Modern Solid State NMR Strategies for the Structural Characterization of

Disordered Materials

Hellmut Eckert

Instituto da Física São CarlosUniversidade de São Paulo

Disordered States of Matter

Non-Stoichiometric CompoundsPlastic Crystals

Glasses, Gels, CeramicsNanocomposites

CompositionPreparation, Processing

PropertiesStructureDynamics

O estado vítreo: aspectos termodinâmicos

gás

cristal

vidro

líquidotransição vítrea

Temperatura

En

talp

ia, v

olu

me

Distance distributions in states of matter

Ion Conducting Glasses

Network formers: SiO2,B2O3,P2O5,Al2O3

Network modifiers: alkaline, alkaline-earth orsilver oxides

Short Range Order

B

O

M

networkmodifier

networkformer

directly bonded neighbors

Coordination numbers and symmetries

Site quantification

200-300 pm

B, Si, P

O

Li-Cs

Medium-range Order in Glasses

Spatial distribution of modifiers

Network former-network modifier correlation

Network former connectivity

300-600 pm

Nano- and Microstructure

• Chemical Segregation,• Phase Separation,• Nucleation/growth

> 1nm

Solid State NMR

experimentelly flexible

Element selectiveLocally selectiveInherently quantitative

h

B0 E

0ΔE = B

H = HZ + HD + HCS + HQ

Distances Bonding geometry

selective - averaging

rot

zr

θ

B0 o7.54

Interações Dipolares Anisotropia de Desvio Químico - CSA

Interações Quadrupolares de Primeira Ordem

H = HZ + HD + HCS + HQiso 2nd.

Haniso= A . {3 cos2 – 1}

Magic Angle Spinning - MASMAS

Current Research Agenda

NMR Methods Glass Li Ion Battery Optical CatalystsDevelopment Science Components Materials Biomaterials

SSNMR, ESR Structure Electrode Luminescent FLP, ZeoliteDipolar Dynamics, Electrolytes, Ceramics, NanocompositesTechniques Sol-Gel CeramicsHybrids Bioceramics

Support

Industry: Corning, Schott, Ivoclar, Nippon GlassDFG, DFG-SFB, IRTG, BMBF

CNPq Universal, FAPESP, CEPID, CNPq- 1B

H. Eckerteckert@ifsc.usp.br

Mixed Network Former EffectIn Ion-Conducting Glasses

In a glass system with fixed network modifier content:How do the physical properties change

when we vary the network former composition ?

Often these changes are non-linear,requiring fundamental understanding

on a structural basis

Mixed network former effect in the (M2O)0.33[(P2O5)1-x(B2O3)x ]0.67 – System (M = Li, K, Cs):

Glass Transition Temperatures

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

400

450

500

550

600

650

700

750

800

x(B2O

3)

M2O =

Li2O

K2O

Cs2O

T

g / K

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-14

-13

-12

-11

-10

-9

-8

log 10

(D

C

×cm)

M2O =

Li2O

K2O

Cs2O

x(B2O

3)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.70

0.75

0.80

0.85

0.90

0.95

1.00

x(B2O

3)

M2O =

Li2O

K2O

Cs2O

EA /

eV

DC- conductivity (300 K) Activation Energies

Mixed network former effect in the (M2O)0.33[(P2O5)1-x(B2O3)x ]0.67 – System (M = Li, K, Cs)

100 50 0 -50 -100

x = 0.4500 K

(7Li) / ppm

400 K

220 K

240 K

260 K

280 K

300 K

320 K

340 K

360 K

380 K

200 K

420 K

440 K

460 K

480 K

200 250 300 350 400 450 500

0

1000

2000

3000

4000

5000

6000

7000

/

Hz

x = 0.0 x = 0.2 x = 0.4 x = 0.6 x = 0.8 x = 1.0

Dynamic characterization by static 7Li NMR

SingleNetwork former

Mixed network former

M. Storek, R. Böhmer, S. W. Martin, D. Larink, H. Eckert, J. Chem. Phys. 2012

Structural Issues Regarding the Mixed-Network Former Effect

• Network former speciations – Coordination polyhedra– Types of anionic and neutral species present

• Connectivity distributions– Random Linkages ?– Connectivity Preferences ?– Clustering/Phase separation ?

