The persistent phosphorescence and thermoluminescence of SrAl2O4:Eu2+:Dy3+ is reported for a variety of different excitation wavelengths and excitation temperatures, to provide new insights in the mechanism of the trapping and detrapping. These measurements reveal that the trapping is strongly dependent on the wavelength and temperature. First, with increasing loading temperature, the thermoluminescence peak shifts to lower temperatures which corresponds to a change of trap population. Secondly, the integrated thermoluminescent intensity increases with increasing loading temperature. All wavelength and temperature dependent experiments indicate that the loading of the traps is a thermally activated processes. Utilizing different wavelengths for loading, this effect can be enhanced or reduced. Furthermore excitation with UV-B-light reveals a tendency for detrapping the phosphor, reducing the resulting thermoluminescent intensity and changing the population of the traps.
Single crystals of tetragonal RCuGa3 (R=La, Pr, Nd and Gd), with BaNiSn3 type structure (space group I4 mm), have been grown by high temperature solution growth technique using Ga as flux. Their magnetic properties were determined by heat capacity and the measurement of magnetization and electrical resistivity along [100] and [001] directions. Except LaCuGa3, the compounds order magnetically. PrCuGa3 undergoes a ferromagnetic transition with Curie temperature of 4.6 K. NdCuGa3 shows a bulk magnetic transition at 3.3 K. The data on GdCuGa3 indicate combined characteristics of spin glass and antiferromagnetic behavior at low temperatures. From the Schottky heat capacity data the crystal electric field level energy spectra have been determined. Further we have performed temperature dependent measurements of electron spin resonance (ESR) on GdCuGa3 between 11 K and room temperature. The ESR data indicate an enhancement of magnetic fluctuations associated with spin reorientation and both homogeneous and inhomogeneous thermal broadening of the linewidth.
 
Europium doped crystalline Ba7F12Cl2 phosphors have been prepared at temperatures between 650 and 900 °C using alkali chloride fluxes, yielding both disordered (with the incorporation of small amounts of Na) and ordered crystal modifications. The white emission spectrum excited in the near UV consists roughly of two broad emission bands at ca 450 and 590 nm, as well as weak sharp Eu2+ 4f-4f emission bands around 360 nm. The incorporation of Eu2+ is further studied using EPR spectroscopy on single crystals, and reveals a significant zero field splitting. The emission spectrum can be significantly tuned by varying the excitation wavelength between 300 and 390 nm. Fine tuning may also be achieved by chemical substitutions to form Ba7-xMyF12Cl2-zBrz (M = Na, Ca,Eu). Quantitative measurements of the light produced using commercial near UV LEDs show that the color temperature ranges between 4000 and 9700 K with CIE chromaticity coordinates close to the ideal values of x=y=0.333. The best color rendering index (CRI) found was 0.83, and the highest light to light conversion yield was 171 lumen/W. These results show that the title compound is a very promising candidate for white light generation using near UV LED excitation.
  
  • Broadband ultraviolet-visible transient absorption spectroscopy in the nanosecond to microsecond time domain with sub-nanosecond time resolution
    B. Lang, S. Mosquera-Vazquez, D. Lovy, P. Sherin, V. Markovic and E. Vauthey
    Review of Scientific Instruments, 84 (7) (2013), p73107
    DOI:10.1063/1.4812705 | unige:28965 | Abstract | Article HTML | Article PDF
A combination of sub-nanosecond photoexcitation and femtosecond supercontinuum probing is used to extend femtosecond transient absorption spectroscopy into the nanosecond to microsecond time domain. Employing a passively Q-switched frequency tripled Nd:YAG laser and determining the jitter of the time delay between excitation and probe pulses with a high resolution time delay counter on a single-shot basis leads to a time resolution of 350 ps in picosecond excitation mode. The time overlap of almost an order of magnitude between fs and sub-ns excitation mode permits to extend ultrafast transient absorption (TA) experiments seamlessly into time ranges traditionally covered by laser flash photolysis. The broadband detection scheme eases the identification of intermediate reaction products which may remain undetected in single-wavelength detection flash photolysis arrangements. Single-shot referencing of the supercontinuum probe with two identical spectrometer/CCD arrangements yields an excellent signal-to-noise ratio for the so far investigated chromophores in short to moderate accumulation times.
 
