Burrs - SEM imaging - thoughts & theories

[ToddS]

...
The metal in the burr looks solid (photo in post No. 1), with the exception of some spalled metal debris on the perimeter. That metal had to come from the blade edge, and I'm not seeing how it could get there in that form other than by plastic flow.

Do you mean the curls of swarf? These are are loose particles that were floating in the water and collected on the edge.

I'm also a little confused about the apex width issue that HeavyHands raised. In the first post, Josh says: "One of the interesting things that I found was that the edge does indeed become thinner at the very apex the further up in grit you go. This has been theorized but I had not seen it proven until now." Are you saying that the apex width is not a function of the honing grit?

It depends on how you measure width:
The width of the apex, what I am calling keenness, is essentially not dependent on grit. With the Shapton progression there is a slight improvement in keenness. With a DMT progression there is no clear change. The blade I imaged above (DMT325) easily popped arm hair 1 cm above the skin.
However, the width of the blade 3 microns from the apex (what I am calling sharpness) does decrease with increasing grit. That 325DMT edge has a final bevel angle of 20-21 degrees while the spine-defined angle is only 16.5 degrees. In other words, that keenness comes from convexity and at the expense of sharpness.

There is an example of what I am trying to say here: https://scienceofsharp.wordpress.com/2014/04/13/the-bevel-set/

 

[REK Knives]

Do you mean the curls of swarf? These are are loose particles that were floating in the water and collected on the edge.



It depends on how you measure width:
The width of the apex, what I am calling keenness, is essentially not dependent on grit. With the Shapton progression there is a slight improvement in keenness. With a DMT progression there is no clear change. The blade I imaged above (DMT325) easily popped arm hair 1 cm above the skin.
However, the width of the blade 3 microns from the apex (what I am calling sharpness) does decrease with increasing grit. That 325DMT edge has a final bevel angle of 20-21 degrees while the spine-defined angle is only 16.5 degrees. In other words, that keenness comes from convexity and at the expense of sharpness.

There is an example of what I am trying to say here: https://scienceofsharp.wordpress.com/2014/04/13/the-bevel-set/

Now that is interesting about that 325 diamond plate and the edge width... I think there are several factors here that we may be missing.

1. waterstones vs. diamonds, what are the effects of each?
2. are you using edge leading or edge trailing passes?

The reason why I made that statement in the OP is because of the progression you posted here Todd, and that combined w/ Dr. Verhoeven's work led me to believe that with an increase in grit, the apex width is reduced.

 

[chiral.grolim]

It depends on how you measure width:
The width of the apex, what I am calling keenness, is essentially not dependent on grit. With the Shapton progression there is a slight improvement in keenness. With a DMT progression there is no clear change. The blade I imaged above (DMT325) easily popped arm hair 1 cm above the skin.
However, the width of the blade 3 microns from the apex (what I am calling sharpness) does decrease with increasing grit. That 325DMT edge has a final bevel angle of 20-21 degrees while the spine-defined angle is only 16.5 degrees. In other words, that keenness comes from convexity and at the expense of sharpness.

There is an example of what I am trying to say here: https://scienceofsharp.wordpress.com/2014/04/13/the-bevel-set/

This is all just awesome, I have to say. Many thanks for the efforts. :thumbup: Will his evolve into a published work of academic literature?


On topic, why did you set upon the "3 microns from the apex" definition of "sharpness"? The apex does the cutting (or crushing) while the material behind it, be it 1 micron or 3, simply separates the cut (or crushed) material and provides structural support to the apex, not so? The behind-the-apex thickness need only be low enough so as not to prevent the apex from penetrating sufficiently deep into the medium to admit completion of the cut - i.e. if the apex-angle is too large then the apex will only make a shallow penetration and the material being cut will instead be bent/torn out of the way much like what is happening to the blade-material as it is abraded by the particles in the hone...

To what do you attribute the higher convexity (arc) produced by the DMT hone?

Does it surprise anyone that 1200 grit DMT, which is proffered as 9-micron, produces scratches that are "one micron wide and a few hundred nanometers deep" ?

 

[ToddS]

...
1. waterstones vs. diamonds, what are the effects of each?
2. are you using edge leading or edge trailing passes?

The diamond plates leave a keener edge, but also seem to cause more deflection and therefore more micro-convexity.
I haven't looked at edge trailing passes on hones in any detail - the stone/hone images I have shown are all edge leading.

