changing values of a column in R while drawing reference from another column

Question

I have a dataset as follows:-

RATE    PriceDifference
84        0 
84        0
85        0
85        0
85        0
84        0
83.1      0

I want to replace all the values of 2nd column with the difference between this row's RATE and the previous row's RATE.

An example: The second row should have the value (84 - 84 =) 0 in PriceDifference. Similarly, the last row should have a value of -0.9 because 83.1 - 84 = 0.9