Loss of atoms from the surface of the material: How does it work?

[PatrickP2]

Good morning! A question from a mere layman, so I hope you won't eat me :D

Some time ago I read that every time one solid body makes some contact with another solid body, several billion atoms are lost from the surface of both the first and the second. On the Internet, I once read a post claiming that with every step we take, the sole of our shoes shrinks by 10^13 atoms. So my question is, how does this relate to harder materials such as diamond, coatings of all kinds, etc.?

According to one study, a well applied DLC (diamond-like carbon) coating with a thickness of 3 micrometers at low loads is able to last up to 85 years. What about the silicon sphere from Project Avogadro, which was supposed to be the roundest man-made object? Every time someone touches it, does that mean we deprive it of those few billion (billiard?) atoms?

And finally, what about the kilogram standard? Did it, too, with each cleaning change its mass? Thank you in advance for your answer. I hope my questions are not off the top of my head :D Greetings!

 

[jack action]

what about the kilogram standard? Did it, too, with each cleaning change its mass?

https://en.wikipedia.org/wiki/International_Prototype_of_the_Kilogram#Stability_of_the_IPK

Beyond the simple wear that check standards can experience, the mass of even the carefully stored national prototypes can drift relative to the IPK for a variety of reasons, some known and some unknown. Since the IPK and its replicas are stored in air (albeit under two or more nested bell jars), they gain mass through adsorption of atmospheric contamination onto their surfaces. Accordingly, they are cleaned in a process the BIPM developed between 1939 and 1946 known as "the BIPM cleaning method"[27] that comprises firmly rubbing with a chamois soaked in equal parts ether and ethanol, followed by steam cleaning with bi-distilled water, and allowing the prototypes to settle for 7–10 days before verification. Before the BIPM's published report in 1994 detailing the relative change in mass of the prototypes, different standard bodies used different techniques to clean their prototypes. The NIST's practice before then was to soak and rinse its two prototypes first in benzene, then in ethanol, and to then clean them with a jet of bi-distilled water steam. Cleaning the prototypes removes between 5 and 60 μg of contamination depending largely on the time elapsed since the last cleaning. Further, a second cleaning can remove up to 10 μg more. After cleaning—even when they are stored under their bell jars—the IPK and its replicas immediately begin gaining mass again. The BIPM even developed a model of this gain and concluded that it averaged 1.11 μg per month for the first 3 months after cleaning and then decreased to an average of about 1 μg per year thereafter. Since check standards like K4 are not cleaned for routine calibrations of other mass standards—a precaution to minimise the potential for wear and handling damage—the BIPM's model of time-dependent mass gain has been used as an "after cleaning" correction factor.

Because the first forty official copies are made of the same alloy as the IPK and are stored under similar conditions, periodic verification using a number of replicas—especially the national primary standards, which are rarely used—can convincingly demonstrate the stability of the IPK. What has become clear after the third periodic verification performed between 1988 and 1992 is that masses of the entire worldwide ensemble of prototypes have been slowly but inexorably diverging from each other. It is also clear that the IPK lost perhaps 50 μg of mass over the last century, and possibly significantly more, in comparison to its official copies.[17][28] The reason for this drift has eluded physicists who have dedicated their careers to the SI unit of mass. No plausible mechanism has been proposed to explain either a steady decrease in the mass of the IPK, or an increase in that of its replicas dispersed throughout the world.[Note 5][29][30][31] Moreover, there are no technical means available to determine whether or not the entire worldwide ensemble of prototypes suffers from even greater long-term trends upwards or downwards because their mass "relative to an invariant of nature is unknown at a level below 1000 μg over a period of 100 or even 50 years".[28] Given the lack of data identifying which of the world's kilogram prototypes has been most stable in absolute terms, it is equally valid to state that the first batch of replicas has, as a group, gained an average of about 25 μg over one hundred years in comparison to the IPK.[Note 6]

What is known specifically about the IPK is that it exhibits a short-term instability of about 30 μg over a period of about a month in its after-cleaned mass.[32] The precise reason for this short-term instability is not understood but is thought to entail surface effects: microscopic differences between the prototypes' polished surfaces, possibly aggravated by hydrogen absorption due to catalysis of the volatile organic compounds that slowly deposit onto the prototypes as well as the hydrocarbon-based solvents used to clean them.[31][33]