The reason why I made that statement in the OP is because of the progression you posted here Todd, and that combined w/ Dr. Verhoeven's work led me to believe that with an increase in grit, the apex width is reduced.

This is one of the reasons I like to define keen and sharp as I have; sharpness increases with grit while keenness is somewhat independent. In general, honing is for sharpness and stropping is for keenness.

... Will his evolve into a published work of academic literature?

I expect so, but for now I'm still in the learning stage of this project. It's just something I work on when I have a few minutes to spare.

On topic, why did you set upon the "3 microns from the apex" definition of "sharpness"? The apex does the cutting (or crushing) while the material behind it, be it 1 micron or 3, simply separates the cut (or crushed) material and provides structural support to the apex, not so? The behind-the-apex thickness need only be low enough so as not to prevent the apex from penetrating sufficiently deep into the medium to admit completion of the cut - i.e. if the apex-angle is too large then the apex will only make a shallow penetration and the material being cut will instead be bent/torn out of the way much like what is happening to the blade-material as it is abraded by the particles in the hone...

Mainly because this is the scale at which I observe micro-convexity. It is more straight forward to measure the width at 3 microns than to to measure the final bevel angle (micro-convexity) since there is sometimes curvature in that region. Also, looking at the whisker images that Josh posted, the key to shaving is penetrating the hard keratin plates on the whisker - 3 microns is the appropriate scale for that as well.

To what do you attribute the higher convexity (arc) produced by the DMT hone?

My working theory is that this is the same mechanism that leads to a raised burr. On each stroke, the apex is deflected away from the stone. On the return stroke that projecting metal is abraded, leaving the apex "short" Since diamond plates are so efficient are shearing off that projecting metal, they lead to a greater micro-convexity than waterstones.

Does it surprise anyone that 1200 grit DMT, which is proffered as 9-micron, produces scratches that are "one micron wide and a few hundred nanometers deep" ?

I think the 'bed of nails' is a good analogy for what happens - it doesn't matter how long the nails are.

 

[chiral.grolim]

...This is one of the reasons I like to define keen and sharp as I have; sharpness increases with grit while keenness is somewhat independent. In general, honing is for sharpness and stropping is for keenness.
...
... It is more straight forward to measure the width at 3 microns than to to measure the final bevel angle (micro-convexity) since there is sometimes curvature in that region. Also, looking at the whisker images that Josh posted, the key to shaving is penetrating the hard keratin plates on the whisker - 3 microns is the appropriate scale for that as well.

This makes sense, penetrating those first 3 microns of plates is the key.
I am still concerned about this use of the terms "sharp" vs "keen" given colloquial use and also their antonyms "dull" and "blunt". The DMT bevel is thicker but "keener" in your use, certainly not "dull" as it is more likely to make the cut because of initial penetration. The ability to make that penetration is what defines "sharp" - it is task-specific. In contrast, the Chosera bevel is thinner but is indeed "blunt" in comparison - less likely to accomplish initial penetration. Straight-razors tend to be honed at 15-20 degrees inclusive, yes? Yet shaving can be accomplished with a "keen" blade honed to 30-40 degrees inclusive - quite thick. Thickness behind the apex provides a significant increase in rigidity, durability, at the expense of some efficiency. If a blade is thinner but too blunt at the apex to make the initial cut, I have difficulty considering it to be "sharp". So why not simply use "keen" and "thick"? Also important is the side-view presenting the "teeth" of the edge - focused penetration points that can make a less "keen" edge penetrate some media better (i.e. sharper) than a keen-edge with shallower points. For example, if two blades are sharpened to the same angle but one is given a more coarse finish with more and taller "teeth", the other has a finer finish with a keener apex but much smaller/fewer teeth, the coarse-edge will more easily cut through the skin of a tomato because of the focus pressure at those high points, i.e. it is "sharper".

Those are just some random thoughts.

The diamond plates leave a keener edge, but also seem to cause more deflection and therefore more micro-convexity.
...
My working theory is that this is the same mechanism that leads to a raised burr. On each stroke, the apex is deflected away from the stone. On the return stroke that projecting metal is abraded, leaving the apex "short" Since diamond plates are so efficient are shearing off that projecting metal, they lead to a greater micro-convexity than waterstones.

I had wondered if it had to to with the waterstone releasing abrasive and swarf in fairly uniform fashion so the edge continues to be hit by particles vs diamond-hone collecting swarf that causes a slight alteration of the angle/depth of abrasion on each pass...

