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Simple method for making deeply curved mesh
Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 64–67
Contents lists available at ScienceDirect
Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Short communication
Simple method for making deeply curved mesh László Tóth a,b , Hiroyuki Matsuda a,b , Hiroshi Daimon a,b,∗ a b
Nara Institute of Science and Technology (NAIST), 8916-5 Takayama, Ikoma, Nara 630-0192, Japan CREST, Japan Science and Technology Agency, Saitama 332-0012, Japan
a r t i c l e
i n f o
Article history: Received 28 March 2008 Received in revised form 21 February 2009 Accepted 21 February 2009 Available online 6 March 2009 Keywords: Mesh lens Curved mesh Ellipsoidal mesh Woven-mesh Electrostatic lens
a b s t r a c t For the purpose of making deep ellipsoidal stainless steel woven-mesh lenses used in electron optical systems, we have developed some new methods and tools. We succeeded in decreasing the diameter of wires in a simple controlled way in acids just by measuring the time. We used the thermal expansion in our pressing mold to produce a strong pressing force not just at the bottom but in all directions and resulting in good shaped strongly fixed wires. Using these methods, we could make deep ellipsoidal stainless steel woven-mesh lenses, which can be effectively applied in an electrostatic lens system. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Mesh lenses are frequently used in electron optical instruments [1–5]. These are usually flat or spherical [1,2] where the latter can be formed by a simple pressing method. However, in some cases, such as wide acceptance angle electron optics [3–5], deeper lenses are needed. We have developed a new method for making more deeply curved stainless steel woven-mesh lenses which can be used in many fields. A deep ellipsoidal deformation of a woven mesh sheet shows a characteristic form (Fig. 1). That is, at certain directions (in this case horizontal and vertical) the original square-hole structure remains almost distortion free (black lines in Fig. 1(b and c)) while in other directions strong shearing deformations occur (white lines in Fig. 1(b and c)). These distort the transmittance (Tr) of the mesh lens in different directions and cause some other difficulties. One of these difficulties is that at a certain lens diameter (d) the maximum depth (Zmax ) of the ellipsoidal deformation without folding depends on the maximum shearing deformation of the mesh which finally depends on the wire diameter (Ø)/distance (w) ratio of the given mesh sheet (see Fig. 1(d)). Therefore, for a certain density mesh, Zmax and Tr can be increased by choosing a smaller Ø mesh. Although there are several kinds of woven mesh with small Ø, usually these are woven too tightly, resulting in strong friction force against a deep deformation. This force, however, can be decreased by decreasing the Ø, e.g. by solving the wire in acid. The
solving method has been used by Eastman et al. to make a shallow ellipsoidal mesh [1]. The next step is the pressing where we had to solve two main problems. One of these is how to strongly press the side wall while reducing the downward shearing motion and the other is how to fix the wires in the mesh lens without deforming them. The first problem can be solved entirely and the second partly by using a new mold where following the downward motion the inner part is heated while the outer cooled to produce a strong pressing force in all directions using the thermal expansion. The complete resolution of the wire fixing problem requires an additional special shaped fixing ring which is spot-welded at the bottom of the mesh lens. 2. Solving the mesh in HNO3 + 3HCl solution In order to decrease the wire radius (r = Ø/2), we solved the mesh in HNO3 + 3HCl solution. However, to realize a certain r it was necessary to know the change of the radius as a function of solution time (t) in the acid without direct radius measurements. We created a model to describe the r = r(t) function for a certain acid temperature, concentration and mesh material. In our work we solved 120 mm × 120 mm size #100 line/inch and #400 line/inch SUS 316 mesh where in both cases the length (l) of the individual wires were much longer than their radius (r0 ) as l 2r0
(1)
which is true even for smaller pieces (e.g. 10 mm × 10 mm size) of mesh. Then, we assumed that ∗ Corresponding author at: Nara Institute of Science and Technology (NAIST), 8916-5 Takayama, Ikoma, Nara 630-0192, Japan. Tel.: +81 743 72 6020. 0368-2048/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2009.02.013
V = −c1 t
(2)
L. Tóth et al. / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 64–67
65
Fig. 1. Deep ellipsoidal deformation of a woven-mesh sheet. The arrows in (a) show the direction of deformation and the thin solid lines represent the net structure of the mesh sheet that is not visible at this magnification. (b and c) The top view and the side view of a ready made mesh lens, respectively. (d) shows definitions of r0 , Ø and w.
