Crystal Growth Kinetics and Viscous Behavior in Ge2Sb2Se5

Subscriber access provided by UNIV OF CALIFORNIA SAN DIEGO LIBRARIES

Article 2

2

5

Crystal Growth Kinetics and Viscous Behavior in GeSbSe Undercooled Mel Jaroslav Barták, Petr Koštál, Veronika Podzemna, Jana Shán#lová, and Jiri Malek J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b05455 • Publication Date (Web): 21 Jul 2016 Downloaded from http://pubs.acs.org on July 25, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Crystal Growth Kinetics and Viscous Behavior in Ge2Sb2Se5 Undercooled Melt Jaroslav Barták*1, Petr Koštál2, Veronika Podzemná1, Jana Shánělová1,Jiří Málek1 1

2

Department of Physical Chemistry, University of Pardubice, Studentská 573, Pardubice 532 10, Czech Republic

Department of Inorganic Technology, University of Pardubice, Doubravice 41, Pardubice 532 10, Czech Republic

*corresponding author: [email protected]; tel.: 00420466037346

ABSTRACT The crystal growth, viscosity, and melting were studied in Ge2Sb2Se5 bulk samples. The crystals formed a compact layer on the surface of the sample and then continued growing from the surface to the central part of the sample. The formed crystalline layer grew linearly with time which suggests that the crystal growth is controlled by liquid-crystal interface kinetics. Combining the growth data with measured viscosities and melting data, the crystal growth could be described on the basis of standard crystal growth models. The screw dislocation growth model seems to be operative to describe the temperature dependence of crystal growth rate in the studied material in a wide temperature range. A detailed discussion about the relation between the kinetic coefficient of crystal growth and viscosity (ukin∝η-ξ) is presented. The activation energy of crystal growth was found to be higher than the activation energy of crystallization followed by DSC, which covers the whole nucleation-growth process. This difference is considered and explained under the experimental conditions.

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

INTRODUCTION The chalcogenide glasses have been studied for many decades due to their unique properties, which predetermine these materials for usage in different optoelectronic, photonics, photoconducting, sensing and memory devices applications1, 2. Generally, the chalcogenide glasses are transparent from the visible to the infrared (IR) spectral region. Different sulfide, selenide and telluride glasses, as well as mixed selenide-telluride glasses, were developed for optical components for the far infrared spectral region, which have been exploited commercially1, 3. The chalcogenide found their application also in fibers, where these materials are used for laser power delivery, chemical sensing, temperature monitoring, thermal imaging, or near field microscopy4. Some chalcogenide materials exhibit a pronounced difference of optical and electronic properties in amorphous and crystalline phases. Moreover, a rapid and reversible switching between these phases takes place under certain conditions. Such phase change materials (PCM) can be used in data storage applications5-7. Thermal stability, thermomechanical properties, nucleation, and crystal growth play a key role in preparation, processing, and possible usage of the mentioned materials. The crystallization process needs to be prevented to obtain an ideal glass, or, on the other hand, the controlled transformation from amorphous to crystalline state is a cardinal process of the considered technology. The understanding of nucleation-growth process is then a fundamental phenomenon, either, to prevent or control the amorphous-to-crystalline transformation. The applicability of crystal growth kinetics and viscosity to describe the crystallization process in glasses and undercooled melts can help to predict crystallization behavior in a wide temperature range. Such a description can provide a possibility to predict crystallization behavior in similar materials by revealing the basic properties and mechanisms of the material. This article is focused on a detailed study of viscous flow and crystal growth kinetics in bulk glasses of Ge2Sb2Se5. This glass belongs to a broad family of Ge-Sb-Se chalcogenide glasses which are known for their low transmission loss, high transparency in infrared region (2-16 µm), and high thermal stability8-14. The chosen composition (Ge2Sb2Se5) is the selenium analog of the GST-225 (Ge2Sb2Te5), which is a well-known PCM exhibiting extremely fast amorphous-to-crystalline transformation6, 15. Utilization of these materials requires a deep understanding of thermal and thermodynamic properties, and involved kinetic processes. This article provides a novel and extensive study of crystal growth, viscosity and melting in the Ge2Sb2Se5 amorphous material. The viscosity, growth and melting data were combined and used to describe wide temperature range crystallization behavior in the chosen Ge2Sb2Se5 bulk glass.

CRYSTAL GROWTH THEORY The crystal growth rate in glasses and undercooled melts is usually driven by the interface mechanism. The crystal growth rate (u) can be generally expressed as16:

u = f (T ) ⋅ D(T ) ≈

f (T ) (1), η (T )


