New ОСНОВЫ СПАРК ПЛАЗМЕННОГО СПЕКАНИЯlemc-lab.mephi.ru/content/file/news/olevsky_0.pdf · 2013. 6. 17. · ОСНОВЫ СПАРК-ПЛАЗМЕННОГО

ОСНОВЫ СПАРК-ПЛАЗМЕННОГО СПЕКАНИЯ

FUNDAMENTALS OF SPARK-PLASMA SINTERING

ОЛЕВСКИЙ ЕВГЕНИЙ АЛЕКСАНДРОВИЧ

EUGENE A. OLEVSKY

2й Научный семинар «Перспективные технологии консолидации материалов

с применением электромагнитных полей»

Москва, 20-23 мая 2013 г.

Лаборатория Электромагнитных Методов Производства Новых Материалов

Национальный Исследовательский Ядерный Университет «МИФИ»

San Diego State University, USA

Powder Technology Laboratory

FUNDAMENTALS OF SPARK PLASMA SINTERING:

INTRODUCTION

SPS PUBLICATION STATISTICS

Web of Science

Overwhelming majority of ~ 3000 refereed publications on SPS describe empirical

trial-and-error attempts to consolidate various powder material systems.

About 80 publications include theoretical studies. In our publications*, sintering

constitutive equations are expanded to include the contribution of SPS-specific

factors.* E. Olevsky and L. Froyen, Constitutive modeling of spark-plasma sintering of conductive materials, Scripta

Mater., 55, 1175-1178 (2006)

E. Olevsky, S. Kandukuri, and L. Froyen, Consolidation enhancement in spark-plasma sintering: Impact of

high heating rates, J. App. Phys., 102, 114913-114924 (2007)

E. Olevsky and L. Froyen, Influence of thermal diffusion on spark-plasma sintering, J. Amer. Ceram.

Soc., 92, S122-132 (2009)

E. Grigoryev and E. Olevsky, Thermal Processes during high voltage electric discharge consolidation of

powder materials, Scripta Mater. , 66, 662-665 (2012)

W. Li, E. A. Olevsky, J. McKittrick, A. L. Maximenko, and R. M. German, Densification mechanisms of spark

plasma sintering: multi-step pressure dilatometry, J. Mater. Sci., 47, 1-11 (2012)

Citations in Each Year

as of Summer 2010 as of Fall 2012

W. L. Voelker, Improvements in the Manufacture of Filaments of Incandescing Electric

Lamps and in Means applicable for use in such Manufacture, GB Patent 6149 (1899)

Moscow Engineering Physics University San Diego State University

Field-Assisted Powder Consolidation

High-Voltage Techniques Low-Voltage Techniques

High Vs. Low Mode Field-Assisted Techniques

< 300 s Up to 30kV 500 kA/cm2

High-Voltage Electric Discharge Compaction

< 50 kN < 10V < 1500 A

Spark-Plasma Sintering

HVEDC PUBLICATION STATISTICS

В. Д. Деменюк, М. С. Юрлова, Л. Ю. Лебедева, Е. Г. Григорьев, Е. А. Олевский, Методы

электроимпульсной консолидации: альтернатива спарк-плазменному спеканию, Ядерн. Физ.

Инжин. (2012) – в печати

Олевский Е.А., Александрова Е.В., Ильина А.М., Новоселов А.Н., Пельве

К.Ю, Григорьев, Е.Г., Исследования процессов консолидации порошковых материалов

пропусканием электрического тока, проводившиеся на территории бывшего Советского

Союза, Физ. Хим. Обраб. Матер. (2012) – в печати

cleaner grain boundaries in sintered ceramic materials

a remarkable increase in superplasticity of ceramics

higher permittivity in ferroelectrics

improved magnetic properties

improved electrical properties

improved bonding quality

improved thermoelectric properties

reduced impurity segregation at grain boundaries

improved oxidation and corrosion resistance

improved optical transmission

SPS promotes:

SPS process: unique capabilities to densify

nanostructured ceramic, intermetallic and composite

materials in bulk form.