BaFCl single crystals doped with Sm3+ ions were studied by using the EPR method. Several types of paramagnetic Sm3+ centres were found. The parameters of the corresponding spin Hamiltonians were determined. Structural models and ground states of the observed centres are proposed.
  
A tetragonal La2+ center (symmetry C4v) was identified in single crystals of BaFCl and SrFCl doped with lanthanum with the aid of electron paramagnetic resonance (EPR)/electron-nuclear double resonance (ENDOR). This center forms a donor-acceptor couple with initially present F(F-) centers. Switching takes place by illumination of appropriate wavelength. The kinetics of the process was monitored by EPR as La2+ and the unswitched F center are paramagnetic. The results of our experimental investigation of this kinetics are presented. A foregoing spectroscopic characterization of the La2+ center allowed one to identify a d-d (the B1-E) transition, a charge-transfer band (for BaFCl at 10940cm-1 and at 17890cm-1, respectively) and to obtain a value of 710cm-1 for the spin-orbit coupling constant in the ground state. In order to narrow the choice of possible acceptor-donor partners a detailed EPR/optical search was further done to identify a number of lattice defects and oxygen centers—in addition to a La-oxygen molecular structure.
 
The Yb3+ paramagnetic center of the trigonal symmetry (“oxygen” paramagnetic center T2) in CaF2 and SrF2 single crystals is studied by EPR and optical spectroscopy. The Stark level energies of the Yb3+ multiplets are established from absorption, luminescence and excitation luminescence spectra and the crystal field parameters are calculated.
Results of EPR and optical spectroscopic investigation of the trigonal paramagnetic Yb3+ ion in SrF2 (‘oxygen’ paramagnetic center — T2) are presented. The energy level scheme of the center is determined from its optical spectra and the parameters of the crystal field potential are calculated.
Electron paramagnetic resonance, electron-nuclear double resonance, and optical spectroscopy of the tetragonal Yb3+ center in KMgF3 are reported here. The results of these experiments allow us to conclude that a previously given structural model as well as the interpretation of the optical spectrum of this center are incorrect. A model is presented and experimentally and theoretically justified. In particular, the values of the hyperfine and transferred hyperfine interaction parameters were determined as well as an experiment-based energy-level scheme. Its parametrization is performed by including simultaneously the crystal field and the spin-orbit interaction within the 7F term. Furthermore, a theoretical analysis of the transferred hyperfine interaction (THFl) parameters is presented. It is further shown from optics and from microscopic calculations of the THFI parameters that g and ghave opposite signs and that the rule of correspondence between the cubic g factor and g̃=1/3(gx+gy+gz) does not depend on the relative magnitude of the cubic and low-symmetry crystal field acting on the rare-earth ion.
  
The optical and paramagnetic properties of X-irradiated silver doped SrF2 crystals were investigated. The freshly irradiated crystals show a complex absorption spectrum between approximately 200 and 650 nm. Subsequently, systematic heat treatments were applied and absorption, photoluminescence and its polarization dependence, thermo- and radio-luminescence experiments have been undertaken. The resulting experimental data were mutually correlated with the aid of the factor analysis technique and six different origins of the observed spectra were identified. Models of the underlying silver-defect structures are discussed and crystal preparation is further presented.
Single crystals of the new host Ba12F19Cl5 doped with Eu2+ were grown and studied by electron paramagnetic resonance (EPR) and luminescence emission spectroscopy. Three different Eu2+ sites were observed. Two of them had orthorhombic point symmetry while the last one was monoclinic. Physico-chemical and symmetry arguments allowed us to establish correspondence between the different Eu2+centres and the host cation lattice sites. All three centres presented in their ground state important crystal field splitting. The 80 K luminescence emission spectrum consisted of one broad unsymmetrical f-d band peaking at 22 700 cm-1. No 4f-4f transitions of the Eu2+ ion were observed between room temperature and 80 K.
 
