NEW CHALCOGENIDE-BASED PHASE-CHANGE
MATERIALS FOR POTENTIAL DATA STORAGE
APPLICATIONS
By
Joseph B. Wachter

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Chemistry
2010

ABSTRACT
NEW CHALCOGENIDE-BASED PHASE-CHANGE
MATERIALS FOR POTENTIAL DATA STORAGE
APPLICATIONS
By
Joseph B. Wachter
Phase-change materials are defined here as materials that undergo reversible, thermallyactivated glass-to-crystal transformations. These materials are utilized commercially in data
storage media such as rewriteable CDs and DVDs as a way to reversibly encode binary data.
The current industry standards for these materials are Ge2 Sb2 Te5 and several nonstochiometric alloys of Ag, Sn, Sb, Ge, In, and Te. The next generation of data storage devices calls
for faster switching rates, higher storage density, and better cyclability, for which the currently used materials may not be sufficient. This thesis will present several new chalcogenidebased phase-change materials that contain alkali metals and the lighter chalcogenides S and
Se. These materials, including K1-x Rbx Sb5 S8 , K2 Sb8 Se13 , and K2 Bi8 S13 , can be reversibly,
thermally interconverted between glassy and crystalline phases. They are semiconductors
and have optical band gaps in the range of 0.9-1.8 eV, which permits encoding by visible
or ultraviolet laser irradiation. The 1-x Rbx Sb5 S8 family of solid solutions shows the ability
to tune the thermal and optical properties of these materials by changing the value of x.
K2 Sb8 Se13 shows the extremely rare behavior of polyamorphism wherein there exists two
distinct amorphous phases as well as a crystalline phase, and each is stable and can be isolated at room temperature. Formed as a thin film on glass and silicon substrates, K2 Bi8 S13
was shown by kinetic measurements to have the potential to switch faster than existing materials. These compounds were characterized by thermal and optical analysis (DTA, DSC,
UV-Vis), X-ray diffraction (XRPD, PDF), and electron microscopy (TEM, SEM).

To Nora and Ethan.

iii

ACKNOWLEDGMENTS

The author would like to acknowledge the National Science Foundation, Grant DMR0443785, for funding this project. Additionally, collaborators on this project are acknowledged for their invaluable contributions.

iv

TABLE OF CONTENTS

LIST OF TABLES

vii

LIST OF FIGURES

viii

1 Introduction
References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
5

2 Local structure and influence of bonding on the phase-change behavior of
the chalcogenide compounds K1-x Mx Sb5 S8 (M= Rb, Tl)
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Experimental section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Electron microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Powder X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Synchrotron radiation diffraction experiments . . . . . . . . . . . . .
2.2.5 Thermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Raman scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.7 Thermal conductivity measurements . . . . . . . . . . . . . . . . . .
2.2.8 Electronic structure calculations . . . . . . . . . . . . . . . . . . . . .
2.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Phase-change behavior . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Glass-forming ability (GFA) . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Local structure: crystal versus glass . . . . . . . . . . . . . . . . . . .
2.3.4 Electronic absorption and Raman spectroscopy . . . . . . . . . . . .
2.3.5 Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 K2 Sb8 Se13 : a phase-change material exhibiting polyamorphism
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Experimental section . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Differential Scanning Calorimetry (DSC) . . . . . . . . . . .
3.2.3 X-ray powder diffraction . . . . . . . . . . . . . . . . . . . .

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3.2.4 Synchrotron radiation diffraction experiments
3.2.5 Optical energy band gaps . . . . . . . . . . .
3.2.6 Pyncnometry . . . . . . . . . . . . . . . . . .
3.3 Results and discussion . . . . . . . . . . . . . . . . .
3.3.1 Structural analysis . . . . . . . . . . . . . . .
3.3.2 Optical properties . . . . . . . . . . . . . . . .
3.3.3 Density measurements . . . . . . . . . . . . .
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . .
References and Notes . . . . . . . . . . . . . . . . . . . . .
4 Investigation into the switching mechanisms of the
genide K2 Sb8 Se13
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
4.2 Experimental section . . . . . . . . . . . . . . . . . .
4.2.1 Synthesis . . . . . . . . . . . . . . . . . . . .
4.2.2 Differential Scanning Calorimetry (DSC) . . .
4.3 Results and Discussion . . . . . . . . . . . . . . . . .
4.3.1 Kissinger analysis . . . . . . . . . . . . . . . .
4.3.2 Ozawa-Flynn-Wall analysis . . . . . . . . . . .
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . .
References and Notes . . . . . . . . . . . . . . . . . . . . .

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polyamorphic chalco.
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APPENDICES
A.1 Design of an analytical laser-switching device . . . . . . . . . . . . . . . . . .

82
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5 Synthesis and phase-change behavior of K2 Bi8 S13
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
5.2 Experimental section . . . . . . . . . . . . . . . . .
5.2.1 Synthesis of crystalline K2 Bi8 S13 . . . . . .
5.2.2 Synthesis of amorphous K2 Bi8 S13 thin films
5.2.3 Differential Scanning Calorimetry (DSC) . .
5.2.4 Transmission electron microscopy (TEM) . .
5.2.5 Scanning electron microscopy (SEM) . . . .
5.3 Results and discussion . . . . . . . . . . . . . . . .
5.3.1 Structural analysis . . . . . . . . . . . . . .
5.3.2 Analysis of films . . . . . . . . . . . . . . .
5.3.3 Electron microscopy . . . . . . . . . . . . .
5.3.4 Thermal analysis . . . . . . . . . . . . . . .
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . .
References and Notes . . . . . . . . . . . . . . . . . . . .

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LIST OF TABLES

2.1

Dependence on the reduced glass transition temperature Trg , the supercooled
liquid region ∆Txg and Hruby parameters Kgl and Kgl from Rb content for
K1-x Rbx Sb5 S8 at a heating rate of 10o C/min. . . . . . . . . . . . . . . . . .

15

3.1

Energy gaps and density of the three states of K2 Sb8 Se13 . . . . . . . . . . .

48

4.1

Comparison of crystallization energy, Ec , and rate constant, k(T ), of
K2 Sb8 Se13 with KSb5 S8 and Ge2 Sb2 Te5 at 20 K/min heating rate. . . . . .

57

5.1

Comparison of crystallization energy, Ec , and reduced glass transition temperature, Trg = Tg /Tm (3 ), of K2 Bi8 S13 with KSb5 S8 , K2 Sb8 Se13 and Ge2 Sb2 Te5 . 72

A.2 Connections from Atmega128 to AD5206. . . . . . . . . . . . . . . . . . . . .

85

A.3 Connections from Atmega128 to MAX9483. . . . . . . . . . . . . . . . . . .

85

vii

LIST OF FIGURES

2.1

Powder X-ray diffraction patterns of as-synthesized glasses of K1-x Rbx Sb5 S8
(a-c, x = 0.25, 0.5, 0.75, respectively) and TlSb5 S8 (d), showing their amorphous nature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

X-ray diffraction patterns of: (a) K0.25 Rb0.75 Sb5 S8 glass, as-synthesized. (b)
K1-x Rbx Sb5 S8 after annealing for 2 h at 300o C. (c) KSb5 S8 calculated from
crystal structure ( monoclinic P n; a = 8.1374 ˚; b = 19.5013 ˚; c = 9.0620
A
A
˚) (11 ). The difference in low-angle peak ((020) reflection) between the pure
A
K structure and the 75% Rb structure is 0.402o in 2θ. . . . . . . . . . . . . .

14

DSC thermograms of K1-x Rbx Sb5 S8 amorphous alloys with heating rate
10o C/min. (a) x = 0.0, (b) x = 0.25, (c) x = 0.5, and (d) x = 0.75. The
glass transition (Tg ) was determined by the intersection of the curve and the
halfway line between the two base lines. . . . . . . . . . . . . . . . . . . . . .

16

Dependence of the glass transition (Tg ), crystallization peak (Tp ) and the
onset of melting point (Tm ) on the Rb content (x) in 1-x Rbx Sb5 S8 . . . . . .

17

DSC thermograms with heating rate 10o C/min: (a) RbSb5 S8 , (b) TlSb5 S8 ,
first heating and (c) TlSb5 S8 , second heating. . . . . . . . . . . . . . . . . .

19

2.6

Experimental structure functions of crystalline and glassy KSb5 S8 . . . . . . .

21

2.7

(a) PDF plot of crystalline KSb5 S8 , experimental, (b) PDF plot of glassy
KSb5 S8 , (c) Sb coordination environment of KSb5 S8 . . . . . . . . . . . . . .

22

Solid state UV-Vis reflectance spectra of K0.75 Rb0.25 Sb5 S8 converted to absorption via the Kubelka-Monk procedure. The spectra for K0.5 Rb0.5 Sb5 S8
and K0.25 Rb0.75 Sb5 S8 glasses are similar. Band gaps extrapolated linearly to
0 are 1.50, 1.47, and 1.51 eV respectively. . . . . . . . . . . . . . . . . . . .

25

2.2

2.3

2.4

2.5

2.8

viii

2.9

Raman scattering data on crystalline (a) and glassy (b) KSb5 S8 at room
temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

2.10 Raman scattering data of glassy KSb5 S8 at various temperatures along the
heating curve, The crystallization event is shown by the sharpening of peaks
between 210 and 335o C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

2.11 Raman scattering data of KSb5 S8 cooled from the molten state. Crystallization is evidenced by the sharpened features near 338, 321, 310, 298, and 280
cm-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

2.12 Temperature dependence of thermal conductivity of the crystalline and glassy
KSb5 S8 (4-300K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

3.1

The crystal structure of K2 Sb8 Se13 . . . . . . . . . . . . . . . . . . . . . . . .

42

3.2

(A) crystalline K2 Sb8 Se13 . (B) material obtained by quenching molten
K2 Sb8 Se13 (glass-β). (C) X-ray powder diffraction patterns from the three
phases of K2 Sb8 Se13 : i) as-synthesized glass-β; (ii) glass-α after heating to
225o C and (iii) crystalline phase after heating above 263o C. (Cu Kα radiation). 43

3.3

DSC thermogram of K2 Sb8 Se13 ribbon. Three phase changes are observed
from glass-β to glass-α (227o C), from glass-α to crystal (263o C), and melting
(443o C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

(A) Pair-distribution function analysis of the three phases of K2 Sb8 Se13 : assynthesized glass-β; glass-α after heating to 220o C and crystalline phase after
heating to 270o C. (B) Optical absorption spectra showing energy gaps for
crystalline and glass-α K2 Sb8 Se13 . . . . . . . . . . . . . . . . . . . . . . . .

46

Baseline-corrected, nonisothermal DSC traces of K2 Sb8 Se13 at heating rates
β of 5, 10, 15, and 20 K/min. . . . . . . . . . . . . . . . . . . . . . . . . . .

56

Kissinger plot of K2 Sb8 Se13 glass β to glass α, ln(β/Tp ) vs. 1000/T and the
straight regression line (β in K s−1 ) . . . . . . . . . . . . . . . . . . . . . . .

58

Kissinger plot of K2 Sb8 Se13 glass α to crystal, ln(β/Tp ) vs. 1000/T and the
straight regression line (β in K s−1 ) . . . . . . . . . . . . . . . . . . . . . . .

58

3.4

4.1

4.2

4.3

ix

4.4

OFW plot of ln(β) vs. 1/T for different values of α during the first phase
transition (glass β-to-glass α) of K2 Sb8 Se13 . . . . . . . . . . . . . . . . . . .

60

OFW plot of ln(β) vs. 1/T for different values of α during the first phase
transition (glass β-to-glass α) of K2 Sb8 Se13 . . . . . . . . . . . . . . . . . . .

61

XRPD of K2 Bi8 S13 film after annealing at temperatures (from top) of 350,
325, 275, 250, 150, and 100o C, showing the glass-to-crystal phase change and
stability of the crystal up to 350o C. . . . . . . . . . . . . . . . . . . . . . . .

69

TEM image of K2 Bi8 S13 film after annealing. Crystalline Bi2 S3 domains are
visible. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

5.3

SEM image of as-synthesized K2 Bi8 S13 glass film. . . . . . . . . . . . . . . .

71

5.4

DSC trace of K2 Bi8 S13 glass film at a heating rate of 15 K/min. The exotherm
at 181o C shows crystallization of the glass, confirmed by XRPD after the scan. 73

5.5

Kissinger plot of K2 Bi8 S13 film for heating rates of 5, 10, and 15 K/min.
2
Regression line has the equation ln(β/Tp ) = 14.48/Tp − 12756.88. . . . . . .

74

5.6

Ozawa-Flynn-Wall plots, ln β vs. 1/T for α=0.2-0.85, of K2 Bi8 S13 film. . . .

75

5.7

Activation energy of crystallization Ec vs. extent of reaction α for K2 Bi8 S13
film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

4.5

5.1

5.2

5.8

JMA-Matusita plot of K2 Bi8 S13 films at heating rates of 5, 10, and 15 K/min. 77

A.9 Schematic of data flow in the laser device. . . . . . . . . . . . . . . . . . . .

83

A.10 The extracted laser diode module. . . . . . . . . . . . . . . . . . . . . . . . .

84

A.11 The user input module (Olimex AVR-MT-128). . . . . . . . . . . . . . . . .

