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Phase transitions in K and Rb under pressure
Volume 99A, number 8
PHYSICS LETTERS
19 December 1983
PHASE TRANSITIONS IN K AND Rb UNDER PRESSURE H. OLIJNYK and W.B. H O L Z A P F E L Experimentalphysik, Universitiit - G H - Paderborn, D-4790 Paderborn, Fed. Rep. Germany
Received 20 July 1983
The crystal structures of K and Rb are studied by energy-dispersive X-ray diffraction at room temperature and pressures up to 35 GPa. Phase transitions occur in K at 11 GPa and around 20 GPa, and in Rb at 7 GPa, 14 GPa, 17 GPa and around 20 GPa. Structural systematics of the alkali metals and their relation to s ~ d transfer are discussed.
1. Introduction. At ambient conditions, all the alkali metals crystallize in the bcc structure. For Cs at room temperature, four phase transitions in the 10 GPa range are well known [1] : at 2.2 GPa Cs transforms to fcc, at 4.2 GPa it collapses into another fcc phase and at 4.4 GPa into a body-centered tetragonal (Cs-IV) structure [2]. Around 10 GPa Cs transforms to phase V [3], the structure o f which is not yet determined [2]. Recent X-ray diffraction studies showed bcc ~ fcc transitions around 7 GPa in Rb [4] and in Li [5]. Furthermore electrical resistance measurements [6,7] and optical reflectivity studies [4,8] revealed the existence of additional high pressure phases in Rb and K. 2. Experimental. The structures of K and Rb were studied by energy-dispersive X-ray diffraction (EDXD) using a conical slit system [9] which has been modified for simultaneous pressure determination by the ruby fluorescence method. The linear pressure scale with dX/dp = 3.65 A [10] was adopted. The samples were cut and m o u n t e d into a gasketed diamond anvil cell [ 11] under silicon oil, together with a ruby splinter for pressure determination. The high pressure study on K up to 35 GPa was done at HASYLAB using synchrotron radiation, but the beam conditions at that time allowed only to detect diffraction lines up to 30 keV [12]. 3. Results. K transformed from bcc (K-I) to fcc (K-II) at 11 GPa and V = 0.45 V 0. The analysis of
0 . 0 3 1 - 9 1 6 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 03.00 © 1983 North-Holland
an X-ray diffraction pattern for fcc K at 11.6 GPa is given in table 1. In agreement with electrical and optical studies, we found the next phase transition to K-Ill around 20 GPa. Table 1 lists also the d values of the first 5 diffraction lines of this phase which remained stable up to 35 GPa, the highest pressure in the present experiments on K. The b c c - f c c transition in Rb was observed in the present study at 7 GPa. Figs. la and l b show the EDXD patterns of RB-I (bcc) and Rb-II (fcc) at 6.5 GPa and 11 GPa respectively. Around 14 GPa fcc Rb transformed into a new structure, Rb-III. The diffraction pattern of this phase is shown in fig. lc. On further compression, around 17 GPa another phase transition to Rb-IV is observed (fig. ld), however, the present patterns of Rb-llI and Rb-IV did not allow for a unique indexing. Around 20 GPa another
Table 1 Experimental d-spacings and observed and calculated intensity ratios for K-II (fcc) at 11.7 GPa and observed d-spacings and intensity ratios for K-Ill around 25 GPa. K-II (fcc)
K-Ill
hkl
dob s [A]
lobs
Icalc
dob s [A]
lob s
111 200 220 311
2.961 2.564 1.814 1.550
100 60 65 25
100 50 45 60
3.186 3.064 2.335 2.163 2.104
15 30 100 10 25 381
Volume 99A, number 8
PHYSICS LETTERS
RbI bcc6 G
i
J
Rbl] fcc
Ii i
eq 0,4
b)
°
01Ft-
6
!It
O fk-J
k, r"l
¢/3 -4-r 'Z3 O t..a
2
~s GpoI
~
,#'
0
m O
"7 4-r-OJ
E
t~
,,--,
6
go
!~
Io
Rbg Csl~-sf e) ~ 28 GP°
o~
TM
g
l I[ /twAv_.~/',~ V d ' LEA . _
._j ...j j
i
2z~
3z+
z,z,
i
5z+