It has been possible to rule out many explanations of the observed divergences in the masses of the world's prototypes proposed by scientists and the general public. The BIPM's FAQ explains, for example, that the divergence is dependent on the amount of time elapsed between measurements and not dependent on the number of times the prototype or its copies have been cleaned or possible changes in gravity or environment.[34] Reports published in 2013 by Peter Cumpson of Newcastle University based on the X-ray photoelectron spectroscopy of samples that were stored alongside various prototype kilograms suggested that one source of the divergence between the various prototypes could be traced to mercury that had been absorbed by the prototypes being in the proximity of mercury-based instruments. The IPK has been stored within centimetres of a mercury thermometer since at least as far back as the late 1980s.[35] In this Newcastle University work six platinum weights made in the nineteenth century were all found to have mercury at the surface, the most contaminated of which had the equivalent of 250 μg of mercury when scaled to the surface area of a kilogram prototype.

 

[berkeman]

Welcome to PF, @PatrickP2

"I read somewhere" and "On the Internet, I once read" are not good sources to use for thread starts at PF. It is always best to link to the actual sources, and ask questions about the reading you've been doing at those sources. Thanks.

 

[PatrickP2]

Welcome to PF, @PatrickP2

"I read somewhere" and "On the Internet, I once read" are not good sources to use for thread starts at PF. It is always best to link to the actual sources, and ask questions about the reading you've been doing at those sources. Thanks.

Ahh, sure! Referring to the DLC coating, here I have a study on the subject: https://www.mdpi.com/2076-3417/11/10/4445

 

[Baluncore]

So my question is, how does this relate to harder materials such as diamond, coatings of all kinds, etc.?

The study of friction, lubrication, and wear, at moving material interfaces, is now called tribology. It is a multidisciplinary subject that will take some exploration and Google searching. Start here ...
https://en.wikipedia.org/wiki/Tribology

 

[PatrickP2]

The study of friction, lubrication, and wear, at moving material interfaces, is now called tribology. It is a multidisciplinary subject that will take some exploration and Google searching. Start here ...
https://en.wikipedia.org/wiki/Tribology

I have already searched for information on this topic on Google, but I did not find an answer to my question, so I decided to write a post here and ask a question. What I'm most curious about is whether the atoms we remove with every touch of our hands can be counted in millions, billions or maybe trillions? What would happen if I rubbed the surface of a diamond/DLC with my hand continuously for, say, a hundred years? Are there any studies on this topic?

 

[Baluncore]

What would happen if I rubbed the surface of a diamond/DLC with my hand continuously for, say, a hundred years?

Your finger would wear out first, then you would die of old age.

Diamond dust is used to polish diamonds, so you must specify if your fingers are cleaned, or do fragments of dirt or diamond dust break away, to become embedded in your skin?

The availability of oxygen will be important in diamond surface wear. Under friction, or higher temperatures, diamond burns to CO2 in air. Diamonds are now cut with IR lasers.

Are there any studies on this topic?

There must be studies, but you must learn the terminology while searching them out. Knowing the best search terms is something that you are yet to discover.

Tribology becomes very involved and specific very quickly. That means general questions cannot be simply answered. You must start by looking at all the possible implications of your situation.
https://www.tribonet.org/wiki/wear/

 

[PatrickP2]

I found a study on the abrasion of diamond against aluminum, in which the disks were loaded against the cube face of diamond in the [010] direction. The sliding speed was 88 mm s^-1and the load 2.2 N. After 8000 min the scar depth was about 0,45 micrometers and the scar volume 10^-5mm³. The corresponding rate of wear is 1.2x10^-10mm³N^-1m^-1.
Also, I once found a post on an online forum in which someone counted how many atoms of the rubber sole of shoe are left behind with each step and after doing the calculations it was found that there are 1.189 × 10¹³ atoms removed.
Then, having a study on aluminum and diamond, can we roughly estimate how many carbon atoms from diamond have been wiped off?
Here are the links to the paper and the Reddit: https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1973.0072

 

[Baluncore]

@PatrickP2
As I wrote,

Tribology becomes very involved and specific very quickly. That means general questions cannot be simply answered.

