The debye (symbol: D) (; Dutch: [dəˈbɛiə]) is a CGS unit (a non-SI metric unit) of electric dipole moment named in honour of the physicist Peter J. W. Debye. It is defined as 1×10−18 statcoulomb-centimeters. Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10−10 statcoulomb (generally called e.s.u. (electrostatic unit) in older literature), which were separated by 1 Ångström. This gave a convenient unit for molecular dipole moments.
Typical dipole moments for simple diatomic molecules are in the range of 0 to 11 D. Symmetric homoatomic species, e.g. chlorine, Cl2, have zero dipole moment, and highly ionic molecular species have a very large dipole moment, e.g. gas-phase potassium bromide, KBr, with a dipole moment of 10.5 D.The debye is still used in atomic physics and chemistry because SI units are inconveniently large. The smallest SI unit of electric dipole moment is the yoctocoulomb-meter, which is roughly 300,000 D. There is currently no satisfactory solution to this problem of notation without resorting to the use of scientific notation.
I am trying to check if an expression is dimensionless. If it is, then I have done things correctly. However, I am stuck on how to deal with a (Debye^2) term. How can I break it down to find out if it cancels out with the other units I have left? I know this is probably a trivial question...
So really i am just unsure how to answer the last part of the question. I am unsure how to apply the low and high temperature limits the way i have done it. Do i set upper/lower limits on the integral and solve? If so i am not sure what to put
Here is what he book has for 3d
this is my attempt of a solution , but my only equation is should i convert Θ to Celsius , and if i did the specific heat of the other
substance is greater , how is that if its inversely proportional with temperature ! . and the other Θ is 200 K so it should be less ?!
Since in Debye aproximation Debye's frecuency is defined as the maximum frecueny , the corresponding wavelenght should be the minimum one, due to the inverse relation among those
λ=v/f=v·2π/ω=5.9 Å , which is higher than the given result.
I believe I should be using the information 'cubic...
Hi all, I have trouble understanding some ideas relating to the Debye model.
In my text (Oxford Solid State Basics by Steven Simon, page 11), it was stated that Debye wrote the following expression
⟨E⟩=3∑→kℏω(→k) [nB(βℏω(→k))+12]
What was not stated was the meaning of this expression. The only...
I keep hearing people saying DEB-EYE.
If it is a Dutch name, surely it is pronounced DAB-HEY-YEAH (not quite like that, but I'm trying to find something close to unambiguous syllables).
Who's Dutch here that can cover this for me, please?
Homework Statement
Show that, in the Debye theory, the number of excited vibrational modes in the frequency range ##\nu## to ##\nu+d\nu##, at temperature T, is proportional to x2e-x, where ##x=h\nu/kT##. The maximum in this function occurs at a frequency ##\nu'=2kT/h##; hence ##\nu'→0## as...
Hi everyone, I need a little help understanding how periodic reciprocal space applies to the Debye model for solids. Many thanks in advance!
If we start with the general derivation of a dispersion relation for a 1D system, with atoms coupled by springs, one gets the following relation
$$\omega...
Hi all, I have trouble understanding some ideas relating to the Debye model.
In my text (Oxford Solid State Basics by Steven Simon, page 11), it was stated that Debye wrote the following expression
$$\langle E \rangle = 3\sum_{\vec{k}} \hbar \omega (\vec{k}) \ [ n_B (\beta \hbar \omega...
Hi all, I have a few questions related to Debye's model of solids. Any assistance is greatly appreciated.
##\textbf{1)}##
My current understanding is that unlike Einstein's model, he views a 1D solid as a chain of atoms similar not unlike a 1D chain of masses coupled with springs. Thus a chain...
I calculated the energy density of capillary waves with Debye method (pretty much Debye model in 2D), and I assumed there is a frequency cutoff for capillary waves as well. However, when I checked my work with solution I was quite surprised that the solution suggests there is no such a cuttoff...
The debye length is the effective length over which electrostatic potential disturbances are "screened out" in a plasma.
So if I drop a charged point particle in a plasma, then I expect after some Debye Length, D, from this point charge, I can see no difference between any other point in the...
Dear all,
In the wiki article about Debye solid :
https://en.wikipedia.org/wiki/Debye_model , in the section 'Another derivation', below Eq. 6, the following statement is provided:
Here, I understand the right hand side, which is nothing but the density of states/modes at the frequency \nu...
Homework Statement
Na has a bcc structure with molecular mass of 22.99 gr/mol, mass density of 0.971 gr/cm^3.
