Structural Changes in Vitreous GeSe4 under Pressure - The Journal of

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Structural Changes in Vitreous GeSe4 under Pressure L. B. Skinner,† C. J. Benmore,‡,§ S. Antao,|| E. Soignard,^ S. A. Amin,^ E. Bychkov,# E. Rissi, J. B. Parise,†,3 and J. L. Yarger*,§,^ †

Mineral Physics Institute & Department of Geosciences, Stony Brook University, Stony Brook, New York 11794-2100, United States X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Illinois 60439, United States § Department of Physics and ^Department of Chemistry & Biochemistry, Arizona State University, Tempe, Arizona, United States Department of Geoscience, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada # LPCA, UMR 8101 CNRS, Universite du Littoral, 59140 Dunkerque, France. 3 Photon Science Division, Brookhaven National Laboratory, Upton, New York 11973, United States

)

‡

ABSTRACT: High-energy X-ray diffraction experiments have been performed on GeSe4 glass up to pressures of 8.6 GPa, and the equation of state has been measured up to 10 GPa. The X-ray structure factors reveal a decrease in the first sharp diffraction peak intensity and broadening with pressure, which signifies a break-up of the intermediate range order in the glass. In contrast, the principal peak in the structure factor shows an increase in intensity and a sharpening with pressure, which is attributed to an increase in extended range order and coherence of the compacted units. The average nearest neighbor coordination number is found to remain constant in GeSe4 glass (within experimental error) over the pressure range measured. This is in contrast with the gradual increase found in GeSe2 glass. Rather, in GeSe4 glass the densification mechanism is shown to be associated with large inward shifts of the second neighbor and higher coordination shells. These features appear as additional correlations at 3.3 and 5.3 Å in the differences taken between adjacent pair distribution functions with increasing pressure.

’ INTRODUCTION The structures of GexSe1
x glasses have been intensively studied over the past decades because of their potential applications in infrared optics1
6 from a fundamental viewpoint looking at glass formation over a wide compositional range7
9 and the floppy to rigid network transition.10
14 Previous high-pressure studies on the rigid network GeSe2 glass have revealed a minimum in the shear wave velocity, discontinuities in elastic moduli, and anomalous behavior in Poisson’s ratio at 4 GPa,15 which have been attributed to a network rigidity minimum originating from competition between two very different densification mechanisms. The GeSe4 composition glass is also of special interest because it lies in the so-called intermediate phase between an underconstrained elastically floppy network and an overconstrained stressedrigid network.16 The purpose of this study is to compare the densification mechanisms in this “borderline” network glass (GeSe4) compared with a fully connected and very rigid network glass (GeSe2). The density and the degree of intermediate range ordering (IRO) signified by the height of the first sharp diffraction peak (FSDP) for Ge
Se glasses over a wide compositional range is plotted in Figure 1. This Figure shows three main regions at low Ge concentrations (labeled I); the structure consists of isolated Ge centered tetrahedral, which are randomly distributed in the Se matrix. At higher Ge concentrations (region II), the tetrahedra start to form connections7 with the system reaching a density maximum around GeSe4, where the average nearest neighbor coordination reaches 2.4. Percolation theory predicts that this is r 2011 American Chemical Society

the minimum number of connections required for the formation of a rigid 3D network.16,17 At Ge-rich compositions beyond the GeSe2 composition (region III) the network is overconnected and has to form increasingly more defective connections to maintain charge balance. Different possible bonding schemes associated with GexSe1
x glasses are plotted in Figure 1b. At the composition GeSe2, the glass has been observed to contain Ge
Ge (labeled e in Figure 1b) and Se
Se (labeled 1) homopolar bonds as well as corner and edge-shared tetrahedra (labeled c and d, respectively).18 Moreover, under pressure, Raman scattering has confirmed that the fraction of edge-sharing tetrahedra reduces in GeSe220 resulting in an increase in the intertetrahedral Ge
Se
Ge bond angle distribution. Although the reduction of edge sharing itself requires more volume, it has been argued that it allows the network more flexibility, enabling the collapse of large rings during the densification process.16 However, at the GeSe4 composition, the low concentration of Ge suggests that edge sharing tetrahedra and homopolar Ge
Ge are expected to have a low probability of occurrence (both less than ∼10%), at ambient pressure.21,14 Special Issue: Chemistry and Materials Science at High Pressures Symposium Received: July 15, 2011 Revised: November 21, 2011 Published: November 21, 2011 2212