85

A.12 The MAX9483 laser driver mounted to a printed circuit board. Extension
pins are spaced 0.001” apart. . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

x

CHAPTER 1

Introduction

With the volume of data carried and processed by the world increasing at a substantial
rate, the need for ultra-high-density data storage becomes more prevalent. Conventional
non-volatile storage media, such as magnetic hard disks, will run into a spot size barrier
well before the predicted need of 20 nm spots because of inherent limitations such as supermagnetic effects (1 ). Phase-change materials are promising in this area since they allow for
extremely small spots that are thermally stable in a large temperature range and unaffected
by electric or magnetic fields. (2 –5 )
Most conventional phase-change materials, such as the widely used Ge2 Sb2 Te5 , exhibit
glassy and crystalline phases that can be interconverted with heat. The glass forms upon
cooling from the melt. Reheating the glass causes it to go through a glass transition and
then a glass-crystal transition below the melting point. After this point, the material is
cooled and maintains its crystallinity, where re-melting can again afford the glass. A useful
material should exhibit excellent cyclability without significant degradation. (6 , 7 )
The methods for heating the material vary greatly, leading to an assortment of promising
devices for non-volatile data storage. Currently in wide use are the laser-activated rewriteable
compact discs (CD) and digital versatile discs (DVD). In these devices, a polycarbonate disc
is coated with a thin film of phase-change material in the glass form. The data are written by
focusing a laser with frequency above the band gap of the material on a spot and heating just
beyond the crystallization temperature. The disc is read by a less powerful laser measuring

1

the difference in refraction between glassy and crystalline spots as binary data.
Because of the limitations of laser-written, disc-based media, new methods of data storage have been investigated, many utilizing phase-change materials. Current-induced phase
changes, heating the material with an electrical current rather than a laser (Joule heating), have become attractive for their fast access times, potentially smaller spot sizes, and,
in some cases, no moving parts. Phase-Change Random Access Memory (PC-RAM), also
called Ovonic Unified Memory (OUM), seeks to replace the current RAM-hard drive tandem
used in virtually all computers with a single device. The capacitance-driven RAM currently
used in computers can be accessed extremely fast, but the data must eventually be written to a hard drive as the RAM is volatile and will degrade after a short period of time.
PC-RAM solves this problem by storing the data in a way that is thermally and electrically
stable. The spots are read in this case by measuring the difference in resistance between
the crystalline and glassy phases as binary data. Simulations using conductive transparent
probes have achieved spot sizes as low as 20 nm, leading to nearly 1 terabit/inch2 storage
density, hundreds of times greater than today’s best materials. (2 )
For all the research and development going into new technology based on phase-change
materials, there is little research into new materials. New PC-based devices, from the latest
in high-density DVD’s to the current-based systems mentioned above, all utilize either a
Ge/Sb/Te phase (most often Ge2 Sb2 Te5 ) or the non-stoichiometric Ag/In/Sb/Te phases (8 ).
Progress in the area of new materials exhibiting phase-change properties could positively
impact whichever technology becomes the industry standard, and advances in the properties
of the materials stand to benefit the efficacy of the device from the most basic level; therefore,
research into the most fundamental materials is crucial to the success of the format.
In order to synthesize new phase-change materials with the desirable properties of high
interconversion speed, good cyclability and stability, the underlying chemistry should be
examined. For a fast interconversion time, there should be a large driving force, such as
a large energy difference between the amorphous and crystalline structure, and the atoms

2

should not need to travel a long distance. For good cyclability, the composition of the
structure should be stoichiometric so as to avoid phase separation. The material should
also be a semiconductor, allowing it to be interconverted by lasers and used in optical data
storage devices. (9 )
The alkali (or pseudoalkali) antimony sulfides are a promising system to explore for
new phase-change materials. They are semiconductors with a range of band gaps. Most
compounds have well-defined stoichiometries and are charge-balanced. The variety in the
coordination environment of antimony can also be a factor in its ability to form phase-change
materials. The mostly inert lone pair in Sb3+ is expressed by distorting the coordination
away from octahedral. This may contribute to the phase-change behavior exhibited in several
antimony chalcogenides.
Currently, there are no known bismuth-based phase-change materials in the literature.
Antimony seems to occupy a ”sweet spot” between As and Bi with regard to its ability
to vary its coordination, leading to phase-change behavior. Many phosphorus and arsenic
compounds vitrify easily (10 ); indeed, they may be more difficult to crystallize, while Bi
compounds are often more symmetric and more difficult to vitrify. This does, however,
make Bi a likely target for exceptionally fast PCMs, as the quenching rate needed to form
the glass has been implicated in the speed of the glass-to-crystal phase transition.

3

References and Notes

4

References and Notes

[1] Lee, K. M.; Polycarpou, A. A. 2006, 20, 1322 – 1337.
[2] Murashita, T. Mat. Res. Soc. Symp. Proc. 2004, 803, HH1 – 3 – 1.
[3] Kado, H.; Tohda, T. Appl. Phys. Lett. 1995, 6, 296.
[4] Peng, C.; Cheng, C.; Mansuripur, M. J. Appl. Phys. 1997, 82, 4183.
[5] Gotoh, T.; Sugawara, K.; Tanaka, K. J. Non-Cryst. Solids 2002, 299-302, 968.
[6] Yamada, N.; Ohno, E.; Nishiuchi, K.; Akahira, N.; Takao, M. Journal Of Applied Physics
1991, 69, 2849 – 2856.
[7] Yamada, N.; Matsunaga, T. Journal Of Applied Physics 2000, 88, 7020 – 7028.
[8] Wright, C. D.; Armand, M.; Aziz, M. M.; Senkader, S.; Yu, W. Mat. Res. Soc. Symp.
Proc. 2004, 803, HH1 – 2 – 1.
[9] Feringa, B.; Jager, W.; Delange, B. Tetrahedron 1993, 49, 8267 – 8310.
[10] Chung, I.; Jang, J. I.; Gave, M. A.; Weliky, D. P.; Kanatzidis, M. G. Chem. Commun.
2007, 4998 – 5000.

5

CHAPTER 2

Local structure and influence of bonding on the phase-change
behavior of the chalcogenide compounds K1-x Mx Sb5 S8 (M= Rb,
Tl)

2.1

Introduction

Phase-change materials are gaining increasing interest because of their use in the data storage media crucial to the information technology industry. (1 , 2 ) These materials exhibit
reversible glass-to-crystal phase transitions and can be used in applications as diverse as
non-volatile memory (3 ), digital video disks (4 ), polarized holograms (5 ), opto-mechanical
actuators (6 ) and infrared optical waveguides (7 ). There are two major classes of phasechange materials: stoichiometric and non-stoichiometric. Stoichiometric phase-change materials, such as the industry standard Ge2 Sb2 Te5 (8 ), consist of a single crystallographically
distinct structure, which is recovered in pure form upon recrystallization. Non-stoichiometric
glasses tend to crystallize into a mixture of two or more structures. An example of this is
the (Li2 S)x (Sb2 S3 )1-x , x=0-0.17 system, which crystallizes into a mixture of LiSbS2 and
Sb2 S3 (9 ). The stoichiometric materials are more advantageous due to faster crystallization
rates, better cyclability and long lifetimes.
The compound KSb5 S8 is isostructural to TlSb5 S8 , the mineral parapierrotite, and is
a stoichiometric phase-change material that exhibits a rapid and reversible glass-to-crystal
transition (10 ). The crystalline phase melts at 441o C and does not recrystallize on rapid

6

cooling. Upon subsequent heating, there is a glass transition at 223o C followed by a rapid
crystallization at 287o C. Its structure is made of undulating [Sb5 S8 ]- layers with K+ ions
seated in between the layers. The layers however interact strongly with one another forming
essentially a three-dimensional [Sb5 S8 ]- network, Figure 2.1(a) (11 ). This system is an
interesting study case because it presents a combination of covalent bonding (i.e. Sb–S bonds)
and ionic K—S bonding both of which can influence the phase-change behavior. Almost
all materials that have been studied so far possess exclusively covalent bond frameworks.
KSb5 S8 is a semiconductor with a band gap of 1.82 eV for the crystalline phase and 1.67 eV
for the glass. The activation energy of crystallization for KSb5 S8 is 167±3.1 kJ/mol and the
rate constant for the peak temperature was found to be comparable to that of Ge2 Sb2 Te5
(12 ). The crystallization process appears to proceed via a bulk multi-step crystallization
mechanism, where the nucleation rate increases with time. (13 )
To further understand the KSb5 S8 system we investigated the isostructural solid solutions
of the type K1-x Rbx Sb5 S8 . By partially substituting K for Rb the properties can be subtly
altered while preserving the structure and the phase-change capacity. For example, the
same ASb5 S8 structure forms with K+ , Rb+ and Tl+ and thus it is possible to prepare
solid solutions of the type K1-x Rbx Sb5 S8 and K1-x Tlx Sb5 S8 (11 , 14 ). These represent small
but significant perturbations on the parent phase that could allow a better assessment of
how changes in ionic bonding affect the phase-change and other properties of KSb5 S8 . Such
studies could lead to a deeper understanding of the relationship of ionic vs. covalent bonding
and crystallization kinetics in phase-change materials. Here we report on the evolution of
physical, thermal and phase-change properties of a representative set of K1-x Rbx Sb5 S8 solid
solutions. We discuss structure-property relationships though local structure studies using
pair distribution function analysis (PDF), electronic structure and bonding analysis using
density functional theory (DFT) band structure calculations. We also performed Raman and
optical spectroscopic studies recorded during a phase-change event. In addition we report
thermal conductivity measurements for KSb5 S8 . The thermal conductivity is a key property

7

Intensity (arb. units)

(a)

(b)
(c)
(d)
0

20

40

60

80

100

120

2θ, deg

Figure
X-ray diffraction patterns
glasses of K1-x
Figurex12.1. Powder0.75, respectively) and TlSb of as-synthesizedtheir amorphousRbxSb5S8
. 0.25, 0.5,
(a-c, =
S (d), showing
nature.
5 8

8

in phase-change switching materials and it is highly favorable in this case as it is one of the
lowest known for solid-state materials.

2.2
2.2.1

Experimental section
Synthesis

K2 S and Rb2 S were prepared by the reaction of a stoichiometric mixture of potassium or
rubidium metal and sulfur in liquid ammonia at -78o C until no trace of the metal was left
(approx. 12 h). The ammonia was then allowed to evaporate and the resulting pale yellow
powder was dried under vacuum for 24 h. Sb2 S3 was prepared by reacting a stoichiometric
mixture of Sb and S powders in a silica tube at 750o C for 24 h, then quenched in air to room
temperature. K1-x Rbx Sb5 S8 solid solutions were prepared by a stoichiometric combination
of potassium sulfide, rubidium sulfide, and antimony sulfide, where the potassium sulfide to
rubidium sulfide ratio was allowed to vary. A mixture of K2 S (1-x mmol, 0 < x < 1), Rb2 S
(x mmol), and 1.698 g Sb2 S3 (5.00 mmol) was loaded in a silica tube under a dry nitrogen
atmosphere in a Vacuum Atmospheres Dri-Lab glovebox and flame-sealed under reduced
pressure (< 10−4 mbar). The mixture was heated in a flame until a homogeneous, orange
melt was achieved, which was then quenched in air to form a silver, glassy ingot. The yield
was quantitative. Crystalline K1-x Rbx Sb5 S8 was formed by annealing the glassy ingot above
the crystallization point, which ranged from 278 to 314o C depending on composition. Glassy
TlSb5 S8 was prepared by the reaction of a stoichiometric combination of Tl metal, Sb2 S3 ,
and sulfur powder. The reactants were loaded into in a silica tube under a dry nitrogen
atmosphere in a Vacuum Atmospheres Dri-Lab glovebox and flame-sealed under reduced
pressure (< 10−4 mbar). The mixture was heated in a furnace at 800o C for 1 d, then quickly
removed and quenched in ice water to afford the TlSb5 S8 glass.

9

2.2.2

Electron microscopy

Quantitative microprobe analyses of the compounds were performed with a JEOL JSM-35C
scanning electron microscope (SEM) equipped with a Tracor Northern energy-dispersive
spectroscopy (EDS) detector. Data were acquired using an accelerating voltage of 25 kV
and a 1-min acquisition time.

2.2.3

Powder X-ray diffraction

The samples were examined by X-ray powder diffraction for identification and to assess phase
purity. Powder patterns were obtained using a CPS 120 INEL X-ray powder diffractometer
with Ni-filtered Cu Kα radiation operating at 40 kV and 20mA and equipped with a positionsensitive detector. The purity of phases was confirmed by comparison of the X-ray powder
diffraction patterns to ones calculated from single crystal data using the NIST Visualize
1.0.1.2 software.

2.2.4

Synchrotron radiation diffraction experiments

Synchrotron radiation scattering experiments were carried out at the beamline 11-ID-C at
the Advanced Photon Source at Argonne National Laboratory using X-rays of energy 115.68
keV (λ = 0.1072 ˚ ). The higher energy X-rays were used to obtain diffraction data to higher
A
values of the wave vector, Q, which is important for the success of atomic PDF analysis. The
measurements were carried out in symmetric transmission geometry and scattered radiation
was collected with an intrinsic germanium detector connected to a multi-channel analyzer.

2.2.5

Thermal analysis

Differential thermal analysis (DTA) was performed with a computer-controlled Shimadzu
DTA-50 thermal analyzer. The crushed powders (∼ 25 mg total mass) were sealed in silica
ampoules under reduced pressure (< 104 mbar). A silica ampoule of equal mass was sealed
and placed on the reference side of the detector. The samples were heated to 850o C at a rate

10

of 10o C/min where they were isothermed for 5 min followed by cooling at 10o C/min to room
temperature. The differential scanning calorimetric (DSC) measurements were carried out
with a Setaram DSC141 calorimeter. Temperature and energy calibrations of the instrument
were performed, for different heating rates, using the well-known melting temperatures and
melting enthalpies of high-purity zinc and indium supplied with the instrument. Bulk-shaped
specimens weighing about 7 mg were crimped in aluminum crucibles; an empty aluminum
crucible was used as reference. A constant flow of nitrogen was maintained to provide
a constant thermal blanket within the DSC cell, thus eliminating thermal gradients and
ensuring the validity of the applied calibration standard from sample to sample. In the DSC
measurements, the heating rate was 10o C/min.

2.2.6

Raman scattering

Raman spectra were measured on a Jobin-Yvon LABRAM 28 spectrometer equipped with a
LINKAM high-temperature cell. To eliminate artifacts from oxidative sample decomposition,
all the experiments were repeated with the samples sealed in silica ampules. A solid-state
diode laser was used for all measurements, generating 10mW power at an excitation wavelength of 785 nm. Scattered radiation was collected with a CCD. For each run, two scans
were accumulated at a scanning time of 60 s, generating a spectrum with a resolution of 0.7
cm-1 . Raman spectra were also obtained with a Holoprobe Raman spectrograph equipped
with a CCD camera detector using 633nm radiation from a HeNe laser for excitation and a
resolution of cm-1 .

