Hi there,

maybe someone knows the answer to the following
question that has been puzzling me for some time now.

Thermodynamic stability of a paramagnetic system seems to
require a nonnegative magnetic susceptibility (convexity of the free
energy). This is somehow equivalent to the requirement of a
positive compressibility for mechanical stability of a substance.
However, real materials also show diamagnetism, which,
by definition, corresponds to a _negative_ magnetic susceptibility.
Why doesn't this lead to stability problems? Does anyone care to
explain this to me or cite a good reference where this is discussed?

In article <45f83663$0$11352$3b214f66@usenet.univie.ac.at>, beheiger wrote:
Hi there,

maybe someone knows the answer to the following
question that has been puzzling me for some time now.

Thermodynamic stability of a paramagnetic system seems to
require a nonnegative magnetic susceptibility (convexity of the free
energy). This is somehow equivalent to the requirement of a
positive compressibility for mechanical stability of a substance.
However, real materials also show diamagnetism, which,
by definition, corresponds to a _negative_ magnetic susceptibility.
Why doesn't this lead to stability problems? Does anyone care to
explain this to me or cite a good reference where this is discussed?

First I'll give you a reference. For all my thermodynamic needs, I
usually turn to the excellent books by Landau & Lifshitz. For this
question specifically, you want to look at vol.VII (Electrodynamics of
Continuous Media), sections 14 (for the dielectric case) and 32 for the
magnetic case. Now, I'll try to summarize their argument.

First, you are slightly mistaken in your assesment of the situation.
Thermodynamic stability only requires the total permittivity
(epsilon = epsilon_0 (1 + chi_E)) and total permeability
(mu = mu_0 (1 + chi_M)) to be positive, where the chi_E and chi_M are
respectively the dielectric and magnetic susceptibilities.

So the constraints on chi_E and chi_M are just that they are > -1. This
allows for paramagnetism (chi_M > 0) and diamagnetism (chi_M < 0). On
the other hand, you are right the we can improve the constraint on the
polarizability to chi_E > 0. The real question is How?

I've got to run now. I hope to say more on this later.

Hope this helps.

Igor

We can easily make solids with random unpaired electron spins
(paramagnets; transition, lanthanide, actinide metal salts, organic
stable free radicals), aligned unpaired electron spins (ferromagnets;
94% of Alnico 5 magnetic field), and aligned electron orbital angular
momenta (37% of Sm2Co17 magnetic field). The few transparent
ferromagnetic solids have very high refractive indices - but that is
expected. Is there anything special about these guys compared to
Plexiglas?

We can easily make corresponding solids with permanent electric
dipoles - poled ferroelectrics, electrets. Bulk water at 20 C has
epsilon = 80.1, and that is an impressively large number. N-Methyl
formamide, epsilon = 182.4 (308 at -40); N-methyl acetamide, epsilon =
191.3. Bulk KTaNbO3 has epsilon = 34,000 at 0 C. Is there anything
special about these guys compared to benzene at epsilon = 2.28 or
cyclohexane at epsilon = 2.02?

--
Uncle Alhttp://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)http://www.mazepath.com/uncleal/lajos.htm#a2

On Mar 17, 8:29 pm, Uncle Al <Uncle...@hate.spam.net> wrote:
[snip]

We can easily make corresponding solids with permanent electric
dipoles - poled ferroelectrics, electrets. Bulk water at 20 C has
epsilon = 80.1, and that is an impressively large number. N-Methyl
formamide, epsilon = 182.4 (308 at -40); N-methyl acetamide, epsilon =
191.3. Bulk KTaNbO3 has epsilon = 34,000 at 0 C. Is there anything
special about these guys compared to benzene at epsilon = 2.28 or
cyclohexane at epsilon = 2.02?

How lossy are these materials at radio frequencies?