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Figure 2. Pressure
volume equation of state for amorphous GeSe4. Experiments were performed in a hydrostatic medium of a 4:1 methanol/ethanol mixture. Compression results are represented by the filled circles and decompression shown by the open circles. A third-order isothermal Birch
Murnaghan equation of state (EoS) fit to the experimental compression data is given by the blue dashed line.

Figure 1. TOP: Compositional dependence of density (filled circles and triangles) and FSDP (open circles) in GexSe1
x glasses at ambient pressure. The behavior shows three distinct regions. Region I is random distribution of Ge centered tetrahedral in the Se matrix. Region II is where the tetrahedral network forms. Region III is a fully connected network with increasing concentration of defect edge sharing and homopolar Ge
Ge connections. GeSe4 falls in the middle of the network formation range close to the density maximum, where the system is in an intermediate phase between a floppy and a rigid network. BOTTOM: Schematic diagrams of the connection types reported to occur in Ge
Se glasses. Right to left: (e) represents Ge
Ge homopolar bonds, which is the shortest Ge
Ge separation, (d) is edge sharing tetrahedra, (c) is “normal” corner sharing, which produces only longer (∼3.985 Å) Se
Se separations (labeled 2), (b) is tetrahedra linked by a Se
Se homopolar bond (this creates a short Se
Se separation (∼2.32 Å, labeled 1)), and (a) tetrahedra separated by 2 Se atoms (this would produce different Ge
Se
Se and Se
Se
Se bond angles and larger Ge
Ge separation).

Historically it has been debated whether Ge
Se
Se linkages (schemes a and b in Figure 1b) are formed in glassy GeSe4.5,11,12,19,22,23 The absence of such bonds implies that the GeSe4 tetrahedra are clustered and fully connected (by corner or edge sharing) leading to a heterogeneous structural model on the order of a few nanometers.12,19,11 Alternatively, if Ge
Se
Se connections are present (schemes a and b in Figure 1b), then this would provide the bonding variability to support a homogeneous distribution of Ge ions and a predominantly tetrahedral local structure.5,22,23 X-ray scattering and neutron diffraction data have been used to support the homogeneous structural model because no signature of any clustering process was observed in the small angle signal.1,2,8,24 However, NMR studies observe only two spectral lines attributed to homopolar Se
Se
Se and tetrahedral Ge
Se
Ge connections with no evidence of Ge
Se
Se linkage in the network,11 which lends support to the heterogeneous model. However, small angle scattering is limited by the low scattering contrast between Ge and Se atoms, and NMR is limited by sensitivity because of the low natural abundance of 77Se. We also

note that fast relaxation processes for Se-rich GexSe1
x glasses observed by high-pressure Raman studies can be attributed to floppy modes from the damping or jumping motion of the rotating Sen chain segments.25 In addition, a recent ab initio molecular dynamics (MD) study,14 which agrees very well with experimentally determined structure factors8
10 has provided further support for the homogeneous model. The ab initio MD study finds significant Ge
Se
Se connections as well as homopolar Se
Se
Se and tetrahedral Ge
Se
Ge connection types. In this work, in situ high-pressure high-energy X-ray diffraction experiments were performed to study the structure of GeSe4 glass at ambient pressure and to study the densification mechanism of this glass under pressure up to 8.6 GPa. Total scattering by neutrons or X-rays gives a direct measurement of the topology of the glass (i.e., they closely approximate Bhatia
Thornton number
number pattern). This is because the Ge and Se scattering cross sections are nearly identical for both X-rays and neutrons. Determining the detailed atomic structure, however, is uniquely difficult for two main reasons: (i) the Ge and Se atoms have comparable sizes and (ii) there is a range of bonding schemes, including direct Ge
Ge and Se
Se homopolar bonds.26
28

