Development of tomography–transmission electron microscope (TEM) specimen holder stable under acoustic disturbances

Abstract

This paper focuses on the development of tomography—transmission electron microscope (TEM) specimen holder stable under environment effect that allows atomic resolution. The successful holder must be dynamically stable for accuracy and image processes to obtain an atomic resolution, with a minimum controllable drift of the sample position. Different strategies to reduce the effect of acoustic disturbances are investigated. The approach to the problem has been two-fold, numerical and experimental. The effect of mechanical and acoustic noise is analyzed. Finite element results match very well previous experimental results and observations. Theoretical analysis showed that air pressure fluctuations have a significant impact on microscopes with side entry goniometers, especially when the exciting frequency matches a vibration mode of the sample holder. For example, finite element analysis (FEA) predicts that the tip deflections are 4.5 Å and 0.09 Å under air pressure excitation of 64 and 40 dB respectively. Utilizing a sandwiched constrained damping shell layer made of viscoelastic material that partially covers the inner part of TEM holder body successfully decreased the vibration. Finite element simulations predict that a shell layer of viscoelastic material with a thickness equal to the 1/10 of the body holder diameter reduces the vibrations by 30%. The viscoelastic layer shell thickness, loss factor, and elastic modulus have a strong effect on the damping behavior and the optimal combination should be determined.

Keywords

Noise in situ TEM instrumentation finite element analysis atomic resolution dynamic responses

Introduction

Transmission Electron Microscopy (TEM) is an imaging method where a beam of electrons is passed through an ultra-thin specimen. TEMs are capable of imaging at ultra-high resolution. The TEM is used heavily in both physical and biological sciences. Due to the advancement in nanotechnology, TEM has become the desired method for examining nanoscale materials. TEM analysis provides information that is directly related to their structure, morphology, and composition. This information and data can be used to enhance the commercializing of the production of nanotechnologies. The small physical gap between the microscope pole pieces has limited the ability to perform in situ experimentation. In a TEM, the specimen is placed into this pole piece gap and needs to be translated in 3D and tilted along a primary axis and often a secondary axis. For ultra-high resolution TEMs, the pole piece gap is on the order of 2.2 mm. 3D information can be obtained by using a tomography holder that allows tilting the specimen up to +/−70°.¹

Recent developments in TEM technology have allowed the capability to perform examinations at atomic scale levels. The effects of environmental disturbances become more apparent at atomic resolution. To obtain high-quality transmission electron microscopy (TEM) images, it is necessary to reduce several types of environmental influence. Environmental effects include, but are not limited to, electromagnetic field, temperature changes,² ground vibration, airflow across the column, and air pressure changes. The effect of these disturbances might not be meaningful for many operations at the micrometer scale, however, they become an important limiting factor when nanometric precision is required.^3
–5 Several studies have identified the effect of electromagnetic interference on image resolution and proposed solutions to minimize its effect.^6
–10,11 The causes and solutions for the image distortions due to sample drift are discussed in.^{6,10,12
–17}

Image distortions due to vibrations are seen at atomic resolution.^3,6,14,18,19 The mains sources of vibrations are; air movement inside the microscope room, motors of the two turbopumps, acoustic disturbances, alternating current (AC) motors, ground vibration, computer fans.^14,19 Hence, reducing both the vibration disturbances and the sensitivity of the TEM to these vibrations have received significant attention by many researchers.^{10
–14,18
–22} Vibration isolators are not effective at high magnification levels (40,000 times). It was found that the distortion caused by vibrations could not be eliminated with a simple filter.¹⁴ Ground vibration reaches the microscope through two paths; via the bedrock on which the building sits, and movement of the building itself. Introducing vibration isolation has been extensively studied.^23,24 The design of vibration isolation utilizes slab-on-grade^7,11 and suspended structures²⁰ were presented. Vibration isolations on most microscopes are very effective when the exciting frequency is above 100 Hz. On the other hand, they can amplify noise at low frequencies (below 10 Hz) depending on their resonance frequency.²⁵ This forms a serious problem since the natural frequencies around 5–10 Hz for most buildings.¹⁴ If the vibration frequency is above a few hundred Hertz, the sample holder will have a significant response to these acoustic vibrations. Muller et al. observed that when the frequency below 60 Hz, the floor vibrates more than the column.²⁶ However, the holder is vibrating more than the floor when the frequency above 60 Hz. Muller's et al. results show that the microscope was also sensitive to acoustic noise at 60 Hz and below.²⁶ Acoustic shielding at these low frequencies is difficult. It is worth mentioning that conventional sound damping material made from polyurethane or other foams are almost completely ineffective in the 0–125 Hz band. The most common vibrations at industrial sites are caused by alternating current (AC) motors which operate at 30, 60, and 120 Hz.

