Phenomenological approach of the thermodynamic properties of CDW (SDW) systems

M. Saint-Paul; P. Monceau

arxiv: 1907.01206 · v1 · pith:M4QFT5KFnew · submitted 2019-07-02 · ❄️ cond-mat.str-el

Phenomenological approach of the thermodynamic properties of CDW (SDW) systems

M. Saint-Paul , P. Monceau This is my paper

Pith reviewed 2026-05-25 11:08 UTC · model grok-4.3

classification ❄️ cond-mat.str-el

keywords charge density wavespin density wavespecific heatelastic constantsmean field theoryphase transitionthermodynamic properties

0 comments

The pith

Thermodynamic jumps at CDW and SDW transitions increase with the transition temperature following mean-field BCS behavior.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper collects measurements of the specific heat jump and the change in longitudinal elastic stiffness across the charge-density-wave transition in several compounds. These include the quasi-one-dimensional blue bronze, the transition-metal dichalcogenide 2H-NbSe2, rare-earth tritellurides, and the intermetallic Lu5Ir4Si10, plus spin-density-wave cases in chromium and CuGeO3. In each case the size of the thermodynamic discontinuity grows larger when the transition occurs at higher temperature. The authors conclude that this pattern indicates the systems obey the classical mean-field description familiar from BCS theory, even though strong fluctuations are expected in lower-dimensional materials.

Core claim

Across a range of CDW and SDW materials the magnitude of the specific heat jump ΔCp and the relative softening ΔC11/C11 at the transition both increase with the transition temperature TCDW, leading to the conclusion that the thermodynamic properties follow classical mean-field BCS-type behavior despite the presence of large fluctuations.

What carries the argument

The positive correlation between the size of the thermodynamic discontinuities (ΔCp and ΔC11/C11) and the CDW transition temperature TCDW.

If this is right

The mean-field BCS framework remains applicable to the thermodynamics of real CDW systems in various dimensions.
Materials with higher transition temperatures should exhibit larger specific-heat and elastic anomalies.
The same scaling relation applies to spin-density-wave transitions as well as charge-density-wave ones.
Fluctuation effects do not override the mean-field jump behavior in the examined systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the trend is general, the gap magnitude inferred from thermodynamics should also scale with TCDW across these materials.
Similar measurements on additional CDW compounds could test whether the relation continues to hold outside the listed examples.
The observed scaling might be used to estimate expected thermodynamic signatures in predicted but unmeasured density-wave systems.

Load-bearing premise

The chosen materials are representative of CDW and SDW systems in general rather than reflecting only special cases or selection biases.

What would settle it

Observation of a CDW or SDW material in which the specific heat jump or elastic stiffness change decreases or remains unchanged as the transition temperature increases would falsify the general tendency.

read the original abstract

The microscopic description of the CDW phase transition is still debated and remains controversial. The question is how to extend the Peierls picture to real systems in higher dimensions. A general tendency is found in the thermodynamic properties such as the specific heat jump DCp and the decrease of the longitudinal elastic stiffness constant DC11/C11 at the CDW phase transition in several materials, such as quasi-one dimensional (K0.3MoO3), transition metal dichalcogenide compounds (2H-NbSe2), rare earth tritellurides (TbTe3, ErTe3, HoTe3) and intermetallic compound (Lu5Ir4Si10). DCp and DC11/C11 increase as the temperature of the phase transition TCDW and TCDW2 respectively. The same tendency is found at the spin density phase transition in chromium and CuGeO3.Thermodynamic properties of almost all CDW systems, although it has been recognized to exhibit large fluctuations, follow the classical mean field BCS type behavior.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper compiles jump sizes from eight CDW/SDW compounds and notes they grow with transition temperature, but the limited sample and lack of fluctuation comparisons leave the mean-field claim under-supported.