’ EXPERIMENTAL DETAILS GeSe4 glasses were synthesized from high-purity elements (Ge: 99.9999%, Se: 99.999%, Aldrich Chemicals) at the Universite du Littoral, France using established methods.29 The in situ equation of state (EoS) of GeSe4 glass was measured as a function of pressure up to 10 GPa using a diamond anvil cell (DAC) at room temperature. The area of a thin GeSe4 glass sample in a hydrostatic medium of a 4:1 methanol/ethanol mixture was determined by collecting three digital photographs of the sample at the same magnification at each pressure point, and the error bars were determined by calculating the standard deviation of the three imaged surface areas. Samples with a thickness 300 to avoid tilting errors. High-resolution images were taken with 8 megapixel Sony DSC cameras. The sample 2213

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Figure 4. Close up of the SX(Q) patterns to highlight the behavior of the FSDP and PP under pressure. The solid lines from bottom to top are at pressures of 0, 1.5, 3, 4.3, 6, 7, and 8.6 GPa; the black dashed line overlapping with the 1.5 GPa data is the decompressed glass. The thick dashed blue line overlapping the 0 GPa data is the Lorentzian peak fit for that pressure, and the dotted gray lines are the individual peaks.

Figure 3. High-energy X-ray structure factors of GeSe4 glasses during compression (solid lines). These curves were obtained by removing unphysical correlations below 0.95 Å in the pair distribution function and back transforming. The upper blue dashed line is the raw SX(Q) for 8.6 GPa to demonstrate the typical difference between the raw and backtransformed data. The black dashed line superimposed over the 1.5 GPa pattern is obtained from the decompressed glass. The structure and density of this recovered glass are both very close to that for the 1.5 GPa compressed glass.

area was determined by detecting the edges of each sample using standard image processing algorithms based on the Canny method (in Matlab 2010b). The pressures and hydrostatic nature of the sample were determined using ruby fluorescence,31 where a minimum of five ruby chips at various locations with the diamond cell sample chamber was used to ensure the sample was hydrostatic. The in situ high-pressure X-ray diffraction measurements were conducted on beamline 1-ID at the APS using an incident beam of area 50  50 μm2 and a beam energy of 80.0 keV.30 Pressure was applied to the sample using a Merrill
Bassett type DAC allowing reliable diffraction patterns to be taken in a large solid angle up to Q ≈ 15 Å
1. The GeSe4 glass samples were packed into the DAC without a pressure medium. Hence, the sample was under nonhydrostatic conditions. The pressures in all DAC experiments were determined to within an accuracy of (10% using ruby fluorescence.31 The high-energy X-ray data were analyzed using the software programs Fit2D32 and PDFGETX2.33 Details of the experimental set up and analysis procedure have been previously reported.29

’ RESULTS The measured volume change of glassy GeSe4 as a function of pressure, P, is shown in Figure 2. The experimental data were fitted by using a third-order isothermal Birch
Murnaghan EoS34 "


