D. Loidl et al. Carbon 41(2003)563-570 0010020.030.04005006 3,48 56 2[A Fig. 8.(a) The effective shear modulus ger obtained from Eq. (8b) increases with increasing orientation parameter. The symbols are defined in Fig. 2. The lines are the values obtained for the single crystallites ge by Eq.(3)for MPP- and PAN-based fibers.(b)The eff shear modulus plotted versus the layer spacing dooz There is an additional increase in the shear modulus geff, calculated from Eq. (8b), with increasing orientation 1. The Young's modulus er of the graphene planes parameter as well as with increasing lattice distance dooz decreases with increasing orientation parameter, but (Fig. 8). This effect is much greater than the relatively shows a constant value of e=1140+ 10 GPa for fibers small increase of the crystallite shear modulus for MPP with the highest preferred orientation. This value is fibers and is equally observed for PAN fibers, where the larger than that of graphite, but is coincident with actual crystallite shear modulus was nearly constant( Fig. 6). The measurements of the Youngs modulus of carbon results may be described by supplementing the effective nanotubes constant shear modulus ger by an additional part g(zo -Zi) 2. The half-width of the 002 reflection decreases with depending on the orientation parameter, gerr=gr+ ng load nearly linearly for PAN-based fibers g(zo -Zi). We give here two possible interpretations of MPP-based fibers exhibit a much stronger and these results, which do not necessarily exclude each other linear decrease, which is not predicted by the One is that cross-links located at the crystallite boundaries models are responsible, which are favored by greater misorient- 3. The mean value of the shear modulus ger of the tion angles of the crystallites. The other possibility is that crystallites was evaluated to be g=4.5+0.2 GPa the fibers are built up as(nano-)composites, which would MPP-based and ger 13.6*0.9 GPa for PAN-based also lead to an increase in the shear modulus. The latter fibers. Whereas nearly no dependence of crystallite assumption is supported by the possible existence of two shear modulus on stress was observed for pan fibers it phases, in particular in MPP fibers [30], and by experimen- increases to a greater extent the higher the orientation of tal observation of the arrangement of the crystallites in the mPp fibers aligned micro-domains as suggested by HR-SEM [ 40. 4. With the additional knowledge of the effective Youngs However, concise theoretical models should be developed modulus of the fibers, the shear modulus g er can be to clarify the role of the crystallites, their elastic properties obtained within the framework of the uniform stress of the intel model, which increases from the value of g. with creasing orientation parameter Cross-links located at the crystallite boundaries or a composite cha 6. Conclusions he material are possible explanations for this behavior. 5. Existing models based on crystallites with identical and Microbeam X-ray diffraction is able to provide detailed onstant modulus and only different orientation should quantitative information on the development of the inner be improved. The experimental results suggest that structure and its relation to the mechanical properties of neither the Youngs modulus of the crystallites nor the carbon fibers during in-situ loading. The following param- effective shear modulus are constant, but depend on the eters show a dependence on the applied stress initial orientation parameter.D. Loidl et al. / Carbon 41 (2003) 563–570 569 Fig. 8. (a) The effective shear modulus geff obtained from Eq. (8b) increases with increasing orientation parameter. The symbols are defined as in Fig. 2. The lines are the values obtained for the single crystallites g by Eq. (3) for MPP- and PAN-based fibers. (b) The effective cr shear modulus plotted versus the layer spacing d . 002 There is an additional increase in the shear modulus g , eff calculated from Eq. (8b), with increasing orientation 1. The Young’s modulus e of the graphene planes cr parameter as well as with increasing lattice distance d decreases with increasing orientation parameter, but 002 (Fig. 8). This effect is much greater than the relatively shows a constant value of e 5 1140610 GPa for fibers cr small increase of the crystallite shear modulus for MPP with the highest preferred orientation. This value is fibers and is equally observed for PAN fibers, where the larger than that of graphite, but is coincident with actual crystallite shear modulus was nearly constant (Fig. 6). The measurements of the Young’s modulus of carbon results may be described by supplementing the effective nanotubes. constant shear modulus g by an additional part g(Z 2 Z ) 2. The half-width of the 002 reflection decreases with cr 0 1 depending on the orientation parameter, g 5 g 1 increasing load nearly linearly for PAN-based fibers. eff cr g(Z 2 Z ). We give here two possible interpretations of MPP-based fibers exhibit a much stronger and non- 0 1 these results, which do not necessarily exclude each other. linear decrease, which is not predicted by the actual One is that cross-links located at the crystallite boundaries models. are responsible, which are favored by greater misorienta- 3. The mean value of the shear modulus g of the cr tion angles of the crystallites. The other possibility is that crystallites was evaluated to be g 5 4.560.2 GPa for cr the fibers are built up as (nano-)composites, which would MPP-based and gcr 5 13.660.9 GPa for PAN-based also lead to an increase in the shear modulus. The latter fibers. Whereas nearly no dependence of crystallite assumption is supported by the possible existence of two shear modulus on stress was observed for PAN fibers, it phases, in particular in MPP fibers [30], and by experimen- increases to a greater extent the higher the orientation of tal observation of the arrangement of the crystallites in the MPP fibers. aligned micro-domains as suggested by HR-SEM [40]. 4. With the additional knowledge of the effective Young’s However, concise theoretical models should be developed modulus of the fibers, the shear modulus g can be eff to clarify the role of the crystallites, their elastic properties obtained within the framework of the uniform stress and the properties of the interface. model, which increases from the value of g with cr increasing orientation parameter. Cross-links located at the crystallite boundaries or a composite character of 6. Conclusions the material are possible explanations for this behavior. 5. Existing models based on crystallites with identical and Microbeam X-ray diffraction is able to provide detailed constant modulus and only different orientation should quantitative information on the development of the inner be improved. The experimental results suggest that structure and its relation to the mechanical properties of neither the Young’s modulus of the crystallites nor the carbon fibers during in-situ loading. The following param- effective shear modulus are constant, but depend on the eters show a dependence on the applied stress: initial orientation parameter