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Temperature and pressure derivatives of the elastic constants of cubic rubidium cyanide
Solid State Communications, Vol. 32, p. 181—183. Pergamon Press Ltd. 1979. Printed in &eat Britain.
TEMPERATURE AND PRESSURE DERIVATWES OF THE ELASTIC CONSTANTS OF CUBIC RUBIDIUM CYANIDE S. HaussUhl Institut für Kristallographie, Universitat zu KOIn, Zulpicher Str. 49, 5000 KOln I, West Germany (Received 2 May 1979 by B. Muhlschlegel)
The temperature and pressure derivatives of all elastic constants of rubidium cyanide have been from 133 to 380 respectively 2 measured by ultrasonic methods. The Kthermoelastic from 0 to 1500 x iO~ Nrn behaviour resembles that of KCN and NaCN. A strong softening of the shear resistance c,~approaching the transition temperature from higher temperatures is observed. The pressure derivatives are also quite similar to those of KCN and NaCN, but fully different from those of normal alkali halides of rocksalt-type. This behaviour confirms a rule already observed in other isotypic crystal groups: the quasi..invariant pressure derivatives are shifted in a characteristic way for a certain structure type, if rare-gas-like ions are replaced by asymmetric ions. The nonlinear elastic behaviour is qualitatively interpreted by interactions of volumeconserving type as existing in fluids.
IN CONTINUATION of earlier investigations on cubic
After several runs the quality of the crystals deteriorated considerably (inclusions, milky areas). Therefore each ingot was used only three times. All properties, e.g. cleavage, hygroscopic behaviour, plasticity, and transition properties are KCN-like. The cubic phase of RbCN [5] is stable from melting temperature at ca. 820 K down to 133 K, where a first transition occurs. The structure of the new phase might be similar to the corresponding orthorhombic phase of KCN and NaCN which first has been studied in the case of NaCN by Verweel and Bijvoet [6] That phase possesses a parallel alignment of the CN-dipoles with a certain head-and-tail disorder. At a still lower temperature (ca. 70K) a third fully ordered phase is expected [7] which was concluded from drastic changes of dielectric properties. Passing through the transition temperature at ca. 133 K the crystals become strongly inhomogeneous due to the formation of domains of different orientation.
alkali cyanides of quasi-rocksalt-structure-type [1—3] the temperature and pressure derivatives of single crystals of cubic RbCN have now been determined. The dominating question is whether RbCN exhibits a similar anomalous elastic behaviour as NaCN and KCN or not. Siniultaniously a Brillouin scattering study was undertaken the results of which have been published recently [4]. 1. EXPERIMENTAL
.
Single crystals of RbCN with dimensions up to 10mm were grown from aqueous solutions by ternperature-controlled slow cooling in the range between 315 and 305 K. The raw material was prepared by reacting of an aqueous solution of RbOH with an equivalent amount of liquid hydrocyanic acid. The purity of both reagents was better than 99%. An excess of RbOH of ca. 5% was added in order to prevent polymerisation processes. Such solutions kept stable over several months, if they were stored in a sealed container. The solution grown crystals exhibit cube {i 00) and octahedron {l 11) faces. The crystals possess areas of optical quality. However, often small inclusions of solution are observed. Better results were achieved by the Czochralski technique employing solution grown crystals as raw material (alumina crucible, argon atmosphere; growth velocity between 3 and 6mm h~,seed-crystal rotation ca. 30 r.p.m.). The crystals obtained were of optical quality and had diameters up to 15mm and lengths up to 30mm.