Air movement inside the microscope room can lead to pressure fluctuation which leads to image distortion.¹⁹ Airflow across the column must be less than 0.075 m/s for 0.2 nm resolution⁷ (see Figure 1). A change in air pressure a few Pascal can be detected and deflects the specimen stage by a few angstroms.⁷ Muller et al. used a high precision barometer and found that 1 Pascal of air pressure change leads to sample deflection by 0.1 nm.⁷ Faria et al. reported that acoustic noise with low power levels (46 dB) has a severe effect on the sample, when its frequency matches a vibration mode of the sample holder.¹⁹ Moreover, they observed that the effect of acoustic pressure can be also noticed in everyday situations, that is, conversations in the room, as the first mode of their samples falls within the range of the human speech frequencies. Finally, they concluded that small pressure variations can have large effects on samples if a frequency composing the disturbance matches a resonant mode of a component inside the microscope. The sharpness of the mechanical resonance peak is larger in a vacuum than in air due to lack of air damping. Marks et al. reported that using a silicone oil dashpot (conceptually similar to an automotive shock absorber) can reduce the tip vibration amplitude to ~5 nm.²¹

Figure 1.

Limits of air speed through the microscope column in order to obtained sub 0.3 and 0.2 nm STEM against several environmental sources.^12,13

Careful design and implementation of microscope sites have been the main approach considered to obtain atomic resolution. The optimal building design should have minimal vibration, air flow/fields, and temperature fluctuations. It is recommended to build a new clean building in a clean site. Despite the extensive research, the optimal building designs did not completely eliminate the environmental effects. Control strategies work for a certain limited region of the frequency band. Estimating the sensitivity of a microscope to mechanical or acoustic noise is often not practical. The noises occur at a wide range of frequency band where the sensitivity is a function of the microscope itself. It has been observed that each microscope’s resonances differ from instrument to instrument. It is worth mentioning that thin, tall columns will be more likely to detect air movement than short fat ones.²⁷ One of the main challenges of developing a new holder design is to ensure that the sensitivity of the TEM is maintained while increasing the functionality. The previously discussed reasons are the motivation for this study to develop tomography holder that are stable under extreme environment. Developing this technology allows the possibility to capture 3D information of the material at atomic levels. The objective of this paper is to develop a holder that overcomes the technical problems associated with the current assemblies. This holder must be dynamically stable for accuracy and image processes while simultaneously subjecting it to varying environments, with a minimum controllable drift of the sample position. The most common environmental problem is analyzed herein: Air Pressure Fluctuations. Both numerical and experimental approaches have been used to assess the stability of the sample holder. This study investigates the effectiveness of utilizing constrained shell layer tube as damper to suppress the vibration of the holder tip.

Methods

This study presents dynamics analyses of a tomography TEM holder assembly. In order to develop TEM holder that allows accurate in situ measurements, a formal methodology is developed and presented in the following sections. The damping characteristics of TEM holders incorporating the viscoelastic sandwich shell are investigated. The analyses were performed with the finite element package ANSYS.