SPS-processed

(SDSU) TaC

powder specimen:

99% dense;

maximum

temperature

2300°C;

maximum pressure

50 MPa;

SPS time – 8 min

Microstructure of TaC specimens fabricated by spark plasma

sintering

E. Khaleghi, Y.-S. Lin, E. Olevsky, and M. Meyers, Spark plasma sintering of tantalum carbide, Scripta

Mater., 63, 577-580 (2010)

A bulk nanocrystalline Al–5 at.% Fe alloy was synthesized by mechanical

alloying and spark plasma sintering. The alloy exhibited a very high

compressive yield strength of 1 GPa with a plastic strain of 0.3. The alloy

consists of coarse α-Al grains that form from powder boundaries and

nanocrystalline regions composed of α-Al and Al6Fe phases. The

combination of the coarse and nanoscale grains are considered to be the

reason for the large plastic strain in such a high-strength material.

A high-strength bulk nanocrystalline Al–Fe alloy processed

by mechanical alloying and spark plasma sintering

spark plasma sintered Al–5 at.% Fe alloy.SEM image of the alloy that was deformed to a

strain of 0.08. This micrograph indicates the

coarse α-Al grains were mainly deformed.

E. Olevsky, S. Kandukuri, and L. Froyen, Consolidation enhancement in spark-plasma sintering: Impact of high heating rates, J. App.

Phys., 102, 114913-114924 (2007)

The SPS was carried out in an argon atmosphere at 1850 C and 100 MPa

Debrupa Lahiri, Evan Khaleghi, Srinivasa Rao Bakshi, Wei Li, Eugene A. Olevsky, and Arvind Agarwal, Graphene-

induced strengthening in spark plasma sintered tantalum carbide–nanotube composite, Scripta Materialia 68 (2013)

285–288

Graphene-induced strengthening in spark plasma

sintered tantalum carbide–nanotube composite

Fracture surfaces for TaC, TaC–LC and TaC–SC

High-magnification SEM micrographs

of TaC–SC fracture surface revealing:

(a) transformed graphene platelets with

straight edges; (b) graphene platelets

sandwiched at TaC grain boundaries; (c)

pulledout graphene platelet forming a

strong interface with the TaC matrix

SEM OF FRACTURE SURFACES: HUMAN DENTIN

Longitudinal

Transverse

Collagen fibers

Micro-channels

1µm

SPS 1200C, 50MPa, 5min

SPARK-PLASMA SINTERING OF HAP POWDER

Hydroxyapatite(Ca10(PO4)6(OH)2), 0.5

Melting point: 16700C, density: 3.14g/cm3

The main component in human bones and teeth

SEM IMAGES OF MICRO CHANNEL STRUCTURE AFTER FPSPS

The channel diameters decrease with the increase of the initial slurry concentration

100µm

15vol%

20µm

15vol%

100µm

20vol%

20µm

20vol%

100µm

25vol%

25vol%

20µm

Y.-S. Lin, M. A. Meyers, and E. A. Olevsky, Microchannelled hydroxyapatite components by sequential freeze drying and

free pressureless spark plasma sintering, Adv. App. Ceram., 111, 269-274 (2012)

SPS-FPSPS PROCESSING SEQUENCE

Complex shape HAp-based dental

implant prototype produced by SPS-

FPSPS sequence

FPSPSSPS

500nm500nm 500nm

Y.-S. Lin, M. A. Meyers, and E. A. Olevsky, Microchannelled hydroxyapatite components by sequential freeze drying and

free pressureless spark plasma sintering, Adv. App. Ceram., 111, 269-274 (2012)

H2 H2H2

Representation of adsorption bed settling, based on observations by:

[Qin et. al, 2000, Collins et. al, 2007, and Ubago-Pérez et. al, 2006].