Optical or acoustic measurements on specimens in that state yield only unsatisfactory results. Therefore only properties of the high temperature cubic phase are reported here. The retransition into the high-temperature phase takes place after a hysteresis of several degrees. The elastic constants CU and thermoelastic constants d log c~ Tu = dT have been derived from velocities of transverse and longitudinal elastic waves propagating in the directions [100] and [110]. They were measured from 133 to 181
182
ELASTIC CONSTANTS OF CUBIC RUBIDIUM CYANIDE
Vol. 32, No.2 2] and thermoelastic constants ~ [10~ /K] ofrubidium cyanide. Nm
Table 1. Elastic cj~c[1010 Estimated limitsconstants of error are 11 0.8%, c12: 1.5%; c~:3%; T11, T12, T~:~%. The constants at room temperature possess limits of errors smaller than halfof these values T [K] c11 c12 c~ T12 T1~ T~ 133 1.498 1.380 0.0213 1.56 —1.60 57 140 1.514 1.365 0.0297 1.49 —1.60 40 150 1.536 1.343 0.0412 1.39 1.62 27.7 160 1.557 1.321 0.0525 1.30 —1.63 20.8 170 1.577 1.300 0.0632 1.21 1.65 16.7 180 1.595 1.278 0.0735 1.14 1.66 13.7 190 1.613 1.257 0.0833 1.06 1.67 11.6 200 1.630 1.236 0.0928 0.99 1.69 10.0 210 1.646 1.216 0.1018 0.92 —1.70 8.66 220 1.660 1.195 0.1103 0.86 —1.71 7.61 230 1.674 1.175 0.1186 0.80 —1.72 6.73 240 1.687 1.155 0.1264 0.74 —1.72 6.01 250 1.699 1.135 0.1338 0.68 —1.73 5.39 260 1.710 1.115 0.1408 0.63 —1.73 4.85 270 1.721 1.096 0.1475 0.58 —1.74 4.37 280 1.731 1.077 0.1537 0.53 1.74 3.95 290 1.739 1.058 0.1596 0.48 1.74 3.57 300 1.747 1.040 0.1652 0.44 —1.74 3.24 310 1.755 1.022 0.1703 0.40 —1.74 2.93 320 1.762 1.004 0.1751 0.36 1.74 2.65 330 1.768 0.987 0.1796 0.32 —1.73 2.40 340 1.773 0.970 0.1837 0.28 1.72 2.16 350 1.778 0.954 0.1875 0.25 1.71 1.94 360 1.782 0.938 0.1910 0.22* 1.70 1.74 370 1.786 0.923 0.1942 0.19* —1.68 1.55 380 1.789 0.908 0.1970 0.16* 1.66 1.37 420 1.792 0.0* 480 1.779 —0.39~ 3/K. * Limits of error <0.03 x 10 Table 2. Pressure derivatives dcj~/dpofelastic constants ofrubidium cyanide and comparable crystals for 293 K. Estimated limits of error in parentheses —
— — —
—
— —
—
— — —
—
NaCN [3]
KCN [3]
RbCN
NaCI [10]
KC1 [11]
RbC1 [121
5.55
4.43
4.46(10)
11.85
12.93
12.50
5.98
5.90
5.38(20)
2.06
1.58
1.48
—0.36
—0.11
—0.125(10)
0.37
—0.39
—0.64
380 K by diffraction of monochromatic light by ultrasonic waves in plates with a thickness of ca. 10mm at
third order polynomial approximations for the measured quantities c 11, c~,c’ = (c11 + c12 + 2c~)/2,and c” = frequencies of ca. 15 MHz (Schaefer—Bergmann method). (c11 c12)/2 in the temperature range between 133 and These values were controlled by recording the resonance 380 K yields the values of CU and T1, given in Table 1. frequencies of such plates and by conventional pulse Further, the pressure derivatives of the elastic constants echo technique. A least squares fit employing individual at 293 K were determined from the shifts of resonance —
Vol. 32, No.2
ELASTIC CONSTANTS OF CUBIC RUBIDIUM CYANIDE
frequencies, induced by hydrostatic pressures up to 1500 x l0~Nm2 (Table 2). That method has been outlined in detail recently [81.The density p = 2.328 g cm3 at 293 K was determined by the flotation method. The coefficient of linear thermal expansion, which is needed for the correction of specimen thick. ness at different temperatures, was measured by an inductive gauge dilatometer to be approximately 50 x 10-6 per degree K in the whole range, a value which corresponds to that of KCN. The lattice constant for 293 K as determined with the Bragg method on a large crystal is a = 0.6828 nm. This value agrees with the experimental density within 0.1%, giving an indication of the high purity of the crystals. 