The flight instructor reported that, during takeoff, the solo student pilot realized he had a crosswind from the right and applied right aileron and right rudder. He added that, as the student rotated the airplane, it drifted left. The student then lost airplane control, pulled the engine power to idle, and aborted the takeoff. Subsequently, during touchdown, the airplane veered hard to the left and exited the runway, and the nose landing gear collapsed. The airplane sustained substantial damage to the forward fuselage. The student pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The automated weather observation system at the accident airport reported that, about the time of the accident, the wind was calm. The student pilot was departing from runway 1.