Adsorbent

ہ Activated Carbon from Biomass Sources

ہ Structural stability; prevent reduction of system efficiency

ہ Material Parameter Focus: Specific Surface Area

250 µm

Optical micrograph of 40MPa SPS SiCNW-AC compostie

20 µm 5 µm

ہ Conventional SPS of SiCNW-AC Composite

ہ 50C/min to 1300C, 15min hold in vac.

ہ Structurally stable sample of thickness

Comparative Analysis of SSA Values

ہ Lack of SSA retention under pressure-assisted conditions

ہ Significant structural stability in both cases

ہ Additional SSA retention with SiC-AC composite

SSA data for the precursor material and the SPS consolidated SiC-AC compact

ہ Enhanced low pressure and porosity control

ہ Potential application to reactive SPS systems

ہ Significant tool for study of fundamental SPS mechanisms

Design and demonstration of a novel FPSPS

method

15 and 10mm FPSPS dies with unsintered and sintered zirconia spacers respectively

As produced CNW structures – morphologies marked by arrowsPlatelet CNF structures – interstitial spacing marked by arrows

Nanofiber and Nanowire Morphology3-D CNF Textured Structure

Fe and Mg content observed by analyzing the center of the nanowire structure.

Tailoring Nano-scale Synthesis Template Properties

Nanowire cluster characterization reveals presence of Mg, Ca, and K.

Biomass is carbon source for CNF growth, initiated by inherent metallic particles.

Synthesized during processing of AC biomass templatesPlatelet CNF and CNW growth may increase specific surface area, interstitial spacing and preferential adsorption of hydrogen.

W. Bradbury and E. Olevsky, Synthesis of carbide nano-structures on monolithic agricultural-waste biomass-activated carbon

templates, Int. J. App. Ceram. Techn., 8 [4] 947–952 (2011)

Nanoscale necking between monolithic AC-stalk materials

Stable 3-D 10mm SiC-AC Sample

ہ Significant Structural Enhancement

ہ Production of stable porous compact

FPSPS Processing of Biomass-Derived Silicon Carbide

W.L. Bradbury and E.A. Olevsky, Scripta Materialia, Production of SiC-Ccomposites by free-pressureless spark plasma sintering (FPSPS), 63 [1](July, 2010) 77-80.

Comparative Analysis of SSA Values

ہ Improved SSA retention under pressure-less conditions

ہ Significant structural stability obtained

SSA data for the precursor material, SPS and FPSPS SiC-AC compacts

High-Voltage Electric Discharge Consolidation:

Manufacturing of Pressing Tools with High Wear Resistance

Specimen WC, diameter 9мм

J = 90 кА/см2, P = 200 МPаSpecimen WC, diameter 9мм

J = 90 кА/см2, P = 130 МPа

Steel Р6М5,

J = 256 кА/см2, P = 350 МPа

Steel Р6М5,

J = 296 кА/см2, P = 350 МPа

Specimen WC, axial cross-section:

High-Voltage Electric Discharge Consolidation: Structure

Inhomogeneity and Control

E. Grigoryev and E. Olevsky, Thermal Processes during high voltage electric discharge consolidation of powder

materials, Scripta Mater. , 66, 662-665 (2012)

Flash Sintering Experimentation

u Performed by Rishi

Raj et.al.

u Yitria stabilized

Zirconia powder

u Vertical Tube Furnace

u Dog bone specimen

u Pt Electrodes

u Shrinkage recorded

via CCD camera

Pt Electrode

Tube FurnaceSpecimen

Flash Sintering Results

u Sintering rate depends on

applied electric field

u Sintering rate becomes

unstable ~40V/cm

u Small particle contacts

necessary for flash

sintering to occur

Source: Flash Sintering of Nanograin Zirconia in o5 s at

8500C, Rishi Raj et. al., J. Am. Ceram. Soc., 93 [11] 3556–

3559 (2010)

SPS: ENHANCEMENT OF MASS TRANSPORT

electromigration

(diffusion enhancement)

electroplasticity

(electron wind,

magnetic depinning of

dislocations)

dielectric breakdown of

oxide films at grain

boundaries

ponderomotive forces

“pinch effect”

surface plasmons

Field Effects in SPS

high heating rates

high local non-

uniformities of

temperature distribution

(local melting and

sublimation)

macroscopic

temperature gradients

thermal diffusion

thermal stresses

Thermal Effects in SPS


INFLUENCE OF HIGH HEATING RATES

Micromechanical Model

E. A. Olevsky, B. Kushnarev, A.

Maximenko, V. Tikare and M.