read the letter

The core observation is that specific-heat and elastic jumps at the CDW or SDW transition increase with the transition temperature in the listed materials. The authors collect numbers for K0.3MoO3, 2H-NbSe2, three rare-earth tritellurides, Lu5Ir4Si10, Cr, and CuGeO3, then note that the jumps follow the classical BCS pattern even though fluctuations are acknowledged to be large. That cross-check across different families is the main concrete thing the manuscript adds; it makes the scaling tendency easy to see in one place. The data themselves come from prior experiments, so the work is observational rather than a new derivation or measurement. The trend is presented clearly enough that a reader already working on these compounds could check it against their own notes. The main limitation is the small set of compounds. No count of known CDW materials appears, no selection criteria are stated, and there is no test of whether the correlation survives adding other systems or direct comparison to Ginzburg-Landau or renormalization-group predictions that include fluctuations. The phrasing “almost all CDW systems” therefore sits on a narrow base. The paper does not introduce free parameters or circular fits, and the citations track back to the original measurements. Specialists who track thermodynamic signatures in density-wave materials would find the tabulated trend convenient to have on hand. It is not a new framework, but the pattern is worth a referee’s look to verify the data sources and to ask whether the trend is robust beyond the chosen examples. I would send it out for review rather than desk-reject.

Referee Report

2 major / 1 minor

Summary. The manuscript presents a phenomenological analysis of thermodynamic properties at CDW and SDW transitions. It reports that the specific-heat jump ΔCp and the relative elastic-stiffness change ΔC11/C11 increase with transition temperature TCDW (or TCDW2) across eight listed compounds (K0.3MoO3, 2H-NbSe2, TbTe3, ErTe3, HoTe3, Lu5Ir4Si10, Cr, CuGeO3) and concludes that, despite acknowledged large fluctuations, the thermodynamic properties of almost all CDW systems follow classical mean-field BCS-type behavior.

Significance. If the reported positive correlation between jump size and transition temperature proves robust across a wider set of materials, the observation would indicate that mean-field descriptions remain quantitatively useful for CDW thermodynamics even when fluctuations are large, thereby constraining the parameter regimes in which fluctuation-corrected theories are required.

major comments (2)

[Abstract] Abstract: the assertion that 'almost all CDW systems' exhibit the described mean-field BCS behavior rests on tabulated or plotted values for only eight specific compounds; no count of known CDW materials, selection criteria, or demonstration that the trend survives inclusion of additional systems is provided, rendering the generality claim unsupported.
[Abstract] Abstract: although large fluctuations are explicitly recognized, the manuscript contains no quantitative comparison of the observed ΔCp(TCDW) or ΔC11/C11(TCDW) trends against predictions from fluctuation-corrected theories (e.g., 1D/2D Ginzburg-Landau or renormalization-group calculations), which is required to substantiate that the data nevertheless follow classical mean-field behavior.

minor comments (1)

[Abstract] Abstract: notation 'DCp' and 'DC11/C11' should be written consistently as ΔCp and ΔC11/C11 to match standard thermodynamic usage.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major points below.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion that 'almost all CDW systems' exhibit the described mean-field BCS behavior rests on tabulated or plotted values for only eight specific compounds; no count of known CDW materials, selection criteria, or demonstration that the trend survives inclusion of additional systems is provided, rendering the generality claim unsupported.

Authors: The eight compounds were selected because they are the systems for which both specific-heat jumps and elastic-stiffness changes have been reliably measured and reported in the literature; they also span distinct material classes and dimensionalities. We do not assert that every known CDW material has been examined. To avoid any implication of exhaustive coverage we will revise the abstract and main text to replace 'almost all CDW systems' with 'the CDW (SDW) systems examined here'. revision: yes
Referee: [Abstract] Abstract: although large fluctuations are explicitly recognized, the manuscript contains no quantitative comparison of the observed ΔCp(TCDW) or ΔC11/C11(TCDW) trends against predictions from fluctuation-corrected theories (e.g., 1D/2D Ginzburg-Landau or renormalization-group calculations), which is required to substantiate that the data nevertheless follow classical mean-field behavior.

Authors: The work is phenomenological and therefore limited to the empirical observation that the measured jumps follow the mean-field BCS dependence on transition temperature. While fluctuation-corrected theories exist, performing a material-specific quantitative comparison would require additional microscopic parameters (Ginzburg number, anisotropy, etc.) that are not uniquely determined for each compound and lie outside the scope of the present study. We will add a short paragraph in the discussion noting that the observed trend remains consistent with mean-field expectations despite the acknowledged fluctuations. revision: partial

Circularity Check

0 steps flagged

No circularity: observational correlations from independent experiments, no derivation or self-referential fitting.