We have studied the solid-liquid equilibrium of the system Sr1–yBayFCl1–xBrx using DTA and X-ray diffraction techniques. The entire composition range in this system yields solid solutions which crystallize in the PbFCl (Matlockite) structure type. The melting points of the entire composition range have been parametrized (within 5°C rms error) using a biquadratic fit of the available data obtained by experiment and from the literature.
  • Electron nuclear double resonance of the cubic Dy3+ center in KZnF3 single crystal
    M.L. Falin, V.A. Latypov, H. Bill and D. Lovy
    Applied Magnetic Resonance, 14 (4) (1998), p427-434
    DOI:10.1007/BF03161852 | unige:2957 | Abstract | Article PDF
ENDOR measurements on the 19F- nuclei in the first four shells of KZnF3 containing Dy3+ ions in the cubic site are reported. The values and signs of the hyperfine and transferred hyperfine interaction parameters are determined. The local deformation of the crystal lattice in the vicinity of the impurity ion is estimated. The theoretical analysis of the THFI parameters for the first coordination shell of the F- ions has been carried out. For the Dy3+ ion the influence of spin polarization of the closed 5s and 5p shells is considered for the first time. Spin polarization is shown to play a significant role in the mechanism of rare-earth ion-ligand coupling. 
  
A recent investigation of the (BaF2–MgF2) phase diagram produced several new compounds which are suitable hosts for Rare Earth impurities. We present results on single crystals of Ba2Mg3F10 doped with Eu2+. The local structure and optical properties of this system were investigated by luminescence emission and by EPR. We observed two different Eu2+ sites. Both show Cs point symmetry and an important ground state splitting. Correlating our EPR and optical results with the new Ba2Mg3F10 structure data allowed the assignment of each of them to a specific barium lattice site. The luminescence emission of both the 4f7–4f65d and the 4f7–4f7 transitions is observed. The relative importance of the two emissions is strongly temperature dependent. The emission intensities of the intra f-shell 6P7/28S7/2transitions increase strongly on going from 295 K to 77 K. Thus, the lowest levels of the 4f65d configuration are approximately degenerate with the 6P7/2 manifold.
 
Eu2+ was introduced into pure and oxygen codoped BaMgF4 single crystals. A detailed EPR study of this ion (S=7/2) was realized on both types of systems. The result is that only one spectrum was observed involving a strong crystal field. The associated site symmetry of the impurity is Cs. It occupies very closely a Barium lattice site as was established by correlating the EPR results with those of a refined X-ray structure analysis on a Ba0.8Eu0.2MgF4 single crystal realized in our laboratory. The oxygen codoped crystals exhibited this same Eu2+EPR spectrum (the only one). Optical emission and excitation experiments were performed between 13 000 and 53 000 cm−1. The results due to the Eu2+ impurity are given and discussed qualitatively within the 4f7  4f65d1 scheme.
  
We study the ionic conductivity versus temperature and frequency of large Na2S single crystals by using a calibrated impedance apparatus. The experimental setup used for the ionic conductivity measurements up to 1350 K and its calibration are described. The apparatus allows to measure complex impedances between 0.1 Ω and 10 GΩ. The high temperature conductivity data were analyzed in terms of the conventional Frenkel defect model. We assume that cation vacancies and cation interstitials are the dominant intrinsic defects. The energy of motion was found to be 0.61 ± 0.05 eV for a cation vacancy. The energy of formation of a Frenkel defect pair is 2.51 ± 0.05 eV. Results are given that show clear evidence of a superionic behaviour close to the melting point, similar to the one found in alkaline earth fluorides and several halides. Furthermore, X-ray diffraction experiments on a high optical quality single crystal were performed. The cell parameter and the population parameter of Na+ were accurately determined (6.5373 Å and 0.988, respectively).
  • Defect association, Jahn-Teller or off-center effect in CaF2:Copper, BaF2:Silver ?
    V. Lefevre, A. Monnier, M. Schnieper, D. Lovy and H. Bill
    Zeitschrift fr Physikalische Chemie, 200 (1997), p265-273
    unige:2810 | Abstract
The results of a detailed optical and paramagnetic-resonance study performed on copper in CaF2 and silver in BaF2 are presented. Two different Ag+ centers were identified in BaF2. One is associated with an interstitial F- ion whereas the other one has a cubic surrounding. The Cu2+ ion in CaF2 was shown to reorient at 4.2 K between 6 equivalent minima of D2h symetry. This fact is interpreted with the aid of a T2gx(T2g+Eg) type Jahn-Teller effect. The nonlinear mixed coupling terms are shown to play an important role. The Cu+ impurity in CaF2 is presumably off-center in the F- sublattice without associated defect or impurity.
  • High-temperature spectral hole burning on Samarium(II) in single crystals of the lead fluorohalide structure family and thin films of calcium fluoride
    H. Bill, R. Jaaniso, H. Hagemann, D. Lovy, A. Monnier and M. Schnieper
    Optical Engineering, 34 (8) (1995), p2333-2338
    DOI:10.1117/12.201813 | unige:3537 | Abstract | Article PDF
 