 

[REK Knives]

This makes sense, penetrating those first 3 microns of plates is the key.
I am still concerned about this use of the terms "sharp" vs "keen" given colloquial use and also their antonyms "dull" and "blunt". The DMT bevel is thicker but "keener" in your use, certainly not "dull" as it is more likely to make the cut because of initial penetration. The ability to make that penetration is what defines "sharp" - it is task-specific. In contrast, the Chosera bevel is thinner but is indeed "blunt" in comparison - less likely to accomplish initial penetration. Straight-razors tend to be honed at 15-20 degrees inclusive, yes? Yet shaving can be accomplished with a "keen" blade honed to 30-40 degrees inclusive - quite thick. Thickness behind the apex provides a significant increase in rigidity, durability, at the expense of some efficiency. If a blade is thinner but too blunt at the apex to make the initial cut, I have difficulty considering it to be "sharp". So why not simply use "keen" and "thick"? Also important is the side-view presenting the "teeth" of the edge - focused penetration points that can make a less "keen" edge penetrate some media better (i.e. sharper) than a keen-edge with shallower points. For example, if two blades are sharpened to the same angle but one is given a more coarse finish with more and taller "teeth", the other has a finer finish with a keener apex but much smaller/fewer teeth, the coarse-edge will more easily cut through the skin of a tomato because of the focus pressure at those high points, i.e. it is "sharper".

Those are just some random thoughts.

I think what we are discussing, Chiral, is the definitions of "sharp" and "cutting ability". The way I see it is: Sharp is where the two sides of the edge form to create an apex (obviously you have different apex widths though so some are "sharper") and this can be at any degree, 10 dps or 30 dps it doesn't matter. Then you have "cutting ability" which has to do with the actual angle of the edge and the angle of the primary grind, the thickness of the edge, etc. So technically you could have a sharp (.1 um thick apex) 30 dps edge that is .030" thick at the shoulder, and a dull (say 3-5 micron wide apex) edge that is 10 dps w/ a .005" thick edge (at the shoulder) and the latter will likely cut through most mediums much better. I may be wrong but this just seems to be the case from what I have experienced...

I had wondered if it had to to with the waterstone releasing abrasive and swarf in fairly uniform fashion so the edge continues to be hit by particles vs diamond-hone collecting swarf that causes a slight alteration of the angle/depth of abrasion on each pass...

man! this is a great observation/theory, I don't know why I didn't even think of it! Good point!

Todd, when you are sharpening w/ the waterstones, how clean are they and how much slurry is on them?

 

[ToddS]

This makes sense, penetrating those first 3 microns of plates is the key.
I am still concerned about this use of the terms "sharp" vs "keen" given colloquial use and also their antonyms "dull" and "blunt". The DMT bevel is thicker but "keener" in your use, certainly not "dull" as it is more likely to make the cut because of initial penetration. The ability to make that penetration is what defines "sharp" - it is task-specific. In contrast, the Chosera bevel is thinner but is indeed "blunt" in comparison - less likely to accomplish initial penetration.

The definitions have not been well received; however, for lack of better, I think they are suitable terms. I try to avoid using the absolute terms sharp and keen, but rather comparing sharpness and keeness.

Straight-razors tend to be honed at 15-20 degrees inclusive, yes? Yet shaving can be accomplished with a "keen" blade honed to 30-40 degrees inclusive - quite thick.

I don't know that anyone chooses to use a straight razor simply to "accomplish" shaving. 14-17 degrees (inclusive) is typical for a reason.

Thickness behind the apex provides a significant increase in rigidity, durability, at the expense of some efficiency. If a blade is thinner but too blunt at the apex to make the initial cut, I have difficulty considering it to be "sharp". So why not simply use "keen" and "thick"? Also important is the side-view presenting the "teeth" of the edge - focused penetration points that can make a less "keen" edge penetrate some media better (i.e. sharper) than a keen-edge with shallower points. For example, if two blades are sharpened to the same angle but one is given a more coarse finish with more and taller "teeth", the other has a finer finish with a keener apex but much smaller/fewer teeth, the coarse-edge will more easily cut through the skin of a tomato because of the focus pressure at those high points, i.e. it is "sharper".
...

Geometrically, an edge can't have sharpness unless it is also has keenness; they are not unrelated.
There is almost always non-uniformity along the bevel, so edge width is an average.