where V is the volume of an individual wire and c1 is a constant. Since any of the small l length parts of the long wire is solved in the acid in the same way, therefore A V = = −c2 lt t
(3)
where A (t) = r 2 (t)
(4)
is the cross section of an individual wire and c2 is a constant. Solving Eq. (3) we get A(t) = r02 − c2 t
(5)
Solving the combination of Eqs. (4) and (5) we get
r(t) =
r02 −
c2 t
(6)
From the time tmax when the wires are totally solved, i.e. r(tmax ) = 0, one can determine c2 easily: c2 =
r02
(7)
tmax
Fig. 2. Solution of a stainless steel mesh (#400 line/inch, Ø 30 m SUS 316) in HNO3 + 3HCl solution. The temperature (T) changed from the initial 26.5 ◦ C to 27 ◦ C and the acid concentration was kept quasi-constant by using continuous stir and a much larger volume of acid than the volume of the mesh. The error-bars in the figure include the error in the difference of materials of different direction wires.
Substituting Eq. (7) into Eq. (6) finally we get
r(t) = r0
1−
t tmax
(8)
for describing the changes of mesh wire radius r as a function of solution time t with the initial radius r0 and the time tmax that is needed for the entire solution of a certain material wire at a certain temperature and acid concentration. In order to keep the solving velocity of Eq. (3) constant, the quantity of the acid should be several tens times larger than the minimum quantity to solve the entire mesh. This tmax can be determined easily by solving a small piece (e.g. 10 mm × 10 mm size) of mesh entirely in the acid and measuring the elapsed time. The validity of Eq. (8) is shown in Fig. 2 where we put 10 mm × 10 mm size #400 line/inch, Ø: 30 m, SUS 316 meshes into HNO3 + 3HCl solution and measured the average wire diameter as a function of elapsed time. The measured data fit well with the calculated curves, which means that Eq. (8) can be applied to control the diameter changes of a thin long wire in acid as a function of nothing else than the solution time. Fig. 2 shows that the different direction (X and Y) wires of the used woven-mesh have different speed of the change of diameter, which shows that there is a rather
wide distribution in the rate even for the same material. However, this formula is useful even in such a case and also useful in any other case where similar diameter decreasing is needed. 3. Pressing mesh by thermal expansion A typical mold (like Fig. 3(d)) is able to press mainly at the bottom and applies shearing force with little or no pressure on the side wall. In our case, this method was not possible because a thin wire can easily break even by a small force produced by the friction and shearing forces between the inner and outer walls of the mold. Furthermore, after the pressing, in contrast to a solid material, the individual wires in the woven-mesh can shift from its position thus deforming the final required shape. To avoid this deformation it is necessary to fix the wires, e.g. by a strong perpendicular pressing force, not just at the bottom but also at the side wall. This pressing force perpendicular to the side wall at the entrance of the mesh can be calculated as 0.5 of the pressing force if Z/d = 0.29 for spherical shape because the perpendicular angle is 60◦ from vertical direction, and cos 60◦ = 0.5. This shape of curved mesh is widely used for LEED apparatus. This ratio 0.5 of the pressing force seems
66
L. Tóth et al. / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 64–67
Fig. 3. Basic processes of mesh-lens forming.