When modern spectral hole burning applications for high-density information storage under noncryogenic temperatures are envisioned, it is necessary to develop new frequency-selective photoactive materials for this purpose. Mixed compounds of the PbFCl family, doped with samarium(II) ions, exhibit promising and true room-temperature hole burning capabilities. We investigate this class of systems (and related ones) by combining material synthesis and high-resolution spectroscopy. Whole groups of isomorphous crystals were synthesized with varying degrees of halide anion and/or cation substitutions. Thin films of fluoride-based materials were made in a laboratory-built molecular beam epitaxy system. An extended x-ray study, differential thermal analysis, luminescence, and Raman measurements allowed the characterization of the materials. Formal models were developed for both the inhomogeneous zero-phonon optical line shapes of the samarium(II) and the time evolution of the hole burning.
  • ENDOR and transferred hyperfine interaction of impurity rare-earth ions with nearest diamagnetic ions in crystals
    M.L. Falin, M.V. Eremin, H. Bill and D. Lovy
    Applied Magnetic Resonance, 9 (3) (1995), p329-354
    DOI:10.1007/BF03161957 | unige:2867 | Article PDF
The tetragonal Er3+ ion associated with the interstitial F ion along the [100] axis in CaF2 is studied using ENDOR. The parameters of the transferred hyperfine interaction and of the nuclear Zeeman interaction of the surrounding fluorine ions are determined. Anomalously large values of the pseudo-nuclear Zeeman effect on the F nuclei are found. The theoretical analysis of these parameters is carried out in a frame of operator techniques in the theory of transferred hyperfine interactions. A number of useful relations for practical calculations of the values of the local field at ligand nuclei are reported.
  • Raman Optical Activity of (β)-citronellene
    H. Hagemann, A. Lucken, D. Lovy and H. Bill
    in "Proc. XIV th Conference on Raman Spectroscopy" Eds. N.T. Yu, X.Y. Ku, J. Wiley and sons, Singapore, 14 (1994), p1072-1073
  • Thermolysis and chemiluminescence of monocyclic 1,2,4-trioxan-5-ones
    C.W. Jefford, M.C. Josso, M. Da Graa H. Vicente, H. Hagemann, D. Lovy and H. Bill
    Helvetica Chimica Acta, 77 (7) (1994), p1851-1860
    DOI:10.1002/hlca.19940770716 | unige:2888 | Abstract | Article PDF
The 3,6-substituted 1,2,4-trioxan-5-ones 11-14, on heating to 170-200°, underwent unimolecular thermolysis to generate electronically excited singlet ketones with an efficiency of ca. 0.2%. The chemiluminescence quantum yields (ΦoSCL) depended on the nature of the 6-substitutents and increased linearly with temperature. The Arrhenius activation energies were obtained by measuring the rate of decay of luminescence and determined as 22.9, 30.4, 35.6, and 34.2 kcal/mol for 11-14, respectively. Step analysis of the chemiluminescence of 14 afforded an average activation energy of 44.3 kcal/mol. This latter result is explicable in terms of two decomposition paths, higher and lower in energy, leading to excited and 'dark' products, respectively. The thermolysis of trioxanones 12-14 lacking a H-atom at the 6-position is interpreted as involving successive rupture of the peroxide bond, excision of ketone at the 3-substituted end, and loss of CO2, to finally produce ketone originating from the 6-position (see Scheme 4).
Copper and silver, respectively, were introduced into single crystals of CsCdF3. Our detailed electron paramagnetic resonance (EPR) study showed that both elements enter the Cd lattice site—copper as Cu2+, silver as Ag+, which then was converted into Ag2+ by x raying the corresponding samples. Cu2+ and Ag2+ were shown to present in their ground state a pseudostatic Jahn–Teller effect. Motional effects were observed in the respective EPR spectra and studied in some detail for Cu2+ as they are seen over a wide temperature range. Predictions of a stochastic Kubo model [J. Phys. Soc. Jpn. 9, 935 (1954)] were compared with the temperature dependent linewidths of the motionally averaged EPR spectrum. A power law (Tn with n≂1.9) was determined for the temperature dependence of the reorientation frequency between 30 and 90 K.
  • Determination of the angular dependence of Hc2 in high Tc single crystals by a microwave technique
    D. Shaltiel, H. Bill, A. Grayevsky, A. Junod, D. Lovy, S. Sadowski and E. Walker
    Superconductor Science and Technology, 4 (1S) (1991), p85-87
    DOI:10.1088/0953-2048/4/1S/014 | Abstract | Article PDF
It is shown that using an ESR spectrometer with magnetic field modulation and sweeping the temperature across Tc (at a constant and a very low magnetic field), is equivalent to temperature modulation. The signal intensity obtained when crossing Tc is proportional to 1/( delta Hc2/ delta T) at T=Tc. Using the WHH relation Hc2(T=0)=0.7 Tc( delta Hc2/ delta T)T=Tc enabled the measurement of the relative angular variation of Hc2 in single crystals of YBaCuO with Tc approximately 85 K. The data fit the Ginzberg-Landau theory. This very sensitive technique can be used to characterize properties of high Tc superconducting materials. Results on thin films is also be presented.
  
