(Go to SRIM Menu)

(Go to Stopping in Compounds)

Stopping of Ions in Compounds

Core and Bond Corrections

There have been more than 400 papers which discuss methods of calculating the stopping of ions in compounds (Compound Citations listings). Many recent papers tend to be rather rigorous and apply molecular orbital calculations to single systems. Our interest is to find an accurate solution which can be used for any ion / compound situation with limited input from the user. The most basic information is still necessary: the chemical nature of the compound. From this rudimentary information, SRIM then estimates the corrections needed to produce stopping which is accurate to a few percent. (SRIM's input requirements are discussed below.)

The method which is used is called the Core and Bond (CAB) approach, which was first proposed by a group at the University of Cologne (Köln, Germany).[1] They proposed approaching the problem by reducing each target atom to two parts: the core electrons which are unperturbed by bonding, and the bonding electrons. An example would be for carbon atoms, with a core of the nucleus and the inner shell electrons, and then separate outer shell contributions depending on how the carbon was bound into the compound. 

The problem is to determine the Core and Bond values for common elements.  The Core stopping contributions would simply follow Bragg's rule for the atoms of the compound, which suggests a linear addition of the stopping from each of the elements in the compound. The chemical bonds of the compound would then contain a correction to this basic stopping. The bonds would be evaluated depending on the simple chemical nature of the compound. For example, for hydrocarbons, carbon in C-C, C=C and CðC structures would have different bonding contributions (C=C indicates a double-bond structure and CðC is a triple bond). The contribution to stopping  by a carbon atom in a C=C bond is almost twice that of a carbon atom single-bond state. And a carbon atom in a triple-bond state contributes even greater stopping powers. By merely specifying the bonding of the atoms in the compound, for example, SRIM can then generate a stopping correction required for the compound with this bonding arrangement.

The Core and Bond values may be determined by analyzing the stopping of ions over a great number of targets, and solving for the contribution from the Cores and the Bonds. We use the stopping of light ions, H, He and Li, in 162 different stopping experiments.  The compounds contained 30 different elements. We will assume that for the targets with 12 heavy elements, the stopping is dominated by the non-bonding electrons (discussion below). But 114 of these compounds contained only light elements, and their stopping is significantly altered by their bonding. The light elements we consider are:  H, C, N, O, F, S and Cl. For each of these elements there is a core contribution, and a separate bonding contribution. The bonds which appear in the 114 compounds with only light elements that we studied were:

Compound Bonds which were Evaluated

 (Table 1)

where "-" denotes a single bond, "=" denotes a double bond and "ð" denotes a triple bond. These 16 bonds are considered unknown parameters. The scaling of ion stopping from H to He to Li  are also considered unknowns.  Finally the stopping effect of the phase-state of the target is another unknown parameter. This gives a total of (16 bonds) + (3 ions) + (2 phase states) = 20 parameters that will be extracted from the data of 114 experiments. For H in targets, we assume there is no core (only one electron is available) and all its stopping is in the bonding electron. For the other elements, each possible bond is considered separately.

It is clear that we have an "over-defined" problem, in which there are many more equations than the number of unknowns, and this improves the accuracy of the solutions. The solving of the multiple equations was done in a standard iterative method for over-defined problems.

The limitations of this approach should be mentioned.

1. The most important limitation might be that of the target band-gap. Experiments on insulating targets dominate the experimental results that we use. For compounds which are conducting, there might be an error with the suggested stopping correction. It might be too low. Theoretically, band gap materials are expected to have lower stopping powers than equivalent conductors because the small energy transfers to target electrons are not available in insulators. It is not clear what the magnitude of this effect is, but about 50 papers have discussed the stopping of ions in metals and their oxides, e.g. targets of Fe, Fe₂O₃ and Fe₃O₄. (Examples are shown below: Bragg's Rule and Heavy Elements) These experiments evaluated similar materials with and without band-gaps. No significant differences were found that could be attributed to the band-gap. Measurements have also been made of the stopping of H and He ions into ice (solid water) with various dopings of salt (NaCl). No change of energy loss was observed for up to 6 orders of magnitude change in resistivity of the ice.