Page 2 of 20

Page 3 of 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where D(T) represents temperature dependence of molecular diffusion and is proportional to reciprocal shear viscosity η(T) through Stokes-Einstein equation. The term f(T) differs in various growth models used for description of the crystal growth kinetics. According to eq. 1, it is necessary to know the temperature dependence of diffusion or viscosity and the appropriate growth mechanism. On the basis of different kinetic approaches to crystal-liquid interface, there are three basic phenomenological growth models17, 18: normal, screw dislocation, and 2D surface nucleated growth model. The normal growth assumes a rough surface on atomic scale, where the growth units are oriented to the sites with the lowest energy. The crystal growth rate can be expressed as:

u=

 k ⋅T  ∆G  ⋅ 1 − exp −  (2), 2 3π ⋅ a0 ⋅ η   R ⋅ T 

where T is temperature, η is viscosity, a0 is the mean interatomic distance in the interface layer, k is Boltzmann constant, R is universal gas constant, and ∆G is change of Gibbs free energy between the undercooled melt and the crystalline phase. The screw dislocation growth is based on a lattice distortion in which the attachment of growth units to the crystal surface results in the development of a spiral growth pattern or a screw dislocation. The crystal growth rate is then expressed as:

u=

k ⋅T ∆T ⋅ 2 3π ⋅ a0 ⋅η 2π ⋅ Tm

  ∆G ⋅ 1 − exp −  R ⋅T 

  (3), 

where ∆T is undercooling of the system with respect to temperature of melting Tm (∆T = Tm – T). The 2D surface nucleated growth is controlled by formation of 2-dimensional nuclei on the smooth surface of a growing crystal and by subsequent addition of growth units to the nucleus. The crystal growth rate can be expressed as:

u=

B   ⋅ exp −  (4), η  T ⋅ ∆T 

C

where B and C are parameters of the model. Jackson et al.19 showed that the operative crystal growth model can be assessed from the dependence of reduced crystal growth rate (UR) on undercooling of the system (∆T). The UR is given by the following equation:

UR =

u ⋅η (5)  ∆G  1 − exp −   R ⋅T 

The operative crystal growth model can be then assessed from a plot of UR vs. ∆T, where if the plot results in a shape of horizontal line, the normal crystal growth model should be used. For screw



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

dislocation growth model, the plot results in a straight line with positive slope, and for the 2D surface nucleated growth model, the plot is expected to be in the form of a curve of increasing positive slope.19 As obvious from eqs. 2 – 5, it is necessary to know the temperature dependence of change of Gibbs free energy between undercooled melt and crystalline phase (∆G). With knowledge of temperature dependencies of heat capacities of the undercooled melt (Cpm) and the crystalline phase (Cpcr), the ∆G can be directly calculated: T

T

m ∆T m dT ∆G = ∆H m − ∫ ∆C p dT + T ∫ ∆C p (6a), Tm T T T

∆Cp = C pcr − Cpm (6b), where ∆Hm is enthalpy of melting. Nevertheless, the heat capacity data for undercooled melts are not often available, because of the difficulties connected to their measurements. Owing to the missing data, several simpler expressions were found to calculate the ∆G20-23. The relation proposed by Turnbull 20 is the most used approximation of ∆G:

∆G = ∆H m

∆T (7) Tm

The standard crystal growth models assume a simple inverse proportionality of crystal growth rate to viscosity, as was shown in eqs. 1 – 3. This is valid for small undercooling where the amorphous-to-crystalline kinetic process is assumed to be similar to that which governs selfdiffusion, and the diffusion constant can be described by the inverse shear viscosity24. Nevertheless, several authors25-28 showed that the viscosity and crystal growth rate can decouple with increasing undercooling. The decoupling can be caused by break-down of the Stokes-Einstein relationship between diffusivity and viscosity. Ediger25 proposed a power law dependence of kinetic coefficient ukin on viscosity:

u kin ∝ η −ξ (8), where ξ ≤ 1 represents extent of decoupling of crystal growth rate and viscous flow in terms of Stokes-Einstein equation. The ukin is the crystal growth rate corrected for thermodynamic factor:

u kin =

u (9)  ∆G  1 − exp −   R ⋅T 

EXPERIMENTAL The bulk glasses of the Ge2Sb2Se5 composition were prepared by weighing of appropriate amounts of pure elements (5N, Sigma Aldrich) into a silica ampule. The ampule was evacuated (103 Pa) and sealed and was placed into a rocking furnace. The synthesis was performed at 800 °C for 24


Page 4 of 20

Page 5 of 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


hours. After the synthesis, the ampule was quenched in cold water. The amorphous character of the prepared glass was checked by X-ray diffraction analysis. For crystal growth experiments the samples were prepared in small pieces of size cca 3 x 3 x 2 mm3. The samples were heat-treated for various times at selected temperatures in a computercontrolled furnace (central hot zone was constant within ± 0.5 °C). After the heat treatment the samples were quickly cooled down to room temperature and examined by Olympus BX51 microscope equipped with an XM10 infrared camera. Some samples were characterized also by scanning electron microscope (SEM) JEOL JSM-7500F (1 kV, gentle beam mode). Because of the surface crystallization, the samples were broken and the surface layer was examined. The viscous behavior was studied using a thermomechanical analyzer TMA CX 03 (RMI, Czech Republic). The viscosity was measured using penetration method 29. The bulk samples of approximate size 6 x 6 x 2.5 mm3 were used for these measurements. Two different shapes of indenters were used: stainless steel cylindrical indenter (1 mm in diameter), and corundum hemispherical indenter (3.98 mm in diameter). More details about the instrument and experimental arrangement can be found elsewhere 30, 31.The temperature was calibrated on melting of pure metals (Ga, In, Zn, Sn, Pb, Al). Crystallization and melting of amorphous samples, and melting of fully crystallized samples (same size as used for microscopy measurement, cca 35 – 50 mg) of the studied system were measured by differential scanning calorimetry (DSC) in open silica ampules at a heating rate of 2 °C/min in SensysEvo DSC (Setaram co.). The heat flow was calibrated using the Joule effect method. Because special silica ampules were used for the experiments, the calibration of heat flow and real temperature were verified using melting of pure Zn. The typical error of the heat flow was about 7 % and the deviation of temperature was lower than 1 °C. The XRD analysis was performed using a Bruker AXS X-ray diffractometer D8 Advance equipped with a scintillation counter, utilizing Cu Kα radiation (40 kV, 30 mA). The scans were taken over scattering angles 2θ from 10 to 70° with scanning rate 0.02 ° / 20 s.

