Nanoclusters in model ferroelastics Hg2Hal2

E.M.Roginskii

A.F.Ioffe Physical-Technical Institute, Russia

Outline

1. Introduction

2. Model of Phase Transitions

3. Raman scattering investigations

4. X-Ray analysis

5. Conclusion

Hg2Hal2 (Hal=Br,Cl,I) unit cell

 

 

Table of basic physical properties

]011[ 011/110

Table1. Physical properties of univalent mercury halides

Lattice constants, Å

Transparency spectral range, m

Transverse (TA) sound velocity along [110] polar. on , m/sec.

Birefringence n(=6328 Å)

Acousto-optical coefficient M2, (CGS)

for [100]/[100] and

 

Hg2Cl2

a=4,480b=10,910

 

0,35 - 20 

347 

0.6650610-18

64010-18

 

Hg2Br2

a=4,640b=11,100

 

0,42 - 30 

282 

0.8599110-18

180410-18

 

Hg2I2

a=4,920b=11,610

 

0,55 - 40 

254 

1.48224610-18

428410-18

Hg2Hal2

property

Comparison with physical characteristics of often used materials

Acousto-optical coefficient for

longitudinal wave Sound velocity

Ferroelastic Phase transition172

174 hh DD

Hg2Cl2 Tc=186K

Hg2Br2 Tc=144K

Hg2I2 incipient PT Pc=9Kbarr

Model of Phase transition 172

174 hh DD

y

[0 1 0 ]X

[11 0 ]_

x[1 0 0 ]

Y[11 0 ]

g

g

SoftMode

SM at approaching Tc

D 1 74 h D 1 7

2 h

H alH g

H g H a l2 2

Brillouin Zone

X

X

1

2 Г

Z

z[00 1]

y

x

[1 00]

[0 10]

Experimental technique

Eigen vectors of vibrations in Hg2Hal2 crystals. Rrefers to Raman-active vibrations, and IR, to vibrations

active in infrared absorption (reflection).

Raman spectra of Hg2I2 and Hg2Br2 single crystals taken at room temperature. Dashed lines correspond to XZ(YZ) polarization, and solid lines, to ZZ polarization. Star denotes the 1 overtone.

0 50 100 150 200

*

4

3

2

1

x20 x20

Hg2I2

Inte

nsity

x10x10

4

3

2

1

Hg2Br2

, cm-1

Low-Temperature (10K) low frequency Raman Spectra for Hg2(Br1-xIx)2

0 25 50 75 100 0 25 50 75 100

x 10

sm

2

1 x=0

Int

ensi

ty

0.12

0.18

0.30

*

5

0.50

Hg2(Br1-xIx)2

XZ(YZ)

*

0.75

0.90

x=1

, cm-1

HgHg22BrBr22

HgHg22II22

Low-Temperature (10K) high frequency Raman Spectra for Hg2(Br1-xIx)2

100 150 200 250 100 150 200 250

Hg2(Br1-xIx)2

ZZx=0

4

3

x 10

Br

BrI3

0.18

0.12

0.30

Intensity

0.50

6

0.75

0.90

3I

x=1

, cm-1

HgHg22BrBr22

HgHg22II22

Soft Mode Raman Spectra

-20 0 20

sm

sm

Hg2Br22

sm2

sm

10K

40K

125K

135K

80K

100K

144K

170K

190K

200K

230K

260K

293K

Inte

nsi

ty,

arb

. u

nits

(cm-1)

172

174 hh DD (X (X ))

TTcc=144=144 TTcc=100=100

-20 -10 0 10 20

2 2

sm

sm

Hg2(Br0.88I0.12)2

* *

sm

sm

10K

25K

70K

50K

90K

100K

150K

170K

200K

250K

293K

Inte

nsity

, arb

. uni

ts

(cm-1)

Domain Structure

100 150

BrI3

0.18

0.12

Hg2(Br

1-xIx)2

ZZ

0.30

Intensity

, cm-1

Concentration dependence of frequency and intensity

0.0 0.2 0.4 0.6 0.8 1.00

50

100

150

200

{BrI I

Br

cm-1

3

5

3

6

4

3

2

1

Hg2I2

Hg2Br

2

,

x

0.0 0.2 0.4 0.6 0.8 1.0

Hg2I2Hg

2Br

2

Hg2(Br,I)2

Hg2I2Hg2Br2

Inte

nsi

ty, a

rb.u

nits

x

X-ray analysis

Brillouin Zone

X

X

1

2 Г

Z

z[00 1]

y

x

[1 00]

[0 10]

X-ray experiment

2

SampleMonochromator

Source

Detector

Slit

Reciprocal Lattice

X

Z

Z

Г

(0,0,0) (1,0,0) (2,0,0) (3,0,0) (4,0,0)

(0,4,0)