2.2.7

Thermal conductivity measurements

The thermal conductivity was determined with a longitudinal steady-state method over the
temperature range 4-300 K. In this case, samples were attached (using either a low melting
point solder or silver-loaded epoxy) to the cold tip of the cryostat, while the other end of
the sample was provided with a small strain gauge resistor (thin film), which serves as a

11

heater. Temperature difference across the sample was measured using differential chromelconstantan thermocouple. Both crystalline and glassy KSb5 S8 materials were measured. The
polycrystalline samples were cylindrical in shape with diameter 4 mm and length about 5
mm. Radiation loss is an unavoidable error in all thermal conductivity measurements made
using a longitudinal steady-state technique manifested in deviations from the true value
that increase with temperature above about 200 K. In order to determine the radiation loss
experimentally, we made a subsequent measurement with the sample detached from the heat
sink (sample hangs by thin connecting wires). We determined the amount of heat needed to
supply to the heater that raises the temperature of the entire sample to the same average
temperature as during the actual measurement of the thermal conductivity. The values of
the thermal conductivity were then corrected for this radiation loss.

2.2.8

Electronic structure calculations

Electronic structure calculations were performed using the self-consistent full-potential linearized augmented plane wave (LAPW) method (15 ) within DFT (16 ), using the generalized
gradient approximation (GGA) of Perdew et al. (17 ) for the exchange and correlation potential. Convergence of the self-consistent iterations was performed for 20 k points inside
the irreducible Brillouin zone to within 0.0001 Ry with a cutoff of –6.0 Ry between the
valence and the core states. Scalar relativistic corrections were included and a spin-orbit
interaction was incorporated using a second variational procedure (18 ). The calculations
were performed using the WIEN2K program (19 ).

2.3
2.3.1

Results and discussion
Phase-change behavior

Solid solutions of the form K1-x Rbx Sb5 S8 were synthesized with x = 0, 0.25, 0.5 and 0.75
by quenching the corresponding melts in air or water. They were obtained as shiny, gray
metallic-like glasses, which are red-purple in fine powdered form and are amorphous by
12

powder X-ray diffraction (Figure 2.1(b)). The crystalline phases exhibit the same color
difference between bulk and powder, though the crystalline form is a dull, silver ingot rather
than mirror-like. Powder X-ray diffraction of these samples obtained after annealing above
the crystallization temperature showed them to be isostructural to the parent KSb5 S8 (20 ).
The increasing incorporation of the larger Rb atom in K1-x Rbx Sb5 S8 is confirmed by the shift
of the (200) reflection in the X-ray diffraction pattern from 9.031 to 8.601 in 2θ (Figure 2.2).
The effect of this substitution on the thermal properties of the materials was measured
with DTA and DSC experiments. We observed systematic evolution of the crystallization as
a function of temperature, and in some cases incongruent melting as indicated by the two
melting endotherms. The thermograms of the four different samples with x = 0, 0.25, 0.50
and 0.75 are presented in Figure 2.3 where the glass transition (Tg ), the crystallization peak
(Tp ) and the melting point (Tm ), considered as the onset of melting peak, temperatures are
shown. There is a pronounced differentiation in phase-change behavior as the Rb fraction
increases in the compound. As shown by the sharp exothermic crystallization peaks in
the range 280 - 310o C, each of these glasses is a phase-change material with a well-defined
crystallization process.
The melting point decreases with enrichment (Figure 2.4), which is most probably due
to the larger size of Rb+ as compared to K+ (1.60 ˚ vs. 1.51 ˚ ) giving rise to longer and
A
A
weaker Rb2 S bonds thereby softening the lattice. This follows the general trend in alkali
metal chalcogenides of a decrease in melting point with increasing alkali metal size (21 ). This
trend is followed until x = 0.50 (eutectic point) and then it reverses as we move towards
pure RbSb5 S8 . A similar trend is observed in the crystallization peaks. The increase of x
(Rb content) up to 0.25 results in quite a small shift of the crystallization peak to lower
temperatures, and then for x = 0.25 is observed a shift to higher temperatures, indicating
a minimum value at about x = 0.25. The shifts in crystallization temperature could be
attributed to a destabilization of the glass up to a minimum between x = 0.25 and 0.50
(melting point temperature trend), and then a locking in of the structure nearing total K

13

Intensity (arb. units)

400

(a)

200

(b)

(c)
0
20

40

2θ, deg

Figure 2.
Figure 2.2.

60

80

X-ray diffraction patterns of: (a) K0.25 Rb0.75 Sb5 S8 glass, as-synthesized. (b)
K1-x Rbx Sb5 S8 after annealing for 2 h at 300o C. (c) KSb5 S8 calculated from crystal structure
( monoclinic P n; a = 8.1374 ˚; b = 19.5013 ˚; c = 9.0620 ˚) (11 ). The difference in lowA
A
A
angle peak ((020) reflection) between the pure K structure and the 75% Rb structure is
0.402o in 2θ.

14

K1-x Rbx Sb5 S8 x(Rb) Trg
0.00
0.25
0.50
0.75

0.68
0.69
0.71
0.72

∆Txg (K) Kgl Kgl
52.7
0.31 0.29
58.5
0.48 0.37
65.9
0.58 0.48
69.9
0.61 0.56

Table 2.1. Dependence on the reduced glass transition temperature Trg , the supercooled
liquid region ∆Txg and Hruby parameters Kgl and Kgl from Rb content for K1-x Rbx Sb5 S8
at a heating rate of 10o C/min.

occupancy leading to the increase in the crystallization temperature.
The compounds TlSb5 S8 and RbSb5 S8 were not examined in-depth because of their
propensity to phase separate when undergoing transitions, both in melting and crystallization. The glass formed by melting a stoichiometric mixture of Rb2 S and Sb2 S3 and quenching it in water was found to recrystallize at 311 and 391o C, respectively, before melting at
421o C (Figure 2.5(a)). Annealing the Rb-containing glass at 320o C showed crystallization
to RbSb5 S8 , RbSbS2 , and Sb2 S3 , as determined with X-ray diffraction.
The initial glass of TlSb5 S8 crystallizes at 294 o C and melts rather congruently at 417o C
(Figures 2.5(b) and 2.5(c)). Upon cooling, however, a mixture of the crystalline phases
TlSbS2 , Sb2 S3 , and TlSb5 S8 were identified. This is consistent with the phase diagram of
the Tl2 S/Sb2 S3 system reported previously (22 ).
2.3.2

Glass-forming ability (GFA)

GFA as related to the ease of devitrification is a crucial property for understanding the origins
of glass formation and also important for designing and developing new bulk glasses (23 ). In
K1-x Rbx Sb5 S8 , following the initial heating treatment, the samples were cooled from 500o C
to RT at rates of 10 and 25o C/min. It was observed that the parent KSb5 S8 phase (x =
0) crystallizes completely upon slow cooling (10 or 25o C/min) from 500o C, whereas for x
= 0.25 and 0.50 the compound crystallizes partially under these conditions and complete
vitrification was observed for x = 0.75. Thus, the incorporation of Rb tends to enhance
GFA.

15

Figure 2.3. DSC thermograms of K1-x Rbx Sb5 S8 amorphous alloys with heating rate
10o C/min. (a) x = 0.0, (b) x = 0.25, (c) x = 0.5, and (d) x = 0.75. The glass transition (Tg ) was determined by the intersection of the curve and the halfway line between the
two base lines.

16

300

Tm

440

295
430
290

o

o

285

T ( C)

T ( C)

420

410

Tp

280

400
275

Tg
390

270
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

x (Rb content)

igure 4
Figure 2.4. Dependence of the glass transition (Tg ), crystallization peak (Tp ) and the onset
of melting point (Tm ) on the Rb content (x) in 1-x Rbx Sb5 S8 .

17

The GFA of a melt is evaluated in terms of critical cooling rate (Rc ) for glass formation,
which is the minimum cooling rate necessary to keep the melt amorphous without precipitation of crystals during solidification. The smaller the Rc , the higher the GFA of a system;
however, Rc is a parameter that is difficult to measure precisely. As a result, many criteria
have been proposed to reflect the relative GFA on the basis of the characteristic temperatures
measured by DTA (24 ). The most extensively used criteria are the reduced glass transition
temperature Trg (glass transition temperature Tg over liquidus temperature Tl or melting
temperature Tm ) and the supercooled liquid region ∆Txg (the temperature difference between the onset crystallization temperature Tx and the glass transition temperature Tg ).
Generally, the larger the temperature interval ∆Txg the higher the GFA. Another parameter
Kgl suggested by Hruby (25 ) is also used as a measure of the glass-forming tendency of
materials:
Kgl = (Tx − Tg )/(Tm − Tx )

(2.1)

or Kgl where Tl instead of Tm is used (26 ). According to Hruby, the higher the value of Kgl
in a glass, the higher is its stability against crystallization on heating and, presumably the
higher its vitrifiability on cooling.
In Table 2.1, we present the values of all the characteristic parameters (Trg , ∆Txg , Kgl ,
Kgl ) for the K1-x Rbx Sb5 S8 system. All the calculated parameters increase with the decrease
in the K+ ion fraction, indicating that glass stability and GFA increase with an increase in x.
This stabilization means that the melt need not be cooled as quickly to afford the glass and
implies a much higher energy barrier of atomic realignment towards the crystal resulting in a
slower crystallization speed. This effect is believed to be caused by the greater polarizability
and larger size of the Rb atom as compared to K, which results in lower mobility in the
lattice and slows down the conversion process to the ordered crystalline phase. Furthermore,
the longer Rb2 S bonds and increased structural disorder of the solid solution result in a
decreased absolute lattice energy compared to the pristine KSb5 S8 . This diminishes the
thermodynamic driving force to transform from the higher energy glass state to the lower

18

Figure 2.5. DSC thermograms with heating rate 10o C/min: (a) RbSb5 S8 , (b) TlSb5 S8 , first
heating and (c) TlSb5 S8 , second heating.

19

lying crystalline state.

2.3.3

Local structure: crystal versus glass

The structures of crystalline and glassy KSb5 S8 and several K1-x Rbx Sb5 S8 compositions
were probed with X-ray scattering using PDF analysis (27 ). Deeper structural clues were
sought as to the nature of glass vis-a-vis crystal by investigating similarities and differences
in the structure of both forms at the atomic level. The atomic PDF technique has emerged
recently as a powerful tool for the characterization and structure refinement of materials
with intrinsic disorder. The utility of the technique stems from the fact that it takes into
account the total diffraction, that is Bragg as well as diffuse scattering, and so it can be
applied to both crystalline (28 ) and amorphous materials (29 ). Therefore, the technique is
both a local and an extended structure probe and thus a powerful tool that can be used to
identify differences in structural features between the crystalline and glassy versions of these
materials (30 ).
The PDF, G(r), is obtained from the experimentally determined total-scattering structure function, S(Q), by a sine Fourier transform
2 ∞
Q[S(Q) − 1] sin(Qr)dQ
π 0
= 4πr[ρ(r) − ρ0 ]

G(r) =

(2.2)
(2.3)

where ρ is the distance between two atoms and Q the magnitude of the scattering vector,
and S(Q) is the corrected and properly normalized powder diffraction pattern of the material
(also called the structure function). ρ(r) and ρ0 are the local and average atomic number
densities, respectively, and ρ is the radial distance. Experimental structure functions S(Q)
for crystalline and glassy KSb5 S8 are shown in Figure 2.6 on an absolute scale. The structure
of crystalline KSb5 S8 was analyzed and refined based on the PDF data to obtain a basis
for the structural comparisons of the glass forms and the results were in excellent agreement
with those of the single crystal refinement (11 ). In the glass, the Bragg peaks are lacking and

20

0.60

0.48

Q[S(Q)-1]

0.36

KSb5S8 (crystalline)

0.24

0.12

KSb5S8 (glass)

0.00

-0.12
0

3

6

9

12

15

18

21

24

27

-1

Wavevector Q, Å

Figure 6 2.6. Experimental structure functions of crystalline and glassy KSb5 S8 .
Figure

21

30

Figure 2.7. (a) PDF plot of crystalline KSb5 S8 , experimental, (b) PDF plot of glassy KSb5 S8 ,
(c) Sb coordination environment of KSb5 S8 .

22

only diffuse scattering is observed; however, the scattering profile tracks closely the profile of
the crystalline form. Beyond 8 ˚-1 , both scattering patterns merge into a slowly oscillating
A
diffuse component.
The experimental PDFs for both forms of KSb5 S8 are shown in Figures 2.7(a) and (b),
respectively. They were obtained from the synchrotron radiation diffraction data following
the usual data reduction procedures described previously (28 ). As can be seen in Figure 2.7
the experimental PDFs peak at characteristic distances separating pairs of atoms and thus
reflect the local atomic-scale structure. In the crystalline phase, these molecular units are
arranged into a 3D periodic structure and the corresponding experimental PDF oscillates out
to high interatomic vectors (see Figure 2.7(a)). In particular, the first peak in both PDFs is
located between 2.4 and 2.8 ˚, reflecting the Sb-S bonds in the sample. As determined from
A
the crystal structure of KSb5 S8 , there are several SbS6 and SbS7 coordination polyhedra
with a spread of Sb-S bond lengths. One typical such fragment is shown in Figure 2.7(d).
The second and third PDF peaks occur at approximately 4 and 6 ˚ and reflect mostly the
A
nearest Sb-Sb and S-S atomic neighbor distances and possibly some longer Sb-S distances.
The three PDF peaks, which occur within the first 7 ˚, correspond to a well-defined and
A
compact structural fragment of SbS7 shown in Figure 2.7(d). The calculated PDF of the
molecular SbS7 fragment is shown for comparison in Figure 2.7(c). It is clear that the three
correlation peaks due to Sb-S bond and S-S second neighbor distances are very similar to
those observed experimentally (Figures 2.7(a) and (b)). The PDFs of the K1-x Rbx Sb5 S8
members (not shown) were similar to that of the parent compound suggesting they possess
the same local structure.
In the glass, the experimental PDF is seen to decay to zero at ∼15 ˚. Obviously, its
A
structural coherence length is much shorter than that observed in the crystal. This coherence length, however, is much longer than those of more conventional glasses such as SiO2
and underscores a much more organized and well-defined local structure in the amorphous
[Sb5 S8 ]- framework. Based on the strong similarity of the G(r) of the two forms up to 7 ˚,
A

23

see Figures 2.7(a) and (b), we surmise that this structural fragment is essentially invariant
in both the glass and the crystal. The glass structure consists essentially of the same rigid
SbSn fragments as the crystalline KSb5 S8 structure except that they are connected in a
disordered fashion. If the basic building units that define the structure of KSb5 S8 are intact
in the glass, only a small reorganization would be required to regain the periodic crystalline
state. This is consistent with the rapid and facile crystallization processes in this system.

