In the crystal growth process, the temperature distribution and concentration distribution at the solid-liquid interface edge are always the hot problems. In this paper, we study the concentration distribution at the solid-liquid interface edge under the natural convection conditions, we find that the concentration field is oscillating exponential decline or rose along the crystal growth direction. We also study the dendrite morphology of Al-La alloys using the experimental method, the results show that the microstructure of Al-35%La alloys is different from the common microstructure of hypereutectic alloy during the conventional casting process, the first crystalline phase is Al11La3, which composition is discontinuous along the growth direction, the main dendrite is composed of α-Al alternating with Al11La3, the results of SEM and XRD show that the chemical composition along the main dendrite exhibits periodic behavior, therefore, this microstructure is named as periodic diphase dendrite structure.