Material

General considerations

In nature, materials (chemical compounds, mixtures) are made of elements, and elements are made of isotopes. Geant4 has three main classes designed to reflect this organization. Each of these classes has a table, which is a static data member, used to keep track of the instances of the respective classes created.

G4Isotope

This class describes the properties of atoms: atomic number, number of nucleons, mass per mole, etc.

G4Element

This class describes the properties of elements: effective atomic number, effective number of nucleons, effective mass per mole, number of isotopes, shell energy, and quantities like cross section per atom, etc.

G4Material

This class describes the macroscopic properties of matter: density, state, temperature, pressure, and macroscopic quantities like radiation length, mean free path, dE/dx, etc.

Only the G4Material class is visible to the rest of the toolkit and used by the tracking, the geometry and the physics. It contains all the information relevant to its constituent elements and isotopes, while at the same time hiding their implementation details.

Introduction to the Classes

G4Isotope

A G4Isotope object has a name, atomic number, number of nucleons, mass per mole, and an index in the table. The constructor automatically stores “this” isotope in the isotopes table, which will assign it an index number. The G4Isotope objects are owned by the isotopes table, and must not be deleted by user code.

G4Element

A G4Element object has a name, symbol, effective atomic number, effective number of nucleons, effective mass of a mole, an index in the elements table, the number of isotopes, a vector of pointers to such isotopes, and a vector of relative abundances referring to such isotopes (where relative abundance means the number of atoms per volume). In addition, the class has methods to add, one by one, the isotopes which are to form the element.

The constructor automatically stores “this” element in the elements table, which will assign it an index number. The G4Element objects are owned by the elements table, and must not be deleted by user code.

A G4Element object can be constructed by directly providing the effective atomic number, effective number of nucleons, and effective mass of a mole, if the user explicitly wants to do so. Alternatively, a G4Element object can be constructed by declaring the number of isotopes of which it will be composed. The constructor will “new” a vector of pointers to G4Isotopes and a vector of doubles to store their relative abundances. Finally, the method to add an isotope must be invoked for each of the desired (pre-existing) isotope objects, providing their addresses and relative abundances. At the last isotope entry, the system will automatically compute the effective atomic number, effective number of nucleons and effective mass of a mole, and will store “this” element in the elements table.

A few quantities, with physical meaning or not, which are constant in a given element, are computed and stored here as “derived data members”.

Using the internal Geant4 database, a G4Element can be accessed by atomic number or by atomic symbol (“Al”, “Fe”, “Pb”…). In that case G4Element will be found from the list of existing elements or will be constructed using data from the Geant4 database, which is derived from the NIST database of elements and isotope compositions. Thus, the natural isotope composition can be built by default. The same element can be created as using the NIST database with the natural composition of isotopes and from scratch in user code with user defined isotope composition.

G4Material

A G4Material object has a name, density, physical state, temperature and pressure (by default the standard conditions), the number of elements and a vector of pointers to such elements, a vector of the fraction of mass for each element, a vector of the atoms (or molecules) numbers of each element, and an index in the materials table. In addition, the class has methods to add, one by one, the elements which will comprise the material.

The constructor automatically stores “this” material in the materials table, which will assign it an index number. The G4Material objects are owned by the materials table, and must not be deleted by user code.

A G4Material object can be constructed by directly providing the resulting effective numbers, if the user explicitly wants to do so (an underlying element will be created with these numbers). Alternatively, a G4Material object can be constructed by declaring the number of elements of which it will be composed. The constructor will “new” a vector of pointers to G4Element and a vector of doubles to store their fraction of mass. Finally, the method to add an element must be invoked for each of the desired (pre-existing) element objects, providing their addresses and mass fractions. At the last element entry, the system will automatically compute the vector of the number of atoms of each element per volume, the total number of electrons per volume, and will store “this” material in the materials table. In the same way, a material can be constructed as a mixture of other materials and elements.

It should be noted that if the user provides the number of atoms (or molecules) for each element comprising the chemical compound, the system automatically computes the mass fraction. A few quantities, with physical meaning or not, which are constant in a given material, are computed and stored here as “derived data members”.

Some materials are included in the internal Geant4 database, which were derived from the NIST database of material properties. Additionally a number of materials frequently used in HEP is included in the database. Materials are interrogated or constructed by their names ( Material Database). There are UI commands for the material category, which provide an interactive access to the database. If material is created using the NIST database by it will consist by default of elements with the natural composition of isotopes.