Cad Model of tomography holder

Solid modeling has been successfully used in the design of many mechanical systems. Developing a solid model was the first step in developing an accurate tomography holder. Solid modeling can be used to evaluate the model for proper fits and clearances. This is achieved by conducting kinematics motion of the assembly. The final revised solid model is transferred directly into ANSYS software for further dynamic analyses.

Finite element analysis (FEA) is a great design tool, especially for complex shapes and assemblies. Generally, elementary calculations cannot be used for complex irregular shapes. The idea of FEA is to discretize the complex geometry into convenient small geometries whose boundary conditions are known.

A solid model for the proposed design is shown in Figure 2. It is a 10 mm cylindrical rod. The total length is approximately 250 mm that is inserted into the TEM’s goniometer stage. The tip was designed to allow large tilt and long fields of view in high-resolution TEMs with narrow gap pole pieces. Life and physical sciences applications require high-specimen tilt and large viewable area at angles in excess of 70°. Beryllium copper is largely used for the holder assembles because of its desirable X-ray characteristics.

Figure 2.

Solid Model of tomography holder.²⁸

Experimental works

To investigate the effect of pressure fluctuations on the stability and resolution of TEM experimentations, we designed an experimental set up as shown in Figure 3. The qualitative data obtained was used to demonstrate the sensitivity of the TEM holder assembly to air pressure fluctuations. The reasons behind that are the holder is different from the one that is used in FE model, the sample is different, the microscope is different and the clamping mechanism is different. The sound generated from the speaker at known frequencies induces air pressure fluctuations on the amount of 73 dB. Off-shelf sound generator is used to generate audio frequency ranging from 50 HZ to 10,000 HZ. Hand help meter is attached close to the end of the tip holder is used to accurately measure the air pressure levels in dB. A charge-coupled device (CCD) camera was incorporated to show the images on the computer screen. Figure 4 shows a snapshot of the sample (needle) using X330,000 magnifications. As can be seen in Figure 4(a) that the image is rich and steady which creates possibility for accurate examination. Figure 4(b)–(e) shows that the sample experiences vibrations when the speaker is turned on.

Figure 3.

Layout diagram of experimental set up.

Figure 4.

TEM image at several excitation frequencies.³² (a) Speaker off. (b) Excitation frequency = 776 Hz Y-direction. (c) Excitation frequency = 786 Hz in X-direction. (d) Excitation frequency = 3430 Hz in Y-direction. (e) Excitation frequency = 3436 Hz in X-direction. (f) Excitation frequency = 5576 Hz in X-direction.

Theoretical model

Dynamic stability is strict demand on high precision instruments. Sources that distort the images obtained from TEM can originate from both inside and outside of the microscope. Vacuum pump and circulating of the coolant inside the microscope are examples of internal sources. The acoustic disturbances vibrations can be created from both inside TEM room and outside TEM room. Traffic, aircrafts, trains, noise generated from nearby machineries, and other laboratory equipment are considered external sources of acoustic vibration. Fans, electronic noise, and human noise inside the microscope room are the main source of acoustic internal vibration. Maximizing the natural frequencies of the system has been successfully used to minimize the effect of vibrations. Another method for decrease vibration problems is by increasing the structural damping of the structure. Moreover, special damping layers made of viscoelastic materials are widely applied in structures subjected to dynamic loading to reduces the vibrations.28 –32

The vibration analyses were performed using the commercially available package ANSYS. The acoustic noise in this study is restricted to vibrations caused by internal sources (human voice and fans, etc.). Sound is a wave motion in the air or in other elastic media which creates vibrations in the surrounding medium. It is caused by the objects vibrating at specific frequencies. Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average, or equilibrium) atmospheric pressure, caused by a sound wave. In the air, sound pressure can be measured using a microphone. The human voice can cause harmonic variations in air pressure about atmospheric mean. The frequency of the typical human voice ranges between 100 and 10,000 Hz.³³ The sound pressure levels range between 40 and 60 dB. Sound pressure level (SPL) or acoustic pressure level is a logarithmic measure of the effective pressure of a sound relative to a reference value. Sound pressure level, denoted L_p and measured in dB, is defined by Bies and Hansen,³⁴ Roeser and Valente³⁵