The average speed of sound in Na (at room temperature=300K) is 3200 m/s.
Calculate the Debye temperature for Na
Homework Equations
I worked out this equation to calculate the Debye...
In class we derived the relationship between temperature and heat capacity for the Debye model. We found that in 3D the heat capacity is proportional to temperature cubed. My question is, would this relationship change in a metallic system?
Homework Statement
Calculate the Debye temperature for gold
Homework Equations
$$Θ_D = \hbar \frac{v_s}{k_b} \sqrt[3]{6π^2 \frac{N}{V}}$$
Speed of sound in gold: $$v_s=3240 m/s$$
The Attempt at a Solution
I used the equation for ΘD and for the concentration I used the value for atom density...
Hi! I feel like I've understood none of this stuff!
A 1D chain of springs and masses modeling a chain of atoms has a dispersion relation ala ## \omega## ~ ##|sin(k a /2) |##, where ##k## is the wave vector and ##a## the distance between atoms. As far as I have understood, the debye model (in...
Resistivity. Take this graph for example, is the Debye temperature relavant here? Would the Debye temperature be the point where the semiconductor starts to become like a metal? i.e. where the curve goes from minimum to linear?
I understand the heat capacity relation i.e. from T^3 to 3nNk but...
Homework Statement
(a) Find debye frequency.
(b) Find number of atoms.
Homework EquationsThe Attempt at a Solution
Part(a)
[/B]
Density of states is given by
g(\omega) = \frac{3V\omega^2}{2 \pi^2 c^3} = N \left[ \frac{12 \pi \omega^2}{(2\pi)^2 n c^3} \right] = 9N \frac{\omega}{\omega_D^3}...
I was doing some calculations earlier and tried the ratio between a metal's fermi temperature ##T_F## and debye temperature ##\theta_D##:
\frac{T_F}{\theta_D} = (6 \pi^2)^{\frac{1}{3}} \left( \frac{\lambda}{a} \right)
where ##\lambda = \frac{\hbar}{2 m_e c}## and lattice spacing is ##a##.
I...
Homework Statement (a) Find fermi temperature and debye temperature. Calculate them for copper.
(b) Show the scattering wave relation
(c) What does ##\lambda## mean?
Homework EquationsThe Attempt at a Solution
Part(a)
The fermi temperature and debye temperature is given by:
T_F = \frac{\hbar^2...
Homework Statement
(c) (i) Neglecting hydrogen-bonding, calculate the interaction energy between (i) H3O+ and H2O and (ii) H3O+ and H3O+ , if each pair is separated by 0.3 nm and assuming that the aqueous solvent can be treated as a medium with constant relative permittivity. Using your result...
If the young's modulus(E), poisson's ratio(v) and density(rho) of gallium arsenide is given how to find its debye temperature
K=c11+c12/2
G=c11-c12/3
Debye temp = (h/k)*(9N/4*3.14*V)^(1÷3)*(2/ut^3+1/ul^3)^(-1/3)
Using E and rho i found out the c11 and c12 and then found out bulk modulus(G)...
Hello, I am new here.
I was reading Wangsness electromagnetic fields and he delves into a short discussion about poisson-boltzman equation/Debye length before introducing the point-form of Ohm's Law. Just wondering what the significance of this was and how these two things are related.
Hi all
Homework Statement
The Debye temperature of argon is 92 K and that of silicon is 345 K. Rank the following in order of thermal conductivity (largest value first):
(i) A 1 cm3 cube of silicon at 6 K
(ii) A 512 mm3 cube of silicon at 2 K
(iii) A 1 mm3 cube of argon at 4 K
(iv)...
Homework Statement
Using the Debye dispersion approximation, calculate the heat capacity of a harmonic, monatomic, 1D lattice. Next, find the temperature dependence in the low temperature limit. (Assume that the longitudinal mode has spring constant CL = C, and the two transverse modes both...
In the Einstein model, atoms are treated as independent oscillators. The Debye model on the other hand, treats atoms as coupled oscillators vibrating collectively. However, the collective modes are regarded here as independent. What is the meaning of this independence and how does it contrast...
Dear Fellows,
In Debye Huckle Rule, how does Relaxation effect occurs in the presence of electric field.Logically it is not possible in the presence of electric field.Please help me out.
Thanks
Faisal
Hi everyone
I have trouble with this task
Homework Statement
the specific heat cv is given by
c_v =\frac {N_A k_b \hbar^2}{{\Omega_D}^3 {k_b}^2 T^2} \int \limits_{0}^{\Omega_D} \! \frac {\Omega^4 exp\frac{\hbar \Omega}{k_b T}}{{(exp\frac{\hbar \Omega}{k_b T}-1})^2} \, d\Omega
I...