Braginsky, Modelling of

anisotropic sintering in crystalline

ceramics, Philosophical Magazine,

85, (19), 2123-2146 (2005)

2

p

a

p

cr

a

2

p

c

p

ar

c

2

1 2 3x x x xb y b y b

2

1 2 3y y y yb x b x b

0

sin2

ap

xx

c cdx c

c

( ) ;xc

cr

0 0 0xx yy

22 33 1 1 3 3 1 1 3

sin sin2 2 2 2 2 2 2

x xx p p

c c

c c y c cc r c c c r c

where is the surface tension, is the dihedral angle, a and c

are the grain semi-axes; x - effective (far-field) external stress in

the x-direction (compressive x is negative). Parameter

px

c c

c

is a local stress on the grain boundary (

pc c

c

is the

stress concentration factor).

23 1 1

sin2

gb gb pxgbx

cp p

D c c

kT c r c ca a c c

gb gbgb xy

DJ

kT y

( )

2

gb

y

gbx

p p

J c

a a c c

gb

yJ is the flux of matter in the direction of the

axis y caused by the grain boundary diffusion,

gbD is the coefficient of the grain boundary

diffusion, gb is the grain boundary thickness,

k – Boltzman constant; T – absolute temperature.

Influence of High Heating Rates

E. Olevsky, S. Kandukuri, and L. Froyen, Consolidation

enhancement in spark-plasma sintering: Impact of high

heating rates, J. App. Phys. 102, 114913-114924 (2007)

For an aluminum alloy

powder

, ,x gbx crx f G

4

22

4 2

31 1 1

8

s sD

kTG

x

θ= e= ε

1-θ

3

1.3400

fd GG GG

G is the porous material’s grain growth rate, 0fdG

is the grain growth rate of the fully-dense material

with the grain size 0G , 0G is the initial grain size of

the porous (powder) material

Du and Cocks

4 16.67 10 3.55 10

0

fd fd TG G t

Beck et al. fdG is the current grain size of the fully-dense material; 0

fdG is the initial grain size of the fully-

dense material; t is time, s; and T is temperature, K

3

4 1.3400

1 235 /6.67 10 ln , 533

0, 533

GK sG if T K

G K G

if T K

dT

dt = const is the heating rate, K/s

Influence of High Heating Rates

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 1000 2000 3000

Time, s

Po

ros

ity

200C/min

100C/min

50C/min

25C/min

10C/min

For aluminum powder


INFLUENCE OF THERMAL DIFFUSION

Influence of Thermal Diffusion

J is the vacancy flux, D is the coefficient of diffusion, vC is the vacancy concentration,

vC is the vacancy concentration gradient, *Q is the heat of vacancy transport, T is the

temperature gradient.

*

v v

Q TJ D C C

kT T


Ludwig-Soret effect of thermal diffusion causes

concentration gradients in initially homogeneous two-

component systems subjected to a temperature gradient.J. Chipman, The Soret effect, Journal of the American Chemical Society, 48, 2577-2589 (1926)

For the case of atomic and vacancy diffusion in crystalline

solids, this effect was studied by a number of authors

including it’s theoretical interpretation by Shewmon and

Schottky.P. Shewmon, Thermal diffusion of vacancies in zinc, Journal of Chemical Physics, 29, (5), 1032-1036 (1958)

G. Schottky, A theory of thermal diffusion based on lattice dynamics of a linear chain, Physica Status Solidi, 8, (1),

357 (1965)