L p = 20 \log_{10} (\frac{p}{p_{o}}) d B

(1)

Where p is the root mean square sound pressure, p₀ is the reference sound pressure, the commonly used reference sound pressure in air is p₀ = 20 μPa.³⁴ Most sound-level measurements will be made relative to this reference, meaning 1 Pa will equal an SPL of 94 dB. High values of dB are considered in this study to account for various forms of acoustic disturbances in a very conservative manner.

Modal analysis is a free vibration analysis used to determine natural frequencies and mode shapes of a structure. The natural frequencies and mode shapes are important parameters in the design of a structure for dynamic loading conditions. It also can be a starting point for another, more detailed, dynamic analysis, such as a transient dynamic analysis, a harmonic response analysis, or a spectrum analysis.

These two vibration characteristics are key factors that determine the response of parts under dynamic loads. Furthermore, it is a necessary step for performing dynamic analysis. The equation of motion for free an undamped system can be written in matrix form as:

[M] {\vec{\overset{..}{U}}} + [K] {\vec{U}} = {0}

(2)

Where $\overset{..}{U}$ is the 2nd time derivative of the displacement, [K] is the stiffness matrix, and [M] is the mass matrix. A harmonic solution is assumed for the solution of free—vibration problem as:

\vec{\overset{..}{U}} = λ \vec{U}

(3)

where λ is the eigenvalue. The equation of motion reduces to

[M] λ {\vec{U}} + [K] {\vec{U}} = {0}

(4)

This is an eigenvalue problem. Including some structural damping into the equation of motion, the free vibration problem can be written as:

[M] {\overset{\leftarrow}{\overset{..}{U}}} + [C] {\vec{\dot{U}}} + [K] {\vec{U}} = {0}

(5)

where [C] is the damping matrix. The dynamic response of the system is given by

{u}_{i} = {ϕ}_{i} e^{λ_{i} t}

(6)

where ψi is the eigenvectors and λ_i is the complex eigenvalue.

Harmonic response analysis is used to study the dynamic response of bodies under the effects of forced vibrations. It is a technique used to determine the steady-state response of a linear structure to loads that vary sinusoidally (harmonically) with time. The idea is to calculate the structure's response at several frequencies and obtain a graph of some response quantity (usual displacements) versus frequency. “Peak” responses are then identified on the graph and stresses reviewed at those peak frequencies. The transient vibrations, which occur at the beginning of the excitation, are not accounted for in a harmonic response analysis. The dynamic behavior is well studied by plotting the maximum displacements against several exciting frequencies. The governing equations for the motion of the linear system can be writing as:

[M] {\vec{\overset{..}{U}}} + C {\vec{\dot{U}}} + [K] {\vec{U}} = {\vec{F}}

(7)

where F is the force vector. The damping matrix using the Rayleigh Damping coefficients α and β is given as:

[C] = α [M] + β [K]

(8)

The displacements for damped linear structure can be written in complex a form as:

{u} = {u_{\max} e^{j ϕ}} e^{j Ω t}

(9)

where u_max is the maximum displacement, Ω is the exciting circular frequency (rad/s), and φ is the displacement phase shift (radians). The methodology for solving such equations using finite element methods can be explained in detail in many references.³⁶ The damping matrix is usually not well identified. Estimates for Rayleigh damping parameters is used in this study.