Homework Statement
I have seen case studies of the 3D Debye model where the vibrational modes of a solid is taken to be harmonic with dispersion relation \omega = c_sk. It is said that for temperatures much less than the Debye temperature, the heat capacity at constant volume C_V\sim T^3...
Hello,
In the low temp. limit of Debye law for specific heat, we encounter the following integral:
∫(x4 ex)/(ex-1)2 dx, from 0 to ∞.
The result is 4∏2/15.
I have searched and found this to be related to zeta function but zeta functions do not have ex in the numerator so I am unable...
Homework Statement
A solid's thermal expansion coefficient is defined as
δ= \left(\frac{1}{V}\frac{∂V}{∂T}\right)
In the Debye model and at the low-temperature limit, show that δ is a positive quantity and is proportional to T^{3}. At the high-temperature limit, show that δ is still...
Diamond has a Debye temperature of Dt = 2000 K and a density of 3500 kg/m3.
The distance between nearest neighbors is 0.15 nm. Determine the velocity of
sound using the Debye approximation.
I have no idea where to even start with this question. Most books don't even mention the Debye...
Homework Statement
Consider phonons propagating on a one-dimensional chain of N identical atoms of mass M interacting by nearest-neighoour spring constants of magnitude C.
a) Show that the Debye frequency can be written as \omega_{D}=\pi(C/M)^{1/2}.
b) Show that when the temperature is...
This is a short question from an old final exam I'm studying from.
If you're given the graph of the dispersion curves for some material (I attached an example, but pretend the axes have numerical values on them), how would I go about estimating the Debye frequency?
My initial thought was just...
Homework Statement
Hello everyone!
I'm using the text:
"Elements of Solid State Physics - JP Srivastava (2006)"
I have followed the argument leading up to the derivation of the Debye formula for specific heat capacity, so we now have;
C_V = \frac{9N}{\omega_D^3} \frac{\partial}{\partial T}...
Homework Statement
Consider a positive point charge +q, immersed in plasma. Show that the net charge in the Debye shielding cloud exactly cancels the test charge. Assume the ions are fixed and that e*phi <<< kTe.
Homework Equations
f(u) = A exp [-(1/2*m*u^2 + q*phi)/k_b*T_e]
u is the...
Homework Statement
Consider a positive point charge +q, immersed in plasma. Show that the net charge in the Debye shielding cloud exactly cancels the test charge. Assume the ions are fixed and that e*phi <<< kTe.
Homework Equations
f(u) = A exp [-(1/2*m*u^2 + q*phi)/k_b*T_e]
u is the...
Homework Statement [/b]
Debye considered atoms to oscillate from 0 up to a nu max. It is explained further in the text that the complication (i.e., not all atoms oscillating at same frequency as shown in Einstein's formula) is accounted for, by averaging over all the frequencies present...
Homework Statement
Consider phonons propagating on a one-dimensional chain of N identical atoms of mass M interacting by nearest-neighbour spring constants of magnitude C.
Show that the Debye frequency can be written as w_{D}=\pi \left(\frac{C}{M}\right)^{1/2}.
Homework Equations
The...
Homework Statement
In Atkins's physical chemistry textbook it is written that Debye considered atoms to oscillate from 0 up to a nu max. It is explained further in the text that the complication (i.e., not all atoms oscillating at same frequency as shown in Einstein's formula) is accounted...
Hello everyone,
I have two questions about the Debye model (one historical and the other theoretical).
1. Debye models oscilators as standing waves. Where did his idea come from? Is there any physical reason to suppose this? I guess he didn't compute 1000 models just to see that this one...
I'm trying to fill out my bibliography in a report and I need to reference the papers by Debye and Falckenhagen that laid out their Induction Effect. London gives them as being
P. Debye, Physik. Z., 1920, 21, 178
H. Falckenhagen, Physik. Z., 1922, 23, 87
and I find some random paper...
I'm working from Feynman's definition of internal energy for the Debye theory of heat capacity. I'm trying to use that to derive the normal definition of heat capacity that I've seen. But I'm running into a problem. Note, in the following V_0 is frequency, whereas V is volume (that's how Feynman...
Homework Statement
I'm struggling to understand the relationship between the Debye temperature and the speed of sound in a substance. An example problem given is:
Estimate the Debye Temperature of Silicon and Lead, given that their respective speeds of sound are 9150 m/s and 1320 m/s. (not...