2. The scaling of ion stopping from H to He to Li  is assumed to be independent of target material, This assumption has been evaluated with 27 targets which have been measured for two of the three ions (at the same ion velocity) and 6 of these targets have been measured for all three ions (see listings in Table 2). In all cases, the stopping scaled identically within 4%. That is, for H (125 keV) and He (500 keV) and Li (875 keV) the scaling of stopping powers was 1 : 2.7 : 4.7 for the 27 targets (average error was <4%). (For those unfamiliar with stopping theory, the primary parameter for the scaling of stopping powers is the ion velocity, which reduces to scaling in units of kev/amu. This is reviewed in the section on Stopping History.)

3. The light elements of He and Ne are missing from the above list of target bonding atoms. No comparative experiments have been done on the stopping into He in solid / gas phases. However studies of stopping into targets of  Ne and Ar have been conducted in both gas and solid form. These papers show no significant difference between the stopping in gas and solid phases. It appears that the van der Waals forces which hold noble gases together in frozen form, are too weak to effect the energy loss of ions. Of particular note is the extensive work done in the paper: F. Besenbacher, J. Bottiger, O. Graversen, J. Hanse and H. Sorensen, "Stopping Power of Solid Argon for Helium Ions", Nucl. Inst. Methods, 188, 657-667 (1981).

4. The light target atoms of Li, Be and B are missing from the list of bonding atoms. This is a serious defect. The number of papers that have looked at compounds which contain significant amounts of these three elements is too limited to allow their evaluation. Target atoms of these three elements are considered by SRIM to have no bonding correction, which is clearly not true. But without experimental data, there is no reliable way to evaluate the contribution of their bonds in compounds.

Reference [1] G. Both, R. Krotz, K. Lohman and W. Neuwirth, Phys. Rev., A28, 3212 (1983).

Table 2 shows the compounds used for the extraction of Core and Bond parameters.

       Compounds used to extract Bonding Contributions (Table 2)

The simultaneous fitting of ion stopping in all of these compounds yielded the following Bonding Corrections, see Table 3. The corrections are for H, He and Li ions at 125 keV/amu (about the peak of their stopping power curve) and all strengths are normalized to the C-C bond. The evaluations were done at several ion velocities, both higher and lower than 125 keV/amu, and the relative magnitude of the bonds changed. The spread of the relative effects was significantly reduced for higher ion energies. For lower energies, the spread of  relative strengths slightly increased, but not very much.

 Relative Strength of Bonding in Compounds (Table 3)

The relative strength of the target atom "cores" were also extracted, see Table 4. The contribution of the hydrogen core was set to zero because its only electron is used in bonding. All core strengths are shown relative to carbon. The core contribution to stopping was found to be relatively independent of the ion velocity, in contrast to the contribution of bonding, above.

Relative Strength of Atomic Cores (Table 4)

Bragg's Rule and Heavy Target Elements

We have concentrated on the analysis of the stopping of ions in compounds made up of light elements. For compounds with heavier atoms, many experiments have shown that deviations from Bragg's rule disappear. In Table 5 is shown representative examples of ion stopping in various compounds containing heavy elements. None show measurable deviations from Bragg's rule. The citations for these measurements are tabulated in the Compound Citation page. Many articles with similar results were reviewed in the 1980s.[1,2] 

Bragg's Rule Accuracy in Heavy Compounds (Table 5)

For compounds which contain elements with atomic numbers greater than 12, it is possible to combine the CAB approach with Bragg's rule. The CAB approach can be used for the small atomic number cores and bonds, and these can be combined with the normal stopping contribution of the other components of the compound. 