(0,3,0)

(0,2,0)

(0,1,0)

X

X

X X

Typical scans for Hg2Br2 and Hg2I2 crystals

3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2

0

1

2

3

4

5

6

(4.5,3.5,0)

x100

(5,3,0)

(4,4,0)C

ou

nts

x 1

0-5/2

s

Wavevector

Hg2I

2 15K

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

0

1

2

3

4

5

(3,1,0)

(2,2,0)

x 10

Co

un

ts x

10-3

/2s

Wavevector

Hg2Br

2 160K

(2.5,1.5,0)

Diffuse maxima

4.2 4.3 4.4 4.5 4.6 4.7 4.80

500

1000

4.2 4.3 4.4 4.5 4.6 4.7 4.80

500

1000

4.2 4.3 4.4 4.5 4.6 4.7 4.80

500

1000

4.2 4.3 4.4 4.5 4.6 4.7 4.80

500

1000

4.4 4.5 4.60

500

1000

4.4 4.5 4.60

500

1000

4.4 4.5 4.60

500

1000

4.4 4.5 4.60

500

1000

Wavevector

T=13K

30K

50K

80K

Cou

nts/

30s

0

1000

2000

3000

0

1000

2000

3000

2.45 2.50 2.550

1000

2000

3000

0

1000

2000

3000

0

1000

2000

3000

2.48 2.50 2.520

1000

2000

3000

Cou

nts/

2s

Wavevector

150K

144K

140K

Hg2Br2 Hg2I2

Temperature dependence of integral intensity

100 200 3000

200

400

600

800

T, K

Inte

nsit

y, a

rb. u

nits

Tc

Hg2Br

2

(2.5,1.5,0)soft

hard

0 20 40 60 800

20

40

60

Inte

nsit

y, a

rb.u

nits

T, K

Hg2I2

(4.5,3.5,0)

soft

hard

Halfwidth temperature dependence

=2/

Correlation radius

100 150 200 250 300

0.05

0.10

0.15

0.20

0.25

T, K

Hal

fwid

th(

), 2/

a

Hg2Br

2

(2.5,1.5,0) soft

hard

0 20 40 60 80 1000.0

0.1

0.2

0.3

Hal

fwid

th(

), 2/

a

T, K

soft

hard

Hg2I2

(4.5,3.5,0)

log-log scale Hg2Br2

A~A~ ~~

=(T-T=(T-Tcc)/T)/Tc c – reduce temperature– reduce temperature

-2.0 -1.5 -1.0 -0.5 0.0

1.8

2.4

3.0

3.6

-2.0 -1.5 -1.0 -0.5 0.0

-2.4

-1.8

-1.2

-0.6

lg(A

)

lg()

hard

soft

lg(

)lg()

log-log scale Hg2I2

A~A~ ~~

=(T-T=(T-Tcc)/T)/Tc c – reduce temperature– reduce temperature

0.2 0.4 0.6 0.81.8

2.0

2.2

2.4

2.6

0.2 0.4 0.6 0.8

-1.5

-1.0

-0.5

lg(A

)

lg()

lg(

)lg()

soft

hard

Temperature dependence of susceptibility in Hg2I2

0.000

0.002

0.004

0.006

0.008

0.010

-20 -10 0 10 20 30 40 50 60 70 80 90

100

150

200

250

300

350

Inve

rse

Inte

nsity

Inte

nsity

, arb

. uni

ts

T,K

Conclusion•The Effects of the phase transition such as nucleation of low-The Effects of the phase transition such as nucleation of low-temperature phase clusters in high-temperature tetragonal matrix temperature phase clusters in high-temperature tetragonal matrix and soft mode appearance in ferrophase was observed.and soft mode appearance in ferrophase was observed.

•Appearance of “ferroelectric” and “antiferroelectric” nanoclusters Appearance of “ferroelectric” and “antiferroelectric” nanoclusters in mixed crystals Hgin mixed crystals Hg22(Br,I)(Br,I)2 2 was investigated. Their appearance was investigated. Their appearance

induced by Hginduced by Hg22(BrI)(BrI)22 – mixed molecules existing in these – mixed molecules existing in these

compounds.compounds.

•Anisotropic diffuse X-ray scattering maxima associated with Anisotropic diffuse X-ray scattering maxima associated with order-parameter fluctuations and nucleation of low-temperature order-parameter fluctuations and nucleation of low-temperature orthorhombic clusters in the high-temperature tetragonal matrix orthorhombic clusters in the high-temperature tetragonal matrix have been found to exist at X-points. have been found to exist at X-points.

•New information has been obtained on the temperature New information has been obtained on the temperature dependence of the susceptibility and correlation length, cluster size dependence of the susceptibility and correlation length, cluster size shape and anisotropy, and the critical exponents.shape and anisotropy, and the critical exponents.