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X-ray measurement of the Debye temperature for diamond at low temperatures
Solid State Communications,
Vol.7, pp. 15—18, 1969.
Pergamon Press.
Printed in Great Britain
X-RAY MEASUREMENT OF THE DEBYE TEMPERATURE FOR DIAMOND AT LOW TEMPERATURES F.R.L. Schoening and L.A. Vermeulen Department of Physics, University of the Witwatersrand, Johannesburg, South Africa (Received 4 September 1968)
-
The X-ray Debye temperature, ~ was measured at liq. He, liq. N2 and room temperature for two diamond powders of industrial quality, having a mean particle size of 6~and 780A respectively. The results are compatible with 6~~ 1880°Kfor the fine and °M~1500°K for the coarse powder. A slight decrease of OM at low temperatures is possible within the experimental errors. Because no use is made of the atomic scattering factor, the claim is not substantiated that previous results around 1500°Knecessitate a revision of the scattering factor curve for carbon.
INTRODUCTION
diamonds were used. Electron micrographs of the
THE X-RAY Debye temperature, °M, for diamond has attracted attention because its change at low temperature differs from that of Si and Ge and because of the large spread in its experimental values. Recent calculations of OM are based on dispersion curves measured by Warren et at.’ in inelastic neutron experiments. 2 havescattering fitted a lattice model toDolling the and Cowley dispersion curves and calculated frequency distributions which have a long parabolic region suggesting a nearly constant °M at low temperatures. Their data give 0M = 1860°K at 09< and 1869°Kat 77°K. In a similar approach Blanchard and Varshni3 obtain 1860°Kat 409< and 1882°Kat 300°K. Barron el al.4 estimate from heat capacity data that °M = 1890°Kat 0°K, 1920°K at room and 1970°Kat high temperatures. A decrease of 0M with decreasing temperature is indicated in these cases. In sharp contrast are 1491°Kand 1549°Kobtained for OM in reliable X-ray experiments at room temperatures (see review by Herbstein5).
coarse powder show well ‘rounded’ particles with a mean projected diameter of 6~. The small particles are very ragged having a mean diameter of 780A as confirmed by X-ray line broadening. The integrated intensities of the 533, 642, 822, 911, 664 and 844 reflections were measured at liq. He, liq. and room temperature using Mo radiation andN2a crystal monochromator between sample and detector. A few measurements were done at 300°Kand 673°K in a high temperature attachment. The poor peak to backround ratio (1.2—1.7) required long counting times and frequent repetitions. For the usual plot of the logarithm of the intensity ratios vs. A2 sin2O (James6), all data were corrected for thermal diffuse scattering and were combined by adjusting factors which were independent of ?C2 sin2 0. In general, the large particle data were well represented by straight lines, whilst the small particle data were sometimes difficult to fit by straight lines as is evident from the large uncertainties in some of the slopes. Equation (1) of reference 6 shows that the experimental slope depends on 0Mi and 0M2 which are characteristic of the low and high
EXPERIMENTAL A coarse and a fine powder of industrial 15
16
X-RAY MEASUREMENT FOR DIAMOND AT LOW TEMPERATURES
T
2400
2200 ~
L
0—c
-
2000
;isoo_j
Vol.7, No. 1
~
1600—I
1400
(
I
0
I
300 T(’K)
600
°M = 1880°Kat 300°K points a (large particles) and b (small particles) are obtained. Assuming 0M = 1500°K for the large particles points c are obtained. Calculations3 using the frequency spectrum give the horizontal curve.
FIG. 1. Assuming
temperatures T Slope
=
1 and T2 of the experiment. 1913 + T, ~F~-~--) /OM1\ 1 — MI
I
T 2
—
If it is assumed that the two samples have 0M values shown by the points a andforb the in Fig. obtained. To explain the points large1 are = 1880°Kat 300°K,constant volume
1
f6M2\
~jr-~
1
—
(1)
.
