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In situ X-ray diffraction study of germanium at pressures up to 11 GPa and temperatures up to 950 K
Journal of Physics and Chemistry of Solids 64 (2003) 2113–2119 www.elsevier.com/locate/jpcs
In situ X-ray diffraction study of germanium at pressures up to 11 GPa and temperatures up to 950 K G.A. Voronina,*, C. Panteaa,c, T.W. Zerdaa, J. Zhangb,c, L. Wangb, Y. Zhaoc b
a Department of Physics and Astronomy, Texas Christian University, TCU Box 298840, Fort Worth, TX 76129, USA Center for High Pressure Research and Mineral Physics Institute, State University of New York, Stony Brook, NY 11794-2100, USA c LANSCE, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Received 9 April 2003; revised 9 June 2003; accepted 17 June 2003
Abstract In situ X-ray diffraction measurements on germanium were conducted in the pressure range of 5 – 11 GPa and temperatures up to 950 K. Using our data a better defined P– T diagram for germanium is presented. The coordinates of the triple point between GeI – GeII – GeL have been determined to a better degree of precision. The onsets of the GeI – GeII transition were found both under hydrostatic and non-hydrostatic conditions. Anisotropy of thermal expansion coefficient for the GeII is characterized from the c=a ratios in the temperature interval 473– 823 K. Phases GeIII and GeIV are shown to be metastable forms of germanium. q 2003 Elsevier Ltd. All rights reserved. Keywords: C. X-ray diffraction; C. High pressure
1. Introduction High-pressure polymorphism in germanium and silicon has been the subject of numerous earlier studies, starting from 1955. A number of pressure induced modifications, metastable phases, and sluggish and irreversible transitions complicate the determination of the P –T diagrams of these elements. Hall [1] was the first to report behavior of Ge in the pressure range up to 7 GPa and found a large negative slope of the melting line. Solid– solid phase transition in germanium from semi-conducting phase GeI with cubic diamond type structure (space group Fd3m) to a metallic phase GeII was reported later [2,3]. Subsequently Jamieson [4] studied this transition by in situ X-ray diffraction technique and found the structure of GeII to be a tetragonal b-Sn structure (space group I41 =amd) with c=a ¼ 0:551; which is stable only at high pressures. Bundy and Kasper [5] and Bates et al. [6] discovered the metastable semi-conducting * Corresponding author. Tel.: þ1-817-257-6393; fax: þ 1-817257-6393. E-mail address: [email protected] (G.A. Voronin).
phases GeIII (tetragonal body centered ST12, space group P43 21 2) and GeIV (cubic body centered BC8, space group Ia3). Bates et al. [6] found GeIII in samples compressed for long periods of time (several days) to 2.5 GPa at room temperature. GeIV was found in the samples held at 11– 13 GPa at room temperature for 10 – 40 h and then pressure quenched. Bates et al. [6] proposed that GeIII is stable in the pressure range between 2.5 and 11 GPa while GeIV above 11 GPa which can be obtained as a result of direct GeI – GeIII, GeII –GeIV transitions, respectively. The I – II, II– III, and II– IV phase transitions of Ge were studied more precisely at room temperature by in situ X-ray diffraction measurements by several investigators [7 –13]. It was found that the I – II transition is very sluggish and extends over a wide pressure region. Under quasi-hydrostatic conditions the onset of the transition was found to be 10.5 GPa [9], 10.6 GPa [12], or 10.7 GPa [8], while under non-hydrostatic conditions the pressures were 8.0 GPa [7], 7.5 GPa [11], 8.1 GPa [12], and even as low as 6.7 GPa [9]. The formation of GeIII was observed only during the decompression from the region of stability of GeII [9 – 12]. Malyuitskaya and Kabalkina [11], and Menoni et al. [12]
0022-3697/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0022-3697(03)00278-6
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concluded that (contrary of Ref. [6]) GeIII is a metastable phase at all pressures, and is produced from GeII as a result of kinetic factors. Different authors have reported contradictory details of the GeII – (GeI þ GeIII) transition. Quadri et al. [9] stated that the decrease of pressure from 12 to 10.4 GPa resulted in an almost total transformation of GeII to a mixture of GeI and GeIII phases. Under better hydrostatic conditions, they observed that GeII converted completely into GeIII. On the other hand, Menoni et al. [12] found that GeII transformed into GeIII at 7.6 GPa under rapid depressurization, whereas a slow release of pressure and hydrostatic conditions resulted in partial conversion to phase GeI þ GeIII. Nelmes et al. [13] have reported different result. According to them fast decompression favored formation of GeIV, while slower rate yielded mostly GeIII with some GeIV. Under ambient conditions GeIV transformed within several hours into the GeV phase with hexagonal Wurtzite type structure [13]. Later studies have reported that GeII phase is stable up to 75 GPa. In the pressure range 75 – 190 GPa and room temperature four new phases of Ge were found by in situ X-ray diffraction studies using diamond anvil cells [14 – 16] An intermediate orthorhombic phase (space group Imma) was observed at 75 – 80 GPa [15], a primitive hexagonal phase (space group P6=mmm) at 80 – 100 GPa [14,16], an orthorhombic structure of Cs –V type (space group Cmca) at 100 – 160 GPa, and a hexagonal close-packed phase at 180 GPa [16]. While phase transitions of Ge at high pressures have been extensively studied at room temperature, the behavior at high pressures and high temperature has not been investigated thoroughly. Cannon [17] analyzed previous studies of GeI melting curve, determined by differential thermal analysis (DTA) and resistance methods [18 – 21] and concluded that the results obtained by Vaidya et al. [21] are the most reliable. However, there is hardly any reliable data on melting of GeII. According to Ref. [22], GeII melts at about 823 K at 12 GPa. From all the data reported [18 –21], Cannon [17] drew a phase diagram which is shown in Fig. 1. In this diagram the coordinates of the GeI – GeII – GeL triple point are P ¼ 9:5 GPa and T ¼ 773 K: Brazhkin et al. [22] studied phase transitions of Ge by resistance measurements at different temperatures and pressures up to 11 GPa. Their data is also shown in Fig. 1, which is noticeably different from the diagram proposed by Cannon [17]. Based on X-ray diffraction data obtained at ambient conditions they suggested the following sequence of phase transitions for GeII on decreasing temperature: GeII – GeI (above 420 K), GeII –GeIII, GeII – GeIV, and GeII – Gea (amorphous Ge). Malyuitskaya and Kabalkina conducted in situ X-ray diffraction study of the GeI – GeII transition during compression at temperatures 298, 573 and 673 K [11]. At 573 and 673 K the GeII peaks were found at 8.8 ^ 0.5 and 9.1 ^ 0.5 GPa, respectively, and the onset of the I– II transition at room temperature at 7.5 ^ 0.5 GPa. The later
Fig. 1. Former P –T phase diagrams of germanium. Solid lines— Cannon [17], A—Vaidya et al. [21], O—Bundy [19], K—Bundy (Cannon [17]), dotted lines—Brazhkin et al. [22], and dashed line— Malyuitskaya and Kabalkina [11].