RESULTS Crystal Growth The crystal growth in bulk glasses of Ge2Sb2Se5 composition was studied ex-situ using infrared (IR) microscopy and scanning electron microscopy (SEM). The samples were isothermally heat-treated at selected temperature for various times. In fig. 1 the typical formed crystals are shown. As is shown in fig. 1a, the nucleation takes place at random positions on samples surface. The formed crystals grow as hemispherical particles (fig. 1b), until the whole surface is covered by a compact crystalline layer (fig. 1c). Then the formed crystalline layer continues growing (figs. 1c and 1d) uniformly around the whole sample. The structure of the formed crystals is shown in detail in the SEM pictures in fig. 2. SEM images of the partially and fully crystallized samples show that the crystals start growing from one point and the crystals show dendritical growth structure starting at the sample surface. After the whole surface



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

is crystallized the dendrites are diversely intertwined and continue growing in the direction from the surface to the central part of the sample. The layer then grows as an assemblage of thin fibers, which are growing from the surface to the inside of the sample.

Fig.1 Crystal growth and morphology in glassy Ge2Sb2Se5: a) sample surface, T = 267.9 °C, t = 1260 min, IR microscopy; b) sample fracture, T = 306.8 °C, t = 30 min, SEM; c) sample fracture, T = 306.8 °C, t = 90 min, IR microscopy; d) sample fracture, T = 306.8 °C, t = 120 min, IR microscopy.


Page 6 of 20

Page 7 of 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 2 SEM micrographs of structure of the formed crystals in Ge2Sb2Se5: a,b) show surface of the partially crystallized samples; c,d) show the interior of fully crystallized samples.

The isothermal crystal growth was measured in the temperature range of 265 – 350 °C as the thickness of the formed crystalline layer in samples, where the layer was compact. Or, for the lower temperatures (265 – 290 °C), the growth was measured as the radius of the formed crystals on the surface of the sample. The crystals grew linearly with time as shown in fig. 3. From the slopes of linear dependencies of crystal size on preheating time, the crystal growth rates were evaluated and are listed in table 1. In a narrow temperature region, a simple exponential behavior of crystal growth rate on temperature can be expected. The linear dependence of log u vs. 1/T (fig. 4) is then used to evaluate the activation energy of crystal growth, which was found to be EG = 340 ± 5 kJ/mol.

Table 1 Crystal growth rates and viscosities in Ge2Sb2Se5 bulk glasses. The temperature accuracy is ± 0.5 °C and reproducibility of the viscosity data is ± 0.1 log units. T (°C) 267.9 271.9 283.2 283.5 288.2

u (µm/min) 0.0043 0.0077 0.058 0.042 0.072

± ± ± ± ±

0.0003 0.0006 0.003 0.003 0.006

T (°C)

log (η/Pa·s)

229.6 233.2 236.4 237.9 241.0

12.60 12.28 12.11 11.88 11.71



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

291.1 294.2 299.0 300.0 306.8 308.7 310.4 311.8 312.6 314.4 318.6 320.5 321.0 322.5 325.5 329.2 331.5 334.5 339.4 340.0 340.3 346.9 352.2 357.3 359.3 361.0

0.135 0.292 0.444 0.479 0.83 2.3 1.66 2.27 2.11 3.2 4.5 5.80 6.8 9.40 11.8 16.3 20.8 24.6 41 54 62 97 113.9 214 238 305

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.003 0.008 0.018 0.010 0.03 0.3 0.06 0.05 0.10 0.2 0.3 0.12 0.3 0.10 1.3 1.6 1.9 1.8 4 5 3 4 1.3 21 18 56

242.0 243.2 245.6 249.1 251.0 251.3 255.8 262.1 264.6 265.8 267.6 269.5 272.2 272.9 273.4 277.7 281.4 284.0 285.4 286.5 289.4 290.2 295.6

Page 8 of 20

11.55 11.55 11.25 11.02 10.91 10.82 10.48 10.01 9.90 9.73 9.50 9.43 9.19 9.22 9.13 8.80 8.53 8.39 8.26 8.14 7.95 7.98 7.58

Fig.3 Time dependence of thickness of the formed crystalline layer (290 – 350 °C) or radius of formed crystals (265 – 290 °C) on time at different temperatures: a) in temperature range 267 – 309 °C, b) in temperature range 310 – 350 °C. The typical deviation of the crystalline layer thickness was in the range of 5 – 10 %.


