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Temperature and pressure variation of the electric field gradient in arsenic metal
TEMPERATURE
21 July 1980
PHYSICS LETTERS
Volume 78A, number 2
AND PRESSURE VARIATION
OF THE ELECTRIC FIELD GRADIENT
IN ARSENIC METAL
T.J. BASTOW, R.J.C. BROWN and H.J. WHITFIELD CSIRO Division of Chemical Physics, Clayton, Victoria, Australia 3168
Received 12 March 1980 Revised manuscript received 12 May 1980
The variation of the NQR frequency 75VQ for arsenic metal has been measured at 195 and 295 K for pressures up to 2 kbar and at atmospheric pressure between 77 and 525 K. The data are compared with those for other metallic elements.
Following our initial report of the 75 As nuclear quadrupole resonance frequency for metallic arsenic [l] we report here the detailed measurement of the temperature and pressure variation of This now brings to six the number of metals for which NQR data as a function of both temperature and pressure are available. Furthermore, it provides for the first time the basis for a comparison between two metals, viz. As and Sb, with the same structure. A small anomaly in the slope of the temperature dependence of was noted for arsenic. To check that this was not due to artefacts, such as thermocouple calibration, the temperature dependence of the 121Sb (3/2, 5/2) transition of metallic antimony [2] was recorded and is also presented here. The various factors involved in interpreting the present data are discussed. The arsenic was 99.999% pure granulated material from British Drug Houses and was sieved to obtain 100 mesh powder. The antimony was MARZ grade (99.999%) rod from Materials Research Corporation crushed to a similar mesh. The crushed metals were mixed with alumina powder, of particle size 1 p, to provide electrical insulation between particles, The NQR spectra were recorded with a conventional Zeeman-modulated noise-controlled spectrometer. Temperatures above room temperature were obtained with a furnace. Temperatures below room temperature were obtained by means of slow drift upwards from liquid nitrogen temperature vQ
vQ.
vQ
198
to dry ice temperature and then to room temperature in two stages, each stage taking about 12 h. Several high and low temperature runs were carried out alternately and temperatures were measured using a chromel-alumel thermocouple. The pressure dependence in arsenic at 295 K was measured in a conventional oil-filled system. The maximum pressure used was 2.0 kbar. Pressures were read with a calibrated Bourdon gauge. A signal-to-noise ratio of at least 10: 1 was observed with the sample in the pressure vessel. The temperature of the pressure vessel was monitored with a mercury thermometer, and the frequencies corrected to 295 K using the measured temperature dependence. The pressure dependence at 195 K was obtained using a 1: 1 mixture of neo-pentane and isopentane as the pressure medium. The Viton O-ring seal on the piston was replaced by a Bridgman seal arrangement using a lead O-ring. The pressure vessel was surrounded by a cylindrical container of dry ice, and measurements were taken when a monitoring thermometer indicated that thermal equilibrium had been achieved. It has been observed that the temperature dependence of the nuclear quadrupole resonance frequencies for a number of metals and alloys can be well represented by a power law of the form [3,4] vQ(T)=a
tbT7
(7% 1.5).
(1)
Metallic arsenic is no exception and our data can be fitted very well by eq. (1) over a substantial range of temperature (77-300 K) with y = 1.5 as shown in fig. I
21 July 1980
PHYSICS LETTERS
Volume 7 8A, number 2
T(K)
200
100
300
I
500
400
I
1
I
- 23.0
235-
20*0-
2Ct5.200
2000
4000
6000
0000
WOO
~&~
+&3/2)
Fig. 1. Temperature variation of NQR frequencies of 75As and 12’ Sb in arsenic and antimony metal.
The apparent change of slope near 300 K does not appear to mark a discontinuity in any other reported physical property (although data on physical properties of As above room temperature are sparse), and probably just marks the upper limits of applicability of the simple power law representation. Certainly no discontinuity was observed at this temperature in the equally detailed power-law temperature plot for metallic antimony also displayed in fig. 1. The a and b coefficients for As and Sb are given in table 1. However, we believe that this T1.5 representation
has no deep physical significance beyond reflecting the dependence (linear to lowest order) of the e.f.g. on the mean square amplitude of vibration (x2jT, which is measured in diffraction experiments as the Debye-Waller factor. In a large number of both metals and dielectric compounds where accurate DebyeWaller measurements are available, these data are accurately fitted by a power law of the form eq. (1) with y = 1.5 [5,6] . This is at first sight surprising, since on physical grounds (x2>* is expected to take the form
Table 1 The parameters II and b in eq. (1) for metallic arsenic and antimony.