5=3 # 3B0 V
7=3 V P¼
V0 V0 2 " !#

2=3 3 V
1 ð1Þ 3 1 þ 4ðB1
4Þ V0

where the isothermal bulk modulus B0 = 10.4(14) GPa and the first pressure derivative B1 = 6.0(11) and the bracketed numbers are the 95% confidence bounds in the last two digits. Figure 3 shows the X-ray total structure factors SX(Q) for glassy GeSe4 at pressures up to 8.6 GPa, together with the recovered glass at ambient pressure. The FSDP at 1.13(1) Å
1 at normal pressure is a signature of IRO, which is often a result of directional bonding in amorphous solids and an open network.23 The FSDP height and area in GeSe4 glass is much lower than that for GeSe2 glass. Isotopic substitution experiments on GeSe2 glass have confirmed that the FSDP in GeSe2 arises predominantly from the real-space ordering of the Ge
Ge correlations at intermediate length scales (where intermediate denotes the range g2 to 4 nearest neighbor separations).35 For GeSe4 glass, the most significant changes in the measured SX(Q) pattern with pressure occur in the FSDP and principle peaks (PPs) shown in Figure 4, where the PP is the second peak in S(Q), which is also the highest peak at the highest densities. The results of Lorentzian fits to these two peaks are shown in Figure 5. The Lorentzian form is chosen based on the work of Wright.43 HighQ oscillations and the first peak in real space are consistent with a regular Ge centered tetrahedral unit. From Figures 4 and 5, it is observed that the FSDP in GeSe4 shifts to lower Q values, broadens, and reduces in area with increasing pressure. This indicates a significant rearrangement of the IRO upon compression.36 The FSDP position, width, and area of the recovered glass all relax back to approximately the same as those observed in the 1.5 GPa X-ray diffraction pattern. The principal peak (PP) has been associated with the extended range ordering of the network,37 and this peak also shifts to lower Q, but it also sharpens and remains constant in area as pressure increases. The decrease in intensity of the FSDP and concomitant increase in the PP intensity therefore reflects the collapse of the preferred open network geometry of the ambient pressure glass and the increased extended range order as the density increases. It is noted that like the FSDP, the PP position, width, and area of the recovered glass are also close to the 1.5 GPa values. The peak fits parameters, coordination numbers, and densities used to obtain the above results are given in Table 1. The pair distribution function g(r) is obtained by Fourier transform of the SX(Q) functions. g(r) is density normalized and tends to zero at low r and 1 at high r. The function T(r) = 4πFrg(r) 2214

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Figure 5. (a
c) Results of Lorentzian peak fits to the FSDP (open circles) and PP (filled circles) in glassy GeSe4 divided by their ambient values. The peaks both shift position in a similar fashion, but the FSDP broadens whereas the PP sharpens with increasing pressure. Also, the FSDP area reduces significantly, whereas the width PP remains constant (within error). (d) Height of the FSDP in glassy GeSe4 compared with glassy GeSe2.

Table 1. Parameters from the Measured Structure Factor SX(Q) Including the First Sharp Diffraction Peak (FSDP) and Principal Peak (PP) Fits and the Nearest Neighbor Average Coordination Numbera FSDP pressure

Figure 6. T(r) = 4πFrg(r) pair distribution function. The upper solid lines (labeled data) are the direct Fourier transforms of the raw SX(Q) data using a maximum Q value of 14.85 Å
1. The gray arrow indicates increasing pressure, with each line corresponding to the data sets measured at 0, 1.5, 3, 4.3, 6, 7, and 8.6 GPa. The black dashed line is the recovered glass pattern. Low-r oscillations are shown down to the 0.95 Å cut off used for the back transform procedure. The gray dotted lines are the r < 0.95 Å data for 0 and 8.6 GPa. The red dashed line labeled fit represents a fitted Gaussian atom distribution convoluted with the Q-dependent weighting and transform modifications (shifted down 0.5 for clarity). This is plotted to show that the peak at 2.88 Å is largely due to the truncation artifacts. The lower curves labeled “diff” are the 0 and 8.6 GPa patterns after subtraction of the first peak fit line. This shows the small but significant correlations around 2.70 Å (below the vertical dashed line) as well as the slight encroachment of the second shell into this region at high pressure.

PP

pos

fwhm

area

0

1.128

0.405

1.5

1.158

0.44

3

1.167

4.3

1.191

6 7

pos

fwhm

area

density coord

0.231 2.072

0.715

1.61

0.0339

2.35

0.181 2.12

0.649

0.156

0.0377

2.39

0.434

0.159 2.13

0.658

1.60

0.0403

2.43

0.454

0.128 2.173

0.617

1.566

0.0421

2.46

1.222

0.502

0.107 2.214

0.595

1.576

0.0441

2.48

1.235

0.537

0.081 2.247

0.571

1.573

0.0452

2.46

8.7

1.262

0.597

0.072 2.303

0.549

1.625

0.0468

2.45

Recov.

