We report the structural, magnetic, and magnetocaloric properties of Co$_2$Cr$_{1-x}$Ti$_x$Al ($x=$ 0--0.5) Heusler alloys for spintronic and magnetic refrigerator applications. Room temperature X-ray diffraction and neutron diffraction patterns along with Rietveld refinements confirm that the samples are of single phase and possess a cubic structure. Interestingly, magnetic susceptibly measurements indicate a second order phase transition from paramagnetic to ferromagnetic where the Curie temperature (T$_{rm C}$) of Co$_2$CrAl increases from 330~K to 445~K with Ti substitution. Neutron powder diffraction data of the $x=$ 0 sample across the magnetic phase transition taken in a large temperature range confirm the structural stability and exclude the possibility of antiferromagnetic ordering. The saturation magnetization of the $x=$ 0 sample is found to be 8000~emu/mol (1.45~$mu_{rm B}$/{it f.u.}) at 5~K, which is in good agreement with the value (1.35$pm$0.05~$mu_{rm B}$/{it f.u.}) obtained from the Rietveld analysis of the neutron powder diffraction pattern measured at temperature of 4~K. By analysing the temperature dependence of the neutron data of the $x=$ 0 sample, we find that the change in the intensity of the most intense Bragg peak (220) is consistent with the magnetization behavior with temperature. Furthermore, an enhancement of change in the magnetic entropy and relative cooling power values has been observed for the $x=$ 0.25 sample. Interestingly, the critical behavior analysis across the second order magnetic phase transition and extracted exponents ($betaapprox$ 0.496, $gammaapprox$ 1.348, and $deltaapprox$ 3.71 for the $x=$ 0.25 sample) suggest the presence of long-range ordering, which deviates towards 3D Heisenberg type interactions above T$_{rm C}$, consistent with the interaction range value $sigma$.
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