Diamond and Related Materials, 2 (1993) 859-861
Thermal expansion of synthetic diamond single crystals at low temperatures K. Haruna Faculty q( b2ngineering, Tamagawa University, 6-1-1 Tamagawa-gakuen, Machida, Tokyo 194 (Japan)
H. Maeta Department q[' Physics, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, lbaraki 319-11 (Japan)
Abstract The thermal expansion of the lattice parameter of synthetic diamond single crystals has been measured in the range 4.2 H320 K by the Bond method. The thermal expansion coefficient calculated from the experimental results is very small (of the order of l0 v or less) and no definite evidence of negative thermal expansion is found within our relative experimental accuracy of the order of _+lxtO ~. We measured the temperature dependence of the lattice parameter of the synthetic diamond single crystals irradiated by high energy accelerated heavy ions, but its thermal expansion behaviour does not show a marked change.
Usually the lattice parameter of a cubic crystalline material increases with increasing temperature; so the linear thermal expansion coefficient is positive. Physically this positive thermal expansion is attributed to the fact that the lattice separation becomes wider with increasing temperature. However, there are many materials that show a negative thermal expansion coefficient, including Si, Ge, Gap and InP [! 3]. Such tetrahedrally bonded solids show negative values for the thermal expansion coefficient below approximately 100 K. These materials basically have diamond structures. Therefore it is very interesting to determine whether the diamond crystal has a negative thermal expansion coefficient or not in the low temperature region. Novikova  measured a relative change in length of the diamond crystal and reported a small negative thermal expansion between 40 and 90 K. Parsons , however, pointed out that Novikova's result was of the same order as the experimental error and the confirmation was incomplete. Since then no substantial measurement has been reported. In order to resolve this situation, we measured the lattice parameter of a synthetic diamond crystal using the Bond method with a relative accuracy of _+1 x 10 6 at low temperatures . Then we calculated the thermal expansion coefficients from our experiments. The negative thermal expansion was not confirmed even with this accuracy in our measurements . We have measured the lattice parameter of the irradiated single G a P crystals
and found a dose dependence of the thermal expansion behaviour in low temperature regions . This enables us to examine irradiated diamond crystal. The behaviour of thermal expansion does not show a marked change after irradiation by heavy ions.
The synthetic diamond single crystals used in our experiment were purchased from Sumitomo Denko Co., Ltd. The specimens were Ib type which contained less than 80 ppm N and had a yellow colour. They were thin square plates with dimensions of 3.5ram x 3.5 mm x 0.3 mm. The surfaces of the specimens were oriented parallel to the (100) plane. We measured two kinds of specimen: one as grown and the other irradiated with 100 MeV C 6+ ions up to fluences of 3.5 × 1015 ions cm 2 nearly at liquid-nitrogen temperature using a tandem accelerator. After the irradiation, the specimen was warmed to room temperature. The measurements were performed in a specially designed glass cryostat . To attain the highest possible accuracy, a finely focused K[3 line from an iron target was used, together with reflection from the (400) plane since these represented the highest possible reflection angle corresponding to (100) planes. The wavelength of the K[3 line was taken as 1.756 53 A. Before each measurement, the tilt angle of the specimen was carefully adjusted and the relative accuracy of + 1 x 10 6 was maintained in determining the lattice parameter. The temperature was varied
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K. Haruna, H. Maeta / Thermal expansion of diamond single crystals at low T
in the range 4.2-320 K and a precision of +0.1 K was maintained during the experiment.
3. Results and discussion
In Fig. 1, the lattice parameters of unirradiated diamond crystal in the temperature range 4.2-320 K are plotted (as open circles). The values are corrected for refraction, absorption and Lorentz factors. It is clearly shown that the lattice parameter is more or less constant between 4.2 and 90 K. This feature is considerably different from those observed in other tetrahedrally bonded solids. Since there is no distinct minimum in the lattice parameter in this wide temperature range, we conclude that diamond does not have negative thermal expansion behaviour within the precision of our measurement. The full circles in this figure show the lattice parameters of irradiated diamond. There is also no distinct minimum in the lattice parameter of this specimen at low temperatures, but overall lattice parameters of the irradiated diamond crystal increase at a rate of 4.32 x 10 -3 The thermal expansion coefficients are calculated from the observed lattice parameter values. The linear thermal expansion coefficient is defined by
1 da a(He) d T where a(He) is the lattice constant at liquid-He temperature. The calculated results are plotted in Fig. 2. The open circles shows the as-grown diamond data. The full curves give reasonable values of thermal expansion coefficients that are fitted to the fourth-order polynomial. These coefficients, determined by the method of least squares, are shown in Table 1. This shows that diamond has a very small thermal 3.5672
E 0 (3L
0 ° ° ~ ° ° ° ° ° ° ° ° ° °
3.5666 ~oo=~c~cooo=ooo o o ° ° 0
Temperature (K) Fig. 1. T e m p e r a t u r e d e p e n d e n c e of the lattice p a r a m e t e r for s y n t h e t i c single-crystal diamond.
P, e~ x
~ %~-~. 0 ~ 0
Fig. 2. Temperature dependence of the thermal expansion coefficient for syntheticsingle-crystaldiamond. T A B L E 1. Coefficients fitted to the f o u r t h - o r d e r p o l y n o m i a l for the t h e r m a l e x p a n s i o n coefficients o f s y n t h e t i c single c r y s t a l d i a m o n d ao al a2
0.00 5.05 x 10 - 1 ° - - 5 . 0 4 x 10 lz
a3 a4 __
7.79 x 1 0 - 1 4 - 1 . 0 1 × 10 16 __
expansion coefficient (of the order of 10 -s) below 100 K and that the lattice parameter is more or less constant between 4.2 and 90 K. This is caused by the very strong binding force of diamond. Recently Xu et al.  reported their theoretical result of the thermal expansion of diamond. They state that diamond does not show the same results as Si. The directional covalent bonding is much stronger in diamond than in Si. Thus the angular forces are dominant in diamond; the non-central forces favour positive Grfineisen behaviour. Their results support our experimental result. We may conclude that synthetic single-crystal diamond does not show a negative thermal expansion at low temperatures within our experimental precision. We measured the lattice parameter of the unirradiated G a P single crystals in the same temperature regions. The result shows a very small lattice parameter change at low temperatures . Then we measured the lattice parameter of the irradiated GaP single crystals. So we found the change in the thermal expansion behaviour in the low temperature regions . Therefore we measured the irradiated diamond crystal. The full circles in Fig. ! show the temperature dependence of thermal expansion coefficients of the specimen irradiated by high energy accelerated heavy ions. The measured temperature region is the same as for the unirradiated specimen. Since there is no distinct minimum in the plot of the lattice parameter over a wide low temperature range, we
K. Haruna, H. Maeta / Thermal expansion of diamond single crystals at low T
also observe that there is no negative thermal expansion in the irradiated diamond single crystal as far as the precision of our measurement allows. The reason why the diamond behaviours is different from the irradiated GaP crystal behaviour is due to the very large binding force of diamond.
4. Conclusions We measured the temperature dependence of the lattice parameters for as-grown synthetic diamond single crystals and a specimen irradiated by high energy accelerated heavy ions in the temperature range 4.2-320 K. Diamond has nearly constant lattice parameters between 4.2 and 90 K. We calculated the thermal expansion coefficients of the as-grown diamond single crystal. From these results, we concluded that diamond does not show a negative thermal expansion coefficient phenomenon within our experimental error. Further, we
conclude that the irradiation of the high energy accelerated heavy ions does not affect the thermal expansion of diamond.
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