M2
M2J
RESULTS AND DISCUSSION Table 1 shows that between 4°Kand 77°K the slope for the small particles is positive whilst that for the large particles could be positive within one standard deviation. From (1) follows that the results are therefore compatible with a decrease of 0M with decreasing T. The large particle slopes are always more negative thereby indicating a lower average °M• However, on closer inspection widely different 0M vs. T curves can be derived from the experimental slopes. Table 1. Experimental slopes in Temperatures
Small
Particles
A2
particles the rather unlikely postulate has to be made that the frequency spectrum has changed 0MGe. withThese considerably towards that for Si and two elements show an increase of decreasing T. Within the errors, the data for the small particles agree with the predictions based on the frequency spectrum. If at room temperature 0M = 1500°K for the large particles, then points c are obtained. These are now reasonable in the sense that ~ is constant and, within the errors of the experiment, could decrease at low temperatures. Although such low 0M~ have been reported, the difference between the samples remains to be explained. In view of the use of industrial quality powders and stones in this and other relevant experiments, some possible explanations might
Large
be discussed. It is unlikely that the difference reflects a genuine surface or size effect. The
liq. N 2 —liq. He room—liq. N He room—liq. 2 673°K300°K
+0.038 —0.006 —0.029 —0.043
±0.009 ±0.040 ±0.023 ±0.034
—0.016 —0.083 —0.078 —0.114
±0.021 ±0.004 ±0.007 ±0.007
influence of7)crystal size0Mcanforbethe estimated to reduce small powder (Schoening by 5—12°K,depending on temperature. Specific 0M by about surface vibrations might reduce
Vol.7, No.1
X-RAY MEASUREMENT FOR DIAMOND AT LOW TEMPERATURES
12—15°K (Kothari). The observed differences are either much larger (points a and b) or in the opposite sense (points b and c). during Whether the different results are due to different grades of diamonds is difficult to decide because of the ill-defined origin of the powders. The X-ray patterns are identical but the E.S.R. spectra show a difference.* The slopes reflect any intensity changes which are temperature dependent and are a function of the diffraction angle. Static lattice distortions, if temperature dependent and originating from point defects, would affect the slopes, To raise the points c to the level of those for the small particles would require static displacements whose temperature change is of the same order of magnitude as that of the thermal displacements. The origin of such hypothetical static displacements is obscure.
*
Professor J.H.N. Loubser and Mr. L.A. Balona found for the fine powder the usual, although rather intense, nitrogen spectrum and for the coarse powder an additional, strong, broad line at g slightly larger than 2.0024.
17
All powders were boiled in aqua regis after milling. Some of the inclusions, which must have been in the large particles, have been exposed fracture and, subsequently might have been dissolved by the acids. It can therefore be expected that the small particles are, on the average, more perfect. In conclusion, there is no obvious explanation and the possibility of obtaining X-ray results around 1500°Kand around 1900°Kcannot be excluded. The suggestion by Barron et a!.4 that previously determined X-ray values around 1500°K require a revision of the atomic scattering curve for carbon, is not supported by the present result because they are independent of the atomic scattering factor.
Acknowledgements—The authors like to thank Dr. J.Vl. Matthews for taking the electron micrographs, Dr. P.T. Wedepohi for commenting on the manuscript and Mr. D.C. MacMurray for assistance with the experiments. An equipment grant from the Council for Scientific and Industrial Research is gratefully acknowledged. The diamond powders were kindly supplied by the Diamond Research Laboratory.
REFERENCES 1.
WARREN J.L., WENZEL R.G. and YARNELL J.L., Inelastic Scattering of Neutrons Vol.1, p.361. I.A.E.A., Vienna (1965).
2.
DOLLING G. and COWLEY R.A., Proc. phys. Soc. 88, 463 (1966).
3.
BLANCHARD R. and VARSHNI Y.P., Phys. Rev. 159, 599 (1967).
4.
BARRON T.H.K., KLEIN M.L., LEADSETTER A.J., MORRISON J.A. and SALTER L.S., Proc. 8th mt. Conf. Low Temperature Physics p. 415. Butterworths, London (1963).
5. 6.
HERBSTEIN F.H., Phil Mag. Suppi.. 10, 313 (1961). JAMES R.W., The Optical Principles of the Diffraction of X-rays. Bell, London (1962).
7.
SCHOENING F.R.L., Acta Crystallogr. A, in press.
8.
KOTHARI L.S., Phys. Lett. 24A, 382 (1967).
18
X-RAY MEASUREMENT FOR DIAMOND AT LOW TEMPERATURES
Die Debye Temperatur, 0M, von zwei industriellen Diamant Pulvern mit Teilchengrossen von 6~und 780A wurde mittels Rontgenbeugung bei Zimmertemperatur und den Temperaturen von flüssigem Helium und Stickstoff gemessen. Die Resultate sind verträglich mit 0M = 1880°Kfür das feine Pulver und 0M = 15000 für das grobe Pulver. Innerhalb der Fehlergrenzen ist em geringer Abfall von °M bei tiefen Temperaturen moglich. Da der Atomare Streufaktor nicht benutzt wurde, ist der Anspruch, dass frühere Resultate um 1500°K eine Revision des Streufaktors für Kohienstoff bedingen, nicht bestãtigt worden.
