Monte Carlo simulation of lattice analysis of complex LaCeTh0.1CuOy using ion bombardment technique

M. E. Emetere

Abstract Ion bombardment analysis of perovskite materials is challenging owing to their peculiar structure. This shortcoming renders the reliability on the technique somewhat questionable. In this research, three structured modifications (i.e., scan angle, low energy, and large ion bombardment) were adopted to improve the ion bombardment analysis of 99,999 ions using Monte Carlo simulations. The modified technique was used to analyze the effects of a chemically pressurized ‘‘A’’ site in the perovskite lattice system. The LaCeTh0.1Cu2Oy compound was used in this experiment. Despite the low probing energy, it was observed that the high number of ions bombarding the material resulted in external pressure on the lattice structure of the material. Moreover, the chemically pressurized ‘‘A’’ site perovskite material was characterized by lattice mismatch, lattice fluctuations, grain boundary collapse, and oxygen displacement. The novel discovery of this research is the inter- and intra-extended lattice mismatches that are likely to connect.Hence,further investigation of the connection between inter- and intraextended lattice mismatches is recommended as they may enable fabrication of room-temperature superconductors.

Keywords Lattice mismatch · Ion bombardment ·Chemical pressure · Scan angle

1 Introduction

The chemical structure of cuprates (i.e., similar to the perovskite oxides) is an ABO3composition with the ‘‘A’’site representing an alkaline earth or rare earth element,the‘‘B’’ site representing transition metal elements, and the‘‘O’’ site representing octahedron oxygen ions [1]. The ABO3composition favors the interplay of atomic properties, such as charge and spin degrees of freedom. A modification of the ABO3composition is expected to influence the orbital and lattice formation of the compound. This modification also influences the electronic interactions within the lattice degree of freedom.Hence,it is possible to have varying symmetry and electronic states within a complex lattice system.

In this study, a complex lattice system was suggested such that the ‘‘A’’ site is reordered with two lanthanide elements and doped with an actinide metal. This phenomenon is expected to create multi-electronic states in the lattices. One of the likely lattice variations may be caused by orthorhombic strain due to the differences in the lattice stiffnesses [2]. Most notably, there may be a lattice mismatch at room temperature due to chemical pressure on the transition oxide (i.e., copper oxide) plane. The chemical pressure causes a lattice mismatch and affects the transition temperature of the material[2,3].In this case,the external pressure that can lead to the lattice mismatch may be caused by ion injection or bombardment [4, 5]. Chemical and external pressures may lead to lattice anharmonicity alongside this mismatch. A physical illustration of this event is synonymous to a cross section of a pizza with different gaps. In this circumstance, the gap in the lattice represents the oxygen displacement.Reference[6]reported that oxygen displacements are a clear indication of a lattice deformity otherwise known as lattice fluctuations. However, there is a clear possibility of lattice anharmonicity due to the covalent and ionic bonds present in the complex material [7]. In other words, lattice anharmonicity and lattice fluctuations may coexist within the LaCeTh0.1CuOycompound.

In this study, the features of the inherent lattice system of LaCeTh0.1CuOywere investigated using the ion bombardment technique.Here,the ion bombardment technique is used as diagnostic tool [8, 9]. The use of ion bombardment as a characterization technique has been previously demonstrated in cuprate samples. For example, ion irradiation of 50 keV or 130 keV He+has been used to analyze YBCO.In that experiment,transitions of the crystal lattice from an orthogonal to a tetragonal shape were observed[10]. In some cases, ion beam analysis of cuprate compound was able to show that the insulating phase of cuprates contains a granular structure of superconducting islands [11, 12]. For example, at certain degree of ion bombardment, the physical properties of polymers are affected.Hence,one of the challenges of ion bombardment is the tendency of the electrons to cause material damage due to the transition of a chemical bond from a bonding to an anti-bonding state [13, 14].