full rationale

The paper collects tabulated or plotted thermodynamic data (ΔCp, ΔC11/C11) from eight distinct materials and reports an observed positive correlation with transition temperature. No equations, ansatz, fitted parameters, or uniqueness theorems are introduced whose output is then relabeled as a prediction. The central statement that 'almost all CDW systems follow classical mean-field BCS behavior' is presented as a direct phenomenological summary of the listed measurements rather than a quantity derived from any internal definition or self-citation chain. External literature on fluctuations is acknowledged but not used to close a logical loop. The analysis therefore contains no load-bearing step that reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that mean-field BCS theory remains applicable to these fluctuating systems and that the chosen materials illustrate a universal rather than idiosyncratic behavior.

axioms (1)

domain assumption Mean-field BCS theory applies to CDW/SDW transitions despite large fluctuations
Abstract states that properties follow BCS-type behavior even while noting recognized large fluctuations.

pith-pipeline@v0.9.0 · 5713 in / 1171 out tokens · 29672 ms · 2026-05-25T11:08:06.109299+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages

[1]

Grüner, Density Waves in Solids ed

G. Grüner, Density Waves in Solids ed. D. Pines (Addison-Wesley) 1994 and Rev. Mod. 60,1129 (1988)

work page 1994
[2]

Frölich, Poc.R

H. Frölich, Poc.R. Soc. London A223, 296, (1954)

work page 1954
[3]

J. W. Brill, “ Elastic properties of low dimensional materials in Chap.10 in Handbook of Elastic Properties of Solids (VolumeII) Liquid and Gases, Levy, Bass, and Stern, Eds, Academic Press, (2001)

work page 2001
[4]

Monceau, Electronic crystals : An experimental overview, Advances in Physics, Vol 61, 325-581, (2012)

P. Monceau, Electronic crystals : An experimental overview, Advances in Physics, Vol 61, 325-581, (2012)

work page 2012
[5]

M. D. Johannes, I. Mazin, Fermi Surface nesting and the origin of charge density waves in metals Phys. Rev B 77 165135 (2008)

work page 2008
[6]

X. Zhu, J. Guo, J. Zhang, E. W. Plummer, J. D. Guo Classification of charge density waves based on their nature Proc. Natl. Acad. Sci. 112 (2015) 2367-2371

work page 2015
[7]

X. Zhu, J. Guo, J. Zhang, E. W. Plummer, Misconception associated with the origin of charge density waves Adv. Phys. 2 622-640 (2017)

work page 2017
[8]

Manzeli, D.Ovchinnikov, D

S. Manzeli, D.Ovchinnikov, D. Pasquier, O. V. Yazyev, A. Kis 2D transition metal dichacogenides Nature Reviews/Materials 2 (2017) 17033. [9 J. A. Wilson, F. Di Salvo, S. Mahajan Charge density waves and superlattices in the metallic layered transition metal Advances in Physics 24 117 (1975)

work page 2017
[9]

Rossnagel On the origin of charge density waves in selected layered transition metal dichalcogenides Journal of Physics: Condensed Matter 23, 213001 (2011)

K. Rossnagel On the origin of charge density waves in selected layered transition metal dichalcogenides Journal of Physics: Condensed Matter 23, 213001 (2011)

work page 2011
[10]

J. W. Brill, M. Chung, Y.-K. Kuo, E. Figueroa, G. Mozurkewich Thermodynamics of the Charge-Density-Wave Transition in Blue Bronze, Phys. Rev. Lett. 74 1182 (1995)

work page 1995
[11]

J. A. Aronovitz, P. Goldbart, G. Mozurkewich Elastic singularities at the Peierls transition Phy. Rev. Lett 64, 2799-2802 (1990)

work page 1990
[12]

Tomic, K

S. Tomic, K. Biljakovic, D. Djurek, J. R . Cooper, P. Monceau, A. Meerschaut Calorimetry study of the phase transition in Niobium Triselenide NbSe 3 Solid. State. Commun. 38, 109-112 (1981)

work page 1981
[13]

J. W. Brill, N. P. Ong , Young's modulus of NbSe 3 Solid State Commun. 25, 1075-1078 (1978)

work page 1978
[14]

Eremenko, V

V. Eremenko, V. Sirenko, V. Ibulaev, J. Bartomomé, A. Arauzo, G. Reményi, Heat capacity, thermal expansion and pressure derivative of critical temperature at the superconducting and charge density wave (CDW) in NbSe2 Physica 469, 259-264 (2009)

work page 2009
[15]

