solidstate physics

7/29/2019 solidstate physics

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Whats this course about?

earn ng ec ves To introduce what this course is about.

To introduce the concepts of deformation and failure.

To introduce the assumptions used in mechanics.

To introduce the fundamental aspects of deformation.

Prof. M.L. Weaver


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IntroductionIntroduction

As engineers we use materials for various purposes.

All materials have structures that can be defined atvarious length scales.

Structure can have a large influence on properties,

, .

Perhaps nowhere is this more important than in

mechanical properties.

Prof. M.L. Weaver

In this course we will address the linkages between the

structures of materials and their mechanical properties.


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IntroductionIntroduction

All engineered structures must endure mechanical loads.

components properly and/or selecting materials for a givenapplication to satisfy specific performance criteria.

us, or mos eng neers, a e a e un ers an ng o e

influences of microstructure on properties is secondary.

applying physical processes that occur within a material during

mechanical loading to satisfy specific performance criteria.

It is critical that engineers understand both approaches. In

a few pages I will demonstrate why using a series of

Prof. M.L. Weaver

.


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Mechanical Properties / Mechanical BehaviorMechanical Properties / Mechanical Behavior

Addresses how materials respond to forces/loads.

Macro-scale Solid mechanics

Micro-scaleMicromechanics

Nanomechanics -

This sub ect involves the a lication of mathematics

chemistry and physics.*

Prof. M.L. Weaver

*The reader is referred to Chapter 1 inMechanics and Materials: Fundamentals and Linkages (JohnWiley & Sons, 1999). This chapter describes the linkage between mechanics and materials.


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Pertinent length scales in materials and structuresPertinent length scales in materials and structures

DETERMINE PROPERTIES AT THESE LENGTH SCALES

-

100

100

-

100

Sheet

polycrystalline

continuum

I-beam or other

structural memberEngineered structure

1000100

nano-scale

2.3 1.0 m 40 m

micro-scale

Atomic structure

Dislocation and solute

elastic fields

meso-scale

Grains and

precipitates

Prof. M.L. Weaver

Figure Relative length scales for a typical structural materials spanning thirteen orders of magnitude. Figure derived fromR.H. Wagoner and J-L. Chenot, Fundamentals of Metal Forming, (John Wiley & Sons, New York, 1996) p. 93.

STRUCTURAL DEFECTS AT THESE LENGTH SCALES


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Pertinent length scales in materials and structuresPertinent length scales in materials and structures

Mesolevel

MATERIALS STRUCTURES INFRASTRUCTURE

Nanolevel Microlevel Macrolevel S stems

integration

Molecular scale Microns Meters Up to km scale

Mesomechanics

Interfacial structures

Com osites

Nanomechanics

Self-assembly

Nanofabrication

Micromechanics

Microstructures

Smart Materials

Beams

Columns

lates

Bridge systems

Lifelines

Air lanes

Etc.Etc. Etc. Etc. Etc.

. . , . . , . . , ,3rd Edition, (John Wiley & Sons, New York, 2010) p. 7.

Mechanical behavior s ans all len th scales. Therefore,

Prof. M.L. Weaver

we need to understand how all length scales link together.


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Lets start with a very general discussion

of how materials res ond to loadin

Prof. M.L. Weaver


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What types of forces actWhat types of forces act

Surface forces/ loads: forces from contact

r c on,

point load,

etc

Volume forces/ loads: forces that act over the entire body

,

magnetic forces,

etc

Surface forces are usually more significant than volume

forces; but there are exceptions

Prof. M.L. Weaver

can you think of any?


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Different categories of surface forcesDifferent categories of surface forces

Static: Independent of time.

Constant in magnitude,

Constant in direction,

Constant in location.

Quasi-static: Vary slowly with time.

Dynamic: Vary with time

Stead -state maintain the same character fre uenc ,

amplitude, etc.) over a long time.

Transient change their character with time (e.g., decay).

Prof. M.L. Weaver


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What happens to a material or structure when itWhat happens to a material or structure when itis exposed to mechanical or thermal loading?is exposed to mechanical or thermal loading?

Deformation Fracture1 2

Macroscopically

Macroscopically

Etc. ???

In general these processes are not mutually

exclusive.

Prof. M.L. Weaver


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What is deformation?What is deformation?

Shape

Change

CATEGORIES of DEFORMATION:CATEGORIES of DEFORMATION:

Viscoelastic*

*

Elastic*

*

Prof. M.L. Weaver


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TimeTime--independent deformationindependent deformation

1. Elastic deformation: reversible deformation.

Analogous to the stretching of atomic bonds.