Enerqy (keV) Fig. 1. EDXD patterns of Rb-I (bcc), Rb-II (fcc), Rb-III, Rb-IV and Rb-V (Cs-IV-structure) at various pressures. phase transition to Rb-V occurs. The diffraction pattern of Rb-V at 28 GPa is reproduced in fig. le, which shows that all the lines can be assigned to the Cs-IV structure with a = 2.883 A and c = 10.760 A. The axial ratio c/a decreases from 3.745 at 20 GPa to 3.72 at 35 GPa, the maximum pressure in the experiments on Rb. 382
19 December 1983
4. Discussion. For a discussion of these data we use our preliminary equation of state data together with tile data for Li [5], Na [13] and Cs [2] to evaluate the atomic radii RA(P) and scale the radii with respect to the ionic radii R I at ambient pressure [14] to determine the radius ratio RA/R I for tile different elements at ambient conditions and at the various phase transitions as shown in fig. 2. In this representation, K, Rb and Cs transform from bcc to fcc at a conrmon radius ratio RA/R l ~ 1.5. Tile fcc -+ fcc transition in Cs and the fcc -> Rb-llI transition in Rb also occur at a common radius ratio RA/R l --- 1.38, while K transforms from fcc to K-III at a higher value of RA/R I ~ 1.42. Bandstructure calculations for these dements [15-- 18] show that the occupied sbands rise relative to tile empty d bands with the result of an s -+ d transfer. Correlations between d-band occupation number and crystal structure stability have been established previously for the rare earth metals [19] and the alkaline earth metals [20] and a relationship between d-band occupation number and the fraction of the atomic volume occupied by the ion core was noticed [19]. We conclude therefore that the I -* II transitions and the II -+ IlI transitions in K, Rb and Cs occur also at a critical d-electron occupation number. Theoretical calculations on fcc Cs [18] indicate that the bottom of the 6s band should be shifted above the Fermi level at V ~ 0.25 V0, which corresponds to a pressure of roughly 15 GPa and this is in the range where Cs-V is stable. One may therefore conclude that the Cs-V structure is typical for the heavy alkali metals after completion of the s -+ d transfer. The differences in structures for K-Ill, Rb-III and Rb-IV, and Cs-IIl as well as the different radius ratios R A/R1 for the occurrence of the Cs-IV structure in Rb and Cs indicate, however, that minor differences in the band structure may be responsible for the different behavior of these elements as long as the s -* d transfer is not completed. On the other hand, the light alkali metal Li behaves quite differently as can be seen from fig. 2. This difference is expected within the present picture, since there are no nearby d-bands in Li. Also for Na, the first empty d-band is quite far from the Fermi level, and from theoretical calculations only a transition to hcp is expected in the 100 GPa region [21].
Volume 99A, number 8
PHYSICS LETTERS
19 December 1983
Radius ratio %/R I
2.5 i
Li No
Rb
I
O-bee
2.0 i
i
i
I
6.9 I fcc-
I
1.5 i
i
i
i
I
i
i
i
1.0 I
Transition I~
bcc ¢ - -
bcc
~)
bcc
11 19 I fcct-77 13.5 17 20 t fcc -Jr ?nk 7-~/sr7-
Pressures in OPa
/~2/4, 10 I fccntj JrCslgnt Cs2 fEE cam--~ fcc -*p(ex-~CslV * Cs~ Z2
Cs
0"- bcc
Genera[ trend
bcc
Fig. 2. Structures, transition pressures and radius ratios for the alkali metals under compression. Transition pressures are given for compression at ambient temperature without correction for hysteresis.
This w o r k was s u p p o r t e d in p a r t b y t h e Bundesm i n i s t e r i u m ffir F o r s c h u n g u n d T e c h n o l o g i e a n d p a r t l y p e r f o r m e d at H A S Y L A B .
References [1] J.F. Cannon, J. Phys. Chem. Ref. Data 3 (1974) 788. [2] K. Takemura, S. Minomura and O. Shimomura, Phys. Rev. Lett. 49 (1982) 1772. [3] R.A. Stager and H.G. Drickamer, Phys. Rev. Lett. 12 (1964) 19. [4] K. Takemura and K. Syassen, Solid State Commun. 44 (1982) 1161. [5] A.W. Olinger and J.W: Shaner, Science 219 (1983) 1071. [6] R.A. Stager and H.G. Dfickamer, Phys. Rev. 123 (1973) 124.