Final Considerations

The classes will automatically decide if the total of the mass fractions is correct, and perform the necessary checks. The main reason why a fixed index is kept as a data member is that many cross section and energy tables will be built in the physics processes “by rows of materials (or elements, or even isotopes)”. The tracking gives the physics process the address of a material object (the material of the current volume). If the material has an index according to which the cross section table has been built, then direct access is available when a number in such a table must be accessed. We get directly to the correct row, and the energy of the particle will tell us the column. Without such an index, every access to the cross section or energy tables would imply a search to get to the correct material’s row. More details will be given in the section on processes.

Isotopes, elements and materials must be instantiated dynamically in the user application; they are automatically registered in internal stores and the system takes care to free the memory allocated at the end of the job.

Recipes for Building Elements and Materials

The Listing 44 illustrates the different ways to define materials.

Listing 44 A program which illustrates the different ways to define materials.
#include "G4Isotope.hh"
#include "G4Element.hh"
#include "G4Material.hh"
#include "G4UnitsTable.hh"

int main() {
G4String name, symbol;             // a=mass of a mole;
G4double a, z, density;            // z=mean number of protons;
G4int iz, n;                       // iz=nb of protons  in an isotope;
                                   // n=nb of nucleons in an isotope;
G4int ncomponents, natoms;
G4double abundance, fractionmass;
G4double temperature, pressure;

G4UnitDefinition::BuildUnitsTable();

// define Elements
a = 1.01*g/mole;
G4Element* elH  = new G4Element(name="Hydrogen",symbol="H" , z= 1., a);

a = 12.01*g/mole;
G4Element* elC  = new G4Element(name="Carbon"  ,symbol="C" , z= 6., a);

a = 14.01*g/mole;
G4Element* elN  = new G4Element(name="Nitrogen",symbol="N" , z= 7., a);

a = 16.00*g/mole;
G4Element* elO  = new G4Element(name="Oxygen"  ,symbol="O" , z= 8., a);

a = 28.09*g/mole;
G4Element* elSi = new G4Element(name="Silicon", symbol="Si", z=14., a);

a = 55.85*g/mole;
G4Element* elFe = new G4Element(name="Iron"    ,symbol="Fe", z=26., a);

a = 183.84*g/mole;
G4Element* elW = new G4Element(name="Tungsten" ,symbol="W",  z=74., a);

a = 207.20*g/mole;
G4Element* elPb = new G4Element(name="Lead"    ,symbol="Pb", z=82., a);

// define an Element from isotopes, by relative abundance
G4Isotope* U5 = new G4Isotope(name="U235", iz=92, n=235, a=235.01*g/mole);
G4Isotope* U8 = new G4Isotope(name="U238", iz=92, n=238, a=238.03*g/mole);

G4Element* elU  = new G4Element(name="enriched Uranium", symbol="U", ncomponents=2);
elU->AddIsotope(U5, abundance= 90.*perCent);
elU->AddIsotope(U8, abundance= 10.*perCent);

G4cout << *(G4Isotope::GetIsotopeTable()) << G4endl;
G4cout << *(G4Element::GetElementTable()) << G4endl;

// define simple materials
density = 2.700*g/cm3;
a = 26.98*g/mole;
G4Material* Al = new G4Material(name="Aluminum", z=13., a, density);

density = 1.390*g/cm3;
a = 39.95*g/mole;
G4Material* lAr = new G4Material(name="liquidArgon", z=18., a, density);

density = 8.960*g/cm3;
a = 63.55*g/mole;
G4Material* Cu = new G4Material(name="Copper"   , z=29., a, density);

// define a material from elements.   case 1: chemical molecule
density = 1.000*g/cm3;
G4Material* H2O = new G4Material(name="Water", density, ncomponents=2);
H2O->AddElement(elH, natoms=2);
H2O->AddElement(elO, natoms=1);

density = 1.032*g/cm3;
G4Material* Sci = new G4Material(name="Scintillator", density, ncomponents=2);
Sci->AddElement(elC, natoms=9);
Sci->AddElement(elH, natoms=10);

density = 2.200*g/cm3;
G4Material* SiO2 = new G4Material(name="quartz", density, ncomponents=2);
SiO2->AddElement(elSi, natoms=1);
SiO2->AddElement(elO , natoms=2);

density = 8.280*g/cm3;
G4Material* PbWO4= new G4Material(name="PbWO4", density, ncomponents=3);
PbWO4->AddElement(elO , natoms=4);
PbWO4->AddElement(elW , natoms=1);
PbWO4->AddElement(elPb, natoms=1);

