Talk:Bulk modulus

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For the adiabatic definition, I think that means constant entropy, not enthalpy. see http://scienceworld.wolfram.com/physics/AdiabaticBulkModulus.html Ojcit 20:05, 1 September 2006 (UTC)

Dead links

Links to hyperphysics.phy-aster.gsu.edu are non-existant. These links are located in the reference section of the page.

Currently reads http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html, and comes out at the front of the site. Would be useful to embed the link deeper into the site.

—DIV (128.250.204.118 09:21, 19 March 2007 (UTC))

Nomenclature

Is there any special reason for calling this K? B also seems common. —DIV (128.250.204.118 09:21, 19 March 2007 (UTC))

Bulk modulus (B) Compressibility (K)

Sorry to the person who did the bulk of the writing on this page, but you've got the symbols backward. B is for bulk modulus and K is for compressibility. When I get some time, I will try to repair the damage, but it's going to take a lot of work as the error is spread across several pages. Elert 20:48, 2 December 2007 (UTC)elert

Actually using B (it's actually a lower-case beta, but that's neither here nor there) for compressibility, and K for Bulk modulus is the correct way to do it. It is logically a little backwards, but is nonetheless correct. 128.118.175.36 (talk) 18:26, 4 September 2008 (UTC)

K has always been used to express Bulk Modulus, also not sure why B has to be used for Compressibility considering that it is the reciprocal of K anyway - 1/K is easier for the reader to immediately understand the relationship. However, I would propose to broaden the current formula definition to differentiate between solids and gases. While the current definition refers to both solids and gases, the nature of the higher compressibility of gases lends itself to a change in density (due to the change in volume). Hence I would propose the Bulk Modulus formula for gases to also be stated as follows: K = ρ0(δp/δρ)0 , where ρ0 is the equilibrium density of the gas, δp is the change in pressure to realise δρ, the change in density of the gas and K expressed as Nm-2. Grathan (talk) 09:59, 22 August 2010 (UTC)

I've also seen β used for bulk modulus (in https://www.semanticscholar.org/paper/Multicomponent-Multiphase-Equation-of-State-for-Kerley-Chhabildas/cb0d52699ffda4efa2781fcd9236a14b34bf5958). Someone on the compressibility talk page said that conventions differ about whether bulk modulus is B or K. The same person said they'd seen β or κ for compressibility. It looks like the Wikipedia pages are currently mostly going with K for bulk modulus and κ for compresibility.DubleH (talk) 08:42, 31 March 2021 (UTC)

This is a situation where different fields and different authors use different notation. Nothing wrong with the page explaining that, of course - especially since folks seem to have strong beliefs about which notation is "right" or "wrong." Personally I'm agnostic. KeeYou Flib (talk) 20:56, 31 March 2021 (UTC)

Directionality

"the bulk modulus is not the same in all directions" I don't think the bulk modulus varies with direction. Also, I would like to include the equation that B = ratio of hydrostatic stress to volumetric strain. I know this is implied by the thermodynamic definition, but it is a much more useful relationship for mechanics of materials.And it points up that even for an anisotropic crystal, the bulk modulus is a scalar. —Preceding unsigned comment added by Tibbits (talk • contribs) 16:40, 30 June 2008 (UTC)

It does in single crystals. A typical bar of steel, for instance, will have a great many grains facing every which way, masking the effect. An extreme example of anisotropy would be a layered material like the cuprate high temperature superconductors - clearly the in-plane bonding differs significantly from the cross-plane electronic structure. A less extreme example can be seen in the regular trivalent rare earth structural sequence, where hexagonal structures transform under pressure to be more close-packed by compressing preferentially along the c-axis (the height of the right hexagonal prism). - Eldereft (cont.) 22:27, 30 June 2008 (UTC)

I agree that the elastic modulus varies with the orientation of measurement with respect to the crystalline axes of anisotropic crystals. I disagree that the bulk modulus varies. Change in volume does not refer to the direction of the deformation. The bulk modulus is a scalar. Tibbits (talk) 14:33, 2 April 2010 (UTC)

I would like to see the anisotropy section of the bulk modulus page removed. K = dP/(dV/V) = dP/(e_x + e_y + e_z). Note that the denominator of the rightmost expression is an invariant of the strain tensor, hence insensitive to orientation of coordinate system, as is pressure as well. This reinforces the argument that both pressure and volumetric strain are scalars, so their ratio is also a scalar.Tibbits (talk) 05:17, 4 April 2010 (UTC)

1/e?