The study investigates different strategies to reduce the effect of acoustic disturbances. To further enhance the damping characteristics of the holder, a constrained viscoelastic shell layer is utilized to cover the portion of the holder. A single sandwich system is investigated in this study. The properties of viscoelastic materials depend on frequency and temperature. Classical Hooke law cannot be used to describe the behavior of viscoelastic material. Viscoelasticity is implemented through the use of the Prony series. The shear and volumetric responses are separated, and the well-known relationships between shear modulus G and bulk modulus K are shown below:

The kernel functions are represented in terms of the Prony series, which assumes that

G (t) = G_{\infty} + \sum_{i = 1}^{n_{G}} G_{i} e^{- \frac{t}{τ_{i}^{G}}}

(10)

K (t) = K_{\infty} + \sum_{i = 1}^{n_{G}} K_{i} e^{- \frac{t}{τ_{i}^{G}}}

(11)

where G_i is shear modulus, G_∞ is final shear modulus, K_i is the bulk modulus, K_∞ is the final bulk modulus. τ_i^G and τ_i^K are relaxation time of the Prony series component. These equations imply that the shear and bulk moduli are represented by a decaying function of time t. Introducing relative moduli, the kernel functions can be expressed as:

G (t) = G o [α_{\infty}^{G} + \sum_{i = 1}^{n_{G}} α_{i}^{G} e^{- \frac{t}{τ_{i}^{G}}}]

(12)

K (t) = K o [α_{\infty}^{G} + \sum_{i = 1}^{n_{G}} α_{i}^{G} e^{- \frac{t}{τ_{i}^{G}}}]

(13)

where G₀ and K₀ denote instantaneous shear and bulk moduli respectively. A detailed descript of the constitutive model for the viscoelastic materials is given in Park and Schapery.³⁷

Numerical model

The ANSYS software program was used in conjunction with 3D computer-aided-design (CAD) to study the dynamic behavior of the TEM holder assembly. The results obtained from this software can evaluate the design performance and provide guidelines on how to revise the design. ANSYS software has been successfully used to study the dynamic response of structures. The actual assembly ‘solid model’ created was imported into ANSYS. No geometry simplifications were required. Dynamic analysis requires input data such as density, modulus of elasticity, and Poisson’s ratio for each part in the assembly. After performing a mesh independent study, a model composes of 88,000 elements is used. SOLID187 and SOLID186 were chosen for all parts of the assembly because have a quadratic displacement behavior and are well suited to modeling irregular meshes. Targe170 and Conta174 were used between contacting bodies. A finer mesh is created at critical parts of the assembly, mainly, at the holder tip and at TEM goniometer stage.

Figure 5 shows a solid model for the proposed tomography holder. The TEM goniometer stage was modeled as three 3 mm silver spheres 120° apart at two locations along the holder as shown in Figure 5. The X-axis lies along the length of the holder. The Y-axis is perpendicular to the sample face. Of the three spheres at each support location, the sphere that was located along the Y-axis was assumed to be attached to a spring-damper. The loading condition for free vibration analysis requires only a constraint from rigid body motion. This loading condition for free vibration analysis (modal) is a fixed support at the six spheres. We assumed that the clamping mechanism between the sample and the sample grid fully constrained the sample. A contact bond was used to satisfy this condition. We also assumed that the clamping mechanism between the sample grid and the holder tip was bonded. Standard contact conditions were used between the spheres and the holder body. In addition to the previous assumptions, we assumed there are no thermal strains due to irradiation from the electron beam. The finite element model is shown in Figure 6.

Figure 5.

Solid Model of tomography holder showing support.²⁸

Figure 6.

Finite elements model.²⁸

A simplified model of symmetric constrained shell tube of viscoelastic material inserted inside the TEM body is built to investigate the damping effect. Figure 7 shows the geometry of TEM holder with a viscoelastic shell damping layer. Viscoelastic shell layer is in contact with both the inner surface and the outer surface of the sample holder. In ANSYS, viscoelasticity is implemented through the use of Prony series. The shear and volumetric responses are separated, and the well-known relationships between shear modulus G and bulk modulus K are shown below:

G (t) = \frac{E (t)}{2 (1 + ν)}, K (t) = \frac{E (t)}{3 (1 - 2 ν)}

(13)

where E(t) is the relaxation modulus determined by experimental data. Table 1 list the material properties. Table 2 Parameters of the Prony series.²⁸

Figure 7.