2. DISCUSSION The elastic and thermoelastic behaviour of RbCN resembles that of KCN and NaCN [1, 2]. The main feature is the anomalous softening of the shear resistance c~approaching the transition temperature. The 2 observed near smallest value c~~ 0.02 1 x iO’°Nm the transition temperature is similar to that found in NaCN and KCN indicating a similar mechanism of transition. The decreasing transition temperatures in the sequence NaCN, KCN, RbCN reflects the geometrical situation of the cyanide ions within the octahedral cage of cations. As the lattice constants and therefore also the voids within the octahedral cages increase with the atomic number of the monovalent cations under investigation (due to the higher ionic radii), the barrier for the hindred librational and rotational motions of the cyanide ions is weakened in the sequence and therefore the thermal energy necessary to onset these motions is lowered. The higher volume compressibility K = 3/(c 11 + 2c12) of RbCN in the whole temperature range also is a consequence of the larger lattice constant r, due to the rhi.law which is valid in isotypic ionic crystals [91. Expanding the measurements of c11 and c’ up to 480 K, the temperature of maximum values could be determined to be 415 K for c11 and 307 K for c’. At higher temperatures, T11 and T’ tend to behave normally (T11, T’ <0). The elastic constants determined by ultrasonic methods at ca. 15 MHz coincide within the limits of error with the values obtained by Brillouin scattering [41. The dispersion of all elastic wave velocities is therefore less than 4% up to frequencies of lOb Hz.
183
Finally the prissure derivatives dcu/dP (P hydrostatic pressure) are compared with those of NaCN, KCN, and regular alkali halides like NaCl, KC1, and RbCl (Table 2). The differences between the cyanides are surprisingly small in view of the different transition temperatures. But there exist distinct differences between the regular alkali halides and the cyanides which might be interpreted as mainly originating from interactions similar to those dominating in fluids as was pointed out earlier [3]. In fluids c 11 equals c1~and c~vanishes. The same happens with the pressure derivatives. In fact, the constants dc11 /dP and dc12/dP have the same order of magnitude in the cyamdes, the coefficient dc~/dPis substantially smaller. This behaviour is another macroscopic manifestation of the librational and rotational motions of the cyanide ions and their coupling with lattice vibrations. The new data may provide a further chance to improve the theoretical developed for the interpretation of themodels anomalous elasticrecently behaviour of alkali cyanides and similar systems [13—16]. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. i0. 11. 12. 13. 14. 15. 16.
S. HaussUhl, Solid State Commun. 13, 147 (1973). S. Haussuhl, J. Eckstein, K. Recker & F. Walirafen, Acta Cryst. A33, 847 (1977). S. HaussUhl & W. Michaelis,Acta Cryst. A35, 240 (1979). W. Krasser, B. Janik, K.D. Ehrhardt & S. HaussUhi, Solid State Commun. 30, 33 (1979). J.A. Dissertation, Utrecht (1942). H.J. Lely, Verweel & J.M. Bijvoet, Z. Krisrallogr. 100, 201 (1938). Y. Kondo, D. Schoemaker & F. Lüty, Private communication (1979). 5. Haussühl & P. Preu, Acta C,yst. A34, 442 (1978). S. Haussuhl, Z Kristallogr. 110, 67 (1958). K.D. Swartz, J. Acoust. Soc. Amer. 41, 1083 (1967). J.R. Drabble & R.E.B. Strathen, Proc. Phyn Soc. London 92, 1090 (1967). M. Ghafelehbashi, D.P. Dandekar & A.L. Ruoff, ,J~~ Phy& 41,652 (1970). C.J. Bifi, H. Jex & M. Mullner,Phyn Lett. A56, 320 (1976). K.H. Michel & J. Naudts, J~Chem. Phys. 67, 547 (1977). W. Rehwald, J.R. Sandercock & M. Rossinelli, Phys. Status Solidi A42, 699 (1977). B.J. Mokross & R. Pirc, .1. Chem. Phys. 68, 4823 (1978).