[7] K. Ullrich, Thesis, Universitiit KiSln (1979); Report K 171, Jiilich No. 1634 (1980). [8] K. Takemura and K. Syassen, to be published (1983). [9] W.B. Holzapfel and W. May, in: High pressure research in geophysics, eds. S. Akimoto and M.H. Manghnani (Centre of Academic Publication, Japan, 1982) p. 73. [10] G.J. Piermarini, S. Block, J.D. Barnett and R.A. Forman, J. Appl. Phys. 46 (1975) 2774.
[11] K. Syassen and W.B. Holzapfel, Eur. Conf. Abstr. 1A (1975) 75. [ 12] J. Staun Olsen, B. Buras, L. Gerward and S. Steenstrup, J. Phys. E l 4 (1981) 1154. [13] I.V. Alexandrov, S.M. Stishov, V.N. Kachinsky and I. Makarenko, Conf. Abstract, 20th EHPRG meeting (Stuttgart, 1982). [14] C. Kittel, in: Introduction to solid state physics, 5th Ed. (Wiley, New York, 1976) p. 100. [15] M.S.T. Bukowinski, Geoph. Res. Lett. 3 (1976) 491; in: High pressure science and technology, eds. K.D. Timmerhaus and M.S. Barber, Vol. 2 (Plenum, New York, 1979) p. 237, and references therein. [16] J.-P. Jan, A.H. MacDonald and H.C. Skriver, Phys. Rev. B21 (1980) 5584. [17] A.K. McMahan, Phys. Rev. B17 (1978) 1521. [18] D. Gl~Stzel and A.K. McMahan, Phys. Rev. B20 (1979) 3240, and references therein. [19] J.C. Duthie and D.G. Pettifor, Phys. Rev. Lett. 38 (1977) 564. [20] H.C. Skriver, Phys. Rev. Lett. 49 (1982) 1768. [21] J.A. Moriarty and A.K. McMahan, Phys. Rev. Lett. 48 (1982) 809.
383
PHYSICS LETTERS
19 December 1983
PHASE TRANSITIONS IN K AND Rb UNDER PRESSURE H. OLIJNYK and W.B. H O L Z A P F E L Experimentalphysik, Universitiit - G H - Paderborn, D-4790 Paderborn, Fed. Rep. Germany
Received 20 July 1983
The crystal structures of K and Rb are studied by energy-dispersive X-ray diffraction at room temperature and pressures up to 35 GPa. Phase transitions occur in K at 11 GPa and around 20 GPa, and in Rb at 7 GPa, 14 GPa, 17 GPa and around 20 GPa. Structural systematics of the alkali metals and their relation to s ~ d transfer are discussed.
1. Introduction. At ambient conditions, all the alkali metals crystallize in the bcc structure. For Cs at room temperature, four phase transitions in the 10 GPa range are well known [1] : at 2.2 GPa Cs transforms to fcc, at 4.2 GPa it collapses into another fcc phase and at 4.4 GPa into a body-centered tetragonal (Cs-IV) structure [2]. Around 10 GPa Cs transforms to phase V [3], the structure o f which is not yet determined [2]. Recent X-ray diffraction studies showed bcc ~ fcc transitions around 7 GPa in Rb [4] and in Li [5]. Furthermore electrical resistance measurements [6,7] and optical reflectivity studies [4,8] revealed the existence of additional high pressure phases in Rb and K. 2. Experimental. The structures of K and Rb were studied by energy-dispersive X-ray diffraction (EDXD) using a conical slit system [9] which has been modified for simultaneous pressure determination by the ruby fluorescence method. The linear pressure scale with dX/dp = 3.65 A [10] was adopted. The samples were cut and m o u n t e d into a gasketed diamond anvil cell [ 11] under silicon oil, together with a ruby splinter for pressure determination. The high pressure study on K up to 35 GPa was done at HASYLAB using synchrotron radiation, but the beam conditions at that time allowed only to detect diffraction lines up to 30 keV [12]. 3. Results. K transformed from bcc (K-I) to fcc (K-II) at 11 GPa and V = 0.45 V 0. The analysis of
0 . 0 3 1 - 9 1 6 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 03.00 © 1983 North-Holland
an X-ray diffraction pattern for fcc K at 11.6 GPa is given in table 1. In agreement with electrical and optical studies, we found the next phase transition to K-Ill around 20 GPa. Table 1 lists also the d values of the first 5 diffraction lines of this phase which remained stable up to 35 GPa, the highest pressure in the present experiments on K. The b c c - f c c transition in Rb was observed in the present study at 7 GPa. Figs. la and l b show the EDXD patterns of RB-I (bcc) and Rb-II (fcc) at 6.5 GPa and 11 GPa respectively. Around 14 GPa fcc Rb transformed into a new structure, Rb-III. The diffraction pattern of this phase is shown in fig. lc. On further compression, around 17 GPa another phase transition to Rb-IV is observed (fig. ld), however, the present patterns of Rb-llI and Rb-IV did not allow for a unique indexing. Around 20 GPa another