value led them to believe that the slope of the GeI – GeII equilibrium line is greater than that given in Ref. [17]. Germanium quenched from melt in the region of GeI stability (at pressures 2 – 7 GPa) was studied by DTA by Zhang and Wang [23] and He et al. [24] These authors concluded that during melt quenching at pressures above 4 GPa liquid germanium first crystallizes into GeII, and during subsequent cooling transforms into GeI þ GeIII þ GeIV. Although the X-ray diagrams made after decompression showed presence of GeIII and GeIV in the samples, the statement that liquid germanium crystallizes into GeII at 4 – 7 GPa contradicts existing versions of P – T phase diagrams of germanium [17,22,25]. It is evident from the above survey that the high temperature region of the P– T diagram of germanium is ill defined. Data to support an equilibrium phase diagram of Ge are fragmentary and sometimes contradictory. It is unclear if GeIII and GeIV have a region of stability at high pressures and temperatures. The positions of the GeII melting line and the GeI – GeII – GeL triple point have been only roughly estimated. There are no data on high temperature properties of GeII. The goal of this work is to fill these gaps by conducting an in situ X-ray diffraction study of Ge at pressures 5 – 11 GPa and temperatures 300– 950 K, and collect data on phase transitions and structure of various phases, and to obtain a more precise P– T diagram of germanium.
2. Experimental procedures In situ X-ray diffraction experiments were performed in a DIA-6 type cubic-anvil apparatus (SAM-85) [26,27] installed on beamline X17B1 of the National Synchrotron
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Light Source (NSLS) at Brookhaven National Laboratory. The experiments were conducted using tungsten carbide anvils with of 4 £ 4 mm2 faces. For pressure medium a mixture of amorphous boron and epoxy resin was used. The graphite heater was isolated from the pressure medium by alumina. The detailed description of cell assembly used in our experiments can be found in Ref. [28]. Samples were encapsulated in a hexagonal boron nitride chamber with NaCl þ BN powder for pressure calibration. Temperature was measured by a W/Re 25% – W/Re 3% thermocouple, and pressures were calculated using the Decker’s equation of state for NaCl [29]. Errors in temperature measurements are estimated to be ^ 10 K and the uncertainty in pressure measurements was , 0.2 GPa (see Refs. [28,30] for details). The incident X-ray beam was collimated to 100 £ 100 mm2. The diffraction data were collected at the fixed angle of 2u ¼ 6:3888 in the energy range up to 100 keV, with a Ge solid-state detector. Typical duration for collecting a diffraction pattern with acceptable resolution was 150–200 s. Ge powder from Alfa Aesar of 99.999% purity was used in all experiments. Two different powder samples containing Ge were prepared. The first sample was a mixture of finely powdered Ge and hexagonal boron nitride, BNh, (Alfa Aesar, 99.5% purity) powders in the mass proportion 1:3. The second sample was a mixture of Ge and diamond powder (GE industrial diamond, grain size 5 – 10 mm) in the same mass proportion. Because of the low yield stress of BNh, Ge particles in the Ge/BNh mixture should be under quasi-hydrostatic conditions. In contrast, very high yield stress and elastic moduli of diamond represented a nonhydrostatic environment in the Ge/Cd mixture. Two different runs were made using the same cell design and materials, labeled as A and B. Their P –T paths are shown in Figs. 2 and 3, respectively. An initial pressure of 5.5 GPa (run A) and 5.0 GPa (run B) was applied at room temperature. Then the pressure and temperature were changed as shown in Figs 2 and 3, and X-ray diffraction
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Fig. 3. P –T path in run B.
patterns of Ge/BNh, Ge/Cd samples and the pressure calibrants NaCl/BNh were recorded at each point. In run A the maximum pressure (11.1 GPa) was applied at room temperature straightaway, and then temperature was raised to 950 K. Data collection was done at selected temperatures and constant ram load. Pressure in the cell decreased during the first heating cycle due to stress release and consequent flow of cell assembly material [31,32]. The next heating cycle was started after the pressure was dropped to a desired level. These steps were repeated several times. In run B we studied in detail the regularities of the GeI – GeII transition by changing pressure in the cell at two temperatures, 473 and 673 K. After a pressure of 5.0 GPa was first applied, the sample was heated to 473 K and then the pressure was increased further, as illustrated in Fig. 3.
3. Results and discussion 3.1. Ge/BNh samples
Fig. 2. P –T path in run A.
For the Ge/BNh mixtures, in run A, no peaks of GeII were observed at room temperature until the pressure reached 11.1 GPa (see Fig. 4(b)). The fact that the GeI – GeII phase transition starts at such a high pressure indicates that the stress state of Ge grains in soft BNh matrix is very close to hydrostatic conditions [10,12]. Increasing temperature greatly facilitated the transition. At 473 K most of GeI transformed to GeII (Fig. 4(c)) and at 573 K no GeI peaks were observed (see Fig. 4(d)). The diffraction patterns of Ge/BNh remained unchanged with temperature increase until its melting point (890 K, 10.2 GPa, point 6 in Fig. 2), at which the GeII peaks disappeared. During the subsequent cooling stage GeII crystallized at 887 K and 10.0 GPa. However, only very strong (101) and weak (420) diffraction peaks of GeII were found (Fig. 4(e)). This effect could be due to oriented crystallization of GeII. The X-ray diffraction
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Fig. 4. Selected X-ray spectra of the Ge/BNh sample as a function of pressure and temperature from run A (see P –T path in Fig. 2). A— GeI (111), (220), (311) peaks, K—GeII (200), (101) peaks, and W— BNh (002), (100), (101), (102) peaks. The peaks of each phase, in this and the following figures, are listed in left to right sequence.