TEMPERATURE AND PRESSURE DERIVATWES OF THE ELASTIC CONSTANTS OF CUBIC RUBIDIUM CYANIDE S. HaussUhl Institut für Kristallographie, Universitat zu KOIn, Zulpicher Str. 49, 5000 KOln I, West Germany (Received 2 May 1979 by B. Muhlschlegel)
The temperature and pressure derivatives of all elastic constants of rubidium cyanide have been from 133 to 380 respectively 2 measured by ultrasonic methods. The Kthermoelastic from 0 to 1500 x iO~ Nrn behaviour resembles that of KCN and NaCN. A strong softening of the shear resistance c,~approaching the transition temperature from higher temperatures is observed. The pressure derivatives are also quite similar to those of KCN and NaCN, but fully different from those of normal alkali halides of rocksalt-type. This behaviour confirms a rule already observed in other isotypic crystal groups: the quasi..invariant pressure derivatives are shifted in a characteristic way for a certain structure type, if rare-gas-like ions are replaced by asymmetric ions. The nonlinear elastic behaviour is qualitatively interpreted by interactions of volumeconserving type as existing in fluids.
IN CONTINUATION of earlier investigations on cubic
After several runs the quality of the crystals deteriorated considerably (inclusions, milky areas). Therefore each ingot was used only three times. All properties, e.g. cleavage, hygroscopic behaviour, plasticity, and transition properties are KCN-like. The cubic phase of RbCN [5] is stable from melting temperature at ca. 820 K down to 133 K, where a first transition occurs. The structure of the new phase might be similar to the corresponding orthorhombic phase of KCN and NaCN which first has been studied in the case of NaCN by Verweel and Bijvoet [6] That phase possesses a parallel alignment of the CN-dipoles with a certain head-and-tail disorder. At a still lower temperature (ca. 70K) a third fully ordered phase is expected [7] which was concluded from drastic changes of dielectric properties. Passing through the transition temperature at ca. 133 K the crystals become strongly inhomogeneous due to the formation of domains of different orientation.
alkali cyanides of quasi-rocksalt-structure-type [1—3] the temperature and pressure derivatives of single crystals of cubic RbCN have now been determined. The dominating question is whether RbCN exhibits a similar anomalous elastic behaviour as NaCN and KCN or not. Siniultaniously a Brillouin scattering study was undertaken the results of which have been published recently [4]. 1. EXPERIMENTAL
.
Single crystals of RbCN with dimensions up to 10mm were grown from aqueous solutions by ternperature-controlled slow cooling in the range between 315 and 305 K. The raw material was prepared by reacting of an aqueous solution of RbOH with an equivalent amount of liquid hydrocyanic acid. The purity of both reagents was better than 99%. An excess of RbOH of ca. 5% was added in order to prevent polymerisation processes. Such solutions kept stable over several months, if they were stored in a sealed container. The solution grown crystals exhibit cube {i 00) and octahedron {l 11) faces. The crystals possess areas of optical quality. However, often small inclusions of solution are observed. Better results were achieved by the Czochralski technique employing solution grown crystals as raw material (alumina crucible, argon atmosphere; growth velocity between 3 and 6mm h~,seed-crystal rotation ca. 30 r.p.m.). The crystals obtained were of optical quality and had diameters up to 15mm and lengths up to 30mm.
