress

Fields

Relative

size


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Interstitial C sitting in the octahedral void in HT FCC-Fe

rOctahedral

void

/ rFCC

atom

= 0.414 rFe-FCC

= 1.29

rOctahedral

void

= 0.414 x 1.29 = 0.53

rC

= 0.71

Compressive strains around the C atom

Solubility limited to 2

wt% (9.3 at%)

Interstitial C sitting in the octahedral void in LT BCC-Fe

rTetrahedral

void

/ rBCC

atom

= 0.29

rC

= 0.71

rFe-BCC

= 1.258

rTetrahedral

void

= 0.29 x 1.258 = 0.364

But C sits in smaller octahedral void-

displaces fewer atoms

Severe

compressive strains around the C atom Solubility limited to 0.008 wt% (0.037 at%)


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Equilibrium Concentration of Vacancies

Formation of a vacancy leads to missing bonds and distortion of

the

lattice

The potential energy (Enthalpy) of the system increases

Work required for the formaion

of a point defect

Enthalpy of formation (Hf

)

[kJ/mol or eV/defect]

Though it costs energy to form a vacancy its formation leads to

increase in configurational entropy

above zero Kelvin there is an equilibrium number of vacancies

Crystal Kr Cd Pb Zn Mg Al Ag Cu Ni

kJ / mol 7.7 38 48 49 56 68 106 120 168eV / vacancy 0.08 0.39 0.5 0.51 0.58 0.70 1.1 1.24 1.74

G = H

T S ln( )ConfigS k


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T (C) n/N

500 1 x 1010

1000 1 x 105

1500 5 x 104

2000 3 x 103

Hf

= 1 eV/vacancy

= 0.16 x 1018

J/vacancyG(

Gibbsfre

eenergy)

n (number of vacancies)

Gmin

Equilibrium

concentration

G (perfect crystal)

Certain equilibrium number of vacancies are preferred at T > 0K

Vacancies play a role in:

Diffusion

Climb

Electrical conductivity

Creep etc.


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1D

(Line defects)


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2

Gm

The shear modulus of metals is in the range 20

150 GPa

DISLOCATIONS

Actual shear stress is 0.5

10 MPa

I.e. (Shear stress)theoretical

> 100 * (Shear stress)experimental

!!!!

The theoretical shear stress will bein the range 3

30 GPa

Dislocations weaken the crystal


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EDGE

DISLOCATIONS

MIXED SCREW

Usually dislocations have a mixed character andEdge and Screwdislocations are the ideal extremes


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Motion of

Edgedislocation

Conservative(Glide)

Non-conservative

(Climb)

For edge dislocation: as b

t they define a plane the slip plane

Climb involves addition or subtraction of a row of atoms below the

half plane

+ve

climb = climb

up removal of a plane of atoms

ve

climb = climb

down addition of a plane of atoms

Motion of dislocations

On the slip plane

Motion of dislocation

to the slip plane


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Mixed dislocations

b

tb

Pure EdgePure screw


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Slip

Role of Dislocations

FractureFatigue

CreepDiffusion

(Pipe)

Structural

Grain boundary

(low angle)

Incoherent Twin

Semicoherent

InterfacesDisc of vacancies~ edge dislocationCreep

mechanisms in

crystalline

materials

Dislocation climb

Vacancy diffusion

Cross-slip

Grain boundary sliding


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2D

(Surface / Interface)


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Grain Boundary

The grain boundary region may be distorted with atoms belonging toneither crystal

The thickness may be of the order of few atomic diameters

The crystal orientation changes abruptly at the grain boundary

In an low angle boundary the orientation difference is < 10

In the low angle boundary the distortion is not so drastic as thehigh-angle boundary can be described as an array of

dislocations Grain boundary energy is responsible for grain growth on heating

~ (>0.5Tm

)

Large grains grow at the expense of smaller ones The average no. of nearest neighbours

for an atom in the grain

boundary of a close packed crystal is 11


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Type of boundary Energy (J/m2)

Grain boundary between BCC crystals 0.89

Grain boundary between FCC crystals 0.85

Interface between BCC and FCC crystals 0.63

Grain boundaries in

SrTiO3

T i B d


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Twin Boundary

The atomic arrangement on one side of the twin boundary is related to

the other side by a symmetry operation (usually a mirror)

Mirror twin boundaries usually occur in pairs such that the orientationdifference introduced by one is restored by the other

The region between the regions is called the twinned region

Annealing twins (formed during recrystallization)

Deformation twins (formed during plastic deformation)

Twin

[1] Transformations in Metals, Paul G. Shewmon,McGraw-Hill Book Company, New York, 1969.