• Competition for the network modifier– Proportional sharing vs. preferential attraction

• Relation to physical properties

20 10 0 -10

a)

()/ ppm

x= 0.1

x= 0.2

x= 0.3

x= 0.4

x= 0.5

x= 0.6

x= 0.7

x= 0.8

x= 0.9

x= 1.0

20 0 -20 -40 -60

(P) ppm

x = 0.9

x = 0.8

x = 0.7

x = 0.6

x = 0.5

x = 0.4

x = 0.3

x = 0.2

x = 0.1

x = 0.0

11B

SOLID STATE NMR CHARACTERIZATION

31PB(3) B(4) P(1) P(2) P(3)

D. Larink, H. Eckert, M. Reichert, S.W. Martin, J. Phys. Chem. 126, 26162-26176 (2012)

Structural speciation in the (K2O)0.33[(P2O5)1-x(B2O3)x ]0.67 – system

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00

10

20

30

40

50 B4

B3

B2

P3

P2

P1

x(B2O

3)

Str

uktu

rein

heit

en in

%

0 < x < 0.5: P(2) units successively replaced by B(4) units0.5 < x 1.0: P(3) units successively replaced by B(3) units

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.2

1.3

1.4

1.5

1.6

1.7

x(B2O

3)

M2O =

Li2O

K2O

Cs2O

[O]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

400

450

500

550

600

650

700

750

800

x(B2O

3)

M2O =

Li2O

K2O

Cs2O

Tg /

KTg-value and network connectedness

Glass transition temperature number of bridging oxygen per network former unit

0 < x < 0.5: P(2) units successively replaced by B(4) units0.5 < x 1.0: P(3) units successively replaced by B(3) units

x=45%

x=40%

x=35%

x=30%

x=25%

20 10 0 -10 -20 / ppm

x=20%BO3

BO4

11B- MAS –NMR Spectra of Borophosphate Glasses 50% Ag2O * x P2O5 * (50%-x) B2O3

Connectivity with phosphorus ??

S

I

ˆˆ ˆsin( )ISD r z zH D t I S

Modulation of HD under Sample Rotation

Magic- Angle Spinning (MAS)

Rotational Echo Double Resonance (REDOR)

+

-ˆ ISDH

Tr

+ +ˆ ISDH

Tr

I-channel pulse

ˆ ˆ( )z zI I

11B

31P

REDOR Pulse Sequence

[ Tr ]

0 1 2 3 4

/2

/2

S0- S

S0

=S0

S

11B

11B

31P

31P

11B {31P}-REDOR on50% Ag2O - 25% B2O3 - 25% P2O5

Site Connectivities in Borophosphate Glasses:

spin echo

spin echo with dephasing

difference

BO3 BO4

REDOR Pulse Sequence

[ Tr ]

0 1 2 3 4

/2

/2

S0

S

11B

11B

31P

31P

strength of interaction (# neighbors, distance)

dipolar evolution timeN . Tr

depends on:

222

0

1( ) ( )

( 1)r r

SNT M NT

S I I

Analysis of REDOR Curves in Glasses

22 2 2 60

2

4( 1)

15 4 I S ISS

M S S r

.

11B{31P} REDOR of Crystalline BPO4

.

0.0000 0.0005 0.0010 0.0015 0.00200.0

0.2

0.4

0.6

0.8

1.0

M2meas

= 15.8 ± 0.2 kHz2

M2

theo = 18.48 kHz

2

Measurement Simulation

(S0-S

)/S 0

NTr (s)

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

0,0

0,2

0,4

0,6

0,8

1,0

1,2 B4

B3

x = 0.6M

2(11B(B4){31P}) = 7.6×106 (+/- 10 %) rad2s-2

M2(11B(B3){31P}) = 2.1×106 (+/- 10 %) rad2s-2

N×Tr / ms

(S0-S

)/S 0+

(S 0-S

')/S 0

Network connectivity: 11B{31P} REDOR

No B(3)-O-P connectivity

M2 = 4-5 . 106 rad2/s2 per B-O-P linkage

S/So = 4/3 M2 (N.Tr)2

M2 ~ rij-6

Network connectivityvia O-1s XPS:

538 536 534 532 530 528 526

x = 1.0

x = 0.9

x = 0.8

x = 0.7

x = 0.6

x = 0.5

x = 0.4

x = 0.3

x = 0.2

x = 0.1

Bindungsenergie / eV

x = 0.0

Binding energy [eV]

P-O-P NBOP-O-B B-O-B

Constant linewidthPeak position changing monotonicallyAreas consistent with compositionModel compound validation

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

0

10

20

30

40

50

60

70

80

90

100

Sau

erst

offu

mge

bung

in %

x(B2O

3)

NBO P-O-P P-O-B B-O-B

P-O-P

NBO P-O-BB-O-B

Quantification of network connectivity: Chemical ordering scenario

maximized B(4)-O-P Connectivityno B(3)-O-P Connectivityno B(4)-O- B(4) Connectivity; no P(2)

2B units

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

20

40

60

80

100 P-O-B P-O-P B-O-B

Con

cent

rati

on [

%]

x(B2O

3)

Structure-property correlations in the (M2O)0.33[(P2O5)1-x(B2O3)x ]0.67 – system

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00

10

20

30

40

50 B4

B3

B2

P3

P2

P1

x(B2O

3)

Str

uktu

rein

heit

en in

%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-14

-13

-12

-11

-10

-9

-8

log 10

(D

C

×cm)

M2O =

Li2O

K2O

Cs2O

x(B2O

3)

Speciation electrical conductivities

Charge delocalization near P31B and B4 0P units creates shallow

Coulomb traps, favoring ionic mobility

Summary

• Quantification of Mixed Network Former Effects– Site Quantifications– Connectivity distributions– Network modifier sharing

– Structure/Property correlations: Tg,

• Tendency for heteratomic linkages decreases:– Borophosphate -> Germanophosphate – ->Tellurophosphate -> Thioborophosphate

• Other systems studied: – Alumoborate, Alumophosphate,– Alumophosphosilicat

Solid State NMR as a tool in complex phosphate glasses

• Aluminophosphate or -borate matrices• Rare-Earth (RE) ion emitters embedded in

a glassy or ceramic environment• Luminescence intensity (excited state

lifetime, quantum yield) critically controlled by RE local environment and spatial distribution

Optical Glasses and CeramicsWaveguides, NLO-materials,

Matrices for RE dopants for potential laser applications

Fundamental Problem: NMR of fluorescent rare earth ions is impossible due to their strong f-electron paramagnetism

Structural Magnetic Resonance Approaches

1. NMR analysis of diamagneticmimics to RE species. 45Sc, 89Y-NMR

2. NMR analysis of paramagneticeffects on host constituentnuclei: HZ and T1

3. EPR analysis of electron-nucleardipolar couplings (studied by ESEEM)

1. NMR analysis of diamagneticmimics to RE species.´45Sc, 89Y-NMR

2. NMR analysis of paramagneticeffects on host constituentnuclei: HZ and T1

= Sc3+, Y3+= RE3+

NMR properties of the isotopes

nuclide 45Sc 89Y 139La 171Yb 175Lu

Spin 7/2 1/2 7/2 1/2 7/2

% abundance 100 100 99.9 14.3 97.4

Q/1028m2 0.22 0 0.2 0 2.8

/MHz (11.7T) 121 24.5 71.2 88.0 57.2

1. The Diamagnetic Mimic Approach

89Y MAS NMR of yttrium aluminoborate glasses and crystalline model compounds

20(Al20(Al22OO33)-20Y)-20Y22OO33-60B-60B22OO33

11B MAS NMR of 40-y(Al40-y(Al22OO33)-yY)-yY22OO33-60B-60B22OO33 (10 (10 y y 25) 25)

BO4

BO33-

(orthoborates)

BO32-

(pyroborates)

BO3-

(metaborates)

H. Deters, A. S. S. de Camargo, H. Eckert, et al. J. Phys. Chem. C 113, 16216 (2009)

Prior to crystallization

60 40 20 0 -20 -40

VC-Y10

VC-Y15

VC-Y25

(11B) / ppm

VC-Y20

YAl3(BO

3)4

YBO3

glassy B2O

3

11B MAS NMR of vitroceramics in the40-y(Al40-y(Al22OO33)-yY)-yY22OO33-60B-60B22OO33 system (10 system (10 y y 25) 25)

