KAHIBARO
8.1. Material Definitions
Table of Contents
Elements
In GATE, every material is built from more basic building blocks called elements. An element represents a pure chemical species such as hydrogen, carbon, or oxygen, with a defined atomic number $Z$ and atomic mass $A$. GATE relies on the Geant4 material system, so when you define materials in GATE you are effectively defining Geant4 elements and using them to construct more complex materials.
An element serves two main roles in a simulation. First, it determines which interaction cross sections and physical processes apply to the atoms in a material. Second, it defines the relative probability of different atomic interactions based on $Z$ and $A$. For example, the dominant gamma interaction process can change as $Z$ changes, so distinguishing between elements like carbon and lead is essential for realistic physics.
Conceptually, to define an element you need:
its chemical symbol or name, its atomic number $Z$, and its atomic mass $A$ in units of g/mol. Internally, Geant4 uses these to compute quantities such as the number of atoms per volume, once the material density is known. In practice, you usually do not need to work with the element directly during geometry construction, but you must know which elements appear in a material and in what proportions.
Many common elements are already available through the Geant4 NIST material database, which GATE can access. This database provides standardized definitions of elemental properties, which helps avoid inconsistencies between simulations. When you build your own materials, it is good practice to reuse these existing element definitions when possible, rather than redefining basic elements with slightly different atomic masses.
In medical physics simulations, a relatively small set of elements appears frequently. For example, hydrogen, carbon, nitrogen, oxygen, phosphorus, and calcium form the basis of most biological tissues, while elements such as barium or iodine appear in contrast agents, and high‑$Z$ elements like lead or tungsten are common in shielding. Detector materials also rely on specific elements, such as lutetium and silicon in LYSO, or bismuth and germanium in BGO. Understanding which elements make up your detector or phantom is the first step before constructing compounds or mixtures.
Because materials are ultimately defined by the combination of their elements, a consistent element definition is important whenever you compare different simulations or validate results. Using the same element definitions across different projects makes it easier to interpret differences in dose, attenuation, or detector response as real physical effects instead of artifacts of slightly different material definitions.
An element in GATE is defined by its atomic number $Z$, atomic mass $A$ in g/mol, and a unique name or symbol. Always reuse standard element definitions from the Geant4 NIST database whenever possible to ensure consistent physics across simulations.
Compounds
A compound in GATE represents a chemically pure substance composed of two or more elements combined in a fixed stoichiometric ratio. Examples include water ($\text{H}_2\text{O}$), carbon dioxide ($\text{CO}_2$), and calcium carbonate ($\text{CaCO}_3$). In medical physics simulations, compounds such as water and plastics are particularly important, both for phantoms and for components of detectors and equipment.
Conceptually, a compound is defined in two layers. First, you specify which elements are present and how many atoms of each element appear in the chemical formula. Second, you assign a mass density in g/cm$^3$ to describe how much mass is contained in a given volume. The combination of stoichiometry and density allows Geant4 to compute the number of atoms of each element per unit volume. These atomic number densities are what the physics models really use during transport.
For example, for water you specify two hydrogen atoms and one oxygen atom. From the atomic masses of hydrogen and oxygen, you can compute the molar mass of water:
$$
M_{\text{H}_2\text{O}} = 2 M_{\text{H}} + 1 M_{\text{O}}.
$$
Given the density $\rho$ of water, Geant4 derives the number of water molecules per unit volume, then multiplies by the number of atoms of each type per molecule. You do not need to perform these calculations yourself, but it is useful to understand that the stoichiometric formula and density together define the microscopic composition that governs particle interactions.
The distinction between compounds and mixtures is important. A compound has a fixed and well defined microscopic structure, for example every molecule of water contains exactly two hydrogen atoms. A mixture, in contrast, may represent a macroscopic blend of different substances, such as a mixture of water and air. In practice, GATE uses the same underlying mechanism to handle both, but you choose the representation that best matches the physical nature of what you are modeling.