Annealing twins in Austenitic StainlessSteel

[1]

T i b d i F d d S TiO bi t l ( ifi i ll d)


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Twin boundary in Fe doped SrTiO3

bicrystals

(artificially prepared)

[1] S. Hutt, O. Kienzle, F. Ernst and M. Rhle, Z Metallkd, 92 (2001) 2

Twin plane

Mirror related

variants

High-resolution micrograph


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Grain size and strength

dk

iy y

Yield stress

i

Stress to move a dislocation in single crystal

k Locking parameter (measure of the relative

hardening contribution of grain boundaries)

d

Grain diameterHall-Petch

Relation


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Defects:Defects:

Further EnquiryFurther Enquiry


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Random

DEFECTS

Structural

Based on

origin

Vacancies Dislocations Ledges

The role played by a random defect is very different from the role played by astructural defect in various phenomenon


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b

2h2

Low Angle Grain Boundaries


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No visibleGrain

Boundary

2.761

Fourier filtered image

Dislocationstructures atthe Grain

boundary

~8

TILT BOUNDARY IN SrTiO3

POLYCRYSTAL


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Random

DEFECTS

Ordered

Based on

position

Ordered defects become part of the structure and hence affect the basic symmetryof the structure

Vacancies Stacking Faults


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Crystal with vacancies

Vacancy ordering

E.g. V6

C5

, V8

C7

Effect of Atomic Level Residual Stress


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Effect of Atomic Level Residual Stress

Yield Point Phenomenon

(GPa)

x ()

y(

)

Interaction of the stress fields ofdislocations

with Interstitial atoms


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3D

(Volume defects)

&

MICROSTRUCTURES


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T.J. Konno, K. Hiraga and M. Kawasaki, Scripta mater. 44 (2001) 23032307

HAADF

micrographs of the GP zones:

(a) Intercalated monatomic Cu layers several nm in width are clearly resolved,(b) a GP-zone two Cu layers thick can chemically

be identified.

Bright field TEM micrograph of an Al-

3.3% Cu alloy, aged at room temperaturefor 100 days, showing the GP-I zones.


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Precipitate particleb

b

Hardening effect Part of the dislocation line segment (inside theprecipitate) could face a higher PN stress

Increase in surface area due to particle shearing

Pi i ff t f th i it t


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Pinning effect of the precipitate

Can act like a Frank-Reed source

rGb2~


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Controlling microstructures:Controlling microstructures:

Examples

EutecticFe-Cementite diagram


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%C

T

Fe Fe3

C

6.74.30.80.16

2.06

PeritecticL +

Eutectic

L

+ Fe3

C

Eutectoid

+ Fe3

C

L

L +

+ Fe3C

1493C

1147C

723C

Fe-Cementite

diagram

Austenite () FCC

Ferrite () BCC

Cementite

(Fe3

C) Orthorhombic

Fe3C

[1] rruff.geo.arizona.edu/doclib/zk/vol74/ZK74_534.pdf

[1]

Time- Temperature-Transformation (TTT) Curves Isothermal Transformation


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Austenite

Austenite

Pearlite

Pearlite + Bainite

Bainite

Martensite100

200

300

400

600500

800

723

0.1 1 10 102 103 104 105

Eutectoid temperature

Ms

Mf

Coarse

Fine

t (s)

T

Eutectoid steel (0.8%C)

[1] Physical Metallurgy for Engineers, D S Clark and W R Varney, Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962