For the electric-current assisted sintering, the effect of

thermal diffusion was analyzed by Kornyushin and co-

workers. Later, for rapid densification, the role of

temperature gradients was studied by Searcy and by Young

and McPherson.Y. V. Kornyushin, Influence of external magnetic and electric-fields on sintering, structure and properties, Journal of

Materials Science, 15, (3), 799-801 (1980)

A. W. Searcy, Theory for sintering in temperature-gradients - role of long-range mass-transport, Journal of the

American Ceramic Society, 70, (3), C61-C62 (1987)

R. M. Young and R. McPherson, Temperature-gradient-driven diffusion in rapid-rate sintering, Journal of the

Influence of Thermal DiffusionJ is the vacancy flux, D is the coefficient of diffusion, vC is the vacancy concentration,

vC is the vacancy concentration gradient, *Q is the heat of vacancy transport, T is the

temperature gradient.

*

v v

Q TJ D C C

kT T

2

v fC HC T

kT

*v fDC T

J H QkT T

*

m fQ H H

Schottky:

Young &

McPherson:

Wirtz:

Kornyushin:

mH is the enthalpy of vacancy migration;

fH is the enthalpy of vacancy formation

vm

DC TJ H

kT T

;

v m f TT

C H HJ D T

k T T

did not include the term vC ! Otherwise:

T is the thermal diffusion ratio ( T is

the spatial average of temperature)

v mT

C H

k T We re-define:

TdivJ D TT

The driving force for

the vacancy migration:

T

TT q

dt

C

Heat transfer equation:

T is the thermal conductivity; C is heat capacity; t is time; and q is the

heat production per unit volume of the material and per unit time, which in the case of SPS can be represented as

2

eq E , where e is the specific

electric conductivity, and E is the electric field intensity 2T

e

T

TdivJ D E

T t

C


22 2gb Ttd gb gb eT

TJ divJ G D E G

T t

C2T e

T

TdivJ D E

T t

C

2

2 2

2

gbgb gb Ttd td

gbx e

Tp p

DJ T GE

T tG r G r

C

_ ,gbx gbx

curvature driven th diffusion driven

x crx f G

x

θ= e= ε

1-θ

3

10 1.3401.5 10 /G

G m sG

E. Olevsky and L. Froyen, Influence of thermal diffusion on spark-plasma sintering, J. Amer. Ceram. Soc. 92, S122-132 (2009)

T is the thermal conductivity; C is heat capacity; t is time; and q is the

heat production per unit volume of the material and per unit time, which in the case of SPS can be represented as

2

eq E , where e is the specific

electric conductivity, and E is the electric field intensity

is porosity; G is the average grain size


25

125

225

325

425

525

625

0 200 400 600 800 1000

Time, s

Te

mp

era

ture

, C

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Po

ros

ity

Temperature

Porosity - Model

Porosity - Experiment

25

207

389

571

753

936

1118

1300

0 70 141 211 281 352 422

Time, s

Te

mp

era

ture

, C

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Po

ros

ity

Temperature

Porosity - Model

Porosity - Experiment

Porosity kinetics during SPS of aluminum

powder. Comparison of the developed model

taking into account the impact of thermal

diffusion with experimental data of Xie et al.,

Effect of interface behavior between particles on

properties of pure al powder compacts by spark

plasma sintering, Materials Transactions, 42, (9),

1846-1849 (2001)

Porosity kinetics during SPS of alumina powder.

Comparison of the developed model taking into

account the impact of thermal diffusion with

experimental data of Shen et al., Spark plasma

sintering of alumina, J. Amer. Ceram. Soc., 85, (8),

1921 (2002)

3

2

11

2 223

4 24

0

2

2

2

3 32 129 2 23

1 4 1 9 1 2 exp 1

3 2

2 1

m

m m

xx

gb gb ref

gbx

cr

gb gb v m

e

T

G G

D G

QkTGA G

RT

D C H TE

t Gk T

C

curvature-driven grain boundary diffusion thermal diffusion power-law creep


INFLUENCE OF ELECTROMIGRATION

Major Components of Densification-Contributing Mass Transfer

During SPS (model including electromigration):

EC C J E

Nernst-Einstein equation

grain-boundary diffusion power-law creep

driving sources

externally applied loadsintering stress

electromigration

*gb gb

E q

DC Z e

kT

Blech’s formula

gb gbD

CkT

where is the atomic volume, *Z is the valence of a migrating ion, and qe is

the electron charge (the product * qZ e is called “the effective charge”).