Optical or acoustic measurements on specimens in that state yield only unsatisfactory results. Therefore only properties of the high temperature cubic phase are reported here. The retransition into the high-temperature phase takes place after a hysteresis of several degrees. The elastic constants CU and thermoelastic constants d log c~ Tu = dT have been derived from velocities of transverse and longitudinal elastic waves propagating in the directions [100] and [110]. They were measured from 133 to 181
182
ELASTIC CONSTANTS OF CUBIC RUBIDIUM CYANIDE
Vol. 32, No.2 2] and thermoelastic constants ~ [10~ /K] ofrubidium cyanide. Nm
Table 1. Elastic cj~c[1010 Estimated limitsconstants of error are 11 0.8%, c12: 1.5%; c~:3%; T11, T12, T~:~%. The constants at room temperature possess limits of errors smaller than halfof these values T [K] c11 c12 c~ T12 T1~ T~ 133 1.498 1.380 0.0213 1.56 —1.60 57 140 1.514 1.365 0.0297 1.49 —1.60 40 150 1.536 1.343 0.0412 1.39 1.62 27.7 160 1.557 1.321 0.0525 1.30 —1.63 20.8 170 1.577 1.300 0.0632 1.21 1.65 16.7 180 1.595 1.278 0.0735 1.14 1.66 13.7 190 1.613 1.257 0.0833 1.06 1.67 11.6 200 1.630 1.236 0.0928 0.99 1.69 10.0 210 1.646 1.216 0.1018 0.92 —1.70 8.66 220 1.660 1.195 0.1103 0.86 —1.71 7.61 230 1.674 1.175 0.1186 0.80 —1.72 6.73 240 1.687 1.155 0.1264 0.74 —1.72 6.01 250 1.699 1.135 0.1338 0.68 —1.73 5.39 260 1.710 1.115 0.1408 0.63 —1.73 4.85 270 1.721 1.096 0.1475 0.58 —1.74 4.37 280 1.731 1.077 0.1537 0.53 1.74 3.95 290 1.739 1.058 0.1596 0.48 1.74 3.57 300 1.747 1.040 0.1652 0.44 —1.74 3.24 310 1.755 1.022 0.1703 0.40 —1.74 2.93 320 1.762 1.004 0.1751 0.36 1.74 2.65 330 1.768 0.987 0.1796 0.32 —1.73 2.40 340 1.773 0.970 0.1837 0.28 1.72 2.16 350 1.778 0.954 0.1875 0.25 1.71 1.94 360 1.782 0.938 0.1910 0.22* 1.70 1.74 370 1.786 0.923 0.1942 0.19* —1.68 1.55 380 1.789 0.908 0.1970 0.16* 1.66 1.37 420 1.792 0.0* 480 1.779 —0.39~ 3/K. * Limits of error <0.03 x 10 Table 2. Pressure derivatives dcj~/dpofelastic constants ofrubidium cyanide and comparable crystals for 293 K. Estimated limits of error in parentheses —
— — —
—
— —
—
— — —
—
NaCN [3]
KCN [3]
RbCN
NaCI [10]
KC1 [11]
RbC1 [121
5.55
4.43
4.46(10)
11.85
12.93
12.50
5.98
5.90
5.38(20)
2.06
1.58
1.48
—0.36
—0.11
—0.125(10)
0.37
—0.39
—0.64
380 K by diffraction of monochromatic light by ultrasonic waves in plates with a thickness of ca. 10mm at
third order polynomial approximations for the measured quantities c 11, c~,c’ = (c11 + c12 + 2c~)/2,and c” = frequencies of ca. 15 MHz (Schaefer—Bergmann method). (c11 c12)/2 in the temperature range between 133 and These values were controlled by recording the resonance 380 K yields the values of CU and T1, given in Table 1. frequencies of such plates and by conventional pulse Further, the pressure derivatives of the elastic constants echo technique. A least squares fit employing individual at 293 K were determined from the shifts of resonance —
Vol. 32, No.2
ELASTIC CONSTANTS OF CUBIC RUBIDIUM CYANIDE
frequencies, induced by hydrostatic pressures up to 1500 x l0~Nm2 (Table 2). That method has been outlined in detail recently [81.The density p = 2.328 g cm3 at 293 K was determined by the flotation method. The coefficient of linear thermal expansion, which is needed for the correction of specimen thick. ness at different temperatures, was measured by an inductive gauge dilatometer to be approximately 50 x 10-6 per degree K in the whole range, a value which corresponds to that of KCN. The lattice constant for 293 K as determined with the Bragg method on a large crystal is a = 0.6828 nm. This value agrees with the experimental density within 0.1%, giving an indication of the high purity of the crystals. 