M. H. Jericho, A. M. Simpson, R. F. Frindt , Velocity of ultrasonic waves in 2H-NbSe 2, 2H-TaS 2 and 1T-TaS 2 Phys. Rev B 22, 4907-4914 (1980)

work page 1980
[16]

Caillé, Y

A. Caillé, Y. Lepine, M. H. Jericho, A. M. Simpson , Thermal expansion, ultrasonic velocity and attenuation measurements in TiS 2,TiSe 2 and TiS 0.5 Se 1.5 Phys. Rev. B 28, 5454 (1983)

work page 1983
[17]

R. A. Craven, F. J. Di Salvo, F. S. L. Hsu, Mechanism for the 200 K transition in TiSe 2: A measurement of the specific heat Solid State Commun. 25, 39-42 (1978)

work page 1978
[18]

N. Ru, C. L. Condron,G. Y. Margulis, K. Y. Shin, J. Laverock, S. B. Dugdale, M. F. Toney, I. R. Fisher Effect of chemical pressure on the charge density wav transition in rare earth tritellurides RTe 3 Phys. Rev. B 77 035114 (2008)

work page 2008
[19]

Brouet, W

V. Brouet, W. L. Yang, X. J. Zhou, Z. Hussain, R. G. Moore, R. He, D. H. Lu, Z. X. Shen, J. Laverock, S. B. Dugdale, N. Ru, I. R. Fisher, Angle resolved photoemission study of the evolution, of band structure and charge density wave properties in RTe 3 (R=Y,La, Ce, Sm, Gd, Tb and Dy). Phys.Rev. B 77 235104 (2008)

work page 2008
[20]

Saint-Paul, C

M. Saint-Paul, C. Guttin, P. Lejay, G. Remenyi, O. Leynaud, P. Monceau , Elastic anomalies at the charge density wave transition in TbTe 3. Solid State Commun.233, 24-29 (2016)

work page 2016
[21]

Saint-Paul, G

M. Saint-Paul, G. Reményi, C. Guttin, P. Lejay, P. Monceau , Thermodynamic and critical properties of the charge density wave system ErTe 3 Physica B 504, 39-46 (2017)

work page 2017
[22]

Saint-Paul, C

M. Saint-Paul, C. Guttin, P. Lejay, O. Leynaud, P. Monceau, Elastic anomalies at the charge density wave transition in HoTe 3. International Journal of Modern Physics B 32, 1850249 (2018)

work page 2018
[23]

Van Smaalen, M

S. Van Smaalen, M. Shaz, L. Palatinus, P. Daniels, F. Galli, G. J. Nieuwenhuys, J. A. Mydosh, Multiple charge-density-waves in R 5Ir 4Si 10 (R=Ho, Er, Tm, and Lu) Phys. Rev. B 69 014103 (2004)

work page 2004
[24]

Y.-K. Kuo, C. S. Lue, F. H. Hsu, H. H. Li, H. D. Yang , Thermal properties near the charge-density-wave transition Phys. Rev. B 64 125124 (2001)

work page 2001
[25]

Mansart, M

B. Mansart, M. J. G. Cottet, T. J. Penfold, S. B. Dugdale, R. Tediosi, M. Chergui, F. Carbone, Evidence for a Peierls phase transition in a three-dimensional multiple charge-density waves in solid. Proc. Natl. Acad. Sci. (2011)

work page 2011
[26]

Saint-Paul, C

M. Saint-Paul, C. Opagiste, C. Guttin , Elastic properties at the charge density wave transition in Lu 5Ir 4Si 10 Journal of Physics and Chemistry of solids (to be published)

work page
[27]

S. L. Bud’ko, S. A. Law, P. C. Canfield,G. D. Samolyuk M. S. Torikachvili G. M. Schmiedeshoff , Thermal expansion and magnetostriction of pure and doped RAgSb2 (R=Y, Sm, La) single crystals. Journal of Physics: Condensed Matter, vol. 20, 115210 (2008)

work page 2008
[28]