2.3.4

Electronic absorption and Raman spectroscopy

The effect of the substitution of Rb+ into the structure on the electronic properties was
probed with optical reflectance spectroscopy in the glasses (Figure 2.8). Each glass member
showed a band gap Eg ∼ 1.50 eV, which is slightly lower than that of the parent KSb5 S8
glass of 1.67 eV. There was no significant variation in the experimentally measured band
gaps of the solid solutions as a function of x which may be due to the competing effects of
the larger, more polarizable nature of the Rb+ ion, which should decrease the band gap, and
the increased ionicity of the more electropositive Rb+ ion, which should increase it. This is
consistent with the bonding insights obtained by the electronic band structure calculations
on KSb5 S8 (14 )
Figure 2.8 compares the Raman spectra of glassy and crystalline KSb5 S8 measured at
room temperature. While the crystalline material shows five well-defined peaks between 280
and 345 cm-1 , which can be attributed to vibrations involving the [Sb5 S8 ]- framework, the
spectrum observed in the glass is extremely broad, suggesting a wide distribution of bond
angles. Nevertheless, the centers of gravity of both spectra roughly coincide, supporting
the close structural resemblance of both phases inferred from the PDF study discussed
above. The amorphous KSb5 S8 phase at room temperature shows Raman shifts on top of
a broad feature centered at 100-150 cm-1 and a characteristic broad peak in the 250-350
cm-1 range. Essentially identical room temperature spectra were observed for the mixedalkali K1-x Rbx Sb5 S8 glasses, further supporting the interpretation that all of these spectral

24

Figure 2.8. Solid state UV-Vis reflectance spectra of K0.75 Rb0.25 Sb5 S8 converted to
absorption via the Kubelka-Monk procedure. The spectra for K0.5 Rb0.5 Sb5 S8 and
K0.25 Rb0.75 Sb5 S8 glasses are similar. Band gaps extrapolated linearly to 0 are 1.50, 1.47,
and 1.51 eV respectively.

25

Figure 2.9. Raman scattering data on crystalline (a) and glassy (b) KSb5 S8 at room temperature.

26

Figure 2.10. Raman scattering data of glassy KSb5 S8 at various temperatures along the
heating curve, The crystallization event is shown by the sharpening of peaks between 210
and 335o C.

27

400 °C

300 °C

200 °C

0

100

200

300

cm

400

500

-1

re 9c
Figure 2.11. Raman scattering data of KSb5 S8 cooled from the molten state. Crystallization
is evidenced by the sharpened features near 338, 321, 310, 298, and 280 cm-1 .

28

features can be attributed to vibrations involving only the framework atoms of antimony
and sulfur.
To obtain further insight into the local structure of the glass and the phase-change process, we conducted temperature–dependent Raman scattering experiments in an attempt to
observe the crystallization process in situ. The Raman spectra as a function of temperature
of a KSb5 S8 glass sample are shown in Figure 2.10. As long as the temperature remained
below the glass transition temperature of 220o C, no significant changes were observed in
the Raman spectra of the glass. Above Tg , well-defined features are observable, which are
successively developed above 240o C. The new features include intense peaks at 81 and 150
cm-1 , as well as features near 230 and 305 cm-1 with a shoulder near 330 cm-1 . When the
temperature exceeded the compound’s melting point, this spectrum disappeared giving rise
to a similar one observed for the glass at room temperature. While the nucleation of crystals above Tp is easily detected in the Raman spectra, the comparison of the spectra above
240o C (Figure 2.10) with that of the fully crystallized material (Figure 2.8(a)) reveals that
the sharpening of these Raman peaks is only gradual. That the Raman peaks do not entirely
sharpen in this temperature region indicates that the nucleated material is still strongly disordered above Tp , and extra energy is needed to fully crystallize and lock the atoms into their
crystallographic coordinates. DTA studies conducted on KSb5 S8 during melt cooling reveal
no crystallization exotherms, suggesting the formation of glassy material under these conditions (10 ). Nevertheless, Raman spectra obtained during melt cooling (Figure 2.11) reveal
the same features as those obtained above Tp during the heating cycle, indicating that small
crystalline nuclei have formed under these (relatively slow) cooling conditions. This is most
clearly seen by the appearance of peaks near 338, 321, 310, 298, and 280 cm-1 (reflecting
peak positions observed in crystalline KSb5 S8 ) which become increasingly well-defined with
decreasing temperature. The sizes of the nuclei generally depend on the cooling rate and in
the case of the Raman experiments the cooling rate was considerably slower that those used
in the DTA experiments (10o C/min).

29

2.5

κ (W/m.K)

2

glassy
crystalline

1.5

1

0.5

0
0

50

100

150

200

250

300

T (K)
Figure 2.12. Temperature dependence of thermal conductivity of the crystalline and glassy
KSb5 S8 (4-300K).

Figure 10

30

2.3.5

Thermal conductivity

In phase-change materials, besides optical response, the thermal behavior is important for
reasons involving heating, quenching and switching speeds, cyclability and suppression of
thermal cross talk (31 ). A low thermal conductivity is necessary to ensure fast, localized
heating over a minimum area. Optimization for thermal performance requires accurate
knowledge of the thermal conductivity of both glass and crystalline states and it is therefore
imperative to have an accurate estimation of the thermal transport properties of these materials. The thermal conductivity of bulk crystalline and glassy KSb5 S8 was measured with
a steady-state technique over the temperature range of 4-300K (Figure 2.12). Because both
forms of KSb5 S8 have a very low electrical conductivity (e.g. < 10−8 S/cm) the data shown
essentially represent the lattice thermal conductivity.
The thermal conductivity of crystalline KSb5 S8 exhibits the expected Umklapp peak at
low temperatures (about 8K) and is characteristic of crystalline materials (32 ). It is caused
by the competition between the phonon-boundary scattering and Umklapp phonon-phonon
interactions. On the other hand, glassy KSb5 S8 shows no such peak at low temperatures,
which is a typical behavior for amorphous materials and presents significantly lower values
as expected due to the structural disorder (33 ).
At higher temperatures, the thermal conductivity for both samples is similar regarding
both magnitude and trend. The thermal conductivity of crystalline KSb5 S8 at room temperature is an amazingly low 0.4 W/mK. This value in fact represents an upper bound in this
family of materials as we expect the solid solutions K1-x Rbx Sb5 S8 to be even less thermally
conducting.
The thermal conductivity of KSb5 S8 is lower than that of Ge2 Sb2 Te5 , which is 0.55
W/mK (34 ). This may appear surprising since KSb5 S8 consists of lighter elements than
Ge2 Sb2 Te5 and is generally expected to have higher lattice thermal conductivity (35 ). The
lower values in the sulfide compound can be attributed to the characteristically lower crystal
symmetry, the relatively large unit cell, and the presence of weakly bound K atoms (i.e. K —

31

S ionic bonding). All of these are absent in Ge2 Sb2 Te5 . This finding implies that in certain
cases KSb5 S8 may have an advantage over Ge2 Sb2 Te5 in sustaining smaller spot sizes and
higher packing densities without thermal cross talk.

2.4

Conclusions

KSb5 S8 is a good example of a phase-change material with a mixed ionic/covalent bonding. The K site in the structure can be used to modulate the glass-forming properties and
crystallization rates of the system via isomorphic substitution with Rb. In this work we
introduced perturbations on the ionic bonding, i.e. K(Rb) — S, which affects the phase
change properties of the system significantly. The members of the K1-x Rbx Sb5 S8 series
exhibit phase-change properties with greater GFA than KSb5 S8 . The GFA increases with
increasing Rb content. In this case, the random alloy disorder in the alkali metal sublattice
seems to predominate over the increased degree of ionicity in going from K — S to Rb — S
bonding and works to stabilize the glass forms in K1-x Rbx Sb5 S8 and slow the crystallization
process compared to pure KSb5 S8 . Tl ions also substitute for K but the Tl analog itself
is not stable on melting and therefore its phase change behavior is relatively complicated.
Property modification could not be accomplished with neither Sb nor S site substitution in
the structure of KSb5 S8 as these sites do not lend themselves for similar substitutions with
e.g. Bi, Se, respectively. Band structure calculations on KSb5 S8 and TlSb5 S8 suggest a wide
indirect energy gap with the Tl — S interactions being slightly stronger than those of K —
S (14 ).
In-depth studies are needed in chalcogenide systems in which the ionic/covalent bonding
ratio can be varied. In this regard, KSb5 S8 and related A/Sb/Q (A = alkali metal, Q = S,
Se) phases could be excellent study cases. Of particular interest would be to compare the
behavior of K/ Sb/S systems to that of K/Sb/Se counterparts and some of these results are
reported in Chapters 3 and 4 of this thesis. The glass possesses relatively long-range order (up
to 7 ˚) compared to most known glasses. The glassy and the crystalline states share large,
A

32

well-defined local coordination polyhedral SbS7 fragments of an approximate length scale
of 7 ˚. This represents a substantial degree of built-in pre-organization in the amorphous
A
form that sets the stage for facile crystallization. Finally, the thermal conductivity of both
glass and crystalline KSb5 S8 is among the lowest known for any dense inorganic solid-state
material.

33

References and Notes

34

References and Notes

[1] (a) Hesselink, L.; Mijiritskii, A. E. Advanced data storage materials and characterization techniques. MRS Proceedings, 2003; p 803, references therein; (b) Borg, H. J.; van
woudenberg, R. Journal Of Magnetism And Magnetic Materials 1999, 193, 519 – 525;
(c) Popescu, M.; Sava, F.; Anghel, A.; Lorinczi, A.; Kaban, I.; Hoyer, W. Journal Of
Optoelectronics And Advanced Materials 2005, 7, 1743 – 1748; (d) Gidon, S.; Lemonnier, O.; Rolland, B.; Bichet, O.; Dressler, C.; Samson, Y. Applied Physics Letters 2004,
85, 6392 – 6394.
[2] (a) Lankhorst, M. H. R.; Ketelaars, B. W. S. M. M.; Wolters, R. A. M. Nature Materials 2005, 4, 347 – 352; (b) Teteris, J.; Reinfelde, M. Journal Of Optoelectronics And
Advanced Materials 2003, 5, 1355 – 1360; (c) Hisakuni, H.; Tanaka, K. Science 1995,
270, 974 – 975.
[3] (a) Edwards, A. H.; Pineda, A. C.; Schultz, P. A.; Martin, M. G.; Thompson, A. P.;
Hjalmarson, H. P. Journal Of Physics-Condensed Matter 2005, 17, L329 – L335; (b)
Ahn, D. H.; Kang, D. H.; Cheong, B. K.; Kwon, H. S.; Kwon, M. H.; Lee, T. Y.;
Jeong, J. H.; Lee, T. S.; Kim, I. H.; Kim, K. B. IEEE Electron Device Letters 2005,
26, 286 – 288.
[4] Ohta, T. Journal Of Optoelectronics And Advanced Materials 2001, 3, 609 – 626.
[5] Spektor, B.; Lisiansky, M.; Shamir, J.; Klebanov, M.; Lyubin, V. Applied Physics Letters
2000, 76, 798 – 800.
[6] Tikhomirov, V. K.; Elliott, S. R. Physical Review B 1994, 49, 17476 – 17479.
[7] Lucas, J. Current Opinion In Solid State and Materials Science 1999, 4, 181 – 187.
[8] (a) Yamada, N.; Ohno, E.; Nishiuchi, K.; Akahira, N.; Takao, M. Journal Of Applied
Physics 1991, 69, 2849 – 2856; (b) Yamada, N.; Matsunaga, T. Journal Of Applied
Physics 2000, 88, 7020 – 7028.
[9] de la Parra, S.; Torres-Gonzalez, L. C.; Torres-Martinez, L. M.; Sanchez, E. Journal Of
Non-Crystalline Solids 2003, 329, 104 – 107.