3

14

2

13

1

12

0

11

-1

10 DSC peaks

-2

9

-3

8

-4

log (η/Pas)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


log (u/µmmin-1)

Page 9 of 20

7 1.5

1.6

1.7

1.8

1.9

2.0

1000/T (1/K)

Fig. 4 Temperature dependence of crystal growth rate and viscosity for Ge2Sb2Se5 composition. The dashed line shows a temperature region where maxima of crystallization peaks followed by DSC can be found for different heating rates (1 – 30 °C/min)11. Dashed line corresponds to the calculated screw dislocation growth model (see the Discussion for more details).

Viscosity The viscosities of Ge2Sb2Se5 bulk samples were measured in the region of undercooled melt and glass by use of penetration method. The viscous flow was measured in the temperature range of 230 – 290 °C, and the viscosity data are listed in table 1. The plot of log η vs. 1/T(fig. 4) shows linear dependence. The temperature dependence of viscosity was then fitted by Arrhenius type equation and the activation energy of viscous flow (Eη) was evaluated: Eη = 421 ± 3 kJ/mol. From the linear fit of log η vs. 1/T the temperature T12 was calculated. The temperature T12 is known as the viscosity glass transition temperature and corresponds to the temperature when the viscosity value reaches 1012Pa·s. The T12 was found to be 237 ± 2 °C. With knowledge of the T12, kinetic fragility parameter (m)32 can be calculated from the dependence of logarithm of viscosity on the reduced temperature T12/T:

     d logη  (10) m=  T12    d      T  T →T12 Using the eq. 10, the kinetic fragility parameter was evaluated: m = 43.1 ± 0.4.

Structure The amorphous and crystallized samples were examined by XRD analysis. The samples of Ge2Sb2Se5 belong to the pseudobinary system GeSe–Sb2Se3. The diffraction pattern shown in fig. 5



indicates diffraction lines corresponding to the crystalline phases of Sb2Se3, GeSe and GeSe2. Then, it can be expected, that the crystalline phase found for Ge2Sb2Se5 samples is formed by some mixed crystals of the mentioned compounds. The diffraction pattern is shown in fig. 5 Nevertheless, this crystalline phase has not been described yet.

Ge2Sb2Se5 GeSe GeSe2 intensity (a.u.)

Sb2Se3

10

20

30

40

50

60

70

2θ (°)

Fig. 5 The XRD pattern of fully crystallized Ge2Sb2Se5 sample. The full points show positions and relative intensity of the possible formed phases.

Melting The thermal behavior of the Ge2Sb2Se5 bulk material was measured using DSC under nonisothemal conditions at a heating rate of 2 °C/min. Fig. 6 shows crystallization and melting of amorphous material and melting of fully crystallized sample from crystal growth experiment.

0.3

amorphous 0.2

Φ (W/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 20

0.1

fully crystallized 0.0

-0.1 200

300

400

500

600

T (°C)

Fig. 6 Crystallization and melting in Ge2Sb2Se5 bulk material at heating rate 2 °C/min.


Page 11 of 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 6 shows an incongruent melting of the Ge2Sb2Se5 material. After the crystallization (∼344 °C), one part of the material melts with the minimum of melting peak at approximately 410 °C. The first melting is followed by melting of another part of the material (∼445 °C), which is turned into recrystallization manifested by a sharp exothermal effect at ∼448 °C, and subsequently followed by another melting (∼470 °C). Then the melting of the materials is followed by a very broad peak (∼545°C) which probably corresponds to the evaporation of a part of the material as indicated by condensed material at colder wall of the testing silica ampules. The temperature of melting of the Ge2Sb2Se5material was then found as the onset of the first melting peak, Tm = 392.4 ± 1.5 °C.

DISCUSSION The crystal growth in Ge2Sb2Se5 bulk glass and undercooled melt has been studied. The crystal growth rate exhibits a simple exponential behavior in the explored temperature range (fig. 4). The calculated activation energy of crystal growth (EG = 340 ± 5 kJ/mol) can be compared with the activation energy of crystallization obtained from DSC experiments (EA = 245 ± 14 kJ/mol)11, 14. The difference in activation energy of crystal growth from the direct/microscopic observation and activation energy of crystallization followed by DSC can be explained by the different temperature regions in which the experiments were performed (fig. 4). The dependence of log u on 1/T can be, in fact, highly nonlinear in wide temperature region, especially when the temperature is close to the temperature the maximum of crystal growth rate33. The non-linearity is shown in fig. 4 using the calculated dependence of crystal growth rate on temperature described by screw dislocation growth model (see the following text for more details). It is also important to mention that the activation energy of crystallization calculated from DSC data includes the whole nucleation-growth process. The knowledge of viscous behavior of any glass-former is very important. Viscosity is quite essential for description of structural relaxation. The activation energy of viscous flow (421 ± 3 kJ/mol) is nearly identical to the activation energy of enthalpic structural relaxation (414 kJ/mol)12. Similar behavior has been confirmed also for other glass-forming systems34-38. From this point of view it seems that the structural relaxation in materials is in fact continuation of viscous flow below Tg though significantly more complex with pronounced non-exponential and non-linear character. Viscosity also plays a key role in study and description of crystal growth in undercooled liquids. As anticipated in the Results section, the crystals formed a compact crystalline layer which grew linearly from the surface of the bulk samples. The linear isothermal growth (fig. 3) is typical for crystal growth controlled by liquid-crystal interface kinetics and the growth can be then described using one of the three basic phenomenological growth models which were mentioned in the Introduction. Nevertheless, these growth models are based on simple proportionality of crystal growth rate to viscosity. This assumption can be tested by plotting the logarithm of ukin (eq. 9) on logarithm of η. From the linear dependence in fig. 7, the coefficient ξ can be calculated and is equal to 0.90 ± 0.01. The value of the exponent ξ is close to the value of 1 over five orders of magnitude of



