L.C. Leu et al. Materials Chemistry and Physics 56(1998)256-261 thus results. Substituting the above values into Eqs.(1)and (2), volumes of the cap and the droplet of about 1. 136r. and 4.135ra are obtained, respectively. Fig 3(a)was obtained erupting the vapor-phase reaction at the end of the nucleation stage. The constituents of SiC whiskers should be about to be saturated in the liquid droplet in order to be able to precipitate at the solid-liquid interface. It is reasonable to argue that the volume of the liquid droplet (or liquid cap) ge, since no significant volume increase due to all Fig. 4. Schematic cross sections taken through the center of wh would be possible, As a consequence, the assumption of constant volume for both the liquid cap on the graphite sub rate and liquid droplet on the whisker tip could be employe to estimate their dimensional relationships. The following impurities were used as liquid-forming agents for SiC expression can be deduced whisker growth, respectively. The reported values of the ratio of the droplet diameter(2ra) to the whisker diameter(2rw) fell within the ranges 1.7-2. 1 and 3-3.5, respectively, as After appropriate algebraic operat compared to about 1. 5-2 for whiskers obtained from Ni n. a rato containing droplets in the present study [15]. The difference 1. 538: 1 is obtained. The value of rw. as shown in Fig. 2(b)is in the values accounts for the fact that droplet size as well as equal to the product of ra and sin Bz. The dimensional rela- tionship between re, ra and rw is therefore represented the ratio of droplet diameter to whisker diameter cannot nec essarily be the dominant factor in determining the diameter with experimentally measured values for the whisker indi- of the whiskers grown. The conclusion can generally be cated by an arrow in Fig 3(b), where the values of the anism. another observation to explain the effect of wetting diameter(2re, 2ra and 2rw )measured at different sections of whisker are 13. 1,8.8 and 4.5 mm, respectively. A measured characteristics on whisker diameter is the presence of knotted dimensional relationship of 1.49: 1: 0.51 can be obtained. In whiskers or the periodic variation of whisker diameter along its axis with essentially the same volume of liquid droplet view of the changes in wetting characteristics of liquid drop- located on the whisker tip. It was found that changes in wet- lets during whisker growth, especially at the transient growth stage exhibiting a consequently variable whisker diameter, ting characteristics caused by perturbations in supersaturation the reported conclusion 10] that the diameter of whiskers is of the liquid solution might give rise to the growth of a determined by the diameter of liquid droplets can only be whisker with variable diameter along its axis [14, 17] valid in the steady-state growth stage with the characteristic In addition to the abovementioned factor in determinin of an essentially constant contact angle the diameter of whiskers grown by the vls mechanism, the According to the above results and discussion, a general effect of CVd of Sic on the lateral surface of whiskers should conclusion can be drawn that applies to all whiskers grown also be discussed. That is, the thickening process by two- by the VLS mechanism. The exact factor for determining th diameter of a VLS-grown whisker is the contact area of the during CVD should not be overlooked. The JANAF Ther solid-liquid interface from which the crystal precipitates. The mochemical Tables [18] indicate that the Gibbs free energy wetting behavior, characterized by the value of the contact change for the decomposition of MTS becomes negative at angle, may vary during whisker growth. It is especially true temperatures higher than 800C. However, due to the exis that at the initial stage of whisker growth a tapered cross tence of a nucleation barrier for the formation of Sic crystal section grown from a liquid droplet with increasing contact lites, nothing could be found even at temperatures above angle will be found prior to the transition to the steady-state 1150"C with the low reactant concentration employed in the growth stage. Even with the appropriate choice of the kind deposition runs without the addition of liquid-forming agent of liquid-forming agent, the volume of liquid droplets is ne [12]. Under conditions when the nucleation barriers are once not necessarily the decisive factor for determining the reduced by the assistance of other kinetic factors, the vapor- whisker diameter. As a consequence, a liquid droplet with a solid(vs)deposition of Sic could occur continuously and large volume located on a whisker having a small diameter contribute to the increase in the radial dimension of whiskers. might be possible due to its large contact angle. On the other The growth kinetics concerning the increase in the radial nd,a small contact angle for a liquid cap on a whisker dimension during Ni-activated whisker preparation have crystal would lead to the growth of a whisker with the same been found and will be discussed in detail elsewhere [15] diameter for only a small volume of liquid-forming agent An explanation underlying the nucleation and growth mech- added. The results are depicted in Fig 4 and can be verified anism for whisker thickening will be employed to clarify the as compared with those reported by Bootsma et al. [14] and apparently contradictory arguments mentioned above. Wag DeJong and Mc Cauley [6], where iron and iron-containing ner and Ellis [2] proposed a mechanism in which the pres-L-C. Leu et al. / Materials Chemistry and Physics 56 (1998) 256-262 259 thus results. Substituting the above values into Eqs. ( 1 ) and (2), volumes of the cap and the droplet of about 1.136r; ~ and 4.135rd 3 are obtained, respectively. Fig. 3(a) was