for T > BD, the Debye temperature. The first term is due to harmonic interactions (classical equipartition of energy) and the second term is the lowest-order anharmonic correction. The next term in the expansion is O(T-I) [7]. Kolk [8] has drawn attention to the simple algebraic fact that optimum matching of an expression of the form (x2jT = c t dT7 to eq. (2) can be obtained for
Temperature range (K)
u (MHz)
b (MHz K-j’?)
As
77-300 300-525
23.69 23.57
0.181 0.160
Sb
200-430
23.05
0.300
(x2), = AT + BT2 t ... ,
.y= 3/2 + [I - 8oE2),/((x24
(2)
- (x~,~)] li2,
(3) 199
Volume 78A, number 2
21 July 1980
PHYSICS LETTERS Table 3 Separation of volume effects on 295 K.
Table 2 Pressure coefficients for metallic arsenic a).
VQfor
metallic arsenic at
[kHz (MPa)-’ ] (MPa
295 19.5
-1.04 -0.94
K-‘)
1.69
(Joe4 K-l) -2.74
(low4 K-‘) (10m4 K-r) --_ _ ._ -2.00
-0.74
_.. .~_~_ a) 1 MPa = 10 bar.
where (x2>, = c and (x2), = c t dTr, with T1 the temperature at which both forms yield identical values for (x2),. When (x2), > 9 (x2), a value of y = 1.5 results. However, the physics of the situation appears to be contained in eq. (2). Linear frequency-pressure plots were observed at both temperatures, and the slopes given in table 2. There is no substantial difference between the two. The negative sign of the NQR pressure coefficient for both As and Sb [9] is consistent with the X-ray studies of Morosin and Schirber [I 0] which indicate a trend to cubic, i.e., c/a + fi u + l/4 under pressure. The observed temperature and pressure coefficients can be analysed very simply [I I] on the assumption that v = v(V, T), to yield [avQ/aT] v in terms of the thermal expansion coefficient [ 121 and the isothermal compressibilities [lo] . However, as pointed out by O’Sullivan and Schirber [9] , because of the anisotropic nature of the crystal structure at least four parameters are needed, i.e., v = V(V, T, c/a, u), and at present there are insufficient independent measurements to obtain explicit dependence of on all these parameters. However, if, as a first approximation we ignore these complications then the simple analysis of ref. [ 111 yields vQ
[~~QPU v = Pv~laTlp + (dP)[av~laPl T, where a! is the bulk thermal expansion,
200
and /3is the
(4)
isothermal compressibility. The values derived for rhombohedral arsenic on the basis of eq. (4) are given in table 3. It can be seen that the purely volume dependent term is a relatively small component, indicating qualitatively that the temperature dependence is due primarily to the vibration amplitudes, with only relatively small contributions from the volume change of the crystal. This is consistent with our remarks in the previous section. Similar behaviour for Sb, Cd, In, 01Ga and fl-Ga was noted by Brown and Segel [ 1 l] . References [l] T.J. Bastow and H.J. Whitfield, Solid State Commun. 18 (1976) 955. [2] R. Hewitt and B.F. Williams, Phys. Rev. 129 (1963) 1188. [3] J. Christiansen et al., Z. Phys. B24 (1976) 177. [4] E.N. Kaufman and R.J. Vianden, Rev. Mod. Phys. 51 (1979) 161. [5] T.J. Bastow, S.L. Mair and S.W. Wilkins, J. Appl. Phys. 48 (1977) 494. [6] T.J. Bastow, Phys. Lett. 60A (1977) 487. [ 71 T.H.K. Barron, A.J. Leadbetter, J.A. Morrison and L.S. Salter, Acta Cryst. 20 (1966) 125. [8] B. Kolk, J. de Phys. C2 (1979) 680. [9] W. O’Sullivan and J.E. Schirber, J. Chem. Phys. 41 (1964) 2212. [lo] B. Morosin and J.E. Schirber, Solid State Commun. 10 (1972) 249. [ll] R.J.C. Brown and S.L. Segel, J. Phys. FS (1975) 1073. [12] G.K. White, J. Phys. C5 (1972) 2731.