35

[10] Kyratsi, T.; Chrissafis, K.; Wachter, J.; Paraskevopoulos, K. M.; Kanatzidis, M. G.
Advanced Materials 2003, 15, 1428 – 1431.
[11] Berlepsch, P.; Miletich, R.; Armbruster, T. Zeitschrift Fur Kristallographie 1999, 214,
57 – 63.
[12] Park, J.; Kim, M. R.; Choi, W. S.; Seo, H.; Yeon, C. Japanese Journal Of Applied
Physics Part 1-Regular Papers Short Notes and Review Papers 1999, 38, 4775 – 4779.
[13] Chrissafis, K.; Kyratsi, T.; Paraskevopoulos, K. M.; Kanatzidis, M. G. Chemistry Of
Materials 2004, 16, 1932 – 1937.
[14] Wachter, J. B.; Chrissafis, K.; Petkov, V.; Malliakas, C. D.; Bilc, D.; Kyratsi, T.;
Paraskevopoulos, K. M.; Mahanti, S. D.; Torbr¨gge, T.; Eckert, H.; Kanatzidis, M. G.
u
J. Solid State Chem. 2007, 180, 425 – 436.
[15] Singh, D. Pseudopotential and the LAPW method ; Kluwer Academic, Boston, MA,
1994.
[16] (a) Hohenberg, P.; Kohn, W. Physical Review 1964, 136, B864 – B871; (b) Kohn, W.;
Sham, L. J. Physical Review 1965, 140, A1133 – A1138.
[17] Perdew, J. P.; Burke, K.; Ernzerhof, M. Physical Review Letters 1996, 77, 3865 – 3868.
[18] Koelling, D. D.; Harmon, B. N. Journal Of Physics C-Solid State Physics 1977, 10,
3107 – 3114.
[19] Blaha, P.; Schwarz, K.; Madsen, G.; Kvasnicka, D.; Luitz, J. WIEN2K, An Augmented
Plane Wave+Local Orbitals Program for calculating Crystal Properties; Karlheinz
Schwarz Technical University, Wien, 2001.
[20] Attempts to prepare solid solutions of KSb5 S8 with respective Bi and Se substitutions
were not successful.
[21] TB. Massalski (Ed.), ASM International (Corporate Author), H. Okamoto (Ed.), Compare Melting Points of A2 Q Systems (A = alkali metal, Q = S, Se, Te): Binary Alloy
Phase Diagrams, 1986.
[22] Jumas, J. C.; Olivierfourcade, J.; Rey, N.; Philippot, E. Revue De Chimie Minerale
1985, 22, 651 – 665.
[23] Turnbull, D. Contemporary Physics 1969, 10, 473 – and.
[24] Li, Y.; Ng, S. C.; Ong, C. K.; Hng, H. H.; Goh, T. T. Scripta Materialia 1997, 36, 783
– 787.
[25] Hruby, A. Czechoslovak Journal of Physics 1972, 78, 1187.
36

[26] Zhang, Z.; Wang, W. H.; Hirotsu, Y. Materials Science And Engineering A-Structural
Materials Properties Microstructure And Processing 2004, 385, 38 – 43.
[27] (a) Toby, B. H.; Egami, T. Acta Crystallographica Section A 1992, 48, 336 – 346; (b)
Egami, T. Journal Of Physics And Chemistry Of Solids 1995, 56, 1407 – 1413.
[28] Petkov, V.; Jeong, I. K.; Chung, J. S.; Thorpe, M. F.; Kycia, S.; Billinge, S. J. L.
Physical Review Letters 1999, 83, 4089 – 4092.
[29] Waseda, Y. The Structure of Non-crystalline Materials; McGraw Hill, New York, 1980.
[30] Billinge, S. J. L.; Kanatzidis, M. G. Chemical Communications 2004, 749 – 760.
[31] Ohta, T.; Inoue, K.; Uchida, M.; Yoshioka, K.; Akiyama, T.; Furukawa, S.; Nagata, K.;
Nakamura, S. Japanese Journal Of Applied Physics Part 1-Regular Papers Short Notes
and Review Papers 1989, 28, 123 – 128.
[32] Berman, R. Thermal Conduction in Solids; Clarendon, Oxford, 1976.
[33] (a) Kittel, C. Physical Review 1949, 75, 972 – 974; (b) Zeller, R. C.; Pohl, R. O.
Physical Review B 1971, 4, 2029 – and.
[34] Konstantinov, P. P.; Shelimova, L. E.; Avilov, E. S.; Kretova, M. A.; Zemskov, V. S.
Inorganic Materials 2001, 37, 662 – 668.
[35] Spitzer, D. P. Journal Of Physics And Chemistry Of Solids 1970, 31, 19 – and.

37

CHAPTER 3

K2 Sb8 Se13 : a phase-change material exhibiting polyamorphism

3.1

Introduction

Phase-change materials have been widely studied over the past two decades, most notably
for their utility as data storage media. (1 –4 ) The ability for a material to exist in two stable states at room temperature distinguishable by a simple measurement, usually optical
reflectance or electronic resistance, makes it a perfect fit for the binary system ubiquitous in
the computing world. Additionally, the ability for the material to be rapidly switched from
one state to another, generally using heat, allows for the facile writing and erasing of data.
Because of the permanent nature of written data in PC materials and the relative ease of
rewriting, it is postulated that further advancement of these materials could lead to their
replacing the conventional 3-step computer memory process of electrical memory¡magnetic
memory¡optical memory with a single memory device. (2 , 5 , 6 ) The utility of most PC
materials is based upon their ability to exist as both crystalline and amorphous structures at
room temperature, and all currently-used materials have this property. Here we report the remarkable behavior of potassium antimony selenide K2 Sb8 Se13 (PASE: potassium-antimonyselenide), a material that shows a glass¡glass, polyamorphic phase change as well as a
glass¡crystal phase change, making it a three-state PC system. Polyamorphism is a phenomenon that is well-studied in several binary compounds (e.g. SiO2 , GeO2 , H2 O, BeF2 )
and some pure elements (C, Si, Ge, Bi, Se, Te, I), often under high pressures, but is, in
general, quite rare. (7 –9 ) Recent discoveries of polyamorphism in liquid phosphorus (10 )
38

and Al2 O3 -Y2 O3 (11 , 12 ) have further proven the existence of these systems, but represents
the first example of a stoichiometric, chalcogenide-based polyamorphic material functioning
at ambient pressure. Unlike these examples, K2 Sb8 Se13 is a single phase with a well-defined
crystal structure and contains both ionic and covalent bonds.

3.2
3.2.1

Experimental section
Synthesis

Crystalline PASE was synthesized by combining 0.345 g K2 Se, 0.122 g Sb, and 0.079 g Se
powders under a nitrogen atmosphere in a 13 mm diameter, fused silica tube, which was
then sealed under reduced pressure (<10-4 torr) and heated at 850o C for 24 h, when heating
was ceased and the tube was allowed to cool in the furnace. The resulting ingot was proven
to have the K2 Sb8 Se13 stoichiometry by energy dispersive X-ray elemental analysis. The
ingot was then crushed and loaded into a 9 mm fused silica tube whose bottom had been
drawn out to a sharp point and ground to reveal a hole <0.5 mm in diameter. This tube
was loaded into a nitrogen atmosphere glove box and suspended ∼2 cm over two copper
cylinders, each 2 in. in diameter, rotating in opposite directions. The powder in the bottom
of the tube was heated by a small heating element until molten, where it was held in the tube
by surface tension until the tube was lightly pressurized by nitrogen, immediately forcing
the molten K2 Sb8 Se13 through the hole to be flattened and rapidly cooled by the rotating
copper cylinders. The resulting thin glassy ribbon was ∼150 µm thick.

3.2.2

Differential Scanning Calorimetry (DSC)

The differential scanning calorimetric (DSC) measurements were carried out with a Shimadzu
DSC-50 calorimeter. Temperature and energy calibrations of the instrument were performed,
for different heating rates, using the well-known melting temperatures and melting enthalpies
of high-purity zinc, indium and tin. Bulk-shaped foil specimens weighing about 5 mg were
crimped in aluminum crucibles; an empty aluminum crucible was used as reference. A
39

constant flow of nitrogen was maintained to provide a constant thermal blanket within
the DSC cell, thus eliminating thermal gradients and ensuring the validity of the applied
calibration standard from sample to sample.

3.2.3

X-ray powder diffraction

The samples were examined by X-ray powder diffraction for confirmation of their amorphous
nature and evidence of crystallization. Powder patterns were obtained using a CPS 120 INEL
X-ray powder diffractometer with Ni-filtered Cu Kα radiation operating at 40 kV and 20
mA and equipped with a position-sensitive detector.

3.2.4

Synchrotron radiation diffraction experiments

The local structure was solved using atomic pair distribution function (PDF) analysis. Powder of crystalline and glass K2 Sb8 Se13 was packed in a flat aluminum plate with thickness of
1.0 mm sealed with kapton tape. Diffraction data were collected at 300 K using the rapid acquisition pair distribution function (RA-PDF) technique (13 ). Data were collected using an
MAR345 image plate detector and ∼100 keV energy X-rays (λ = 0.123515 ˚) at the 6-IDD
A
beam line at the Advanced Photon Source (APS). Measurements were repeated 4-5 times
per sample to improve counting statistics. The data were combined and integrated using
the program FIT2D (14 ). Various corrections were made to the data, such as subtraction of
background, Compton and fluorescence scattering, geometric corrections, absorption, and so
on, as described in reference. Corrections were made using the program PDFgetX2 (15 ). Finally, S(Q) was truncated at Qmax of 25 ˚-1 before the PDF was calculated (16 ). Structural
A
models are fit to the data using the program PDFFIT (17 ).

3.2.5

Optical energy band gaps

Optical band gaps were determined at room temperature using Kubelka-Munk theory (18 ) on
data collected by diffuse reflectance UV/Vis spectroscopy on finely ground sample portions

40

of the foil. A background was collected before each scan using BaSO4 . A spectrum was
collected for the region of 200-2500 nm with a Shimadzu UV-3101 PC double-beam, doublemonochromator spectrophotometer.

3.2.6

Pyncnometry

Density was calculated from the sample mass (∼40mg) and the volume determined from a
Micromeritics AccuPyc 1340 gas pycnometer at 293 K. Samples of glass α were obtained by
heating glass β to 230o C in a Shimadzu DSC-50 and rapidly cooling to obtain the desired
glassy phase.

3.3

Results and discussion

3.3.1

Structural analysis

The structure of K2 Sb8 Se13 is a three-dimensional, dense array of octahedral blocks. The
structure is similar to that of β-K2 Bi8 Se13 (19 ) and includes two different interconnected
types of Sb/Se rod-shaped building blocks forming a framework with parallel tunnels filled
with K+ atoms (Figure 3.1). The triclinic structure is an ordered variant of the monoclinic
structure of K2 Bi8 Se13 with two types of blocks designated as NaCl(111) - and NaCl(100) because they represent excised fragments of the NaCl structure with cuts along the (111)
and (100) plane respectively. The blocks are connected to each other by shared Sb atoms.
Figures 3.2A and 3.2B show typical sample fragments of crystalline and glass-β PASE. The
as-synthesized PASE foil (glass-β) was found to be amorphous by X-ray powder diffraction
(Figure 3.2c).
The three broad features visible at 13-17o , 23-35o , and 42-58o 2θ angle indicate a high
degree of order in the glass, though it clearly has no periodic structure. Upon heating, the
material undergoes two well defined exothermic transitions, as evidenced by differential scanning calorimetry (DSC, Figure 3.3 and XRPD, Figure 3.2C. The first transition, beginning
at 220o C, represents reorganization to another amorphous structure (glass-α). The powder
41

Figure 3.1. The crystal structure of K2 Sb8 Se13 .

42

Figure 3.2. (A) crystalline K2 Sb8 Se13 . (B) material obtained by quenching molten
K2 Sb8 Se13 (glass-β). (C) X-ray powder diffraction patterns from the three phases of
K2 Sb8 Se13 : i) as-synthesized glass-β; (ii) glass-α after heating to 225o C and (iii) crystalline
phase after heating above 263o C. (Cu Kα radiation).

43

diffraction data confirm the amorphous nature of this product (Figure 3.2C); however, there
is clearly some change in structure as suggested by the fact that the broad peak at 23-35o has
sharpened, and the other peaks are starting to show definition beyond their counterparts
in the β glass. Upon further heating to 263o C, the structure undergoes another exothermic
reorganization, this time to a crystalline product, as shown by XRPD (Figure 3.2). In this
XRPD pattern, all peaks corresponding to the K2 Sb8 Se13 structure are present, and no
amorphous background is observed. The exothermic nature of the two transitions suggests
the metastable nature of glass-α and glass-β.
To examine the consequences of these transitions on the local structure of the materials,
the pair-distribution function (PDF) was examined for each structure (Figure 3.4A). The
PDF was determined from the processing of X-ray diffraction data of a Synchrotron source
and validates the existence of three distinct phases. In the as-synthesized glass-β (Figure
3.4A), the presence of atomic pair correlations indicate ordering to nearly 10 ˚, a considerable
A
distance for a glass. There are clear peaks at 2.6 ˚, showing Sb–S bonds and at ∼4 ˚ & 6.5
A
A
˚, showing 2nd- (Se· · · Se and Sb· · · Sb) and 3rd-nearest neighbor distances. On conversion
A
to glass-α, more order is observed (Figure 3.4A). Peaks have developed at 4.9 ˚, 7.1 ˚, 10.7
A
A
˚, 12.4 ˚, showing that the transition from glass-β to α has indeed resulted in a change in
A
A
the local structure, and that this new structure is more ordered than glass-β. The PDF of
the crystallized compound (Figure 3.4A) shows a further sharpening of the peaks, as well
as new features at much longer radial distances, demonstrating full crystallization of the
material.

3.3.2

Optical properties

The other unusual property in this material is the shifting of the band gap from 1.43 eV
to 1.3 eV to 0.74 eV as the material is switched from βαcrystal. All other PC materials
show the canonical behavior: a slight increase (usually 0.1-0.2 eV) in the band gap as
the material is switched from glassAcrystal, attributed to the removal of ”band tailing”

44

Figure 3.3. DSC thermogram of K2 Sb8 Se13 ribbon. Three phase changes are observed from
glass-β to glass-α (227o C), from glass-α to crystal (263o C), and melting (443o C).

45

Figure 3.4. (A) Pair-distribution function analysis of the three phases of K2 Sb8 Se13 : assynthesized glass-β; glass-α after heating to 220o C and crystalline phase after heating
to 270o C. (B) Optical absorption spectra showing energy gaps for crystalline and glass-α
K2 Sb8 Se13 .
46

effects in the glass. A change of nearly double in energy in the opposite direction must be
attributed to a major change in electronic structure. One way to account for this is that
the coordination number of antimony has changed. Several systems are known in which
an increase of chalcogenide atoms coordinated to a central metal leads to a sharp decrease
in band gap. CdS undergoes a pressure-induced phase transition from a wurtzite structure
to a rock salt structure around 3 GPa (20 ) As it moves from tetrahedral coordination in
the wurtzite structure to octahedral coordination in the rock salt structure, the band gap
decreases from 2.5 eV to 1.5-1.7 eV (21 ) A similar effect is seen in HgS, which transitions
from the two-coordinate cinnabar structure (band gap = 2.3 eV) to the four-coordinate
zinc blende structure, where the band gap collapses and the material becomes metallic (22 )
Though it is not a phase transition, we can also draw similarities to K2 Bi8 S13 . K2 Bi8 S13
has a band gap of 0.06-0.25 eV (19 , 23 ) and contains primarily octahedral Bi atoms. This
can be compared with the trigonal pyramidal Bi atoms in Bi2 S3 , which has a larger band
gap of 1.1 eV (24 ). The contribution of potassium can be ignored here because, in general,
increased ionicity will afford a wider band gap (25 ). These examples support the hypothesis
that the glass of PASE contains a greater number of 3-coordinate Sb sites, while the crystal,
as shown by X-ray crystallography, contains primarily 6-coordinate Sb.