2. DISCUSSION The elastic and thermoelastic behaviour of RbCN resembles that of KCN and NaCN [1, 2]. The main feature is the anomalous softening of the shear resistance c~approaching the transition temperature. The 2 observed near smallest value c~~ 0.02 1 x iO’°Nm the transition temperature is similar to that found in NaCN and KCN indicating a similar mechanism of transition. The decreasing transition temperatures in the sequence NaCN, KCN, RbCN reflects the geometrical situation of the cyanide ions within the octahedral cage of cations. As the lattice constants and therefore also the voids within the octahedral cages increase with the atomic number of the monovalent cations under investigation (due to the higher ionic radii), the barrier for the hindred librational and rotational motions of the cyanide ions is weakened in the sequence and therefore the thermal energy necessary to onset these motions is lowered. The higher volume compressibility K = 3/(c 11 + 2c12) of RbCN in the whole temperature range also is a consequence of the larger lattice constant r, due to the rhi.law which is valid in isotypic ionic crystals [91. Expanding the measurements of c11 and c’ up to 480 K, the temperature of maximum values could be determined to be 415 K for c11 and 307 K for c’. At higher temperatures, T11 and T’ tend to behave normally (T11, T’ <0). The elastic constants determined by ultrasonic methods at ca. 15 MHz coincide within the limits of error with the values obtained by Brillouin scattering [41. The dispersion of all elastic wave velocities is therefore less than 4% up to frequencies of lOb Hz.
183
Finally the prissure derivatives dcu/dP (P hydrostatic pressure) are compared with those of NaCN, KCN, and regular alkali halides like NaCl, KC1, and RbCl (Table 2). The differences between the cyanides are surprisingly small in view of the different transition temperatures. But there exist distinct differences between the regular alkali halides and the cyanides which might be interpreted as mainly originating from interactions similar to those dominating in fluids as was pointed out earlier [3]. In fluids c 11 equals c1~and c~vanishes. The same happens with the pressure derivatives. In fact, the constants dc11 /dP and dc12/dP have the same order of magnitude in the cyamdes, the coefficient dc~/dPis substantially smaller. This behaviour is another macroscopic manifestation of the librational and rotational motions of the cyanide ions and their coupling with lattice vibrations. The new data may provide a further chance to improve the theoretical developed for the interpretation of themodels anomalous elasticrecently behaviour of alkali cyanides and similar systems [13—16]. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. i0. 11. 12. 13. 14. 15. 16.
S. HaussUhl, Solid State Commun. 13, 147 (1973). S. Haussuhl, J. Eckstein, K. Recker & F. Walirafen, Acta Cryst. A33, 847 (1977). S. HaussUhl & W. Michaelis,Acta Cryst. A35, 240 (1979). W. Krasser, B. Janik, K.D. Ehrhardt & S. HaussUhi, Solid State Commun. 30, 33 (1979). J.A. Dissertation, Utrecht (1942). H.J. Lely, Verweel & J.M. Bijvoet, Z. Krisrallogr. 100, 201 (1938). Y. Kondo, D. Schoemaker & F. Lüty, Private communication (1979). 5. Haussühl & P. Preu, Acta C,yst. A34, 442 (1978). S. Haussuhl, Z Kristallogr. 110, 67 (1958). K.D. Swartz, J. Acoust. Soc. Amer. 41, 1083 (1967). J.R. Drabble & R.E.B. Strathen, Proc. Phyn Soc. London 92, 1090 (1967). M. Ghafelehbashi, D.P. Dandekar & A.L. Ruoff, ,J~~ Phy& 41,652 (1970). C.J. Bifi, H. Jex & M. Mullner,Phyn Lett. A56, 320 (1976). K.H. Michel & J. Naudts, J~Chem. Phys. 67, 547 (1977). W. Rehwald, J.R. Sandercock & M. Rossinelli, Phys. Status Solidi A42, 699 (1977). B.J. Mokross & R. Pirc, .1. Chem. Phys. 68, 4823 (1978).