# What is Debye: Definition and 69 Discussions

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.

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1. ### A Can a Solid Vibrate at Debye Max Frequency?

Can a solid vibrate with only one frequency-Debye maximal frequency?
2. ### A Einstein, Debye and Peierls approaches of the Heat Transfer

What is the difference between the approaches of Einstein, Debye and Peierls regarding the heat transfer?!
3. ### I How to ensure an equation is dimensionless when it includes "Debye"

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...
4. ### Debye Approximation of Heat Capacity in 1D

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
5. ### A question about the specific heat and Debye temperature

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 ?!
6. ### Minimum wavelength of phonons under the Debye aproximation

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...
7. ### A Debye Model Q&A: Interpreting Expression & Link to Einstein's

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...
8. ### I How is Peter Debye's name pronounced?

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?
9. ### The number of vibrational modes g(v)dv in Debye theory

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...

12. ### I Questions on Debye's Model of solids

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...
13. ### I Is there a frequency cutoff for Debye theory of capillary waves?

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...
14. ### I Does the Debye Length Change with Applied Potential Strength in a Plasma?

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...
15. ### Are energy levels in a Debye solid equivalent to particles?

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...
16. ### Why Is My Calculated Debye Temperature for Sodium Higher Than Literature Values?

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...
17. ### Does the heat capacity change for a metallic system?

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?
18. ### Debye temperature for gold

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...
19. ### Why Does Iron Have a Higher Molar Specific Heat Than Its Debye Value?

Why does iron have molar specific heat greater than Debye value 3R?
20. ### Understanding the Vacuum Debye Screening Length: Importance and Calculation

What is the correct value for the vacuum Debye screening length?
21. ### Understanding the Debye Model for Solids: Masses and Springs

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...
22. ### Is it possible to label the Debye temperature on a graph of

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...
23. ### Number of phonons - Which length should I use?

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}...
24. ### What does this length represent?

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...
25. ### Electron-Phonon Scattering

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...
26. ### Interaction Energies and Debye Length

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...
27. ### Find Debye Temp of GaAs: E,v,rho Given

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)...
28. ### Exploring the Relationship Between Debye Length and Ohm's Law

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.
29. ### Thermal conductivity and Debye temperature

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)...
30. ### Heat capacity using Debye dispersion relation

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...
31. ### Einstein Model vs Debye model.

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...
32. ### Debye-Hückel Rule: Relaxation Effects in Electric Fields

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
33. ### Approximation of specific heat, Debye model

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...
34. ### Debye model in Statistical Physics

Was Debye's basic idea for a solid body to neglect the dispersion Einstein talked about in his model?
35. ### Debye model and dispersion relation

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...
36. ### Zeta function for Debye Low Temp. Limit

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...
37. ### Thermal expansion coefficient of a Debye solid

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...
38. ### Calculating Sound Velocity in Diamond Using Debye Approximation

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...
39. B

### Show that when the temperature is such that T Debye temperature, the specific

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...
40. ### Estimating Debye Frequency from Dispersion Curves: What's the Proper Approach?

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...
41. ### Derivation of the Debye Specific Heat Capacity

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}...
42. ### What is the Debye Shielding Problem?

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...
43. ### Plasma Physics Debye Shielding

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...
44. ### What Determines the Equilibrium Separation Between Atoms in a Lattice?

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...
45. ### Debye Frequency for 1D atomic chain

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...
46. ### How did Debye derive nu max and nu average?

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...
47. ### Debye Model of Solids: Questions & Answers

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...
48. ### Trying to find papers of Debye and Falckenhagen's Induction Effect.

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...
49. ### Debye internal energy for heat capacity

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...
50. ### Relationship between Debye Temperature and Speed of Sound in Metals

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...