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Designing glasses to meet specific mechanical properties

Tanguy ROUXELLARMAUR, FRE-CNRS 2717, Université de Rennes 1

Introduction: The Scales of Concern

Elastic Moduli And The Short To Medium Range Order In Glass

Hardness And Indentation Behavior

2

Strength of simply annealed window glass ~ 45 MPa CEN EN 572-2

Strength of heat strengthened float glass ~ 70 MPa CEN EN 1863-2

Strength of coated float glass ~ 120 MPa CEN EN 12150-2

Strength of tempered glass ~ 150 to 250 MPa

Strength of ion-exchanged glass ~ 450 to 750 MPa

Theoretical strength ~ 10 to 15 GPa!

Young’s modulus of window glass ~ 72 MPa

No change since the 17th century!

J.T. Littleton said « We never test the strength of glass: all we test isthe weakness of its surface » (1941)F.W. Preston added, « We do not test the properties of the glass at all,but only those of the surrounding atmosphere »

(J. App. Phys. 13, [10], 623-634 (1942))

There is much room for improvement!

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Chemical-Physics

Mechanical behavior (constitu

tive law)

Modelling (FEM) - A

pplication

Typical multiscale approach in mehanical design

Q1: Can we applied this approach to glass parts?Q2: What for? Since glass is mostly not bearing the load!

Cathedral of Notre Dame, Paris

Glass has played an important role inarchitecture as the material thatopens up a building to light

Considered functions: transparency,aesthetics, insulation

Major drawback: glass windowsweaken the structure

Grandes Serres of “La cité des sciences etde l’industrie” at la Villette (Paris)

Although glass appeared to take aleading role it was still only a materialthat separated the interior andexterior untill some twenty years agowhen loaded glass sheets started tobe used in large structures

Apple store, New York

TU Delft all glass paviljon 2004

TU Delft project of a beam-shape aquarium

(Courtesy F.A. Veer, TU Delft, Netherlands)

Q: How far can we go?

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Search for glasses possessing high elastic moduli:

Increase computer hard disk rotating speed

Lower the weight of windows (saving energy in transportation systems)

Increase structure stiffness (buildings, bio-materials implants)

Optimize ceramic sintering additives

Design glass and glass-ceramic matrices with better performance foraerospace industry

I. Elasticity

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There is no direct correlation between E and Tg

Elastic moduli are expressed in Pascals, i.e. in J/m3 , and are thusgoverned by the volume density of energy

J. Am. Ceram. Soc. 90 [10] 3019-3039 (2007)

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High temperature measurementsMeasurements at ambient temperature

Measurement of elastic moduli by ultrasonic echography

Generator

Receiver

Signal analyser

Magnetostrictive Transducer (100 – 400kHz)

Ar-7%H2

Furnace Sample

Tungsten guide

Refractory cement

Thermocouple

(Fourier's analysis)

E = ρ Vl2

L

Long beam bar mode : e<<L and e << λ (10 to 100 mm)

e

Oscilloscope

Sample

Transmitter/receiver

Piezoelectrictransducer (5 to 20MHz)

Signal

Time synchronization

Elastic wave in semi-infinite medium : λ<<L and λ << Η

E = ρ (3Vl2-4Vt

2)/((Vl/Vt)2-1)G= ρ Vt

2

ν=E/(2G)-1

Where: ρ: specific massVl: longitudinal wave velocityVt: transverse wave velocity

HL

Small size specimens: Acoustic microscopyWhen (L,H)<λ, regular piezoelectric transducers are

unable to efficiently promote the propagation of shear wavesthrough the specimen. Focused piezoelectric transducers canbe used to propagate surface-type waves, also calledRayleigh waves, which velocity is given by: VR=ζVt, whereζ is a function of Poisson´s ratio, or of the Vl/Vt ratio. VRand Vl are measured and Vt is optimised to satisfy thefollowing equation:

)/V(V-0.750

))/V(V-(0.715VV

lt

2

ltt

2

R =

K = Vo U9V

mn

V2

U2

o

oVo

=!

!

Simple (simplistic) case of a Lennard-Jones potential (1st Grüneisen rule)

Multiconstituent glass:

><V

U

o

o = Σ fiΔHai /(Σ fiMi/ρi)

)ByAx(Hf)g,B(Hf

y)g,A(Hfooo

!"!+!ΔHai =x

For the ith constituent AxBy, according to an ordinary Born-Haber cycle:

ρi : densityfi : molar fraction of the ith constituent Mi molar mass of the ith constituent

From the atom and to the continuum

K = Vo U9V

mn

V2

U2

o

oVo

=!