// define a material from elements.   case 2: mixture by fractional mass
density = 1.290*mg/cm3;
G4Material* Air = new G4Material(name="Air  "  , density, ncomponents=2);
Air->AddElement(elN, fractionmass=0.7);
Air->AddElement(elO, fractionmass=0.3);

// define a material from elements and/or others materials (mixture of mixtures)
density = 0.200*g/cm3;
G4Material* Aerog = new G4Material(name="Aerogel", density, ncomponents=3);
Aerog->AddMaterial(SiO2, fractionmass=62.5*perCent);
Aerog->AddMaterial(H2O , fractionmass=37.4*perCent);
Aerog->AddElement (elC , fractionmass= 0.1*perCent);

// examples of gas in non STP conditions
density     = 27.*mg/cm3;
pressure    = 50.*atmosphere;
temperature = 325.*kelvin;
G4Material* CO2 = new G4Material(name="Carbonic gas", density, ncomponents=2,
                                     kStateGas,temperature,pressure);
CO2->AddElement(elC, natoms=1);
CO2->AddElement(elO, natoms=2);

density     = 0.3*mg/cm3;
pressure    = 2.*atmosphere;
temperature = 500.*kelvin;
G4Material* steam = new G4Material(name="Water steam ", density, ncomponents=1,
                                      kStateGas,temperature,pressure);
steam->AddMaterial(H2O, fractionmass=1.);

// What about vacuum ?  Vacuum is an ordinary gas with very low density
density     = universe_mean_density;                //from PhysicalConstants.h
pressure    = 1.e-19*pascal;
temperature = 0.1*kelvin;
new G4Material(name="Galactic", z=1., a=1.01*g/mole, density,
                   kStateGas,temperature,pressure);

density     = 1.e-5*g/cm3;
pressure    = 2.e-2*bar;
temperature = STP_Temperature;                      //from PhysicalConstants.h
G4Material* beam = new G4Material(name="Beam ", density, ncomponents=1,
                                      kStateGas,temperature,pressure);
beam->AddMaterial(Air, fractionmass=1.);

// print the table of materials
G4cout << *(G4Material::GetMaterialTable()) << G4endl;

return EXIT_SUCCESS;
}

As can be seen in the later examples, a material has a state: solid (the default), liquid, or gas. The constructor checks the density and automatically sets the state to gas below a given threshold (10 mg/cm3).

In the case of a gas, one may specify the temperature and pressure. The defaults are STP conditions defined in PhysicalConstants.hh.

An element must have the number of nucleons >= number of protons >= 1.

A material must have non-zero values of density, temperature and pressure.

Materials can also be defined using the internal Geant4 database. Listing 45 illustrates how to do this for the same materials used in Listing 44. There are also UI commands which allow the database to be accessed. The list of currently available material names ( Material Database) is extended permanently.

Listing 45 A program which shows how to define materials from the internal database.
#include "globals.hh"
#include "G4Material.hh"
#include "G4NistManager.hh"

int main() {
  G4NistManager* man = G4NistManager::Instance();
  man->SetVerbose(1);

  // define elements
  G4Element* C  = man->FindOrBuildElement("C");
  G4Element* Pb = man->FindOrBuildMaterial("Pb");

  // define pure NIST materials
  G4Material* Al = man->FindOrBuildMaterial("G4_Al");
  G4Material* Cu = man->FindOrBuildMaterial("G4_Cu");

  // define NIST materials
  G4Material* H2O  = man->FindOrBuildMaterial("G4_WATER");
  G4Material* Sci  = man->FindOrBuildMaterial("G4_PLASTIC_SC_VINYLTOLUENE");
  G4Material* SiO2 = man->FindOrBuildMaterial("G4_SILICON_DIOXIDE");
  G4Material* Air  = man->FindOrBuildMaterial("G4_AIR");

  // HEP materials
  G4Material* PbWO4  = man->FindOrBuildMaterial("G4_PbWO4");
  G4Material* lAr    = man->FindOrBuildMaterial("G4_lAr");
  G4Material* vac    = man->FindOrBuildMaterial("G4_Galactic");

  // define gas material at non STP conditions (T = 120K, P=0.5atm)
  G4Material* coldAr = man->ConstructNewGasdMaterial("ColdAr","G4_Ar",120.*kelvin,0.5*atmosphere);

  // print the table of materials
  G4cout << *(G4Material::GetMaterialTable()) << G4endl;

  return EXIT_SUCCESS;
}

The Tables