J. P. Pouget, L. P. Regnault, M. Ain, B. Hennion, J. P. Renard, P. Veillet, G. Dhalenne, and A. Revcolevschi, Structural evidence for a spin Peierls ground state in the quasi one dimensional compound CuGeO 3 Phys. Rev. Lett. 72, 4037 (1994)

work page 1994
[29]

Saint-Paul, G

M. Saint-Paul, G. Reményi, N. Hegmann, P. Monceau, G.Dhalenne, A. Revcolevschi , Ultrasonic Study o magnetoelastic effects in the spin -Peierls state of CuGeO3 Phys. Rev. B 52, 15298 (1995). [31]R. Weber, R. Street , The heat capacity anomaly of chromium at 311 K (antiferromagnetic to paramagnetic transition Journal of Physics F: Metal Physics 2 873-877 (1972)

work page 1995
[30]

D. I. Bolef, J. De Klerk , Anomalies in the elastic constants and thermal expansion of chromium single crystals Phys. Rev B 129, 1063-1067 (1963)

work page 1963
[31]

Saint-Paul and P

M. Saint-Paul and P. Monceau, Survey of the thermodynamic properties of the charge density wave systems Advances in condensed matter (Hindawi) (2019) 2138264 doi /10.1155/2019/2138264

work page doi:10.1155/2019/2138264 2019
[32]

W. L. McMillan , Landau theory of charge density waves in transition-metal dichalcogenides Phys. Rev. B 12 1187-1196 (1975)

work page 1975
[33]

Allender, J

D. Allender, J. W. Bray, J. Bardeen , Theory of fluctuation superconductivity from electron-phonon interactions in pseudo- one-dimensional systems Phys. Rev. B 9, 119 (1974). [36 L. Landau and E. Lifshitz, Statistical Physics, Pergamon Press, 1968 and K. Binder, Theory of first order phase transitions Rep. Prog. Phys. 50 783859 (1987)

work page 1974
[34]

L. R. Testardi, Elastic modulus, thermal expansion, and specific heat at a phase transition Phys. Rev. B 12 3849-3853 (1975)

work page 1975
[35]

Rehwald, The study of structural phase transitions by means of ultrasonic experiments Adv

W. Rehwald, The study of structural phase transitions by means of ultrasonic experiments Adv. Phys. 22 721-755(1973). Table 1 Anomalies of Specific heat and sound velocity at the CDW phase transition. Molar volume V m. Materials Specific heat jump Velocity decrease Quasi-one-dimensional conductors K0.3 MoO 3 Vm=3.6×10 -5 m3 NbSe 3 Vm=4.1×10 -5 m3 T CDW =1...

work page 1973

[1] [1]

Grüner, Density Waves in Solids ed

G. Grüner, Density Waves in Solids ed. D. Pines (Addison-Wesley) 1994 and Rev. Mod. 60,1129 (1988)

work page 1994

[2] [2]

Frölich, Poc.R

H. Frölich, Poc.R. Soc. London A223, 296, (1954)

work page 1954

[3] [3]

J. W. Brill, “ Elastic properties of low dimensional materials in Chap.10 in Handbook of Elastic Properties of Solids (VolumeII) Liquid and Gases, Levy, Bass, and Stern, Eds, Academic Press, (2001)

work page 2001

[4] [4]

Monceau, Electronic crystals : An experimental overview, Advances in Physics, Vol 61, 325-581, (2012)

P. Monceau, Electronic crystals : An experimental overview, Advances in Physics, Vol 61, 325-581, (2012)

work page 2012

[5] [5]

M. D. Johannes, I. Mazin, Fermi Surface nesting and the origin of charge density waves in metals Phys. Rev B 77 165135 (2008)

work page 2008

[6] [6]

X. Zhu, J. Guo, J. Zhang, E. W. Plummer, J. D. Guo Classification of charge density waves based on their nature Proc. Natl. Acad. Sci. 112 (2015) 2367-2371

work page 2015

[7] [7]

X. Zhu, J. Guo, J. Zhang, E. W. Plummer, Misconception associated with the origin of charge density waves Adv. Phys. 2 622-640 (2017)

work page 2017

[8] [8]

Manzeli, D.Ovchinnikov, D

S. Manzeli, D.Ovchinnikov, D. Pasquier, O. V. Yazyev, A. Kis 2D transition metal dichacogenides Nature Reviews/Materials 2 (2017) 17033. [9 J. A. Wilson, F. Di Salvo, S. Mahajan Charge density waves and superlattices in the metallic layered transition metal Advances in Physics 24 117 (1975)

work page 2017

[9] [9]