critical limit for simple pressing. Hence simple pressing method seems not to be used for deeper mesh of Z/d > 0.3. Such strong perpendicular pressing force can be produced easily by thermal expansion if the inner mold is heated while the outer is kept at room temperature (Fig. 3). Fig. 4 shows how the real pressing mold looks. As a first step of the pressing process the lens holder ring is fitted into the hole at the top of the outer mold (Fig. 3(a)). Following that, a solved square-shaped mesh sheet is put on it (Figs. 1 and 3(b)), and then the pressing disc (Fig. 3(c)) is put on it to keep the mesh sheet tight and smooth during the processes. The next step is a slow downward motion of the inner mold until it touches the bottom (Fig. 3(d)). Then a downward pressing force of about 30 N/mm2 is applied using screws and almost perpendicular pressing force of about 40 N/mm2 is applied using thermal expansion by heating the inner mold to 70 ◦ C and sudden cooling the outer mold to 20 ◦ C (Fig. 3(e)) by water. Because this force is estimated to be between 20% and 80% of the capacity to resist [endure] pressure of the mesh
material of SUS316, the contact area can be increased to be more than 20% of the total area. After applying this pressure several times, the mesh sheet and a special shaped ring were spot-welded to the holder ring (Fig. 3(f)) to fix the lower part of the lens in the correct shape and position. Finally, following an additional heated pressing, the mesh lens is ready and can be removed carefully from the mold (Figs. 1(g) and 5(b)). One of our prepared mesh lenses is shown in Fig. 5. The original mesh sheet (#100 line/inch, Ø: 50 m, stainless steel, woven type) was solved in HNO3 + 3HCl solution that resulted in Ø: 30 ± 2 m for the x and Ø: 34 ± 2 m for the y direction wires. The shape differences from the ideal ellipsoid are less than 0.5 mm. The shiny surface is a result of the strong pressing force of thermal expansion. The position-dependent total deformation, as well as the transmittance Tr of our mesh lens, can be estimated easily by applying the following assumptions. At the top of the mesh, there is no dis2 tortion and Tr is (1 − /w) = 0.8742 = 0.76. The length of the wire did not change in x and y axes in Fig. 1(a). The size of the present
Fig. 4. The cutaway view and picture of the thermal expansion type pressing mold.
L. Tóth et al. / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 64–67
67
When we use the same Ø/w value as that in the vertical direction, the Tr at the bottom is (1 − 0.34) × 0.874 = 0.58. The total transmittance of the present mesh lens thus is estimated to be more than 60% on average. 4. Summary
Fig. 5. One of our prepared mesh lenses. The original mesh sheet (#100 line/inch, Ø: 50 m, stainless steel, woven type) was solved in HNO3 + 3HCl solution that resulted in Ø: 30 ± 2 m for the x and Ø: 34 ± 2 m for the y direction wires. The shape differences from the ideal ellipsoid are less than 0.5 mm. The shiny surface is a result of the strong pressing force of thermal expansion.
mesh is d = 42.8 mm, Z = 36.4 mm, S = 46.0 mm. The number of wires included in the large circle in Fig. 1(a) is therefore 1450. Hence the wire occupies 1450 × (0.030 + 0.034)/2 = 46.4 mm of the circumference of the small circle of Fig. 1(b) of × d = 135 mm, which is 34%.
For making deep ellipsoidal stainless steel woven-mesh lenses, some new methods and tools have been developed here. Because the maximum depth of the ellipsoidal deformation of a given mesh sheet, as well as its transmittance, depends on the wire diameter distance ratio, a decrease of the ratio is necessary, and we have found a simple controlled way by just solving in acid and controlling the time. The ratio is a function of solving time in acid. To avoid the shear and to produce strong pressing force not just at the bottom but also in all directions we used thermal expansion in our pressing mold resulting in good shape and strongly fixed wires. By these methods we succeeded in making deep ellipsoidal stainless steel woven-mesh lens for an electrostatic lens system. References [1] D.E. Eastman, J.J. Donelon, N.C. Hien, F.J. Himpsel, Nucl. Instrum. Methods Phys. Res. 172 (1980) 327. [2] H. Daimon, Rev. Sci. Instrum. 59 (1988) 545. [3] H. Matsuda, H. Daimon, M. Kato, M. Kudo, Phys. Rev. E 71 (2005) 066503. [4] H. Matsuda, H. Daimon, Phys. Rev. E 74 (2006) 036501. [5] H. Matsuda, H. Daimon, L. Toth, F. Matsui, Phys. Rev. E 75 (2007) 046402.