! n=1 and m=9

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Silicate glasses: Glass formers (Si, Al, B, Zr) Modifyers and charge compensators (Li, Na, K, Ca, Ba) Anions: O, N or C

Cation substitution: modifyers ⇒ Uo ; formers ⇒ CgIntermediate elements occupying former or interstitial sites: Hf, Be,Zr, Ti, Li and Th.Electronegativities: 1.25 to 1.75.Emax=145 GPa: magnesium aluminates + 25 mol.% de BeO.

Si Si

Si Si

Si Si

Si Si

Si Si

Si Si

O

O

O

O N C

O

O

Anionic substitutions: more efficient but Tg

However: UoSiC(447) kJ/mol)~UoSi-N(437 kJ/mol)<UoSi-O(800 kJ/mol)E oxycarbides and E oxynitrides >> E oxides

This is more the architecture (reticulation) of the network than the individualbond stiffnes that governs the glass elasticity

15

50

70

90

110

130

150

170

190

210

230

250

0 5 10 15 20 25

Carbon or nitrogen content (at %)

Yo

un

g's

mo

du

lus (

GP

a)

YSiAlON (Y/Si/Al=28/56/16 eq%)CaSiAlONSiOCYSiAlON (Y/Si/Al = 55/25/20 eq.%)

Partial cristallization

Residual free carbon

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Examples: TAS: Te2As3Se5 / GeSe4 / 2S2G: Ga5Sb10Ge25Se60 / GASIR: Ge22As20Se58

Chalcohalogenide glasses

Chalcogen elements (S, Se, Te) (Col. 16)Groups III, IV or/and V

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Atoms with much different atomic radii favour a chemical disorder and are used tosynthesize BMG’s: A metal (Be, Al, ...) + A transition metal (groups 3 to 12) from the right-hand side of the periodic table (Cu, Ni,...) + A transition metal from the left-hand side (Zr,Ti, Hf, Nb, ...), and a metalloid

Ex: Zr60Al10Ni10Cu15Pd5 ; Zr65Al10Ni10Cu15

As a result, BMG’s are characterized by a high atomic packing density and exhibitrelatively high elastic moduli

Bulk Metallic Glasses

Much different atomic radii are required to favour achemical disorder:A metal (Be, Al, ...) + A transition metal from theright-hand side of the periodic table (Cu, Ni,...) + Atransition metal from the left-hand side (Zr, Ti, Hf,Nb, ...), and a metalloid

Zr60Al10Ni10Cu15Pd5Zr65Al10Ni10Cu15

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Diferent chemical systems lead to identical elastic moduli

This observation stems from the fact that BMG’s show up with very differentatomic packing density depending on their composition. For instance, Pt-basedglasses have much higher packing density than Cu-Based alloys

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SeSe

SeSe

SeSe

SeSe

Ge

Ge

GeSeSe

SeSeSe

Se

SeSe

SeSe

SeSeSe

Se Ge

OSiO

OO

SiO

OO

SiOO

O

SiO

OO

Si

OOO

Si OO

O

N

CSi

OOO Si

OOO

SiOO

O

SiOO

O

Si

OOO

Si OO

O

Substitution of 3O2- for 2N3-

Substitution of 2O2- for 1C4-

1D: Chains and rings

2D: Layers

3D: 3D units andcrosslinking

0D: Clusters, litlle short to medium range ordering

Molecular scale:

Influence of the atomic packing density

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Atomic packing density, Cg

Po

iss

on

's r

ati

o

SiO2-Na2ORare-earth silicatesOxynitridesLead vanadatesSilico-aluminatesMetallicOxycarbidea-SiO2Soda-lime-silicates(Mg,Ca)-silicatesa-B2O3Lead silicatesRare-earth aluminatesBorosilicateK2O-SiO2

SiO1.6C0.8

SiO2

Pd40Cu30Ni10P20

Steels

Poisson’s ratio and dimensionality

Poisson’s ratio and atomic network dimensionality

ΔL

ΔD

D

Lν = -εt/εl = - L/DxΔD/ΔL

ΔV/V=Trace ε=(1-2ν)σ/E

σ

ν≈ 0.163D

ν≈ 0.2862D

ν≈ 0.3231D

ν≈ 0.370D?