1.17

0.475

0.212 2.094

0.636

1.542

0.039

Fit range for the FSDP was 0.7 to 1.5 Å
1. The fit range for the PP was from 1.75 to 2.0 to 2.25 to 2.40 (increasing with pressure). a

is shown at different pressures in Figure 6. Because the structural features between 2 and 4 Å are sharper than the π/Qmax of our measurement window, Lorch modification significantly broadens the measured structure. Instead, to help distinguish real structure from transform artifacts, the contribution of a Gaussian peak is calculated in Q-space and transformed over the same Q-range as the data as described by Narten.38 The first real feature in the pair distribution function centered at 2.36(1) Å is assigned to tetrahedral Ge
Se bonds and homopolar Se
Se bonds. No pressure-induced bond elongation of the first peak in real space is observed during compression. A very slight asymmetry of the first peak is observed as a higher minimum on the high-r side compared with the ideal peak. This asymmetry increases very

Figure 7. Solid lines are pair distribution functions, obtained from transforming the raw SX(Q) patterns without a window function. The gray arrow indicates increasing pressure. The inset is the variation of the average coordination number of the 1st peak in g(r) glasses as a function of pressure. The open circles are glassy GeSe4 data obtained from integrating the plotted function between the two minima either side of the first peak. The filled circles are GeSe2 data from Mei and Benmore.29 The blue triangles are ambient data from Petri and Salmon.18

slightly with increasing pressure and accounts for the 0.1 increase in the average coordination number of the first peak with pressure (Figure 7). The features for short- and intermediate-range order in the ambient pressure pattern include peak maxima at 3.76, 4.45, 4.90, and 5.64 Å. All of these features are associated with Ge
Se or Se
Se correlations due to the low weighting of Ge
Ge correlations. (The approximate weightings are 4% GeGe, 64% SeSe, and 32% GeSe.) The Fourier transformation of the structure 2215

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factors with a Lorch function confirms that the peaks at 4.45 and 4.90 Å are due to real structural features rather than transform artifacts. Subtraction of the Gaussian peak truncated at the experimental Qmax shows the feature at 2.88 Å to be mainly a transform artifact with a very small underlying real structural peak centered at ∼2.70 Å. Upon compression, the broad peak centered at 3.76 Å dramatically shifts to lower r and broadens asymmetrically. The peak at 5.65 Å shifts to 5.42 Å and sharpens between ambient pressure and 8.6 GPa.

’ DISCUSSION Because Ge and Se have a similar number of electrons, the X-ray patterns obtained here approximate to the Bhatia
Thornton number
number partial structure factor SNN(Q) and partial pair
distribution function gNN(r). (The GeGe, SeSe, and GeSe weightings are all within 4% of the ideal number
number values.) Therefore the average coordination number irrespective of species type n can be deduced from8,9,24 4πF

Z r2 2 r1

r gx ðrÞ dr ¼

Z r2 r1

Figure 8. Differential pair distribution function D(r) = 4πFr(g(r)
1) shows the same data transformed using a Lorch modification function. This formalism removes the bulk density and highlights the higher-r correlations without transforming artifacts but at the cost of slightly broadening of lowest-r features. The vertical gray dashed line indicates the low-r cutoff used to generate the back transformed S(Q) patterns.

rTx ðrÞ dr≈n̅ ¼ ≈n̅

Se Se Ge ¼ cGe ðn̅ Ge ̅ Ge Þ þ cse ðn̅ Se þ n̅ Se Þ Ge þ n ð6Þ

where F is the atomic number density and nβα is the mean coordination number of chemical species β around α in a volume defined by two concentric spheres of radii r1 and r2. Figure 6 compares the average coordination number (n) as a function of pressure for GeSe4 glass with that of previously measured GeSe2 glass,29 computed from the data in Figure 5. For GeSe4, the average coordination number increases from 2.35(10) at ambient pressure to 2.45(10) at 8.6 GPa, which is