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Growth of Bi–Sb gradient crystals for X-ray monochromators
Journal of Crystal Growth 198/199 (1999) 811—814
Growth of Bi—Sb gradient crystals for X-ray monochromators Stefan Penzel*, Wolfgang Neumann Institut fu( r Physik, Kristallographie, Humboldt-Universita( t zu Berlin, Invalidenstrasse 110, 10115 Berlin, Germany
Abstract Bi—Sb single crystals with a well defined slope of composition have been grown by the gradient projection method (GPM). The gradient crystals obtained exhibit a lattice parameter gradient of *a/aN /dz"0.835%/cm and *c/cN /dz"0.79%/cm. The concentration profiles of the grown crystals show a good approximation to a linear distribution. By adjusting the growth rate and using a single crystalline seed the quality of the grown crystals could be drastically increased. 1999 Elsevier Science B.V. All rights reserved. PACS: 81.10.Fq; 07.85.Fv Keywords: Crystal growth; Gradient crystals; X-ray monochromator
1. Introduction To change the divergence of an X-ray bundle or a neutron beam a Bragg reflector with a laterally varied lattice parameter is a suitable instrument. Such a Bragg reflector can be realised by a graded multilayer optic [1] or a gradient crystal [2—4]. Bent gradient crystals are of special interest for short wavelength X-ray and neutron beams. In contrast to multilayer systems an asymmetric beam geometry is possible. The paper presents new results of crystal growth in the system Bi—Sb using a single crystalline seed. Bismuth and antimony are completely miscible.
* Corresponding author. Fax: #49 30 20937760; e-mail: [email protected].
The system is characterised by strong segregation during crystallisation from the melt. The differences in the lattice parameters are *a/aN "5.4% and *c/cN "5.1%. 2. The gradient projection method The GPM is a special technique developed to grow crystals with a well defined variation of composition. It is based on the determination of a concentration gradient via a temperature gradient (Fig. 1) [5]. From a melt, whose composition will be specifically varied according to the solidus of the phase diagram an alloy composition crystallises if the melt becomes supersaturated with respect to the actual temperature.
0022-0248/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 1 0 5 4 - 9
812
S. Penzel, W. Neumann / Journal of Crystal Growth 198/199 (1999) 811–814
Fig. 1. Scheme of the projection of a temperature gradient into a concentration gradient.
a controlled rise in temperature at the dissolving interface [6].
3. Experimental set-up
Fig. 2. Cleaved (0 0 0 1)-plate reflecting the logo of Humboldt University.
The growth velocity is determined by the dissolving rate of the higher melting component whose concentration in the melt becomes gradually higher. It is controlled by a continuous rise and shift of the temperature profile. This gives rise to a constant temperature gradient along the growing crystal and
All growth experiments have been carried out in a 3-zone-furnace where all zones are controlled via EUROTHERM atemperators. The axial temperature profiles are symmetric with respect to the centre of the furnace. The effective length of the temperature region was about 140 mm with a maximally attainable gradient of temperature of approximately 10 K/cm. The accuracy of the temperature control of the whole growth system is $0.1 K. A continuous rise and shift of the temperature profile produces an increasing temperature gradient which will result in a linear concentration profile according to the gradient projection (Fig. 1). The furnace was used in a horizontal position without rotation of the ampoule. The movement of the furnace was driven by a stepmotor. The simultaneous rise and shift of the temperature profile were controlled by a computer.
S. Penzel, W. Neumann / Journal of Crystal Growth 198/199 (1999) 811–814
813
The orientation of the single crystalline seeds was (1 1 0 0). 4. Results and discussion After crystal growth the ingots were cut along the growth axis. Samples for characterisation have been produced by cleaving (0 0 0 1)-surfaces. A photograph of a cleaved (0 0 0 1)- plate is given in Fig. 2. The diameter of the grown crystals is 15 mm, the grown length is about 20 mm. The axial element distribution was measured along different lines parallel to the growth direction by wavelength-dispersive X-ray spectroscopy (WDXS) using an electron microprobe. The diameter of the excited sample area was in the order of 1—2 lm and the axial step width was 250 lm. All grown crystals show qualitatively similar concentration profiles exhibiting a good approximation to a linear distribution. The variation of composition for Bi Sb is 1(x(0.7. A typical V \V axial concentration profile for crystals grown in the 3-zone-furnace is given in Fig. 3. For a crystal length of 2 cm the gradient attained in the lattice parameters is *a/aN /dz"0.835%/cm and *c/cN / dz"0.79%/cm. The shape of the isoconcentration planes was determined by additional WDXS measurements at different positions z perpendicular to the growth direction (Fig. 4). The profiles measured show a uniform curvature of the growing interface. The asymmetric shape of the concentration profiles with higher Bi-concentration at small z-values belongs to the concave curvature of the whole interface. The relationship between composition x and the lattice parameters a and c in the system Bi—Sb is characterised as follows [7]: a"0.47867#0.02398x, c"1.186294!0.058632[1#1.26((1!x)\!1)]\. To detect the strong effect of the lattice constant gradient of 0.8%/cm X-ray diffraction measurements have been carried out. For a given reflection, the Bragg angles at different positions along the sample have been detected. Fig. 5 shows the results of the rocking curve measurements of the 124reflection carried out using Cu K radiation and ?