obtained by interrupting the vapor-phase reaction at the end of the nucleation stage. The constituents of SiC whiskers should be about to be saturated in the liquid droplet in order to be able to precipitate at the solid-liquid interface. It is reasonable to argue that the volume of the liquid droplet (or liquid cap) would be essentially the same after passing the nucleation stage, since no significant volume increase due to alloying would be possible. As a consequence, the assumption of constant volume for both the liquid cap on the graphite sub￾strate and liquid droplet on the whisker tip could be employed to estimate their dimensional relationships. The following expression can be deduced: V~ ~r = 1.136re 3 = 4.1351h 3 = Vdropie t After appropriate algebraic operation, a ratio rc:rd = 1.538:1 is obtained. The value of rw as shown in Fig. 2 (b) is equal to the product of ru and sin0,. The dimensional rela￾tionship between to, rd and r,,, is therefore represented as ro:rd:rw = 1.538:1:0.5. The result is in reasonable agreement with experimentally measured values for the whisker indi￾cated by an arrow in Fig. 3(b), where the values of the diameter ( 2r¢, 2r~ and 2r,,.) measured at different sections of a whisker are 13.1, 8.8 and 4.5 re_m, respectively. A measured dimensional relationship of 1.49:1:0.51 can be obtained. In view of the changes in wetting characteristics of liquid drop￾lets during whisker growth, especially at the transient growth stage exhibiting a consequently variable whisker diameter, the reported conclusion [ 10] that the diameter of whiskers is determined by the diameter of liquid droplets can only be valid in the steady-state growth stage with the characteristic of an essentially constant contact angle. According to the above results and discussion, a general conclusion can be drawn that applies to all whiskers grown by the VLS mechanism. The exact factor for determining the diameter of a VLS-grown whisker is the contact area of the solid-liquid interface from which the crystal precipitates. The wetting behavior, characterized by the value of the contact angle, may vary during whisker growth. It is especially true that at the initial stage of whisker growth a tapered cross section grown from a liquid droplet with increasing contact angle will be found prior to the transition to the steady-state growth stage. Even with the appropriate choice of the kind of liquid-forming agent, the volume of liquid droplets is now not necessarily the decisive factor for determining the whisker diameter. As a consequence, a liquid droplet with a large volume located on a whisker having a small diameter might be possible due to its large contact angle. On the other hand, a small contact angle for a liquid cap on a whisker crystal would lead to the growth of a whisker with the same diameter for only a small volume of liquid-forming agent added. The results are depicted in Fig. 4 and can be verified as compared with those reported by Bootsma et al. [ 14] and DeJong and McCauley [6], where iron and iron-containing d,, Fig. 4. Schematic cross sections taken through the center of whiskers with the same diameter but gTown from liquid droplets having different volumes. (Volume of droplet A is smaller than that of droplet B.) impurities were used as liquid-forming agents for SiC whisker growth, respectively. The reported values of the ratio of the droplet diameter (2re) tO the whisker diameter (2r,~) fell within the ranges 1.7-2.1 and 3-3.5, respectively, as compared to about 1.5-2 for whiskers obtained from Ni￾containing droplets in the present study [ 15]. The difference in the values accounts for the fact that droplet size as well as the ratio of droplet diameter to whisker diameter cannot nec￾essarily be the dominant factor in determining the diameter of the whiskers grown. The conclusion can generally be applied to various whisker crystals grown by the VLS mech￾anism. Another observation to explain the effect of wetting characteristics on whisker diameter is the presence of knotted whiskers or the periodic variation of whisker diameter along its axis with essentially the same volume of liquid droplet located on the whisker tip. It was found that changes in wet￾ting characteristics caused by perturbations in supersaturation of the liquid solution might give rise to the growth of a whisker with variable diameter along its axis [ 14,17]. In addition to the abovementioned factor in determining the diameter of whiskers grown by the VLS mechanism, the effect of CVD of SiC on the lateral surface of whiskers should also be discussed. That is, the thickening process by two￾dimensional nucleation and growth in the radial direction during CVD should not be overlooked. The JANAF Ther￾mochemical Tables [18] indicate that the Gibbs free energy change for the decomposition of MTS becomes negative at temperatures higher than 800°C. However, due to the exis￾tence of a nucleation barrier for the formation of SiC crystal￾lites, nothing could be found even at temperatures above 1150°C with the low reactant concentration employed in the deposition runs without the addition of liquid-forming agent [ 12 ]. Under conditions when the nucleation barriers are once reduced by the assistance of other "kinetic factors, the vapor￾solid (VS) deposition of SiC could occur continuously and contribute to the increase in the radial dimension of whiskers. The growth kinetics concerning the increase in the radial dimension during Ni-activated whisker preparation have been found and will be discussed in detail elsewhere [ 15]. An explanation underlying the nucleation and growth mech￾anism for whisker thickening will be employed to clarify the apparently contradictory arguments mentioned above. Wag￾ner and Ellis [2] proposed a mechanism in which the pres-