A Stiff diagram, or Stiff pattern, is a graphical representation of chemical analyses, first developed by H.A. Stiff in 1951. It is widely used by
hydrogeologists and
geochemists to display the major ion composition of a
water sample. A polygonal shape is created from four parallel horizontal axes extending on either side of a vertical zero axis.
Cations
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
are plotted in
milliequivalents
An equivalent (symbol: officially equiv; unofficially but often Eq) is the amount of a substance that reacts with (or is ''equivalent'' to) an arbitrary amount (typically one mole) of another substance in a given chemical reaction. It is an archa ...
per liter on the left side of the zero axis, one to each horizontal axis, and
anions
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
are plotted on the right side. Stiff patterns are useful in making a rapid visual comparison between water from different sources. An alternative to the Stiff diagram is the
Maucha diagram A Maucha diagram, or Maucha symbol, is a graphical representation of the major cations and anions in a chemical sample. R. Maucha published the symbol in 1932.
It is mainly used by biologists and chemists for quickly recognising samples by their ...
.
Stiff diagrams can be used:
:1) to help visualize ionically related waters from which a flow path can be determined, or;
:2) if the flow path is known, to show how the ionic composition of a water body changes over space and/or time.
A typical Stiff diagram is shown in the figure (right). By standard convention, Stiff diagrams are created by plotting the equivalent concentration of the cations to the left of the center axis and anions to the right. The points are connected to form the figure. When comparing Stiff diagrams between different waters it is important to prepare each diagram using the same ionic species, in the same order, on the same scale.
Environmental laboratories typically report concentrations for anion and cation parameters using units of mass/volume, usually mg/L. In order to convert the mass concentration to an equivalent concentration the following mathematical relationship is used:
:(mass concentration) * (ionic charge) / (molecular weight) = (equivalent concentration)
For example, a water with a calcium concentration of 120 mg/L would have the following calcium equivalent concentration:
:(120 mg/L) * (2 meq/mmol) / (40 mg/mmol) = 6 meq/L
Software programs in common use
HyCACommercial software available fro
KWR waterwareAqQACommercial software available fro
RockWare, Inc.AquaChemCommercial software fro
Schlumberger Water ServicesChemPoint ProCommercial software fro
Starpoint software, Inc.Commercial software fro
Sanitas Technologies LLC*
The Geochemist's Workbench Commercial software fro
Aqueous Solutions LLCGWB Community EditionFree community edition of the popular geochemical modeling software package.
*
RockWorks Utilities Commercial software from RockWare, Inc.
*
EnviroInsite Commercial software from HydroAnalysis, Inc.
Python ScriptsFree open-source
Python scripts that can plot stiff diagrams.
References
*Fetter. ''Applied Hydrogeology'', 4th Edition. 2001. p. 376
*Drever, James I. ''The Geochemistry of Natural Waters, Surface and Groundwater Environments'', Third Edition. Upper Saddle River, NJ:
Prentice Hall
Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari B ...
, 2002.
*Stiff, H.A., Jr., 1951, The interpretation of chemical water analysis by means of patterns: Journal of Petroleum Technology, v. 3. no. 10, section 1: p15,16 and section 2: p3.
Analytical chemistry
Water chemistry