Fig. 3. Axial slope of composition in Bi Sb (WDXS V \V measurement).
Fig. 4. Radial distribution of composition for different axial positions z in Bi Sb (WDXS measurement). V \V
Fig. 5. Rocking curves of the 124-reflection detected at different positions.
a Ge 400 collimator. In this case, the distance between two points of measurement was 2 mm. The average halfwidth of the rocking curves was 45 . The measured rocking curves show a significant shift in the Bragg angle. Assuming the validity of the correlation of the composition and the lattice parameter given by Berger et al., the concentration determined by X-ray diffraction at a given position
814
S. Penzel, W. Neumann / Journal of Crystal Growth 198/199 (1999) 811–814
was compared with the concentration profile measured by WDXS. The X-ray diffraction measurements are in good agreement with the spectroscopic data described above. 5. Conclusions The completely miscible system Bi—Sb is suitable for growth of gradient crystals. The GPM enables the tailoring of well defined concentration profiles. In particular, a significant increase in crystal quality is made possible by using a single crystalline seed and controlling the growth velocity via adjusting the dissolution rate. Gradient Bi Sb single V \V crystals exhibit the same cleavage systems as the single crystals of the pure components. Acknowledgements The authors would like to thank Dr. R. Mitdank for EPMA measurements, Dr. P. Scha¨fer for
assisting the X-ray measurements and Mrs. A.-K. Bluhm and Mr. W. Krumbein for technical assistance. This project was financially supported by the Deutsche Forschungsgemeinschaft under contract NE 646/3-2.
References [1] H.E. Go¨bel, M. Schuster, J. Phys. D 28 (1995) A270. [2] R.K. Smither, Rev. Sci. Instrum. 53 (1982) 131. [3] R.K. Smither, P.B. Fernandez, Rev. Sci. Instrum. 63 (1992) 1755. [4] H. Bradaczek, G. Hildebrandt, W. Uebach, Coll. Abstr. XVI Congr. and General Assembly of IUCr, Beijing, China, 1993, p. 374. [5] P. Gille, M. Hollatz, H. Kleessen, M. Schenk, J. Crystal Growth 139 (1994) 165. [6] S. Penzel, H. Kleessen, W. Neumann, Cryst. Res. Technol. 32 (8) 1137. [7] H. Berger, B. Christ, J. Troschke, Cryst. Res. Technol. 17 (1982) 1233.
Growth of Bi—Sb gradient crystals for X-ray monochromators Stefan Penzel*, Wolfgang Neumann Institut fu( r Physik, Kristallographie, Humboldt-Universita( t zu Berlin, Invalidenstrasse 110, 10115 Berlin, Germany
Abstract Bi—Sb single crystals with a well defined slope of composition have been grown by the gradient projection method (GPM). The gradient crystals obtained exhibit a lattice parameter gradient of *a/aN /dz"0.835%/cm and *c/cN /dz"0.79%/cm. The concentration profiles of the grown crystals show a good approximation to a linear distribution. By adjusting the growth rate and using a single crystalline seed the quality of the grown crystals could be drastically increased. 1999 Elsevier Science B.V. All rights reserved. PACS: 81.10.Fq; 07.85.Fv Keywords: Crystal growth; Gradient crystals; X-ray monochromator
1. Introduction To change the divergence of an X-ray bundle or a neutron beam a Bragg reflector with a laterally varied lattice parameter is a suitable instrument. Such a Bragg reflector can be realised by a graded multilayer optic [1] or a gradient crystal [2—4]. Bent gradient crystals are of special interest for short wavelength X-ray and neutron beams. In contrast to multilayer systems an asymmetric beam geometry is possible. The paper presents new results of crystal growth in the system Bi—Sb using a single crystalline seed. Bismuth and antimony are completely miscible.
* Corresponding author. Fax: #49 30 20937760; e-mail: [email protected].
The system is characterised by strong segregation during crystallisation from the melt. The differences in the lattice parameters are *a/aN "5.4% and *c/cN "5.1%. 2. The gradient projection method The GPM is a special technique developed to grow crystals with a well defined variation of composition. It is based on the determination of a concentration gradient via a temperature gradient (Fig. 1) [5]. From a melt, whose composition will be specifically varied according to the solidus of the phase diagram an alloy composition crystallises if the melt becomes supersaturated with respect to the actual temperature.
0022-0248/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 1 0 5 4 - 9
812
S. Penzel, W. Neumann / Journal of Crystal Growth 198/199 (1999) 811–814
Fig. 1. Scheme of the projection of a temperature gradient into a concentration gradient.
a controlled rise in temperature at the dissolving interface [6].
3. Experimental set-up
Fig. 2. Cleaved (0 0 0 1)-plate reflecting the logo of Humboldt University.