Fig. 5. Selected X-ray spectra of Ge/BNh sample after the GeII – (GeI þ GeIII þ GeIV) transition (run A). A—GeI (111), (220), (311) peaks, K—GeII (200), (101), (220) peaks, B—GeIII (201), (112), (222) peaks, O—GeIV (211), (321) peaks, and W—BNh peaks.
patterns remained unchanged at points 9 – 11. The same patterns were observed in run B after crystallization of GeII from the liquid state. The pressure release at 303 K from 8.3 to 7.3 GPa (point 12 in Fig. 2) leads to the GeII – (GeI þ GeIII þ GeIV) transition (Fig. 5(a)). GeII transformed into GeIII þ GeIV, although small peaks of GeI and remnants of GeII were also detected. At this pressure, increasing the temperature initiated the (GeIII þ GeIV) – GeI transition. GeIII and GeIV peaks became significantly lower at 473 K (Fig. 5(b)) and totally disappeared at 608 K (Fig. 5(c)). This fact strongly suggests that GeIII and GeIV have no region of stability, and were formed from GeII as a result of kinetic factors. During subsequent heating, melting of GeI was detected at 853 K and 8.0 GPa (point 13). Upon cooling no Ge peaks were found (point 14) down to 623 K at P ¼ 8:3 GPa (point 15). This can be attributed to a highly oriented crystallization of germanium, or due to an amorphous form. We believe that the latter possibility is more likely. Subsequent pressure release and temperature changes resulted in the emergence of GeI peaks in the X-ray spectra. Melting of GeI was observed at 920 K when P was 7.0 GPa (point 16). In run B, the onset of the GeI – GeII transition was found at 9.7 GPa when T was 473 K (point 2 in Fig. 3). Diffraction
pattern recorded at this point (see Fig. 6(b)) shows clearly the (200) peak of GeII. From peak intensities (Fig. 6(c)) we estimate that at 10.1 GPa (point 3) about half of GeI had transformed into GeII. Intensities of GeII peaks decreased noticeably during subsequent pressure release, as seen in Fig. 6(d) (8.2 GPa and 473 K), indicating the beginning of the reverse GeII – GeI transition. No GeIII and GeIV peaks were found in the diffraction pattern shown in Fig. 6(d), and we suggest that diffusion at 473 K is large enough to ensure the direct conversion of GeII to GeI. Measurements at 673 K showed that the GeI – GeII transformation was complete at 9.5 GPa (point 4). Melting of GeII was observed at 873 K when the pressure was 9.4 GPa. Based on our results we present a modified P– T diagram of germanium shown in Fig. 7. The GeI melting points are in very good agreement with the results of Vaidya et al. [21]. However, the position of the GeII melting curve is significantly higher, by more than 70 K, than that proposed in Refs. [17,22]. The intersection of the GeI and GeII melting lines gives the following position for the GeI – GeII – GeL triple point (GeL—the liquid phase): 833 ^ 20 K and 8.7 ^ 0.2 GPa. In Fig. 7 the dotted line depicts the estimated boundary between the region where phases GeI and GeII coexist during
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Fig. 6. Selected X-ray spectra of Ge/BNh sample as a function of pressure and temperature from run B (see P –T path in Fig. 3). A— GeI (111), (220), (311) peaks, K—GeII (200), (101), (220) peaks, and W—BNh peaks.
Fig. 7. Corrected P – T phase diagram of germanium. A—melting points (Vaidya et al. [21]), W—melting points, present work, dotted line—estimated boundary between GeI þ GeII and GeII phases during compression, short-dashed line—boundary between GeI þ GeII and GeI phases during decompression, and dashed line—the estimated GeI – GeII equilibrium line. The area between the short-dashed and dotted lines represents conditions where both phases may coexist. See text for further explanations.
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compression and the region where only the GeII phase exists. Similarly, the short-dashed line denotes the estimated boundary between the region where both GeI and GeII phases coexist during decompression and the region where there is only one phase—GeI. From all room temperature data it seems reasonable to place the equilibrium GeI –GeII point at about 9 GPa [17,25]. Connecting this point with the presently obtained triple point gives us a boundary for the GeI – GeII which has a small negative slope (dashed line in Fig. 7). We have estimated the volume effects associated with the GeI – GeII transition at its onset, taking into account the compressibility of GeI at different temperatures and pressures, from the lattice parameter measurements. The GeI compressibility data are plotted in Fig. 8. Table 1 summarizes the results obtained at the onset of the GeI – GeII transition at 298 K (run A) and 473 K (run B). Data from Refs. [4,7,10,12] obtained at room temperature are also listed for comparison. The onset of the GeI – GeII transition in run B at 473 K was found at 9.7 GPa (point 2, Fig. 2). Under these conditions only the (200) peak of GeII was well resolved. Therefore for the volume calculations we used the next point at a slightly higher pressure (10.1 GPa), in which all GeII peaks were well resolved. The data in Table 1 indicate that increasing temperature, from 298 to 473 K, leads to a significant decrease in pressure at which the GeI – GeII transition starts, and to an increase in the c=a ratio of the GeII unit cell from 0.551 to 0.554. In run A an identical increase of the c=a ratio was observed upon heating from 298 to 473 K (Table 2). We conclude that the ratio c=a ¼ 0:553 – 0:554 is typical for GeII under hydrostatic conditions at temperatures 298–473 K, while the c=a ratio of 0.551 corresponds to a non-hydrostatically stressed GeII at the beginning of the GeI – GeII transition at room temperature. Furthermore, the c=a ratio increases with increasing temperature and reaches 0.555– 0.556 at 823 K (Table 2). This implies a large anisotropy of GeII thermal expansion coefficient.