a-SiO2 GeSe4 a-Se Zr55Cu30Al10Ni5

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HIGH TEMPERATURE ELASTICITY

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27

0

20

40

60

80

100

120

140

160

200 400 600 800 1000 1200 1400 1600

T (K)

Yo

un

g's

mo

du

lus (

GP

a)

SiOC Window glassSe Ge10Se90Ge15Se85 Ge25Se75Ge30Se70 YSiAlOYSiAlON(7.5 at% N) YSiAlON(11.2 at% N)YSiAlON(Si/Al=1.5) YSiAlON(Si/Al=1.95)YSiAlON(Si/Al=3.75) YMgSiAlONZrCuAlNi GlycerolGe22As20Se58 a-SiO2Pd42.5Ni71Cu30P20 ZBLANDiopside Grossulara-B2O3

Soda-lime-silica

(window)

SiOC

Chalcogenides

Oxynitride

Bulk metallicBasaltic

a-SiO2

Tg

J. Am. Ceram. Soc. 90 [10] 3019-3039 (2007)

28

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

20 60 100 140 180 220 260 300 340 380 420 460

Temperature (°C)

No

rma

lize

d Y

ou

ng

's m

od

ulu

s (

E/E 2

0°C

)

Se

Ge10Se90

Ge15Se85

Ge25Se75

Ge30Se70

29For glasses with E>10 GPa: E=E(Tg)Tg/T

You

ng’s

mod

ulus

(GP

a)

30

31

!

" =1

1#T

E

$E

$T

« Strong » versus « Fragile » Glasses (Angell)

Glass Tg (K) E (293 K)

(GPa)

E (Tg)

(GPa)

dE/dT(Tg+)

(MPa/K) (~Tg)2) 3)

(littérature)

Glycérol170 186 6 9.5 -190 0.2 0.65174or 0.435175

Ge10Se90165 365 12.1 10 -230 0.07 0.6176

Ge15Se85165 383 13.8 10.3 -80 0.22 0.62176

Ge25Se75165 501 16.1 12.8 -38 0.38 0.63176

Ge30Se70165 573 17.9 15.5 -34 0.42 0.63176

Ge22As20Se58166 565 18 16.4 -29 0.43 0.63176

Y12.3Si18.5Al7O54.7N7.540 1183 150 122 -103 0.45 0.8177

Y4.86Mg6.3Si16.2Al11.8O54.9N5.92171 1120 134 122 -105 0.52 0.75178

Zr55Cu30Al10Ni5172 673 81.4 72.9 -108 0.65 0.7179

Window glass1) 173 835 72 56 -67 0.53 0.55173 or 0.45175

SiC0.375O1.2558 1623 110 84.8 -52 0.61 0.6658

Φ(t)=σ(t)/σ(0)=exp[-(t/t)β]

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ν as a probe of the depolymerization process

J. Am. Ceram. Soc. 90 [10] 3019-3039 (2007)

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Conclusion

ELASTICITY

1) There is no direct relationship between elastic moduli and Tg.

2) Poisson's ratio (ν) correlates with the atomic packing density and with the glassnetwork dimensionality (polymerization degree)

3) High elastic moduli are favoured by structural disorder and in the search for stiffglasses, atomic packing density seems to predominate over the bond strength

4) The temperature dependence of the elastic properties above Tg can be discussedin the light of the "fragile" versus "strong" character of the liquid. Thetemperature sensitivity of ν in the liquid range can be viewed as a consequenceof the depolymerization occurring above Tg. ν depends much on temperatureabove Tg but stays mostly lower than 0.5 up to T=1.3 Tg except for weakly cross-linked materials such as chain-polymers.

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Acknowledgements:

Ralf Riedel, TU Darmstadt, GermanyGian-Domenico Sorarù, University of Trento, ItalyStuart Hampshire, University of Limerick, IrelandSatoshi Yoshida, University of Shiga prefecture, JapanYoshihito Kawamura, University of Kumamoto, JapanYoshihiko Yokoyama, University of Tohoku, Sendai, JapanChristian Gault, Hervé Lemercier et Marc Huger, ENSCI, LimogesPascal Gadaud, ENSMA, Poitiers, FranceFranck Augereau, LAIN, Montpellier, FranceVincent Keryvin, jean-Pierre Guin et Jean-Christophe Sangleboeuf,LARMAUR, Rennes, FranceThe glass and ceramics laboratory, Rennes, France