..
Todd, when you are sharpening w/ the waterstones, how clean are they and how much slurry is on them?

I generally lap my waterstones with an Atoma 400 prior to each use and rinse well, so no slurry.

 

[HeavyHanded]

A couple of items come to mind, especially looking at some of the images from part two of this work-up. Is amazing that some of the curling appears to be very localized, even on the images of unstropped edges there appears to be a bit of flow back and forth over the theoretical midpoint on a scale that would seem to preclude human error with force or angle control. The ones from charged stropping might almost indicate variations in the density of the backing, but how to explain the ones straight off the stone? I have seen some of this on my optical microscope, but is much more difficult to gauge how much deviation as most of it is within the focal depth of the aperture and can only be guestimated by moving the stage up and down right at the edge of focus.

Another thought - the human eye can see a candle flame at distance over 10 miles under the right conditions. I found that a lot of the defects I could pick up even at 1000x were sometimes visible to the naked eye under the right lighting, and certainly with a 15 or 20x loupe. Couldn't tell what the actual state was, but could spot non-uniform reflectance.

 

[chiral.grolim]

The definitions have not been well received; however, for lack of better, I think they are suitable terms. I try to avoid using the absolute terms sharp and keen, but rather comparing sharpness and keeness.
...
Geometrically, an edge can't have sharpness unless it is also has keenness; they are not unrelated.
There is almost always non-uniformity along the bevel, so edge width is an average.

This is why I advise using "sharp" as task-specific, "keen" as levels of sharpness based on apex-diameter, and everything behind the apex is just "thickness". Backing up to the macroscopic scale, a "hard-use" utility knife will commonly have a primary bevel ground to <10 degrees inclusive just as a light-use paring knife, and each will commonly be sharpened to 30 degrees inclusive at the edge as this provides an excellent compromise between durability and cutting efficiency (2:1 ratio of bevel height to thickness). It is the same angle used for wood-planers and chisels, for chainsaws and mower blades. But what differs in these different blades is the thickness behind said bevel - a tool for harder use requires more support for durability and so a thicker blade often in the range of 0.030" while a light-use slicer can be as thin as 0.005". Both tools can be made "shaving-sharp", i.e. equally "keen" at the apex with the difference being that one is thicker than the other. But what if the thin blade wasn't "shaving-sharp"? You would shave with the thick blade instead.

Cutting-efficiency, the force required to complete the cut, is a function blade thickness at a given bevel-height, that height corresponding to the depth of the cut required to overcome resistance of the medium. Some media is "loose" - it easily separates or falls away and offers little/no resistance to the bevels of the blade as it is forced through behind the apex (e.g. loose fibers in rope or hair on a macroscopic scale). Other media is "stiff" - it offers continual resistance to the progress of the blade as it wedges its way through (e.g. stiff cardboard). In the former instance, the thin blade has little/no advantage over the thick blade if they are equally "keen". Only in the later instance does that thickness come into play due to the impact of wedging/drag on the bevels. But the thick-blade would still not be considered "dull" in comparison to the thin blade, just thick.

Similarly you have two razor-blades where one is less "keen" than the other at the microscopic level. IF the task required a smaller apex-diameter to make a proper cut (e.g. cutting tissue samples for SEM imaging ) then the thin blade with the less "keen" edge will be called "dull"because it cannot complete the cut (it can only crush) despite being thinner behind the apex, and the thicker blade would be called "sharp" because it CAN complete the cut despite being thicker behind the apex. Yet in another task where an apex-diameter 10X larger would still be sufficient to complete the cut, BOTH knives would be considered "sharp" indeed indistinguishably so because the difference in "keeness" is lower than the required threshold.

So that is my argument: "sharp" refers to the cutting application at hand, "keen" refers to the average apex-diameter, and differences in behind the apex thickness are precisely that - thicker vs thinner.

I don't know that anyone chooses to use a straight razor simply to "accomplish" shaving. 14-17 degrees (inclusive) is typical for a reason.

Do you happen to know that reason? Because my suspicion is that it was simply the angle achieved when grinding down a simple 1"x 1/4" blank. Before the advent of the modern Sheffield (17th century), I have no guess. Verhoeven's experiments suggest that going below that angle makes it exceedingly difficult to achieve a uniform stable edge unless the material is very hard.

I generally lap my waterstones with an Atoma 400 prior to each use and rinse well, so no slurry.