[1] D. I. Thwaites, Nucl. Inst. Methods, B12, 84 (1985).

[2] D. I. Thwaites, Nucl. Inst. Methods, B27, 293 (1987).

Examples of Stopping Correction for Compounds

Stopping Correction for a target of  Ethylene 

When you use SRIM, you are given the option of using the Compound Dictionary. This menu lists about 200 compounds, and provides stopping corrections for a great number of them. Below is a typical example for Ethylene, C₂H₄, which has a total 12% stopping correction. Below on the left is the SRIM Compound Dictionary window for Ethylene. The Bonding Correction is 8.33%. Below this is the density for Ethylene in gas phase, and the chemical formula and the bonding information in schematic form. Below this is the composition of Ethylene in both atomic percent and mass percent. The term "Core Stopping" is the same as the Table 4 above, but in different units. Finally, at the bottom the bonding information is listed. There are four (H-C) single bonds, and one (C=C) double bond. The effect of these cores and bonds is to make a 8.3% correction. SRIM also makes an automatic correction for the phase change for carbon in the target if the "Gas Phase" box is checked in SRIM (we are assuming gaseous Ethylene in this example). The gas-phase correction is about 4% for carbon. This makes the total correction to be 12%. 

Shown in figure "He into Ethylene (gas)" is the stopping of He ions into Ethylene showing the Bragg's rule stopping estimate for (2 Carbon) + (4 Hydrogen) atoms (black curve). These values are clearly too small. There are two corrections that are made. The stopping of He in Carbon assumes a solid-phase target. The stopping in gas-phases usually increases the stopping. Shown in the curve is the stopping due to carbon solid (solid green line) and carbon in gas phase (dashed green line). Then we must consider the bonding effects. The ethylene molecule contains 4 H-C single bonds, and a C=C double bond. From the discussion above, the C=C bond adds significantly to the stopping power near the peak of the stopping. SRIM calculates that this increase is 8.3%.  So the two corrections make the total adjustment to the stopping to be about 12%, and it brings the calculation into reasonably accurate agreement with the data. 

Stopping Correction for a target of  Polystyrene 

Another example of a large correction is that necessary for a target of Polystyrene, C₈H₈. Shown below is the Compound Dictionary  in SRIM for Polystyrene (which is also identified by the ICRU #226). This compound will have two corrections, one to convert stopping in H (gas) to stopping in H (solid). This will tend to decrease the stopping power. The second correction will be for the bonding of the compound, which will increase the stopping. The result will be a net increase of about 6%. The chemical form of Polystyrene is rather complex since it contains 8 (H-C) bonds, 6 (C-C) bonds and 3 (C=C) bonds. Note that the density of Polystyrene is quite variable, and you must be careful that your target density is correctly entered.

Shown in figures "H into Styrene" and "He into Styrene" are the stopping of H and He ions into Polystyrene. They show the Bragg's rule stopping estimate for (8 Carbon) + (8 Hydrogen) atoms (black curve). These values are too small. There are two corrections that must be made. The stopping of ions in Hydrogen assumes a gas-phase target. The stopping in gas-phases has higher stopping than for solid phase. Shown in the curve is the stopping due to hydrogen in gas phase (dashed green line) and hydrogen solid (solid green line).  Then we must consider the bonding effects. The Polystyrene molecule contains 8 H-C single bonds, 6 C-C single bonds,  and 3 C=C double bonds (see the molecular structure in SRIM's Compound Dictionary). From the discussion above, the C=C bond adds significantly to the stopping power near the peak of the stopping. SRIM calculates that the bonding correction is +6.6%.  In this case the two corrections work opposite to each other. The phase-change correction for hydrogen  reduces the stopping, while the bond correction increases the stopping. The total adjustment to the stopping is about 6%, and it brings the calculation into reasonably accurate agreement with the data for both H and He ions. 

(Go to SRIM Menu)

(Go to Stopping in Compounds)