viscosity, and therefore it seems that the Stokes−Einstein relaVonship is nearly fulﬁlled in the studied system even at higher undercooling.

3

2

log (ukin/µmmin-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 20

1

0

-1

-2

-3 4

5

6

7

8

9

10

log (η/Pas)

Fig. 7 The linear dependence of log ukin vs. log η. The straight line represents a linear fit of the data.

With knowledge of crystal growth data, temperature dependence of viscosity, and melting parameters (Tm, ∆Hm), the reduced crystal growth rate (UR) can be calculated according to eq. 5. Nevertheless, melting process in this system, Ge2Sb2Se5, is very complicated (Fig. 6). According to the phase diagram of the ternary Ge–Sb–Se system published by Bordas and Clavaguera-Mora39, this system exhibits quite complicated melting and even a slight change of composition of a sample, caused by crystallization, partial melting, or evaporation, can result in a significant change of melting behavior. Such a subtle composition change may significantly affect the melting enthalpy. Due to this fact we prefer to replace melting enthalpy in eq. 7 by crystallization enthalpy change. The enthalpy of crystallization corresponds directly to the studied crystal growth process, unlike the melting process during which the crystalline phase probably disintegrates and recrystallizes in different components. The enthalpy of crystallization was found to be ∆Hc = -35 ± 2 J/g, and the temperature of melting was found as the onset of first melting peak (Fig. 6): Tm = 392.4 ± 1.5 °C. Using the enthalpy of crystallization and the initial temperature of melting, the reduced crystal growth (UR) rate was calculated. The plot of UR vs. ∆T is shown in fig. 8. The average standard deviation is shown by one point. The UR dependence on undercooling shown in fig. 8 does not clearly show which crystal growth model can be assumed for the presented data. Because of the comparatively high errors of the UR and the relatively short temperature region, two growth models can be assumed19: the screw dislocation or the 2D surface nucleated model which are expressed by eqs. 3 and 4, respectively. Both the mentioned models were then used to fit the crystal growth data to find the appropriate one. The fitted curves are compared in fig. 9 with the experimental data.


Page 13 of 20

3.5 3.0

UR (N/m)

2.5 2.0 1.5 1.0 0.5 0.0 0

50

100

150

∆T (K)

Fig.8 Reduced crystal growth rate dependence on undercooling in the Ge2Sb2Se5 system. The average standard deviation is shown.

600

1E+03 1E+02

500

1E+01

300

u (µm/min)

1E+00

400

u (µm/min)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1E-01 1E-02 1E-03 1E-04

experimental data Screw dislocation model 2D Surface nucleated model

1E-05

200

1E-06 250

300

350

400

T (°C)

100

0 250

300

350

400

T (°C)

Fig. 9The growth data in the system Ge2Sb2Se5 fitted by the screw dislocation and 2D surface nucleated growth model. The inset shows the data with growth rates in logarithmic scale.

Fig. 9, respectively, the inset of fig. 9, shows that the screw dislocation growth model fits the experimental data better than the 2D surface nucleated one, which underestimates the growth rates at lower temperatures. The screw dislocation growth model has only one fitting parameter – the interatomic distance in the interface layer a0 (eq. 3), which can be equated with the size of the building units. The value of the parameter was found to be 0.0325 ± 0.0004 Å. Despite the parameter is more than ten times smaller than the covalent radii of the component elements in Ge-Sb-Se glasses (Ge ∼1.22 Å, Sb ∼1.40 Å, Se ∼1.17 Å)40, it provides the best fit of the experimental data within the screw dislocation model.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Coming back to the proposed 2D surface nucleated growth model – it was found that the screw dislocation growth model describes the growth rate data better. Nevertheless, the 2D surface nucleated growth model is very often used for description of crystal growth in oxide26, 41 and chalcogenide27, 42 glasses, especially in sulfur-analog Ge-Sb-S system28, 43-47. Looking in fig. 9, the calculated 2D surface nucleated growth model is close to the experimental data, and therefore an analysis of calculated parameters of this model in the presented Ge2Sb2Se5 material could provide useful information, especially in comparison with other systems. The parameters of the 2D surface nucleated model for crystal growth in Ge2Sb2Se5 were determined from the nonlinear regression: B = (37.4 ± 4.8)·103 K2 and C = 0.120 ± 0.027 N/m, the specific surface energy of the melt-crystal interface σE can be at least assessed from the parameter B17, 19, 41:

