Three serious misuses of the phi-notation have developed since its introduction by Krumbein as the expression of a logarithmic transformation of grain diameters in millimeters. These misuses are: 1) the mistaken correlation of "phi " and "millimeters," 2) the misuse of phi in the expression of values of the standard deviation, and 3) the misuse of "phi-units" as dimensions. These errors have led to a confused interpretation of the meaning of phi . The suggested redefinition of phi as the negative logarithm of the ratio of a grain diameter to a standard diameter is shown to rectify the confusion.
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Dean A. McManus (1963) studied this question.