On each pass of the blade, material is ground from both waterstone and blade = slurry that can be washed away to provide a clean abrasive surface for each pass and also for the continued passage of the blade on a single pass. On a diamond-hone, abraded material is more likely to collect with each pass, indeed it may collect off the edge of the blade and so prevent what is behind it from making as deep of contact with the particles of the hone, resulting in a more sloped apex.
Just a theory.

 

[REK Knives]

This is why I advise using "sharp" as task-specific, "keen" as levels of sharpness based on apex-diameter, and everything behind the apex is just "thickness". Backing up to the macroscopic scale, a "hard-use" utility knife will commonly have a primary bevel ground to <10 degrees inclusive just as a light-use paring knife, and each will commonly be sharpened to 30 degrees inclusive at the edge as this provides an excellent compromise between durability and cutting efficiency (2:1 ratio of bevel height to thickness). It is the same angle used for wood-planers and chisels, for chainsaws and mower blades. But what differs in these different blades is the thickness behind said bevel - a tool for harder use requires more support for durability and so a thicker blade often in the range of 0.030" while a light-use slicer can be as thin as 0.005". Both tools can be made "shaving-sharp", i.e. equally "keen" at the apex with the difference being that one is thicker than the other. But what if the thin blade wasn't "shaving-sharp"? You would shave with the thick blade instead.

Cutting-efficiency, the force required to complete the cut, is a function blade thickness at a given bevel-height, that height corresponding to the depth of the cut required to overcome resistance of the medium. Some media is "loose" - it easily separates or falls away and offers little/no resistance to the bevels of the blade as it is forced through behind the apex (e.g. loose fibers in rope or hair on a macroscopic scale). Other media is "stiff" - it offers continual resistance to the progress of the blade as it wedges its way through (e.g. stiff cardboard). In the former instance, the thin blade has little/no advantage over the thick blade if they are equally "keen". Only in the later instance does that thickness come into play due to the impact of wedging/drag on the bevels. But the thick-blade would still not be considered "dull" in comparison to the thin blade, just thick.

Similarly you have two razor-blades where one is less "keen" than the other at the microscopic level. IF the task required a smaller apex-diameter to make a proper cut (e.g. cutting tissue samples for SEM imaging ) then the thin blade with the less "keen" edge will be called "dull"because it cannot complete the cut (it can only crush) despite being thinner behind the apex, and the thicker blade would be called "sharp" because it CAN complete the cut despite being thicker behind the apex. Yet in another task where an apex-diameter 10X larger would still be sufficient to complete the cut, BOTH knives would be considered "sharp" indeed indistinguishably so because the difference in "keeness" is lower than the required threshold.

So that is my argument: "sharp" refers to the cutting application at hand, "keen" refers to the average apex-diameter, and differences in behind the apex thickness are precisely that - thicker vs thinner.




Do you happen to know that reason? Because my suspicion is that it was simply the angle achieved when grinding down a simple 1"x 1/4" blank. Before the advent of the modern Sheffield (17th century), I have no guess. Verhoeven's experiments suggest that going below that angle makes it exceedingly difficult to achieve a uniform stable edge unless the material is very hard.




On each pass of the blade, material is ground from both waterstone and blade = slurry that can be washed away to provide a clean abrasive surface for each pass and also for the continued passage of the blade on a single pass. On a diamond-hone, abraded material is more likely to collect with each pass, indeed it may collect off the edge of the blade and so prevent what is behind it from making as deep of contact with the particles of the hone, resulting in a more sloped apex.
Just a theory.

+1 Well written and I agree about the definitions... they seem more feasible to me.

As far as angles of straight razors go, in my esperience they range between 10-15 dps. I have a Dovo I will be doing tonight... i will measure it.

 

[eKretz]

Hmm, for me, deflection doesn't explain the micro-convexity at all. Deflection should cause the opposite, as if the hone-side of the apex deflected while being honed, it would tend to produce a more acute bevel, not more convex/obtuse. I think a better explanation would be that the diamond is somehow causing the apex (which is of course very thin and weak) to be pulled down into the hone surface farther - possibly due to the diamonds biting harder/farther into the steel than other abrasives, which then results in the apex springing back to center after removal of contact with the diamond surface - I think this would more likely explain the result of the "micro-convexity" or more obtuse angle at the apex.