No evidence of meta- or pyroborate groups in the vitroceramics

30 20 10 0 -10

(11B) / ppm

S0 and S

S0-S

VC-Y20NT

R=0.0093 s

0.00 0.01 0.02 0.03

0.0

0.2

0.4

0.6

0.8

1.0

S/S

0

NTR / s

YAl3(BO

3)4 Y20

VC Y20

Change in B-O-Al connectivity upon crystallizationdetected by 11B{27Al} REDOR

43% of the B(3) units are not linked to aluminum in the vitroceramic

20Y2O3 - 20Al2O3 - 60B2O3

g-B2O3

8 10 12 14 16 18 20 22 24 260

10

20

30

40

50

60

70

11B

sig

nal f

ract

iona

l are

a

mol % Y2O

3

YAl3(BO

3)4

B2O

3

YBO3

Glass - to - vitroceramic transition for the system40-y (Al40-y (Al22OO33) - y Y) - y Y22OO3 3 – 60 B– 60 B22OO33

(B2O3)0.6(Al2O3)0.4-y)(Y2O3)y {(0.8/3) - (2y/3)} YAl3(BO3)4 + {(8y/3)-0.8/3} YBO3 + 0.2 B2O3

= Fermi + dip + dia

()Fermi {µB2/kBT}gisoBo ~ M

(2) dip ~ {µB2/kBT}r-3{gzz

2- ½(gxx2 + gyy

2)}(3cos2-1)

Rapid electron Zeeman state fluctuations (short T1e):

(1)Isotropic shift contribution(2)Isotropic shift contribution + broadening effects

2nd Approach: NMR Analysis of paramagnetic effects uponthe constituent matrix nuclei: HZ and T1

XZZZZZSol IBSIASISH IS ωω

60 40 20 0 -20 -40

Y20Nd0.75

Y20Nd0.50

Y20Nd0.35

Y20Nd0.20

Y20Nd0.10

ppm

Y20

60 40 20 0 -20 -40

ppm

Y20Er0.75

Y20Er0.50

Y20Er0.35

Y20Er0.25

Y20Er0.10

Y20

60 40 20 0 -20 -40

ppm

Y20Yb0.75

Y20Yb0.50

Y20Yb0.35

Y20Yb0.20

Y20Yb0.10

Y20

0,0 0,2 0,4 0,6 0,80

1000

2000

3000

LB /

Hz

x / mol% RE2O

3

Er3+-doped

Yb3+-doped

Nd3+-doped

BO3/2

0,0 0,2 0,4 0,6 0,80

1000

2000

3000

BO4/2

-

LB /

Hz

x / mol% RE2O

3

Er3+-doped

Yb3+-doped

Nd3+-doped

Al2O3)0.2(Y2O3)0.2(B2O3)0.6 : Nd3+, Er3+,and Yb3+ subst.

BO4BO3

Nd3+ Er3+ Yb3+

Distribution of the RE ions in the ceramics: 27Al MAS-NMR results

Linewidths and areas of new Al site are proportional to Yb/Y ratio

60 40 20 0 -20 -40 -60

VC-Y10Yb1.0

VC-Y10Yb0.5

VC-Y10Yb0.2

(27Al) / ppm

VC-Y10

60 40 20 0 -20 -40 -60

VC-Y20Yb2.0

(27Al) / ppm

VC-Y20Yb1.0

VC-Y20Yb0.5

VC-Y20Yb0.2

VC-Y20

10Y-30Al-60B 20Y-20Al-60B YAl3(BO3)4 YAl3(BO3)4 in phase mixture

H. Deters, A. S. S. De Camargo, C. N. Santos, H. Eckert, J Phys. Chem. C 114,14618 (2010)

0 2 4 6 8 10

100

200

300

400

[Yb]/([Y]+[Yb]) / %

VC-Y20Ybx (YAB)

Line

wid

th (

89Y

) / H

z VC-Y10Ybx (YAB)

0 2 4 6 8 100

500

1000

1500

2000

VC-Y20YbxYAB: B(3)-II

Line

wid

th (

11B

) / H

z

[Yb]/([Y]+[Yb]) / %

VC-Y10YbxYAB: B(3)-II

0 2 4 6 8 10

600

800

1000

1200

1400

1600

[Yb]/([Y]+[Yb]) / %

VC-Y20Ybx (YAB)