Fig. 8. Pressure–volume–temperature relation for GeI A—298 K, W—473 K, and K—823 K.
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Table 1 Volume effects at the onset of the GeI –GeII transition
Present work, 298 K (run A) Present work, 473 K (run B) Jamieson [4] Baublitz and Ruoff [7] Olijnyk et al. [10] Menoni et al. [12] a b c d
Pt (GPa)
VI ðPt Þ=VI ð0Þ
VII ðPt Þ=VI ð0Þ
ðVI – VII Þ=VI ðPt Þ
c=a
11.1 9.7 10.1 12.0 8.0 10.3 8.1b 9.8c 10.6d
0.885 0.898a 0.892a 0.875 0.915 0.895 0.916 0.910 0.903
0.736 – 0.746 – – 0.74 0.740 0.760 0.732
2 0.168 – 2 0.173 2 0.207 2 0.192 – 2 0.192 2 0.165 2 0.189
0.551 – 0.554 0.551 0.551 – 0.552 0.554 0.548
VI ð0ÞT¼473 K ¼ 1:0033VI ð0ÞT¼298 K according to Ref. [33]. No pressure medium. 4:1 methanol–ethanol pressure medium. NaCl pressure medium.
3.2. Ge/diamond samples At room temperature, for the Ge/Cd samples small GeII peaks were observed in both runs at relatively low pressures of 5.5 GPa (point 1, Fig. 2) and 5.0 GPa (point 1, Fig. 3), compare Fig. 9(b). The striking decrease of the onset pressure of the GeI – GeII transition must be due the existence of large micro-scale stresses in this powder mixture, as evidenced by the broadened GeI peaks. The GeII peaks intensities increased at higher pressure (Fig. 6(c)), indicating further conversion to GeII phase. When the temperature was increased at 11.1 GPa, the GeII peak intensities diminished, while the GeI peaks became narrow. At 473 K the GeII peaks became very weak (Fig. 6(d)) and completely disappeared at 890 K. From this we infer that the volume fraction of the GeII phase was reduced as a result of stress redistribution in Ge crystals due to a significant decrease in the yield stress of Ge with increasing temperature. The averaged pressure experienced by the Ge grains must be lower than the applied external pressure due to the presence of the rigid diamond matrix. This is
supported by the experimental observation that GeI in the Ge/diamond mixture did not melt even at 950 K when the external pressure was 10.2 GPa (point 7, Fig. 2) indicating that the hydrostatic component of stresses in Ge grains mixed with diamonds did not exceed 7.5– 8 GPa estimated from the phase diagram in Fig. 7. Similar results were obtained in run B. In the Ge/Cd sample, the peaks of GeII were recognizable at 5 GPa and
Table 2 Cell parameters ðc; aÞ and cell volume V for GeII at selected points of runs A and B. The standard deviations (in parentheses) refer to the uncertainty in the last digit ˚) Run/ P (GPa) T (K) c (A Point #
˚) a (A
c=a
˚ 3) V (A
A/2 A/3 A/4 A/5 A/8 A/9 A/10 B/3 B/5
4.945(4) 4.955(3) 4.964(2) 4.980(2) 4.978(4) 4.962(3) 5.000(4) 4.968(2) 4.995(3)
0.5509(6) 0.5522(5) 0.5536(3) 0.5560(5) 0.5556(6) 0.5534(5) 0.5564(6) 0.5537(5) 0.5552(5)
66.61(9) 67.17(8) 67.71(5) 68.67(6) 68.54(9) 67.61(8) 69.55(9) 67.90(6) 69.19(8)
11.1 10.8 10.5 10.3 9.8 9.2 9.3 10.1 9.5
298 373 473 823 783 303 873 473 829
2.724(2) 2.736(2) 2.748(1) 2.769(2) 2.766(2) 2.746(2) 2.782(2) 2.751(2) 2.773(2)
Fig. 9. Selected X-ray spectra of Ge/Cd sample as a function of pressure and temperature from runs A and B. A—GeI (111), (220), (311) peaks, K—GeII (200), (101), (220) peaks, V—diamond (111) peak, and W—BNh peaks.
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room temperature. They disappeared when the sample was heated to 473 K. We conclude that under non-hydrostatic conditions the stress concentration is responsible for a significant decrease of the onset of the GeI –GeII transition. These effects could account for the results reported in Refs. [7,9,11,12].
4. Conclusions In situ X-ray diffraction studies on germanium were carried out in the pressure–temperature range 5–11 GPa and 298–950 K. The data obtained has enabled us to define the P–T diagram more precisely. Accordingly the GeI –GeII –GeL triple point is placed at 833 ^ 20 K and 8.7 ^ 0.2 GPa. The position of the GeII melting curve was found to be significantly higher, by 70– 100 K, than previously reported values [17,22,25]. The GeI – GeII equilibrium line is shown to have a negative slope. Both GeIII and GeIV phases are formed from GeII during decompression at room temperature. These are metastable phases, which transform to GeI at temperatures 473–623 K, near the GeI –GeII boundary ðP ¼ 7:5 – 7:8 GPaÞ: The volume effects at the beginning of the GeI – GeII transition at 298 and 473 K were calculated. The c=a ratio of GeII increases from 0.553 – 0.554 to 0.555 – 0.556 in the temperature interval 473– 823 K, implying a large anisotropy in the thermal expansion coefficient of GeII. In the diamond powder matrix, the GeI – GeII transformation starts at a relatively low pressure, namely , 5 GPa. This is attributed to large stress concentrations in grain contact zones. Stress relaxation in Ge during subsequent heating at a constant load is the origin of the observed GeII – GeI transformation.
Acknowledgements We thank M. Vaughan and J. Chen for their help in the DIA experiments. This study has been supported by the US Department of Energy under contract No. W-7405-ENG-36 and TCU RCA Fund. The Center for High Pressure Research (CHiPR) is jointly supported by National Science Foundation under the grant EAR 89-17563 and by the State University of New York at Stony Brook. The X-17B1 beamline at the NSLS is supported by the US Department of Energy under contract No. DE-AC02-76CH00016.