Hookes law applies: =E.

2. Plastic deformation: permanent deformation.

NOT recovered upon unloading.Begins at the proportional limit. At this point the material is said to

o

Hookes law fails.

Prof. M.L. Weaver

between and .


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TimeTime--dependent deformationdependent deformation

3. Creep / viscoplastic: permanent deformation.

.

Occurs at high homologous temperatures (i.e., T/Tmp 0.4).

n a ma er a a s su ec e o a cons an oa or s ress a s

often far below the yield point.

4. Viscoelastic: reversible deformation.

e orma on s recovere over a per o o me.

Rubbery behavior.

Prof. M.L. Weaver

This behavior is exhibited by all materials (at some level).


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What is fracture?What is fracture?

When something

separates into pieces.

CATEGORIES of FRACTURE:CATEGORIES of FRACTURE:

High cycle fatigue

Low cycle fatigue

Brittle

Ductile / ductile rupture

a gue crac growCorrosion fatigue

reep rup ureEnvironmental

Prof. M.L. Weaver


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How do we classify fractures?How do we classify fractures?

1. Ductile: lots of plastic deformation prior to

rac ure.

2. Brittle: little or no plastic deformation prior

to fracture.

Prof. M.L. Weaver


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Is fracture the same as failure?Is fracture the same as failure?

NOT NECESSARILY!

Failure = n hin h mi h m n n

to lose its structural tolerances, thus preventing itfrom serving its intended purpose.

Generally this means:(i) fracture,

(ii) or plastic deformation,

or excess ve e as c e orma on.

Prof. M.L. Weaver

We design and select materials to avoid failure.


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StressStress--dependent modes of failuredependent modes of failure

Elastic ta ePlastic

Excessive deformationElastic (buckling)(static loading)

,

Creep (collapse, buckling)Excessive deformation Increment

al collapse

Brittle fractureFracture

Low-stress brittle fracture(static loading)

Fracture Fatigue(cyclic loading)

, , ,o so e y s ress-dependent stress corrosion

Creep and fatigue (cyclic creep)Combined modes

Prof. M.L. Weaver

a gue o owe y ow-s ress r e rac ure

Table adapted from B. Derby, D. Hills, and C. Ruiz, Materials Engineering: A FundamentalDesign Approach, (Longman Scientific & Technical, Essex, UK, 1992) p. 8.


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Engineers approach for explainingEngineers approach for explaining

1. Strength of materials / Continuum mechanicsa. Stress

b. Strain

.

d. Plasticity

2. Micromechanics / Material physicsa. Consider properties of constituents

i. Grain orientations / texture

ii. Crystal / atomic structureiii. Defect content

Prof. M.L. Weaver

. .


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Engineers Approach to Mechanical BehaviorEngineers Approach to Mechanical Behavior

material response. (statics, dynamics, and strength ofmaterials, etc.).

Applied regularly in engineering design. Very useful and

eas ! Finite element n l sis/modelin b sed on this

The advantages are that relatively few constants are

nee e o pre c mec an ca e av or .

Prof. M.L. Weaver


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General assumptionsGeneral assumptions

The member is in s i e ilibri m Fi=0; Mi=0 (external forces = internal resisting forces)

The body is continuous It contains no voids, holes, or spaces.

The body is homogeneous It has properties that are identical at any point

e o y s so rop c Properties dont vary with direction or orientation.

Prof. M.L. WeaverAllows for simple mathematical treatment in design


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Problems with general assumptionsProblems with general assumptions

The member is in s i e ilibri m Fi=0; Mi=0 (external forces = internal resisting forces)

The body is continuous It contains no voids, holes, or spaces.

ALL materials contain flaws on some level.

The body is homogeneous It has properties that are identical at any point

ALL materials and structures contain local inhomogeneities.

e o y s so rop c Properties dont vary with direction or orientation.

Prof. M.L. Weaver

.


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Engineers ApproachEngineers Approach contd.contd.

Problem: general theories break down when the atomicna ure o ma er a s .e., ma er a s ruc ure s n ro uce .

Examples:

Generation and accumulation of dislocations leads to hardening.

Creep (a form of high temperature deformation). Microstructurechanges with time.

Stress concentrations at crack tips. Local stress may be higher

.

Ductile-to-brittle transition temperature (DBTT) in steels due to .

Fundamental changes in the material behavior cause a brittle

Prof. M.L. Weaver

solid to function like a plastic material.

Etc.


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Engineers ApproachEngineers Approach contd.contd.

In spite of the deficiencies, strength of materialsapproaches are still usedin engineering design.