Rossnagel On the origin of charge density waves in selected layered transition metal dichalcogenides Journal of Physics: Condensed Matter 23, 213001 (2011)

K. Rossnagel On the origin of charge density waves in selected layered transition metal dichalcogenides Journal of Physics: Condensed Matter 23, 213001 (2011)

work page 2011

[10] [10]

J. W. Brill, M. Chung, Y.-K. Kuo, E. Figueroa, G. Mozurkewich Thermodynamics of the Charge-Density-Wave Transition in Blue Bronze, Phys. Rev. Lett. 74 1182 (1995)

work page 1995

[11] [11]

J. A. Aronovitz, P. Goldbart, G. Mozurkewich Elastic singularities at the Peierls transition Phy. Rev. Lett 64, 2799-2802 (1990)

work page 1990

[12] [12]

Tomic, K

S. Tomic, K. Biljakovic, D. Djurek, J. R . Cooper, P. Monceau, A. Meerschaut Calorimetry study of the phase transition in Niobium Triselenide NbSe 3 Solid. State. Commun. 38, 109-112 (1981)

work page 1981

[13] [13]

J. W. Brill, N. P. Ong , Young's modulus of NbSe 3 Solid State Commun. 25, 1075-1078 (1978)

work page 1978

[14] [14]

Eremenko, V

V. Eremenko, V. Sirenko, V. Ibulaev, J. Bartomomé, A. Arauzo, G. Reményi, Heat capacity, thermal expansion and pressure derivative of critical temperature at the superconducting and charge density wave (CDW) in NbSe2 Physica 469, 259-264 (2009)

work page 2009

[15] [15]

M. H. Jericho, A. M. Simpson, R. F. Frindt , Velocity of ultrasonic waves in 2H-NbSe 2, 2H-TaS 2 and 1T-TaS 2 Phys. Rev B 22, 4907-4914 (1980)

work page 1980

[16] [16]

Caillé, Y

A. Caillé, Y. Lepine, M. H. Jericho, A. M. Simpson , Thermal expansion, ultrasonic velocity and attenuation measurements in TiS 2,TiSe 2 and TiS 0.5 Se 1.5 Phys. Rev. B 28, 5454 (1983)

work page 1983

[17] [17]

R. A. Craven, F. J. Di Salvo, F. S. L. Hsu, Mechanism for the 200 K transition in TiSe 2: A measurement of the specific heat Solid State Commun. 25, 39-42 (1978)

work page 1978

[18] [18]

N. Ru, C. L. Condron,G. Y. Margulis, K. Y. Shin, J. Laverock, S. B. Dugdale, M. F. Toney, I. R. Fisher Effect of chemical pressure on the charge density wav transition in rare earth tritellurides RTe 3 Phys. Rev. B 77 035114 (2008)

work page 2008

[19] [19]

Brouet, W

V. Brouet, W. L. Yang, X. J. Zhou, Z. Hussain, R. G. Moore, R. He, D. H. Lu, Z. X. Shen, J. Laverock, S. B. Dugdale, N. Ru, I. R. Fisher, Angle resolved photoemission study of the evolution, of band structure and charge density wave properties in RTe 3 (R=Y,La, Ce, Sm, Gd, Tb and Dy). Phys.Rev. B 77 235104 (2008)

work page 2008

[20] [20]

Saint-Paul, C

M. Saint-Paul, C. Guttin, P. Lejay, G. Remenyi, O. Leynaud, P. Monceau , Elastic anomalies at the charge density wave transition in TbTe 3. Solid State Commun.233, 24-29 (2016)

work page 2016

[21] [21]

Saint-Paul, G

M. Saint-Paul, G. Reményi, C. Guttin, P. Lejay, P. Monceau , Thermodynamic and critical properties of the charge density wave system ErTe 3 Physica B 504, 39-46 (2017)

work page 2017

[22] [22]

Saint-Paul, C

M. Saint-Paul, C. Guttin, P. Lejay, O. Leynaud, P. Monceau, Elastic anomalies at the charge density wave transition in HoTe 3. International Journal of Modern Physics B 32, 1850249 (2018)

work page 2018

[23] [23]