21 July 1980
PHYSICS LETTERS
Volume 78A, number 2
AND PRESSURE VARIATION
OF THE ELECTRIC FIELD GRADIENT
IN ARSENIC METAL
T.J. BASTOW, R.J.C. BROWN and H.J. WHITFIELD CSIRO Division of Chemical Physics, Clayton, Victoria, Australia 3168
Received 12 March 1980 Revised manuscript received 12 May 1980
The variation of the NQR frequency 75VQ for arsenic metal has been measured at 195 and 295 K for pressures up to 2 kbar and at atmospheric pressure between 77 and 525 K. The data are compared with those for other metallic elements.
Following our initial report of the 75 As nuclear quadrupole resonance frequency for metallic arsenic [l] we report here the detailed measurement of the temperature and pressure variation of This now brings to six the number of metals for which NQR data as a function of both temperature and pressure are available. Furthermore, it provides for the first time the basis for a comparison between two metals, viz. As and Sb, with the same structure. A small anomaly in the slope of the temperature dependence of was noted for arsenic. To check that this was not due to artefacts, such as thermocouple calibration, the temperature dependence of the 121Sb (3/2, 5/2) transition of metallic antimony [2] was recorded and is also presented here. The various factors involved in interpreting the present data are discussed. The arsenic was 99.999% pure granulated material from British Drug Houses and was sieved to obtain 100 mesh powder. The antimony was MARZ grade (99.999%) rod from Materials Research Corporation crushed to a similar mesh. The crushed metals were mixed with alumina powder, of particle size 1 p, to provide electrical insulation between particles, The NQR spectra were recorded with a conventional Zeeman-modulated noise-controlled spectrometer. Temperatures above room temperature were obtained with a furnace. Temperatures below room temperature were obtained by means of slow drift upwards from liquid nitrogen temperature vQ
vQ.
vQ
198
to dry ice temperature and then to room temperature in two stages, each stage taking about 12 h. Several high and low temperature runs were carried out alternately and temperatures were measured using a chromel-alumel thermocouple. The pressure dependence in arsenic at 295 K was measured in a conventional oil-filled system. The maximum pressure used was 2.0 kbar. Pressures were read with a calibrated Bourdon gauge. A signal-to-noise ratio of at least 10: 1 was observed with the sample in the pressure vessel. The temperature of the pressure vessel was monitored with a mercury thermometer, and the frequencies corrected to 295 K using the measured temperature dependence. The pressure dependence at 195 K was obtained using a 1: 1 mixture of neo-pentane and isopentane as the pressure medium. The Viton O-ring seal on the piston was replaced by a Bridgman seal arrangement using a lead O-ring. The pressure vessel was surrounded by a cylindrical container of dry ice, and measurements were taken when a monitoring thermometer indicated that thermal equilibrium had been achieved. It has been observed that the temperature dependence of the nuclear quadrupole resonance frequencies for a number of metals and alloys can be well represented by a power law of the form [3,4] vQ(T)=a
tbT7
(7% 1.5).
(1)
Metallic arsenic is no exception and our data can be fitted very well by eq. (1) over a substantial range of temperature (77-300 K) with y = 1.5 as shown in fig. I
21 July 1980
PHYSICS LETTERS
Volume 7 8A, number 2
T(K)
200
100
300
I
500
400
I
1
I
- 23.0
235-
20*0-
2Ct5.200
2000
4000
6000
0000
WOO
~&~
+&3/2)
Fig. 1. Temperature variation of NQR frequencies of 75As and 12’ Sb in arsenic and antimony metal.
The apparent change of slope near 300 K does not appear to mark a discontinuity in any other reported physical property (although data on physical properties of As above room temperature are sparse), and probably just marks the upper limits of applicability of the simple power law representation. Certainly no discontinuity was observed at this temperature in the equally detailed power-law temperature plot for metallic antimony also displayed in fig. 1. The a and b coefficients for As and Sb are given in table 1. However, we believe that this T1.5 representation
has no deep physical significance beyond reflecting the dependence (linear to lowest order) of the e.f.g. on the mean square amplitude of vibration (x2jT, which is measured in diffraction experiments as the Debye-Waller factor. In a large number of both metals and dielectric compounds where accurate DebyeWaller measurements are available, these data are accurately fitted by a power law of the form eq. (1) with y = 1.5 [5,6] . This is at first sight surprising, since on physical grounds (x2>* is expected to take the form
Table 1 The parameters II and b in eq. (1) for metallic arsenic and antimony.
for T > BD, the Debye temperature. The first term is due to harmonic interactions (classical equipartition of energy) and the second term is the lowest-order anharmonic correction. The next term in the expansion is O(T-I) [7]. Kolk [8] has drawn attention to the simple algebraic fact that optimum matching of an expression of the form (x2jT = c t dT7 to eq. (2) can be obtained for
Temperature range (K)
u (MHz)
b (MHz K-j’?)
