Pearl Nacre Thickness Estimate

Model minimum/maximum nacre thickness around eccentric spherical nucleus with exact nonoverlap shell volume; ideal measured geometry does not establish natural/cultured origin or actual uniform nacre quality.

Description

Nacre thickness around a spherical nucleus varies when that nucleus is offset inside the pearl.

Nacre thickness around a spherical nucleus varies when that nucleus is offset inside the pearl. An ideal spherical model can report extreme thicknesses without assuming a centered nucleus.^[1]

When to use Pearl Nacre Thickness Estimate

Use this tool to model minimum/maximum nacre thickness around eccentric spherical nucleus with exact nonoverlap shell volume; ideal measured geometry does not establish natural/cultured origin or actual uniform nacre quality.

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.

How to use Pearl Nacre Thickness Estimate and understand its results

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
Enter outerPearlRadiusMm, nucleusRadiusMm, nucleusCenterOffsetMm using the field table and calculation rules, then run the tool.
Read minimumModelNacreThicknessMm, maximumModelNacreThicknessMm, sphericalShellVolumeMm3. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
outerPearlRadiusMm	Outer pearl radius mm	number	Required
nucleusRadiusMm	Nucleus radius mm	number	Required
nucleusCenterOffsetMm	Nucleus center offset mm	number	Required

Use positive outer radius, nonnegative nucleus radius and center offset in mm, with nucleus radius+offset≤outer radius. Return minimum/maximum thickness and shell mm³ using a stable factored volume difference.

minimum/maximum thickness=outer radius−nucleus radius∓offset; shell volume=4π(R³−r³)/3

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
minimumModelNacreThicknessMm	Minimum model nacre thickness mm	number
maximumModelNacreThicknessMm	Maximum model nacre thickness mm	number
sphericalShellVolumeMm3	Spherical shell volume mm3	number

json

{
  "input": {
    "outerPearlRadiusMm": 5,
    "nucleusRadiusMm": 3,
    "nucleusCenterOffsetMm": 1
  },
  "output": {
    "minimumModelNacreThicknessMm": 1,
    "maximumModelNacreThicknessMm": 3,
    "sphericalShellVolumeMm3": 410.5014400690663
  }
}

Limitations and assumptions

Actual non-spherical geometry, nacre quality and natural/cultured origin are not established.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Pearl Size Millimeter Sieve Classifier: Classify measured pearl diameter with caller sieve bands and boundary uncertainty, preserving multiple possible sizes; no invented exact size at ambiguous screen boundary. For a complementary task, use Opal Doublet Thickness Check: Correct caller microscopy top/backing intercepts for oblique section geometry and audit top fraction; two-layer geometry does not identify opal, treatment or adhesive condition.

References

Pearl Nacre Thickness Estimate — tool.io

Similar or alternative tools

Pearl Size Millimeter Sieve Classifier
Classify measured pearl diameter with caller sieve bands and boundary uncertainty, preserving multiple possible sizes; no invented exact size at ambiguous screen boundary.
Opal Doublet Thickness Check
Correct caller microscopy top/backing intercepts for oblique section geometry and audit top fraction; two-layer geometry does not identify opal, treatment or adhesive condition.