  • Microwave absorption across Tc: Determination of the angular dependance Hc2(θ) / Hc2
    D. Shaltiel, H. Bill, A. Grayevsky, A. Junod, D. Lovy, W. Sadowski and E. Walker
    Physical Review B, 43 (16) (1991), p13594-13597
    DOI:10.1103/PhysRevB.43.13594 | Abstract | Article PDF
It is shown that measuring microwave absorption in high-Tc superconductors at constant and very low magnetic fields, using magnetic-field modulation, is, under some conditions, equivalent to temperature modulation when sweeping the temperature across Tc. Using an ESR spectrometer, the derivative of microwave absorption is measured close to Tc. This allows a determination of the relative angular variation of dHc2/dT at T=Tc in single crystals of Y-Ba-Cu-O. The data fit the Ginzburg-Landau theory on the relative angular variation of Hc2. The ratio (dHc2/dT)T=Tc parallel and perpendicular to the Cu planes was found to be 2.7 and 5.3 for two Y-Ba-Cu-O single crystals with Tc=89 and 86 K, respectively. These values obtained at 1010 Hz are close to the values obtained by conventional dc methods.
 
The construction of a new high-resolution multichannel low-cost pulse generator is reported. It is fully computer controlled through a simple RS232 serial interface. Its features are 1 ns resolution within any time, pulse delays up to 16 ms and pulse lengths up to 65 mu s, and pulse sequence repetition rate from 66 Hz up to 250 kHz. It has fully programmable sequencing, including step increments for any pulse delay or length. It governs a pulsed ESR spectrometer, which is also described, but it could be used in a very wide range of experimental set-ups. A few examples of spin-echo detected ESR and ESEEM of some paramagnetic centres are shown.
The effect of externally applied stresses of eg and t2g symmetry on the cubic Eg(X)eg Jahn-Teller (JT) system Y2+ in SrCl2 is studied. Coupling constants were obtained with the aid of EPR and by relying on a Ham-type cluster JT Hamiltonian, in conjunction with a random strain distribution. This is established from a critical review of the contributing strain sources (including possible percolation effects due to the isotopic composition of natural SrCl2). The stress of t2g symmetry shows strong effects. The authors conclude that the cubic Ham factor q is nearly one and that the experiments allow, as a function of this latter stress, one to pass gradually towards a trigonal JT effect. The optical absorption spectrum assigned to Y2+ is given in addition.
  • Unusual behavior of the Gd ESR in single crystals of GdyY1-yBa2Cu3O6+x with x=0.1-0.8 and y=0.03-0.06: evidence for a magnetic interaction in the superconductors
    D. Shaltiel, S.E. Barnes, H. Bill, M. Franois, H. Hagemann, J. Jegondaz, D. Lovy, P. Monod, M. Peter, A. Revcolevschi, W. Sadowski and E. Walker
    Physica C: Superconductivity, 161 (1) (1989), p13-20
    DOI:10.1016/0921-4534(89)90036-1 | unige:3071 | Abstract | Article PDF
The ESR of small concentration of Gd 0.03<y<0.06 substituting for Y in single crystals of GdyY1−yBa2Cu3O6−x has been measured. In the insulating compound, with x ~ 0.1, and the superdconducting materials with 30 K < Tc < 80 K, the measurements were performed at X-band, 9.3 GHz, and Kα-band, 36 GHz, over a large temperature range above Tc. Angular dependence measurements exhibit a spectrum which is fully resolved in certain directions, but only partially resolved, because of exchange narrowing, in other directions. Comparisons between the spectra in the insulating and superconducting compounds shows similar angular dependent behavior. This seems to indicate that the origin of the exchange narrowing is the same in both compounds. Since this narrowing in the insulating compound arises from interaction with, or via, the Cu magnetic system, it is implied that there is a similar, perhaps fluctuating, system in the superconducting state. Preliminary measurements of the temperature dependence of the line widths may indicate the presence of spin pairing at about 110 K, above the actual Tc of 70 K. The crystal field parameters are D = 3B02 = 1307 MHzB04 = 3.014 MHz and B44 = -11.43 MHz, for the semiconducting sample. The g-value is 1.989 ± 0.005. These values change only slightly in the superconducting crystals.