BTW Todd: thanks very much for doing this and taking the time to discuss it here as well. I have always found your photos and posts most interesting and thought-provoking.

 

[HeavyHanded]

Hmm, for me, deflection doesn't explain the micro-convexity at all. Deflection should cause the opposite, as if the hone-side of the apex deflected while being honed, it would tend to produce a more acute bevel, not more convex/obtuse. I think a better explanation would be that the diamond is somehow causing the apex (which is of course very thin and weak) to be pulled down into the hone surface farther - possibly due to the diamonds biting harder/farther into the steel than other abrasives, which then results in the apex springing back to center after removal of contact with the diamond surface - I think this would more likely explain the result of the "micro-convexity" or more obtuse angle at the apex.

BTW Todd: thanks very much for doing this and taking the time to discuss it here as well. I have always found your photos and posts most interesting and thought-provoking.

I was thinking similarly. Was also wondering if this is being prepared freehand or on a guide, if there is added grab from the diamonds at the start of the pass, one would expect to see this sort of thing.

Even the diamond edges display localized swaying of the edge line over the theoretical center, that is most intriguing to me.

 

[ToddS]

A couple of items come to mind, especially looking at some of the images from part two of this work-up. Is amazing that some of the curling appears to be very localized, even on the images of unstropped edges there appears to be a bit of flow back and forth over the theoretical midpoint on a scale that would seem to preclude human error with force or angle control. The ones from charged stropping might almost indicate variations in the density of the backing, but how to explain the ones straight off the stone? I have seen some of this on my optical microscope, but is much more difficult to gauge how much deviation as most of it is within the focal depth of the aperture and can only be guestimated by moving the stage up and down right at the edge of focus.

The key point is that the apex at bevel angles below 10dps is extremely flexible - the deflections you see here are typical of a straight razor edge. A spec of dust on the strop or hone can cause these. Also, I usually rinse the blade to remove swarf and blow dry with compressed air - that can cause deflections of the edge as well.

...I found that a lot of the defects I could pick up even at 1000x were sometimes visible to the naked eye under the right lighting, and certainly with a 15 or 20x loupe. Couldn't tell what the actual state was, but could spot non-uniform reflectance.

Essentially this is the same principle as dark-field imaging, where we look only at the scattered light - defects, scratches, specs of dust are easily viewed in darkfield, and often with the naked eye at a glancing angle to the surface.

This is why I advise using "sharp" as task-specific, "keen" as levels of sharpness based on apex-diameter, and everything behind the apex is just "thickness". Backing up to the macroscopic scale, a "hard-use" utility knife will commonly have a primary bevel ground to <10 degrees inclusive just as a light-use paring knife, and each will commonly be sharpened to 30 degrees inclusive at the edge as this provides an excellent compromise between durability and cutting efficiency (2:1 ratio of bevel height to thickness). It is the same angle used for wood-planers and chisels, for chainsaws and mower blades. But what differs in these different blades is the thickness behind said bevel - a tool for harder use requires more support for durability and so a thicker blade often in the range of 0.030" while a light-use slicer can be as thin as 0.005". Both tools can be made "shaving-sharp", i.e. equally "keen" at the apex with the difference being that one is thicker than the other. But what if the thin blade wasn't "shaving-sharp"? You would shave with the thick blade instead.

Cutting-efficiency, the force required to complete the cut, is a function blade thickness at a given bevel-height, that height corresponding to the depth of the cut required to overcome resistance of the medium. Some media is "loose" - it easily separates or falls away and offers little/no resistance to the bevels of the blade as it is forced through behind the apex (e.g. loose fibers in rope or hair on a macroscopic scale). Other media is "stiff" - it offers continual resistance to the progress of the blade as it wedges its way through (e.g. stiff cardboard). In the former instance, the thin blade has little/no advantage over the thick blade if they are equally "keen". Only in the later instance does that thickness come into play due to the impact of wedging/drag on the bevels. But the thick-blade would still not be considered "dull" in comparison to the thin blade, just thick.

Similarly you have two razor-blades where one is less "keen" than the other at the microscopic level. IF the task required a smaller apex-diameter to make a proper cut (e.g. cutting tissue samples for SEM imaging ) then the thin blade with the less "keen" edge will be called "dull"because it cannot complete the cut (it can only crush) despite being thinner behind the apex, and the thicker blade would be called "sharp" because it CAN complete the cut despite being thicker behind the apex. Yet in another task where an apex-diameter 10X larger would still be sufficient to complete the cut, BOTH knives would be considered "sharp" indeed indistinguishably so because the difference in "keeness" is lower than the required threshold.