3.3.3

Density measurements

Moving from a structure with 3-coordinate Sb to the known crystal structure of PASE with
6-coordinate Sb should lead to an increase in density, which we probed using a pycnometer.
Density values are reported in Table 3.1 for each phase. Consistent with the PDF and X-ray
data, the density data show a slight increase in density upon transition from glass β Aα
and then a more pronounced change to the crystalline form. This lends further proof to the
increase in coordination and clear evidence of a polyamorphic transition. (11 )

47

Phase

glass β

glass α

Density (g/cm3 )
Energy gap (eV)

4.949(1) 5.060(1)
1.43(1) 1.30(1)

crystal
5.278(1)
0.74(1)

Table 3.1. Energy gaps and density of the three states of K2 Sb8 Se13 .

3.4

Conclusions

The glassAglass transition discovered in K2 Sb8 Se13 is unique in that this is both the
first example of a true ternary polyamorphic system as well as the first ambient pressure
chalcogenide-based polyamorphic system. The suitability of chalcogenides for use as functional materials in phase-change memories (PCMs) has been well-documented (26 ), so the
new tri-state system described here could see application in data storage and novel computing
devices utilizing ternary logic mechanisms (27 ) rather than the current binary systems (28 ).
The tri-stability property found in PASE raises the prospect of additional systems yet to
be discovered with similar properties. If tri-stability is more common than we currently
imagine, then materials with ideal three-state behavior may soon emerge as new platforms
for a variety of experimentation relevant to higher than binary logic. Additionally, the PASE
system should be ideal for fundamental studies of the rare polyamorphic phenomenon, as
both glasses α and β are stable at standard temperature and pressure, and are not reactive
with air or water.

48

References and Notes

49

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– 1474.
[20] Batlogg, B.; Jayaraman, A.; Vancleve, J. E.; Maines, R. G. Physical Review B 1983,
27, 3920 – 3923.
[21] Cervantes, P.; Williams, Q.; Cote, M.; Zakharov, O.; Cohen, M. L. Physical Review B
1996, 54, 17585 – 17590.
[22] Yoffe, A. D. Advances in Physics 2001, 50, 1 – 208.
[23] Chung, D. Y.; Choi, K. S.; Iordanidis, L.; Schindler, J. L.; Brazis, P. W.; Kannewurf, C. R.; Chen, B. X.; Hu, S. Q.; Uher, C.; Kanatzidis, M. G. Chem. Mater.
1997, 9, 3060 – 3071.
[24] Nkum, R. K.; Adimado, A. A.; Totoe, H. Mater. Sci. Eng., B 1998, 55, 102 – 108.
[25] Axtell, E. A.; Park, Y.; Chondroudis, K.; Kanatzidis, M. G. J. Amer. Chem. Soc. 1998,
120, 124 – 136.
[26] (a) Yamada, N.; Ohno, E.; Nishiuchi, K.; Akahira, N.; Takao, M. Journal Of Applied
Physics 1991, 69, 2849 – 2856; (b) Kolobov, A. V.; Fons, P.; Frenkel, A. I.; Ankudinov, A. L.; Tominaga, J.; Uruga, T. Nature Materials 2004, 3, 703 – 708.
[27] (a) Rusu, M. I.; Miclos, S.; Savastru, D.; Popescu, M. New phase-change materials to
achieve cognitive computing - Overview and future trends. In Icton 2007: Proceedings
of the 9th International Conference on Transparent Optical Networks, 2007; pp 287 –
289; (b) Ovshinsky, S. R.; Pashmakov, B. In Innovation providing new multiple functions in phase-change materials to achieve cognitive computing.; Ahner, J. W., Levy, J.,
Hesselink, L., Mijiritskii, A., Eds.; 2004; Vol. 803, pp 49 – 60.
[28] (a) Bogdanov, Y. I.; Chekhova, M. V.; Krivitsky, L. A.; Kulik, S. P.; Penin, A. N.;
Zhukov, A. A.; Kwek, L. C.; Oh, C. H.; Tey, M. K. Physical Review A 2004, 70,
year; (b) Bechmann-Pasquinucci, H.; Peres, A. Phys. Rev. Lett. 2000, 85, 3313 – 3316;
(c) Ghosh, P.; Das, P. P.; Mukhopadhyay, S. In An alternative proposal of arithmetic
and image operations in optical parallel computation.; Marsh, J. H., Bhattacharya, P.,
Wada, O., Eds.; 2001; Vol. 4598, pp 175 – 181.

51

CHAPTER 4

Investigation into the switching mechanisms of the polyamorphic
chalcogenide K2 Sb8 Se13

4.1

Introduction

K2 Sb8 Se13 was the first phase-change material to show both glass-to-glass and crystal-tocrystal transitions (1 ). Several techniques have been developed to probe the kinetic and
thermodynamic properties of solid state phase changes (2 , 3 ), but few studies have been
done on stoichiometric materials akin to K2 Sb8 Se13 . Chrissafis et. al. have studied the stoichiometric KSb5 S8 system, which is similar to the K2 Sb8 Se13 described here (4 ). Several
kinetic and thermodynamic factors must be calculated to determine the nature and underlying mechanisms of these transformations. Analysis of these transformations is often based
upon the single-step kinetic equation
dα
= k(T )f (α)
dt

(4.1)

where α is the extent of reaction, t is the time, T is the temperature (in Kelvin), k(T ) is
the rate constant, and f (α) is the reaction model. This equation shows that dependence of
the reaction on time is proportional to the reaction model f (α), and that the rate constant
depends upon temperature. If the rate constant is replaced by the Arrhenius equation, the
explicit temperature dependence is revealed:
dα
= A exp
dt
52

−E
RT

f (α)

(4.2)

where A is the Arrhenius preexponential factor, E is the crystallization energy (also from
the Arrhenius equation), and R is the gas constant. Since the measurements here will be
nonisothermal, it is more appropriate to replace dα/dt in Equation 4.2 with the heating rate,
β.
β(dα/dT ) =

dT
dt

(4.3)

The rate of change of fractional extent of reaction with respect to time (dα/dt) is proportional
to the measured specific heat flow φ, normalized to sample mass, so these measurements are
well suited to differential scanning calorimetry (DSC), where α can be calculated from the
normalized integration of heating curves.
Crystallization kinetics can be interpreted in terms of the standard nucleation-growth
model first developed by Johnson and Mehl (5 ) and later refined by Avrami (2 ) (JMA).
Their model shows the time dependence of α and is often written thusly:
α = 1 − exp[−(kt)n ]

(4.4)

where k, the rate constant, depends on temperature, crystal growth rate, and nucleation
frequency. The exponent n depends on the phase change mechanism and can reflect the
nucleation frequency and/or the growth morphology. Differentiation of Equation 4.4 with
respect to time gives
dα
= kn(1 − α)[− ln(1 − α)]1−1/n
dt

(4.5)

Equation 4.5, referred to as ”the JMA equation,” is frequently used to describe thermal
crystallization data; however, there are several assumptions upon which its validity depends.
First, the phase change occurs under isothermal conditions; second, crystal growth is highly
isotropic; third, the nucleation occurs at randomly dispersed phase-changed particles; fourth,
the growth rate of the new phase is controlled by temperature and completely independent
of time. Since the validity of these assumptions is not usually known a priori for a new
phase-change material, several methods have been developed for testing a given system’s
adherence to the JMA model.
53

The most popular method for testing the applicability of the JMA model to a new,
nonisothermal system is to test the linearity of the JMA plot. Matusita et al. have suggested
an equation applicable to nonisothermal crystallization given by
ln[− ln(1 − α)] = −n ln(β) − 1.052

mEa
+ constant
RT

(4.6)

where β is the heating rate, m and n depend on the nucleation and growth of the new phase,
and Ea is the crystallization energy (6 , 7 ). It was suggested that n = (m + 1) for a perfectly
quenched glass with no nuclei and n = m2 0 for a glass with a large number of nuclei (6 ).
The value of m is given by the dimensionality of crystal growth (1,2, or 3). The plot of
ln[− ln(1 − α)] vs. reciprocal temperature should be linear to show the applicability of the
JMA model; however, any double logarithmic function is not very sensitive to changes in
its arguments, so substantial linearity in these plots is often observed even when the JMA
model is not the strongest model of the system under investigation. Ultimately, more realtime methods, such as time-resolved electron microscopy, will need to be developed to gain a
more complete understanding of the complex and varied mechanisms at work in phase-change
systems, especially with regard to nucleation and growth.

4.2
4.2.1

Experimental section
Synthesis

Crystalline K2 Sb8 Se13 was synthesized by combining 0.345 g K2 Se, 0.122 g Sb, and 0.079
g Se powders under a nitrogen atmosphere in a 13 mm diameter, fused silica tube, which
was then sealed under reduced pressure (<10-4 torr) and heated at 850o C for 24 h, when
heating was ceased and the tube was allowed to cool in the furnace. The resulting ingot was
proven to have the K2 Sb8 Se13 stoichiometry by energy dispersive X-ray elemental analysis.
The ingot was then crushed and loaded into a 9 mm fused silica tube whose bottom had
been drawn out to a sharp point and ground to reveal a hole <0.5 mm in diameter. This
tube was loaded into a nitrogen atmosphere glove box and suspended ∼2 cm over two copper
54

cylinders, each 2 in. in diameter, rotating in opposite directions. The powder in the bottom
of the tube was heated by a small heating element until molten, where it was held in the tube
by surface tension until the tube was lightly pressurized by nitrogen, immediately forcing
the molten K2 Sb8 Se13 through the hole to be flattened and rapidly cooled by the rotating
copper cylinders. The resulting thin glassy ribbon was ∼150 m thick.

4.2.2

Differential Scanning Calorimetry (DSC)

The differential scanning calorimetric (DSC) measurements were carried out with a Shimadzu
DSC-50 calorimeter. Temperature and energy calibrations of the instrument were performed,
for different heating rates, using the well-known melting temperatures and melting enthalpies
of high-purity zinc, indium and tin. Bulk-shaped foil specimens weighing about 5 mg were
crimped in aluminum crucibles; an empty aluminum crucible was used as reference. A
constant flow of nitrogen was maintained to provide a constant thermal blanket within
the DSC cell, thus eliminating thermal gradients and ensuring the validity of the applied
calibration standard from sample to sample. DSC data were analyzed with OriginPro 7.0
software.

4.3

Results and Discussion

K2 Sb8 Se13 shows a rare glass-to-glass transition at 227o C and glass-to-crystal transition at
263o C. To better understand the nature of these transitions, quantitative kinetic analyses
were performed on the DSC data (Figure 4.1). Each thermogram shows two exothermic
events: the first, broad peak arises from the glass-to-glass transition and the second, sharp
peak from the glass-to-crystal transition.

4.3.1

Kissinger analysis

Calculating the activation energy Ec of each phase transition can give insight into their
mechanisms and relative speeds. The dependence of peak temperature, Tp , on heating rate

55

Figure 4.1. Baseline-corrected, nonisothermal DSC traces of K2 Sb8 Se13 at heating rates β
of 5, 10, 15, and 20 K/min.

56

Material
K2 Sb8 Se13
K2 Sb8 Se13
KSb5 S8
Ge2 Sb2 Te5

glass
glass
glass
glass

Ec (kJ/mol) k(T ) (s−1 )

Transition

1 - glass 2 245
2 - crystal 316
- crystal
167
- crystal
215

2.4 × 10−3
2.6 × 10−3
2.1 × 10−2
2.45 × 10−2

Table 4.1. Comparison of crystallization energy, Ec , and rate constant, k(T ), of K2 Sb8 Se13
with KSb5 S8 and Ge2 Sb2 Te5 at 20 K/min heating rate.

β is given by Equation 4.7 (8 )
Tp = A + B log β

(4.7)

where A and B are constants for a given composition. Kissinger analysis (9 ), which combines
the single-step mechanism with the Arrhenius equation, can give a rough estimation of the
2
activation energy of a solid-solid phase transition from the slope of a ln(β/Tp ) vs. 1/Tp plot

(see Equation 4.8, where R is the universal gas constant).
2
ln(β/Tp ) = −Ec /RTp + ln(A · R/Ec )

(4.8)

Kissinger plots for both peaks are shown in Figures 4.2 and 4.3. The data show good
linearity, though this is not surprising considering the logarithmic relationship. The values of
the activation energies Ec1 and Ec2 were found to be 245 kJ/mol and 316 kJ/mol respectively,
and preexponential factors A1 and A2 were calculated as 1.05 × 1023 s−1 and 2.10 × 1028
s−1 from the intercept. By substituting the Arrhenius equation into the single-step kinetic
equation (Equation 4.9), the rate constants k(T ) were calculated (Equation 4.10) to be
2.4 × 10−3 s−1 for peak 1 and 2.6 × 10−3 s−1 for peak 2 at β = 20 K/min.
dα/dt = Ae−E/RT f (α)

(4.9)

k(T ) = Ae−Ec /RTp

(4.10)

Table 4.1 shows the comparison of these kinetic parameters with previously studied phasechange materials KSb5 S8 and Ge2 Sb2 Te5 . These data seem to indicate that the transitions
in K2 Sb8 Se13 are slower than those in comparable materials, but the assumption of the
57

Figure 4.2. Kissinger plot of K2 Sb8 Se13 glass β to glass α, ln(β/Tp ) vs. 1000/T and the
straight regression line (β in K s−1 )

Figure 4.3. Kissinger plot of K2 Sb8 Se13 glass α to crystal, ln(β/Tp ) vs. 1000/T and the
straight regression line (β in K s−1 )

58

Kissinger method, that the phase transitions are single-step, may not be applicable in this
case. This is not surprising, as the unusual nature of the glass Aglass polyamorphic transition
may require more sophisticated kinetic analysis.