The mean range of an ion in a material provides a rough estimation of the mean thickness of a material, while the stopping power (S) of the material is the rate of change of energy (-dE/dT) within the material thickness (T). The stopping power depends on the energy E of the ion. It is proposed in this research that the varying mean ranges of ion bombardments on a thin-film cuprate material under appreciable ion energy of 20 keV could help determine salient features of the lattice system.

2 Methodology

Monte Carlo simulations of ion transport through LaCeTh0.1CuOywere performed in the Transport of ions in matter(TRIM)module of the SRIM software package[15]to determine the Monte Carlo stopping range. TRIM calculations assume the target temperature to be absolute zero.SRIM was used because it has the ability to determine the smallest impact parameter that occurs over the path length[16].All target atoms were stationary.The ion range in the material was taken at different angles at the same energy,i.e., 20 keV. The He+ion and its energy were adopted based on the Rutherford backscattering experiment reported in Ref [2]. The thickness of the material was 1.68 cm.Based on Fig. 1,we propose that the ion range in the lattice system will be able to map out the lattice of the material.The ion range in the material was measured as depth X,lateral Y, and lateral Z. The varying 3D lattice map was reconstructed at several angles, i.e., 0°, 15°, 20°, 30°, and 60°.The chosen angles were expected to capture any lattice information present via He+.

The Monte Carlo simulation of the bombardment of LaCeTh0.1CuOywith 99,999 He+was performed. The statistics of the ion range for all 99,999 ions was partitioned and analyzed in ten sections, i.e., 0–1000 ions(section A), 9000–10,000 ions (section B), 20,000–21,000 ions (section C), 30,000–31,000 ions (section D),40,000–41,000 ions (section E), 50,000–51,000 ions (section F), 60,000–61,000 ions (section G), 70,000–71,000 ions (section H), 80,000–81,000 ions (section I), and 90,000–91,000 ions (section J). The statistics of sections A–J was calculated to follow the changes in the material as it goes through the bombardment by 99,999 ions.The beta diversity of each section was calculated to capture the physics of the lattice deformation, mismatch, or anharmonicity.

The statistical analysis was then compared with a 3D reconstruction of the ion bombardment. The structure of the LaCeTh0.1CuOycompound was then constructed to understand why the sputtering yield changes with varying angles of the incident ions.

3 Results and discussion

The ion range (i.e., depth X) histogram of sections A–J for each angle is presented in Fig. 2.The figure shows that the bell-shaped normal distribution is generally skewed to the left for all five different angles. However, at 60°, the histogram was even more skewed to the left than in any other scan angle. This effect occurs because sputter yields vary with the incidence angle of the ions. The sputtering yield is related to the surface structure of the target material;hence,it is believed that the scan angle reveals special details about LaCeTh0.1CuOy.The peak of the histogram’s normal fit depicts an active depth penetration (with the highest frequency) of the ions at 600 mm for all angles.However,the highest frequency changed depending on the incidence angle: At 0°, it was at 500 mm and 750 mm; at 15°,it was at 800 mm; at 20°, it was at 800 mm; at 30°,it was at 550 mm;and at 60°,it was at 270 mm.Hence,when ion bombardment is incident on the material at an angle of 0°, two main events most likely occur. Further, the histogram shows that at 0°,the response of the target material is most stable (Fig. 2a). Figure 2c (20°) reveals that the stability of the ion bombardment on the target material is not directly proportional to the scan angles but rather to the components of the target material.For higher angular(i.e.,15° and 20°) ion bombardments, the highest depth occurs as a result of the two events. In addition, the ion range(depth X) at 30° and 60° shows that the histogram has a truncated distribution.This event shows that the lattice has different features caused by bonding and anti-bonding events in the material [13, 14]. The ion range (i.e., lateral Y) histogram of sections A–J of each angle is presented in Fig. 3. It can be seen that the bell-shaped normal distribution defines the gradual left skew with increasing scan angle. For example, the peak of the histogram normal fit shows the following: At a scan angle of 0°, the peak position was at 0; at 15°, the peak position was at 300; at 20°,the peak position was at 200;at 30°,the peak position was at 450; and at 60°, the peak position was at 600. This shows that the lateral Y ion range in the sample is dynamic at wider scan angles. Figure 2 also reveals that ion bombardments are more uniform at 0°. First, it can be inferred from the lateral Y ion range that the lattice system comprises of different patterns. This is an evidence of lattice mismatch. Second, it can be inferred that the lattice mismatches consist of different lengths [17, 18]. The implications of different lattice mismatches are that the material possesses different lattice constants due to the existence of strained sub-lattices. However, a strain estimation cannot be determined statistically. The conventional technique to determine mismatch in cuprates is given by [19] in Eq. 1:

