Determination of constant strain gradients of elastically bent crystal using X-ray mirage fringes

Two experimental approaches are studied to determine a parameter of the strain gradient in an elastically bent crystal. In one approach, the parameter is determined by measuring the third peak of the X-ray mirage interference fringes and in the other, by measuring the region where no mirage diffraction beam reaches on the lateral surface of the crystal. Using the X-rays from synchrotron radiation, the mirage fringes have been observed in the 220 reflection of the Si crystal whose strain is controlled in cantilever bending. These two approaches both give accurate values of the parameter of the strain gradient, showing good agreement with the values calculated using elastic theory. In addition, the residual strain due to gravity is observed by measuring mirage fringes when the bending force becomes zero.