Folded acoustic phonons in InAs-AlAs strained-layer superlattices
Raman spectroscopy is used to characterize highly mismatched (7%) InAs‐AlAs superlattices grown by atomic layer molecular beam epitaxy. In particular, folded acoustic modes are presented and compared with two different theoretical models (Rytov and linear chain). We find good agreement between theory and experiments. We estimate, with a simple model, the magnitude of the effect of the strain on the phonon frequency shifts.
Specific heat and thermal expansion coefficient of AlP, AlAs and AlSb
Abstract The temperature dependence of specific heat CV and thermal expansion coefficient α for AlP, AlAs and AlSb are studied theoretically from first principle by using the lattice dynamical method. No such experimental data are available for AlP and AlAs. The compression effect on phonon frequencies vi(q), i.e. the mode Gruneisen parameters γi(q) are also computed. The theoretical values of α for AlP and AlAs become slightly negative at low temperatures (below 30 K), a fact which differs other tetrahedral crystals. Our data of γi(q), Cv and α for AlP, AlAs and AlSb should be useful for discussing experimental information and for studying the anharmonic properties of these compounds.
Positive Rights and State Constitutions: The Limits of Federal Rationality Review
INTRODUCTION ............................................................................................................................. 1132 I. STATE CONSTITUTIONAL WELFARE PRACTICE ............................................................. 1144 A. A Mandatory Obligation: The New York Example .................................................. 1144 B. A Typology of Current State Court Decisions .......................................................... 1145 IT. RECONSIDERING FEDERAL RATIONALITY REVIEW IN STATE CONSTITUTIONAL WELFARE CASES ................................................................................ 1153 A. Rationality Review and Positive Rights .................................................................. 1155 B. Rationality Review and Democratic Legitimacy .................................................... 1157 C. Rationality Review and Judicial Finality ............................................................. xi61 D. Rationality Review and Federalism ......................................................................... i166 E. Rationality Review Revisited .................................................................................... 1169 III. TOWARD A NEW STANDARD OF REVIEW ......................................................................... 1169 A. The Need for Judicial Review .................................................................................. 1170 B. Institutional Competence and Welfare Litigation ................................................... 1175 I. State Courts as Fact Gatherers ......................................................................... 1175 2. State Courts as Policymakers ......................................................................... " 179 3. State Courts as Rights Enforcers ..................................................................... 1182 C. A Jurisprudence of Consequences .............................................................................. 1183 D. Why Education and Not Welfare? ........................................................................... i86 E. Implications for Welfare Litigation ........................................................................... i9i IV. CONCLUSION ........................................................................................................................ 1194