4.3.2

Ozawa-Flynn-Wall analysis

The isoconversional method first developed by Ozawa, Flynn and Wall (3 ) uses a model-free
approach by measuring the temperatures at each value of α (extent of reaction) and plotting
them at different heating rates (Equation 4.11).
ln(β) = ln[Af (α)/dα/dT ] − Ec /RT

(4.11)

The plots of ln(β) vs. 1/T are shown in Figure 4.4. According to the OFW equation
(Equation 4.11), the slopes are proportional to the activation energy (−Ec /R). If the activation energy is calculated to be similar for different values of α, it can be reasonably concluded
that the transition proceeds via a single-step mechanism; however, if there is a substantial
change in slope with increasing degree of conversion, then the separation of variables involved
in the OFW analysis is no longer appropriate, indicating a more complex reaction mechanism. Figure 4.4 shows the OFW plots for the glass β-to-glass α transition of K2 Sb8 Se13
and Figure 4.5 shows the relationship of activation energy with extent of conversion α. The
inconsistency of activation energy calculations for each α show that there are likely variations
in mechanism throughout the phase change, showing the polyamorphic transition to be of a
complex mechanism and most likely multi-step. Since this is a unique example of polymorphism at ambient pressure, it is reasonable to expect that the phase transition mechanisms
will be significantly different from previously studied systems (10 –12 ).

4.4

Conclusions

Kinetic studies on K2 Sb8 Se13 glass showed great variability in mechanism and form, its nonadherence to classical models underscoring the novelty of this system. Kissinger analysis of

59

Figure 4.4. OFW plot of ln(β) vs. 1/T for different values of α during the first phase
transition (glass β-to-glass α) of K2 Sb8 Se13 .

60

Figure 4.5. OFW plot of ln(β) vs. 1/T for different values of α during the first phase
transition (glass β-to-glass α) of K2 Sb8 Se13 .

61

DSC data showed linearity, but the isoconversional OFW method showed a clear deviation
from the model. As this represents the first example of a polyamorphic material stable in
both glass forms at ambient temperature and pressure, it may be an excellent candidate for
developing new models to describe the kinetics of polyamorphic phase transitions.

62

References and Notes

63

References and Notes

[1] Wachter, J. B.; Chung, D.-Y.; Kyratsi, T.; Malliakas, C.; Chrissafis, K.; Sootsman, J. R.;
Kanatzidis, M. G. Science 2010, submitted, .
[2] Avrami, M. J. Chem. Phys. 1941, 9, 177.
[3] Ozawa, T. J. Therm. Anal. 1970, 2, 301.
[4] Chrissafis, K.; Kyratsi, T.; Paraskevopoulos, K. M.; Kanatzidis, M. G. Chemistry Of
Materials 2004, 16, 1932 – 1937.
[5] Johnson, W. A.; Mehl, R. F. Trans. Am. Inst. Min. (Metall.) Eng 1939, 135, 416.
[6] Matusita, K.; Sakka, S. Phys. Chem. Glasses 1979, 20, 81.
[7] Matusita, K.; Konatsu, T.; Yokota, R. J. Mater. Sci. 1984, 19, 291.
[8] Lasocka, M. Mater. Sci. Eng. 1976, 1976, 173.
[9] Kissinger, H. E. J. Res. Natl. Bur. Stand. 1956, 57, 217.
[10] McMillan, P. F.; Wilding, M. C. J. Non-Cryst. Solids 2008, 354, 1015 – 1025.
[11] Aasland, S.; McMillan, P. F. Nature 1994, 369, 633 – 636.
[12] Angell, C. A. Science 1995, 267, 1924 – 1935.

64

CHAPTER 5

Synthesis and phase-change behavior of K2 Bi8 S13 thin films

5.1

Introduction

The previous chapters have reported on several new antimony chalcogenide-based phase
change materials. Attempts to quench bismuth chalcogenides were unsuccessful in that the
glassy phases could not be formed through standard quenching techniques such as water,
air, and splat quenching (1 ). The more rigid frameworks in bismuth-based structures (2 )
require ultra-rapid quenching to afford the amorphous phase; however, this makes those
phases particularly lucrative from a data storage material standpoint, as the resulting glasses
should crystallize exceptionally fast (3 ).
Gutwirth et al. (4 ) have demonstrated the synthesis of Ag-Sb-S glasses, which are unable
to be synthesized through rapid bulk quench methods, by pulsed-laser deposition. In this
technique, a target of the bulk, crystalline sample is irradiated by a high energy, pulsed
laser, releasing a plume of small particles that settle onto a substrate placed in front of the
target (5 ). The rapid cooling of the particles as they settle on the substrate results in the
amorphous structure.
An additional advantage of producing films of the phase-change materials is to investigate
their utility in data storage devices and media. All currently-used, phase-change materialbased solid state memory devices require thin layers of the material to be deposited onto
the device, often layered with electrodes (6 ). Synthesizing films of A-Sb/Bi-S-type PCMs
has been difficult using conventional techniques such as chemical vapor deposition (CVD)
65

because of the great variation in vapor pressures among alkali metal ions, antimony, bismuth,
and sulfur, though there has been some success with solution techniques (7 ).
Here we describe the first synthesis of glassy K2 Bi8 S13 films, using the pulsed-laser deposition technique. The films, which have phase-change properties, were analyzed using
conventional solid-state techniques and found to exhibit excellent potential for use in data
storage devices.

5.2
5.2.1

Experimental section
Synthesis of crystalline K2 Bi8 S13

Crystalline K2 Bi8 S13 was synthesized by combining K2 S, and Bi2 S3 powders in a 1:4 ratio
under a nitrogen atmosphere in a 13 mm diameter, fused silica tube, which was then sealed
under reduced pressure (<10-4 torr) and heated at 850o C for 24 h, when heating was ceased
and the tube was allowed to cool in the furnace. The resulting ingot was proven to have the
K2 Bi8 S13 stoichiometry by energy dispersive X-ray elemental analysis and its crystallinity
and structure were confirmed by powder X-ray diffraction.

5.2.2

Synthesis of amorphous K2 Bi8 S13 thin films

Thin films of K2 Bi8 S13 were synthesized by irradiating the ingot with a 200 mJ/pulse KrF
laser (λ = 248 nm) under reduced pressure (∼ 10−2 torr) at 20 Hz for 10 min. A glass slide
was placed in front of the ingot, onto which the film deposited. The amorphous nature of
the thin film was confirmed by powder X-ray diffraction.

5.2.3

Differential Scanning Calorimetry (DSC)

The differential scanning calorimetric (DSC) measurements were carried out with a Shimadzu
DSC-50 calorimeter. Temperature and energy calibrations of the instrument were performed,
for different heating rates, using the well-known melting temperatures and melting enthalpies
of high-purity zinc, indium and tin. Material from several film samples (∼ 0.7 mg) was
66

scraped off the glass substrates and into an aluminum crucible; an empty aluminum crucible
was used as reference. A constant flow of nitrogen was maintained to provide a constant
thermal blanket within the DSC cell, thus eliminating thermal gradients and ensuring the
validity of the applied calibration standard from sample to sample.

5.2.4

Transmission electron microscopy (TEM)

Transmission electron microscopy was performed on as-deposited and annealed K2 Bi8 S13
films using a JEOL 2200FS field emission TEM running at 200kV. Samples were prepared
by pulsed-laser deposition as described above, using a copper grid as the substrate.

5.2.5

Scanning electron microscopy (SEM)

Images and quantitative microprobe analyses of the compounds were performed with a JEOL
JSM-35C scanning electron microscope (SEM) equipped with a Tracor Northern energydispersive spectroscopy (EDS) detector. Data were acquired using an accelerating voltage
of 25 kV and a 1-min acquisition time. Samples were coated with carbon prior to analysis.

5.3
5.3.1

Results and discussion
Structural analysis

Crystalline K2 Bi8 S13 was first reported by Kanatzidis et al (2 ). Like other members of the
A-Bi-S system, it is made up of NaCl- or Bi2 Te3 -type and CdI2 -type rod-shaped fragments
along the b axis that connect via highly coordinated Bi atoms to form tunnels. Unlike most
other alkali bismuth (or antimony) chalcogenides, the K+ ions are not found in these tunnels
but are disordered with one of the Bi3+ ions. It is postulated that the disorder, coupled
with the rigidity of the cubic fragments, leads to the rich phase change chemistry recently
observed in these systems (8 –10 ). Amorphous K2 Bi8 S13 could not be synthesized through
quenching of the melt, either with traditional water-quench techniques or with the more
rapid splat-quenching.
67

5.3.2

Analysis of films

The high energy involved in pulsed-laser deposition allowed the material to cool quickly
enough to form an amorphous film, which was previously inaccessible by other techniques.
Figure 5.1 shows XRPD patterns for the as-synthesized K2 Bi8 S13 film and for annealed
films at progressively higher temperatures, showing a clear transformation from amorphous
to crystalline. Annealing at higher temperatures did not alter the structure, highlighting
the robust nature of the crystalline phase. The small amount of material in the film led to
a low signal-to-noise in the XRPD, so long scans (16 h) were required in order to determine
the crystal structure of the crystalline phase.
Comparison with calculated XRPD patterns showed that the annealed film contained
a Bi2 S3 -type structure, with no other crystalline phase observed. This was unexpected,
since similar systems have been shown to undergo stoichiometric phase transitions, and the
structure of the crystalline film here was clearly not K2 Bi8 S13 . Therefore, the K must have
either formed a Kx Bi2-x S3 -type solid solution, a compound that has not been previously
reported, or the phase change was nonstoichiometric, that is, upon crystallization the glass
phase separates into pure Bi2 S3 and an amorphous, K-containing phase. The local structure
of the crystalline film was further examined using TEM.

5.3.3

Electron microscopy

TEM of the annealed films showed clearly visible crystalline domains throughout the sample
(Figure 5.2), confirmed by electron diffraction. Energy-dispersive X-ray analysis (EDS) and
scanning transmission electron microscopy (STEM) show an absence of K in crystalline
domains, giving an average composition of Bi1.88 S3 , a good match for bismuth sulfide.
This evidence shows the non-stoichiometric nature of the glass-to-crystal phase transition in
K2 Bi8 S13 , indicating that the reversibility and long-term cycling ability of the phase transition may be compromised and therefore less suitable for use in electronic devices that require
more robust phase-change behavior.

68

Figure 5.1. XRPD of K2 Bi8 S13 film after annealing at temperatures (from top) of 350, 325,
275, 250, 150, and 100o C, showing the glass-to-crystal phase change and stability of the
crystal up to 350o C.

69

Figure 5.2. TEM image of K2 Bi8 S13 film after annealing. Crystalline Bi2 S3 domains are
visible.

70

Figure 5.3. SEM image of as-synthesized K2 Bi8 S13 glass film.

71

Material

Ec (kJ/mol) Trg

K2 Bi8 S13
K2 Sb8 Se13
KSb5 S8
Ge2 Sb2 Te5

120
316
167
215

0.44
0.63
0.78
0.46

Table 5.1. Comparison of crystallization energy, Ec , and reduced glass transition temperature, Trg = Tg /Tm (3 ), of K2 Bi8 S13 with KSb5 S8 , K2 Sb8 Se13 and Ge2 Sb2 Te5 .

Side-on SEM images of the as-synthesized film (Figure 5.3) showed a homogeneous glass
4.5 µm thick. EDS analysis gave an average composition of K2.17 Bi7.97 S13 , indicating stoichiometric transfer of material during the laser deposition process.

5.3.4

Thermal analysis

Though the glass-to-crystal phase change of K2 Bi8 S13 was found to be non-stoichiometric,
it can still have utility as a phase-change material provided the crystallization process is
rapid, as several currently-used PCMs display non-stoichiometric phase changes (11 –13 ). A
DSC measurement of the as-synthesized K2 Bi8 S13 film is shown in Figure 5.4. There is clear
evidence of crystallization at 181o C and glass transition ∼100o C. Kissinger analysis (14 ) of
the DSC data (15 ), shown in Figure 5.5 allows for the calculation of activation energy of
crystallization, Ec , and rate constant k(T ). These values are shown in Table 5.1 compared
to other phase-change materials (8 , 9 , 16 , 17 ). The low activation energy of crystallization
and reduced glass transition temperature (3 ) demonstrate the unusually rapid nature of
glass-to-crystal conversion in K2 Bi8 S13 ; indeed, it is one of the lowest Trg values reported
in the literature for phase change materials. These values are encouraging for the potential
performance of K2 Bi8 S13 as a data storage material.
To investigate the mechanism of the phase change, Ozawa-Flynn-Wall (18 ) and JohnsonMehl-Avrami (19 , 20 ) analyses were performed on the DSC data. For detailed descriptions
of these kinetic methods, see Chapter 4. The OFW plots (Figure 5.6) show minimal variation
in the activation energy with extent of reaction α (Figure 5.7), demonstrating a possible one-

72

Figure 5.4. DSC trace of K2 Bi8 S13 glass film at a heating rate of 15 K/min. The exotherm
at 181o C shows crystallization of the glass, confirmed by XRPD after the scan.

73

Figure 5.5. Kissinger plot of K2 Bi8 S13 film for heating rates of 5, 10, and 15 K/min.
2
Regression line has the equation ln(β/Tp ) = 14.48/Tp − 12756.88.
step mechanism. This allows for an accurate comparison to the current industry-standard
phase-change material for data storage, Ge2 Sb2 Te5 , which has been shown to undergo a
one-step phase change mechanism (21 ).
Since the mechanism appears to be one step, it is appropriate to use the JMA method
to probe the nucleation and growth mechanism. The Matusita extention (22 ) of the JMA
equation (Equation 4.6) was applied, where α is the fractional extent of reaction, β is heating
rate, and n and m are numerical factors depending on the nucleation process and growth
morphology. Here, n is equal to (m + 1) for a quenched glass containing no nuclei and n is

74

Figure 5.6. Ozawa-Flynn-Wall plots, ln β vs. 1/T for α=0.2-0.85, of K2 Bi8 S13 film.

75

Figure 5.7. Activation energy of crystallization Ec vs. extent of reaction α for K2 Bi8 S13
film.

76

Figure 5.8. JMA-Matusita plot of K2 Bi8 S13 films at heating rates of 5, 10, and 15 K/min.

77

equal to m (23 ) for a glass containing a sufficiently large number of nuclei. Also, m = 3 for
three-dimensional growth of crystal particles, m = 2 for two-dimensional growth, and m = 1
for one-dimensional growth. The Avrami plots are shown in Figure 5.8, showing substantial
linearity; however, double logarithmic functions are known to be insensitive to small changes
in their arguments, so linear JMA plots may not necessarily indicate adherence to the JMA
model.