B=

π ⋅ λ ⋅ Tm ⋅ Vm ⋅ σ E2 3 ⋅ k B ⋅ ∆H m

(11),

where λ and Vm are diameter and molar volume of the crystallized substance, respectively. Unfortunately in this particular case, meaning the crystallization in bulk Ge2Sb2Se5, the structure of the crystallization fraction is not known. Structure of GexSbxSe100-2x bulk glasses was studied by Gunasekera et al.40, who found that the local structure of the glasses consists of basic structural units GeSe4/2 tetrahedra SbSe3/2 pyramids and Se2 chains. With increasing x (x > 18.2) homopolar bonds Ge–Ge and Sb–Sb appear in the network. According to XRD (fig. 5) and direct observation by microscopy (figs. 1 and 2) where no different crystalline phases were observed, we can assume that the crystalline phase is some mixture of GeSe, GeSe2, and Sb2Se3 structural units and corresponds, more or less, to the structure of the glassy matrix. Using this assumption we can use the molar volume of the Ge22Sb22Se56 glass (Vm = 17.3 cm3/mol) 40 to evaluate the specific surface energy. The diameter of a building unit can be estimate as41:

λ =3

Vm (12), NA

where NA is the Avogadro number. The specific surface energy of the crystal-melt interface was determined to be σE = 20.3 mJ/m2. The σE is often represented by α which stands for “surface-liquid interface energy / molar heat of fusion” ratio20:

α=

σE 3 N A ⋅ Vm2 (13) ∆H m

The α is for the studied sample equal to 0.377 what corresponds to the average α = 0.3 obtained from nucleation experiments for a variety of non-metallic materials48-50.

CONCLUSION


Page 14 of 20

Page 15 of 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The crystal growth, viscosity, and melting behavior were studied in Ge2Sb2Se5 bulks using infrared and electron microscopy, thermomechanical analysis, and differential scanning calorimetry, respectively. The crystal growth starts on the surface of a sample and after a compact crystalline layer is formed, the growth continues from the surface to the center of the sample. The crystalline layer grew linearly with time which indicates a growth controlled by liquid-crystal interface kinetics and the crystal growth rates were measured over three orders of magnitude (10-2– 101.5µm/min). The activation energy of crystal growth (EG = 340 ± 5 kJ/mol) is significantly higher than the activation energy of the whole crystallization (nucleation-growth) process calculated from the DSC data. The difference can be explained by the different experimental conditions, especially by the different temperature range. The viscosities were measured in the range of 107.5 - 1012.5 Pa.s. The activation energy of viscous flow (Eη = 421 ± 3 kJ/mol) is nearly identical with the activation energy of enthalpic structural relaxation. The fragility index of the studied material is m = 43.1 ± 0.4. Melting of the Ge2Sb2Se5 material is very complicated with several processes taking part during the melting process. Temperature of melting was evaluated as the onset of the first melting peak on DSC curve (Tm = 392.4 ± 1.5 °C). The relationship between the kinetic coefficient of crystal growth rate and viscosity (ukin∝η-ξ) was tested. The exponent ξ was found to be 0.90 ± 0.01. With the parameter ξ close to 1, the assumption, that the Stokes-Einstein relation between crystal growth rate and viscosity holds even in this highly undercooled system, can be set. Combining the growth, viscosity and melting data an operative crystal growth model was calculated. The screw dislocation growth model seems to be applicable to the measured data. Nevertheless, the calculations provide a physically unrealistic value of the parameter a0 = 0.0325 ± 0.0004 Å, which represents interatomic distance in the interface. On the other hand, only this value of the parameter a0 provides the best fit of the screw dislocation model to the experimental data of crystal growth rates.

AUTHORS INFORMATION Corresponding Author: Jaroslav Barták:[email protected] Co-authors: Petr Koštál: [email protected] Veronika Podzemná: [email protected] Jana Shánělová: [email protected]



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

JiříMálek: [email protected]

AKNOWLWDGEMENT The authors would like to express their gratitude for ﬁnancial support from the Czech Science Foundation under grant no. 16-10562S and from the Czech Ministry of Education, Youth and Sports of the Czech Republic under the Grant LM2015082 Center of Materials and Nanotechnologies and CZ.1.05/4.1.00/11.0251. The author would like to thank Doc., Ing. Ludvík Beneš, CSc. for his help with the XRD measurements.