where r A-O（ ） can be represented by r La-O（ ）,r Ce-O（ ）, and r Th-O（ ）; r Cu-O（ ） is the bond length;and t is the Goldschmidt tolerance factor. The ion range(i.e., lateral Z) histogram of sections A–J of each angle is the highest frequency of all scan angles. This can be interpreted that a scan angle of 15° may adequately focus on the lattice mismatch in the ‘‘A’’ site. Therefore, when the ions range lateral Y and ion range lateral Z are constructed within the 3D lattices, the peak positions are regions with high number of lattice fluctuations.This result is corroborated by the result of the ion range depth X (Fig. 2), i.e., considering the scan at 15°. A full consideration of the histogram shows that the ion range lateral Z is more transient at two extreme scan angles(i.e.,0°andpresented in Fig. 4.Unlike the lateral Y ion range,the peak of the normal fit was at position zero for all scan angles.However,the histogram of the scan angles 0°and 60° was found to be almost the same. The scan at 20° showed a uniform distribution as the normal fit. This indicates that the ion range lateral Z at 20°of the angular scans is a good representation of the copper oxide lattice.As expected,the copper oxide did not receive any lattice damage due to the peculiarity of the plane of the cuprate system. The lattice scan was at 15°. It was observed that the lattice scan had 60°),transient at scan angles of 15°and 30°,and stable at a scan angle of 20°. Hence, this trend can be illustrated in a wave-like diagram(Fig. 5).The trend described above was only observed for the ion range lateral Z. The ion range depth X and ion range lateral Y do not have specific trends along the scan angles.

Table 1 Beta diversity of ion range

The beta diversity of the ion range is presented in Table 1. As observed in the table, the beta diversity along depth X is insignificant. This result occurs when the thickness of a material is uniform. Moreover, Table 1a shows that the diversity parameters are very low or even zero at each point. This means that the lattice of the material was not distorted along the depth of the material.However, significant changes were observed between the lateral Y and the lateral Z.The beta diversity parameter was higher for lateral Y than for lateral Z, except for the Routledge, Mourelle, and Harrison diversity parameters at a scan angle of 0°. Further, the lateral Y was higher than lateral Z for the diversity parameters, i.e., Routledge,Wilson-Shmida, Williams, Mourelle, and Harrison, for angular scans at 15°. When the diversity parameter is higher in lateral Y, this is an evidence of oxygen displacement as it is displaced toward lateral Y, i.e., in the caxis direction [20, 21]. Hence, at a scan angle of 0°, the lattice system is characterized by oxygen displacement, an effect that is reduced with increasing scan angle.Along the scan angles of 20°–60°, the beta diversity parameter for lateral Z was found to be higher than that for lateral Y. Whittaker and Routledge decreased as the scanning angles increased along lateral Y. Based on the beta diversity parameters from the scan angle result, the scans differ from the increasing or decreasing trends of other parameters. This further affirms that the ion ranges in lateral Y depict the ‘‘A’’ site that is characterized by lattice fluctuations.It was observed in the lateral Z analysis along the scan angles that the beta diversity parameter increases uniquely between 0°–20°and 30°–60°.However,this trend is not obeyed in the Wilson-Shmida parameter.