*1gb gbgb x

y q

D UJ Z e

kT l y

U and l are the electric potential and the characteristic length along the

electric field.

( )

2

gb

y

gbx

p

J c

ca a

*

2 2

3 1 1

2

gb gb q pxgbx

pp

D Z e G rU

kT l G r G GG r

is the surface tension, x - effective (far-field) external stress in the x-direction

G a c is the grain size, p p pr a c is the pore radius.

• M. Scherge, C.L. Bauer, and W.W. Mullins, Acta

Met. Mater., 43 (9), 3525-3538 (1995):

electromigration stress of 23MPa along grain

boundaries under an electric field of 500 V/m (in a 1-

thick film) and up to GPa range stresses for grain

structures with closed surface junctions

• M.R. Gungor and D. Maroudas, Int. J. Fracture, 109

(1), 47-68 (2001): electromigration stress of

140MPa in a 1 -thick film under the field of about 425

V/m

• Q.F. Duan and Y.L. Shen, J. Appl. Phys. 87 (8),

4039-4041 (2000): electromigration stress of

450MPa along fast-diffusion length of 15 under 650

V/m

• Z. Suo, Q. Ma, and W.K. Meyer, MRS Symposium

Proceedings, 6p. (2000): electromigration stress in 0.5

-thick Al film under 300 V/m field should reach the

level of 1.5GPa

5

2

13

*2 2

2 2

3 1 1 3 31 1

2 22

m

gb gb q pxx gbx crx x

pp

D Z e G rUA

GkT l G r G GG r

G is the grain size; pr is the pore radius; A and m are power-law creep frequency

factor and power-law creep exponent, respectively; gbD is the coefficient of the

grain boundary diffusion, gb is the grain boundary thickness, k is the Boltzman’s

constant, T is the absolute temperature; is the atomic volume, *Z is the

valence of a migrating ion, and qe is the electron charge (the product *

qZ e is

called “the effective charge”); U and l are the electric potential and the

characteristic length along the electric field; is the surface tension; x - effective (far-field) external stress in the x-direction; is porosity.

E. Olevsky and L. Froyen, Constitutive modeling of spark-plasma sintering of conductive materials, Scripta Mater. 55, 1175-1178 (2006)

shrinkage due to grain-boundary diffusion

shrinkage due to dislocation creep

Constitutive Model of Spark-Plasma Sintering

Densification map for aluminum powder,

T=673K, =28.3MPa

Contribution of different factors to shrinkage under SPS

E. Olevsky and L. Froyen, Constitutive modeling of spark-

plasma sintering of conductive materials, Scripta

Mater. 55, 1175-1178 (2006)

1.E-10

1.E-07

1.E-04

1.E-01

1.E+02

1.E+05

1.E+08

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Porosity

Sh

rin

kag

e R

ate

, 1/s

shrinkage rate due to electromigration (electric current)

shrinkage rate due to sintering stress (surface tension)

shrinkage rate due to power-law creep (punch load)

1.E-10

1.E-07

1.E-04

1.E-01

1.E+02

1.E+05

1.E+08

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Porosity

Sh

rin

kag

e R

ate

, 1/s




1.E-10

1.E-07

1.E-04

1.E-01

1.E+02

1.E+05

1.E+08

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Porosity

Sh

rin

kag

e R

ate

, 1/s




Grain Size: 1Grain Size: 40Grain Size: 100nm

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1.E-08 1.E-07 1.E-06 1.E-05 1.E-04

Grain Size, m

Po

rosit

y

external load

surface tension

electromigration

Contribution of different factors to shrinkage rate of aluminum powder under SPS

417U V

l m , T=6730K, x =28.3MPa

The average particle size is 55m. The applied field is accepted to be of

500V

m (Joule heat generation balance –based estimation), the pressure is

constant and equal to 23.5 MPa.