ESR results are reported on the Ag2+ ion introduced into alkaline earth fluoride crystals. In SrF2 (as in CaF2) a trigonal centre is present which tunnels between four equivalent C3 directions as shown by ESR under uniaxial stress. A T2g ⊗ t2g Jahn-Teller model describes adequately the paramagnetic and stress effects when the strong coupling case is considered. Ag2+ in BaF2 forms a static tetragonal cluster similar to Ag2+ and Cu2+ in SrCl2.
A new phase transition is observed in the KLiSO4 crystals below 77 K using MoO43- as a paramagnetic probe. The EPR spectra of this molecular ion, which substitutes for the host SO42- ion, show triclinic symmetry at 77 K due to the joint action of a trigonal crystal field and a trigonal Jahn-Teller effect of E(X)e type. Above 77 K, motional averaging in the a-b plane occurs; thereby an axial spectrum is observed. Below 64 K, the two sulphate sites are no longer equivalent resulting in the appearance of two distinct EPR spectra of the molybdate ion. The possible space groups of the crystal in the vicinity of the phase transition are discussed. The authors' results indicate that one needs to distinguish carefully between the local dynamics and the structural changes in this crystal.
  • The identification and structure of FSO2 radical trapped in potassium sulphate crystals
    Y. Ravi Sekhar, H. Bill and D. Lovy
    Chemical Physics Letters, 136 (1) (1987), p57-61
    DOI:10.1016/0009-2614(87)87298-6 | Abstract | Article PDF
ESR and ENDOR results on irradiated K2SO4:BF4 crystals are presented. Based on the ESR spectra and their symmetry at the X and Ka bands, a new paramagnetic radical trapped at the sulphate sites is identified. The ENDOR spectra are consistent with the involvement of a fluorine nucleus. The spectra are assigned to the symmetric FSO2 radical.
The authors show that CaF2:Y crystals that have been X-irradiated at low temperatures contain Y2+ ions associated with a trigonally located interstitial F- ion. Experimental results are presented that support this identification and that show that a trigonal Jahn-Teller effect (with warping) is involved. An estimate for the Jahn-Teller energy of EJT approximately=490 cm-1 is obtained.
An EPR study has been carried out on a Cu2+ center in NaF single crystals (with 2 % mole of copper) from 1.6 k – 150 K. The symmetry of the EPR spectra is triclinic at 1.6 K, monoclinic at 4.2 K, tetragonal at T ≥ 40 K. No hyperfine structure has been observed. Models which include both the Jahn-Teller effect and a low symmetry crystal field are proposed.
  
  • Supergiant variability: theoretical pulsation periods and comparison with observations
    D. Lovy, A. Maeder, A. Nols and M. Gabriel
    Astronomy and Astrophysics, 133 (1984), p307-312
    Abstract | Article PDF
Attention is given to the theoretical period-luminosity-color relations of stars evolving with mass loss that cover the upper part of the HRD, and pulsation periods are determined for the fundamental radial mode and first and second overtones. It is noted that the pulsation Q-terms present a minimum near T(eff) of 20,000 K, and that the Q-terms increase both for hot main sequence stars and cool and luminous red supergiants. A comparison of models with observations indicates that about 40 percent of the supergiants have periods which are in agreement with the fundamental mode of radial pulsation.

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