Sketch the monoclinic x-y-z reference axes. The x- and y-axes are separated by 90 degrees. The z-axis is not perpendicular to the x-y plane. The acute angle between the x-y plane and the z-axis changes for different monoclinic materials. The axes do not need to be drawn to scale.
Draw the monoclinic unit cell on the monoclinic reference axes.
Label the points along each axis where the crystal faces intercept the axes. If the unit cell is drawn at the origin of the frame of reference, then there will be three cell faces that pass through the origin and three that do not. Only label the axis-intercepts for those faces that do not pass through the origin. For example, a face that is parallel to the x-z-plane may cut the y-axis at 5. The y-intercept is 5. This face would never cut the x- or z-axis, so the intercepts for those axes are set at infinity.
Find the reciprocal of the intercept points. The reciprocal of a number is found by inverting the number. For example, if the intercepts are x = infinity, y = 5 and z = infinity, then the reciprocal of these intercepts is: 0; 0.2; 0 = 1/infinity; 1/5; 1/infinity.
Write the reciprocal of the intercepts as integers. Find a common denominator and multiply all the intercepts by it. For example, the reciprocal intercepts 0; 1/5; 0 have a common denominator of 5. Multiplying throughout by 5 yields integer reciprocal intercepts of: 0; 1; 0 = (0 x 5); (0.2 x 5); (0 x 5).
Convert the integer reciprocal intercepts to a specific planar Miller index by enclosing the intercepts in brackets. For example, the index of the plane with integer reciprocal intercepts of: 0; 1; 0 is (0; 1; 0).