Shrinkage kinetics during SPS of aluminum powder:

comparison with experiments

Pressure 10 MPa

Field 250 V/m

10 MPa

250 V/m

E. Olevsky and L. Froyen, Constitutive modeling of spark-plasma sintering of conductive materials, Scripta Mater. 55, 1175-1178 (2006)


LOCAL HEAT BALANCE

Total Electric Current Density (A/m2)

Total Electric Current Density in the contact between

two Aluminum particles under SPS conditions

A ratio of neck radius to particle radius of 1/1000 was used for the analysis. This means that the area of

the neck is 106 times smaller than the area of the particle diameter cross-section.

A voltage drop of about 0.4 V across a specimen 4 mm high for an electric field of 100 V/m. When

considering two particles with a 1 m radius - a voltage drop from the center of the top particle to the

center of the bottom particle is of 2x10-4 V.

An average current density of about 3x107 A/m2 in the center cross-section of the particle.

FEM COMSOLTM

software-based

solution:

Applied Voltage 12:2 ms (30 ms) Initial heat-up 12:2 Pulse (30 ms)

The stability of the temperature gradient in the inter-particle contact area is related

to the on and off pulse frequency, which controls the local and, in turn, the

macroscopic heating rate.

Applied Voltage and Initial Heat-Up in the contact

between two Aluminum particles under SPS conditions

FEM COMSOLTM software-based

solution:

Local Temperature Gradients

1.0E-06

1.0E-04

1.0E-02

1.0E+00

1.0E+02

1.0E+04

1.0E+06

1.0E+08

0.0E+00 5.0E-08 1.0E-07 1.5E-07 2.0E-07

Cu

rre

nt D

en

sit

y (

A/m

^2

)

Arc Length (m)

Current Density for 55 "A-Spot" Model

1.0E-06

1.0E-04

1.0E-02

1.0E+00

1.0E+02

1.0E+04

1.0E+06

1.0E+08

1.0E+10

1.0E+12

0.0E+00 5.0E-08 1.0E-07 1.5E-07 2.0E-07

Cu

rre

nt D

en

sit

y (

A/m

^2

)

Arc Length (m)

Current Density for 60 "A-Spot" Model

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0 20 40 60 80 100 120 140 160

Eff

ective C

ond

uctivity,

1/(

Ohm

xm

)

Number of Included Particles - "A-Spots" (r=2nm)

Conductivity of Alumina layer with Aluminum Particles - "A-Spots"

Fritting and channeling:

alumina reduction and

creation of aluminum

conductive “A-spots”

Fritting and channeling: alumina reduction and creation of

aluminum conductive “A-spots”

1000

1010

1020

1030

1040

1050

1060

1070

0 50 100 150

T, K

particle diameter, μm

T, K

h=0.005

h=0.01

h=0.015

T – the average temperature of

the inter-particle contact area

(the temperature in the center

of the particle is 1000K)

h – the specimen’s height, m

(determines the average

voltage per particle)

0

2

4

6

8

10

12

14

16

18

20

0 50 100 150

∆F

, %

particle diameter, μm

ΔF,%:

h=0.005

h=0.01

h=0.015

U, V:

F – the difference between

the shrinkage rates determined

by the difference in

temperatures in the particle

center and the inter-particle

contact area


MACROSCOPIC MODELING

( elV ) 0

CpT

t (kT T) el V

2

ij (W )

Wij

.

1

3

e.

ij

PLij

.

1 e

.