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In situ X-ray diffraction study of germanium at pressures up to 11 GPa and temperatures up to 950 K G.A. Voronina,*, C. Panteaa,c, T.W. Zerdaa, J. Zhangb,c, L. Wangb, Y. Zhaoc b
a Department of Physics and Astronomy, Texas Christian University, TCU Box 298840, Fort Worth, TX 76129, USA Center for High Pressure Research and Mineral Physics Institute, State University of New York, Stony Brook, NY 11794-2100, USA c LANSCE, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Received 9 April 2003; revised 9 June 2003; accepted 17 June 2003
Abstract In situ X-ray diffraction measurements on germanium were conducted in the pressure range of 5 – 11 GPa and temperatures up to 950 K. Using our data a better defined P– T diagram for germanium is presented. The coordinates of the triple point between GeI – GeII – GeL have been determined to a better degree of precision. The onsets of the GeI – GeII transition were found both under hydrostatic and non-hydrostatic conditions. Anisotropy of thermal expansion coefficient for the GeII is characterized from the c=a ratios in the temperature interval 473– 823 K. Phases GeIII and GeIV are shown to be metastable forms of germanium. q 2003 Elsevier Ltd. All rights reserved. Keywords: C. X-ray diffraction; C. High pressure
1. Introduction High-pressure polymorphism in germanium and silicon has been the subject of numerous earlier studies, starting from 1955. A number of pressure induced modifications, metastable phases, and sluggish and irreversible transitions complicate the determination of the P –T diagrams of these elements. Hall [1] was the first to report behavior of Ge in the pressure range up to 7 GPa and found a large negative slope of the melting line. Solid– solid phase transition in germanium from semi-conducting phase GeI with cubic diamond type structure (space group Fd3m) to a metallic phase GeII was reported later [2,3]. Subsequently Jamieson [4] studied this transition by in situ X-ray diffraction technique and found the structure of GeII to be a tetragonal b-Sn structure (space group I41 =amd) with c=a ¼ 0:551; which is stable only at high pressures. Bundy and Kasper [5] and Bates et al. [6] discovered the metastable semi-conducting * Corresponding author. Tel.: þ1-817-257-6393; fax: þ 1-817257-6393. E-mail address: [email protected] (G.A. Voronin).
phases GeIII (tetragonal body centered ST12, space group P43 21 2) and GeIV (cubic body centered BC8, space group Ia3). Bates et al. [6] found GeIII in samples compressed for long periods of time (several days) to 2.5 GPa at room temperature. GeIV was found in the samples held at 11– 13 GPa at room temperature for 10 – 40 h and then pressure quenched. Bates et al. [6] proposed that GeIII is stable in the pressure range between 2.5 and 11 GPa while GeIV above 11 GPa which can be obtained as a result of direct GeI – GeIII, GeII –GeIV transitions, respectively. The I – II, II– III, and II– IV phase transitions of Ge were studied more precisely at room temperature by in situ X-ray diffraction measurements by several investigators [7 –13]. It was found that the I – II transition is very sluggish and extends over a wide pressure region. Under quasi-hydrostatic conditions the onset of the transition was found to be 10.5 GPa [9], 10.6 GPa [12], or 10.7 GPa [8], while under non-hydrostatic conditions the pressures were 8.0 GPa [7], 7.5 GPa [11], 8.1 GPa [12], and even as low as 6.7 GPa [9]. The formation of GeIII was observed only during the decompression from the region of stability of GeII [9 – 12]. Malyuitskaya and Kabalkina [11], and Menoni et al. [12]
0022-3697/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0022-3697(03)00278-6
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concluded that (contrary of Ref. [6]) GeIII is a metastable phase at all pressures, and is produced from GeII as a result of kinetic factors. Different authors have reported contradictory details of the GeII – (GeI þ GeIII) transition. Quadri et al. [9] stated that the decrease of pressure from 12 to 10.4 GPa resulted in an almost total transformation of GeII to a mixture of GeI and GeIII phases. Under better hydrostatic conditions, they observed that GeII converted completely into GeIII. On the other hand, Menoni et al. [12] found that GeII transformed into GeIII at 7.6 GPa under rapid depressurization, whereas a slow release of pressure and hydrostatic conditions resulted in partial conversion to phase GeI þ GeIII. Nelmes et al. [13] have reported different result. According to them fast decompression favored formation of GeIV, while slower rate yielded mostly GeIII with some GeIV. Under ambient conditions GeIV transformed within several hours into the GeV phase with hexagonal Wurtzite type structure [13]. Later studies have reported that GeII phase is stable up to 75 GPa. In the pressure range 75 – 190 GPa and room temperature four new phases of Ge were found by in situ X-ray diffraction studies using diamond anvil cells [14 – 16] An intermediate orthorhombic phase (space group Imma) was observed at 75 – 80 GPa [15], a primitive hexagonal phase (space group P6=mmm) at 80 – 100 GPa [14,16], an orthorhombic structure of Cs –V type (space group Cmca) at 100 – 160 GPa, and a hexagonal close-packed phase at 180 GPa [16]. While phase transitions of Ge at high pressures have been extensively studied at room temperature, the behavior at high pressures and high temperature has not been investigated thoroughly. Cannon [17] analyzed previous studies of GeI melting curve, determined by differential thermal analysis (DTA) and resistance methods [18 – 21] and concluded that the results obtained by Vaidya et al. [21] are the most reliable. However, there is hardly any reliable data on melting of GeII. According to Ref. [22], GeII melts at about 823 K at 12 GPa. From all the data reported [18 –21], Cannon [17] drew a phase diagram which is shown in Fig. 1. In this diagram the coordinates of the GeI – GeII – GeL triple point are P ¼ 9:5 GPa and T ¼ 773 K: Brazhkin et al. [22] studied phase transitions of Ge by resistance measurements at different temperatures and pressures up to 11 GPa. Their data is also shown in Fig. 1, which is noticeably different from the diagram proposed by Cannon [17]. Based on X-ray diffraction data obtained at ambient conditions they suggested the following sequence of phase transitions for GeII on decreasing temperature: GeII – GeI (above 420 K), GeII –GeIII, GeII – GeIV, and GeII – Gea (amorphous Ge). Malyuitskaya and Kabalkina conducted in situ X-ray diffraction study of the GeI – GeII transition during compression at temperatures 298, 573 and 673 K [11]. At 573 and 673 K the GeII peaks were found at 8.8 ^ 0.5 and 9.1 ^ 0.5 GPa, respectively, and the onset of the I– II transition at room temperature at 7.5 ^ 0.5 GPa. The later
Fig. 1. Former P –T phase diagrams of germanium. Solid lines— Cannon [17], A—Vaidya et al. [21], O—Bundy [19], K—Bundy (Cannon [17]), dotted lines—Brazhkin et al. [22], and dashed line— Malyuitskaya and Kabalkina [11].