Vol.7, No. 1
Vol.7, pp. 15—18, 1969.
Pergamon Press.
Printed in Great Britain
X-RAY MEASUREMENT OF THE DEBYE TEMPERATURE FOR DIAMOND AT LOW TEMPERATURES F.R.L. Schoening and L.A. Vermeulen Department of Physics, University of the Witwatersrand, Johannesburg, South Africa (Received 4 September 1968)
-
The X-ray Debye temperature, ~ was measured at liq. He, liq. N2 and room temperature for two diamond powders of industrial quality, having a mean particle size of 6~and 780A respectively. The results are compatible with 6~~ 1880°Kfor the fine and °M~1500°K for the coarse powder. A slight decrease of OM at low temperatures is possible within the experimental errors. Because no use is made of the atomic scattering factor, the claim is not substantiated that previous results around 1500°Knecessitate a revision of the scattering factor curve for carbon.
INTRODUCTION
diamonds were used. Electron micrographs of the
THE X-RAY Debye temperature, °M, for diamond has attracted attention because its change at low temperature differs from that of Si and Ge and because of the large spread in its experimental values. Recent calculations of OM are based on dispersion curves measured by Warren et at.’ in inelastic neutron experiments. 2 havescattering fitted a lattice model toDolling the and Cowley dispersion curves and calculated frequency distributions which have a long parabolic region suggesting a nearly constant °M at low temperatures. Their data give 0M = 1860°K at 09< and 1869°Kat 77°K. In a similar approach Blanchard and Varshni3 obtain 1860°Kat 409< and 1882°Kat 300°K. Barron el al.4 estimate from heat capacity data that °M = 1890°Kat 0°K, 1920°K at room and 1970°Kat high temperatures. A decrease of 0M with decreasing temperature is indicated in these cases. In sharp contrast are 1491°Kand 1549°Kobtained for OM in reliable X-ray experiments at room temperatures (see review by Herbstein5).
coarse powder show well ‘rounded’ particles with a mean projected diameter of 6~. The small particles are very ragged having a mean diameter of 780A as confirmed by X-ray line broadening. The integrated intensities of the 533, 642, 822, 911, 664 and 844 reflections were measured at liq. He, liq. and room temperature using Mo radiation andN2a crystal monochromator between sample and detector. A few measurements were done at 300°Kand 673°K in a high temperature attachment. The poor peak to backround ratio (1.2—1.7) required long counting times and frequent repetitions. For the usual plot of the logarithm of the intensity ratios vs. A2 sin2O (James6), all data were corrected for thermal diffuse scattering and were combined by adjusting factors which were independent of ?C2 sin2 0. In general, the large particle data were well represented by straight lines, whilst the small particle data were sometimes difficult to fit by straight lines as is evident from the large uncertainties in some of the slopes. Equation (1) of reference 6 shows that the experimental slope depends on 0Mi and 0M2 which are characteristic of the low and high
EXPERIMENTAL A coarse and a fine powder of industrial 15
16
X-RAY MEASUREMENT FOR DIAMOND AT LOW TEMPERATURES
T
2400
2200 ~
L
0—c
-
2000
;isoo_j
Vol.7, No. 1
~
1600—I
1400
(
I
0
I
300 T(’K)
600
°M = 1880°Kat 300°K points a (large particles) and b (small particles) are obtained. Assuming 0M = 1500°K for the large particles points c are obtained. Calculations3 using the frequency spectrum give the horizontal curve.
FIG. 1. Assuming
temperatures T Slope
=
1 and T2 of the experiment. 1913 + T, ~F~-~--) /OM1\ 1 — MI
I
T 2
—
If it is assumed that the two samples have 0M values shown by the points a andforb the in Fig. obtained. To explain the points large1 are = 1880°Kat 300°K,constant volume
1
f6M2\
~jr-~
1
—
(1)
.