5.4

Conclusions

K2 Bi8 S13 was successfully quenched into an amorphous form through pulsed-laser deposition.
Though the non-stoichiometric nature of the crystallization of K2 Bi8 S13 , as shown by TEM
and XRPD, is a potential drawback to its use as a multi-use, cyclable phase-change material,
its rapid kinetics of crystallization make it ideal for applications requiring ultrafast switching.

78

References and Notes

79

References and Notes

[1] (a) Nagashio, K.; Kuribayashi, K.; Yamaguchi, O. J. Am. Ceram. Soc. 2007, 90, 238 –
243; (b) Amano, M.; Sasaki, Y.; Watanabe, R. J. Less-Common Met. 1983, 89, 513 –
518.
[2] Kanatzidis, M. G.; McCarthy, T. J.; Tanzer, T. A.; Chen, L. H.; Iordanidis, L.;
Hogan, T.; Kannewurf, C. R.; Uher, C.; Chen, B. X. Chem. Mater. 1996, 8, 1465
– 1474.
[3] Turnbull, D. Contemporary Physics 1969, 10, 473 – and.
[4] (a) Gutwirth, J.; Wagner, T.; Bezdicka, P.; Pokorny, J.; Vlcek, M.; Frumar, M. J.
Non-Cryst. Solids 2005, 351, 3556 – 3561; (b) Gutwirth, J.; Wagner, T.; Frumar, M.;
Bezdicka, P.; Vlcek, M. Phys. Chem. Glasses 2006, 47, 229 – 232; (c) Gutwirth, J.;
Wagner, T.; Nemec, P.; Kasap, S. O.; Frumar, M. J. Non-Cryst. Solids 2008, 354, 497
– 502.
[5] Nemec, P.; Frumar, M.; Jedelsky, J.; Jelinek, M.; Lancok, J.; Gregora, I. J. Non-Cryst.
Solids 2002, 299, 1013 – 1017.
[6] Borg, H. J.; van woudenberg, R. Journal Of Magnetism And Magnetic Materials 1999,
193, 519 – 525.
[7] Mitzi, D. B. Adv. Mater. 2009, 21, 3141 – 3158.
[8] Kyratsi, T.; Chrissafis, K.; Wachter, J.; Paraskevopoulos, K. M.; Kanatzidis, M. G.
Advanced Materials 2003, 15, 1428 – 1431.
[9] Wachter, J. B.; Chung, D.-Y.; Kyratsi, T.; Malliakas, C.; Chrissafis, K.; Sootsman, J. R.;
Kanatzidis, M. G. Science 2010, submitted, .
[10] Wachter, J. B.; Chrissafis, K.; Petkov, V.; Malliakas, C. D.; Bilc, D.; Kyratsi, T.;
Paraskevopoulos, K. M.; Mahanti, S. D.; Torbr¨gge, T.; Eckert, H.; Kanatzidis, M. G.
u
J. Solid State Chem. 2007, 180, 425 – 436.
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80

[12] Balan, V.; Vigreux, C.; Pradel, A.; Ribes, M. Adv. Mater. 2001, 3, 367.
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[15] Kissinger analysis allows for the calculation of activation energy and rate constant by
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81

APPENDICES

82

A.1

Design of an analytical laser-switching device

In order to better compare the newly-synthesized films to the current industry standards, a
laser testing device was constructed. The device was designed to expel a laser pulse of given
intensity and time, which would crystallize or melt the material depending on the incident
power. Existing table top lasers were not the best choices for this device for several reasons.
From a practical standpoint, they are expensive and require large amounts of laser table
space, optics, and power supplies. Also, the lasing threshold for many common large lasers
makes power control difficult or impossible. The time variable is also difficult to control with
large laser systems. For longer pulses, a mechanical shutter can be used, and much research
has been done on very short pulses (on the order of 10−12 s or faster), but the range in which
laser storage devices operate (10−6 − 10−9 s) is best accessed by electronic control. To this
end, a device was constructed based around the Atmel Atmega128 microcontroller, Maxim
MAX9483 laser diode driver, and a 650 nm laser diode extracted from a DVD-RW drive.
In an optical data storage device, the binary data signal is fed at signal level (µA) into
the driver, which amplifies the current to writing level (mA) and drives the laser diode. The
diode is switched on and off in sync with the spinning disc, depending on the binary state
of the input waveform. A similar philosophy is used for this device, but the input waveform
is a constant, pre-determined current and the laser diode driver output is switched on and
off by the microcontroller, which is calibrated by a 16 MHz quartz crystal for precision. A
general flowchart of the signal path is shown in Figure A.9.
The user sets the ”Power” and ”Pulse length” parameters via buttons on the control
board, which in this case is an Olimex AVR-MT-128 development board but could be any
board designed to support the Atmega128 microcontroller.
The ”Power” value is used to set a variable resistor to control the current sent as input
to the driver. The variable resistor used for this device is the Analog Devices AD5206 6channel digital potentiometer. The AD5206 contains six 256-position, digitally-controlled
variable resistor devices with maximum resistances of 10 kΩ. They function in much the
82

Figure A.9. Schematic of data flow in the laser device.
same way as an analog resistor, with two end terminals and a wiper contact that can tap the
resistance. The tap point is determined by a digital 8-bit word loaded into the serial-input
register. Based on the user input, the Atmega128 microcontroller sends the data through
the serial peripheral interface (SPI) into the serial-input register of the AD5206, thus setting
the wiper. The input current for the laser driver passes through this resistor, attenuating it
to the degree necessary based on the user’s power selection.
The microcontroller is also utilized to send a perfectly timed on/off pulse to the laser
driver. The Atmega128’s Timer/Counter0, an 8-bit timer/counter, can be set to count based
upon an input from an external crystal (oscillating at 32.7 kHz) or from the internal oscillator
(running at 16 MHz). Each time the counter register overflows (at 256), an interrupt signal
is actuated and the interrupt subroutine runs before returning to the now-reset count. By
introducing a divider and compare-to-count (CTC) term, the timer can be manipulated to
overflow in a specific amount of time. This timer cycle is then contained in a loop that is
83

repeated depending upon the pulse width as determined by the user.
The laser diode is directly controlled by the Maxim MAX9483 laser diode driver, a
commercial chip used in CD/DVD-RW drives, which accomplishes the dual tasks of providing
the appropriate output current for the laser diode and acting as an ultra-fast gate, turning
the laser on or off as directed by the microcontroller program. It contains a precision current
amplifier with a peak total output current of 400mA and can respond to on/off instructions
in 1.0ns (output-current pulse rise and fall time).

Figure A.10. The extracted laser diode module.

84

Figure A.11. The user input module (Olimex AVR-MT-128).
The devices were connected as shown in Tables A.2 and A.3, with an additional connection between the wiper of RDAC 3 on the variable resistor (W3, pin 14) and the input of
the laser driver (IN1, pin 1).
Function

Connection to Atmega128 Connection on AD5206

Data transfer
Chip select
Serial clock

MOSI/PB2 Pin 12
SS/PB0 Pin 10
SCK/PB1 Pin 11

SDI (Serial Data Input) Pin 7
¯
CS(Chip Select) Pin 5
CLK Pin 8

Table A.2. Connections from Atmega128 to AD5206.

Function

Connection to Atmega128

Connection on MAX9483

Enable device
On/off
Select output

OC1B/PB6 Pin 16
OC1A/PB5 Pin 15
OC0/PB4 Pin 14

ENABLE Pin 7
¯
NE2 Pin 5
OUTSEL Pin 10

Table A.3. Connections from Atmega128 to MAX9483.

The outputs from the Atmega128 microcontroller were connected from the appropriate
output pins on the Olimex board. A standard breadboard was used to connect the AD5206
and MAX9483, and a benchtop power supply was used to supply the input current. The
MAX9483 chip required some additional preparation as it is a QSOP packaged, surface85

mount device and thus cannot be directly connected to the breadboard. A copper printed
circuit board was constructed using the photoresist-etch process to extend the small contacts
on the chip to standard pins, which were spaced appropriately to fit onto the breadboard
(Fig. A.12). The output from the MAX9483 chip (OUT1, pin 15) was connected to the
positive terminal of the laser diode. The laser head itself was extracted from a DVD+RW

Figure A.12. The MAX9483 laser driver mounted to a printed circuit board. Extension pins
are spaced 0.001” apart.
drive. The outer metal casing was easily removed after unscrewing the screws at the corners
of the case, and the laser diode module was removed from the inside of the drive. All optics
were left intact so that the spot size remains the same (Fig. A.10). It should also be noted
that there are two laser diodes in the module, an infrared diode for CD writing and a visible
diode for DVD writing. This device utilizes the visible diode, but either could be used.
In order to function as a stand-alone device (i.e. no computer connection needed while
measuring), the Atmega128 microcontroller was programmed. The C language was used
to write the program, which was compiled into a hex file by AVR Studio and loaded onto
86

the device though the ICSP (intra-circuit serial programmer) interface. The main program
(”laser.c”) is shown below:

#include <sharedCode.h>
#include "lcd.h"
#include <string.h>
#include "laser.h"

int seconds=100;
int amps=255;
char s[6];
char a[6];

void updateData(void)
{
int i;
for (i=0; i<25; i++)
{
msDelay(100);
}
sprintf(s,"%d",seconds);
sprintf(a,"%d",amps);
LCD_moveTo(0,11);
LCD_string("

");

LCD_moveTo(1,11);
87

LCD_string("

");

LCD_moveTo(0,11);
LCD_string(s);
LCD_moveTo(1,11);
LCD_string(a);
}

int main(void)
{
initializeLCD();
//LCD_clear();
LCD_string("Pulse(ms):\0");
LCD_moveTo(1,0);
LCD_string("Power(xx):\0");
spi_setup();
updateData();
while(1==1)
{
if (readButton()==1)
{
seconds += 10;
updateData();
}
if (readButton()==5)
{
seconds -= 10;

88

updateData();
}
if (readButton()==4)
{
amps++;
if (amps<256)
{
updateData();
}
else
{
amps--;
updateData();

}
}
if (readButton()==2)
{
amps--;
if (amps>99)
{
updateData();
}
else
{
amps++;
updateData();

89

}
}
if (readButton()==3)
{
write_pot(0b100,amps);
updateData();
pulseExecute();
}

}
}
}
The functions and subroutines not defined in the above program are taken from spi.c and
sharedcode.c, whose contents are shown below:

#include <sharedCode.h>
#include "lcd.h"
#include "laser.h"

int pot=0;
int resistance=0;

char spi_transfer(volatile char data)
{
SPDR = data;

// Start the transmission

while (!(SPSR & (1<<SPIF)))

// Wait the end of the transmission

{
90

};
return SPDR;

// return the received byte

}

void spi_setup(void)
{
int i;
int clr;
DDRB = (1<<DDB2) | (1<<DDB1) | (1<<DDB0);
PORTB = (1<<PB0);

//set SS high

// SPCR = 01010000
//interrupt disabled,spi enabled,msb 1st,master,clk low when idle,
//sample on leading edge of clk,system clock/4 (fastest)
SPCR = (1<<SPE)|(1<<MSTR);
clr=SPSR;
clr=SPDR;
msDelay(100);
//

for (i=0;i<6;i++)

//

{

//
//

write_pot(i,255);
}

}

void write_pot(int address, int value)
{
PORTB = (0<<PB0); //set SS low
spi_transfer(address);

91

spi_transfer(value);
PORTB = (1<<PB0);

//set SS high

}

#include "sharedCode.h"

//memory routines
void EEPROM_write(unsigned int uiAddress, unsigned char ucData)
{
/* Wait for completion of previous write */
while(EECR & (1<<EEWE))
;
/* Set up address and data registers */
EEAR = uiAddress;
EEDR = ucData;
/* Write logical one to EEMWE */
EECR |= (1<<EEMWE);
/* Start eeprom write by setting EEWE */
EECR |= (1<<EEWE);
}

unsigned char EEPROM_read(unsigned int uiAddress)
{
/* Wait for completion of previous write */
while(EECR & (1<<EEWE))
;
/* Set up address register */

92

EEAR = uiAddress;
/* Start eeprom read by writing EERE */
EECR |= (1<<EERE);
/* Return data from data register */
return EEDR;
}

//IO Section
int readButton(void)
{
int returnValue=0;
int buttonValue;
while(returnValue==0)
{
returnValue=DepressedButton();
//if(buttonValue!=0)
//{
// returnValue=buttonValue;
// while(DepressedButton!=0){}
//}
//msDelay(200);
}

//delay for debounce

// int j;
//for(j=0;j<50;j++)

93

// _delay_ms(1);

return returnValue;
}

int GetBit(int Address, int Bit)
{
return bit_is_set(Address,Bit);
}

void msDelay(int cycles)
{
int j;
for(j=0;j<cycles;j++)
_delay_ms(1);

}

void SetBit(int Address,int Bit)
{
bit_set(Address,Bit);
}

int DepressedButton(void)
{
int result=0;

94

if(GetBit(BUTTON1)==0)
{
_delay_ms(25);
if(GetBit(BUTTON1)==0)
result=1;
}

if(GetBit(BUTTON2)==0)
{
_delay_ms(25);
if(GetBit(BUTTON2)==0)
result=2;
}

if(GetBit(BUTTON3)==0)

{ _delay_ms(25);
if(GetBit(BUTTON3)==0)
result=3;
}

if(GetBit(BUTTON4)==0)

{ _delay_ms(25);
if(GetBit(BUTTON4)==0)

95

result=4;
}

if(GetBit(BUTTON5)==0)

{ _delay_ms(25);
if(GetBit(BUTTON5)==0)
result=5;
}

return result;
}}

The front end of the program, that with which the user interacts, is comprised of a set
of functions meant to read the button inputs and then update the variables seconds and
amps, which control the pulse length and laser power, respectively. As described above, the
amps variable relates to the resulting laser power by controlling the wiper on the digital
potentiometer, attenuating the input current to the laser driver, while seconds tells the
Timer/Counter0 how long to wait before turning the laser off.
Once the appropriate connections are made, the device is powered up by bringing power
to the user input module. In this case, the development board is powered by 12 VDC. The
laser should be positioned above the film to be tested at the desired height. The user then
increases or decreases the pulse length and power by pressing the buttons on the horizontal
and vertical corners, respectively. When the appropriate parameters are set, pressing the
middle button activates the pulseExecute() subroutine, which cycles the laser on and off in
the given time with the appropriate power.

96