,

material forlong term application, the structureof the

material must be considered(at some level).

Macrostructure ( 1)

Microstructure ( 106)

9

All are important!

Prof. M.L. Weaver


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FundamentalFundamental Areas of StudyAreas of Study

Elasticity

Plasticity

Fracture

Fatigue

Creep

Prof. M.L. Weaver


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Lets consider a couple of real materials

roblems to ut thin s into ers ective

Prof. M.L. Weaver


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Process Engineering ProblemProcess Engineering Problem

You are a process engineer at a metal stamping plant thatproduces cans from 304L stainless steel. You produce 20cans/minute. First 1000 cans form perfectly. Ten of the next200 cans failduring stamping. Then, 25 of the next 200 fail.

After that, 100 of the next 200 fail. Production issummarized in the table below.

# cans total # cans #failures, ,

200 1,200 10

200 1 400 25

200 1,600 100

Prof. M.L. Weaver

What is the cause for these failures? What is the solution?


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Whats going on?Whats going on?

Deformation characteristics change with time.

Dislocation generation and motion;

or ar en ng;

Heating/cooling during processing:

Phase transformations (Ms, Mf martensitic);

Change in deformation behavior;

Transformation induced plasticity.

Prof. M.L. Weaver


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Whats going on?Whats going on? contdcontd

Die temperature rises above the Ms temperature during

.

wor ar en ng ra e ur ng process ng.

the amount of uniform plastic elongation; but, also

makes it more difficult to deform the material uniformly.

The solution involves physical metallurgy and intrinsic

Prof. M.L. Weaver

ma er a s proper es, mec an cs, an process ng me o .


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Materials Engineering ProblemMaterials Engineering Problem

Produced via powder

W light bulb filaments

metallurgy.

The filaments fail after a fewthousand hours.

Can we do anything to

Prof. M.L. Weaver

P. Schade, 100 years of doped tungsten wire,International Journal of Refractory metals and Hard

Materials, 28 (2010) 648-660

lifetimes?


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Whats happening?Whats happening?

1. The filament can cree under its

(a)

own weight leading to sagging(see picture on next page).

the sag or shorting due to thetouching of adjacent coils.

can also lead shorting.WEIGHT

(b)

2. Microstructure also changes dueto recrystallization duringservice and can lead to failure.

3. Evaporation can lead to filament(a) The statics of a horizontal light bulb filament. (b) The creep-failure

Prof. M.L. Weaver

nn ng an e eve opmen ohot spots. (corrosion!)

of a tungsten filament. Torsional creep causes the windings to touch,causing overheating or shorting. Figures adapted from H.J. Frost andM.F. Ashby, Deformation-Mechanism Maps, (1982) Pergamon Press,

Oxford, England, pp. 150-153.


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Sagging of an un-doped W filament.

No sagging in adoped W filament.

Non-interlockedgrain structure

Interlocking grainstructure prevents

promotes sag.sag.

Prof. M.L. Weaver

Figures from J.R. Davis editor,ASM Specialty Handbook on Heat-Resistant Metals (ASM

International, Materials Park, OH, 1997) p. 370.


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Whats happening?Whats happening? contdcontd

Drawn wire has fine-grained microstructure w/ grains elongated in the drawing

ecrysta zes- rawn

rec on.

After high temperature exposure, pure W wires recrystallize producing abamboo structure (i.e., grains w/ diameters = wire diameter, grain lengths >>

wire diameter, and grain boundaries essentially perpendicular to the wire axis). Under the stress produced by gravity, these boundaries can slide past one

another via diffusion related mechanisms i.e. cree leadin to ra id failure.

Prof. M.L. Weaver

Figures from C.J.M. Denissen, J. Liebe, and M. van Rijswick, International Journal ofRefractory & Hard Materials, 24 (2006) pp. 321-324.


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1 m

(c)

0.2 m

Micrographs of undoped tungsten. TEM micrographs of (a) as-drawn wire and (b) following annealing at1300C. Note that annealing has resulted in abnormal grain growth. (c) Optical micrograph of hot pressed

-

100 m

Prof. M.L. Weaver

. . .Snow, Metallurgical Transactions A, 10A (1979) 815-821. Figure (c) from P. Szozdowski and G. Welsch,Scripta Materialia, 41 (1999) pp. 1241-1245


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Gravity

Fig. 14.12 Offsets in an undoped W filament caused by prolonged operation at high temperatures.Grain growth followed by grain boundary sliding leads to premature burnout of the filament.Figure adapted from A.M. Russell and K.L. Lee, Structure-Property Relations in NonferrousMetals, (John Wiley & Sons, Hoboken, NJ, 2005) p. 241.