Contents lists available at ScienceDirect
Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Short communication
Simple method for making deeply curved mesh László Tóth a,b , Hiroyuki Matsuda a,b , Hiroshi Daimon a,b,∗ a b
Nara Institute of Science and Technology (NAIST), 8916-5 Takayama, Ikoma, Nara 630-0192, Japan CREST, Japan Science and Technology Agency, Saitama 332-0012, Japan
a r t i c l e
i n f o
Article history: Received 28 March 2008 Received in revised form 21 February 2009 Accepted 21 February 2009 Available online 6 March 2009 Keywords: Mesh lens Curved mesh Ellipsoidal mesh Woven-mesh Electrostatic lens
a b s t r a c t For the purpose of making deep ellipsoidal stainless steel woven-mesh lenses used in electron optical systems, we have developed some new methods and tools. We succeeded in decreasing the diameter of wires in a simple controlled way in acids just by measuring the time. We used the thermal expansion in our pressing mold to produce a strong pressing force not just at the bottom but in all directions and resulting in good shaped strongly fixed wires. Using these methods, we could make deep ellipsoidal stainless steel woven-mesh lenses, which can be effectively applied in an electrostatic lens system. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Mesh lenses are frequently used in electron optical instruments [1–5]. These are usually flat or spherical [1,2] where the latter can be formed by a simple pressing method. However, in some cases, such as wide acceptance angle electron optics [3–5], deeper lenses are needed. We have developed a new method for making more deeply curved stainless steel woven-mesh lenses which can be used in many fields. A deep ellipsoidal deformation of a woven mesh sheet shows a characteristic form (Fig. 1). That is, at certain directions (in this case horizontal and vertical) the original square-hole structure remains almost distortion free (black lines in Fig. 1(b and c)) while in other directions strong shearing deformations occur (white lines in Fig. 1(b and c)). These distort the transmittance (Tr) of the mesh lens in different directions and cause some other difficulties. One of these difficulties is that at a certain lens diameter (d) the maximum depth (Zmax ) of the ellipsoidal deformation without folding depends on the maximum shearing deformation of the mesh which finally depends on the wire diameter (Ø)/distance (w) ratio of the given mesh sheet (see Fig. 1(d)). Therefore, for a certain density mesh, Zmax and Tr can be increased by choosing a smaller Ø mesh. Although there are several kinds of woven mesh with small Ø, usually these are woven too tightly, resulting in strong friction force against a deep deformation. This force, however, can be decreased by decreasing the Ø, e.g. by solving the wire in acid. The
solving method has been used by Eastman et al. to make a shallow ellipsoidal mesh [1]. The next step is the pressing where we had to solve two main problems. One of these is how to strongly press the side wall while reducing the downward shearing motion and the other is how to fix the wires in the mesh lens without deforming them. The first problem can be solved entirely and the second partly by using a new mold where following the downward motion the inner part is heated while the outer cooled to produce a strong pressing force in all directions using the thermal expansion. The complete resolution of the wire fixing problem requires an additional special shaped fixing ring which is spot-welded at the bottom of the mesh lens. 2. Solving the mesh in HNO3 + 3HCl solution In order to decrease the wire radius (r = Ø/2), we solved the mesh in HNO3 + 3HCl solution. However, to realize a certain r it was necessary to know the change of the radius as a function of solution time (t) in the acid without direct radius measurements. We created a model to describe the r = r(t) function for a certain acid temperature, concentration and mesh material. In our work we solved 120 mm × 120 mm size #100 line/inch and #400 line/inch SUS 316 mesh where in both cases the length (l) of the individual wires were much longer than their radius (r0 ) as l 2r0
(1)
which is true even for smaller pieces (e.g. 10 mm × 10 mm size) of mesh. Then, we assumed that ∗ Corresponding author at: Nara Institute of Science and Technology (NAIST), 8916-5 Takayama, Ikoma, Nara 630-0192, Japan. Tel.: +81 743 72 6020. 0368-2048/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2009.02.013
V = −c1 t
(2)
L. Tóth et al. / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 64–67
65
Fig. 1. Deep ellipsoidal deformation of a woven-mesh sheet. The arrows in (a) show the direction of deformation and the thin solid lines represent the net structure of the mesh sheet that is not visible at this magnification. (b and c) The top view and the side view of a ready made mesh lens, respectively. (d) shows definitions of r0 , Ø and w.