Specifically, why are you needing to count atoms and not micrograms?
What is the ultimate aim of this exercise?

 

[PatrickP2]

Out of curiosity. I became interested in the topic because I read that DLC coatings with a thickness of 3 micrometers can last up to 85 years, and then I found a post on the Internet in which someone calculated that the sole of shoes shrinks by trillions of atoms every time we take a step. So the DLC thing seemed unlikely to me. The lenght of carbon-carbon (C-C) bond length in diamond is 154 pm, so a DLC coating would be 3080000 pm thick. I know that diamond is one of the hardest minerals on Earth, but considering that, even if I wipe my finger across the diamond just once and strip it of millions (billions) of atoms, how is it possible for DLC coating to last even 5 years? :D

 

[Chestermiller]

A one carat diamond has a mass of 0.2 grams. That is 1/60 of a gram mole of carbon. There are 6.023 x 10^23 carbon atoms in a mole. That means there are about 1 x 10 ^22 carbon atoms in a one carat diamond. So, if you removed 1 billion atoms (1 x 10^9) from a diamond each time you touched it, you would have to contact it 10 ^13 times to consume the diamond. There are about 30 million seconds in a year. So, if you touched the diamond once a second, it would take you 3 million years to consume the one carat diamond.

 

[Rive]

it would take you 3 million years to consume the one carat diamond

I think one of the most annoying references of 'eternity' in literature is the story about that birdie with the mountain. And its endless variations.

Somewhere, there is a mountain of pure diamond. It takes an hour to climb, and an hour to walk around, and every one hundred years, a bird comes and sharpens it's beak on the mountain. And when the whole mountain has been chiselled away... The first second of eternity has passed

I believe this variation is from The Doctor.

if I wipe my finger across the diamond just once and strip it of millions (billions) of atoms

Though starting from the second wipe you only wipe mostly the residue attached to that diamond from your skin by the first wipe. To clean that up before the second wipe would likely damage the base material more than the second wipe.

Take these kind of 'eternity number exercises' with a pinch of salt. In any real situation it's always about interactions between many different materials, including air (in it's actual constitution). And small changes may induce big differences on long term. And the experiments (assuming there was any) leading to these numbers usually running in a controlled environment, for relative short time.

Ps.: as a live reference, you can consider the numbers often presented (in thousand years) for growth of stalactites - which you can find in any poorly insulated tunnel in decent length after some decades only.

 

[PatrickP2]

Of course, I realize that such exercises should be taken with a pinch of salt.
However, it seems to me that the study conducted may indicate that the DLC coating can last a long time.

"For instance, a covering of just 2 μm of ta-C expands the obstruction of stainless steel against rough wear, changing its lifespan from a week to 85 years. Such ta-C can be viewed as the "unadulterated" type of DLC, as it comprises only sp3-reinforced C ions."

I only asked the question because I'm curious as to how this is possible, since any body-to-body contact causes loss of material counted in trillions of atoms. I don't expect anyone to give me an exact answer, but rather I meant to estimate more or less the number of lost atoms (although I know it's hard to count that too). :)

 

[hutchphd]

estimate more or less the number of lost atoms (although I know it's hard to count that too). :)

My favorite heuristic (as opposed to fact) in this realm is that automobile tires wear at a rate of one monolayer of rubber per tire revolution. I doubt that this represents the actualI mechanism by which they abrade, but it provides a touchstone to the numbers.

 

[jrmichler]

My favorite heuristic (as opposed to fact) in this realm is that automobile tires wear at a rate of one monolayer of rubber per tire revolution. I doubt that this represents the actualI mechanism by which they abrade, but it provides a touchstone to the numbers.

Entire books have been written on the tribology of elastomers, but we can do a ball park calculation. Assume that a car tire lasts 50,000 miles, rotates 700 revolutions per mile, and the tread wears 10 mm in that time:

$0.010 m / 700 {rev}/{mile} / 50,000 miles = 0.3*10^{-9} m/{rev}$

That's 0.3 nanometers per revolution, which sounds about right.

 

[PatrickP2]

Thank you for all the replies!
Could someone please explain to me what exactly the wear of rate equation means 1.2x10
^-10mm³N^-1m^-1? How is it measured?