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![Distribution of vibration amplitude and stress along the waveguide [41].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/6725f61d1bd9545d6f42ef3e/j_msp-2024-0028_fig_005.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKMAP2UW6E%2F20260119%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260119T112103Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEMb%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJIMEYCIQD42JIMT8FAkobAIft8qXE7Dup4%2BALRgUXnp1nABKso2QIhAMvKxnZe8Z%2BaUePUHSy%2F8KVI8KVzB773Jyae8lXtQ%2BIyKsQFCI%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEQAhoMOTYzMTM0Mjg5OTQwIgztCVp8fKC3iJBD4pUqmAWgtkgQ8Q2yfPrG131tbxAVS5mXrikAgdyD5hdYgLlVJyDKGmvhZW6%2BOh3EOJOOsfN48ynOPmglm8OZNY%2Fgj1%2FC%2BIb5swPG3lgLthd3dWPphNT5xqdEzkI2ILrW4xxfrkyUHdBU4OxPt4mAgidHlw3EHzY8FdjdPYNs2KxGSsWMKUrxcGTZFPJ3ezD89wIIl1oajJTITKLXmwJNooQWSYLlnsJYPvuCbQdYmCq1YcWQgIwlAdADKmsFNlbuOGXqF7R7bi8liuM5KCox5FaNA0af269mdILvqw4zXDFsI0KDlsCwIOk88MUBqGRJuLVNVNTihpUo0qG5J08MxNRyOa7iXRFBBnoqabQlX%2BNfkOXlqBo2WhFJ5uLqCZNbjJ3WhkXKrwbX2gbz53pSKKBYnQKHG%2BJkIYaLNhb3LkNhR64EYnI9YmVRXsmHhuxoaCcCSR8rp%2BZAGRmxgF78c2n9jUH2vt3BflbQx9FfPwTukrku8JIxMK0cmr2I%2B9RZ0kgQed9iqa3WGYd%2BuxSUY9zKJuXVZ6GVF%2B7BF9sDsqBC4qcwMbFd7cZ4EC%2BFVVWfZ4S%2B2kfVW2jZt8B7ZSoqKA%2Fk2zRxhVCh3HpgDPoV8S3nA32LALfTkNOUa6m9Vg8OOog2p7ZZ0ZB4X%2FYg%2BGURleuf2Yi6HoHn%2F%2Fdulcin2eAnjsMcjkJu4UXD94s4n0aZAj0AceKBKaonT%2BhrI85hIN06h%2FLjiNa4hEZIJ3jkLGzkLz7fN%2FcmuVd8sR3zMJrAh30PrLU7HmySBYBILnRWsodrIyO9b%2BoxMc4Vu3wTK2d1ocrhid7WdrsNmGYGVvbLTLqM9quPbQYFijEOGdN7Mu3WJxVIA266KuVX%2BtsB2kl94H5keUu1EFZyoZs6MNWFt8sGOrABK9deoz%2BhGAVx50ZdPcGvLTfUA9el8SBSjaF30HYz%2BCOD96yOFz9E7GD8RtSgwI8ANNyL4aLVb17GWGixyAvpLXSMSbDFqZk%2BpZyWHwUbZg38qHtoiUOseTiOKkisdlcVxQF%2BvHJQiUFYW54PIAWR18Lc4GICQFKp09BmKHBD835pAdwkiunizEZU%2Fod%2BWVIqgayY8cnsUypy4wiQ5g%2BpUdm52urD6EFYQt3AQ0gIZ5E%3D&X-Amz-Signature=c5e186b53b843ac3f1899b746abed96693dbc895f7ddf0b0e55d40826f9173d4&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
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Formulas for estimating length of sonotrode depending on its shape_
| Sonotrode shape | First resonance length |
|---|---|
| Cylindrical |
|
| Stepped cylindrical |
|
| Exponential |
|
| Conical |
|
where
| |
Properties of the utilised ink provided by manufacturer [40]_
| Dynamic viscosity (m·Pa·s) | Surface tension (dynes/cm) | Density (g/cm3) | Silver content (%) | Silver powder particle size range (nm) |
|---|---|---|---|---|
| 7.5–10.5 | 28.5–32.5 | 1.1–1.3 | 45 | 3–8 |
Geometry and properties of printed traces_
| Sample | Width (µm) | Height (nm) | Roughness | SOP (%) | ||
|---|---|---|---|---|---|---|
| Total | Without spilled ink | Average value | Sa (nm) | Sz (nm) | ||
| P + S | 406 ± 8 | 311 ± 11 | 586 ± 31 | 123 ± 20 | 995 ± 33 | 17.2 |
| P + H + S | 383 ± 47 | 294 ± 29 | 556 ± 89 | 91 ± 13 | 888 ± 30 | 9.1 |
| P + U + S | 526 ± 56 | 416 ± 35 | 629 ± 106 | 148 ± 21 | 1158 ± 181 | 5.9 |
| P + H + U + S | 415 ± 29 | 302 ± 33 | 722 ± 103 | 92 ± 9 | 1276 ± 198 | 2.7 |