So that is my argument: "sharp" refers to the cutting application at hand, "keen" refers to the average apex-diameter, and differences in behind the apex thickness are precisely that - thicker vs thinner.

First, let me say that I appreciate you taking the time to discuss this. It's not easy to find anyone interested in these sort of details.
You haven't written anything that I disagree with. Clearly, I have not established that the width at 3 microns determines the cutting efficiency of whiskers with a razor (although I am fairly confident of the idea).
At the time I started using these terms, I was thinking only of straight razors. I will give this some more thought.

Do you happen to know that reason? Because my suspicion is that it was simply the angle achieved when grinding down a simple 1"x 1/4" blank. Before the advent of the modern Sheffield (17th century), I have no guess. Verhoeven's experiments suggest that going below that angle makes it exceedingly difficult to achieve a uniform stable edge unless the material is very hard.

I don't know where the 4:1 ratio comes from. I do know that it is difficult to hone a 14 degree (inclusive) razor without pasted-strop convexity to increase the angle near the apex. My experience suggests that beyond 20 degrees (inclusive) the force to cut increases to a level where it is difficult to avoid cutting skin. At the same time, increasing apex angle leads to a less flexible apex and it may be that flexibility that reduces skin cutting.

On each pass of the blade, material is ground from both waterstone and blade = slurry that can be washed away to provide a clean abrasive surface for each pass and also for the continued passage of the blade on a single pass. On a diamond-hone, abraded material is more likely to collect with each pass, indeed it may collect off the edge of the blade and so prevent what is behind it from making as deep of contact with the particles of the hone, resulting in a more sloped apex.
Just a theory.

However, honing on a slurry creates convexity, and the thicker the slurry, the greater the effect.

 

[ToddS]

Hmm, for me, deflection doesn't explain the micro-convexity at all. Deflection should cause the opposite, as if the hone-side of the apex deflected while being honed, it would tend to produce a more acute bevel, not more convex/obtuse. I think a better explanation would be that the diamond is somehow causing the apex (which is of course very thin and weak) to be pulled down into the hone surface farther - possibly due to the diamonds biting harder/farther into the steel than other abrasives, which then results in the apex springing back to center after removal of contact with the diamond surface - I think this would more likely explain the result of the "micro-convexity" or more obtuse angle at the apex.
..

Try drawing a diagram to help visualize what I am suggesting. Even better, simulate the effect with a lump of clay; please take pictures and report back.

I was thinking similarly. Was also wondering if this is being prepared freehand or on a guide, if there is added grab from the diamonds at the start of the pass, one would expect to see this sort of thing.
...

The spine is in contact with the hone and I don't think it can unintentionally lift enough to explain this bevel profile.

 

[chiral.grolim]

I was ... wondering if this is being prepared freehand or on a guide, if there is added grab from the diamonds at the start of the pass, one would expect to see this sort of thing.

Straight-razors provide their own guide via the blade-spine ... I assumed that is what is being used.
The abrasive from each hone should "grab" material as it makes contact but releases that material along with abrasive particles per the nature of crumbling water-stones. Waterstones need to be lapped occasionally to restore flatness because more material in heavily-used areas has abraded away to leave a clean surface for further honing... As a consequence of the easy release of material, the apex continues to cut into the hone-surface or rather the hone-surface continues to cut into the apex. (Just thinking aloud, i know that much of this is obvious to more experienced folk here)

With the non-crumbling diamond-surface (or with ceramic), debris (cut steel) collects amidst the tightly-bound abrasive particles and so requires a thorough scrubbing to dislodge that. Since the material collects as it is grabbed and is not so readily released, the leading portion of the bevel will experience the most "grab" while following bevel-areas will only be grabbed by whatever abrasive material remains uncovered amidst the debris from the leading portion. As a result, the bevel will "ride up" ever-so-slightly on the debris leaving a clean-cut (keen) apex that is no longer impacting abrasive particles (but may show more dramatic "teeth" from the initial abrasive "grabs"). This is of course negated by continued grinding with high pressure to the point of raising a burr...

 

[chiral.grolim]

...honing on a slurry creates convexity, and the thicker the slurry, the greater the effect.