value led them to believe that the slope of the GeI – GeII equilibrium line is greater than that given in Ref. [17]. Germanium quenched from melt in the region of GeI stability (at pressures 2 – 7 GPa) was studied by DTA by Zhang and Wang [23] and He et al. [24] These authors concluded that during melt quenching at pressures above 4 GPa liquid germanium first crystallizes into GeII, and during subsequent cooling transforms into GeI þ GeIII þ GeIV. Although the X-ray diagrams made after decompression showed presence of GeIII and GeIV in the samples, the statement that liquid germanium crystallizes into GeII at 4 – 7 GPa contradicts existing versions of P – T phase diagrams of germanium [17,22,25]. It is evident from the above survey that the high temperature region of the P– T diagram of germanium is ill defined. Data to support an equilibrium phase diagram of Ge are fragmentary and sometimes contradictory. It is unclear if GeIII and GeIV have a region of stability at high pressures and temperatures. The positions of the GeII melting line and the GeI – GeII – GeL triple point have been only roughly estimated. There are no data on high temperature properties of GeII. The goal of this work is to fill these gaps by conducting an in situ X-ray diffraction study of Ge at pressures 5 – 11 GPa and temperatures 300– 950 K, and collect data on phase transitions and structure of various phases, and to obtain a more precise P– T diagram of germanium.
2. Experimental procedures In situ X-ray diffraction experiments were performed in a DIA-6 type cubic-anvil apparatus (SAM-85) [26,27] installed on beamline X17B1 of the National Synchrotron
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Light Source (NSLS) at Brookhaven National Laboratory. The experiments were conducted using tungsten carbide anvils with of 4 £ 4 mm2 faces. For pressure medium a mixture of amorphous boron and epoxy resin was used. The graphite heater was isolated from the pressure medium by alumina. The detailed description of cell assembly used in our experiments can be found in Ref. [28]. Samples were encapsulated in a hexagonal boron nitride chamber with NaCl þ BN powder for pressure calibration. Temperature was measured by a W/Re 25% – W/Re 3% thermocouple, and pressures were calculated using the Decker’s equation of state for NaCl [29]. Errors in temperature measurements are estimated to be ^ 10 K and the uncertainty in pressure measurements was , 0.2 GPa (see Refs. [28,30] for details). The incident X-ray beam was collimated to 100 £ 100 mm2. The diffraction data were collected at the fixed angle of 2u ¼ 6:3888 in the energy range up to 100 keV, with a Ge solid-state detector. Typical duration for collecting a diffraction pattern with acceptable resolution was 150–200 s. Ge powder from Alfa Aesar of 99.999% purity was used in all experiments. Two different powder samples containing Ge were prepared. The first sample was a mixture of finely powdered Ge and hexagonal boron nitride, BNh, (Alfa Aesar, 99.5% purity) powders in the mass proportion 1:3. The second sample was a mixture of Ge and diamond powder (GE industrial diamond, grain size 5 – 10 mm) in the same mass proportion. Because of the low yield stress of BNh, Ge particles in the Ge/BNh mixture should be under quasi-hydrostatic conditions. In contrast, very high yield stress and elastic moduli of diamond represented a nonhydrostatic environment in the Ge/Cd mixture. Two different runs were made using the same cell design and materials, labeled as A and B. Their P –T paths are shown in Figs. 2 and 3, respectively. An initial pressure of 5.5 GPa (run A) and 5.0 GPa (run B) was applied at room temperature. Then the pressure and temperature were changed as shown in Figs 2 and 3, and X-ray diffraction
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Fig. 3. P –T path in run B.
patterns of Ge/BNh, Ge/Cd samples and the pressure calibrants NaCl/BNh were recorded at each point. In run A the maximum pressure (11.1 GPa) was applied at room temperature straightaway, and then temperature was raised to 950 K. Data collection was done at selected temperatures and constant ram load. Pressure in the cell decreased during the first heating cycle due to stress release and consequent flow of cell assembly material [31,32]. The next heating cycle was started after the pressure was dropped to a desired level. These steps were repeated several times. In run B we studied in detail the regularities of the GeI – GeII transition by changing pressure in the cell at two temperatures, 473 and 673 K. After a pressure of 5.0 GPa was first applied, the sample was heated to 473 K and then the pressure was increased further, as illustrated in Fig. 3.
3. Results and discussion 3.1. Ge/BNh samples
Fig. 2. P –T path in run A.
For the Ge/BNh mixtures, in run A, no peaks of GeII were observed at room temperature until the pressure reached 11.1 GPa (see Fig. 4(b)). The fact that the GeI – GeII phase transition starts at such a high pressure indicates that the stress state of Ge grains in soft BNh matrix is very close to hydrostatic conditions [10,12]. Increasing temperature greatly facilitated the transition. At 473 K most of GeI transformed to GeII (Fig. 4(c)) and at 573 K no GeI peaks were observed (see Fig. 4(d)). The diffraction patterns of Ge/BNh remained unchanged with temperature increase until its melting point (890 K, 10.2 GPa, point 6 in Fig. 2), at which the GeII peaks disappeared. During the subsequent cooling stage GeII crystallized at 887 K and 10.0 GPa. However, only very strong (101) and weak (420) diffraction peaks of GeII were found (Fig. 4(e)). This effect could be due to oriented crystallization of GeII. The X-ray diffraction
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Fig. 4. Selected X-ray spectra of the Ge/BNh sample as a function of pressure and temperature from run A (see P –T path in Fig. 2). A— GeI (111), (220), (311) peaks, K—GeII (200), (101) peaks, and W— BNh (002), (100), (101), (102) peaks. The peaks of each phase, in this and the following figures, are listed in left to right sequence.