As
77-300 300-525
23.69 23.57
0.181 0.160
Sb
200-430
23.05
0.300
(x2), = AT + BT2 t ... ,
.y= 3/2 + [I - 8oE2),/((x24
(2)
- (x~,~)] li2,
(3) 199
Volume 78A, number 2
21 July 1980
PHYSICS LETTERS Table 3 Separation of volume effects on 295 K.
Table 2 Pressure coefficients for metallic arsenic a).
VQfor
metallic arsenic at
[kHz (MPa)-’ ] (MPa
295 19.5
-1.04 -0.94
K-‘)
1.69
(Joe4 K-l) -2.74
(low4 K-‘) (10m4 K-r) --_ _ ._ -2.00
-0.74
_.. .~_~_ a) 1 MPa = 10 bar.
where (x2>, = c and (x2), = c t dTr, with T1 the temperature at which both forms yield identical values for (x2),. When (x2), > 9 (x2), a value of y = 1.5 results. However, the physics of the situation appears to be contained in eq. (2). Linear frequency-pressure plots were observed at both temperatures, and the slopes given in table 2. There is no substantial difference between the two. The negative sign of the NQR pressure coefficient for both As and Sb [9] is consistent with the X-ray studies of Morosin and Schirber [I 0] which indicate a trend to cubic, i.e., c/a + fi u + l/4 under pressure. The observed temperature and pressure coefficients can be analysed very simply [I I] on the assumption that v = v(V, T), to yield [avQ/aT] v in terms of the thermal expansion coefficient [ 121 and the isothermal compressibilities [lo] . However, as pointed out by O’Sullivan and Schirber [9] , because of the anisotropic nature of the crystal structure at least four parameters are needed, i.e., v = V(V, T, c/a, u), and at present there are insufficient independent measurements to obtain explicit dependence of on all these parameters. However, if, as a first approximation we ignore these complications then the simple analysis of ref. [ 111 yields vQ
[~~QPU v = Pv~laTlp + (dP)[av~laPl T, where a! is the bulk thermal expansion,
200
and /3is the
(4)
isothermal compressibility. The values derived for rhombohedral arsenic on the basis of eq. (4) are given in table 3. It can be seen that the purely volume dependent term is a relatively small component, indicating qualitatively that the temperature dependence is due primarily to the vibration amplitudes, with only relatively small contributions from the volume change of the crystal. This is consistent with our remarks in the previous section. Similar behaviour for Sb, Cd, In, 01Ga and fl-Ga was noted by Brown and Segel [ 1 l] . References [l] T.J. Bastow and H.J. Whitfield, Solid State Commun. 18 (1976) 955. [2] R. Hewitt and B.F. Williams, Phys. Rev. 129 (1963) 1188. [3] J. Christiansen et al., Z. Phys. B24 (1976) 177. [4] E.N. Kaufman and R.J. Vianden, Rev. Mod. Phys. 51 (1979) 161. [5] T.J. Bastow, S.L. Mair and S.W. Wilkins, J. Appl. Phys. 48 (1977) 494. [6] T.J. Bastow, Phys. Lett. 60A (1977) 487. [ 71 T.H.K. Barron, A.J. Leadbetter, J.A. Morrison and L.S. Salter, Acta Cryst. 20 (1966) 125. [8] B. Kolk, J. de Phys. C2 (1979) 680. [9] W. O’Sullivan and J.E. Schirber, J. Chem. Phys. 41 (1964) 2212. [lo] B. Morosin and J.E. Schirber, Solid State Commun. 10 (1972) 249. [ll] R.J.C. Brown and S.L. Segel, J. Phys. FS (1975) 1073. [12] G.K. White, J. Phys. C5 (1972) 2731.