When the article says: It is defined as the pressure increase needed to decrease the volume by a factor of 1/e, is the 'e' the mathematical constant e? If so, it should have a link.--ML5 (talk) 11:54, 27 September 2011 (UTC)

Is bulk modulus linear until matter degenerates?

Is bulk modulus linear until matter degenerates? Can you compress water 99.99%+ until finally the electrons touch the nucleus? (under what pressure does the equation stop working?) 12.33.223.210 (talk) 23:37, 29 October 2018 (UTC)

Microscopic origin

This section needs editing. The plots use $r$ to represent interatomic spacing, and should have a subscripted $r_{0}$ to indicate the equilibrium spacing. Instead, there is a non-subscripted $r0$.

In addition, the text that accompanies the plots uses a mixture of conventions. In the body paragraphs, it says the spacing is $a$, and equilibrium spacing $a_{0}$, but the equations use $r$ as the spacing, and $r=a_{0}$ to indicate equilibrium spacing.

So, it needs to be edited so that the paragraphs, equations and plots are all using the same convention.

Plus, really, the force plot should be flipped, since attractive force is positive, and repulsive negative. Hermanoere (talk) 23:20, 19 January 2021 (UTC)

...and this is only the tip of the iceberg. many other edits are needed here as well. Qflib, aka KeeYou Flib (talk) 20:40, 20 December 2023 (UTC)

Engineering Mechanics

Bulk modulus is a material property used for both fluids and solids. The definitions given in the definitions section are correct, but not readily amenable to standard engineering mechanics where it is used to relate hydrostatic pressure to volumetric strain. For this, a simple equation such as: p = K * epsilon_volumetric is a good start.

From there we need to define or show how the pressure is calculated from the stress tensor and how volumetric strain is calculated. Namely, p=-I1/3, where I1 is the first invariant of the stress tensor (i.e. its trace) and therefore invariant to rotations of the coordinate system. Volumetric strain = (V_f - V_0)/V_0. For small strains this is approximately equal to the trace of the strain tensor. It would be good to give some indication of when this approximation breaks down.

Also, it would be helpful to have a discussion of how bulk modulus depends on pressure. — Preceding unsigned comment added by Larryhi5 (talk • contribs) 16:15, 21 January 2021 (UTC)

Seems like a good idea. Why don't you add a section? KeeYou Flib (talk) 20:53, 31 March 2021 (UTC)

Measurement

Superhard_material says "The bulk modulus test uses an indenter tool to form a permanent deformation in a material." but the permanent deformation seems more of a hardness (yield strength) test, and it's not mentioned in this article. - Rod57 (talk) 14:09, 25 October 2021 (UTC)

Needs editing

The section on "Microscopic origin" needs very serious editing, if not a complete rewrite, and I've tagged the page for this reason. Many, many typos, poor flow, unexplained formulas and steps... I'm willing to give overhauling this section a try as soon as I get time, but until then anyone else who wants to pitch in should feel free. Qflib, aka KeeYou Flib (talk) 20:39, 20 December 2023 (UTC)

@Qflib, I think the first part #Interatomic potential and linear elasticity is OK but the 2nd part #Relationship with atomic radius is bad hand-waving (incorrect science) from before DFT became possible; you cannot use pair-wise for metals. I suggest deleting that part completely. If you agree I will, and/or we can post to WT:Physics. Ldm1954 (talk) 02:32, 22 February 2024 (UTC)

Agree! Please do. Qflib (talk) 01:38, 24 February 2024 (UTC)

Done Ldm1954 (talk) 01:50, 24 February 2024 (UTC)