Many common compounds used in simulations are already provided in the Geant4 NIST material database, including water, air, and various plastics. Using these predefined compounds has several advantages. The elemental compositions and densities have been carefully chosen, they are widely used in benchmark studies, and they simplify your input files. When such a standard compound exists, it is generally better to use it directly instead of recreating it by hand.
From a physics perspective, the way you define compounds affects key quantities such as attenuation coefficients and stopping powers. Even small changes in density or composition can alter the predicted dose or detector response, especially for high energy photons and charged particles. For this reason, when you build your own compounds, you should take the stoichiometric composition from reliable references, such as ICRU or ICRP reports, and use densities that correspond to the physical state you want to simulate, for example liquid water at room temperature.
A compound in GATE is specified by:
- The list of constituent elements with their stoichiometric ratios, usually given as number of atoms per molecule, and
- The material density in g/cm$^3$.
These together uniquely determine the atomic composition per unit volume that Geant4 uses for particle transport.
Mixtures
A mixture in GATE represents a material composed of two or more distinct components blended together, where each component can itself be an element or a compound. Unlike a pure compound, a mixture does not necessarily have a fixed microscopic chemical formula. Instead, it is described by macroscopic fractions, either by mass or by number of atoms. This flexibility makes mixtures particularly useful for modeling real-world materials such as tissue-equivalent plastics, bone, or composite detector components.
There are two main ways to specify the composition of a mixture. The first is by mass fraction. In this case, you assign to each component a fraction $w_i$ such that
$$
\sum_i w_i = 1,
$$
where $w_i$ is the fraction of the total mass contributed by component $i$. For example, a plastic phantom might be approximated as a mixture of carbon, hydrogen, and oxygen with specified mass fractions taken from a reference. Geant4 uses these fractions, together with the atomic masses, to compute the number of atoms of each element per unit volume.
The second method is by atomic fraction. Here you specify the relative number of atoms of each element, with fractions $f_i$ that satisfy
$$
\sum_i f_i = 1.
$$
Atomic fractions are closer in spirit to chemical formulas, but in practice mass fractions are more commonly available in the literature for tissues and detector materials. Regardless of the method you choose, you must also provide the mass density of the resulting mixture. The density can be measured experimentally, taken from a database, or in some cases computed from the densities of the components if the mixture is simple.
Mixtures are especially important in medical physics applications because most biological tissues cannot be represented accurately as a single compound. For example, cortical bone, lung, and soft tissue are usually modeled as mixtures of basic elements, with mass fractions defined so that their electron density and effective atomic number match measured values. Standard reference compositions are widely used to allow consistent comparison between different Monte Carlo codes and experiments.
From the point of view of the simulation, mixtures and compounds are handled similarly. Both result in a list of elements and their number densities, which determine the interaction probabilities for particles. The difference is conceptual, reflecting whether the material is chemically uniform or a macroscopic blend. For practical purposes, you choose a mixture when you want to approximate a real material whose microscopic composition is complex or not fully known, but whose macroscopic elemental composition or mass fractions are available.
It is important to ensure that the fractions you define are normalized correctly. When using mass fractions, their sum must be exactly 1, within numerical precision. If the fractions do not sum to unity, Geant4 will renormalize them internally, which can hide input mistakes. A small arithmetic error in the fractions might not cause the simulation to fail, but it can shift attenuation or dose by non-negligible amounts, especially in high precision dosimetry studies.
Mixtures also appear in the context of detector modeling. For instance, some scintillators and photodetectors are manufactured from complex glasses or polymers, which you may approximate as mixtures of simpler components. Similarly, shielding structures can be modeled as mixtures when they are made from alloys or composite materials. In each case, accurate mixture definitions help ensure that you predict scattering, absorption, and secondary particle production realistically.
A mixture in GATE is defined by:
- A set of components (elements or compounds) with fractions given either by mass (preferred for tissues and many materials) or by atomic fraction, and
- A material density in g/cm$^3$.
The component fractions must be normalized so that their sum equals 1, otherwise the physical composition of the mixture will be incorrect.
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