Fig. 5. Selected X-ray spectra of Ge/BNh sample after the GeII – (GeI þ GeIII þ GeIV) transition (run A). A—GeI (111), (220), (311) peaks, K—GeII (200), (101), (220) peaks, B—GeIII (201), (112), (222) peaks, O—GeIV (211), (321) peaks, and W—BNh peaks.
patterns remained unchanged at points 9 – 11. The same patterns were observed in run B after crystallization of GeII from the liquid state. The pressure release at 303 K from 8.3 to 7.3 GPa (point 12 in Fig. 2) leads to the GeII – (GeI þ GeIII þ GeIV) transition (Fig. 5(a)). GeII transformed into GeIII þ GeIV, although small peaks of GeI and remnants of GeII were also detected. At this pressure, increasing the temperature initiated the (GeIII þ GeIV) – GeI transition. GeIII and GeIV peaks became significantly lower at 473 K (Fig. 5(b)) and totally disappeared at 608 K (Fig. 5(c)). This fact strongly suggests that GeIII and GeIV have no region of stability, and were formed from GeII as a result of kinetic factors. During subsequent heating, melting of GeI was detected at 853 K and 8.0 GPa (point 13). Upon cooling no Ge peaks were found (point 14) down to 623 K at P ¼ 8:3 GPa (point 15). This can be attributed to a highly oriented crystallization of germanium, or due to an amorphous form. We believe that the latter possibility is more likely. Subsequent pressure release and temperature changes resulted in the emergence of GeI peaks in the X-ray spectra. Melting of GeI was observed at 920 K when P was 7.0 GPa (point 16). In run B, the onset of the GeI – GeII transition was found at 9.7 GPa when T was 473 K (point 2 in Fig. 3). Diffraction
pattern recorded at this point (see Fig. 6(b)) shows clearly the (200) peak of GeII. From peak intensities (Fig. 6(c)) we estimate that at 10.1 GPa (point 3) about half of GeI had transformed into GeII. Intensities of GeII peaks decreased noticeably during subsequent pressure release, as seen in Fig. 6(d) (8.2 GPa and 473 K), indicating the beginning of the reverse GeII – GeI transition. No GeIII and GeIV peaks were found in the diffraction pattern shown in Fig. 6(d), and we suggest that diffusion at 473 K is large enough to ensure the direct conversion of GeII to GeI. Measurements at 673 K showed that the GeI – GeII transformation was complete at 9.5 GPa (point 4). Melting of GeII was observed at 873 K when the pressure was 9.4 GPa. Based on our results we present a modified P– T diagram of germanium shown in Fig. 7. The GeI melting points are in very good agreement with the results of Vaidya et al. [21]. However, the position of the GeII melting curve is significantly higher, by more than 70 K, than that proposed in Refs. [17,22]. The intersection of the GeI and GeII melting lines gives the following position for the GeI – GeII – GeL triple point (GeL—the liquid phase): 833 ^ 20 K and 8.7 ^ 0.2 GPa. In Fig. 7 the dotted line depicts the estimated boundary between the region where phases GeI and GeII coexist during
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Fig. 6. Selected X-ray spectra of Ge/BNh sample as a function of pressure and temperature from run B (see P –T path in Fig. 3). A— GeI (111), (220), (311) peaks, K—GeII (200), (101), (220) peaks, and W—BNh peaks.
Fig. 7. Corrected P – T phase diagram of germanium. A—melting points (Vaidya et al. [21]), W—melting points, present work, dotted line—estimated boundary between GeI þ GeII and GeII phases during compression, short-dashed line—boundary between GeI þ GeII and GeI phases during decompression, and dashed line—the estimated GeI – GeII equilibrium line. The area between the short-dashed and dotted lines represents conditions where both phases may coexist. See text for further explanations.
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compression and the region where only the GeII phase exists. Similarly, the short-dashed line denotes the estimated boundary between the region where both GeI and GeII phases coexist during decompression and the region where there is only one phase—GeI. From all room temperature data it seems reasonable to place the equilibrium GeI –GeII point at about 9 GPa [17,25]. Connecting this point with the presently obtained triple point gives us a boundary for the GeI – GeII which has a small negative slope (dashed line in Fig. 7). We have estimated the volume effects associated with the GeI – GeII transition at its onset, taking into account the compressibility of GeI at different temperatures and pressures, from the lattice parameter measurements. The GeI compressibility data are plotted in Fig. 8. Table 1 summarizes the results obtained at the onset of the GeI – GeII transition at 298 K (run A) and 473 K (run B). Data from Refs. [4,7,10,12] obtained at room temperature are also listed for comparison. The onset of the GeI – GeII transition in run B at 473 K was found at 9.7 GPa (point 2, Fig. 2). Under these conditions only the (200) peak of GeII was well resolved. Therefore for the volume calculations we used the next point at a slightly higher pressure (10.1 GPa), in which all GeII peaks were well resolved. The data in Table 1 indicate that increasing temperature, from 298 to 473 K, leads to a significant decrease in pressure at which the GeI – GeII transition starts, and to an increase in the c=a ratio of the GeII unit cell from 0.551 to 0.554. In run A an identical increase of the c=a ratio was observed upon heating from 298 to 473 K (Table 2). We conclude that the ratio c=a ¼ 0:553 – 0:554 is typical for GeII under hydrostatic conditions at temperatures 298–473 K, while the c=a ratio of 0.551 corresponds to a non-hydrostatically stressed GeII at the beginning of the GeI – GeII transition at room temperature. Furthermore, the c=a ratio increases with increasing temperature and reaches 0.555– 0.556 at 823 K (Table 2). This implies a large anisotropy of GeII thermal expansion coefficient.