The statistics of sections A–J was calculated, where each section is represented as mean position in ‘‘Appendices 1–3.’’ ‘‘Appendix 1’’ shows that the mean depth X decreases as the scan angle increases. It was also observed that the mean depth X decreases slightly in positions 4–6, i.e., sections D–F. Moreover, it was observed that the standard error and standard deviation of depth X were generally low for a scan angle of 60° and varying for other scan angles.It was also observed that the coefficient of variation of the ion range is higher at a scan angle of 60° and varies with other scan angles.

In‘‘Appendix 2,’’it is shown that the mean lateral Y was extremely low and high for scan angles 0° and 15°,respectively. Further, the standard deviation and standard error were lowest for 20°, while they vary for other scan angles. The coefficient of variation of the lateral Y is mostly negative. This indicates that the lateral Y, among other relevant factors, determines the electron seat in the 3D lattice construction.

In‘‘Appendix 3,’’the mean lateral Z and the coefficient of variation fluctuate in both the positive and negative axes.This affirmed that the lateral Z ion range mainly controls the peaks in the 3D lattice.Unlike for depth X and lateral Y,the standard deviation and standard error differ for all scan angles.

After understanding the statistics of the ion ranges for the bombardment with 99,999 ions, the 3D lattice of the compound is constructed.In the 3D construction,the small peaks represent the ‘‘BOx’’ site or copper oxide site in the lattices, the distorted peaks represent the lattice mismatches, the large peaks represent the ‘‘A’’ site of the lattice,and the spaces represent the likely region of oxygen displacements. The alignment between the chemical structure and the 3D lattice system is presented in Fig. 6.

Figure 7a represents the scan angle of 0°over section A.It was observed that lattice mismatches were more visible at the‘‘A’’site of the 3D lattice.Moreover,it was observed that the oxygen displacement occurred around the lattice mismatch. Hence, we propose that oxygen displacements are one of the indications of lattice mismatches[22].It was also observed that the ‘‘A’’ site induced strain on the‘‘BOx’’ site or copper oxides. This result is quite contradictory to the results found in some of the existing literature. Figure 10b represents the scan angle of 15° over section A. The diagram shows that the scan could capture smaller lattice mismatches (as compared to Fig. 7a).However,the lattice mismatch extended from the‘‘A’’site into the ‘‘BOx’’ site or copper oxide plane. This type of lattice mismatch is called an extended lattice mismatch.Very little is known on the effects of extended lattice mismatches onto the electronic or superconducting properties of materials. Further, it was observed that the ‘‘A’’site was clearly visible under the 15° scan angle.

Similar to Fig. 7a,in Fig. 7c a larger lattice mismatch is shown in the‘‘A’’site of the compound.The scan angle of 20° was observed to capture more atoms in the lattice of LaCeTh0.1CuOy. At a scan angle of 30°, there was a clear evidence of an extended lattice mismatch along the ‘‘A’’site. Hence, this gives two types of lattice mismatch,namely intra- and inter-extended lattice mismatches.

Despite the occurrence of intra- and inter-extended lattice mismatches, it is still unclear if the angular scan distorts the sub-lattices. At a scan angle of 60°, a onedirectional strain on the ‘‘BOx’’ site or copper oxide plane was observed. This strain is different from that seen in Fig. 10a, which was a uniform strain on the ‘‘BOx’’ site or copper oxide plane.

The second 3D lattice construction was presented in section D (Fig. 8a). It was observed that there were intraextended lattice mismatches in the ‘‘A’’ site. However,there were no uniform strains, as observed in section A.This indicates that large ion bombardments (99,999) are likely to produce varying lattice information.