Geometry of cylindrical aluminum shell with viscoelastic damping layer.

Table 1.

Material properties of copper and viscoelastic material.

Material	Density [kg/m³]	Modulus of elasticity [Pa]	Poisons ratio
Copper	8300	2.0 × 10¹¹	0.3
Viscoelastic material²⁸	970	2.1 × 10⁶	0.499

Table 2.

Parameters of Prony series.²⁸

G₀ [Pa]	G_∞ [Pa]	$α_{1}^{G} = α_{1}^{K}$	$α_{21}^{G} = α_{2}^{K}$
9.69 × 10⁶	2.36 × 10⁵	0.0579	0.034
$α_{3}^{G} = α_{3}^{K}$	$τ_{1}^{G} = τ_{1}^{K}$	$τ_{2}^{G} = τ_{2}^{K}$	$τ_{3}^{G} = τ_{3}^{K}$
0.6649	30130.7	3013.7	301.307

Table 3.

Undammed natural frequencies with and without viscoelastic shell.

Frequency (HZ)	First order	Second order	Third order	Fourth order	Fifth order	Sixth order	Seventh order
No viscoelastic material	112.9	165.4	1270.8	1403.5	1599.8	1674.1	1864.6
With viscoelastic shell	110.2	162.3	1252.7	1382.3	1573.3	1643.7	1812.7

Results and discussion

Modal analysis

Modal analysis was used to determine the natural frequencies of vibration. The natural frequencies and mode shapes are important parameters in the design for dynamic loading conditions. The natural frequencies of the holder are presented in Table 3. The first and the fourth mode shape are shown in Figure 8. As can be seen in Table 3 that the range of the typical audio exciting frequencies falls within the first set of the holder natural frequencies. Moreover, Table 3 lists the natural frequencies when adding the viscoelastic layer. Finite element simulations are carried out to investigate the system dynamic behavior when exciting frequency near system frequencies.

Figure 8.

Mode shapes: (a) first mode shape and (b) fourth mode shape.²⁸

Harmonic analysis

The harmonic analysis was carried for three-level of sound pressure namely, 40 dB, 68 dB, and 94 db. According to the equation (1), the corresponding air pressure fluctuations around the mean value are 1 Pa, 0.05 Pa, and 0.002 Pa respectively. Since it is extremely difficult to determine accurately the structural damping constants for the complicated assembly, and to improve the reliability of the numerical results, the effect of two values of material damping constants were simulations, namely, β = 0.01and β = 0.05. The Rayleigh Damping coefficients α α is set equal to zero in the entire simulations.

Figure 9 shows the sample displacements in three directions in the vicinity of the first natural frequency under an extremely high value of acoustic pressure level (94 dB). The damped natural frequencies for β = 0.01 and 0.05 are 99.2 HZ and 98.3 HZ respectively which are lower than the undamped natural frequency 112.9 HZ. The finite element simulations predicted that the displacement in the y-direction is considerably higher than the other two directions. Increasing the internal damping has resulted in reducing the damped resonance and the peak response. The tip maximum deflection for β = 0.01 is 11.25 nm, while for β = 0.05, the tip deflection is 2.8 nm. A small amount of internal damping has resulted in reducing the peak amplitude by order of magnitude. As mentioned previously typical values of acoustic pressure level inside the microscope room ranged between 40 and 60 dB. FEA predicts that the tip deflections for β = 0.01 are 4.5 Å and 0.09 Å under air pressure excitation of 64 and 40 dB respectively (see Figure 10). These values are in good agreement with previously published results.²⁶ Increasing the damping constant up to 5%, the tip defections are reduced to 1.4 Å and 0.028 Å under the acoustic sound of 40 dB and 64 dB respectively.

Figure 9.

Sample displacement (m) in all three directions.