where V is the volume of an individual wire and c1 is a constant. Since any of the small l length parts of the long wire is solved in the acid in the same way, therefore A V = = −c2 lt t
(3)
where A (t) = r 2 (t)
(4)
is the cross section of an individual wire and c2 is a constant. Solving Eq. (3) we get A(t) = r02 − c2 t
(5)
Solving the combination of Eqs. (4) and (5) we get
r(t) =
r02 −
c2 t
(6)
From the time tmax when the wires are totally solved, i.e. r(tmax ) = 0, one can determine c2 easily: c2 =
r02
(7)
tmax
Fig. 2. Solution of a stainless steel mesh (#400 line/inch, Ø 30 m SUS 316) in HNO3 + 3HCl solution. The temperature (T) changed from the initial 26.5 ◦ C to 27 ◦ C and the acid concentration was kept quasi-constant by using continuous stir and a much larger volume of acid than the volume of the mesh. The error-bars in the figure include the error in the difference of materials of different direction wires.
Substituting Eq. (7) into Eq. (6) finally we get
r(t) = r0
1−
t tmax
(8)
for describing the changes of mesh wire radius r as a function of solution time t with the initial radius r0 and the time tmax that is needed for the entire solution of a certain material wire at a certain temperature and acid concentration. In order to keep the solving velocity of Eq. (3) constant, the quantity of the acid should be several tens times larger than the minimum quantity to solve the entire mesh. This tmax can be determined easily by solving a small piece (e.g. 10 mm × 10 mm size) of mesh entirely in the acid and measuring the elapsed time. The validity of Eq. (8) is shown in Fig. 2 where we put 10 mm × 10 mm size #400 line/inch, Ø: 30 m, SUS 316 meshes into HNO3 + 3HCl solution and measured the average wire diameter as a function of elapsed time. The measured data fit well with the calculated curves, which means that Eq. (8) can be applied to control the diameter changes of a thin long wire in acid as a function of nothing else than the solution time. Fig. 2 shows that the different direction (X and Y) wires of the used woven-mesh have different speed of the change of diameter, which shows that there is a rather
wide distribution in the rate even for the same material. However, this formula is useful even in such a case and also useful in any other case where similar diameter decreasing is needed. 3. Pressing mesh by thermal expansion A typical mold (like Fig. 3(d)) is able to press mainly at the bottom and applies shearing force with little or no pressure on the side wall. In our case, this method was not possible because a thin wire can easily break even by a small force produced by the friction and shearing forces between the inner and outer walls of the mold. Furthermore, after the pressing, in contrast to a solid material, the individual wires in the woven-mesh can shift from its position thus deforming the final required shape. To avoid this deformation it is necessary to fix the wires, e.g. by a strong perpendicular pressing force, not just at the bottom but also at the side wall. This pressing force perpendicular to the side wall at the entrance of the mesh can be calculated as 0.5 of the pressing force if Z/d = 0.29 for spherical shape because the perpendicular angle is 60◦ from vertical direction, and cos 60◦ = 0.5. This shape of curved mesh is widely used for LEED apparatus. This ratio 0.5 of the pressing force seems
66
L. Tóth et al. / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 64–67
Fig. 3. Basic processes of mesh-lens forming.