[1]348C

[1]278C

Metals Handbook, Vol.8, 8th

edition, ASM, Metals Park, Ohio

[2] Introduction to Physical Metallurgy, S.H. Avner, McGraw-Hill Book Company, 1974

[2]

[2]

Time- Temperature-Transformation (TTT) Curves Isothermal Transformation


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AustenitePearlite

Pearlite + Bainite

Bainite

Martensite100

200

300

400

600

500

800

723

0.1 1 10 102 103 104 105

Eutectoid temperature

Ms

Mf

t (s)

T


+ Fe3C

Eutectoid steel (0 8%C)Different cooling treatments


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100

200

300

400

600

500

800

723

0.1 1 10 102 103 104 105t (s)

T

Waterq

uench O

ilquench

Norm

alizing

Fulla

nnea

l

e e t coo g t eat e ts

M = Martensite

P = Pearlite

Coarse P

PM M + Fine P


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% Carbon Hardness(R

c)

20

40

60

0.2 0.4 0.6

Harness of Martensite

as afunction of Carbon content

Properties of 0.8% C steel

Constituent Hardness (R c

) Tensile strength (MN / m2)

Coarse pearlite 16 710Fine pearlite 30 990

Bainite 45 1470

Martensite 65 -Martensite tempered at 250 oC 55 1990

Cooling


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C1 C2

%C

T

0.80.02

Eutectoid

+ Fe3

C

+ Fe3C

+

+ Fe3C

Fe

C3

[1] Materials Science and Engineering, W.D.Callister, Wiley India (P) Ltd., 2007.

Pro-eutectoid

Cementite

Pearlite

1.4%C [1]

3.4%C, 0.7% Si, 0.6% Mn 2.5% C, 1.0% Si, 0.55% Mn


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White CI

Grey CI

Fully Malleabilized10 m

Ferrite (White)

Graphite (black)

Malleable CI

10 m Ferritic

Matrix Ferrite

Graphite nodules

Nodular CI Ductile

3Fe C Graphite NodulesHeatTreatment

3.4% C,1.8% Si, 0.5% Mn

3.4% C, 0.1% P, 0.4% Mn,1.0% Ni, 0.06%Mg

3 3 3L ( ) ( )Ledeburite Pearlite

Fe C Fe C Fe C

Chang

e

Comp

ositio

n

0%

0.5%

12%

18%

Anisotropy in Material Properties: an example


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Texture can reintroduce anisotropy in material properties

py p p

11E

12E

1

11 12244 E EE

Cubic Crystal

(3 Elastic Moduli)

PolycrystalAnisotropic Isotropic Anisotropic

Texture

Rolling/

Extrusion

Cold Worked

Moly Permalloy: 4% Mo, 79% Ni, 17% Fe

Annealed

Textured samples

EquiaxedElongated

[1] Metals Handbook, Vol.8, 8thEdition, ASM, 1973

[1]

[1]


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CONCLUSIONCONCLUSION

To understand the properties of materials theTo understand the properties of materials the

structurestructure at many differentat many different lengthscaleslengthscales mustmust

be viewedbe viewed


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Ionic Crystals


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Ionic Crystals

Overall electrical neutrality has to be maintained

Frenkel

defect

Cation

(being smaller get displaced to interstitial voids

E.g. AgI, CaF2

Schottky defect


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Schottky

defect

Pair of anion and cation

vacancies E.g. Alkali halides

Other defects due to charge balance


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g

If Cd2+

replaces Na+

one cation

vacancy is created

Defects due to off stiochiometry

ZnO

heated in Zn vapour

Zny

O

(y >1)

The excess cations

occupy interstitial voids

The electrons (2e) released stay associated to the interstitial cation


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FeO

heated in oxygen atmosphere Fex

O

(x


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Cubic48

Tetragonal16

Triclinic2

Monoclinic4

Orthorhombic8

Progressive lowering of symmetry amongst the 7 crystal systems

Hexagonal24

Trigonal12

Increasing

symmetry

Superscript to the crystal system is the order of the lattice point group

Arrow marks lead from supergroups to subgroups


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structure of materials- the key to its properties

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