Figure 10.

Sample displacement (m) in y-direction under two levels of acoustic sound: (a) Acoustic pressure level = 40 dB and (b) Acoustic pressure level = 64 dB

The response around the natural frequencies depends largely on the values of damping coefficients. To investigate the effect of damping on the displacement of the holder tip around the natural frequencies, simulations were carried out. Figure 11 shows the system response as a function of damping constant at the resonance frequency. The results presented in Figure 9 show that increasing the damping coefficient has a significant effect on reducing the magnitude of the displacement. Applying harmonic pressure of magnitude 1 PA, the displacement predicted by FEA is on the order of 1nm. Due to the fact that the exciting frequency ranges between 100 and 10,000 HZ, reducing vibration by altering the natural frequency cannot be effective. In this case, two methods can be utilized to reduce the vibration at resonance, increasing internal damping, and introducing vibration isolation. Using very stiff material that has a high loss factor increases the internal damping. A vibration isolator works by reducing the transmitted force to the holder tip.

Figure 11.

Variation of sample displacement in the y-direction with damping constant.

It is known that beams vibrating under harmonic excitation exhibit a certain amount of internal material damping. The results presented in Figures 9 –11 showed that the material damping is not sufficient to reduce the vibrations under resonant excitation. To decrease the vibration energy of the holder under acoustic disturbances, viscoelastic layers have been commonly used.^28–32 Viscoelastic materials used in such applications are used to dissipate energy when subjected to alternating deformation. The holder as shown in Figure 7 is partially covered by damping a constraining layer. The layers of the holder consist of an isotropic, linear elastic or viscoelastic material.

The effect of viscoelastic layer shell thickness, loss factor, and elastic modulus on the damping performance is numerically investigated. Results presented in Figure 12 clearly demonstrate that a thicker viscoelastic shell reduces the vibration more compared to the thinner layer. The effect of changing both loss factor and elastic on the damping characteristic is studied. The maximum vibration displacement under different parameters is obtained as given in Table 4. It can be seen that vibration displacement is the minimum when the loss factor is chosen as 1.2 and elastic modulus is 0.5 MPa. Its amplitude decreases 44.5% comparing with that when loss factor is chosen as 0.5 and elastic modulus is chosen as 2 MPa.

Figure 12.

Effect of viscoelastic shell in sample displacement in the y-direction, acoustic pressure level = 94 dB.

Table 4.

The maximum displacement of sample [nm] with different loss factor and elasticity modulus of the viscoelastic material, 94 dB acoustic pressure.

Loss factor	0.6	0.8	1	1.2
Elasticity modulus [MPa]
0.5	1.96	1.86	1.73	1.53
1	2.32	2.05	1.76	1.62
1.5	3.18	2.87	2.3	1.75
2	3.44	2.87	2.47	1.86

Conclusion

This paper presents a comprehensive study of the dynamic behavior using finite element tools (ANSYS) for the proposed tomography holder. The proposed tomography holder allows tilting specimen up to +/−70° while maintaining atomic resolution. The atomic resolution requires atomic stability. The optimal design of microscope’s building and the room does not completely eliminate the environmental effect. Vibration isolation and active system work for a limited frequency range. Finite element methods are successfully used to assess design characteristics. Theoretical analysis shows that air pressure fluctuations have a significant impact on microscopes with side entry goniometers. It was found the finite element results are in a good agreement with experimental observations. Air pressure changes of 1 Pa can result in a stage deflection of about 0.1 nm which matches previous studies. To maintain pressure stability, recommend air pressure changes to less than a few Pascal per minute. It was found that the most feasible solution is to increase the damping. Finite element simulations predicted that using viscoelastic shell materials significantly reduce the sample vibrations. The thickness, damping ratio, and the placement of the viscoelastic damping layer should be investigated carefully to determine the optimal combinations.

Footnotes

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Khaled Bataineh

Data availability

data is available through request from the corresponding author.

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