In Fig. 8b,it is shown that the‘‘A’’site was compressed into the‘‘BOx’’site or copper oxide plane.This reflects the collapse of the strained grain boundaries [23]. It was also observed that Fig. 8b characterizes intra-extended lattice mismatches at the‘‘A’’and‘‘BOx’’sites.This may indicate that the lattice mismatch was initiated by chemical pressure.The level of chemical pressure may be further increased via a higher number of ion interactions through ion bombardment.In addition, an inter-extended lattice mismatch was observed.Hence,the scan angle of 15°was able to capture a series of lattice mismatches in the LaCeTh0.1Cu2Oycompound.The same event in Fig. 8b occurred in Fig. 8c.However,the percentage of lattice mismatch in Figs. 8b and 8c is 60% and 45%, respectively. Figure 8d shows a onesided lattice mismatch at the‘‘A’’site of the compound.The grain boundary was found to be homogenous.Hence,apart from the diagnostic applications of scanning different angles, it was affirmed that ion bombardment creates an external pressure on the lattice formation.However,in this case,the ion bombardment positively influenced the inadequacies in the grain boundary.

Figure 9a shows that there is one-sided lattice mismatch in the ‘‘A’’and‘‘BOx’’sites of the compound along the 0°scan angle. Further, there was an inter-extended lattice mismatch. Figure 9b shows the scan angle at 15°. There were intra-and inter-extended lattice mismatches in the‘‘A’’and ‘‘BOx’’ sites of the compound. There was a clear evidence of oxygen displacement in the‘‘A’’site.This trend is initially revealed in Fig. 9a. Figure 9c shows the result of scan angle 20°.The results displayed in Fig. 9c were found to be synonymous to the outcomes observed in Fig. 9b.This indicates that at the third quarter of the ion bombardment(section G), there may be insignificant changes at lower angular scans.Figure 9d shows the result of the scan angle of 30°. There were inter- and intra-extended lattice mismatches.More significant is the unique connection between the inter-and intra-extended lattice mismatches.This result is very important in superconductivity as it likely reveals cooper pair paths[24].Hence,we propose that the quantum state created during superconductivity can only exist at lower temperatures.Therefore,it is proposed that fabricating materials that have inter- and intra-extended lattice mismatch connections may be one of the viable ways of fabricating room-temperature superconductors. Figure 9e shows the results of a scan angle of 60°. Intra-extended lattice mismatches were observed at both the ‘‘A’’ and‘‘BOx’’sites of the compound.

Figure 10a, c shows the intra-extended lattice mismatches in both ‘‘A’’ and ‘‘BOx’’ sites of the compound.Figure 10b, d displays the lattice mismatches in the ‘‘A’’site only. Figure 10c reveals a higher number of intraextended lattice mismatches than in Fig. 10a. Likewise,there are a higher number of lattice mismatches in Fig. 10d than in Fig. 10b. Figure 10e shows a few one-sided intraextended lattice mismatches in the ‘‘A’’ site.

4 Conclusion

The ion bombardment analysis of the lattice of the LaCeTh0.1Cu2Oycompound proved to be a very viable method of investigation, as new facts about the effects of chemically pressurized‘‘A’’site on the lattice system were revealed. We propose that the lateral Y ion range in the sample is dynamic at wider scan angles and its lattice system comprises different patterns. Further, the mean depth X was found to decrease with increasing scan angle.The ion range lateral Y, among other types of ion ranges,determines the electron seat in the 3D lattice construction.Furthermore, apart from the diagnostic applications of the scanning angles, it was affirmed that ion bombardment creates an external pressure on the lattice formation.It was observed that the external pressure caused by the high number of ion bombardment has an influence on the lattice structure. In addition, the chemically pressurized ‘‘A’’ site in perovskite materials clearly leads to lattice mismatches,lattice fluctuations, and oxygen displacement. These can also lead to the collapse of the grain boundaries of the material.The novel discovery of this study is the inter-and intra-extended lattice mismatches.Noticeably,connections can exist between the inter- and intra-extended lattice mismatches. Hence, probing further the connections between the inter-and intra-extended lattice mismatches is recommended, as they might prove to be the means in obtaining a room-temperature superconductor.

Appendix 1

See Fig. 11

Appendix 2

See Fig. 12

Appendix 3

See Fig. 13