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Phase Diagrams & Computational Thermodynamics

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Solder Systems

It is desirable, where practicable, to remove lead-containing components from commercial products for environmental considerations. One area where lead is extensively used is in lead-based solders. New lead-free solders must have the appropriate melting temperatures and freezing ranges, in order to be compatible with existing equipment and components. A thermodynamic database can be used to predict these properties and also show the effects of non-equilibrium solidification. The results from these predictions can be used to eliminate candidate solder alloys for which the calculation revealed unsuitable freezing temperature and range from further testing.

Different types of calculated systems must be distinguished:

  • Assessed systems: A critical evaluation of available experimental data was used to derive a thermodynamic description of the multicomponent system. If experimental data were only available or considered for part of the system then a partial assessment is possible.
  • Extrapolated systems: The analytical descriptions of constituent subsystems are combined and used to predict the multicomponent system, even for compositions and temperatures which have not been experimentally evaluated. Depending on the complexity of the multicomponent system this prediction will be more or less accurate.

This webpage contains a collection of calculated binary and ternary systems that are relevant to solders. The thermodynamic descriptions of these systems are compiled in database files which can be downloaded. Examples for the application of these systems can be found in our papers on solders.

Binary Systems


Ternary Systems


Thermodynamic Database (Sn - Ag - Bi - Cu - Pb)

Condensed Phases

Common NamesPrototypeSpacegroupModel*
Liquidn/aL, L1, L2n/an/a(Ag,Bi,Cu,Pb,Sn)1
FccA1(Ag), (Cu), (Pb)CuFm-3m(Ag,Bi,Cu,Pb,Sn)1(Va)1
BccA2(beta Cu)WIm-3m(Cu,Sn)1(Va)3
HcpA3(zeta Ag), (epsilon Pb)MgP63/mmc(Ag,Bi,Pb,Sn)1(Va)0.5
BctA5(Sn), (beta Sn)beta SnI41/amd(Ag,Bi,Cu,Pb,Sn)1
RhoA7(Bi)alpha AsR-3m(Bi,Pb,Sn)1
Ag3SnD0alphaepsilonbeta Cu3TiPmmn(Ag)0.75(Sn)0.25

*Major species are printed bold face

Thermodynamic Database Files

Thermo-Calc format database file

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