Van Smaalen, M

S. Van Smaalen, M. Shaz, L. Palatinus, P. Daniels, F. Galli, G. J. Nieuwenhuys, J. A. Mydosh, Multiple charge-density-waves in R 5Ir 4Si 10 (R=Ho, Er, Tm, and Lu) Phys. Rev. B 69 014103 (2004)

work page 2004

[24] [24]

Y.-K. Kuo, C. S. Lue, F. H. Hsu, H. H. Li, H. D. Yang , Thermal properties near the charge-density-wave transition Phys. Rev. B 64 125124 (2001)

work page 2001

[25] [25]

Mansart, M

B. Mansart, M. J. G. Cottet, T. J. Penfold, S. B. Dugdale, R. Tediosi, M. Chergui, F. Carbone, Evidence for a Peierls phase transition in a three-dimensional multiple charge-density waves in solid. Proc. Natl. Acad. Sci. (2011)

work page 2011

[26] [26]

Saint-Paul, C

M. Saint-Paul, C. Opagiste, C. Guttin , Elastic properties at the charge density wave transition in Lu 5Ir 4Si 10 Journal of Physics and Chemistry of solids (to be published)

work page

[27] [27]

S. L. Bud’ko, S. A. Law, P. C. Canfield,G. D. Samolyuk M. S. Torikachvili G. M. Schmiedeshoff , Thermal expansion and magnetostriction of pure and doped RAgSb2 (R=Y, Sm, La) single crystals. Journal of Physics: Condensed Matter, vol. 20, 115210 (2008)

work page 2008

[28] [28]

J. P. Pouget, L. P. Regnault, M. Ain, B. Hennion, J. P. Renard, P. Veillet, G. Dhalenne, and A. Revcolevschi, Structural evidence for a spin Peierls ground state in the quasi one dimensional compound CuGeO 3 Phys. Rev. Lett. 72, 4037 (1994)

work page 1994

[29] [29]

Saint-Paul, G

M. Saint-Paul, G. Reményi, N. Hegmann, P. Monceau, G.Dhalenne, A. Revcolevschi , Ultrasonic Study o magnetoelastic effects in the spin -Peierls state of CuGeO3 Phys. Rev. B 52, 15298 (1995). [31]R. Weber, R. Street , The heat capacity anomaly of chromium at 311 K (antiferromagnetic to paramagnetic transition Journal of Physics F: Metal Physics 2 873-877 (1972)

work page 1995

[30] [30]

D. I. Bolef, J. De Klerk , Anomalies in the elastic constants and thermal expansion of chromium single crystals Phys. Rev B 129, 1063-1067 (1963)

work page 1963

[31] [31]

Saint-Paul and P

M. Saint-Paul and P. Monceau, Survey of the thermodynamic properties of the charge density wave systems Advances in condensed matter (Hindawi) (2019) 2138264 doi /10.1155/2019/2138264

work page doi:10.1155/2019/2138264 2019

[32] [32]

W. L. McMillan , Landau theory of charge density waves in transition-metal dichalcogenides Phys. Rev. B 12 1187-1196 (1975)

work page 1975

[33] [33]

Allender, J

D. Allender, J. W. Bray, J. Bardeen , Theory of fluctuation superconductivity from electron-phonon interactions in pseudo- one-dimensional systems Phys. Rev. B 9, 119 (1974). [36 L. Landau and E. Lifshitz, Statistical Physics, Pergamon Press, 1968 and K. Binder, Theory of first order phase transitions Rep. Prog. Phys. 50 783859 (1987)

work page 1974

[34] [34]

L. R. Testardi, Elastic modulus, thermal expansion, and specific heat at a phase transition Phys. Rev. B 12 3849-3853 (1975)

work page 1975

[35] [35]

Rehwald, The study of structural phase transitions by means of ultrasonic experiments Adv

W. Rehwald, The study of structural phase transitions by means of ultrasonic experiments Adv. Phys. 22 721-755(1973). Table 1 Anomalies of Specific heat and sound velocity at the CDW phase transition. Molar volume V m. Materials Specific heat jump Velocity decrease Quasi-one-dimensional conductors K0.3 MoO 3 Vm=3.6×10 -5 m3 NbSe 3 Vm=4.1×10 -5 m3 T CDW =1...

work page 1973