I am curious about this. On a waterstone, the slurry forms off the abrasive-surface, revealing an uncontaminated surface beneathe, so you are not honing "on a slurry". OTOH the slurry forms on a non-crumbling diamond or ceramic surface - i.e. it retains the debris to a greater extent - so you are indeed honing "on a slurry". But convexity on a waterstone may result from wearing the stone into a curved honing surface... *shrug* I'm just theorizing, you're the awesome one with the SEM Thinking of adding a "donations" tab to your blog? I for one might give...

 

[HeavyHanded]

Trying to wrap my head around this one.

Assuming a small amount of temporary flex in the material, Todd's supposition makes a lot of sense.

I'm not sure why the waterstones would be significantly less abrasive on most steel to account for the variation. On plain stainless and carbon, many brands of waterstone are actually faster than comparable grit diamond plates.

Grind speed is not the entire story though, the individual diamonds may very well stand more proud than the waterstone grit, which actually has some mobility in its binder - allowing the apex to pass with less distortion, but the region just behind it is subjected to the maximum amount of friction/grinding action. When it flexes back to its resting state, you have the effect pictured. I have noticed with my optical microscope that waterstones and jointer stones (in my hands) tend to make a very aggressive apex as viewed from the side, yet have less variation back and forth along the cutting line than other media of comparable grit, the more firmly fixed the abrasive is, the greater the back and forth deviation tends to be...generally...in my hands.

Am sitting here with a bunch of sketches trying to piece it out...

 

[chiral.grolim]

Trying to wrap my head around this one.

Assuming a small amount of temporary flex in the material, Todd's supposition makes a lot of sense.

I'm not sure why the waterstones would be significantly less abrasive on most steel to account for the variation. On plain stainless and carbon, many brands of waterstone are actually faster than comparable grit diamond plates.

Abrasiveness depends on the sharpness (cutting ability) or the abrasive particle and its depth of penetration. On softer matrices (fewer/smaller carbides) I'd expect a waterstone with equal size/distribution/sharpness of particles to cut more aggressively than its diamond-plate counterpart because the waterstone-binder releases to uncover a clean surface beneath (new teeth), whereas the diamond-plate must be cleaned/scrubbed of debris clogging the valleys to restore depth of penetration to the same teeth (like a saw).

I don't understand the focus on "flex". I would expect flex to increase as material behind the apex is aggressively removed thus thinning the bevel and reducing stiffness (i.e. what happens during burr-formation).

 

[HeavyHanded]

Abrasiveness depends on the sharpness (cutting ability) or the abrasive particle and its depth of penetration. On softer matrices (fewer/smaller carbides) I'd expect a waterstone with equal size/distribution/sharpness of particles to cut more aggressively than its diamond-plate counterpart because the waterstone-binder releases to uncover a clean surface beneath (new teeth), whereas the diamond-plate must be cleaned/scrubbed of debris clogging the valleys to restore depth of penetration to the same teeth (like a saw).

I don't understand the focus on "flex". I would expect flex to increase as material behind the apex is aggressively removed thus thinning the bevel and reducing stiffness (i.e. what happens during burr-formation).

At this scale I would expect a small amount of flex just pressing it to a surface. Am not sure what the applied force is, but probably in the neighborhood a few ounces spread out over the surface area.

Another thing to consider with waterstones - unless being used under running water, the released abrasive, binder and water form a mud that sometimes seems to speed grinding, but in other instances will slow it down due to the amount of mobility. I could well imagine the abrasive caught between the backbevel and the stone surface to work more aggressively than the abrasive presenting at the apex, especially when used with a leading pass and some flex just behind the apex.

I understand your thoughts, but am not convinced the swarf accumulation can account for the difference. After a few passes there will be swarf deposited all over, on the diamonds I would expect the tips of the diamonds to carry on unimpeded for a time with no real loss of effect, and I cannot imagine it would be so localized when it did show up. And the waterstone might release fresh abrasive faster, but also there is that binder in the mix and any swarf. I don't see any advantage until a lot of work has been done.

All just a guess, I really have no idea. At most I can say the effect is persistent and so there's something discoverable here but am not willing to draw or defend any particular conclusion. What variables could be changed to create additional helpful observation?

 

[REK Knives]

What variables could be changed to create additional helpful observation?

edge leading vs edge trailing on waterstones would be what I love to see, both from side angles and directly down at the edge measuring apex width. Then repeat the same experiment on diamonds and see which ones are optimal for each type of stone.