Page 16 of 20

Page 17 of 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


REFERENCES 1. Hewak, D. W. Chalcogenide Glasses for Photonics Device Applications. In Photonic Glasses and Glass-Ceramics, Murugan, G. S., Ed. Research Signpost: 2010. 2. Adam, J. L.; Zhang, X. Chalcogenide Glasses: Preparation, Properties and Applications. Elsevier Science: 2014. 3. Hilton, A. R.; Jones, C. E.; Brau, M. Non-Oxide IVA-VA-VIA Chalcogenide Glasses. I. GlassForming Regions and Variations in Physical Properties. Physics and Chemistry of Glasses 1966, 7 (4), 105-&. 4. Sanghera, J.; Aggarwal, I. D. Infrared Fiber Optics. Taylor & Francis: 1998. 5. Raoux, S.; Welnic, W.; Ielmini, D. Phase Change Materials and Their Application to Nonvolatile Memories. Chem. Rev. 2010, 110 (1), 240-267. 6. Raoux, S.; Wuttig, M. Phase Change Materials: Science and Applications. Springer US: 2010. 7. Yamada, N.; Ohno, E.; Nishiuchi, K.; Akahira, N.; Takao, M. Rapid-Phase Transitions of GeTeSb2Te3 Pseudobinary Amorphous Thin-Films for an Optical Disk Memory. J. Appl. Phys. 1991, 69 (5), 2849-2856. 8. Goyal, D. R.; Maan, A. S. Far-Infrared Absorption in Amorphous Sb15GexSe85-x Glasses. J. NonCryst. Solids 1995, 183 (1-2), 182-185. 9. El-Sayed, S. Far-Infrared Studies of the Amorphous SbxGe28-xSe72 Glassy Semiconductor. Semicond. Sci. Tech. 2003, 18 (4), 337-341. 10. Hosni, H. M.; Fayek, S. A.; El-Sayed, S. M.; Roushdy, M.; Soliman, M. A. Optical Properties and DC Electrical Conductivity of Ge28−xSe72Sbx Thin Films. Vacuum 2006, 81 (1), 54-58. 11. Svoboda, R.; Malek, J. Particle Size Influence on Crystallization Behavior of Ge2Sb2Se5 Glass. J. Non-Cryst. Solids 2012, 358 (2), 276-284. 12. Svoboda, R.; Honcova, P.; Malek, J. Enthalpic Relaxation in Ge2Sb2Se5 Glass. J. Non-Cryst. Solids 2012, 358 (4), 804-809. 13. Svoboda, R.; Brandova, D.; Malek, J. Crystallization Behavior of GeSb2Se4 Chalcogenide Glass. J. Non-Cryst. Solids 2014, 388, 46-54. 14. Svoboda, R.; Malek, J. Thermal Behavior of Se-Rich Ge2Sb2Se(5-y)Tey Chalcogenide System. J. Alloys Compd. 2015, 627, 287-298. 15. Lacaita, A. L. Phase Change Memories: State-of-the-Art, Challenges and Perspectives. SolidState Electron. 2006, 50 (1), 24-31. 16. Ngai, K. L.; Magill, J. H.; Plazek, D. J. Flow, Diffusion and Crystallization of Supercooled Liquids: Revisited. J. Chem. Phys. 2000, 112 (4), 1887-1892. 17. Uhlmann, D. R. Crystal Growth in Glass-Forming Systems - A Review. In Advances in Nuclection and Crystalline in Glasses, 1972; pp 91-115. 18. Kirkpatrick, R. J. Crystal Growth from the Melt: A Review. Am. Mineral. 1975, 60, 798-814. 19. Jackson, K. A.; Uhlmann, D. R.; Hunt, J. D. On the Nature of Crystal Growth from the Melt. J. Cryst. Growth 1967, 1, 1-36. 20. Turnbull, D. Formation of Crystal Nuclei in Liquid Metals. J. Appl. Phys. 1950, 21, 1022-1028. 21. Hoffman, J. D. Thermodynamic Driving Force in Nucleation and Growth Processes. J. Chem. Phys. 1958, 29 (5), 1192-1193. 22. Thompson, C. V.; Spaepen, F. Approximation of the Free-Energy Change on Crystallization. Acta Metall. 1979, 27 (12), 1855-1859. 23. Singh, H. B.; Holz, A. Stability Limit of Supercooled Liquids. Solid State Commun. 1983, 45 (11), 985-988. 24. Turnbull, D.; Fisher, J. C. Rate of Nucleation in Condensed Systems. J. Chem. Phys. 1949, 17 (1), 71-73. 25. Ediger, M. D.; Harrowell, P.; Yu, L. Crystal Growth Kinetics Exhibit a Fragility-Dependent Decoupling from Viscosity. J. Chem. Phys. 2008, 128 (3), 034709-1 - 034709-6.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