M2
M2J
RESULTS AND DISCUSSION Table 1 shows that between 4°Kand 77°K the slope for the small particles is positive whilst that for the large particles could be positive within one standard deviation. From (1) follows that the results are therefore compatible with a decrease of 0M with decreasing T. The large particle slopes are always more negative thereby indicating a lower average °M• However, on closer inspection widely different 0M vs. T curves can be derived from the experimental slopes. Table 1. Experimental slopes in Temperatures
Small
Particles
A2
particles the rather unlikely postulate has to be made that the frequency spectrum has changed 0MGe. withThese considerably towards that for Si and two elements show an increase of decreasing T. Within the errors, the data for the small particles agree with the predictions based on the frequency spectrum. If at room temperature 0M = 1500°K for the large particles, then points c are obtained. These are now reasonable in the sense that ~ is constant and, within the errors of the experiment, could decrease at low temperatures. Although such low 0M~ have been reported, the difference between the samples remains to be explained. In view of the use of industrial quality powders and stones in this and other relevant experiments, some possible explanations might
Large
be discussed. It is unlikely that the difference reflects a genuine surface or size effect. The
liq. N 2 —liq. He room—liq. N He room—liq. 2 673°K300°K
+0.038 —0.006 —0.029 —0.043
±0.009 ±0.040 ±0.023 ±0.034
—0.016 —0.083 —0.078 —0.114
±0.021 ±0.004 ±0.007 ±0.007
influence of7)crystal size0Mcanforbethe estimated to reduce small powder (Schoening by 5—12°K,depending on temperature. Specific 0M by about surface vibrations might reduce
Vol.7, No.1
X-RAY MEASUREMENT FOR DIAMOND AT LOW TEMPERATURES
12—15°K (Kothari). The observed differences are either much larger (points a and b) or in the opposite sense (points b and c). during Whether the different results are due to different grades of diamonds is difficult to decide because of the ill-defined origin of the powders. The X-ray patterns are identical but the E.S.R. spectra show a difference.* The slopes reflect any intensity changes which are temperature dependent and are a function of the diffraction angle. Static lattice distortions, if temperature dependent and originating from point defects, would affect the slopes, To raise the points c to the level of those for the small particles would require static displacements whose temperature change is of the same order of magnitude as that of the thermal displacements. The origin of such hypothetical static displacements is obscure.
*
Professor J.H.N. Loubser and Mr. L.A. Balona found for the fine powder the usual, although rather intense, nitrogen spectrum and for the coarse powder an additional, strong, broad line at g slightly larger than 2.0024.
17
All powders were boiled in aqua regis after milling. Some of the inclusions, which must have been in the large particles, have been exposed fracture and, subsequently might have been dissolved by the acids. It can therefore be expected that the small particles are, on the average, more perfect. In conclusion, there is no obvious explanation and the possibility of obtaining X-ray results around 1500°Kand around 1900°Kcannot be excluded. The suggestion by Barron et a!.4 that previously determined X-ray values around 1500°K require a revision of the atomic scattering curve for carbon, is not supported by the present result because they are independent of the atomic scattering factor.
Acknowledgements—The authors like to thank Dr. J.Vl. Matthews for taking the electron micrographs, Dr. P.T. Wedepohi for commenting on the manuscript and Mr. D.C. MacMurray for assistance with the experiments. An equipment grant from the Council for Scientific and Industrial Research is gratefully acknowledged. The diamond powders were kindly supplied by the Diamond Research Laboratory.
REFERENCES 1.
WARREN J.L., WENZEL R.G. and YARNELL J.L., Inelastic Scattering of Neutrons Vol.1, p.361. I.A.E.A., Vienna (1965).
2.
DOLLING G. and COWLEY R.A., Proc. phys. Soc. 88, 463 (1966).
3.
BLANCHARD R. and VARSHNI Y.P., Phys. Rev. 159, 599 (1967).
4.
BARRON T.H.K., KLEIN M.L., LEADSETTER A.J., MORRISON J.A. and SALTER L.S., Proc. 8th mt. Conf. Low Temperature Physics p. 415. Butterworths, London (1963).
5. 6.
HERBSTEIN F.H., Phil Mag. Suppi.. 10, 313 (1961). JAMES R.W., The Optical Principles of the Diffraction of X-rays. Bell, London (1962).
7.
SCHOENING F.R.L., Acta Crystallogr. A, in press.
8.
KOTHARI L.S., Phys. Lett. 24A, 382 (1967).
18
X-RAY MEASUREMENT FOR DIAMOND AT LOW TEMPERATURES
Die Debye Temperatur, 0M, von zwei industriellen Diamant Pulvern mit Teilchengrossen von 6~und 780A wurde mittels Rontgenbeugung bei Zimmertemperatur und den Temperaturen von flüssigem Helium und Stickstoff gemessen. Die Resultate sind verträglich mit 0M = 1880°Kfür das feine Pulver und 0M = 15000 für das grobe Pulver. Innerhalb der Fehlergrenzen ist em geringer Abfall von °M bei tiefen Temperaturen moglich. Da der Atomare Streufaktor nicht benutzt wurde, ist der Anspruch, dass frühere Resultate um 1500°K eine Revision des Streufaktors für Kohienstoff bedingen, nicht bestãtigt worden.
Vol.7, No. 1