Prof. M.L. Weaver


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W en a g t u s turne on, t e ament un ergoesthermal expansion along its length. This expansion istransient and non-uniform.

Leads to a tensile force along wire length a force GBs.

After a long enough period of operation, the force will

become large enough to cause intergranular fracture ofthe filament.

Prof. M.L. Weaver

S l tiS l ti


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SolutionSolution

H W D WE LVE THE PR BLEM

n creep an recrys a za on.

.Insoluble in W. Forms bubbles along GBs (see next page).

These bubbles inhibit normal recrystallization of the W wire,leading to the development of an interlocked grain structure thatinhibits grain boundary sliding and increases creep resistance [2].

e mages on t e next ew pages eta t s.[1] J.L. Walter and C.L. Briant, Tungsten wire for incandescent lamps, Journal of Materials Research, 5

Prof. M.L. Weaver

pp. - .[2] C.L. Briant, O. Horacsek, and K. Horacsek, The effect of wire history on the coarsened substructure

and secondary recrystallization of doped tungsten, Metallurgical Transactions A, 24a (1993) 843-851.

SolutionSolution contdcontd


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SolutionSolution cont dcont d(a) (b)

0.2 m

(a) Scanning electron micrograph of the fracture surface of a K-doped W ingot after initial sintering butbefore drawing into fine wire. The larger voids (~1 m) are ordinary sintering pores. They are empty

and will collapse during swaging and wire drawing. The smaller defects (~100 nm) are K bubbles thatformed during initial sintering. These smaller bubbles will also collapse during subsequent cold work,

but they contain minute amounts of solid K that will elongate during the swaging and wire drawing. (b)TEM micrograph showing the bubble arrangement in doped W wire. When the light bulb filament is

Prof. M.L. Weaver

first turned on, these needle-shaped K phases vaporize, forming a string of 10 nm diameter bubbles thatpin grain boundaries and prevent filament sag. Figures adapted from C.L. Briant, O. Horacsek, and K.

Horacsek, Metallurgical Transactions A, 24 (1993) 843-851. Figure (b) from

Wh t h i ?Wh t h i ? tdtd


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Recrystallized structure of W wires.

(a) Doped lamp grade exhibiting (a) 100 m.

(b) Undoped grade exhibiting equiaxedstructure and the beginning of abnormalb 100 m.

(c) Finger-like grain growth in doped Wwire.

Figure adapted from J.R. Davis, editor;ASM Specialty Handbook on Heat-

, ,

Materials Park, OH, 1997) p. 370.

Prof. M.L. Weaver

(c) 100 m


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A Typical Materials Selection ProblemA Typical Materials Selection Problem

Engineers designing computer systems for long-term

era microprocessors as opposed to modern ones.

y

Are there solutions that could potentially allow the

acro- an m cro- ruc ures p ay a ro e

use of modern microprocessors?

Prof. M.L. Weaver

S l tiS l ti


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SolutionSolution

(see ref. [1] for an introduction).

ntense an pro onge rra at on pro uces po nt e ects .

Can impede dislocation motion and hardens the material,

Can agglomerate to form dislocation loops and voids.

When present, point, line, and volume defects degrade theperformance of semiconductor devices.

[1] A.M. Russell and K.L. Lee, Structure-Property Relations in Nonferrous Metals, JohnWile & Sons Hoboken J 1990 . 98-100.

Prof. M.L. Weaver

[2] G.S. Was, Fundamentals of Radiation Materials Science, Springer, New York, NY (2007).

S l tiS l ti tdtd


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SolutionSolution contdcontd

o ern m croprocessors ave muc sma er eature s zes t an smicroprocessors.

Makes them more susceptible to failure due to solar flare radiation and

cosmic rays.

As a result, older technology is generally incorporated into spacecraft.

An account is rovided in Ref. 3 . This a er summarizesobservations from NASAs Galileo program. This paper is worthreading! (Sometimes you can learn more from old papers than

[3] F.L. Bouqet, W.E. Price, and D.M. Newell, Designers guide to radiation effects onmaterials for use on Ju iter fl -b s and orbiters IEEE Transactions on Nuclear Science v.

Prof. M.L. Weaver

NS-26, n. 4 (1979) pp. 4660-4669.


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What does it mean?What does it mean?

Must take in to account more than continuum

.

Must consider structures of materials.

Sometimes structures change in service. Thus propertiescan change. Must be accounted for.

-

performance is concerned.

Prof. M.L. Weaver

solidstate physics

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