26. Nascimento, M. L. F.; Zanotto, E. D. Does Viscosity Describe the Kinetic Barrier for Crystal Growth from the Liquidus to the Glass Transition? J. Chem. Phys. 2010, 133 (17), 174701-1 - 17470110. 27. Podzemna, V.; Bartak, J.; Malek, J. Crystal Growth Kinetics in GeS2 Amorphous Thin Films. J. Therm. Anal. Calorim. 2014, 118 (2), 775-781. 28. Barták, J.; Podzemná, V.; Málek, J.; Eising, G.; Kooi, B. J. Crystal Growth in (GeS2)x(Sb2S3)1-x Thin Films. J. Non-Cryst. Solids 2015, 410, 7-13. 29. Douglas, R. W.; Armstrong, W. L.; P., E. J.; D., H. A Penetration Viscometer. Glass Technol. 1965, 6 (2), 52-55. 30. Malek, J.; Shanelova, J. Viscosity of Germanium Sulfide Melts. J. Non-Cryst. Solids 1999, 243 (2-3), 116-122. 31. Kostal, P.; Malek, J. Viscosity of (GeSe2)x(Sb2Se3)1-x Undercooled Melts. J. Non-Cryst. Solids 2007, 353 (29), 2803-2806. 32. Angell, C. A. Formation of Glasses from Liquids and Biopolymers. Science 1995, 267 (5206), 1924-1935. 33. Barták, J.; Martinková, S.; Málek, J. Crystal Growth Kinetics in Se–Te Bulk Glasses. Cryst. Growth Des. 2015, 15 (9), 4287-4295. 34. Hodge, I. M. Enthalpy Relaxation and Recovery in Amorphous Materials. J. Non-Cryst. Solids 1994, 169 (3), 211-266. 35. Málek, J. Dilatometric Study of Structural Relaxation in Arsenic Sulfide Glass. Thermochim. Acta 1998, 311 (1-2), 183-198. 36. Malek, J. Structural Relaxation of As2S3 Glass by Length Dilatometry. J. Non-Cryst. Solids 1998, 235, 527-533. 37. Malek, J.; Shanelova, J. Structural Relaxation of As2Se3 Glass and Viscosity of Supercooled Liquid. J. Non-Cryst. Solids 2005, 351 (43-45), 3458-3467. 38. Málek, J.; Svoboda, R.; Pustková, P.; Čičmanec, P. Volume and Enthalpy Relaxation of a-Se in the Glass Transition Region. J. Non-Cryst. Solids 2009, 355 (4-5), 264-272. 39. Bordas, S.; Clavaguera-Mora, M. T.; Legendre, B. Phase Diagram of the Ternary System Ge-sbSe. Thermochim. Acta 1982, 56 (2), 161-182. 40. Gunasekera, K.; Boolchand, P.; Micoulaut, M. Elastic Phases of GexSbxSe100–2x Ternary Glasses Driven by Topology. J. Phys. Chem. B 2013, 117 (34), 10027-10034. 41. Reinsch, S.; Nascimento, M. L. F.; Müller, R.; Zanotto, E. D. Crystal Growth Kinetics in Cordierite and Diopside Glasses in Wide Temperature Ranges. J. Non-Cryst. Solids 2008, 354 (52–54), 5386-5394. 42. Shánělová, J.; Málek, J.; Alcada, M. D.; Criado, J. M. Kinetics of Crystal Growth of Germanium Disulfide in Ge0.38S0.62 Chalcogenide Glass. J. Non-Cryst. Solids 2005, 351, 557-567. 43. Málek, J.; Švadlák, D.; Mitsuhashi, T.; Haneda, h. Kinetics of Crystal Growth of Sb2S3 in (GeS2)0.3(Sb2S3)0.7 Glass. J. Non-Cryst. Solids 2006, 352, 2243-2253. 44. Švadlák, D.; Pustková, P.; Koštál, P.; Málek, J. Crystal Growth Kinetics in (GeS2)0.2(Sb2S3)0.8 Glass. Thermochim. Acta 2006, 446 (1-2), 121-127. 45. Švadlák, D.; Zmrhalová, Z.; Pustková, P.; Málek, J.; Perez-Maqueda, L. A.; Criado, J. M. Crystallization Behavior of (GeS2)0.1(Sb2S3)0.9 Glass. J. Non-Cryst. Solids 2008, 354 (28), 3354-3361. 46. Zmrhalová, Z.; Málek, J.; Švadlák, D.; Barták, J. The Crystallization Kinetics of Sb2S3 in (GeS2)0.4(Sb2S3)0.6 Glass. Phys. Status Solidi C 2011, 8 (11-12). 47. Pillai, S. K.; Podzemná, V.; Barták, J.; Málek, J. Nucleation and Growth in Amorphous Thin Films of (GeS2)0.9(Sb2S3)0.1. J. Cryst. Growth 2013, accepted. 48. Turnbull, D. Phase Changes. In Solid State Phys., Frederick, S.; David, T., Eds. Academic Press: 1956; Vol. Volume 3, pp 225-306. 49. Neiman, T. S.; Yinnon, H.; Uhlmann, D. R. Crystallization Kinetics of Lead Metasilicate. J. NonCryst. Solids 1982, 48 (2-3), 393-403.


Page 18 of 20

Page 19 of 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50. James, P. F. Kinetics of Crystal Nucleation in Silicate-Glasses. J. Non-Cryst. Solids 1985, 73 (13), 517-540.



For Table of Content Use Only

0.35

600

DSC

400

0.30

200

0.25

0

0.20

-200 0.15 -400 0.10 -600 250

300

350

400

450

500

550

600

T (°C)


Φ (W/g)

u (µm/min)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 20

Crystal Growth Kinetics and Viscous Behavior in Ge2Sb2Se5

Recommend Documents