A series of polycrystalline SmO1-xFxFeAs bulks (x=0.15, 0.2, 0.3 and 0.4) were prepared by the conventional solid state reaction. Resistivity, susceptibility, magnetic hysteresis, critical current density and microstructure of these samples have been investigated. It is found that critical transition temperature Tc increases steadily with increasing fluorine content, with the highest onset Tc=53 K at x=0.4. On the other hand, the superconductivity seems correlated with lattice constants; that is, Tc rises with the shrinkage of a-axis while resistivity increases with the enlargement of c-axis. A global critical current density of 1.1x10^4 A/cm^2 at 5 K in self field was achieved in the purest sample. A method of characterization of inter-grain current density is proposed. This method gives an inter-grain Jc of 3.6x10^3 A/cm^2 at 5 K in self field, in contrast to the intra-grain Jc of 10^6 A/cm^2. The effect of composition gradients on the inter-grain Jc in SmO1-xFxFeAs is also discussed.
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