Fig. 8. Pressure–volume–temperature relation for GeI A—298 K, W—473 K, and K—823 K.
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Table 1 Volume effects at the onset of the GeI –GeII transition
Present work, 298 K (run A) Present work, 473 K (run B) Jamieson [4] Baublitz and Ruoff [7] Olijnyk et al. [10] Menoni et al. [12] a b c d
Pt (GPa)
VI ðPt Þ=VI ð0Þ
VII ðPt Þ=VI ð0Þ
ðVI – VII Þ=VI ðPt Þ
c=a
11.1 9.7 10.1 12.0 8.0 10.3 8.1b 9.8c 10.6d
0.885 0.898a 0.892a 0.875 0.915 0.895 0.916 0.910 0.903
0.736 – 0.746 – – 0.74 0.740 0.760 0.732
2 0.168 – 2 0.173 2 0.207 2 0.192 – 2 0.192 2 0.165 2 0.189
0.551 – 0.554 0.551 0.551 – 0.552 0.554 0.548
VI ð0ÞT¼473 K ¼ 1:0033VI ð0ÞT¼298 K according to Ref. [33]. No pressure medium. 4:1 methanol–ethanol pressure medium. NaCl pressure medium.
3.2. Ge/diamond samples At room temperature, for the Ge/Cd samples small GeII peaks were observed in both runs at relatively low pressures of 5.5 GPa (point 1, Fig. 2) and 5.0 GPa (point 1, Fig. 3), compare Fig. 9(b). The striking decrease of the onset pressure of the GeI – GeII transition must be due the existence of large micro-scale stresses in this powder mixture, as evidenced by the broadened GeI peaks. The GeII peaks intensities increased at higher pressure (Fig. 6(c)), indicating further conversion to GeII phase. When the temperature was increased at 11.1 GPa, the GeII peak intensities diminished, while the GeI peaks became narrow. At 473 K the GeII peaks became very weak (Fig. 6(d)) and completely disappeared at 890 K. From this we infer that the volume fraction of the GeII phase was reduced as a result of stress redistribution in Ge crystals due to a significant decrease in the yield stress of Ge with increasing temperature. The averaged pressure experienced by the Ge grains must be lower than the applied external pressure due to the presence of the rigid diamond matrix. This is
supported by the experimental observation that GeI in the Ge/diamond mixture did not melt even at 950 K when the external pressure was 10.2 GPa (point 7, Fig. 2) indicating that the hydrostatic component of stresses in Ge grains mixed with diamonds did not exceed 7.5– 8 GPa estimated from the phase diagram in Fig. 7. Similar results were obtained in run B. In the Ge/Cd sample, the peaks of GeII were recognizable at 5 GPa and
Table 2 Cell parameters ðc; aÞ and cell volume V for GeII at selected points of runs A and B. The standard deviations (in parentheses) refer to the uncertainty in the last digit ˚) Run/ P (GPa) T (K) c (A Point #
˚) a (A
c=a
˚ 3) V (A
A/2 A/3 A/4 A/5 A/8 A/9 A/10 B/3 B/5
4.945(4) 4.955(3) 4.964(2) 4.980(2) 4.978(4) 4.962(3) 5.000(4) 4.968(2) 4.995(3)
0.5509(6) 0.5522(5) 0.5536(3) 0.5560(5) 0.5556(6) 0.5534(5) 0.5564(6) 0.5537(5) 0.5552(5)
66.61(9) 67.17(8) 67.71(5) 68.67(6) 68.54(9) 67.61(8) 69.55(9) 67.90(6) 69.19(8)
11.1 10.8 10.5 10.3 9.8 9.2 9.3 10.1 9.5
298 373 473 823 783 303 873 473 829
2.724(2) 2.736(2) 2.748(1) 2.769(2) 2.766(2) 2.746(2) 2.782(2) 2.751(2) 2.773(2)
Fig. 9. Selected X-ray spectra of Ge/Cd sample as a function of pressure and temperature from runs A and B. A—GeI (111), (220), (311) peaks, K—GeII (200), (101), (220) peaks, V—diamond (111) peak, and W—BNh peaks.
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room temperature. They disappeared when the sample was heated to 473 K. We conclude that under non-hydrostatic conditions the stress concentration is responsible for a significant decrease of the onset of the GeI –GeII transition. These effects could account for the results reported in Refs. [7,9,11,12].
4. Conclusions In situ X-ray diffraction studies on germanium were carried out in the pressure–temperature range 5–11 GPa and 298–950 K. The data obtained has enabled us to define the P–T diagram more precisely. Accordingly the GeI –GeII –GeL triple point is placed at 833 ^ 20 K and 8.7 ^ 0.2 GPa. The position of the GeII melting curve was found to be significantly higher, by 70– 100 K, than previously reported values [17,22,25]. The GeI – GeII equilibrium line is shown to have a negative slope. Both GeIII and GeIV phases are formed from GeII during decompression at room temperature. These are metastable phases, which transform to GeI at temperatures 473–623 K, near the GeI –GeII boundary ðP ¼ 7:5 – 7:8 GPaÞ: The volume effects at the beginning of the GeI – GeII transition at 298 and 473 K were calculated. The c=a ratio of GeII increases from 0.553 – 0.554 to 0.555 – 0.556 in the temperature interval 473– 823 K, implying a large anisotropy in the thermal expansion coefficient of GeII. In the diamond powder matrix, the GeI – GeII transformation starts at a relatively low pressure, namely , 5 GPa. This is attributed to large stress concentrations in grain contact zones. Stress relaxation in Ge during subsequent heating at a constant load is the origin of the observed GeII – GeI transformation.
Acknowledgements We thank M. Vaughan and J. Chen for their help in the DIA experiments. This study has been supported by the US Department of Energy under contract No. W-7405-ENG-36 and TCU RCA Fund. The Center for High Pressure Research (CHiPR) is jointly supported by National Science Foundation under the grant EAR 89-17563 and by the State University of New York at Stony Brook. The X-17B1 beamline at the NSLS is supported by the US Department of Energy under contract No. DE-AC02-76CH00016.
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