The growth velocity is determined by the dissolving rate of the higher melting component whose concentration in the melt becomes gradually higher. It is controlled by a continuous rise and shift of the temperature profile. This gives rise to a constant temperature gradient along the growing crystal and
All growth experiments have been carried out in a 3-zone-furnace where all zones are controlled via EUROTHERM atemperators. The axial temperature profiles are symmetric with respect to the centre of the furnace. The effective length of the temperature region was about 140 mm with a maximally attainable gradient of temperature of approximately 10 K/cm. The accuracy of the temperature control of the whole growth system is $0.1 K. A continuous rise and shift of the temperature profile produces an increasing temperature gradient which will result in a linear concentration profile according to the gradient projection (Fig. 1). The furnace was used in a horizontal position without rotation of the ampoule. The movement of the furnace was driven by a stepmotor. The simultaneous rise and shift of the temperature profile were controlled by a computer.
S. Penzel, W. Neumann / Journal of Crystal Growth 198/199 (1999) 811–814
813
The orientation of the single crystalline seeds was (1 1 0 0). 4. Results and discussion After crystal growth the ingots were cut along the growth axis. Samples for characterisation have been produced by cleaving (0 0 0 1)-surfaces. A photograph of a cleaved (0 0 0 1)- plate is given in Fig. 2. The diameter of the grown crystals is 15 mm, the grown length is about 20 mm. The axial element distribution was measured along different lines parallel to the growth direction by wavelength-dispersive X-ray spectroscopy (WDXS) using an electron microprobe. The diameter of the excited sample area was in the order of 1—2 lm and the axial step width was 250 lm. All grown crystals show qualitatively similar concentration profiles exhibiting a good approximation to a linear distribution. The variation of composition for Bi Sb is 1(x(0.7. A typical V \V axial concentration profile for crystals grown in the 3-zone-furnace is given in Fig. 3. For a crystal length of 2 cm the gradient attained in the lattice parameters is *a/aN /dz"0.835%/cm and *c/cN / dz"0.79%/cm. The shape of the isoconcentration planes was determined by additional WDXS measurements at different positions z perpendicular to the growth direction (Fig. 4). The profiles measured show a uniform curvature of the growing interface. The asymmetric shape of the concentration profiles with higher Bi-concentration at small z-values belongs to the concave curvature of the whole interface. The relationship between composition x and the lattice parameters a and c in the system Bi—Sb is characterised as follows [7]: a"0.47867#0.02398x, c"1.186294!0.058632[1#1.26((1!x)\!1)]\. To detect the strong effect of the lattice constant gradient of 0.8%/cm X-ray diffraction measurements have been carried out. For a given reflection, the Bragg angles at different positions along the sample have been detected. Fig. 5 shows the results of the rocking curve measurements of the 124reflection carried out using Cu K radiation and ?
Fig. 3. Axial slope of composition in Bi Sb (WDXS V \V measurement).
Fig. 4. Radial distribution of composition for different axial positions z in Bi Sb (WDXS measurement). V \V
Fig. 5. Rocking curves of the 124-reflection detected at different positions.
a Ge 400 collimator. In this case, the distance between two points of measurement was 2 mm. The average halfwidth of the rocking curves was 45 . The measured rocking curves show a significant shift in the Bragg angle. Assuming the validity of the correlation of the composition and the lattice parameter given by Berger et al., the concentration determined by X-ray diffraction at a given position
814
S. Penzel, W. Neumann / Journal of Crystal Growth 198/199 (1999) 811–814
was compared with the concentration profile measured by WDXS. The X-ray diffraction measurements are in good agreement with the spectroscopic data described above. 5. Conclusions The completely miscible system Bi—Sb is suitable for growth of gradient crystals. The GPM enables the tailoring of well defined concentration profiles. In particular, a significant increase in crystal quality is made possible by using a single crystalline seed and controlling the growth velocity via adjusting the dissolution rate. Gradient Bi Sb single V \V crystals exhibit the same cleavage systems as the single crystals of the pure components. Acknowledgements The authors would like to thank Dr. R. Mitdank for EPMA measurements, Dr. P. Scha¨fer for
assisting the X-ray measurements and Mrs. A.-K. Bluhm and Mr. W. Krumbein for technical assistance. This project was financially supported by the Deutsche Forschungsgemeinschaft under contract NE 646/3-2.
References [1] H.E. Go¨bel, M. Schuster, J. Phys. D 28 (1995) A270. [2] R.K. Smither, Rev. Sci. Instrum. 53 (1982) 131. [3] R.K. Smither, P.B. Fernandez, Rev. Sci. Instrum. 63 (1992) 1755. [4] H. Bradaczek, G. Hildebrandt, W. Uebach, Coll. Abstr. XVI Congr. and General Assembly of IUCr, Beijing, China, 1993, p. 374. [5] P. Gille, M. Hollatz, H. Kleessen, M. Schenk, J. Crystal Growth 139 (1994) 165. [6] S. Penzel, H. Kleessen, W. Neumann, Cryst. Res. Technol. 32 (8) 1137. [7] H. Berger, B. Christ, J. Troschke, Cryst. Res. Technol. 17 (1982) 1233.