Conductive DC

Heat Transfer by Conduction

Stress-Strain Analysis

Densification

Coupled electro-thermo-mechanical FEM calculations

Olevsky E.A. (1998), Theory of sintering: from discrete to continuum. Review, Mater. Sci. & Eng. R: Reports, 40-100

Constitutive Modeling - material model

Constitutive Equation

I. Diffusional creep n = 1 (m = 1)

a.Nabarro-Herring creep (grain lattice diffusion)

b.Coble creep (grain-boundary diffusion)

II. Grain-boundary sliding creep n = 2 (m = 0.5).

III. Dislocation creep

a.Glide-controlled creep, n =3 (m=0.3)

b.Climb-controlled creep, n = 4-5, (m = 0.2 – 0.3)

IV. Dispersion-strengthened alloys n > 8 (m < 0.1).

For Solid Material For Porous Material

SEM Analysis: Morphology of Copper

Powder, (Left) 300X, (Right) 1600X

Copper Powder (Alfa Aesar, MA, USA)

Spherical

High Purity (99.9999%)

Particle Size -170 to + 400 Mesh (38 - 90 μm)

Temperature, Pressure and Densification Profiles

for 625ºC MSPD Experiment

(20-50 MPa)

Strain Rate Sensitivity Component m of

MSPD Experiments at Different

Temperatures (20-50 MPa)

Coupled electro-thermo-mechanical FEM calculations

electrical current density temperature porosity

SPS of an Alumina Specimen

FCT DIE-PUNCH SETUP: TEMPERATURE DISTRIBUTION


SCALABILITY

SPS SCALABILITY (SIZE DEPENDENCE)

Alumina Disk-Shape Specimens (Same Aspect Ratio):

experimental calibration

temperature evolution relative density evolution

15 mm 40 mm 48 mm 56 mm

Sample Height [mm] 3 7.9 9.5 11.1

Radius [mm] 7.5 20 24 28

Die Height [mm] 30 80 96 111.4

Radius [mm] 15 40 47.85 55.7

Punch Height [mm] 15 40 47.8 56

Insert Height [mm] 3.8 10 12 13.9

External Spacers Height [mm] 8 20 20 20

Radius [mm] 30 80 80 80

Transition Height [mm] 30 80 95.7 111.4

Radius 1 [mm] 7.5 20 23.9 27.85

Radius 2 [mm] 30 80 95.7 111.4

voltage evolution

Alumina powder, -325 mesh, 99.99 % pure from Cerac Inc. (now

Materion Advanced Chemicals Inc.) Initial average grain size: 0.38 µm

E.A. Olevsky, W.L. Bradbury, C.D. Haines, D.G. Martin, and D. Kapoor, Fundamental Aspects of Spark Plasma Sintering: I. Experimental Analysis of

Scalability, J. Amer. Ceram. Soc., 95, 2406-2413 (2012)


-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.015 0.030 0.045 0.060

(Po

ros

ity (C

en

ter)

–P

oro

sit

y (S

urf

ac

e))

/ S

am

ple

Ra

diu

s

Die Radius [m]

Porosity Gradient

0.219

0.106

0.216

0.187

0.195

0.153

0.175

0.140


Alumina

powder, -325

mesh, 99.99

% pure from

Cerac Inc.

(now

Materion

Advanced

Chemicals

Inc.) Initial

average

grain size:

0.38 µm

E.A. Olevsky, W.L. Bradbury, C.D. Haines, D.G. Martin, and D. Kapoor, Fundamental Aspects of Spark Plasma Sintering: I. Experimental Analysis of

Scalability, J. Amer. Ceram. Soc., 95, 2406-2413 (2012)


OVERHEATING OF TOOLING

Geometries of (left-to-right): 2 Disks, 3 Disks and 4 Disks Configurations

The Problem Overheating of SPS Tooling

The Problem Overheating of SPS Tooling

QUESTIONS ?

Documents

New ОСНОВЫ СПАРК ПЛАЗМЕННОГО СПЕКАНИЯlemc-lab.mephi.ru/content/file/news/olevsky_0.pdf · 2013. 6. 17. · ОСНОВЫ СПАРК-ПЛАЗМЕННОГО