The relationship between chemical composition, density, and refractive index was proposed as a means of examining gasses and solutions (Gladstone, Dale(1863), Phil. Trans, 153, 317). This relationship is as follows:
(n - 1) / d = constant
Where
n = mean index of refraction
D = density
constant = Gladstone-Dale constant
The practice of using the Gladstone-Dale relationship to minerals only gives an approximation because of the effects that different crystal systems have on the anisotropy of the crystal lattice and the resultant values of n (index of refraction).
Mandarino, in his review of the Gladstone-Dale relationship in minerals (Can, Min, (1981), Vol 19, pp 441-450) proposed the concept of the Compatibility Index in comparing the physical and optical properties of minerals. This compatibility index is a required calculation for approval as a new mineral species (see IMA guidelines).
The compatibility index (CI) is defined as follows:
CI meas = (1 - KPDmeas / KC )
CI calc = (1 - KPDcalc / KC )Where
KP = Gladstone-Dale Constant derived from physical properties
Where
KPDcalc = (n - 1) / Dcalc
KPDmeas = (n - 1) / Dmeasand
KC = SUM OF (k1p1/100 + k2p2/100... + knpn/100). The Gladstone-Dale constant estimated from chemical analysis
Where
kc = Gladstone-Dale constant of chemical phase "n"
kp = Percentage of the chemical phase "n"
The internal consistency of the Compatibility Index is defined by the following Table of values which describe the "Goodness" of the mineral data.
| Compatibility Index | Category |
| ± 0.000 to ± 0.019 | Superior |
| ± 0.020 to ± 0.039 | Excellent |
| ± 0.040 to ± 0.059 | Good |
| ± 0.060 to ± 0.079 | Fair |
| > ± 0.079 | Poor |
The calculation of the Compatibility Index is based on the values of the chemical composition, index of refraction, and calculated or observed density for each mineral species and is included in the optical section of the mineral species description.
The following graph illustrates the application of Mandarino's Compatibility Index (CI) to the minerals in this database:
Of all the minerals (2,679) where the CI is applicable (excluding elements, sulfides, halides, and bad oxide analysis), there are 2,180 minerals with a CI of 0.079 or better.
Conversely, 18.6% of of the 2,679 minerals have a CI rating of "Poor".
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