Table 1 Experimental d-spacings and observed and calculated intensity ratios for K-II (fcc) at 11.7 GPa and observed d-spacings and intensity ratios for K-Ill around 25 GPa. K-II (fcc)
K-Ill
hkl
dob s [A]
lobs
Icalc
dob s [A]
lob s
111 200 220 311
2.961 2.564 1.814 1.550
100 60 65 25
100 50 45 60
3.186 3.064 2.335 2.163 2.104
15 30 100 10 25 381
Volume 99A, number 8
PHYSICS LETTERS
RbI bcc6 G
i
J
Rbl] fcc
Ii i
eq 0,4
b)
°
01Ft-
6
!It
O fk-J
k, r"l
¢/3 -4-r 'Z3 O t..a
2
~s GpoI
~
,#'
0
m O
"7 4-r-OJ
E
t~
,,--,
6
go
!~
Io
Rbg Csl~-sf e) ~ 28 GP°
o~
TM
g
l I[ /twAv_.~/',~ V d ' LEA . _
._j ...j j
i
2z~
3z+
z,z,
i
5z+
Enerqy (keV) Fig. 1. EDXD patterns of Rb-I (bcc), Rb-II (fcc), Rb-III, Rb-IV and Rb-V (Cs-IV-structure) at various pressures. phase transition to Rb-V occurs. The diffraction pattern of Rb-V at 28 GPa is reproduced in fig. le, which shows that all the lines can be assigned to the Cs-IV structure with a = 2.883 A and c = 10.760 A. The axial ratio c/a decreases from 3.745 at 20 GPa to 3.72 at 35 GPa, the maximum pressure in the experiments on Rb. 382
19 December 1983
4. Discussion. For a discussion of these data we use our preliminary equation of state data together with tile data for Li [5], Na [13] and Cs [2] to evaluate the atomic radii RA(P) and scale the radii with respect to the ionic radii R I at ambient pressure [14] to determine the radius ratio RA/R I for tile different elements at ambient conditions and at the various phase transitions as shown in fig. 2. In this representation, K, Rb and Cs transform from bcc to fcc at a conrmon radius ratio RA/R l ~ 1.5. Tile fcc -+ fcc transition in Cs and the fcc -> Rb-llI transition in Rb also occur at a common radius ratio RA/R l --- 1.38, while K transforms from fcc to K-III at a higher value of RA/R I ~ 1.42. Bandstructure calculations for these dements [15-- 18] show that the occupied sbands rise relative to tile empty d bands with the result of an s -+ d transfer. Correlations between d-band occupation number and crystal structure stability have been established previously for the rare earth metals [19] and the alkaline earth metals [20] and a relationship between d-band occupation number and the fraction of the atomic volume occupied by the ion core was noticed [19]. We conclude therefore that the I -* II transitions and the II -+ IlI transitions in K, Rb and Cs occur also at a critical d-electron occupation number. Theoretical calculations on fcc Cs [18] indicate that the bottom of the 6s band should be shifted above the Fermi level at V ~ 0.25 V0, which corresponds to a pressure of roughly 15 GPa and this is in the range where Cs-V is stable. One may therefore conclude that the Cs-V structure is typical for the heavy alkali metals after completion of the s -+ d transfer. The differences in structures for K-Ill, Rb-III and Rb-IV, and Cs-IIl as well as the different radius ratios R A/R1 for the occurrence of the Cs-IV structure in Rb and Cs indicate, however, that minor differences in the band structure may be responsible for the different behavior of these elements as long as the s -* d transfer is not completed. On the other hand, the light alkali metal Li behaves quite differently as can be seen from fig. 2. This difference is expected within the present picture, since there are no nearby d-bands in Li. Also for Na, the first empty d-band is quite far from the Fermi level, and from theoretical calculations only a transition to hcp is expected in the 100 GPa region [21].