critical limit for simple pressing. Hence simple pressing method seems not to be used for deeper mesh of Z/d > 0.3. Such strong perpendicular pressing force can be produced easily by thermal expansion if the inner mold is heated while the outer is kept at room temperature (Fig. 3). Fig. 4 shows how the real pressing mold looks. As a first step of the pressing process the lens holder ring is fitted into the hole at the top of the outer mold (Fig. 3(a)). Following that, a solved square-shaped mesh sheet is put on it (Figs. 1 and 3(b)), and then the pressing disc (Fig. 3(c)) is put on it to keep the mesh sheet tight and smooth during the processes. The next step is a slow downward motion of the inner mold until it touches the bottom (Fig. 3(d)). Then a downward pressing force of about 30 N/mm2 is applied using screws and almost perpendicular pressing force of about 40 N/mm2 is applied using thermal expansion by heating the inner mold to 70 ◦ C and sudden cooling the outer mold to 20 ◦ C (Fig. 3(e)) by water. Because this force is estimated to be between 20% and 80% of the capacity to resist [endure] pressure of the mesh
material of SUS316, the contact area can be increased to be more than 20% of the total area. After applying this pressure several times, the mesh sheet and a special shaped ring were spot-welded to the holder ring (Fig. 3(f)) to fix the lower part of the lens in the correct shape and position. Finally, following an additional heated pressing, the mesh lens is ready and can be removed carefully from the mold (Figs. 1(g) and 5(b)). One of our prepared mesh lenses is shown in Fig. 5. The original mesh sheet (#100 line/inch, Ø: 50 m, stainless steel, woven type) was solved in HNO3 + 3HCl solution that resulted in Ø: 30 ± 2 m for the x and Ø: 34 ± 2 m for the y direction wires. The shape differences from the ideal ellipsoid are less than 0.5 mm. The shiny surface is a result of the strong pressing force of thermal expansion. The position-dependent total deformation, as well as the transmittance Tr of our mesh lens, can be estimated easily by applying the following assumptions. At the top of the mesh, there is no dis2 tortion and Tr is (1 − /w) = 0.8742 = 0.76. The length of the wire did not change in x and y axes in Fig. 1(a). The size of the present
Fig. 4. The cutaway view and picture of the thermal expansion type pressing mold.
L. Tóth et al. / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 64–67
67
When we use the same Ø/w value as that in the vertical direction, the Tr at the bottom is (1 − 0.34) × 0.874 = 0.58. The total transmittance of the present mesh lens thus is estimated to be more than 60% on average. 4. Summary
Fig. 5. One of our prepared mesh lenses. The original mesh sheet (#100 line/inch, Ø: 50 m, stainless steel, woven type) was solved in HNO3 + 3HCl solution that resulted in Ø: 30 ± 2 m for the x and Ø: 34 ± 2 m for the y direction wires. The shape differences from the ideal ellipsoid are less than 0.5 mm. The shiny surface is a result of the strong pressing force of thermal expansion.
mesh is d = 42.8 mm, Z = 36.4 mm, S = 46.0 mm. The number of wires included in the large circle in Fig. 1(a) is therefore 1450. Hence the wire occupies 1450 × (0.030 + 0.034)/2 = 46.4 mm of the circumference of the small circle of Fig. 1(b) of × d = 135 mm, which is 34%.
For making deep ellipsoidal stainless steel woven-mesh lenses, some new methods and tools have been developed here. Because the maximum depth of the ellipsoidal deformation of a given mesh sheet, as well as its transmittance, depends on the wire diameter distance ratio, a decrease of the ratio is necessary, and we have found a simple controlled way by just solving in acid and controlling the time. The ratio is a function of solving time in acid. To avoid the shear and to produce strong pressing force not just at the bottom but also in all directions we used thermal expansion in our pressing mold resulting in good shape and strongly fixed wires. By these methods we succeeded in making deep ellipsoidal stainless steel woven-mesh lens for an electrostatic lens system. References [1] D.E. Eastman, J.J. Donelon, N.C. Hien, F.J. Himpsel, Nucl. Instrum. Methods Phys. Res. 172 (1980) 327. [2] H. Daimon, Rev. Sci. Instrum. 59 (1988) 545. [3] H. Matsuda, H. Daimon, M. Kato, M. Kudo, Phys. Rev. E 71 (2005) 066503. [4] H. Matsuda, H. Daimon, Phys. Rev. E 74 (2006) 036501. [5] H. Matsuda, H. Daimon, L. Toth, F. Matsui, Phys. Rev. E 75 (2007) 046402.