Line

wid

th (

27A

l) / H

z VC-Y10Ybx (YAB)

0 2 4 6 8 10

0

2

4

6

8

10

12

[Yb]/([Y]+[Yb]) / %

VC-Y20Ybxre

lativ

e frac

tion

of th

e

para

mag

netic

27A

l shi

ft VC-Y10Ybx

Linewidth (11B) Linewidth (27Al)

Linewidth (89Y) Peak area (27Al)

Apparent Yb/Y ratio in the YAB component of VC-Y20 lower than predicted

preferential location of Yb in YBO3 componentPreferential location of Nd in YAl3(BO3)4 component

44

3. ESEEM - Electron Spin Echo Envelope Modulation

90°

t+ t

90° 90°

t t

typical excitationwindow

• applied at a particular fixed field strength• systematic variation of the pulse spacing (t+t)

• Modulation effect results from the simultaneous excitation of allowed (ms=±1, mI=0) and partially forbidden (ms=±1, mI≠0 nuclear spin-flip) EPR transitions.

( ) ( ) ( )( ) ttcos1cos12

1 t;t, ttt k

V ( ) ( ) i

iges VV tt t;t t;t

22

I

I BBk

a = [(I + A/2)2 + B2/4]1/2 ß = [(I - A/2)2 + B2/4]1/2

XZZZZZSol IBSIASISH IS ωω

H. Deters, J.F. de Lima, C. Magon, A.S.S. de Camargo, H. Eckert, PCCP 13, 16071 (2011)

5 10 15 20 25 30 35 40

25Y-15Al

20Y-20Al

15Y-25Al

/ MHz

B = 9 kGt = 136 ns

10Y-30Al

10B11B

27Al

ESEEM Spectra of Yb-doped Glasses in the System xY2O3-(40-x)Al2O3-60B2O3

Summary

• Strategy for structural studies of rare earth ions in optical glasses– Influence of rare earth ions upon the framework structure– First 45Sc and 89Y NMR in glasses– First ESEEM of alumoborate glasses

• Study of crystallization mechanism and dopant distributions in Y-alumoborate vitroceramics– Substitution preference for Yb3+ ions

Solid State NMR as a promising tool in optical glasses

Thank you

• Dr. Heinz Deters• Frederik Behrends• Drs. J. F. de Lima, C. J. Magon (IFSC, USP) • Dr. A.S.S. de Camargo (IFSC, USP)

• SFB 458• NRW Graduate School of Chemistry• Fond der Chemischen Industrie

AK Eckert, WWU Münster

Prof. H. EckertProf. H.J. Deiseroth (University of Siegen)S.T. Kong (University of Siegen)

SFB 458

Thanks for your attention!

31P MAS NMR of Li7PS5-xSexCl

PS4 PS3Se PS2Se2 PSSe3 PSe4

Inc

rea

sin

g S

co

nte

nt In

crea

sing

Se c

on

ten

t

Resolution of first and second coordination sphereP-S bonding favored over P-Se bonding

51

31P MAS NMR of Li7PS5-xSexI

PS4 PS3Se PS2Se2 PSSe3PSe4

Clear differentiation of S/Se second coordination spheres Exceptionally good resolution suggests chalcogen/halogen ordering

Inc

rea

sin

g S

co

nte

nt In

crea

sing

Se c

on

ten

t

52

…as proven by 77Se NMR

Complementary Information using Halogen NMR

- Only 127I signal of ordered phase is visible, - In disordered materials EFG too large- Detection of LiI impurities

Paramagnetic broadening of the 207Pb Signal inTm-doped (PLZT) at different levels (wt.% Tm)

undoped 0.1

0.5 2.0

4.0 6.0

-1 0 1 2 3 4 5 6 7

350

400

450

500

550

600

650

700

750

800

M2 (

pp

m2 )

Amount of Tm3+ (weight-%)