Volume 99A, number 8
PHYSICS LETTERS
19 December 1983
Radius ratio %/R I
2.5 i
Li No
Rb
I
O-bee
2.0 i
i
i
I
6.9 I fcc-
I
1.5 i
i
i
i
I
i
i
i
1.0 I
Transition I~
bcc ¢ - -
bcc
~)
bcc
11 19 I fcct-77 13.5 17 20 t fcc -Jr ?nk 7-~/sr7-
Pressures in OPa
/~2/4, 10 I fccntj JrCslgnt Cs2 fEE cam--~ fcc -*p(ex-~CslV * Cs~ Z2
Cs
0"- bcc
Genera[ trend
bcc
Fig. 2. Structures, transition pressures and radius ratios for the alkali metals under compression. Transition pressures are given for compression at ambient temperature without correction for hysteresis.
This w o r k was s u p p o r t e d in p a r t b y t h e Bundesm i n i s t e r i u m ffir F o r s c h u n g u n d T e c h n o l o g i e a n d p a r t l y p e r f o r m e d at H A S Y L A B .
References [1] J.F. Cannon, J. Phys. Chem. Ref. Data 3 (1974) 788. [2] K. Takemura, S. Minomura and O. Shimomura, Phys. Rev. Lett. 49 (1982) 1772. [3] R.A. Stager and H.G. Drickamer, Phys. Rev. Lett. 12 (1964) 19. [4] K. Takemura and K. Syassen, Solid State Commun. 44 (1982) 1161. [5] A.W. Olinger and J.W: Shaner, Science 219 (1983) 1071. [6] R.A. Stager and H.G. Dfickamer, Phys. Rev. 123 (1973) 124.
[7] K. Ullrich, Thesis, Universitiit KiSln (1979); Report K 171, Jiilich No. 1634 (1980). [8] K. Takemura and K. Syassen, to be published (1983). [9] W.B. Holzapfel and W. May, in: High pressure research in geophysics, eds. S. Akimoto and M.H. Manghnani (Centre of Academic Publication, Japan, 1982) p. 73. [10] G.J. Piermarini, S. Block, J.D. Barnett and R.A. Forman, J. Appl. Phys. 46 (1975) 2774.
[11] K. Syassen and W.B. Holzapfel, Eur. Conf. Abstr. 1A (1975) 75. [ 12] J. Staun Olsen, B. Buras, L. Gerward and S. Steenstrup, J. Phys. E l 4 (1981) 1154. [13] I.V. Alexandrov, S.M. Stishov, V.N. Kachinsky and I. Makarenko, Conf. Abstract, 20th EHPRG meeting (Stuttgart, 1982). [14] C. Kittel, in: Introduction to solid state physics, 5th Ed. (Wiley, New York, 1976) p. 100. [15] M.S.T. Bukowinski, Geoph. Res. Lett. 3 (1976) 491; in: High pressure science and technology, eds. K.D. Timmerhaus and M.S. Barber, Vol. 2 (Plenum, New York, 1979) p. 237, and references therein. [16] J.-P. Jan, A.H. MacDonald and H.C. Skriver, Phys. Rev. B21 (1980) 5584. [17] A.K. McMahan, Phys. Rev. B17 (1978) 1521. [18] D. Gl~Stzel and A.K. McMahan, Phys. Rev. B20 (1979) 3240, and references therein. [19] J.C. Duthie and D.G. Pettifor, Phys. Rev. Lett. 38 (1977) 564. [20] H.C. Skriver, Phys. Rev. Lett. 49 (1982) 1768. [21] J.A. Moriarty and A.K. McMahan, Phys. Rev. Lett. 48 (1982) 809.
383