Stepped-frequency acquisitionof full CPMG pulse trains

Second-moment analysis of Spikelet intensity distribution

RE segregation

Structural Investigations of RE doped YAlB Glasses

55

3. Echo Decay and Modulation

0 2000 4000 6000 8000t / ns

15Al-65B

T=164 ns

4K

B = 6.7 kGModulation

FT

0 5 10 15 20 25 30 35 40 / MHz

10B

11B

Glass Composition:0.5Yb2O3-19.5Y2O3-15Al2O3-65B2O3

Experimental Result – Echodecay Fit = Modulation

0 2000 4000 6000 8000

t / ns

15Al-65B

t = 164 ns

T = 4K

B = 6.7 kG

Echodecay Fit

Modulation

0 2000 4000 6000 8000

t / ns

15Al-65B

t = 164 ns

T = 4K

B = 6.7 kG

Echodecay Fit

0 2000 4000 6000 8000

t / ns

15Al-65B

t = 164 ns

T = 4K

B = 6.7 kG

Structural Investigations of RE doped YAlB Glasses

56

3. A brief Introduction to EPR-Spectroscopy

The EPR Hamiltonian for solids (simplification):

further simplifications:

Due to the anisotropy of the hyperfine coupling, the nucleus “sees” an additional hyperfineinteraction perpendicular to the quantization direction.

nuclear spin has a different quantization direction if the electronspin state is |S> than if it is |S>

As a further consequence, nuclear spin flips (mI ≠0) are partially allowed because of the anisotropy of the hyperfine coupling (B)Mixing of electron and nuclear spin states

SAI ZZSol ISH IS ωω

XZZZZZSol IBSIASISH IS ωω

B

O

O OB(n)mP B(n)

mPO

B(n)mP

B(4)0P

B(n)mP

B

O

O OB(n)mP P(n)

mBO

B(n)mP

B(4)1P

B(n)mP

B

O

O OB(n)mP P(n)

mBO

P(n)mB

B(4)2P

B(n)mP

B

O

O OP(n)mB P(n)

mBO

P(n)mB

B(4)3P

B(n)mP

B

O

O OP(n)mB P(n)

mBO

P(n)mB

B(4)4P

P(n)mB

B

O

O B(n)mP

B(3)0P

B(n)mP

1- 1- 1- 1- 1-

O

B(n)mP

B

O

O P(n)mB

B(3)1P

B(n)mP

O

B(n)mP

B

O

O P(n)mB

B(3)2P

B(n)mP

O

P(n)mB

B

O

O P(n)mB

B(3)3P

P(n)mB

O

P(n)mB

B

O

O B(n)mP

B(2)0P

B(n)mP

O

B

O

O P(n)mB

B(2)1P

B(n)mP

O

B

O

O P(n)mB

B(2)2P

P(n)mB

O

1- 1- 1-

P

O

O OP(n)mB

1 -

P(n)mB

O

P

O

O OP(n)mB

1 -

B(n)mP

O

P

O

O OB(n)mP

1 -

B(n)mP

O

P

O

O OP(n)mB P(n)

mBO

P(n)mB

P

O

O OP(n)mB B(n)

mPO

P(n)mB

P

O

O OP(n)mB B(n)

mPO

B(n)mP

P

O

O OB(n)mP B(n)

mPO

B(n)mP

P

O

O O

2-

P(n)mB

O

P

O

O O

2-

B(n)mP

O

P

O

O O

3-

O

P(3)0B P(3)

1B P(3)2B P(3)

3B

P(2)0B P(2)

1B P(2)2B

P(1)0B P(1)

1B P(0)

P

O

O OB(n)mP B(n)

mPO

B(n)mP

P(4)4B

B(n)mP

1+

11 possible PnmB and 15 possible Bn

mB units

BO

O

O

P

OO

O

O

P

OO

O

P

O

O

P

O

O

OO

0.25-

0.25-

0.25-0.25-

O

P

OO

O

O

P

O

O 0.5-

B(4)

B(4)

O

P

O

O 0.75-

B(4)

B(4)

O

B(4)

P32B P3

3B

PP

P

PP

P

PP

P31B

Bond valence Considerations

Competition for the network modifier

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

20

40

60

80

100 M2O =

Li2O

K2O

Cs2O

[QB]

[%]

x(B2O

3)

At all compositions, the phosphate attracts a larger part of the network modifier than predicted by the proportional sharing model.